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Vohra - PhD (GaTech, 2006)

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Page 1: Vohra - PhD (GaTech, 2006)

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p L :KJbJnT�JOc B JnTaUlP�< C�q 9r<mshF@?_Ta< MOEKHtRu? W < Cv EKkn?AE=<N< C ?AEKkw <NJ C kn?AM ^ Ex>DF@?aF@S=FD<yJOc�9�<�Lz:KE=JnTaJOkOU

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Page 2: Vohra - PhD (GaTech, 2006)

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� M C T ^���� MOLmJ W q 81H � ?A>DJ CB JnTaUlP�< C�q 9r<mshF@?_Ta<��Ru? W < Cv E=kn?_E=<N< C ?AE=kw <NJ C kn?AM ^ EK>DF@?aF@S=FD< JOcu9r<�L :KE=JnTAJOkOU

8 � w J�l:KMOTa<� M}FD< C ?AMOT p LN?a<�EKLm<� v E=kn?AE=<N< C ?_E=kw <NJ C kn?AM ^ EK>DF@?aF@S=FD< JOcu9r<�L :KE=JnTAJOkOU

e �� M����V8�T_?� ? � ?AT�� v E � ? C JnExP�<�EGF@MOT v E=kn?AE=<N< C ?AE=kw <NJ C kn?AM ^ EK>DF@?aF@S=FD< JOcu9r<�L :KE=JnTAJOkOU

��� e;<�MOTATacB JnTAUhP�< C q 9�<mslF@?ATa<� Rd? W < C v E=kn?AE=<N< C ?_E=kw <NJ C kn?AM ^ EK>DF@?AF@S=FD< JOc�9�<�Lz:KE=JnTaJOkOU

����� MOEKkB JnTAUhP�< C q 9�<mslF@?ATa<� Rd? W < C v E=kn?AE=<N< C ?_E=kw <NJ C kn?AM ^ EK>DF@?AF@S=FD< JOc�9�<�Lz:KE=JnTaJOkOU

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Page 3: Vohra - PhD (GaTech, 2006)

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^�� JnSKTAH TA? O<-FDJ�F@:KMOE� B�C JOc � � M C T ^���� MOLmJ W qnB5C JOc � p FD<NoZ:=<�E v ��� <�Lz:GFD<�TKMOExH � <�EbFD< C ciJ C 81H � MOEKLm<�Hv EKkn?AE=<N< C ?AEKk Ru? W < C > MOExH Rd?_TAP >�� � 8 v RuR�� M}F � Ta<�P >DJnE c J C o C J � ?AHK?AE=k'oxM C F@?_MOT�c SxEKHK?AE=k ciJ C F@:=<o C J �D<�LmF �

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Page 4: Vohra - PhD (GaTech, 2006)

� � � � � � � � ���� ��� X

��������� ������������������� � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � �����

��� �!�"��#$�%��&'�(��� �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � )*���

��� �!�"��#+#,� ��-/.���� � � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � �0)*�����

�!-1�2�3��.�4 � � � � � �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � �"5!)*�

� �6����.��7�/-��8��� �7� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � 9

: � : B5C JhLm<�> ><;yS=F@TA?_E=< � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � :

: � { � <�TaF p oZ?AEKEK?AEKk � � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � =

: �?> � ?AL C Jn>DF C SKLmF@S C < � � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � :@:

: �BA j C M � JOcu>DoxSKE ` W < C > � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : =

: �?= ; �D<�LmF@? � <�> q 8�>@> SKP�oKF@?aJnEx>-MOExH1C�?APQ?aF@M}F@?aJnEK> � � � � � � �� � � � � � �� � � � � {}|

� � #,�7.��2-/�%����� �7�D�7#$��EF�HGI.��7&'�(��� � � � � � � �� � � � � � �� � � � � JKJ

{ � : � JnEx>D< C � M}F@?aJnE JOc � MO>@> � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � {O{{ � { � JnEx>D< C � M}F@?aJnE JOc � JnP�<�EbF@SKP � � � � � � �� � � � � � �� � � � � � �� � � � � { A{ �?> � JnEx>D< C � M}F@?aJnE JOc v E=< C kOU � �� � � � � � � �� � � � � � �� � � � � � �� � � � � {@L{ �BA � JnEx>DF@?aF@S=F@? � < � <�:KM � ?AJ C� � �� � � � � � � �� � � � � � �� � � � � � �� � � � � {@M{ �?= p JnT_S=F@?aJnE 9�<�Lz:KEK?AghS=< � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � >@=

� �N�3�O��.P���7��EF�6�Q�$�����R�!�(�6G�GI�6��S�7#T#U�6&'��.1�P�6�S� �V�W��E���.��3����/.��UG�.����8���V�!��� � �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � XKY

> � : ^ EGF C JhHKSxLmF@?aJnE �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � > L

> � { v gbSKM}F@?AJnEK> JOc�P�JOF@?aJnE c J C M�` W < C JnEtM C JnTATa< C MOEKH c C <N<f>@oxMOE � � � � �� � � � � > M

> � { � : � JnP�oxM C ?A>@JnE � ?aF@: ` W < C <�ghSKM}F@?aJnEK>?_E F@:=< TA?aFD< C M}F@S C < � � � � �� � � � � A |> �?> 9:K< � JnEK>DF@?aF@SKF@? � < � JlH=<�T �582C�?_E=<�M C TaU v TAMO>DF@?_L � <�TaF � � �� � � � � � �� � � � � A :

> �BA j C M � JnE F@:=< R=<N<�HIe;JnTATa< C �� � � � � � � �� � � � � � �� � � � � � �� � � � � A :

> �BA � : RxSKTAT�>DJnTASKF@?aJnE ciJ C P�J � ?AE=k q >DF C <NF@L :K?AEKk ` W < C > � � �� � � � � � �� � � � � A@A

> �BA � { 8�oKo C J�s=?AP M}FD<�>DJnTAS=F@?AJnE ?AE � :K?_L : MOTATuMOLNLm<�Ta< C M}F@?aJnE FD< C P > M C <�E=<NknTa<�LmFD<�Hc C JnP F@:K< P�JnP�<�EbF@SKP <�ghSKM}F@?aJnEK> � �� � � � � � �� � � � � � �� � � � � = {

> �BA �?> 8�oKo C J�s=?AP M}FD< >@JnTAS=F@?aJnE%?_E � :K?ALz: >DF C <NF@L :K?AEKk MOLNLm<�Ta< C M}F@?AJnE ?_> E=<NknTa<�LmFD<�Hc C JnP F@:K< P�JnP�<�EbF@SKP <�ghSKM}F@?aJnEK> � �� � � � � � �� � � � � � �� � � � � =@>

> �BA �BA � JnP�oxM C ?A>@JnE � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � = A

? �

Page 5: Vohra - PhD (GaTech, 2006)

> �?= j C M � JnE F@:=<fF@M O< �VS=o C JnT_Ta< C � � � � � � � �� � � � � � �� � � � � � �� � � � � = A

> � ~ j C M � ?AE c C <N< >DoxMOEx> � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � = �

> � � � JnExLNTASK>@?aJnE � �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � = �

� � �� ���6�!�%����� �/.�� � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � ���

A � : ^ EGF C JhHKSxLmF@?aJnE �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � = M

A � { v gbSKM}F@?AJnEK> JOc � JOF@?aJnE � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � ~O{A �?> p JnT_S=F@?aJnE � � �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � ~ >A �BA 9:K< 9 � J � p F@M}kO< j C M � B�C JlLm<�>@> � � � � � �� � � � � � �� � � � � � �� � � � � ~ =A �?= p ?_P SKT_M}F@?aJnEK> �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � ~@LA � ~ � JnExLNTASK>@?aJnE � �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � �}~

� #,�6&8��. �/.��U -��!�6�� �/.��U GI�6�Q�2-/���/��. � �V�7��EF��.��3�P�"�7�7����/� ��� �7�� � � � � �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � ���

= � : ^ EGF C JhHKSxLmF@?aJnE �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � ���

= � { v gbSKM}F@?AJnEK> JOc � JOF@?aJnE � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � � L

= �?> � JnEx>DF@?aF@S=F@? � < � JlH=<�T � C�?_E=<�M C TaU v TAMO>DF@?AL � B TAMO>DF@?AL � � � � �� � � � � � �� � � � � � M

= �BA 9:K< 9 � J p F@M}kO< j C M � B�C JlLm<�>@> � ?aF@: M j C M � B ?AE � � �� � � � � � �� � � � � L :

= �?= p JnT_S=F@?aJnE � � �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � L >

= � ~ p ?_P SKT_M}F@?aJnEK> �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � M��

= � � � JnExLNTASK>@?aJnE � �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : | �

� �H� �7�/���(�6�Q� �7# #U�6&'��. �/.�� G�.����8���V�!��� � ��E �2����E������ �8�������� ��E���.��3��� -/�F�,�8���/�6�� � � � �� � � � � � �� � � � � � �� � � � �29K9K9

~ � : � JnEx>DF@?aF@S=F@? � < v gbSxM}F@?aJnE � �� � � � � � � �� � � � � � �� � � � � � �� � � � � :@:@:

~ � { v gbSKM}F@?AJnEK> JOc � JOF@?aJnE � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � :@: {~ �?> p JnT_S=F@?aJnE � � �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � :@: >

~ �BA p ?_P SKT_M}F@?aJnEK> MOEKHtjy?A>@LNSx>@>@?aJnE � � � � � � � �� � � � � � �� � � � � � �� � � � � :@: A

~ �BA � : v <�LmF;JOc <�M}F@?AE=k �� � � � � � � �� � � � � � �� � � � � � �� � � � � :@: A

~ �BA � { v <�LmF;JOcuH C M � oZ?AE :=<�?akn:bF ��� � � � �� � � � � � �� � � � � � �� � � � � : A@A

~ �BA �?> v <�LmF;JOcd`ZEKMOT.F@M O<�S=o C JnTATa< C >Do.<N<�H �� �� � � � � �� � � � � � �� � � � � : A M

� �N� ��EF� ��#U#U���8�2�7# �� �+�/.��U GI�6�Q�1�6�0� �I �H�O������� �/.�� GI.�����8���V��� � � � � � � �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � �29����

� � : v gbSKM}F@?AJnEK> JOc � JOF@?aJnE � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : = ~

Page 6: Vohra - PhD (GaTech, 2006)

� � { p JnT_S=F@?aJnE � � �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : = �

� �?> p ?_P SKT_M}F@?aJnEK> �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : = M

� �BA � JnExLNTASK>@?aJnE � �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : ~ A

� �N� �B�W������.��F�!���6�� ��EF� G�.P���/� �8��� �7��W#,��.S�7�7-/�U�W�2&����F� ��.�����G �.������H�/��GI�����/�����R#U.�� �8��� �7� �$�7�/���,� � � � � �� � � � � � �� � � � �29 � �

L � : ^ EGF C JhHKSxLmF@?aJnE �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : ~ =L � { R C ?ALmF@?aJnE � JhHK<�TA> � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : ~O~L �?> v gbSKM}F@?AJnEK> JOc � JOF@?aJnE � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : ~��L �BA p JnT_S=F@?aJnE � � �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : ~@M

L �BA � : � JnSKTaJnP W c C ?_LmF@?aJnE �� � � � � � � �� � � � � � �� � � � � � �� � � � � : ~@ML �BA � { � C <N<No � C M}FD<fHK<No7<�ExH=<�EGF c C ?ALmF@?aJnE � �� � � � � � �� � � � � � �� � � � � : � :

L �?= p ?_P SKT_M}F@?aJnE � �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : � >

L �?= � : � JnSKTaJnP W c C ?_LmF@?aJnE �� � � � � � � �� � � � � � �� � � � � � �� � � � � : � >

L �?= � { � C <N<No � C M}FD<fHK<No7<�ExH=<�EGF c C ?ALmF@?aJnE � �� � � � � � �� � � � � � �� � � � � : �}~L � ~ jy?A>@LNSx>@>@?aJnE � �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : � L

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Page 7: Vohra - PhD (GaTech, 2006)

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Page 8: Vohra - PhD (GaTech, 2006)

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Page 9: Vohra - PhD (GaTech, 2006)

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JOc-F@:=<�` C >DFy>DF@M}kO< � W <NF � <N<�E � � MOEKH�� � � q { �1?AE F@:=<�` C >DF�c C <N<�>DoxMOE � W <NF � <N<�E�� �MOEKH�� � q > �5JnEQF@:=<1F@M O< �VS=o C JnTATA< C JOc�F@:=<1` C >@F">DF@M}kO<�� W <NF � <N<�E�� MOExH � � q A ��JnEF@:=< c <N<�H C JnTATa< C JOcrF@:=< >D<�LmJnEKH >DF@M}kO< � W <NF � <N<�E � � MOEKH�� � � qK= �-?_E F@:K<y>@<�LmJnEKH c C <N<>DoxMOE � W <NF � <N<�E�� �4MOEKH�� � q MOExH ~ �yJnE F@:=<�F@M O< �VS=o c JnTATa< C JOc-F@:=<�>D<�LmJnEKH%>DF@M}kO<� W <NF � <N<�E��� MOEKH � � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � ~}|

{ A 9:=< >@:KMOHK<�H M C <�M ?AExHK?ALNM}FD<�>4F@:=<'o7J � < C F@:KM}F�LNMOE W < C <�LmJ � < C <�H c C JnP$F@:=< ` W < CM}Fy>Do.<N<�H� MOEKHILmJ C C <�>Do.JnEKHK?AEKk�FD<�EK>@?aJnE���� �� ?A>;F@:=< >Do.<N<�HIJOcdF@:K<fo.< C P MOE=<�EbF@TaU>DF C <NF@Lz:=<�H q SKEKTaJnMOH=<�H ` W < C � �� � � � � � � �� � � � � � �� � � � � � �� � � � � ~��

{ = p o.<N<�H �� � q FD<�EK> ?aJnE ��� � q E=J C P MOTbc J C Lm< o7< C Ta<�E=kOF@: ��� � q c C ?ALmF@?aJnExMOTGc J C Lm<-o7< C Ta<�EKkOF@:����� q MOEKH%FD<�P o7< C M}F@S C <Qo C JO`xTa<�> ��� �yc J C MOE ?A>DJOF@:=< C P MOT�H C M � o C JhLm<�> > � � C Jn>@>D<�>��� �uHK<�E=JOFD<�TaJlLNM}F@?aJnEK> � :=< C < F@:=<;` W < C >u<�?aF@:=< C M}FDF@MOLz:'FDJ J C H=<NoZM C F�c C JnP M C JnTATA< C�qMOEKH LN? C LNTa<�> ��� �fH=<�E=JOFD< TaJhLNM}F@?AJnEK>fJOc F@:K<'?AEx?aF@?AM}F@?aJnE J C Lm<�>@>@M}F@?AJnE JOc�>@TA?ao � p JnT_?AHTA?AEK<�> ��� � �f?AEKHx?ALNM}FD< �NJnE=<�>4JOc;H C M � JnE C JnTATa< C > q HKMO> :=<�H �VH=JOFDFD<�H TA?AEK<�> ��!#"$!#"$! �?AEKHx?ALNM}FD<��NJnE=<�>JOcuE=JQ> TA?ao q MOEKHtH=JOFDFD<�H TA?AE=<�> �$"%"%"&"%"%" � ?AEKHx?ALNM}FD<yc C <N<�>@oxMOEK> � � � � � � :

{O~ p o.<N<�H q FD<�EK>@?aJnE q E=J C P MOTxc J C Lm<1o.< C Ta<�EKkOF@: q c C ?ALmF@?AJnEKMOTKc J C Lm<yo.< C Ta<�EKkOF@: q MOExHQFD<�P �o.< C M}F@S C < o C JO`xTa<�> c J C M H C M � TA?_E=< � ?aF@: :=<�M}FD<�H >D<�LmJnEKH c C <N<�>DoxMOE � � � �� � � � � � A

{�� p o.<N<�H q FD<�EK>@?aJnE q E=J C P MOTxc J C Lm<1o.< C Ta<�EKkOF@: q c C ?ALmF@?AJnEKMOTKc J C Lm<yo.< C Ta<�EKkOF@: q MOExHQFD<�P �o.< C M}F@S C <4o C JO`ZTa<�>;c J C M H C M � TA?AEK< � ?aF@: :=<�M}FD<�H `xExMOT C JnTATA< C MOEKH � ?AF@: # � |�� | = �9:=< H C M � TA?AE=<5TA<�E=kOF@:�?A>�k C <�M}FD< C F@:KMOE4F@:=< o C < � ?aJnSK>�> ?AP SxTAM}F@?aJnEK>rHKS=<-FDJyMOE�MOHKHK<�H�C M}oIJnE F@:=< ` C >DF C JnTATa< C � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � � =

{@L B Jn>@>@? W Ta< oZM}F@:K> ?AE `xTAMOP�<�EbF TaJnMOH � >DF C MO?_E >@oxMOLm<�?AE � :K?ALz:IF@:=<�`xT_MOP�<�EGF >DF C <NF@L :=<�>P�JnE=JOFDJnEx?ALNMOTATaU FDJ >DJnP�< P M s=?AP4SKP >DF C MO?AE(' ���1MOEKH F@:=<�E4SKEKTaJnMOHx> � M ' ��� � ' � �F@:=<SKExTaJnMOHK?AE=ky?A>u<�TAMO>@F@?AL q MOTaJnE=kyF@:=<> MOP�<TA?AE=< MO>uF@:=<TAJnMOHK?AE=k � W ' � � � ' � � '&)MOEKHtL*'+) � ' �� � '+, ��`xT_MOP�<�EGFSxEKTaJnMOHK> � ?AF@: >@TaJOo.<.- � � � � � � � � �� � � � � L}|

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Page 10: Vohra - PhD (GaTech, 2006)

{@M � JnEKLm<�? � M W TA<fH C M � �NJnE=<�>�ciJ C F@:=< F � J �V>DF@M}kO<�H C M � o C JhLm<�>@> � ?aF@:tM H C M � ox?AE � : �JnE F@:=<4ci<N<�H C JnT_Ta< C JOc"F@:=<4` C >DFy>DF@M}kO< � W <NF � <N<�E � � MOEKH�� � � q { �;JnE F@:=<4F@M O< �VS=oC JnTATA< C JOc�F@:=< ` C >DF�>DF@M}kO< � W <NF � <N<�E � MOEKH � � q%> � JnE F@:K< ci<N<�H C JnTATa< C JOc�F@:K<>D<�LmJnEKHI>DF@M}kO< � W <NF � <N<�E � �yMOEKH�� � � q A ��JnE F@:=< H C M � ox?_E � W <NF � <N<�E�� MOEKH�� � � qMOEKH = ��JnE F@:=< F@M O< �VS=o C JnTATA< C JOcrF@:=< >D<�LmJnEKHt>DF@M}kO< � W <NF � <N<�E���� MOExH � � � � � � LO{

> | � MO>D< : JOc�` W < C W <�:KM � ?aJ C JnEIF@:=<�H C M � ox?_E q ?AE � :K?ALz:tF@:=<4` W < C M}FDF@MOLz:=<�>yFDJ F@:K<ox?AE � ?aF@:t>Do.<N<�H � Ta<�>@>F@:KMOEtF@:=<fo C <�Lm<N<�HK?AEKk >D<�LmJnEKH C JnT_Ta< C >Do.<N<�H�� � p S W LNMO>D<: M �r9;:=<�` W < C H=Jh<�> E=JOF c SKTATaU C <�TaJnMOH JnE%F@:K<�ox?AE �� � � � q � :=< C < � H=<�E=JOFD<�>F@:=<fHK<NoxM C F@S C < >@o7<N<�H c C JnP F@:K< ox?AE ��� � � � �� � � � � � �� � � � � � �� � � � � M :

> : p S W LNMO>D< : W �G9:=<` W < C c SKTATAU C <�TaJnMOHK>5JnE�F@:=<oZ?AE W S=F�H=Jh<�>5EKJOF5H C M � ?AEbFDJf?aF@>�`xExMOT>DF@? >DF@M}FD< � � � � � ) � � � � � � � � � �� � � � � � �� � � � � � �� � � � � M :

> { p S W LNMO>D< : L �Z9:=< ` W < C H C M � >?AEbFDJ ?aF@> `ZEKMOT�>DF@? >DF@M}FD<fJnEtF@:=< ox?AE �� )�� � � � � � M >

>@> � MO>D< {;JOc=` W < C W <�:KM � ?aJ C JnEfF@:=< H C M � oZ?AE q ?_E � :K?_L : F@:K<5` W < C M}FDF@MOLz:=<�>uFDJ1F@:=<"oZ?AE� ?aF@: >Do.<N<�H� k C <�M}FD< C F@:xMOEIF@:=< o C <�Lm<N<�HK?_E=kQ>D<�LmJnEKH C JnTATA< C >Do.<N<�H � � p S W LNMO>D<{}M �Z9;:=< ` W < C ?A> E=JOF;H C M � E ?_EGFDJ F@:K< `xEKMOT�>DF@? C <Nkn?aJnEtJnE F@:=< ox?_E �� � � ) � � � M A

> A p S W LNMO>D<f{ W �K9:=< ` W < C H C M � > FDJQ?AF@> `xEKMOT�>DF@? >DF@M}FD<fJnEtF@:=< ox?_E �� � � �) � � � � � M =

>@= ^ >DJOF@:=< C P MOT H C M � o C JlLm<�>@> � ?aF@:=JnS=F4H C M � ox?AEx> �W;yE%F@:=< Ta<Nc F4>@o7<N<�H �� � � > � M C �LNTa<�E=kOF@: � � ��MOEKHQJnEQF@:K< C ?akn:bF5FD<�Ex>@?aJnE ��� � � > � M C LNTa<�E=kOF@: � C�JhLNM}F@?AJnEK>"HK<�E=JOFD<�H W U��� �rM C < � :K< C <"F@:K<-` W < C >�<�?aF@:K< C M}FDF@MOLz:�FDJ J C H=<NoxM C Fuc C JnP2M C JnTATa< C�q ��� �dM C < � :K< C <?AEK?AF@?AM}F@?aJnE J C Lm<�>@>@M}F@?aJnE%JOc">@TA?Ao JnE F@:K< C JnTATa< C >�F@M O<�> oZTAMOLm< q ��� �1?AExHK?ALNM}FD<�H TaJlLNM �F@?aJnEK> � :=< C <fF@:=<4F C MOEK>@?AF@?aJnEK> W <NF � <N<�E >DF@? MOExHI>DJOc F�` W < C W <�:KM � ?aJ C :KM}oKo.<�E � ^ EF@:=< � <�TaJhLN?AFVU�MOEKH FD<�Ex>@?aJnE�o C JO`xTa<�> q ��� � ��M C < �NJnE=<�>5JOc*H C M � JnE C JnTATa< C > q ��!#"$!#"$! �M C < �NJnEK<�>JOc�E=J >@TA?Ao q MOExH �$"%"%"+"%"%" � M C < c C <N<f>DoxMOEK> � � � �� � � � � � �� � � � � M@M

> ~ ^ >DJOF@:=< C P MOT5H C M � o C JhLm<�> > � ?aF@:=JnSKF1H C M � ox?_EK> �1FD<�EK>@?aJnE � > � >Do.<N<�H q : � � � �?AE����� � � � � q { � � �� M}F � � � � q > � � � ?AE�� � � � � � � q � � � )M}F � � � ) q L � � � ?AE �� � � � � � � � � JOFD< F@:KM}F : F@: C JnS=kn: > :KM}oKo.<�E ?AE F@:K<c <N<�HIH C M � JnE F@:=< ` C >DF C JnTATA< C�q MOEKH > F@: C JnSKkn:FL�:KM}oKo.<�E ?AE FDJ c <N<�HtH C M � JnE F@:K<>D<�LmJnEKH C JnTATa< C � �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : | :

> � ^ >DJOF@:=< C P MOT.H C M � o C JlLm<�>@> � ?aF@:'M�H C M � oZ?AE��dF@:=<1H C M � ox?_E J >D<NF � � L#� � : LNP ?_>>@SKLz: F@:KM}FyF@:=<�<msl?aFy>Do.<N<�H� � c C JnP F@:=<�>D<�LmJnEKH C JnTATa< C ?A>�k C <�M}FD< C F@:KMOE F@:=< C JnT_Ta< C>@S C c MOLm< >Do.<N<�H � q >DJ�F@:KM}F F@:=< C < ?A>-F@M O<�S=otH C M � JnE F@:KM}F C JnTATA< C � 9:=<yTa<NciF oxTAJOF@>>Do.<N<�H � > � M C LNTa<�EKkOF@: q MOEKH F@:K< C ?akn:bF FD<�EK>@?aJnE � > � M C LNTA<�E=kOF@: � � � � � � �� � � � � : |n{

> L ^ >DJOF@:=< C P MOT H C M � o C JlLm<�>@> � ?aF@: M H C M � ox?AE ��FD<�EK>@?aJnE � > � >Do.<N<�H � : �� � � �?AE ����� � � � � q { � � � M}F � � � � q<> �� � � ?AE � � � � � � � q ~ � �� � � =@= |�LNP >� � ?AE � ��� � � �� q � � � ) M}F � � � ) q L � � � ��ciJ C�� � � � � JOFD<�F@:KM}F"F@:=<;` W < C E=J � H C M � >�oxM C F@TaU�JnE F@:=<�` C >DF C JnTATa< C � c C JnP : FDJ > � qoxM C F@TAU JnE F@:K< >D<�LmJnEKH C JnT_Ta< C � c C JnP > FDJt~ � q MOEKH oxM C F@TaU JnE F@:=< H C M � ox?AE � c C JnP~�FDJPL � � � � � �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : | A

s

Page 11: Vohra - PhD (GaTech, 2006)

> M ^ >DJOF@:=< C P MOTrH C M � o C JlLm<�>@> � ?aF@:tMQH C M � ox?AE���F@:=< H C M � ox?AE J >D<NF1?A>MOH �@SK>DFD<�H FDJF@:=<�L C ?aF@?_LNMOT � MOTAS=< � , � M#� : �'LNP >DJ F@:KM}FyF@:=<�>Do.<N<�H � JOc�F@:=<�` W < C <msl?aF@?_E=k F@:K<>D<�LmJnEKH C JnTATa< C ?_> <mslMOLmF@TAU � q MOEKHt:=<�EKLm<fF@:=< C <f?A> EKJQH C M � J C SKExTaJnMOHK?AE=k4JnEtF@:K<>D<�LmJnEKH C JnTATa< C � ;yE F@:=<fTa<Nc F?A> F@:K< oxTaJOF JOc�>Do.<N<�H � > � M C LNTa<�E=kOF@: MOEKH JnEtF@:K< C ?akn:bFFD<�EK>@?AJnE � > � M C LNTa<�E=kOF@: � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : | =

A | ^ >DJOF@:=< C P MOT�H C M � o C JhLm<�>@> � ?AF@:'M�H C M � ox?AE � ^ E F@:=<yoxTaJOF JOc�FD<�Ex>@?aJnE � > � >Do.<N<�H : � ��� � ?AE���� � � � � � q { � � ���M}F � � � � qO> � � � ?AE�� � � � � �� q � � � �)yM}F � � � ) q L � � � �fc J C � � � � 9:=<�` W < C E=J � H C M � > JnEKTaUtJnE F@:K<` C >@F C JnTATa< C � c C JnP : FDJ > � q MOEKH JnE F@:K< ox?AE � c C JnP > FDJ�L � � � � � � � � �� � � � � : |n~

A : ^ >DJOF@:=< C P MOT�H C M � o C JhLm<�>@> � ?AF@:'M�H C M � ox?_E :=<�?Akn:GF � � {}|�� : ��LNP q � :K?_L : C <�>@SKTAF@>?AE MOEQ<ms=?aF5>Do.<N<�H �;c C JnP F@:=<1>D<�LmJnEKH C JnTATa< C TA<�>@>�F@:KMOE � q MOExHQ:=<�EKLm<1SKEKTaJnMOHx?AE=kJOcxF@:K<-` W < C JnE4F@:=< >D<�LmJnEKH C JnTATa< C � ;yE4F@:=< Ta<NciF�?A>dF@:=< oxTAJOFrJOc7>Do.<N<�H � > � M C LNTa<�E=kOF@: qMOEKH JnEtF@:=< C ?akn:bF?A> FD<�EK> ?aJnE � > � M C LNTa<�EKkOF@: � � � � � � � �� � � � � � �� � � � � : | L

A { ^ >DJOF@:=< C P MOT7H C M � o C JhLm<�>@> � ?aF@: MfH C M � ox?AE :=<�?Akn:GF � � {}|�� : � LNP q ?AE F@:K<;FD<�EK>@?AJnE� > � >Do.<N<�H'oxTaJOF : � �� � �"c J C � � � � � � q { � � � M}F � � � � qK> � �� � ;ciJ C� � � � � � � q A � �� � � � c J C � � � � � � q = � �� � M}F � � �

�q � � �� )

M}F � � � ) q L � � � � ciJ C � � � � 9:=< ` W < C FD<�EK>@?AJnE H=<�L C <�MO>D<�>1JnEIF@:=<�>D<�LmJnEKHC JnTATA< C c C JnP > FDJ A=q MOEKHQF@:=<�E'?AEKL C <�MO>D<�>"JnE F@:=<;ox?_E c C JnP A FDJ'L � C <�LmJ � < C ?AE=k�c C JnPA FDJ =hq MOEKH F@:=<�EtLmJnP oxTa<NF@?AE=k�F@:K< H C M � c C JnP = FDJPL � � � �� � � � � � �� � � � � : | M

A > Ru? W < C � <�TaJlLN?aFVU� � � � � < C >@Sx> M C LNTa<�E=kOF@: � c J C ?A>DJOF@:=< C P MOT�H C M � � 9:=<�� ?AEKHx?ALNM}FD<o.Jn?AEbF@> JOcdM}FDF@MOLz:KP�<�EbF1MOExHtH=<NF@MOL :xP�<�EGF;c C JnP F@:=< C JnTATA< C > MOEKH � ?AExHK?ALNM}FD<�>>DF@M C FJOc�>@TA?ao � � � � � �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � :@: ~

A@A 9r<�EK>@?aJnE�� � � � � < C > SK>M C LNTa<�EKkOF@: � c J C ?A>@JOF@:=< C P MOT*H C M � � �� � � � � � �� � � � � :@: �

A = R C ?_LmF@?aJnE�� � � � � < C >@SK>M C LNTa<�E=kOF@: � ciJ C ?A>DJOF@:=< C P MOT�H C M � � �� � � � � � �� � � � � :@: L

A ~ 9r<�EK>@?aJnE�� � � � � > � <�TaJlLN?aFVU� � � �-c J C ?A>@JOF@:=< C P MOT�H C M � � � �� � � � � � �� � � � � :@: M

A � 9:=< ` W < C FD<�P�o.< C M}F@S C < ?_EfF@:=< FDJ � ��� � � � � � >�M C LNTA<�E=kOF@: � � � � 9:K<-o.Jn?AEbF@>dJOcx<�EbF C UMOEKH <ms=?aF1FDJ C JnTATa< C >1M C <�TAM W <�Ta<�H � ?aF@: � � 8 :=<�M}FD<�H c C <N<�>DoxMOE � ?aF@: M'F C ?AMOE=knSxTAM CFD<�P�o.< C M}F@S C < k C MOHK?a<�EbF � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : {}|

A L Ru? W < C � <�TaJlLN?aFVU � � � � < C >@SK>*M C LNTA<�E=kOF@: � HKS=<�FDJ;M;:=<�M}FD<�Hfc C <N<�>DoZMOE W <NF � <N<�Ef>D<�LmJnEKHC JnTATA< C MOEKH F@:=<fH C M � oZ?AE ��� � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : {O{

A M Ru? W < C FD<�EK>@?AJnE � � � � � < C >@SK>rM C LNTa<�E=kOF@: � HxS=<�FDJ�M�:=<�M}FD<�H c C <N<�>DoxMOE W <NF � <N<�E4>D<�LmJnEKHC JnTATA< C MOEKHtH C M � ox?AE � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : { >

= | R C ?_LmF@?aJnEfc J C Lm< � � � � � < C >@SK>dM C LNTa<�E=kOF@: � HKS=<�FDJ1M;:=<�M}FD<�H c C <N<�>DoxMOE W <NF � <N<�E4>D<�LmJnEKHC JnTATA< C MOEKHtH C M � ox?AE � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : { A

= : Ru? W < C FD<�EK> ?aJnE � � � � � < C >@SK> � <�TAJhLN?aF U � � � HxS=<tFDJ M :=<�M}FD<�H c C <N<�>DoxMOE W <NF � <N<�E>D<�LmJnEKH C JnTATa< C MOExHtH C M � ox?AE � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : { =

= { 9:=< FD<�P o7< C M}F@S C < o C JO`xTa<yJOcrF@:K<fH C M � TA?AE=< � ?aF@: MQ:=<�M}FD<�Ht`xExMOT.F@M O<�S=o C JnT_Ta< C � � : {O~=@> Ru? W < C � <�TaJlLN?aFVU� � � � � < C > SK>M C LNTa<�EKkOF@: � HxS=< FDJ F@:=<f:K<�M}FD<�HtF@:K? C H C JnTATa< C � � � � � : {��= A Ru? W < C FD<�EK>@?aJnE � � � � � < C >@SK>M C LNTA<�E=kOF@: � HKS=<yFDJ F@:=< :=<�M}FD<�HtF@:K? C H C JnTATa< C � � � � � : {@L

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=@= R C ?_LmF@?aJnE c J C Lm<(� � � � � < C >@SK>M C LNTa<�E=kOF@: � HKS=< FDJ F@:K<f:=<�M}FD<�HtF@:x? C H C JnTATa< C � � � � � : {@M= ~ Ru? W < C FD<�EK>@?aJnE � � � � � < C >@SK> � <�TaJlLN?aF U� � � � HKS=< FDJ F@:=< :=<�M}FD<�HtF@:K? C H C JnTATa< C ��� � � � : > |= � 9:=<fFD<�P�o.< C M}F@S C < o C JO`xTa< JOc�F@:=< H C M � TA?AE=< � ?aF@:tM :=<�M}FD<�H c C <N<�>DoxMOE MOEKHI:=<�M}FD<�H

`xEKMOT.F@M O<�SKo C JnTATA< C � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : > :

= L Ru? W < C � <�TAJhLN?aF U � � � � < C >@Sx>-M C LNTa<�E=kOF@: � ciJ C M�:=<�M}FD<�H c C <N<�>DoxMOE MOEKH':=<�M}FD<�H F@:K? C HC JnTATA< C � � � � � �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : > {

= M Ru? W < C FD<�EK>@?aJnE � � � � � < C >@SK> M C LNTa<�E=kOF@: � ciJ C M�:=<�M}FD<�H c C <N<�>DoxMOE MOEKH :=<�M}FD<�H F@:K? C HC JnTATA< C � � � � � �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : >@>

~}| R C ?_LmF@?aJnE ciJ C Lm<�� � � � � < C >@Sx> M C LNTa<�E=kOF@: � ciJ C M�:=<�M}FD<�Htc C <N<�>@oxMOE MOEKH :=<�M}FD<�H F@:K? C HC JnTATA< C � � � � � �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : > A

~ : Ru? W < C FD<�EK>@?aJnE(� � � � � < C >@SK> � <�TaJlLN?aF U� � � �rc J C M1:K<�M}FD<�H�c C <N<�>DoxMOE�MOEKH�:=<�M}FD<�H�F@:K? C HC JnTATA< C � � � � � �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : >@=

~O{ 9:=<yFD<�P�o.< C M}F@S C < o C JO`xTA<�JOcrF@:=< H C M � TA?AE=< � ?aF@: M�:=<�M}FD<�HtH C M � oZ?AE M}F�M FD<�P o7< C �M}F@S C <fJOc = : > � � � � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : > ~

~ > Ru? W < C � <�TaJlLN?aFVU � � � � < C >@SK>�M C LNTA<�E=kOF@: � J W F@MO?AE=<�H Sx>@?AE=k M :=<�M}FD<�H H C M � ox?AE�?AE�F@:K<H C M � TA?AEK< � � � �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : > L

~ A Ru? W < C FD<�Ex>@?aJnE�� � � � � < C > SK> M C LNTa<�E=kOF@: � J W F@MO?AE=<�H W U'SK>@?AE=k M4:K<�M}FD<�H H C M � ox?AEQ?_EF@:=<fH C M � T_?AE=< ��� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : > M

~ = R C ?_LmF@?aJnE � � � � � < C > SK> M C LNTa<�E=kOF@: � J W F@MO?AEK<�H W U SK>@?AE=k M :=<�M}FD<�H H C M � ox?_E ?_E F@:K<H C M � TA?AEK< � � � �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : A |

~O~ Ru? W < C FD<�Ex>@?aJnE�� � � � � < C >@Sx> � <�TaJlLN?aF U� � � �J W F@MO?AE=<�H W U SK>@?AE=k'M :K<�M}FD<�H H C M � oZ?AE?AE F@:K< H C M � TA?AE=< � � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : A :

~�� � JnP�oZM C ?A>DJnE]JOc H C M � TA?AE=< FD<�EK> ?aJnE]J W F@MO?AE=<�H]Sx>@?AE=k%F@:K<Ic JnTATaJ � ?AE=k FD<�P�o.< C M}F@S C <o C JO`ZTa<�> �u:=<�M}FD<�HQc C <N<�>DoZMOE ��� � � q :=<�M}FD<�H F@:K? C H C JnTATa< C � � � ��� q MOEKH :=<�M}FD<�H'H C M � �ox?AE � � " � " � " � � �� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : A {

~@L � JnP�oZM C ?A>DJnEIJOc�H C M � TA?AE=<yc C ?ALmF@?aJnEIciJ C Lm<�>�J W F@MO?AEK<�HISK>@?_E=k�F@:=<fc JnTATaJ � ?AE=k�FD<�P o7< C �M}F@S C <yo C JO`xTa<�> �u:=<�M}FD<�H c C <N<�>DoxMOE ��� � � q :=<�M}FD<�H F@:K? C H C JnT_Ta< C � � � ��� q MOEKH :=<�M}FD<�HH C M � ox?AE � � " �#" �#" � � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : A >

~@M 9:=<y` W < C FD<�EK>@?AJnE � � � � � > M C LNTa<�E=kOF@: � SKEKH=< C ?A>DJOF@:K< C P MOT.LmJnEKHK?aF@?AJnEK>-ciJ C ��� � �� � : | LNP MOExH � � � � � � � > | LNP � � � � � �� � � � � � �� � � � � � �� � � � � : A =

� | 9:=< ` W < C FD<�EK>@?AJnE � � � � � >'M C LNTa<�E=kOF@: � � ?aF@:]M :=<�M}FD<�H >D<�LmJnEKH c C <N< >DoxMOE]ciJ C��� � � � � : |QLNP MOEKH � � � � � � � > | LNP � �� � � � � � �� � � � � � �� � � � � : A ~

� : 9:=< ` W < C FD<�EK>@?AJnE�� � � � � > M C LNTa<�E=kOF@: � � ?aF@:%MI:K<�M}FD<�H F@:x? C H C JnT_Ta< C c J C ��� � �� � : | LNP MOExH � � � � � � � > | LNP � � � � � �� � � � � � �� � � � � � �� � � � � : A �

�}{ 9:=< ` W < C FD<�EK> ?aJnE � � � � � >'M C LNTa<�E=kOF@: � � ?AF@:]M :K<�M}FD<�H�>@<�LmJnEKH�c C <N<�>@oxMOE MOExH:=<�M}FD<�HIF@:K? C H C JnT_Ta< C ciJ C ��� � � � � : |QLNP MOExH � � � � � � � > | LNP � � �� � � � � : A L

� > 9:=< ` W < C FD<�EK>@?aJnE � � � � � > M C LNTa<�E=kOF@: � � ?aF@: M :=<�M}FD<�H H C M � ox?AE ciJ C ��� � �� � : | LNP MOExH � � � � � � � > | LNP � � � � � �� � � � � � �� � � � � � �� � � � � : = |

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� A 9:=<1` W < C FD<�EK>@?aJnE'?AE F@:=<�FDJ � � � � � � > M C LNTa<�E=kOF@: � SKEKHK< C ?A>@JOF@:=< C P MOT7LmJnEKHK?aF@?AJnEK>c J C ��� > | LNP � ?aF@: `ZEKMOT C JnTATa< C >@S C c MOLm<f>Do.<N<�HK> ��� � � ��� | q � � � � � � A | q MOEKH � �" �#" � " � � : | LNP > � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : = :

� = 9:=<�` W < C FD<�Ex>@?aJnE ?AE F@:=<�FDJ � � � � � � > M C LNTa<�E=kOF@: ��� ?AF@: M :=<�M}FD<�H >D<�LmJnExH c C <N<>DoxMOE c J C � � > | LNP � ?AF@: `ZEKMOT C JnTATa< C >@S C c MOLm<�>Do.<N<�HK> ��� � � ��� | q � � � � � � A | qMOEKH � � " � " �#" � � : | LNP >� � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : = {

�}~ 9:=<�` W < C FD<�Ex>@?aJnE%?AE F@:K<�FDJ � � � � � � > M C LNTA<�E=kOF@: � � ?aF@: M :=<�M}FD<�H F@:K? C H C JnT_Ta< Cc J C ��� > | LNP � ?aF@: `ZEKMOT C JnTATa< C >@S C c MOLm<f>Do.<N<�HK> ��� � � ��� | q � � � � � � A | q MOEKH � �" �#" � " � � : | LNP > � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : =@>

��� 9:=< ` W < C FD<�Ex>@?aJnEt?AE F@:K< FDJ � � � � � � >;M C LNTa<�E=kOF@: � � ?aF@: M :K<�M}FD<�Htc C <N<�>DoxMOEtMOExH:=<�M}FD<�HIF@:K? C H C JnT_Ta< C ciJ C � � > | LNP � ?aF@: `xExMOT C JnTATa< C >@S C c MOLm< >@o7<N<�Hx> ��� � � ��� | q� � � � � � A | q MOEKH � � " �#" � " � � : | LNP >� � � � �� � � � � � �� � � � � � �� � � � � : = A

� L 9:=<f` W < C FD<�EK>@?aJnE ?AE F@:=<fFDJ � � � � � � >�M C LNTa<�E=kOF@: � � ?aF@:tMQ:K<�M}FD<�H H C M � oZ?AE ciJ C� � > |�LNP � ?aF@:'`xEKMOT C JnT_Ta< C > S C c MOLm< >Do.<N<�HK> ��� � � ��� | q � � � � � � A | q MOEKH � � " � "�#" � � : | LNP > � ��� � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : =@=

� M B TAJOF-JOc � < C >@SK> � c J C TaJnMOHK?AEKk JnE W JOF@: C JnTATa< C > q H C M � ox?AE J >D<NF@> M C <�� : |OLNP q : |OLNP � � : ~}|L}| B TAJOF4JOc � < C >@Sx> � ciJ C TaJnMOHx?AE=k ` C >DF C JnTATa< C MOEKH E=J H C M � JnE >D<�LmJnEKH q H C M � oZ?AE

J >D<NF@>�M C < � : |OLNP q : � ~@L}LNP � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � : ~ :L : B TAJOF JOc � < C >@SK> � c J C E=J H C M � JnE ` C >DF C JnTATa< C MOEKH TaJnMOHK?_E=k�JnEt>D<�LmJnEKH q H C M � oZ?AE

J >D<NF@>�M C < � � > L �?> : LNP q : |OLNP � � � � � � � � � �� � � � � � �� � � � � � �� � � � � : ~O{LO{ B TAJOF*JOc � < C >@Sx> � c J C E=JH C M � JnE W JOF@: C JnTATa< C > q H C M � ox?AE1J >@<NF@>�M C < � � > L �?> : LNP q : � ~@L}LNP � � : ~ >L > � JnSKTAJnP W c C ?ALmF@?AJnE P�JlH=<�T�� c C ?ALmF@?aJnEKMOT c J C Lm< o7< C Ta<�E=kOF@: � > � F@:K< C <�TAM}F@? � < >Do.<N<�H

W <NF � <N<�EtF@:=<f` W < C MOEKH C JnTATA< C >@S C c MOLm< � � � �� � � � � � �� � � � � � �� � � � � : ~��L A � C <N<No�� C M}FD<fH=<No.<�EKH=<�EbF c C ?ALmF@?aJnE P�JlH=<�T � � � �� � � � � � �� � � � � � �� � � � � : ~@LL = � <�TaJlLN?aFVU'o C JO`ZTa< � � �"c J C F@:=<y<�EbF@? C < H C M � TA?AEK<�SK>@?_E=k � JnSKTaJnP W c C ?ALmF@?AJnE � ?aF@: # �

|�� { MOExHt>D< � < C MOT � MOTAS=<�>JOcdF@:K< L C <N<No � C M}FD<4H=<No.<�EKH=<�EbF-c C ?ALmF@?AJnE LmJb<('QLN?A<�EGF � ��� � � : L}|LO~ 9:=< � <�TAJhLN?aF U o C JO`xTa< � � �-JnEtF@:=< ` C >@F C JnTATa< C � � � � � � � �� � � � � � �� � � � � : L :

L�� 9:=< � <�TAJhLN?aF U o C JO`xTa< � � �-JnEtF@:=<f>D<�LmJnEKH C JnTATa< C � � � � � �� � � � � � �� � � � � : LO{L@L � C <N<No�� C M}FD<fH=<No.<�EKH=<�EbF c C ?ALmF@?aJnE LmJh<('QLN?a<�EbF � � < C > SK>�� JnE F@:=< >D<�LmJnEKH C JnT_Ta< C � � � : L >

L@M � C <N<No�� C M}FD<fH=<No.<�EKH=<�EbF c C ?ALmF@?aJnE LmJh<('QLN?a<�EbF � � < C > SK>�� �JnE F@:=<f` C >DF C JnT_Ta< C � � � � : L A

M}| 9:=< ` W < C FD<�Ex>@?aJnE�� � � �"oxTaJOFDFD<�HIM}knMO?AEK>DF;M C LNTa<�E=kOF@: � MOTaJnE=k F@:K< FDJ � ���� � � � � : L =

M : Ru? W < C FD<�EK>@?aJnE � � � �"JnEIF@:=< ` C >@F C JnTATa< C � � � �� � � � � � �� � � � � � �� � � � � : LO~MO{ Ru? W < C FD<�EK>@?aJnE � � � �"JnEIF@:=< >D<�LmJnEKH C JnTATa< C � �� � � � � � �� � � � � � �� � � � � : L��

M > � J C P MOT�c J C Lm< o.< C Ta<�EKkOF@: � � � �-MOLmF@?_E=k�JnEtF@:=< ` W < C c J C F@:=<f<�EGF@? C < H C M � TA?AE=< � � � : L@L

M A � J C P MOT�c J C Lm<.� � � �-JnE F@:=< ` C >DF C JnTATA< C � � � �� � � � � � �� � � � � � �� � � � � : L@M

M = � J C P MOT�c J C Lm<.� � � �-JnE F@:=< >@<�LmJnEKH C JnT_Ta< C � � �� � � � � � �� � � � � � �� � � � � : M}|

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Page 14: Vohra - PhD (GaTech, 2006)

MO~ R C ?_LmF@?aJnE c J C Lm< o.< C Ta<�E=kOF@:�� � � � � < C >@Sx>M C LNTa<�E=kOF@: � MOTaJnEKk F@:=< FDJ �� � �� � � � � : M :

M�� R C ?_LmF@?aJnE c J C Lm<(� � � �"JnE F@:=< ` C >DF C JnTATa< C � � � �� � � � � � �� � � � � � �� � � � � : MO{M@L R C ?_LmF@?aJnE c J C Lm<(� � � �"JnE F@:=<f>D<�LmJnExH C JnTATa< C � �� � � � � � �� � � � � � �� � � � � : M >

M@M Ru? W < C � <�TaJlLN?aFVU� � � � � < C > SK>M C LNTa<�EKkOF@: � c J C MOE ?A>DJOF@:=< C PQMOT.o C JlLm<�>@> � � �� � � � � {}|O|: |O| Ru? W < C FD<�P�o.< C M}F@S C < � � � � � < C > SK>M C LNTa<�EKkOF@: � ciJ C MOEI?A>DJOF@:=< C PQMOT.o C JlLm<�>@> � � � � � {}| :: | : Ru? W < C FD<�EK>@?aJnE � � � � � < C >@SK>M C LNTA<�E=kOF@: � ciJ C MOEt?A>DJOF@:=< C P MOT.o C JlLm<�>@> � � �� � � � � {}|n{: |n{ R C ?_LmF@?aJnE c J C Lm<(� � � � � < C >@SK>M C LNTa<�E=kOF@: � ciJ C MOEt?A>DJOF@:K< C P MOT.o C JlLm<�>@> � � �� � � � � {}| >: | > Ru? W < C � <�TaJlLN?aF U� � � � � < C > SK>�M C LNTa<�E=kOF@: � c J C MQH C M � o C JhLm<�> >�LNM C@C ?a<�HtJnS=F1M}F1MOP �

W ?a<�EbF FD<�P�o.< C M}F@S C <f{@M@L � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � {}| A: | A Ru? W < C FD<�P�o.< C M}F@S C < � � � � � < C >@SK>1M C LNTa<�E=kOF@: � ciJ C M'H C M � o C JlLm<�>@>�LNM C@C ?a<�H JnS=F�M}F

MOP W ?a<�EbFFD<�P�o.< C M}F@S C <f{@M@L � � � � � � � � � �� � � � � � �� � � � � � �� � � � � {}| =: | = Ru? W < C FD<�EK> ?aJnE�� � � � � < C >@SK>1M C LNTa<�E=kOF@: � c J C M'H C M � o C JhLm<�>@>1LNM C@C ?A<�HtJnS=FyM}F1MOP �

W ?a<�EbF FD<�P�o.< C M}F@S C <f{@M@L � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � {}|n~: |n~ R C ?_LmF@?aJnE ciJ C Lm< � � � � � < C > SK>yM C LNTa<�E=kOF@: � c J C M'H C M � o C JlLm<�>@>yLNM C@C ?a<�H JnS=FyM}FyMOP �

W ?a<�EbF FD<�P�o.< C M}F@S C <f{@M@L � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � {}| �: | � Ru? W < C � <�TaJlLN?aFVU� � � � � < C >@Sx> M C LNTa<�E=kOF@: � c J C MtH C M � o C JlLm<�>@> LNM C@C ?a<�H JnS=FfSKExH=< C

MOHK?AM W M}F@?AL LmJnEKHK?aF@?AJnEK> � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � {}| L: | L Ru? W < C FD<�P o7< C M}F@S C < � � � � � < C >@SK>'M C LNTa<�E=kOF@: � c J C M H C M � o C JhLm<�> > LNM C@C ?a<�H]JnSKF

SKEKHK< C MOHK?AM W M}F@?AL LmJnExHK?aF@?aJnEK> � � � � � � � � �� � � � � � �� � � � � � �� � � � � {}| M: | M Ru? W < C FD<�EK>@?aJnE�� � � � � < C >@SK> M C LNTA<�E=kOF@: � ciJ C MtH C M � o C JlLm<�>@> LNM C@C ?A<�H JnS=FfSKExH=< C

MOHK?AM W M}F@?AL LmJnEKHK?aF@?AJnEK> � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � { : |:@: | Rdc C ?ALmF@?aJnE ciJ C Lm< � � � � � < C >@SK>yM C LNTa<�E=kOF@: � c J C M H C M � o C JlLm<�>@>yLNM C@C ?A<�HIJnS=F SKExH=< C

MOHK?AM W M}F@?AL LmJnEKHK?aF@?AJnEK> � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � { :@::@:@: Ru? W < C � <�TAJhLN?aF U� � � � � < C >@Sx>�M C LNTa<�E=kOF@: � c J C M1H C M � o C JlLm<�>@> � ?aF@:4My:=<�M}FD<�H�>D<�LmJnEKH

c C <N<�>DoxMOEtM}F > { > � � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � { : {:@: { Ru? W < C FD<�P�o.< C M}F@S C < � � � � � < C >@SK>1M C LNTa<�E=kOF@: � ciJ C M'H C M � o C JlLm<�>@> � ?aF@: M :=<�M}FD<�H

>D<�LmJnEKHIc C <N<�>DoxMOEtM}F > { > � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � { : >:@: > Ru? W < C FD<�EK>@?aJnE(� � � � � < C >@SK>uM C LNTa<�EKkOF@: � ciJ C MyH C M � o C JlLm<�>@> � ?aF@:�My:=<�M}FD<�H�>D<�LmJnEKH

c C <N<�>DoxMOEtM}F > { > � � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � { : A:@: A R C ?_LmF@?aJnE�ciJ C Lm<#� � � � � < C >@Sx>�M C LNTa<�E=kOF@: � ciJ C M H C M � o C JhLm<�>@> � ?aF@:�M :=<�M}FD<�H >D<�LmJnEKH

c C <N<�>DoxMOEtM}F > { > � � � � � � �� � � � � � � �� � � � � � �� � � � � � �� � � � � { : =:@: = p Lz:=<�P M}F@?AL Hx?AM}k C MOP JOc�M W <�TaF F C MOEK> P ?aFDF@?AE=k�M�FDJ C ghS=< � W <NF � <N<�EtF � J oxSKTATa<NUl> � {O{ A

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Page 15: Vohra - PhD (GaTech, 2006)

:@: ~ � <�TaF5FD<�Ex>@?aJnE � � � �uMO>-M c SKEKLmF@?aJnE JOc*M C L;Ta<�EKkOF@: � ciJ C Mf>DF@? W <�TaF � � � { = � q FDJOo �MOEKH M'LmJnP�oxTA?AMOEbF W <�TaF � ��� |�� { � q W JOFDFDJnP ��� � ? C LNTa<�> ��� ��?AEKHx?ALNM}FD< TaJlLNM}F@?aJnEK>�JOcM}FDF@MOL :xP�<�EGF�FDJ1F@:=<"oxSKTATa<NUl> q MOEKH W J�sl<�> � � �*?AEKHK?_LNM}FD<5TaJlLNM}F@?aJnEK>rJOcKH=<NoxM C F@S C < � RKSKT_T>DJnTASKF@?aJnE ��� � � q <�E=kn?AE=<N< C ?AE=k >@JnTAS=F@?aJnE ��! !(! � q MOTaFD< C EKM}FD< >DJnTAS=F@?aJnE �$"%"%" "%"%" � q MOExHLNM}ox>DF@MOE >DJnT_S=F@?aJnE ��!#"$!#"$! � � 9:=<fF@:=<fc SKTAT q <�E=kn?AE=<N< C ?_E=k q MOEKH MOTaFD< C EKM}FD<�>DJnTAS=F@?AJnEK>M C <f?_EKHK?A>DF@?_E=knSK?A>@:xM W Ta< c J C F@:=<f>DF@? W <�TaF LNMO>D< � � � � � � � �� � � � � � �� � � � � { > �

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:@: L � J C P MOT c J C Lm<to.< C SKEx?aF�Ta<�E=kOF@: � � � � c C JnP F@:=< oxSKT_Ta<NUh>4JnE]F@:=< W <�TaF�ciJ C M%>DF@? W <�TaF � � � { = � q FDJOo � MOEKH M LmJnP�oZTA?AMOEbF W <�TaF � � � |�� { � q W JOFDFDJnP ���QRKSxTAT">@J �TAS=F@?AJnE ��� � � q <�E=kn?AE=<N< C ?AE=kt>DJnTASKF@?aJnE ��!�! ! � q MOTaFD< C EKM}FD< >DJnT_S=F@?aJnE �$"%"%" "%"%" � q MOExHLNM}ox>DF@MOE >DJnT_S=F@?aJnE ��!#"$!#"$! � � 9:=<fF@:=<fc SKTAT q <�E=kn?AE=<N< C ?_E=k q MOEKH MOTaFD< C EKM}FD<�>DJnTAS=F@?AJnEK>M C <f?_EKHK?A>DF@?_E=knSK?A>@:xM W Ta< c J C F@:=<f>DF@? W <�TaF LNMO>D< � � � � � � � �� � � � � � �� � � � � { > M

:@: M R C ?_LmF@?aJnEKMOT c J C Lm<to.< C SKEx?aF�Ta<�E=kOF@: � � � � c C JnP F@:=<toxSxTATa<NUl> JnE F@:=< W <�TaF�ciJ C >DF@? W <�TaF � � � { = � q FDJOo � MOEKH M LmJnP�oZTA?AMOEbF W <�TaF � � � |�� { � q W JOFDFDJnP ���QRKSxTAT">@J �TAS=F@?AJnE ��� � � q <�E=kn?AE=<N< C ?AE=kt>DJnTASKF@?aJnE ��!�! ! � q MOTaFD< C EKM}FD< >DJnT_S=F@?aJnE �$"%"%" "%"%" � q MOExHLNM}ox>DF@MOE >DJnT_S=F@?aJnE ��!#"$!#"$! � � 9:=<fF@:=<fc SKTAT q <�E=kn?AE=<N< C ?_E=k q MOEKH MOTaFD< C EKM}FD<�>DJnTAS=F@?AJnEK>M C <f?_EKHK?A>DF@?_E=knSK?A>@:xM W Ta< c J C F@:=<f>DF@? W <�TaF LNMO>D< � � � � � � � �� � � � � � �� � � � � { A |

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Page 16: Vohra - PhD (GaTech, 2006)

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H C M � o C JlLm<�>@> � � J C ox:KJnTaJOkn?ALNMOT MO>Do.<�LmF@> C <�TAM}FD<�H FDJ]H C M � M C < E=JOFtMOHKH C <�>@>D<�H ?AE HK<NF@MO?AT q F@:K?A>M}oKo C JnMOL :'?A>5P MO?_EKTaU�HK? C <�LmFD<�H FDJ SKExH=< C >DF@MOEKHx?AE=k F@:=<1LmJnEK>DF@?aF@S=F@? � < W <�:KM � ?aJ C ?AE M F � J4>DF@M}kO<yH C M �o C JlLm<�>@> � 9;:K?A>4F@MO> ?A>�MOLNLmJnP�oxT_?A>@:=<�H ?AE >D< � < C MOT;>DF@M}kO<�> � 9:=<t>D<NF JOcyLmJnEK>D< C � M}F@?aJnE <�gbSKM}F@?AJnEK>c J C F@:K< ` W < C JnE M C JnTATA< C MOEKH c C <N<'>@oxMOE M C <'HK< � <�TaJOo.<�H ` C >DF � 9;:=<�>D<'<�gbSKM}F@?AJnEK> M C <'J W F@MO?AE=<�HW U%SK>@?AE=k F@:=< LNT_MO>@>@?ALNMOT-LmJnEGF C JnT � JnT_SKP�< M}oxo C JnMOL : JOc;LmJnEbF@?AEhSKSKP P�<�L :xMOEK?ALN> � � U MOS=knP�<�EbF@?AE=kF@:=<fLmJnEx>D< C � M}F@?aJnEI<�ghSKM}F@?aJnEx> � ?aF@:IM LmJnEK>DF@?aF@SKF@? � <fP�JlH=<�T�JOc�F@:=<f` W < C MOEKHI>@JnT � ?_E=k�F@:=< C <�> SKTaF@?AE=k>DUl>DFD<�P JOcd<�ghSKM}F@?aJnEK> q F@:K< � <�TaJlLN?aFVU MOEKH FD<�Ex>@?aJnE JOcuF@:=< ` W < C LNMOE W < o C <�HK?ALmFD<�H �9:K< <�gbSKM}F@?AJnEK>�JOcyP�JOF@?aJnE M C < ` C >DF M}oKoxT_?a<�H FDJ%` W < C H C M � JnE M C JnTATA< C SxEKH=< C ?A>DJOF@:K< C P MOT

LmJnEKHK?AF@?aJnEK>ySK>@?AEKk M > ?AP�oxTa<�TA?AEK<�M C TaU <�TAMO>DF@?_L�` W < C PQM}FD< C ?AMOT�P�JlH=<�T � 9:=<�o C <�HK?ALmFD<�H C <�>Do.JnEK>@<4JOcF@:=< ` W < C ?A>QH=< � <�TaJOo.<�H MO>QM c SKEKLmF@?AJnE JOc�F@: C <N<tE=JnE �VHK?AP <�EK>@?aJnEKMOT-oxM C MOP�<NFD< C > C <(�x<�LmF@?AE=k ` W < C>DF@? E=<�>@> q ` W < C FD<�Ex>@?aJnE q MOEKHIF@:K< Ta<�E=kOF@: JOc�F@:=<�H=<Nc J C P M}F@?aJnE �NJnE=< � 9;:=<fE=< � P�JlH=<�T*F@M O<�> ?AEbFDJMOLNLmJnSKEbF W JOF@: F@:=<�Lm<�EGF C ?Ac S=knMOT�MOLNLm<�TA< C M}F@?aJnE%MOEKH >DF C <NF@L :K?AEKk MOLNLm<�TA< C M}F@?aJnE � R=J C M Lm< C F@MO?_E C MOE=kO<JOc-F@:=<�F@: C <N< E=JnE �VHK?AP�<�EK> ?aJnEKMOTroxM C MOP�<NFD< C > q F@:=<�c SKTATu>DJnTAS=F@?AJnE LNMOE W <�M}oKo C J�s=?AP M}FD<�H <�?AF@:=< C W U

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F@:=< ghSKMO>@? �V>DF@M}F@?_L1>@JnTAS=F@?aJnE W U E=<NknTa<�LmF@?_E=k W JOF@: MOLNLm<�TA< C M}F@?aJnE FD< C PQ> ?AEQF@:K< P�JnP�<�EbF@SKP <�gbSxM}F@?aJnE qLmJnP P�JnExTaU C <Nci< C@C <�H FDJQMO> F@:=<fLNM}oZ>DF@MOEt>DJnTASKF@?aJnE q J C W U F@:K< <�E=kn?AE=<N< C ?_E=k�>DJnTAS=F@?aJnE � :K?AL : C <NF@MO?AEK>JnEKTaU F@:=<fLm<�EbF C ?ac S=knMOT*MOLNLm<�Ta< C M}F@?aJnE �8 P4SKTaF@?A>@F@M}kO< H C M � LmJnEx>@?A>DF JOc>D< � < C MOT C JnTATa< C > � :K?ALz: H C M � F@:=<Q` W < C >@<�gbS=<�EbF@?AMOTATAU � 8 F � J

>DF@M}kO<'H C M � o C JlLm<�>@> ?A> M oZM C F@?ALNSKTAM C LNMO>@<QJOc-F@:=<QP4SKTaF@?A>DF@M}kO< H C M � MOExH%LmJnEK>@?A>@F@> JOc F@: C <N< H C M �C JnTATA< C > � � U SK>@?_E=k M�LmJnEK>@F@?aF@S=F@? � < L :xM C MOLmFD< C ?���M}F@?aJnEtJOc�F@:=< ` W < C >"FDJ M4ox?a<�Lm< � ?_>D<1T_?AE=<�M C TaU�<�T_MO>DF@?AL �oxTAMO>@F@?AL5FDJ LNM}oxF@S C < F@:=< >DJOc FD<�EK?AE=k W <�:KM � ?aJ C JOcZMO> �V>DoxSKE4` W < C >dMOEKH W U ?AEKLmJ C o7J C M}F@?AE=k;FD<�P o7< C M}F@S C <H=<No.<�EKH=<�ExLm< q F@:K< ` W < C W <�:KM � ?AJ C ?_E F@:=<yF � JQ>DF@M}kO<fH C M � ?A> c JnSKEKH W U MO>@>D<�P W TA?_E=k�F@:=<ykOJ � < C EK?_E=k<�ghSKM}F@?aJnEK> c J C ` W < C >1JnE C JnTATa< C > MOEKH ?_E c C <N< >@oxMOEK> q FDJOkO<NF@:K< C � ?aF@: PQM}F@L :K?AEKk W JnSxEKHKM C U LmJnEKHK? �F@?aJnEK> q FDJIo C JhHxSKLm< MtLmJnP�o C <�:=<�EK>@? � < P�JhHK<�TuciJ C MtF � J >@F@M}kO< q EKJnE �V?A>DJOF@:=< C P MOT�?AEKHxSK>DF C ?AMOTdH C M �o C JlLm<�>@> � 9:=<fP JhH=<�T�?A> F@:=<�E <�P oxTaJ UO<�H FDJQ>@?_P SKT_M}FD< C <No C <�>@<�EGF@M}F@? � <4H C M � TA?AE=<�>;:KM � ?AE=k ?A>@JOF@:=< C �P MOT*LmJnExHK?aF@?aJnEK> q :K<�M}FD<�Htc C <N< >DoxMOE q MOExHt:=<�M}FD<�H C JnTATa< C > �^ EIM LmJnPQP�< C LN?AMOTATAU C <�TA< � MOEbF;` W < C H C M � ?AEKk�o C JlLm<�>@> q H C M � oZ?AEK> M C <4SK>D<�H c J C TaJlLNMOTA?���?_E=k MOEKH

<�EK:KMOExLN?AE=k F@:=< ` W < C H C M � �^ EKLNTASx>@?aJnE JOc�M'H C M � ox?AEI?AEGF C JhHKSxLm<�>F@:=< o7Jn> >@? W ?AT_?aFVU JOc�P�<�L :KMOEx?ALNMOTSKEKTAJnMOHK?AE=k ?AE�F@:K<;` W < C�qnC <�>@SKTaF@?AEKky?_EQMOHKHK?AF@?aJnEKMOT=LmJnP�oxTA<msl?aF U�ciJ C F@:=<;<�TAMO>@F@?AL � oxTAMO>DF@?_L ` W < C L :KM C MOL �FD< C ?A>@F@?ALN>�?_EtF@:=<4MOEKMOTaUl>@?A> � ^ EIF@:K<4M W >@<�EKLm<fJOc5SxEKTaJnMOHK?AEKk q F@:=< >@F C <�>@>y?AEtF@:K<f` W < C P JnE=JOFDJnEK?ALNMOTATAU?AEKL C <�MO>D<�> q >@J F@:KM}F5JnExTaU F@:K<;<�TAMO>DF@?_L C <�>Do.JnEK>D< JOc.F@:=<�` W < C <�EGFD< C >"?AEbFDJ F@:=<�MOEKMOTaUl>@?A> �d^ E MOEKMOTaU#��?AE=kMOEQ?_>DJOF@:=< C P MOTlF � J4>DF@M}kO<yH C M � o C JlLm<�>@> � ?aF@:QM H C M � ox?AE�?AE F@:=<;>D<�LmJnEKHQc C <N<>DoxMOE q ?aF�?A>�J W >@< C � <�HF@:KM}F�F@:=< FDJOF@MOTdH C M � ?A>?AE kO<�EK< C MOT�HK?_>DF C ? W SKFD<�H W <NF � <N<�E F@:=< ` C >DF C JnTATa< C q F@:=< >D<�LmJnExH C JnTATA< C�q MOEKHF@:=< H C M � oZ?AE � 9;:=< J >D<NF�TaJlLNM}F@?aJnE JOcF@:=< ox?AE ?A>4>@:=J � E FDJ :KM � < M > ?aknEK?a`xLNMOEbFf< <�LmF�JnE F@:=<HK?A>@F C ? W S=F@?AJnE JOc�F@:=<�H C M � MO> � <�TATxMO>"F@:=<1FD<�EK>@?aJnEQo C JO`xTA< � 81>5F@:x?A>�J >D<NF ?A>"?_EKL C <�MO>D<�H q F@:=<�ExM}F@S C <JOc�F@:K<1H C M � q >DF C <�> > q J C FD<�EK>@?aJnE'JnE'F@:=< >D<�LmJnEKH C JnT_Ta< C Lz:KMOE=kO<�> c C JnP TaJnMOHK?AEKk q FDJ E=<�?AF@:=< C TAJnMOHK?AE=kE=J C SxEKTaJnMOHK?AEKk M}F;M L C ?aF@?ALNMOT.J >D<NF q FDJQSKExTaJnMOHK?AE=k ��� EKH=< C ?A>DJOF@:K< C P MOT�LmJnEKHK?AF@?aJnEK> F@:=< SKExTaJnMOHK?AE=kJOc�F@:=<4` W < C � MO>y<�EbF@? C <�TaUtP�<�Lz:KMOEK?ALNMOTd?AE EKM}F@S C < � R=J C E=JnE �V?A>DJOF@:=< C PQMOT�LmJnEKHK?AF@?aJnEK>;:KJ � < � < C F@:=<SKEKTAJnMOHK?AE=kt?A>4>@S=oxoxTa<�P�<�EbFD<�H W U F@:=< C P MOT-SKEKTaJnMOHx?AE=ktHKS=< FDJ F@:K< >DJOc FD<�EK?AE=k JOcF@:=< ` W < C MO>4F@:=<FD<�P�o.< C M}F@S C <�?_>1?_EKL C <�MO>D<�H � � U MOH �@SK>DF@?AEKkQF@:=< H C M � ox?AE J >D<NF MOEKH F@:=< :=<�M}F@?AEKk ?_E F@:K<�>@<�LmJnEKHc C <N<1>@oxMOE ?aF"?A>-o.Jn>@>@? W Ta< FDJ�MOL :K?A< � < MOE JOoxF@?AP SxP >D<NFDF@?_E=k4?_E � :x?AL : F@:=< C <y?A> E=J�SKEKTaJnMOHK?_E=k JnE'F@:=<>D<�LmJnEKH C JnTATa< C MOEKH%MOTAT�F@:K< H C M � F@M O<�> oxTAMOLm< JnE F@:=< H C M � oZ?AE � 9;:K?A>yJOc LmJnS C >D< :KMO> <�LmJnE=JnPQ?ALW <�E=<N`KF@> c J C F@:=< o C JlLm<�>@> MO> F@:K< HKMOP M}kO< JnE F@:K< >D<�LmJnEKH C JnTATA< C HKS=<yFDJ�c C ?ALmF@?aJnE ?A> P ?aF@?AknM}FD<�HtMOEKH

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>@:K?AciFD<�HQFDJ F@:=<yH C M � oZ?AE � :x?AL : ?A>"PQMOH=<;JOc�M4L :K<�M}o7< C MOEKH C <NoxT_MOLm<�M W Ta<�PQM}FD< C ?AMOT � 81E MOHKHx?aF@?aJnEKMOTc MOLmFDJ C � :K?_L : o.< C P ?aF@>-F@:=< H C M � FDJ W <yF C MOEx>Dci< C C <�H FDJ�F@:=<fH C M � ox?_E ?A> F@:=< `xEKMOT.F@M O<4S=ot>Do.<N<�H �� ?aF@:4F@:=< MOP�JnSKEbFdJOc7TaJnMOHK?AEKk;J C SKEKTaJnMOHx?AE=k;JnE4F@:=< >D<�LmJnExH C JnTATa< C <�>DF@M W TA?_>@:=<�H W UfM1kn? � <�E�F@:K< C P MOTo C JO`ZTa<QMOEKH H C M � ox?_E%J >D<NF q ?aF ?_> o.Jn>@>@? W Ta<�FDJ Lz:KMOE=kO< F@:=< H C M � o C JO`xTa< W U%MOTaFD< C ?AEKkIF@:=< `xEKMOTF@M O< S=o'>Do.<N<�H � 8�>-F@:=<1`xEKMOT C JnTATa< C >Do.<N<�H ?_>"?AExL C <�MO>D<�H'F@:=<yMOP�JnSKEbF"JOc�SxEKTaJnMOHK?AEKk JnE'F@:=<1>@<�LmJnEKHC JnTATA< C H=<�L C <�MO>D<�> � � U%`xE=<'F@SKEK?AEKktF@:=< `xEKMOT C JnTATa< C >Do.<N<�H F@:K<'SKExTaJnMOHK?AE=kIJnE F@:K<'>D<�LmJnExH C JnTATa< CLNMOE W <4HK<�L C <�MO>D<�H FDJ �N< C J MOEKH MOTATdF@:=<�TaJnMOHK?AEKkQJ C H C M � q ?A>�F C MOEK>Dc < C@C <�H FDJ F@:=<�H C M � oZ?AE � 9:=<< <�LmF@? � <�E=<�>@> JOcrF@:=<1H C M � ox?AE H=<No.<�EKHK>5JnE F@:K<1LmJnP�oZTA?AMOEKLm<1JOc*F@:=<1` W < C � R=J C M kn? � <�E ?AEKL C <�P�<�EbF?AE'FD<�EK>@?AJnE F@:K<yMOP JnSKEGF JOcdH C M � ?_EKHKSKLm<�H'?A>-k C <�M}FD< C c J C >DJOc F ` W < C >5F@:xMOE ciJ C >DF@? ` W < C > � p J�?aF ?A>P�J C <f< <�LmF@? � <4FDJ ?_EGF C JlHKSKLm< H C M � ox?AEK> M}F1TaJlLNM}F@?aJnEK> � :=< C < F@:=<f` W < C � <�TaJlLN?aFVUt?AEtF@:=< ` W < C FDJ �LmJ C@C <�>@o7JnExHK> FDJ F@:=< FD<�Ex>@?aJnE � MOTAS=<�>TaUl?AE=k�?AE F@:K< >DJOciF;oxTAM}FD<�MOS �9:K< P JhH=<�TlH=<No.<�EKHx>rJnE�F@:K< c C ?_LmF@?aJnE4o C JO`xTa< � � ?AF@:�F@:=<L C <N<No C M}FD<;HK<No7<�ExH=<�EGFdc C ?ALmF@?aJnE�P�JlH=<�T

F@:=<fPQM}knEK?aF@SKH=< JOcuF@:=<fc C ?_LmF@?aJnE ciJ C Lm<f?A>HK? C <�LmF@TaUQo C JOo.J C F@?aJnEKMOT.FDJ F@:K< C <�TAM}F@? � < � <�TaJhLN?AFVU W <NF � <N<�EF@:=< C JnTATa< C MOEKH F@:=<4` W < C ?AE LmJnEGF C MO>DF FDJ F@:=< � JnSKTaJnP W c C ?ALmF@?aJnE P�JlH=<�T � :=< C <4F@:=< c C ?ALmF@?AJnEtc J C Lm<?A>�H=<No.<�EKH=<�EbFJnEIF@:K<fF@:=<4>@?aknEtJOc�F@:K< C <�TAM}F@? � < � <�TaJlLN?aFVU � � :=< C <�MO>�F@:K< � JnSKTAJnP W c C ?_LmF@?aJnEtP�JlH=<�Tk C M}ox:x?ALNMOTATaU C <�>@<�P W TA<�>�M �@SKP�o�c SKEKLmF@?aJnE q F@:K<L C <N<No C M}FD<H=<No.<�EKH=<�EbFdc C ?_LmF@?aJnE C <NknSKTAM C ? �N<�>rF@:K<>DFD<Noc SKEKLmF@?aJnE�FDJ4M TA?AE=<�M C�C <�TAM}F@?aJnE � 9:=<` W < C � <�TAJhLN?aF U�o C JO`xTa<�>�> :=J � F@:KM}F5M}F5>@S 'QLN?a<�EbF@TaU4T_M C kO< � MOTAS=<�>JOcdF@:=< L C <N<No C M}FD< LmJb<('QLN?A<�EGFF@:K< >DJnTAS=F@?aJnE'o C JO`xTa<�> M}oKo C JnMOL : F@:KM}F J W F@MO?AE=<�H W U'Sx>@?AE=k � JnSKTaJnP Wc C ?ALmF@?aJnE �9:K< > ?aknEK?a`xLNMOEbF�E=< � LmJnEbF C ? W S=F@?AJnE JOc1F@:K?A> � J C FDJ <msl?A>@F@?AE=k TA?aFD< C M}F@S C <'?_E LmJnEGF C MO>@F FDJ%MOTAT

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JnE F@:=<fknTAMO>@> F C MOEx>@?aF@?aJnE FD<�P�o.< C M}F@S C < �9:K<4MOEKMOTAUh>@?_>�JOc"F@:=<�>Dox?AExEK?AE=k�o C JhLm<�>@> Sx>@?AE=k'P MO>@> q P�JnP <�EGF@SKP q MOEKH <�E=< C kOU LmJnEx>D< C � M}F@?aJnE

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Page 25: Vohra - PhD (GaTech, 2006)

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� �?A>5MfLmJnEK>DF@MOEbF � R=J C M � JnE � � < � FDJnEK?AMOE)�xSK?_H�F@:=< � ?A>@LmJn>@?aF U ?A> C M}FD<1H=<No.<�EKH=<�EbF � ;yE=<c C <�ghS=<�EGF@TAUSK>D<�H C <�TAM}F@?AJnE'?_>"M o.J � < C T_M � � :K?ALz:Qkn? � <�>�� � � ��! " � � �#"$ '&% � � :=< C <'� � ?A>"F@:=<��N< C J�>@F C MO?AE � ?A> LmJn>@?aFVUMOEKH)('MOEKH*1M C <f<�P�ox? C ?_LNMOT7LmJnEx>DF@MOEGF@> �

Page 26: Vohra - PhD (GaTech, 2006)

9:K<�FD<�P�o.< C M}F@S C <"H=<No.<�EKH=<�EKLm<�JOc � ?A>@LmJn>@?aF UyJnE FD<�P�o.< C M}F@S C <�>�P4SKL :fk C <�M}FD< C F@:xMOE F@:=<5P <�TaF@?AE=ko.Jn?AEbFu?_>�LNM}oKF@S C <�H W U MOEQ8 C@C :=<�EK?ASK>dF Ubo.< C <�TAM}F@?AJnE�? � < � � ��� � � � � q � :=< C < � � MOEKH��2M C < <�P�oZ? C ?ALNMOTLmJnEK>DF@MOEbF@> � R=J C�C MOE=kO<�>�JOcxFD<�P o7< C M}F@S C < LNTaJn>D< FDJyF@:=< knTAMO>@>dF C MOEx>@?aF@?aJnE�M � CrR FVUho7< C <�T_M}F@?aJnE4kn? � <�EW U � � � � ��� ��� ������ ���� � ������� ?A> Sx>D<�H q � :=< C < � � q

� q M C <Q<�P�ox? C ?_LNMOT�LmJnEK>DF@MOEbF@> MOEKH ��� ?A> F@:=< knT_MO>@>F C MOEK> ?aF@?aJnE FD<�P�o.< C M}F@S C < �

� :=<�E'L C Uh>@F@MOTATA?���M}F@?aJnEQ>D<NF@>"?_E�F@:=< � ?A>@LmJn> ?aFVU�SKEKHK< C kOJb<�>"M C M}oZ?AH ?AEKL C <�MO>D< q p :x?AP ?���S�<NF-MOT � � >@>��

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FDJQ?AExLmJ C o.J C M}FD<yF@:=< < <�LmF�JOcdL C Uh>DF@MOT_TA?AEK?aF U JnE � ?A>@LmJn>@?AFVU � �.?_M W ?AL l?.?AE � A | � :KMO>o C JOo.Jn>D<�H M�P�JlH=<�TJOcuL C Uh>@F@MOTATA?���M}F@?aJnE W MO>@<�H JnE F@:=< ?AH=<�M4F@:KM}FMO>F@:=< o.JnTaUhP < C L C Uh>DF@MOT_TA?��N<�> F@:=< o.JnTaUlP�< C L :KMO?_EK> kO<NF?AEbFD< C LmJnEKE=<�LmFD<�H F@: C JnS=kn: L C Uh>DF@MOT_TA?aFD<�>4? � < � MO>4ox:bUh> ?ALNMOT"L C Jn>@>@TA?AE�h> � 8 F�M Lm< C F@MO?AE L C ?aF@?_LNMOT � MOTAS=<JOcF@:=<'EbSxP W < C JOc F@:=<�>D<'ox:GUl>@?ALNMOT-L C Jn>@> TA?AE l> q F@:K< o.JnTaUlP�< C TAJn>D<�> ?_> �xSx?AHK?aF U MOEKH � ?aF@: c S C F@:=< C?AEKL C <�MO>D< ?AE L C Ul>DF@MOTATA?_EK?aFVU'?aF W <�LmJnP�<�>;P�J C < C ?akn?AH � 9:K< o C JOo.Jn>D<�H � ?A>@LmJn>@?aF U C <�TAM}F@?aJnEt?A> kn? � <�E W U q

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C M}FD< LNTaJn>D< FDJ F@:=<�? C knTAMO>@>'F C MOEK> ?aF@?aJnE FD<�P o7< C M}F@S C < HKS=< TAMOL JOc P�J W ?ATA?AFVU � p J F@:K< P M s=?AP4SKPL C Ul>DF@MOTATA? ��M}F@?aJnE C M}FD< :KM}oKo.<�EK>�M}F >@JnP�<I?AEbFD< C P�<�HK?_M}FD<tFD<�P�o.< C M}F@S C < � 81TA>DJ%? C@C <�>Do.<�LmF@? � < JOc F@:=<FD<�P�o.< C M}F@S C < q F@:K< C <I?A> MOT � M Uh> M%`xEK?AFD<tMOP�JnSKEbF JOcyF@?AP�<IE=<N<�HK<�H FDJ L C Ul>DF@MOTAT_?��N< F@:=<IP M}FD< C ?AMOT � <�EKLm<1?_E Mf>DoZ?AEKTA?AEK<-F@:K<�MOP�JnSKEbF5JOc*L C Uh>DF@MOT_TA?���M}F@?aJnE � ?ATAT=H=<No.<�EKHQJnEQL C Ul>DF@MOTATA? ��M}F@?aJnE l?AE=<NF@?ALN>"MOEKHF@:=<QLmJhJnTA?AEKk C M}FD< � ^ E MOHKHK?aF@?aJnE q F@:=<Qo C <�>D<�EKLm< JOc P�JnTA<�LNSKTAM C J C ?a<�EGF@M}F@?AJnE MOTA>DJ ?AEKL C <�MO>D<�> C M}FD<QJOcL C Ul>DF@MOTATA? ��M}F@?aJnE'JOc�M�o.JnTaUhP < C � 9;:=<y< <�LmF JOcdLmJbJnTA?_E=k C M}FD<yMOExH'L C Uh>DF@MOT_TA?���M}F@?aJnE l?AE=<NF@?ALN> ?A> >@:=J � E?AE Ru?aknS C < > � 9:K<�� L �VLNS C � <��-kO<NF@> >@:K?ac FD<�H FDJ F@:=< TA<NciF <�?AF@:=< C � ?AF@:]?AEKL C <�MO>D<�H]>DF C <�>@>QJ C c MO>DFD< CL C Ul>DF@MOTATA? ��M}F@?aJnE h?_E=<NF@?ALN> C <�>@SxTaF@?AE=k�?AE c MO>DFD< C L C Uh>DF@MOT_TA?���M}F@?aJnE LmJnP�oZM C <�H FDJ F@:=< >DF C <�>@> c C <N<fLNMO>@< �v gbSKM}F@?AJnEK>;c J C L C Ul>DF@MOTATA?���M}F@?AJnE C M}FD<�>yc J C P�<�TaF1>Dox?AEKEx?AE=k M C <�HK? ' LNSKTaFFDJ H=< � <�TaJOo HKSK<fFDJ F@:=<

E=JnE �V?_>DJOF@:=< C P MOT;LmJnEKHK?aF@?aJnEx> MOEKH]HK< � <�TaJOoxP�<�EbFQJOc P�JnTA<�LNSKTAM C J C ?A<�EGF@M}F@?aJnE�HKS=<IFDJ >DF C <�> > � 9:=<

L

Page 27: Vohra - PhD (GaTech, 2006)

��������� � � 9;:=< ?AE��xSK<�EKLm< JOc�LmJbJnTA?_E=k C M}FD<fMOEKH >DF C <�>@>JnEIL C Ul>DF@MOTATA? ��M}F@?aJnE W <�:KM � ?aJ C�q � `xknS C < c C JnP� > A�� � �

F@:=<NJ C U4c J C L C Ul>DF@MOTATA?���M}F@?AJnE�< � <�E ?AE�F@:=<M W >@<�EKLm< JOc�P�JnTa<�LNSKTAM C J C ?a<�EGF@M}F@?AJnE ?A>�E=JOF � <�TATl<�>DF@M W T_?A>@:=<�HMOEKH < � <�E4Ta<�>@>�?A>�lE=J � Ef?AEyF@:=<�o C <�>D<�EKLm<�JOc=P�JnTa<�LNSxTAM C J C ?a<�EbF@M}F@?aJnE � 9rM l?AE=k;F@:=<58 � C MOPQ?O<�gbSxM}F@?aJnE q� :K?_L :f?_>rSK>@<�Hfc J C ?A>DJOF@:=< C PQMOTGL C Ul>DF@MOTATA? ��M}F@?aJnE � ?aF@: q ��� - � � ��� F@:=< L C Uh>@F@MOTATA?���M}F@?aJnE C M}FD< LmJnEK>DF@MOEbFMOEKH �%?_> F@:=<f8 � C MOPQ?�?AEKH=<ms q

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MO>�F@:=< W MO>@?A> �5M P�JhHK<�T"H=< � <�TAJOo7<�H W U � M MOP4S C M <NF � MOT � � {�� q {O~ � ?A> c JnSKEKH FDJ W <'F@:=< W <�>@F c J CE=JnE �V?_>DJOF@:=< C P MOT�LmJnExHK?aF@?aJnEK> q F@:K<fP�JlH=<�T�?A> kn? � <�E W U

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� :=< C < � ?A> F@:=< H=<Nk C <N< JOc;L C Uh>DF@MOT_TA?AEK?aF U � 9;:=<Q< <�LmF�JOc�P�JnTA<�LNSKTAM C J C ?a<�EbF@M}F@?aJnE ?A>�?AEKLNTASKHK<�H W U<mslFD<�EKHK?AE=k F@:=< L C Ul>DF@MOTATA? ��M}F@?aJnE�c MOLmFDJ C FDJ ?_EKLNTASKH=< P�JnTa<�LNSKT_M C J C ?a<�EGF@M}F@?AJnE ? � < � - � - � � � ��� q� :=< C <�� ?_> F@:=< < C P MOEKE � <fJ C ?a<�EbF@M}F@?aJnE c SKEKLmF@?aJnE � 8�c J C P JOc - o C JOo.Jn>D<�H W U �.?_M W ?AL l? � > � � ?A>

- � � � ��� � -�� � � � �� ������ ���� � ��� "�� '�� �� :=< C < � � � �-?A> MOE <�P ox? C ?ALNMOT7oxM C MOP�<NFD< C FDJ W < H=<NFD< C P ?_E=<�H q -���� ?A> F@:=< C M}FD< LmJnEx>DF@MOEGF�M}F � � �

F@:=< FD<�P�o.< C M}F@S C < M}F � :K?ALz: F@:K<yL C Uh>DF@MOT_TA?���M}F@?aJnE C M}FD< ?A> F@:K<yPQM sl?AP4SKP q MOEKH�� ?A>-F@:=< :KMOTac � ?AH=F@:JOc - � > � oxTaJOF � 8�E=JOF@:K< C�C <�TAM}F@?aJnE ?AE SK>@< � MO>�o C JOo7Jn>@<�H W U � M}F@M�UnMOP M <NF MOT � � { A� :KMO>�F@:=<

M

Page 28: Vohra - PhD (GaTech, 2006)

c JnTATaJ � ?AE=k�ciJ C P

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� :=< C <� �� ?A> F@:=<IMOLmF@? � M}F@?aJnE <�EK< C kOU q � ?A>�F@:=< knMO>QLmJnEK>@F@MOEGF q ������� � � � � > | - q � :=< C < � � ?A>F@:=<4knTAMO>@>1F C MOEK> ?aF@?aJnE FD<�P�o.< C M}F@S C < q � � � �

�� � � q :=< C < ��� ?_>;F@:=<�P�<�TaF@?_E=k FD<�P o7< C M}F@S C < SxEKH=< C

ghSK?A>@Lm<�EbF LmJnEKHK?aF@?AJnEK> � 9;:=< � MOTASK<�> JOc - ��MOEKH ��M C < J W F@MO?AEK<�H c C JnP ghS=<�?A> Lm<�EGF L C Ul>DF@MOTAT_?���M}F@?aJnEl?AE=<NF@?ALN> � 9:=< � MOTAS=<�JOc ?_> MOH �DSx>DFD<�H FDJ PQM O<QF@:=<Q> ?AP SxTAM}F@?aJnE M}k C <N< � ?aF@: F@:=< <mslo.< C ?AP�<�EbF@MOTC <�>@SxTaF@> �9:K<"M W J � < HK?A>@LNSx>@>@?aJnEyo.< C F@MO?AEx>*FDJyM;>@?AEKknTa<�`xTAMOP <�EGF � 9:=<"MOLmF@SxMOTb?AExHKSK>DF C ?_MOT}o C JlLm<�>@>r:KJ � < � < C

?A> M P4SKTaF@? � `xT_MOP�<�EGF >D<NF��VS=o ? � < � M W SKEKHKTa< JOc ` W < C > ?A>Q>@oxSKE � <�EKLm< W JOF@:]F@:=< � <�TaJlLN?aF U]MOEKHFD<�P�o.< C M}F@S C <�JOc"F@:=< L C Jn>@> �KJ � MO? C L :xMOE=kO<�> � ?aF@:x?AE F@:=<�` W < C W SKEKHKTA< � :x?AL : ?AP�o.Jn>D<�>yHK? < C <�EbFW JnSKEKHKM C U LmJnExHK?aF@?aJnEK> JnE�F@:=< ?AEKHK? � ?AHxSKMOT-` W < C > � 95Uhox?ALNMOTATAU F@:K< L C Jn>@>��KJ � MO? C � <�TaJlLN?aFVU � ?ATATH=<�L C <�MO>@< MOExH FD<�P o7< C M}F@S C < ?AEKL C <�MO>D< J � < C F@:=< � ?AH=F@: JOc;F@:=< W SKExHKTa< � :x?ATa< W JOF@: F@:=<�>D< < <�LmF@>H=<�L C <�MO>@< M � M�UIc C JnP F@:=< >@ox?AEKE=< C <NF � 8�>�M C <�> SKTaFHK? < C <�EbF;MOP�JnSKEbF;JOc�:=<�M}F1?A> F C MOEx>Dci< C C <�H c C JnPF@:=< ` W < C >-?_E F@:=< W SKExHKTa< C <�>@SKTaF@?_E=k4?_E HK? < C <�EGF>@F C SKLmF@S C < MOExH o C JOo.< C F@?a<�> �81E=JOF@:=< C >@?AP oxTA?a`xLNM}F@?AJnE MOH=JOoKFD<�H � MO> F@:=< MO>@>@SKP oKF@?aJnE JOc SKEK?ac J C P C MOHx?AMOT�HK?A>DF C ? W S=F@?aJnE JOc

FD<�P�o.< C M}F@S C <4MOEKH � <�TaJlLN?aFVU MOL C Jn>@>yF@:=<4`xTAMOP�<�EbF�>@<�LmF@?aJnE � 9:=<4MO>@>@SKP�oxF@?aJnEIJOc5oxS C < <mshFD<�EK> ?aJnEKMOT�KJ � C <�>@SKTaF@?_E=k ?AE SKEx?aciJ C P � <�TaJlLN?aF U MOL C Jn>@>F@:=<y`xTAMOP�<�EbF >D<�LmF@?aJnE ?A> � MOTA?AH SKEKH=< C P�Jn>DFP <�TaF >Dox?AE �EK?AEKk'LmJnEKHx?aF@?aJnEK> � 9:=<�FD<�P�o.< C M}F@S C <�MOExH L C Uh>@F@MOTATA?AEK?AFVUtHK?A>@F C ? W S=F@?AJnEI:=J � < � < C :KM � < W <N<�E c JnSKEKHW U � M}F@M UnMOP MOTr<NF;MOT � � { A�� FDJQ>@:=J � M C MOHK?_MOT � M C ?AM}F@?AJnE �

� SKP�< C ?_LNMOT*>@?AP4SKTAM}F@?aJnE FDJ >DJnT � < F@:=< >D<NF;JOc�P MO>@> q P�JnP�<�EbF@SKE q <�EK< C kOU <�gbSKM}F@?AJnEK>LmJnS=oxTA<�H FDJF@:=<yLmJnEK>DF@?aF@SKF@? � <y<�gbSKM}F@?AJnE MOTaJnEKk � ?aF@:QL C Ul>DF@MOTAT_?���M}F@?aJnE':KMO> W <N<�E H=JnEK<�J � < C F@:=<�UO<�M C > FDJ4o C <�HK?ALmF< � JnTAS=F@?AJnE JOc">D< � < C MOT�o C JlLm<�>@> � M C ?_M W Ta<�>1F@:KM}F o.< C P ?aF@>�F@:=<�o C <�HK?ALmF@?aJnE JOc5` W < C o C JOo.< C F@?A<�>�FDJ W <P MOH=< � p o C SK?a<�TAT � > A�� o C <�>D<�EbF@>Q>@?AP4SKTAM}F@?AJnE C <�>@SKTAF@>�ciJ C C <No C <�>@<�EGF@M}F@? � < o.JnTaUhP < C � ?aF@: ox:bUl>@?ALNMOTo C JOo.< C F@?A<�>TA? O< o.JnTaUnMOPQ?AH=< ~ � ?aF@:IM � < C M}kO<�P�JnTa<�LNSKT_M C � <�?akn:GF�JOc"{ = |O|O| q MOEKH P MO>@>��xJ � C M}FD< JOc{#� = k�� P ?AE c C JnP M LNM}ox?ATATAM C U � Ru?aknS C < A > :=J � >;F@:=< C <�>@SKTaF@> F@:xM}F�LNTAMO?AP FDJ W <fLmJnEK> ?A>DFD<�EbF � ?aF@:IF@:=<<mslo7< C ?AP�<�EbF@MOT�J W >D< C � M}F@?aJnEx> q ciJ C ?AEK>DF@MOExLm< L C Ul>DF@MOTATA? ��M}F@?aJnE%F@M O<�>4oxTAMOLm<'JnEKTaU M}F4F@M O< �VS=o >Do.<N<�HK>?AE <ms=Lm<�>@> JOc = |O|O|OP)� P ?_E � 9:=< JnS=FDoZS=F >@:=J � E ?AE Ru?aknS C < A ?_>�J W F@MO?AE=<�H W U SK>@?AE=k F@:=<tPQMO>@> qP�JnP�<�EbF@SKP q MOEKH�<�E=< C kOU�<�ghSKM}F@?aJnEK>�TA?_>DFD<�H�<�M C TA?a< C � R=J C F@:=< � JnEK>DF@?AF@S=F@? � < W <�:KM � ?aJ C F@:=< c JnTATaJ � ?AE=k

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Page 29: Vohra - PhD (GaTech, 2006)

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Page 41: Vohra - PhD (GaTech, 2006)

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Page 42: Vohra - PhD (GaTech, 2006)

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Page 43: Vohra - PhD (GaTech, 2006)

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Page 44: Vohra - PhD (GaTech, 2006)

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Page 46: Vohra - PhD (GaTech, 2006)

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Page 47: Vohra - PhD (GaTech, 2006)

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Page 48: Vohra - PhD (GaTech, 2006)

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Page 49: Vohra - PhD (GaTech, 2006)

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Page 50: Vohra - PhD (GaTech, 2006)

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Page 51: Vohra - PhD (GaTech, 2006)

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Page 52: Vohra - PhD (GaTech, 2006)

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Page 53: Vohra - PhD (GaTech, 2006)

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Page 55: Vohra - PhD (GaTech, 2006)

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Page 56: Vohra - PhD (GaTech, 2006)

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Page 57: Vohra - PhD (GaTech, 2006)

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9:=< � MOT_S=<;JOc*F@:K<�<�TAMO>@F@?AL�P JhHKSxTASK>�� ?A>5MO> >@SKP�<�H hEKJ � E q F@:=< C < W UQLmJnP�oZTa<NF@?AE=k F@:=<1Lz:KM C MOLmFD< C ? ��M �F@?aJnEQJOc7F@:K<;` W < C > � 9:=<> TA?aoQMOE=knTA< � ?A>5F@M O<�E MO>->Do.<�LN?a`K<�H � 9:=<�>DJnTAS=F@?aJnE JOc�F@:=< W JnSKEKHKM C U � MOTAS=<o C J W Ta<�P2?A>�F@:=< ` W < C FD<�EK>@?AJnE � � � �dMOEKH�>Do.<N<�H � � �uMO>�c SKEKLmF@?aJnEx>uJOc �Gq c C JnP � ��| FDJ � � � � � RKJ CF@:=< oxS C o.Jn>D< JOcZk C M}oZ:K?ALNMOT=HK?A>@oxTAM�UfJOcZF@:=<>@JnTAS=F@?aJnEK> q F@:=<�>D<c SKEKLmF@?aJnEx>dM C << � MOT_SKM}FD<�H M}F�F@:=<HK<NoxM C �F@S C < TAJhLNM}F@?aJnE q F@:=< C < W U ciJlLNSK>@?AEKk4JnEtF@:=< o C <�Hx?ALmF@?aJnEK> JOcdF@:=<fH=<NoZM C F@S C < FD<�EK> ?aJnE�� � � � � � � � � �MOEKH H=<NoxM C F@S C < >Do.<N<�H #� � � � ��� � � q.C <�T_M}F@? � < FDJ'F@:=<4o C <�>@L C ? W <�H � MOTAS=<�>#� � MOEKH� � M}F � � | �� ^ E F@:x?A>-ciJ C P4SKTAM}F@?AJnE q F@:K<y> TA?ao MOEKknTa<��%?A> >Do.<�LN?a`K<�H'MOEKH H=<NoxM C F@S C <1>Do.<N<�H� � ?_>"H=<�HxSKLm<�H MO> oxM C FJOcxF@:K< >@JnTAS=F@?aJnE � C <Nci< C@C ?AE=kyMO:=<�MOH�FDJ F@:=< oxM C <�EbF@:=<NF@?ALNMOT=E=JOFD<M}c FD< C�v ghSKM}F@?aJnE � A | �rc J C M HK?A> LNSK>@>@?aJnEJOcuF@:=< MOTaFD< C ExM}F@? � < c J C P SxTAM}F@?aJnE ?AE � :x?AL :� � ?A> >Do.<�LN?a`x<�H MOEKH�� ?A>;H=<�HKSKLm<�H � �

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Page 61: Vohra - PhD (GaTech, 2006)

^ EfH C M � JnE4Mc <N<�H C JnTATa< C F@:K<5FDJ � ?A>rP�J � ?AE=k�c MO>DFD< C F@:KMOEfF@:=<"SKExH=< C TaUl?AE=k C JnTATA< C >@S C c MOLm< � 9:=<�E qMOLNLmJ C HK?_E=ktFDJIF@:K< >@?aknE LmJnE � <�EbF@?aJnE MOEKH MO> >@SKP ?AEKk � JnSKTaJnP W c C ?ALmF@?aJnE q � ?A> kn? � <�E W U v ghSKM}F@?aJnE� :@: � � 81>;M�> TA?akn:bFHK?ak C <�>@> ?aJnE q=v ghSKM}F@?aJnE � :@: �P�JhHK<�TA> <�MOL : F@:=< c JnTATaJ � ?AE=k�ox:bUh>@?_LNMOT�>@?aF@SKM}F@?aJnEx> �

� � 9:=< ` W < C FDJ � ?_>kOJn?AE=k c MO>@FD< C F@:KMOE M'P�J � ?AE=k C JnTATa< C � ^ EIF@:x?A>;LNMO>D< # � # & q ����| q � � qMOExH � LNMOE W <��N< C JQJ C E=JnE �N< C J �

� � 9:=< ` W < C > M C <4>@TA?aoxox?AE=k JnEIMQ>@F@M}F@?AL C JnTATA< C �5^ E F@:K?A>;LNMO>D< # � # & q � | q � | q MOEKH � LNMOEW <��N< C JQJ C E=JnE �N< C J �

� � � TAJhL � ?_>D<-P JOF@?aJnE � >@TA?ao ��?A>d?AP�o.<�EKHK?_E=kJnE�My>DF@M}F@?AL C JnTATA< C ��# � # � q � | q � | q MOEKH � �� | �

� � p TA?ao ?AE F@:=<fHx? C <�LmF@?aJnE JOc�P�JOF@?aJnEI?A> ?AP�o.<�EKHK?_E=k ��# � # � q � | q �� � q MOEKH � � | �

� ?aF@: EKJ M}oKo C J�s=?AP M}F@?aJnEK> q F@:=<'o.Jn>@>@? W TA< W JnSKExHKM C U � MOTASK<Qo C J W Ta<�P > M C < q c C JnP v ghSKM}F@?aJnEK> � M � q� > A � � ? � < �5v ghSKM}F@?aJnEK> � : A �MOEKH � : = � � MOEKH � :@: � �

G � � ��� � � 9 � p F@M}F@?_L ?AE=<mslFD<�EK>@? W TA<�` W < C > �u?Ac � | MOEKH � ��| q

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R=J C LNMO>D<�> � MOEKH � E=JOFD<4F@:KM}F ����|QMOEKH <�?aF@:=< C � ����| J C � � | q H=<No.<�EKHK?_E=k�JnE ?acuF@:=<4` W < C >?A>1>DF C <NF@Lz:K?AE=k J C E=JOF%�*:=<�EKLm<�?AE F@:=<�>D<�LNMO>D<�>y<�?aF@:K< C G � � � � � � J J C G � � � � � � X ?A>1>DJnT � <�H � RKJ CLNMO>D< � � |tMOEKH � � |IP4SK>DF W <�F C S=< q >@J G � � ��� � � 9 ?A> F@:K< o C J W TA<�P FDJ W <Q>DJnT � <�H � RKJ CLNMO>D< � q ��� |�MOEKH � � | q >@J G � � � � � � J E=<N<�HK>-FDJ W <y>DJnT � <�H � � "�� ��� ��� "!� � � � � � � "���� ��� q F@:=<C <�Ta< � MOEbF;LNMO>D<f?A> � JnEKTaU q MOEKHtF@:=< C <�Ta< � MOEGF;o C J W Ta<�P ?_> G � � � � � � X �

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^ E >D<�LmF@?aJnE > �BA � : F@:K?A>�c SxTAT W JnSKEKHxM C U � MOT_S=<fo C J W Ta<�P ?A>�>@JnT � <�H ciJ C ` W < C FD<�EK>@?aJnE MOEKH >Do.<N<�H q?AE � :K?ALz: W JOF@:'` W < C MOLNLm<�Ta< C M}F@?aJnEK> � Lm<�EbF C ?ac S=knMOT.MOEKH'>DF C <NF@Lz:K?AE=k �"M C <yo C <�>@<�EGF ?AE F@:=< P�JnP�<�EbF@SKP<�ghSKM}F@?aJnEK> � 9 � J'M}oKo C J sl?APQM}FD< o C J W Ta<�P >M C < MOTA>DJ'>DJnT � <�H ciJ C F@:=< oxS C o.Jn>D<�> JOc�LmJnExE=<�LmF@?AE=k � ?aF@:F@:=< W <�TaF�TA?AFD< C M}F@S C <tMOEKH]?A>DJnTAM}F@?AEKk F@:K<t< <�LmF@> JOcyLm<�EGF C ?Ac S=knMOT;MOEKH >DF C <NF@Lz:K?AE=k MOLNLm<�Ta< C M}F@?aJnEK> ?AEF@:=< c SKTAT.>DJnTASKF@?aJnE�� ^ E >D<�LmF@?aJnE > �BA � { F@:=< >DF@MOEKHxM C HtLNM}ox>DF@MOEto C J W Ta<�P ?_E � :K?ALz: W JOF@: ` W < C ?_E=< C F@?AMFD< C P >uM C < E=<NknTA<�LmFD<�H�c C JnP F@:=< P�JnP�<�EbF@SKP <�ghSKM}F@?aJnEK>u?A>u>DJnT � <�H q MOEKH ?_E >D<�LmF@?AJnE�F@:=<-?_EGFD< C P <�HK?AM}FD<M}oKo C J�s=?AP M}FD<�o C J W Ta<�P ?AE � :K?_L : Lm<�EbF C ?ac S=knMOTOMOLNLm<�Ta< C M}F@?AJnE ?A> C <NF@MO?AE=<�H W SKF*>DF C <NF@L :x?AE=kMOLNLm<�Ta< C M}F@?AJnE?AE E=<NknTA<�LmFD<�HI?A> >DJnT � <�H �

X � � � 9 # � � � � � � � �N� ��� � � � ��� )*� � ��� � � ��� � � V� � � � � � � �9:=<fc SKT_T7LmJnSKoxTa<�H o C J W Ta<�P c J C ` W < C FD<�EK> ?aJnEIMOEKHI>Do.<N<�HILmJnEK>@?_>DF@> JOcu<�gbSxM}F@?aJnEK> � > A � � ? � < � v ghSKM �F@?aJnEK> � : A �-MOEKH � : = � � q � > M � q MOExH � :@: � q > S W �D<�LmF"FDJ�F@:=<yF � J W JnSKEKHKM C U LmJnExHK?aF@?aJnEK> � � | � � � �1MOEKH � | �� � � � � 9:K<->DJnT_S=F@?aJnE � � � ��MOEKH � � �rH=<No.<�EKHK>*JnE4F@:=<-F@: C <N< E=JnEKEK<NknM}F@? � < HK?AP�<�EK> ?aJnEKTa<�>@>oxM C MOP <NFD< C > #�� q ! � �

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F@:=<�` W < C > � ?ATAT �KUtJ F@:=< C JnTATa< C � 9:=<�H=<No.<�EKH=<�EKLm<4JOc5F@:=<�P M}knEx?a`xLNM}F@?aJnE ���"�JOc5FD<�Ex>@?aJnE ?AE F@:=<

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0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

35

40

Gv0/ T

0

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0 0.2 0.4 0.6 0.8 10

10

20

30

40

50

60

70

80

90

100

Gv0/ T

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C M}F@?aJ � �� �?AEKL C <�MO>D<�> E=JnEKTA?_E=<�M C TaU MO> ! � �

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:=J � < � < C�q F@:KM}F F@:K?A> W TaJ � ?AE=k S=o JOc F@:=<'H C M � C M}F@?aJ MO> ! � ��"� �

| � ?aF@: ! � �& E=JnE �N< C JIMOEKH `xEK?aFD<LmJ C@C <�>@o7JnExHK>1FDJtF@:=<�ox:bUh>@?_LNMOTATaUIM � � M C H%T_?AP ?aF@>�JOc"<�?AF@:=< C � �4`xEx?aFD< q � � � | q MOEKH � � | q J C�tMOExH � � `ZEK?aFD<fMOEKH�� � ��� � 9:=<4>DJnTAS=F@?AJnE ciJ C F@:=< ox:GUl>@?ALNMOT_TaU C <�MOTA?���M W Ta< TA?AP ?aF JOc��IMOEKH � �`xEK?AFD<1MOEKH � � � | � ?AP oxTaUl?AE=k ! � �

�"�� ! � �& � | �-?A>-F@:=<y>DF@M}F@?AL LNM}oZ>DF@MOE C <�TAM}F@?aJnE q kn? � <�E'?_E'>@<�LmF@?aJnE

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0 0.2 0.4 0.6 0.8 10

5

10

15

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25

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Gv0/ k

T1/

T0

Gv0/ T

0 = 0.1

Gv0/ T

0 = 0.5

Gv0/ T

0 = 0.9

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

35

40

45

50

Gv0/ k

V1/

V0

Gv0/ T

0 = 0.1

Gv0/ T

0 = 0.5

Gv0/ T

0 = 0.9

��������� � � j C M � JnE M c <N<�H C JnTATa< C � ���"�MOEKH�� �

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> � { � Ru?aknS C < : = >@:KJ � >;F@:=< TA?_E=<�M C H=<No.<�EKH=<�ExLm< JOc�F@:=<fFD<�Ex>@?aJnE C M}F@?AJ ��� �JnE ! � �

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J C c MO>DF` W < C > � ! � �� �

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�"�MOEKH ���

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Page 65: Vohra - PhD (GaTech, 2006)

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Page 66: Vohra - PhD (GaTech, 2006)

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Page 67: Vohra - PhD (GaTech, 2006)

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Page 68: Vohra - PhD (GaTech, 2006)

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Page 69: Vohra - PhD (GaTech, 2006)

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Page 70: Vohra - PhD (GaTech, 2006)

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Page 71: Vohra - PhD (GaTech, 2006)

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Page 73: Vohra - PhD (GaTech, 2006)

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Page 76: Vohra - PhD (GaTech, 2006)

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Page 77: Vohra - PhD (GaTech, 2006)

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Page 78: Vohra - PhD (GaTech, 2006)

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Page 79: Vohra - PhD (GaTech, 2006)

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Page 80: Vohra - PhD (GaTech, 2006)

R=J C <�MOL :%JOc F@:=<�>@< >@? s o7Jn> >@? W Ta< oxTAMOLm<�> q H C M � H=Jh<�> E=JOF JlLNLNS C ?ac"F@:=< LmJ C@C <�>Do.JnEKHx?AE=k ?AE=<�ghSKMOTA?aF UM W J � <f?_> ?AEK>DFD<�MOH MOE <�ghSKMOTA?AFVU q < � k � F@:=< C < ?A> E=J H C M � JnE F@:=< F@M O< �VS=o C JnTATa< C JOcdF@:=< >D<�LmJnEKH >@F@M}kO<?ac � � � �� MOEKH � � � � ^ E F@:K<4P�JlH=<�TA?_E=kQJOc�F@:K<4F � J �V>@F@M}kO<QH C M � q � � q � q � � q �� q � � q � qMOEKH�� �1M C < >Do.<�LN?a`K<�H q MOEKH � � q � q � � q � q � q q � q MOEKH� � M C <fH=<�HKSxLm<�H �

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9:=< LmJnEx>D< C � M}F@?aJnE%<�ghSKM}F@?aJnEK> SKEKH=< C >@FD<�MOH=U%LmJnEKHK?aF@?AJnEK>yo C <�>D<�EbFD<�H ?_E � :KM}oKFD< C'> M C < C <NF@MO?_E=<�H �9:=<tLmJnEx>D< C � M}F@?aJnE JOcyP MO>@> ?A>�kn? � <�E W U v ghSKM}F@?aJnE � M � � 9:=<tLmJnEK>@< C � M}F@?AJnE JOc1P JnP�<�EGF@SxP JnEF@:=< C JnTATA< C ?A>�kn? � <�E W U v ghSKM}F@?aJnEx> � : A �1MOExH � : = � q MOEKH W U v gbSxM}F@?aJnE � : L �1?AEIF@:K<4c C <N<�>DoxMOE � 9rJJ W F@MO?AEQF@:=<<�ghSKM}F@?aJnEK>5JOc�P�JOF@?aJnE F@:K<�LmJnEK>D< C � M}F@?aJnEQJOc�P MO>@>5MOExHQP�JnP�<�EbF@SKP M C <�LmJnP W ?AE=<�H � ?aF@:v ghSKM}F@?aJnE � > : � �^ E F@:=< H C M � o C JhLm<�>@>4F@:=< ` W < C >4M C < <�?aF@:=< C ?_E M c C <N<�>DoxMOE J C JnE M C JnTATa< C �"JnE M C JnTATa< C F@:=<

o.Jn>@>@? W Ta<�LmJnEKHx?aF@?aJnEK> M C < EKJ �V>@TA?ao q H C M � JnEtM�c <N<�H C JnTATa< C � ? � < � >@TA?ao � ?aF@: F@:=< ` W < C >-P J � ?AE=k�c MO>DFD< CF@:KMOE�F@:K< C JnTATa< C > S C c MOLm< � q MOEKH H C M � JnE M F@M O< �VS=o C JnTATa< C � ? � < � >@T_?ao � ?aF@:�F@:=<;` W < C >uP�J � ?AE=kf> TaJ � < CF@:KMOE�F@:K< C JnTATa< C > S C c MOLm< � �d^ E�F@:=< c C <N<f>@oxMOE F@:=< C <�TA< � MOEbF�<�ghSKM}F@?aJnEK>�M C < v ghSKM}F@?aJnEK> � M � q � : L � q MOEKH� > : � � � JnP W ?_EK?AE=k4F@:=<�P C <�>@SKTaF@> ?AE

� ���

� � ��� � ��� �� � � ��� ��� A M �

� :=< C < � ��� � MOEKH � ��� � M C < kn? � <�E <mshoZTA?ALN?aF@TaU ?AE v ghSKM}F@?aJnEx> � > { � MOEKH � >@> � � � :=<�E%H C M � JhLNLNS C > JnEF@:=< ci<N<�H C JnTATa< C q ?AEtF@:KM}F1>@TA?ao �NJnE=< F@:K<f` W < C ?_>;P�J � ?AEKkQc MO>DFD< C F@:xMOEIF@:=< C JnTATa< C >@S C c MOLm< � R C ?_LmF@?aJnE?A> l?AE=<NF@?AL4HKS=<4FDJ F@:=<�>@TA?ao q MOEKH o.Jn>@?aF@? � <4MOLNLmJ C Hx?AE=k'FDJ F@:=<�MOH=JOoKFD<�H >@?aknE LmJnE � <�EGF@?AJnE%>DJ v ghSKM �F@?aJnE � :@: ��?A>;SK>@<�H � 9:=< C <�Ta< � MOEGF1<�gbSxM}F@?aJnEK>�ciJ C H C M � JnE MQc <N<�H C JnTATa< C M C <fF@:hSK> v ghSKM}F@?aJnEK> � M � q� : A � q � : = � q � > : � q MOExH � :@: ���KLmJnP W ?AEK?AEKk4F@:K<�P o C JlHKSKLm<�>

� ���

� � ��� � ���� � � � � ��� � � �� � � ��� ��� = | �

� :=<�E H C M � JlLNLNS C >1JnE F@:=<4F@M O< �VS=o C JnTATa< C q ?AE F@:KM}F >@TA?ao �NJnE=<�F@:=<4` W < C ?A>1P�J � ?AEKk > TaJ � < C F@:KMOEF@:=< C JnTATA< C >@S C c MOLm< � R C ?ALmF@?aJnE ?A> l?AE=<NF@?AL�HKS=<1FDJ�F@:=<1> TA?ao q MOEKH E=<NknM}F@? � < MOLNLmJ C HK?_E=k�FDJ4F@:K<yMOHKJOoKFD<�H>@?aknE LmJnE � <�EGF@?aJnE � <�EKLm< v gbSKM}F@?AJnE � : | � W <�LmJnP�<�>�� : { ��9:=< C <�Ta< � MOEbF�<�ghSKM}F@?aJnEK>1c J C H C M � JnE M

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Page 81: Vohra - PhD (GaTech, 2006)

F@M O< �VS=o C JnTATa< C M C < v ghSKM}F@?aJnEK> � M � q � : A � q � : = � q � > : � q MOEKH � : { �%�xLmJnP W ?AEK?AE=k�F@:=<�P o C JlHKSKLm<�>� ���

� � ��� � ���� � � � � ��� � � �� � � ��� ��� = : �

9:K?_>5<�ghSKM}F@?aJnE ?A> � MOTA?AH'?AE F@:=<yF@M O< �VS=o C JnTATA< C H C M � �NJnE=<�> � � � � � �MOEKH�� � � � � ��^ E'F@:=<E=J �V>@T_?ao �NJnEK<�> ��� � � � � � q � � � � � � q MOEKH � � � � � � q F@:=<�` W < C >Do.<N<�H PQM}F@L :=<�>yF@:KM}F JOcF@:=<fSxEKH=< C TaUl?AE=k C JnTATa< C > S C c MOLm< q MOEKHt:=<�EKLm< ?A> LmJnEK>DF@MOEbF � 9:K< C <NciJ C < ?AE F@:=<�>D< C MOE=kO<�>JOc �nq

� ���

� |��� = { �

� � � ����� �� �

^ E%F@:K?A>f>D<�LmF@?aJnE%F@:K<QF@:=< C P J �VP�<�L :KMOEx?ALNMOT W <�:KM � ?aJ C JOc F@:=<Q` W < C > HxS C ?AE=k H C M � ?AEKkt?A> o C <�HK?ALmFD<�H �9:=< LmJnEx>D< C � M}F@?aJnE JOc P MO>@> MOExH%P�JnP�<�EbF@SKP+P4SK>DF W < >@M}F@?A>@`K<�H%MOEKH F@:=< C <�>Do.JnEK>D<�JOc F@:=<�` W < CSKEKHK< C SKEK?_M sl?AMOTuFD<�Ex>@?aJnE ciJ C � M C ?aJnSK> FD<�P o7< C M}F@S C <�>4P SK>@F W <Q?AE=oZS=F � 8 ` W < C P�JlH=<�T5JOcMtc J C P� :K?_L : ?AH=<�MOTA? �N<�>5F@:=< F UboZ?ALNMOT W <�:xM � ?aJ C JOcrSKEKH C M � E B"v 9�` W < C MO>JnS=F@TA?AE=<�H'?AE � :KM}oKFD< C { � ?_TAT W <SK>D<�H �^ E M c SKTATaUILmJnSKoxTa<�H F@:=< C P JnP�<�L :KMOEx?ALNMOT�o C J W Ta<�P q F@:=<QP MO> > q P�JnP�<�EbF@SKP q MOEKH%LmJnEK>DF@?AF@S=F@? � <

<�ghSKM}F@?aJnEK>�JOc1F@:=<tF@:x?A>�>D<�LmF@?aJnE M C <ILmJnP W ?AE=<�H � ?aF@: F@:K< <�E=< C kOU <�gbSxM}F@?aJnE q MOEKH F@:=<�>D<ILmJnSKoxTa<�H<�ghSKM}F@?aJnEK>-M C <y>DJnT � <�H'>@?AP4SKTaF@MOE=<NJnSK> TaU c J C F@:=<;` W < C >Do.<N<�H � � � q FD<�EK>@?AJnE � � � � q MOEKHQFD<�P o7< C M}F@S C <� � � � � 81E MOTAFD< C EKM}F@? � < FDJ >DJnT � ?AE=k c J C FD<�P�o.< C M}F@S C < c C JnP+F@:=< LmJnS=oxTa<�H o C J W Ta<�P+?_> FDJ P�<�MO> S C <?aF JnE �VTA?AE=< � � ?aF@: � � � � lE=J � E q F@:=< P�<�L :KMOEx?ALNMOT5<�ghSKM}F@?aJnEx> H=<�LmJnSKoxTa< � 9:x?A> TAM}FDFD< C M}oKo C JnMOL : ?A>c JnTATaJ � <�H :K< C <�� � ?AF@: � � � �y>Do.<�LN?a`K<�H q MOEKH P MO> > q P JnP�<�EGF@SxP q MOExH%LmJnEK>DF@?aF@SKF@? � <Q<�ghSKM}F@?aJnEK> M C <>DJnT � <�H'c J C � � ��MOEKH�� � � � � 9:hSK>"F@:=<�<�ghSKM}F@?aJnEx>"JOcrP�JOF@?aJnE ?AE <�MOL : JOc*F@:=<yLNMO>D<�> ? � < � > TA?aoQJnE'c <N<�HC JnTATA< C�q >@TA?Ao JnEIF@M O< �VS=o C JnTATA< C�q c C <N<�>DoxMOE q MOEKHIEKJQ>@TA?aoIJnE C JnTATA< C M C < ?_EGFD<Nk C M}FD<�H FDJ J W F@MO?AEILNTAJn>D<�Hc J C P >DJnTASKF@?aJnEK> c J C ` W < C >Do.<N<�H MOEKH FD<�EK> ?aJnE �

e;<Nci< C@C ?AE=k4FDJ Rd?AknS C < { >hq ?AE F@:=<yF � J �V>DF@M}kO< o C JhLm<�> > v gbSxM}F@?aJnE � A M �-?A> � MOT_?AH ?_E F@:K<1c C <N<f>@oxMOEK>� � � � � � MOExH�� � � � � � ��^ EGFD<Nk C M}F@?AE=k v ghSKM}F@?aJnE � A M �"c C JnP F@:=< W <Nkn?AExEK?AE=k FDJQ<�EKH'JOcr<�MOLz:c C <N<�>DoxMOE kn? � <�> �

� � � � �

� ��� � ���� �� � � ��� ���� �� =@> M �

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Page 82: Vohra - PhD (GaTech, 2006)

v ghSKM}F@?aJnEx> � =@> �u?AE � JnT � < F@:=< c JnS C SKE lE=J � EK> � q q � q MOExH �bJnEKLm< F@:=<NU�M C < lE=J � E q F@:=<>Do.<N<�HMO>;M�c SKEKLmF@?AJnE JOcuM C LNTa<�E=kOF@: � ?AF@:K?AE'<�MOL : c C <N<�>DoxMOE ?A> kn? � <�E W U

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��������! �������� ?ac � � � � � � �

� = A �

^ EK>D< C F@?AEKk4F@:x?A> c SxEKLmF@?aJnE ?AEbFDJ F@:=< LmJnEK>@F@?aF@S=F@? � < v gbSxM}F@?aJnE � > | � o C JhHKSxLm<�> ` W < C FD<�EK>@?aJnE�� � � � �e;<Nci< C@C ?AE=k4FDJ�Ru?aknS C <y{ >hq ?_E F@:K<1F � J �V>@F@M}kO<fo C JlLm<�>@> v ghSKM}F@?aJnE � = | �-?A> � MOTA?AH'?AE F@:=<yci<N<�H C JnTATa< C

H C M � �NJnE=<�> � � � � � � � MOExH � � � � � � � �Qv ghSKM}F@?aJnE � = | � ?A> ?AEbFD<Nk C M}FD<�H%c C JnP o.Jn?AEbF JOc >@TA?ao?AEK?AF@?AM}F@?aJnE'FDJ o.Jn?AEbF HK<NoxM C F@S C < c C JnP F@:K< C JnTATa< C c J C <�MOLz:tc <N<�H C JnTATa< C H C M � �NJnEK< FDJQJ W F@MO?_E

� � � � � � � � �� � �

� � � ��� �� ��� � ���� � � � � ��� � � �

� ��� =@= M �

� � � � � � � � �� � �

� � � ��� �� ��� � ���� � � � � ��� � � �

� �� =@= W �

F@:=<;HK<NoxM C F@S C <>@o7<N<�Hx> � MOEKH � H=<�HKSKLm<�H W U�F@:=<;P JhH=<�TxP SK>@F W <?_E�F@:=< C MOEKkO<�> � � � � � � MOEKH�� � � � � � � p JnTAS=F@?aJnEK> � � MOEKH � ��JOc v gbSKM}F@?AJnE � =@= � P4SK>DF;>@M}F@?_>DciU'F@:=< LmJnEKHx?aF@?aJnEK>

� � � � � �� = ~}M �

� � � � � �� = ~ W �

? � < � F@:K< H C M � �NJnEK<4P4SK>DF W < JnEIF@:K< C JnTATA< C � ^ c�c J C M oxM C F@?_LNSKTAM C LmJnEx>DF@?aF@S=F@? � < C <�TAM}F@?aJnE MOEKHIFD<�P �o.< C M}F@S C <yo C JO`xTa<yLmJnEKHK?aF@?aJnE'<�ghSKM}F@?aJnE � = ~}M � ?A> E=JOF>@M}F@?A>@`K<�H W U F@:=< >DJnTASKF@?aJnE'JOc v gbSKM}F@?AJnE � =@= M � qF@:=<�E ?AFu?_> C <NoxTAMOLm<�H W U � � � � � �b? � < � F@:=< C <?_>�E=J H C M � JnE�F@:=< c <N<�H C JnTATa< C JOc7F@:=< ` C >@Fu>@F@M}kO< ��^ c7F@:=<>DJnTASKF@?aJnEtJOc v gbSKM}F@?AJnE � =@= W �;H=Jh<�>�E=JOF1>@M}F@?A>Dc UtLmJnEKHK?AF@?aJnE � = ~ W �F@:=<�E ?aF�?A> C <NoxTAMOLm<�H W U � ��� � � �v ghSKM}F@?aJnEx> � =@= �"?AE � JnT � <;F@:K<�c JnS C SKE lE=J � Ex> � � q � � q � q MOEKH ���bJnEKLm<yF@:=<NU M C < lE=J � E q F@:K<;` W < C>Do.<N<�HtMO>M c SKExLmF@?aJnE JOc � � ?aF@:x?AE'F@:=<fH C M � �NJnE=<�>�?A>

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! �����

� � ?ac � � � � � � � �� = � �

8�knMO?AE q ?_EK>D< C F@?AEKk F@:K?_>�c SKExLmF@?aJnE ?AEGFDJ F@:K<tLmJnEK>DF@?aF@S=F@? � < v ghSKM}F@?aJnE � > | �4o C JhHKSxLm<�> ` W < C FD<�Ex>@?aJnE� � � � �

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Page 83: Vohra - PhD (GaTech, 2006)

v gbSKM}F@?AJnE � = : �yc J C M F@M O< S=o C JnTATa< C ?A> ?AEbFD<Nk C M}FD<�H%c C JnP F@:=<�o.Jn?AEbFyJOc C JnTATa< C M}FDF@MOL :xP�<�EGF FDJF@:=< o.Jn?AEbF JOcd> TA?ao FD< C P ?_EKM}F@?aJnE q

� � � � � � � �� �

� � � ��� �� ��� � ���� � � � � ��� � � �

� ��� = L}M �

� � � � � � � �� �

� � � ��� �� ��� � ���� � � � � ��� � � �

� �� = L W �

F@:=<-M}FDF@MOL :KP�<�EbF�>Do.<N<�HK> MOEKH� �5H=<�HKSKLm<�H W UyF@:=<-P�JhHK<�TnP Sx>DF W <5?AE F@:=< C MOE=kO<�> � � � � � MOEKH � � � � �� � p JnTAS=F@?AJnEtJOc � MOEKH � JOc v ghSKM}F@?aJnEx> � = L ��P4SK>DF W <4LmJnEK>@?A>@FD<�EGF � ?aF@: F@:=<LmJnEKHK?AF@?aJnEK>

� � �� = M}M �

� ����� = M W �

JOF@:=< C � ?A>D<�F@:=<NU M C < C <NoxTAMOLm<�H W U � � � MOEKH � � � q�C <�>@o7<�LmF@? � <�TaU � v gbSKM}F@?AJnEK>�� = L �y?AE � JnT � <F@:=< c JnS C SxE hEKJ � EK> � q � q MOExH� ���KJnEKLm<fF@:K<NU M C < hEKJ � E q F@:=< ` W < C >Do.<N<�HtMO>�M�c SKEKLmF@?aJnE JOc� � ?aF@:K?AE'F@:=< H C M � �NJnEK<�>;?A>

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� >@?AE=k v ghSKM}F@?aJnE � = { �c J C E=JQ>@TA?Ao JnE M C JnTATA< Cfq F@:=< P�JnP <�EGF@SKP o C J �D<�LmF@?aJnE � : A � C <�HKSKLm<�>�FDJMOE <�ghSKM}F@?aJnE c J C F@:K< c C ?_LmF@?aJnE ciJ C Lm< q

� � �� ��� �

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� � � � � � � � � � � � ���� �� � � ���

9:=< W MO>@?_L >DJnT_S=F@?aJnEK>QJOcfF@:=< o C < � ?aJnSK>'>D<�LmF@?aJnE M C < E=J � MO>@>D<�P W Ta<�H FDJ LmJnEx>DF C SKLmF M P�JlH=<�T;JOcF@:=< <�EbF@? C < F � J �V>DF@M}kO< H C M � o C JlLm<�>@> � 9rJ]>@?AP4SKTAM}FD< M oZM C F@?ALNSKTAM C o C JhLm<�>@> q F@:=< FDJ � P4SK>DF W <L :xM C MOLmFD< C ?��N<�H � ?aF@: MOE'<mshoxT_?ALN?aF�LmJnEK>DF@?AF@S=F@? � <1<�gbSKM}F@?AJnE � � �� �� �� � � q MOEKH MfFD<�P o7< C M}F@S C <;o C JO`xTa<� � ��� � �-P4SK>DF W <yo C J � ?_H=<�H �^ E F@:=<Q>@JnTAS=F@?aJnE o C JhLm<�HKS C <�F@:=< c JnS C c C <N< W JnSKEKHxM C ?a<�> � � q � q � � q � W <NF � <N<�E >@TA?ao%MOExH%E=J �

>@TA?Ao�MOEKH c JnS C F C MOEK> ?aF@?aJnE >Do.<N<�HK>� � q q � q � q TAM W <�Ta<�H�?AE Ru?aknS C <%{ > M C < ` C >DF >DJnT � <�H c J C �

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Page 84: Vohra - PhD (GaTech, 2006)

v ghSKM}F@?aJnEx> � =@> � q � =@= � q � = L � M C <Q>@?as <�ghSKM}F@?aJnEK> ciJ C F@:=< <�?akn:bFfSKE lE=J � EK> � � q � q � � q � q � q q � q MOExH� � q MOEKH :K<�EKLm<QF@:=< o C J W TA<�P+?A>fSxEKH=< C �VH=<NFD< C P ?AE=<�H � 9:K< F � J c C <N< oxM C MOP�<NFD< C > ?AE F@:=<o C J W Ta<�P <msl?_>DF W <�LNMOSK>D< F@:K<Q>DFD<�MOH=U c J C P SxTAM}F@?aJnE%?A>fH=Jb<�>fE=JOF HK?_>DF@?AE=knSK?_>@: >@F@M W Ta< >DFD<�MOH=U%>@F@M}FD<�>c C JnP2SKEK>DF@M W TA<">DFD<�MOH=U4>DF@M}FD<�> � 9rJ >D<�Ta<�LmF � :K?ALz:4JOcKF@:=< F � J � oxM C MOP�<NFD< C c MOPQ?ATaU JOcx>DFD<�MOHKU4>DJnT_S=F@?aJnEK>?A> F@:K<f>DJnTAS=F@?AJnE F@:KM}F � ?AT_T W < ox:bUl>@?ALNMOTATaU'>@SK>DF@MO?_E=<�H q <�?aF@:=< C F@:K<f>DF@M W ?AT_?aFVU'JOcrF@:K<f>DFD<�MOH=Ut>DJnT_S=F@?aJnEK>?AEQF@:=<�LmJnEbFD<mshF JOc�F@:=<�F@?AP�<;HK<No7<�ExH=<�EGF5<�gbSKM}F@?AJnEK>"P4SK>DF W <<mslMOPQ?AE=<�H q J C <�E=< C kOU LmJnEK>@?AH=< C M}F@?aJnEK>P4SK>DF W < M}oKo.<�MOTa<�H FDJ � 9;:=< TAM}FDFD< C M}oKo C JnMOL : ?A> ciJnT_TaJ � <�Ht:=< C < �9:K< � <�TaJlLN?aF@?a<�>( � MOExH� M C <'?_H=<�EGF@?A`K<�H MO>�F@:=<'c C <N< oZM C MOP�<NFD< C > q E=JOF@?AE=k F@:KM}F�F@:=<NU P4SK>DF

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>D<�LmJnEKH c C <N<'>@oxMOE q MOEKH F@:K<QF@:K? C H :KMO>4M :K<�M}FD<�H F@:K? C H C JnT_Ta< C � 9:=<�>@<QF@: C <N< o C JlLm<�>@>D<�>4M C < HK?A>��F@?AE=knSx?A>@:=<�H W U F@:=<�FD<�P�o.< C M}F@S C <�o C JO`ZTa< F@:xM}Fy?_>1?_E=oxS=F � ^ E p ?AP4SKTAM}F@?aJnE : F@:=<�FD<�P�o.< C M}F@S C <�?A>yMLmJnEK>DF@MOEbF {@M@L � F@: C JnS=kn:=JnSKFfF@:=<'o C JlLm<�>@> � >D<N<'Ru?aknS C <'{ = � �-E=JOFD< F@:xM}F4?AE F@:K?A> >@?AP4SKTAM}F@?aJnE oxMO>��>@? � < :=<�M}F@?AE=k HKS=< FDJ ?AEGFD< C EKMOTHK?A> >@?aoxM}F@?aJnE c C JnP�c C ?ALmF@?AJnE W <NF � <N<�E]F@:=< ` W < C > MOEKH C JnTATa< C > MOEKH>DF C <NF@Lz:K?AE=k ?A>4E=<NknTa<�LmFD<�H �t^ E p ?AP4SKTAM}F@?aJnE {tF@:=<'FDJ � FD<�P�o.< C M}F@S C <'?A>f>@o7<�LN?A`K<�H%FDJ W < F@:=< >@MOP�<LmJnEK>DF@MOEbF;{@M@L � SKEbF@?ATZF@:=<y>D<�LmJnEKH c C <N< >DoxMOE q J � < C � :K?AL :'?aF C MOP�oZ>5FDJ > { > � � HKSK<1FDJ�M4c C <N< >DoxMOE:=<�M}FD< C � q F@:=<�E C MOP ox> W MOL H=J � E FDJ {@M@L � J � < C F@:=<�` C >@F = LNP JnE F@:=< SKEx:=<�M}FD<�H C JnTATA< C�> � >D<N<Ru?aknS C < {O~ � �t^ E p ?_P SKT_M}F@?aJnE > F@:K<QFD<�P�o.< C M}F@S C < ?A> MILmJnEK>DF@MOEbF {@M@L � SKEGF@?_T�F@:=<Q` W < C LmJnEGF@MOLmF@>F@:=< :=<�M}FD<�H F@:K? C H C JnT_Ta< C�q F@:=<�E J � < C F@:K< ` C >DF = LNP JOc C JnTATa< C�> F@:=< FD<�P o7< C M}F@S C < C MOP�ox>�S=o FDJ= : > � q F@:=< C <�M}c FD< C C <�P MO?AEK?_E=k M}F"F@:K< C JnTATA< C FD<�P�o.< C M}F@S C < = : > � � >D<N<yRd?AknS C <�{�� � � 9;:=< C <�PQMO?AEK?AE=ko C JlLm<�>@>1LmJnEKHK?aF@?AJnEK> c J C F@:=<4F@: C <N<4>@?AP4SKTAM}F@?aJnEx>M C <�HK?A>DoxT_M�UO<�HI?_EI9dM W Ta< > ��� JOFD<�F@:KM}F q MO>@?AH=< F@:=<FD<�P�o.< C M}F@S C < o C JO`xTa<�> q F@:K< o C JlLm<�>@>D<�> JOc p ?_P SKT_M}F@?aJnEK> : MOEKHI{�M C <f?AH=<�EbF@?ALNMOT �^ E MOHKHK?aF@?aJnEIFDJ F@:=< FD<�P o7< C M}F@S C <4o C JO`xTa< q p ?AP4SKTAM}F@?AJnE > HK? < C >c C JnP F@:=<4JOF@:=< C F � J ?AE F@:KM}F

F@:=< C <�?A>�MfTAJ � < C LmJh<('QLN?a<�EbF5JOc.c C ?ALmF@?aJnE W <NF � <N<�E F@:K<` W < C MOEKH�F@:K< C JnTATA< C > � # � | � | = C M}F@:=< C F@:KMOE| � { � q MOExH�F@:=< C <M C < F � J MOEKH�M ghSKM C FD< C �;C M}ox>uJnE�F@:=< ` C >@F C JnTATa< CuC M}F@:=< C F@:KMOE JnE=< MOEKH�M gbSxM C FD< C�qE=<�Lm<�>@> ?aF@M}FD<�H W UtF@:=<�TaJ � c C ?ALmF@?AJnE LmJh<('QLN?a<�EbF � � ^ c�F@:=< C < � < C <�JnEKTAUtJnE=<�MOEKH M gbSKM C FD< C �C M}o ?AEF@:K?A>;>@?AP4SKTAM}F@?aJnE q F@:=< >DJnTAS=F@?aJnEtJOc v gbSxM}F@?aJnE � =@= � � JnSKTAHtUh?a<�T_H � � � � >@> LNP��KF@:=<fE=<NknM}F@? � < � MOTAS=<>@?aknEx?a`K<�>�F@:xM}F-F@:K<yEK<�Lm<�>@>@M C UQH C M � >@S C c MOLm<y?A>-k C <�M}FD< C F@:KMOE � :KM}F ?A> M � MO?ATAM W Ta< � ?AF@: �@SK>DF-JnE=< MOEKHM ghSKM C FD< C �;C M}o q >DJ�F@:=<f` W < C > � JnSxTAH >@TA?ao J � < C F@:=< <�EbF@? C < LmJnEGF@MOLmF � ?aF@: F@:=< C JnTATa< C � �^ E <�MOL :�>@?AP4SKTAM}F@?aJnE�F@:=< ` W < C >@o7<N<�H � � �'MOEKH FD<�EK>@?AJnE � � � � F@: C JnS=kn:=JnSKF'F@:K< H C M � TA?AE=<

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Page 87: Vohra - PhD (GaTech, 2006)

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����# ' � �� � � �� ��� �� ���C <Nc < C <�EKLm<fFD<�P�o.< C M}F@S C <(� � � � � {@M@L {@M@L {@M@LLmJh<('QLN?a<�EbFJOcuc C ?ALmF@?aJnE # |�� { |�� { |�� | =TA?_E=<�M C H=<�EK>@?AFVUQJOcu` W < C � � H=<�EK?a< C � A = | A = | A = |Ta<�EKkOF@: JOcrc C <N<f>@oxMOE : � LNP � = |�� | = |�� | = |�� |Ta<�EKkOF@: JOcrc C <N<f>@oxMOEt{ � LNP � = |�� | = |�� | = |�� |C JnT_Ta< C C MOHK?ASx>� � LNP � : {#� � : {#� � : {#� �EhSKP W < C JOc �C M}ox> JnE C JnTATA< C : : � { = : � { = {#� { =EhSKP W < C JOc �C M}ox> JnE C JnTATA< C { : : :EhSKP W < C JOc �C M}ox> JnE C JnTATA< C,> : : :C JnT_Ta< C : >@S C c MOLm< >Do.<N<�H � � � LNP > � � > MO~ > MO~ > MO~C JnT_Ta< C {�>@S C c MOLm< >Do.<N<�H � � LNP > � � A �}~ A �}~ A �}~C JnT_Ta< C,> >@S C c MOLm< >Do.<N<�H � � � LNP >� � � � A | � A | � A |

M W J � <�F@:=<;>Do.<�LN?a`K<�H4FD<�P�o.< C M}F@S C <o C JO`ZTa< � � ?aF@:�F@:K<LmJnP�oxS=FD<�HQc SKExLmF@?aJnEK> � � � �uMOEKH � � � qhv ghSKM �F@?aJnEK> � : A �yMOEKH � : = � M C < <�P�oxTAJ UO<�H FDJIHK<�HKSKLm<�F@:=< c C ?ALmF@?AJnEKMOTuMOEKH%E=J C PQMOTuciJ C Lm<�>fo.< C Ta<�E=kOF@:��MOEKH�� c C JnP F@:=< C JnTATa< C > JnEIF@:K<f` W < C MO>�c SxEKLmF@?aJnEK>;JOc�o7Jn> ?aF@?aJnE �KF@:K<�>D< M C <4MOTA>DJ'HK?A>DoxT_M�UO<�Ht?AEIF@:=<`KknS C <�> � ^ EIF@:=<�>D<foZTaJOF@> q F@:K< >@S=o.< C ?_P�o.Jn>D<�H >DUhP W JnTA> � � �QTAM W <�T�F@:=<4TaJlLNM}F@?aJnEK> � :=< C <fF@:K<f` W < C >M}FDF@MOL : FDJ MOEKH]H=<NoxM C F�c C JnP F@:=< C JnTATa< C > � F@:K<�>D<ITaJlLNM}F@?aJnEK> M C <t?AE=oxS=F�FDJ%F@:K<IP�JlH=<�T � q MOExH F@:=<>DUlP W JnTA> � � �fTAM W <�T � :K< C <;>@TA?Ao >DF@M C F@>5?_E�ci<N<�H H C M � MOEKH Lm<�MO>D<�> ?AE�F@M O< �VS=o H C M � � F@:=<�>D<1TaJhLNM}F@?AJnEK>M C <4H=<�HKSKLm<�H W U F@:=<4P�JhHK<�T � � 9:=<fM W C S=oKF W <�EKHK>?_EtF@:=<f>@o7<N<�HIoxTaJOF;EKJOF�M}F�MOE � J C ��?_EKHK?ALNM}FD<F@:=< F C MOEK>@?aF@?aJnEx>-?_EGFDJQMOExH JnS=FJOcuF@:=< H C M � oxTAM}FD<�MOStJOcdF@:K< ` W < C �e;<Nci< C@C ?AE=k�FDJQRu?aknS C <�>{ =hq {O~ q MOEKHt{�� q F@:=< FDJOoITa<Nc F oxTaJOFHK?_>DoxTAM Uh>-F@:=< LmJnP�oZS=FD<�H ` W < C >Do.<N<�H

IMO> M c SKEKLmF@?AJnE JOc-M C LNTa<�E=kOF@: �Gq MOEKH F@:=<�FDJOo C ?akn:GF1oxTaJOF HK?_>DoxTAM Uh>�F@:=< LmJnP�oxSKFD<�H ` W < C FD<�Ex>@?aJnE� � � � � � <�TaJ � F@:K?A> oxMO? C M C <'F@:K< LmJnP�oxSKFD<�H EKJ C P MOT"ciJ C Lm<'o.< C TA<�E=kOF@:�� � � � c C JnP$F@:=< C JnTATa< C JnE` W < C�q LmJnP�oZS=FD<�H c C ?ALmF@?aJnEKMOTdc J C Lm< o.< C Ta<�E=kOF@: � � � ��c C JnP F@:K< C JnTATa< C JnE F@:=<�` W < C q MOExH%>Do.<�LN?a`K<�HFD<�P�o.< C M}F@S C < o C JO`xTa< � � � � qGC <�>@o7<�LmF@? � <�TaU �dB5C JlLm<N<�HK?AE=kyc C JnP Ta<Nc FuFDJ C ?akn:bF�?AE4<�MOL :QoxTaJOF q F@:=< ` C >DF �� MOEKH W <Nkn?AEKEK?AEKk JOc*F@:=<1oxTaJOF �5?A>�F@:=<1o.Jn?AEbF5JOc�M}FDF@MOLz:KP�<�EbF ��� � |�LNP)JOc�F@:=<1` W < C FDJ C JnTATA< C : q F@:=<>D<�LmJnEKH � ?A> F@:=<fo7Jn?_EGF JOcuH=<NoxM C F@S C < � � c C JnP C JnT_Ta< C : q F@:=< F@:x? C H � ?A>F@:=< o.Jn?AEGF JOc�M}FDF@MOLz:KP�<�EbF� FDJ C JnTATa< C { q F@:=<c JnS C F@:�� ?A>�F@:K<o.Jn?AEGF�JOc�H=<NoZM C F@S C < � � c C JnP C JnTATa< C { q F@:=<`xciF@: � ?A>�F@:=<;o7Jn?_EGFJOc�M}FDF@MOL :KP <�EGF1FDJQF@:=<fF@:K? C H C JnT_Ta< C�q MOEKH F@:=< >@? slF@: � � MOEKHIFD< C P ?AEKM}F@?AJnE JOcuoxTaJOF �-?A> F@:K< o.Jn?AEGF JOc

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H=<NF@MOLz:KP�<�EbF1c C JnP F@:=< C JnTATa< C�> � 9;:=< ` C >DF �Q?A>�F@:=<4o7Jn?_EGFJOc"?AEK?aF@?AM}F@?AJnE � � JOc�c <N<�H >@TA?ao JnE C JnTATa< C: q F@:=<'>D<�LmJnEKH �t?_> F@:=<'o.Jn?AEGFfJOcLm<�>@>@M}F@?aJnE � JOc F@M O< �VSKo > TA?ao JnE C JnTATA< C { q F@:=<'F@:K? C H � ?A> F@:=<o.Jn?AEbF"JOcu?AEK?aF@?_M}F@?aJnE � ��JOcdci<N<�H >@T_?ao JnE C JnTATa< C { q MOEKH F@:=< c JnS C F@:��4?A>-F@:=< o.Jn?AEbF"JOcuLm<�>@>@M}F@?AJnE � 1JOcF@M O< �VS=o >@TA?ao JnE C JnTATa< C,> �

^ EQF@:K<y?_>DJOF@:=< C P MOT7>@?AP4SKTAM}F@?AJnE � Ru?aknS C < { = �"?aF"?_>5c JnSKEKH F@:KM}F LmJnEKHK?aF@?AJnEK> � = M �-M C < � ?aJnTAM}FD<�H W UF@:=< >DJnT_S=F@?aJnEK>yJOc v ghSKM}F@?aJnEK> � = L �yc J C MOTAT�MOTATaJ � M W Ta< >Do.<N<�HK> � �MOEKH� JOc-M}FDF@MOLz:KP�<�EbF � ?aF@: F@:=<F@M O< �VS=o C JnTATa< C > q � � � )� � MOExH � � � � �� � <�EKLm< ciJ C F@:=< kn? � <�E ` W < C C <�>Do.JnEK>D<c SKEKLmF@?aJnE MOExH o C JlLm<�>@>"LmJnEKHK?aF@?aJnEx>�H C M � H=Jh<�>5EKJOF5JlLNLNS C JnEQ<�?aF@:=< C F@M O< �VSKo C JnTATa< C�q ? � < � F@:K<�P�JlH=<�TH=<�P MOExHK> � � � q � �� �� � 81TA>DJ q >@?AEKLm< F@:=<4` W < C ?A>1?A>DJOF@:=< C P MOT�?AE W JOF@:Ic C <N<�>DoxMOEK> � ���� � � | �MOEKHIF@:=< C < M C < E=JQ?_EGFD< C � <�Ex?AE=k knSK?_H=<�> qxv gbSKM}F@?AJnE � A M �;HK?ALmF@M}FD<�>�F@:KM}F�>Do.<N<�H ?A>;LmJnEK>@F@MOEGF1?AE W JOF@:c C <N<�>DoxMOEK> � 9:=< C <Nc J C <�?AE F@:=< ?A>@JOF@:=< C P MOTdo C JlLm<�>@>yJOc p ?AP4SKTAM}F@?aJnE : q JOc5F@:K< >@? sIo.Jn>@>@? W Ta<foZTAMOLm<�>JOc�H C M � TA?A>@FD<�HtM}F;F@:=< <�EKH JOc�>D<�LmF@?AJnE A � : MOExHI?AEtRu?aknS C < { >hq H C M � JhLNLNS C >JnEKTaU ?AEtF@:=< ` C >@F;MOEKHc JnS C F@: q ? � < � JnE'F@:=<1F � J�ci<N<�H C JnTATA< C > � 9:K?A>"?A>-HKS=<1FDJ�>@o7<�LN?AciUl?AE=k JOc W JOF@:Qo C JhLm<�>@> LmJnEKHx?aF@?aJnEK>-MOEKH`xTAMOP <�EGFLmJnEK>@F@?aF@S=F@? � < C <�>@o7JnEx>D< �

e;<Nci< C@C ?AE=k FDJ Ru?aknS C < { =hq F@:=<t` W < C M}FDF@MOL :K<�> FDJ C JnTATa< C : M}FQF@:=<t` C >DF ��� � ��|�LNP � � ?aF@:FD<�EK>@?AJnE�� � � A � |O| � : | � H=UlE MOEKHtM}F F@:=<f> S C c MOLm< >Do.<N<�H � ��� > MO~�LNP >� � � 9;:=< ` W < C >-o C JlLm<N<�H� ?aF@:KJnS=F >@TA?ao JnE C JnTATA< C : SKEbF@?ATuF@:=< ` C >DF � M}F � � ~��uLNP���?AE F@:K?A> ~��uLNP�JOc E=J >@TA?ao F@:K< >Do.<N<�H qFD<�EK>@?AJnE q MOEKH E=J C PQMOT.ciJ C Lm<fo7< C TA<�E=kOF@:tM C <fMOT_T�LmJnEK>DF@MOEbF q MOEKH F@:=< c C ?ALmF@?AJnE ciJ C Lm<fo7< C TA<�E=kOF@:�� ?A>�N< C J � ��� � � | ?AP oxTA?a<�> � � |�?AE v gbSKM}F@?AJnE � ~ : � � � 9;:=< H C M � �NJnE=< JnE C JnTATa< C : ?A> F@:=< >@> LNP c C JnPF@:=< ` C >DF �� � � � ~��uLNP �FDJ F@:=<4>D<�LmJnEKH � ��� ��� : |O|5LNP � q � :=< C < F@:=<f` W < C >�H=<NoxM C F�F@:=< C JnTATa< C �^ E F@:x?A> H C M � �NJnE=< F@:=< ` W < C >Do.<N<�H ?_EKL C <�MO>D<�>4c C JnP F@:=<'> S C c MOLm< >@o7<N<�H > MO~�LNP]>� � JOc C JnTATa< C :

FDJIF@:K<Q>@S C c MOLm<Q>Do.<N<�H A �}~�LNP > � JOc C JnTATA< C { q MOEKH%F@:=< FD<�EK>@?AJnE%?AEKL C <�MO>@<�> c C JnP A � |O|�� : | � H=UlEFDJ ~#� �}~�� : | � H=UlE � � JOFD< c C JnP F@:=<�o C <�>@<�EKLm<�JOc F@:=< h?_E M}F � �HM@M�LNP$?AE F@:=< � � �1oZTaJOFyF@:KM}FF@:=< ` W < C ?A>H C M � E JnE F@:=< ` C >DF ci<N<�H C JnTATa< C c C JnP ?aF@>?AEx?aF@?AMOT�>DF@? C <�>Do.JnEK>@<f?AEbFDJQ?aF@>>DJOc F;oZTAM}FD<�MOS �R=J C ~��uLNP � � � M@M�LNP F@:=< H C M � ?A>�?AE F@:=< >DF@? o.J C F@?AJnE JOcF@:K<'`ZTAMOP�<�EbF C <�>@o7JnEx>D< q � :=< C < MTAM C kO<y?AEKL C <�MO>D<�?AE FD<�EK>@?AJnE MOLNLmJnP�oZMOEK?a<�> M > P MOTATx?_EKL C <�MO>D<y?AEQ>@F C MO?AE'MOEKH :K<�EKLm<1>@o7<N<�H � RKJ C M@M�LNP� � � : |O|�LNP�F@:K<H C M � ?_>�?AE�F@:=<>DJOc F�o.J C F@?aJnE4JOcZF@:K< `xTAMOP�<�EbF C <�>Do.JnEK>D< q � :K< C <M >@P MOTATl?AExL C <�MO>D<?AE FD<�EK>@?aJnE MOLNLmJnP�oZMOEK?a<�> M�TAM C kO<y?AEKL C <�MO>D<y?AE'>DF C MO?AE MOEKH'>Do.<N<�H �u^ E F@:K<1H C M � �NJnE=<yF@:=<yc C ?ALmF@?aJnEKMOTc J C Lm< JnE F@:=<f` W < C ?A> ?AEKL C <�MO> ?AE=k�MOEKHt?AE F@:K< HK? C <�LmF@?aJnE JOoxo7Jn> ?aFD< FDJ ` W < C P�JOF@?aJnE �

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Page 90: Vohra - PhD (GaTech, 2006)

9:K< = |�LNP W <NF � <N<�E F@:=<4>@<�LmJnEKH � ��� � � : |O|5LNP �MOExHIF@:K? C H � ��� � : = |�LNP �;?A>�F@:=<4` C >DFc C <N< >DoxMOE ��^ E F@:K?_> ?A>DJOF@:=< C PQMOT�c C <N< >DoxMOE � ?AF@:=JnS=F knSK?AH=<�> q >Do.<N<�H MOEKH FD<�EK>@?AJnEtM C < LmJnEK>DF@MOEbF �

� JOFD<�F@:xM}F5F@:=<;>@<�LmJnEKH�� LmJn?AEKLN?AH=<�> � ?aF@:�F@:K<F@:K? C H�� q ?_EKHK?ALNM}F@?AEKk1F@:K<;M}ciJ C <�P�<�EGF@?AJnE=<�H C <�>@SKTaFF@:KM}F F@:=< C <y?_>-EKJ4F@M O< �VSKoIH C M � JnE C JnTATa< C { ��F@:=<y` W < C M}FDF@MOL :=<�>;FDJ C JnTATa< C {�M}F � � � � : = |"LNPMOT C <�MOHKUIM}F ?aF@>y>@S C c MOLm<�>Do.<N<�H � � A �}~�LNP > � � 9:=<4` W < C o C JhLm<N<�HK>yJnE C JnT_Ta< C { � ?AF@:=JnS=Fy>@TA?aoSKEbF@?AT*F@:K<fF@:K? C H�� q � :=< C < ?aF W <Nkn?_EK>FDJ >@TA?ao �KF@:K?A>1H C M � �NJnE=<4JnE C JnTATa< C { ?A>�F@:=< : A LNP c C JnP F@:=<F@:K? C H�� M}F � � � { : ~�LNP FDJ4F@:=<c JnS C F@: � M}F � � � { > |"LNP q � :K< C <F@:=<�` W < C H=<NoxM C F@>5c C JnP C JnTATA< C {MOT C <�MOHKU'M}FF@:K<f>@S C c MOLm< >Do.<N<�H JOc C JnTATA< C,> ��� JOFD< c C JnP F@:=< l?AE ?AE� � � �-F@:KM}FF@:K< ` W < C :KMO> W <N<�EH C M � E JnS=F JOc�?aF@> >@JOciFoZTAM}FD<�MOS JnEtF@:K< >D<�LmJnEKHtc <N<�H C JnT_Ta< C �� <NF � <N<�E F@:K< c JnS C F@: � MOEKH�`Kc F@: � � M}F�� � {@L}|�LNP �'?A> F@:=< >D<�LmJnEKH c C <N< >DoxMOE q M}knMO?AE

?A>DJOF@:K< C P MOT � ?aF@: E=J knSK?_H=<�>yMOEKH :=<�EKLm< � ?aF@:KJnS=F H C M �� 9:=<�c JnS C F@:��'LmJn?AExLN?AH=<�> � ?aF@: F@:=<�`Kc F@:� q M}knMO?AE ?AEKHK?ALNM}F@?_E=ktF@:KM}F4F@:=< C < ?A> E=J F@M O< �VSKo H C M � ?AE F@:K?A>4?A>DJOF@:=< C P MOT�o C JhLm<�>@> � 9:K<Q` W < Co C JlLm<N<�HK> � ?aF@:=JnS=F >@TA?Ao JnEt?aF@> <�EbF@? C < oxM}F@:tJnE C JnTATa< C,> �

Ru?aknS C <I{ = >@:=J � > F@:KM}F M}F F@:=<ITaJlLNM}F@?aJnE � ����~��uLNP � :=< C <I> TA?ao W <Nkn?AEK> q F@:=< C <t?A> M C M}ox?AHW SK?_TAHKS=o'JOcdEKJ C P MOT*MOEKHtc C ?_LmF@?aJnEKMOT.c J C Lm<�> � 81>F@:=<fFDJ � >@F C <NF@L :=<�>�F@:=< E=J C P MOT*MOEKH F@:K< c C ?ALmF@?aJnEKMOTc J C Lm<�> ?_EKL C <�MO>D< q SKEbF@?AT�F@:=<NU � MOEK?A>@: � :=<�E%F@:K<QFDJ � Ta<�M � <�>4F@:=< C JnTATA< C � 9:=< FD<�EK> ?aJnE ?AE%F@:=<QFDJ �?AEKL C <�MO>D<�> SKEK?ac J C P TaU H=J � E�F@:=< H C M � TA?_E=< � 9;:=< ` W < C � <�TaJlLN?aFVU�?AEKL C <�MO>@<�>'> TA?akn:bF@TaU � :=<�E�F@:=<<mslFD<�EK>@?aJnE]JOc F@:=<I` W < C ?_> � ?aF@:x?AE F@:=< ?_EK?aF@?AMOT >DF@? < C C <Nkn?aJnE JOc F@:K< LmJnEK>DF@?AF@S=F@? � < C <�T_M}F@?aJnE � 8 F� � M@M�LNP q F@:=< ` W < C W <�:KM � ?aJ C P�J � <�>;c C JnP F@:K< ` C >DF>@F@? C <Nkn?aJnE FDJ F@:=< LmJnP�oxTA?AMOEbF C <Nkn?aJnE q MOEKHLmJ C@C <�>@o7JnExHK?AE=knTaU F@:=<I>Do.<N<�H JOcyF@:=<tFDJ � ?AEKL C <�MO>D<�> C M}oZ?AHKTaU SKo FDJ F@:=<t>@S C c MOLm< >Do.<N<�H JOc C JnTATa< C{ � � <NF � <N<�E : |O|�LNP+MOEKH { : ~�LNP F@:=<�FDJ � P�J � <�> F@: C JnS=kn: F@:=<�c C <N<�>DoxMOE MOEKH F@:=<�E=J �V> TA?ao �NJnE=<JnE C JnTATa< C { � ?aF@: E=J Lz:KMOE=kO<�>�?AE F@:=<'FD<�EK>@?aJnE MOEKH � <�TaJlLN?aFVU � 8 F � � � { : ~5LNP q F@:=< FDJ � >@F@M C F@>>@TA?AoKox?AE=k W U'P�J � ?AE=k�c MO>DFD< C F@:KMOE F@:=< C JnT_Ta< C >@S C c MOLm< q F@:=< E=J C P MOT�MOExH F@:K< c C ?_LmF@?aJnEKMOTZciJ C Lm<�> W SK?ATAHS=o q MOEKH'F@:=<1FD<�EK>@?aJnE ?AExL C <�MO>D<�> P�JnE=JOFDJnEK?_LNMOTATaU � 9:=< � <�TaJlLN?aFVU'?AEKL C <�MO>D<�> C M}oZ?AHKTaU � :=<�E F@:=<y` W < C >M C <1>DF@?ATATK?_E F@:=<1LmJnP�oxTA?AMOEbF5oZTAM}FD<�MOS q W S=F � :K<�E F@:=<NU�<�EbFD< C F@:=<�>D<�LmJnExH >DF@? < C"C <Nkn?aJnE F@:=<�?AExL C <�MO>D<?AE � <�TaJlLN?aFVUI> TaJ � >1H=J � E � 9:=< C <�M C <�E=J'Lz:KMOE=kO<�> ?AEIF@:=<�FD<�EK>@?aJnE J C � <�TaJlLN?aFVUI?_EIF@:=<�>D<�LmJnEKH c C <N<>DoxMOE q MO> F@:=< o C JhLm<�>@>;?A> >D<NF;S=o �^ E%Ru?aknS C <'{O~ H=<Nox?ALmF@?_E=k p ?AP4SKTAM}F@?aJnE { q M}knMO?AE EKJOFD< F@:=<QS=o � M C H C MOP�o ?AE F@:=< FD<�P o7< C M}F@S C <

o C JO`ZTa<(� � � � W <NF � <N<�E F@:=<fc JnS C F@: ��MOEKHIF@:=<f`Kc F@: � q P JhH=<�T_?AE=k�F@:=< :K<�M}FD<�H >@<�LmJnEKHIc C <N<f>@oxMOE q

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Page 91: Vohra - PhD (GaTech, 2006)

MOEKH F@:=<�H=J � E � M C H C MOP�o ?AE � � � ��ciJ C F@:=<�` C >DF = LNP M}ciFD< C F@:=<�`Kc F@: � q P�JlH=<�TA?AE=k F@:=< LmJhJnTA?AE=kJOcdF@:=<y` W < C > S=o.JnE'LmJnEbF@MOLmF � ?aF@:'F@:=< SKEK:=<�M}FD<�H C JnT_Ta< CU> ��^ E F@:x?A>-o C JlLm<�>@> F@:=< C < ?A> H C M � ?AE ��$ � � �JOc�F@:K< >@? sQo.Jn>@>@? W Ta< �NJnEK<�> q EKMOP�<�TaU'H C M � JnE F@:=< F � J�ci<N<�H C JnTATa< C > � MO>?AE p ?_P SKT_M}F@?aJnE : �-MOExH MOTA>DJH C M � ?AE4F@:=< >D<�LmJnEKH�c C <N< >DoxMOE�HKS=<-FDJyF@:=< o C <�>D<�EKLm< JOcZF@:=< :=<�M}FD< C � 9:=< C < ?A>uE=J H C M � ?AE4F@:=< JOF@:=< CF@: C <N<�o.Jn>@>@? W TA< �NJnE=<�> ��9:=<1P�JhHK<�TK?AEKHK?_LNM}FD<�>�F@:=< C <1?A>5EKJ H C M � JnE F@:=<�F � J F@M O< �VS=o C JnT_Ta< C >�?AEQF@:=<>@MOP�<�P MOExE=< C MO> ?AE p ?AP SxTAM}F@?aJnE : � � <�`xExHIF@:KM}F LmJnEKHx?aF@?aJnEK> � = M �yM C < � ?aJnTAM}FD<�H W U >DJnTAS=F@?AJnEK>;JOcv ghSKM}F@?aJnEx> � = L � c J C MOT_T*MOTATaJ � M W TA<f>Do.<N<�HK> MOEKH� � 9:=< C < ?A>;E=J H C M � ?AE ` C >@Fc C <N<f>DoxMOE >@?AEKLm<?aF?A> ?_>DJOF@:=< C P MOT�MOEKH � ?aF@:=JnSKF knSK?AH=<�> �^ E Ru?aknS C < {O~ F@:=< W <�:KM � ?AJ C JOc F@:=< FDJ � ?A> ?_H=<�EGF@?_LNMOTyFDJ F@:KM}FtJOc4F@:=<%?A>DJOF@:=< C P MOT1o C JlLm<�>@>

JOc p ?AP4SKTAM}F@?aJnE : SKEbF@?ATyF@:=<%:K<�M}FD<�H >D<�LmJnEKH c C <N< >DoxMOE � � :=<�E F@:=< ` W < C > <msho.< C ?a<�ExLm< :x?akn:=< CFD<�P�o.< C M}F@S C < q F@:=<NU W <�:KM � <4?_EIMOLNLmJ C HKMOExLm< � ?aF@: F@:=<�LmJ C@C <�>Do.JnEKHx?AE=k LmJnEK>DF@?AF@S=F@? � <f<�ghSKM}F@?aJnEx>;c J CF@:KM}F-FD<�P�o.< C M}F@S C < qhC <�>@SxTaF@?AE=k ?AE C <�HKSKLm<�HQFD<�EK>@?aJnE ?AE F@:K<;FDJ � MO>-F@:=<�` W < C > W <�LmJnP�<y>DJOciFD< C � p ?AEKLm<F@:=<�` W < C LNMOE%>DF C <NF@Lz: � ?aF@: TaJ � < C FD<�EK>@?AJnE ?_E F@:x?A> C <Nkn?aJnE q F@:=<�>Do.<N<�H JOc5F@:=<�` W < C >y?AExL C <�MO>D<�>y?AEF@:K?A> �NJnE=<Q?AE J C HK< C FDJIP M}F@Lz: F@:K< F@:=< >@S C c MOLm<Q>@o7<N<�H%JOc-F@:K< F@:K? C H C JnTATa< C � 9:K<�FDJ � <�EbFD< C > F@:=<F@:K? C H C JnTATA< C � ?AF@:=JnS=F�> TA?ao q W S=F1F@:=<4HK<�L C <�MO>@?AE=k'FD<�P�o.< C M}F@S C < JOc"F@:=< ` W < C ?AEKHxSKLm<�>;MOE ?AExL C <�MO>D<�HFD<�EK>@?AJnE q MOLNLmJnP oxMOEK?a<�H W UQc C ?_LmF@?aJnEKMOTKMOEKH'E=J C PQMOTxc J C Lm<�> ?AP P�<�Hx?AM}FD<�TaU�M}ciFD< C F@:=<1FDJ � M}FDF@MOL :K<�> FDJF@:=< C JnTATa< C �^ E F@:=<�F@:K? C H >@?AP4SKTAM}F@?aJnE � Ru?aknS C < {�� � q F@:=<�HK? < C <�EKLm<�>yM C <�M TaJ � < C c C ?ALmF@?aJnE LmJh<('QLN?a<�EbF q F � J

MOEKH M�ghSKM C FD< C �C M}ox> JnE C JnTATa< C : � E=JOFD<fF@:KM}F F@:=< HK?A>DF@MOExLm< W <NF � <N<�EIF@:=<y` C >DF � MOEKH F@:=< >@<�LmJnEKH�]?_>E=J � : L}|�LNP C M}F@:=< C F@:KMOE : |O|"LNP � q E=JQc C <N<4>DoxMOEt:K<�M}FD< C > q MOEKHtMQ:K<�M}FD<�H C JnT_Ta< C<> � R=J C F@:K?A>o C JlLm<�>@>fF@:=< C <Q?A>fH C M � JnE W JOF@:%c <N<�H C JnTATa< C > MOExH%E=JIH C M � JnE ` C >DF � SKEK:=<�M}FD<�H �yF@M O< �VS=o C JnTATa< CMOEKH SKEK:=<�M}FD<�H c C <N<'>@oxMOEK> � j1SK< FDJ F@:=<'o C <�>D<�EKLm<'JOcF@:=< :=<�M}FD<�H C JnTATA< C8>hq :=J � < � < C�q F@:=< C < M C <c J C F@:K<1` C >DF-F@?AP�< ?AE F@:=<�>D< >@?AP4SKTAM}F@?aJnEx>">DFD<�MOHKU >DJnTASKF@?aJnEK> � ?aF@: F@M O< �VS=oIH C M � q ?AE � :K?ALz:QF@:=<yFDJ �M}FDF@MOL :K<�>�FDJ C JnTATa< C,> � ?AF@: >Do.<N<�HtTa<�>@> F@:xMOE F@:=< >@S C c MOLm<f>@o7<N<�H JOc C JnT_Ta< CU> �

� :=<�E v ghSKM}F@?aJnE � = L W �;?A>�>@JnT � <�H q F@:=<4>@JnTAS=F@?aJnEK>;JOc � � > M}F@?A>Dc Uh?AEKk � �� M C <4c JnSKEKH ciJ C MOTAT

� MOTAS=<�>-JOc � W <NF � <N<�Et~@L�� � = MOEKH � A |5LNP > � ��v MOL : JOc*F@:K<�>D< � MOT_S=<�>-o C JlHKSKLm<�>-M4>@FD<�MOH=U >DJnT_S=F@?aJnE � � � q � � � � q � � � � q MOExH � � � � � 9;:=Jn>D< � ?aF@: ~@L�� � = � � � � A |5LNP]>� � <msl:K? W ?aFfF@M O< �VSKo JnE F@:=<:=<�M}FD<�H C JnTATA< C �GF@:KM}F � ?aF@: �� � A |�LNP]> � :KMO>"EKJfF@M O< �VS=o H C M � � 8�>-HK?A> LNSK>@>D<�H W <Nc J C < q JnEKTaU�F@:=<>DFD<�MOH=U'>DJnTAS=F@?AJnE � ?AF@:QF@:=< TaJ � <�>@F-<�EK< C kOU � ?AT_T W <1>@F@M W Ta<yMOEKH :=<�EKLm<1o7< C >@?A>DF-?AEQF@:K< C <�MOT � J C TAH �d^ F

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Page 92: Vohra - PhD (GaTech, 2006)

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Page 93: Vohra - PhD (GaTech, 2006)

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Page 94: Vohra - PhD (GaTech, 2006)

?A>"ciJnSxEKHQF@:xM}F-F@:K<y>@JnTAS=F@?aJnE � ?aF@:'E=J F@M O< �VSKoIH C M � :xMO>"F@:K<1TaJ � <�>@F � MOTAS=<1JOc*F@:=<y<�E=< C kOU c SxEKLmF@?aJnE� H=<N`xE=<�H ?AE v gbSxM}F@?aJnE � ~O~ � q MOExH F@:K?A>?A> F@:K<f>DJnTAS=F@?AJnE >@:=J � E ?AE Ru?aknS C <f{�� �9:K< C <�MO>DJnE]ciJ C F@:=<IM W >@<�EKLm<IJOcyF@M O< �VS=o H C M � JnE F@:=<I:=<�M}FD<�H C JnTATa< C�> ?A> c SKEKHxMOP�<�EGF@MOT_TaU

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Page 115: Vohra - PhD (GaTech, 2006)

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Page 116: Vohra - PhD (GaTech, 2006)

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81> C <No C <�>D<�EbFD<�H W UIF@:=<4>@JnTAS=F@?aJnE H=<Nox?ALmFD<�H ?AE Ru?aknS C < >@=hq ?AEIMOE ?A>DJOF@:K< C P MOTrF � J �V>DF@M}kO<QH C M �� ?aF@:KJnS=F5ox?_EK> q H C M � JlLNLNS C >-JnEKTaU MO> c <N<�H H C M � JnE F@:K<�` C >DF C JnTATa< C MOEKH'ci<N<�H H C M � JnE F@:K<y>@<�LmJnEKHC JnTATA< C � �NJnEK<�> � � MOEKH � � ?_E Ru?aknS C < {@M � � R=J C F@:=<�o C JlLm<�>@> ?AE p ?AP4SKTAM}F@?aJnE : q F@:=<�` W < C M}FDF@MOL :=<�>FDJIF@:K<Q` C >@F C JnTATa< C M}FfF@:=< ` C >DF�� � � � |�LNP � � ?AF@: >Do.<N<�H � � � > MO~5LNP >� � � 9:=< ` W < C F@:=<�Eo C JlLm<N<�HK> � ?aF@:=JnS=F�> TA?ao�JnE F@:K<` C >DF C JnTATa< C SKEbF@?ATlF@:=<�` C >DF � M}F � � ~��uLNP �l?AE�F@:K?_>5~��uLNP JOc�E=J >@TA?aoF@:=<4>Do.<N<�HtMOEKHtFD<�Ex>@?aJnEtM C <4LmJnEK>DF@MOEbF � 9:K?A>;E=J �VH C M � o.J C F@?aJnE JOc�F@:K< o C JlLm<�>@>JlLNLNS C >�M}F;o.Jn?AEbF :?AE F@:=< >Do.<N<�H � > � FD<�EK>@?aJnE oxTAJOF?AE Ru?aknS C < > ~ �9:K<;H C M � �NJnE=<�JnEQF@:K<` C >DF C JnTATa< C ?_>�F@:=< >@> LNP c C JnP F@:=<;` C >DF ��� � �� ~���LNP ��FDJ F@:=<�>@<�LmJnEKH

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Page 117: Vohra - PhD (GaTech, 2006)

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Page 118: Vohra - PhD (GaTech, 2006)

>Do.<N<�H A �}~�LNP > � JOc;F@:=< >D<�LmJnEKH C JnTATA< C � M}F�o.Jn?AEbF > � � 9:K<'LmJ C@C <�>Do.JnEKHK?AE=k FD<�EK>@?aJnE ?AEKL C <�MO>D<�>c C JnP A � |O| � : | � H=UlE%FDJ ~#� �}~�� : | � HKUhE � � JOFD< W U h?AE�%M}F � � M@M�LNP � P M C O<�H W U%M � MOEKHEhSKP�< C ?ALNMOTZ{ ��F@:KM}F"F@:=<;` W < C ?A>5H C M � EQJnEQF@:=<�` C >DF5ci<N<�H C JnTATa< C c C JnP ?aF@>5?_EK?aF@?AMOT=>DF@? C <�>Do.JnEK>D<;?AEbFDJ?aF@>�>@JOciF"oxTAM}FD<�MOS��uR=J C ~��uLNP � � � M@M�LNP F@:=<;H C M � ?_>�?AE�F@:=<�?AEK?aF@?AMOTl>DF@? o.J C F@?aJnE JOc7F@:K<`xTAMOP�<�EbFC <�>Do.JnEK>@< q � :=< C <MfTAM C kO<;?AExL C <�MO>D<?AE�FD<�Ex>@?aJnE MOLNLmJnP�oZMOEK?a<�>5Mf>@P MOTAT=?AExL C <�MO>D<;?AE�>@F C MO?AE MOEKHQ:=<�EKLm<>Do.<N<�H � R=J C M@M�LNP � � � : |O|"LNP+F@:=< H C M � ?A> ?AE F@:=<'>DJOciF4o.J C F@?aJnE JOc F@:K<Q`xTAMOP <�EGF C <�>Do.JnEK>D< q� :=< C < M >@P MOTAT�?_EKL C <�MO>D< ?AE FD<�Ex>@?aJnE MOLNLmJnP�oxMOEx?a<�>;M T_M C kO< ?AEKL C <�MO>@<f?AE >DF C MO?_E MOEKHt>Do.<N<�H �9:K<Q` W < C H=<NoxM C F@> F@:=<'` C >DF C JnTATa< C MOT C <�MOH=U%M}F�F@:=< >@S C c MOLm< >@o7<N<�H JOcF@:=< >D<�LmJnEKH C JnT_Ta< C c J C

F � J C <�MO>DJnEK> �;9:=<4c C <N<4>DoZMOE W <NF � <N<�E F@:=<4` C >DFyMOEKH >D<�LmJnEKH C JnTATa< C >;?A>1MOE ?A>DJOF@:=< C PQMOT�c C <N<�>DoxMOE� ?aF@:KJnS=F4H C M � ox?AEx> q MOEKH :=<�EKLm< >Do.<N<�H MOEKH FD<�EK>@?aJnE M C < LmJnEK>DF@MOEbF%� F@:=< = |�LNP ?AE F@:=< FDJOo F � JoxTaJOF@> W <NF � <N<�E F@:K< >@<�LmJnEKH ����� � � : |O|�LNP �4MOEKH F@:K? C H ����� � : = |�LNP �4?A>4F@:=< c C <N< >@oxMOE �9:=<�E q c J C MOTATro7Jn> >@? W Ta< M}FDF@MOL :KP�<�EbFf>Do.<N<�HK> � fFDJ F@:=<�>D<�LmJnExH C JnTATa< C � ? � < � MOTAT � � � � � � � q<�ghSKM}F@?aJnE � ��� �do C <�Hx?ALmF@> � � � �G:=<�EKLm< q MO>�Hx?A>@LNSK>@>@<�HfM}c FD< C <�gbSxM}F@?aJnE � L}| � q c J C F@:x?A>do C JlLm<�>@>dF@:=< C <?A> E=JQF@M O<�S=o H C M � JnE F@:K< >D<�LmJnEKH C JnTATa< C � F@:=<f>@<�LmJnEKH ��MOEKHtF@:K? C H � JnE F@:K< oxTaJOF@>LmJn?_EKLN?AH=< � �9:K< ` W < C M}FDF@MOLz:=<�>�FDJ F@:=< >D<�LmJnEKH C JnTATa< C M}F � � � � : = |�LNP MOT C <�MOH=U'M}F�?aF@> >@S C c MOLm< >Do.<N<�H

� � A �}~�LNP >� � MOEKH o C JhLm<N<�HK> � ?aF@:=JnSKFQ>@TA?ao SxEGF@?ATF@:=<IF@:K? C H � M}F � � � { : ~5LNP �;c C JnP ?aF@>H=<NoxM C F@S C <4c C JnP F@:K<4` C >DF C JnTATa< C SKEbF@?ATrF@:K?A>yTaJlLNM}F@?aJnE F@:=<�` W < C ?A>yM}F o7Jn?_EGF > JnE F@:=<�FD<�EK>@?aJnE � > �>Do.<N<�HIHx?AM}k C MOP � � <NUOJnEKH � � � { : ~5LNP F@:=< ` W < C W <Nkn?AEK> FDJ'>@TA?ao �KF@:K?A>H C M � �NJnE=< JnEIF@:=< >@<�LmJnEKHC JnTATA< C ?A>-F@:=< : A LNP c C JnP)F@:=<yF@:K? C H��fFDJ�F@:=<yc JnS C F@: � M}F � � � { > |�LNP q � :=< C <1F@:=<y` W < C H=<NoZM C F@>c C JnP+F@:=< >D<�LmJnEKH C JnTATa< C MOT C <�MOH=U M}FfF@:=<'>@S C c MOLm<Q>Do.<N<�H JOc F@:=<QF@:K? C H C JnT_Ta< C � 9;:K?A> H C M � JnE F@:=<>D<�LmJnEKH C JnT_Ta< C <mslFD<�EKHK>yc C JnP o.Jn?AEbF > FDJ1LQJOc5F@:=<�>Do.<N<�H � > � FD<�EK>@?AJnE oZTaJOF ��� JOFD<�c C JnP F@:=<�h?AE�P M C O<�H W U'F@:=< >D<�LmJnEKHtF C ?AMOE=knTa< M}F�{ : ��LNP � EhSKP�< C MOT � �-F@:xM}F F@:=< ` W < C ?A> H C M � E JnS=F JOcu?aF@>>DJOc FoxTAM}FD<�MOSIHKS C ?AEKk F@:K?_> ci<N<�HIH C M ��� <NF � <N<�E F@:K<-c JnS C F@:�� MOEKH4`Kc F@:�� � M}F ��� {@L}|�LNP �d?A>dF@:=< >D<�LmJnEKH�c C <N< >DoxMOE q M}knMO?AE�?A>@JOF@:=< C �

P MOT � ?aF@:IEKJ H C M � ox?_EK>MOEKH :=<�EKLm< � ?aF@:=JnS=F�H C M �� ^ EIF@:K?A>o C JhLm<�> ><�ghSKM}F@?aJnE � : |O| �;>@oxS C ?aJnSx>@TaUo C <�Hx?ALmF@> � � � � c J C MOTAT�o.Jn>@>@? W Ta< � q MOEKH%:=<�ExLm< F@:=< C <Q?_> E=JtF@M O<�S=o H C M � M}FfF@:=<Q<�EKH JOc F@:=<>D<�LmJnEKH H C M � >DF@M}kO< q ?AEKHK?ALNM}FD<�H >@= MOEKH > ~ W U F@:=<�ciJnS C F@:�� LmJn?AExLN?AHK?AE=k � ?aF@: F@:=<�`Kc F@: � � 9:=<` W < C o C JlLm<N<�HK> � ?aF@:=JnS=F >@TA?Ao'JnEIF@:=< F@:K? C H C JnTATa< C �

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� � � � � � �N� ��� J �B ?AE MOH �@SK>DFD<�H >DJ F@:xM}FF@:=< C <f?_> H C M � JnE W JOF@: C JnTATa< C > MOEKH F@:=< ox?_E

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MOEKH � : |O| � o C JlHKSKLm<'F@:=< >DoxS C ?aJnSK> C <�>@SKTaF@> � � � MOExH � � � � q�C <�>@o7<�LmF@? � <�TaU �� <�ExLm< q MO>�?AEp ?AP4SKTAM}F@?AJnE : � ?aF@:=JnSKF M H C M � oZ?AE q F@:=< C < ?A>�E=J F@M O<�S=o H C M � JnE <�?AF@:=< C F@:K< >@<�LmJnEKH J C F@:K? C HC JnTATA< C �9:K<Q>DJnTAS=F@?AJnE%?AE p ?_P SKT_M}F@?aJnE { ?A> ?AH=<�EbF@?ALNMOT�FDJ F@:KM}FfJOc p ?_P SKT_M}F@?aJnE : c J C F@:=< ` C >DF >DF@M}kO< JOc

F@:=<tH C M � o C JlLm<�>@> q >@?AEKLm< F@:=< o C JhLm<�> > LmJnEKHK?aF@?AJnEK>�M C <t?AH=<�EbF@?ALNMOT MOEKH F@:=< C <t?A>�E=J%H C M � ox?AE ?AEF@:KM}Ff>@F@M}kO< � 9;:=<�` C >DF EKJOF@?ALm< JOc F@:=< o C <�>D<�EKLm<Q?AE p ?AP SxTAM}F@?aJnE%{ JOc F@:=<Q>@<�LmJnEKH �V>DF@M}kO<'H C M � ox?AE?A>yF@:=< P ?ak C M}F@?aJnE JOc F@:=<�JnEx>D<NF JOc >@TA?ao JnE%F@:K< >D<�LmJnEKH C JnT_Ta< C � F@:=< F@:K? C H � � H=J � EK>DF C <�MOP�?AE F@:=<H C M � o C JlLm<�>@> q LNTaJn>D< C FDJ F@:K<4` W < C <ms=?aF � � c C JnP F@:=<�>D<�LmJnEKH C JnTATA< C � F@:K<4c JnS C F@: � � � � $&� ��� � ���

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9:=<4E=J C P MOT�ciJ C Lm<�?_EIMOTATrLNMO>D<�> � ?aF@:I` W < C JnE C JnTATa< C ?A>;kn? � <�E W U v ghSKM}F@?aJnE � > A W � � e<Nc < C@C ?AEKk FDJ

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� :=<�E%F@:K<Q` W < C ?A> P�J � ?AE=k >@TAJ � < C F@:KMOE F@:=< C JnT_Ta< C >@S C c MOLm< q c C ?_LmF@?aJnE%?A> l?AE=<NF@?_L HKS=<�FDJ >@TA?aoMOEKHtMOLNLmJ C HK?AE=k�FDJ F@:K<fMOH=JOoKFD<�Ht> ?aknEtLmJnE � <�EGF@?aJnEIc C ?ALmF@?aJnE ?A> E=<NknM}F@? � < >DJ v gbSxM}F@?aJnE � : { � ?A> Sx>D<�H �� JnP W ?AEK?_E=k F@:K< C <�Ta< � MOEGF <�ghSKM}F@?aJnEx> ciJ C H C M � q ? � < � � M � q � > A � q � : |n{ � q MOExH � : { � o C JhHKSxLm<�>

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Page 132: Vohra - PhD (GaTech, 2006)

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^ E%F@:K?A> >D<�LmF@?aJnE F@:=<Q< <�LmF@>�JOc FD<�P�o.< C M}F@S C < q H C M � oZ?AE :=<�?akn:bF � q MOEKH%`xExMOT C JnTATA< C >Do.<N<�H ��JnE>D<�Ta<�LmFD<�H H C M � TA?AE=< � M C ?AM W Ta<�> c C JnP � <�TAJhLN?aF U q FD<�EK> ?aJnE q MOEKH c C ?ALmF@?aJnE M C <f>DF@SKHK?A<�H �

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Page 133: Vohra - PhD (GaTech, 2006)

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SKEKTAJnMOHK>QJnE F@:K< >D<�LmJnExH C JnTATa< C � ?aF@: F@:=< ` W < C FD<�Ex>@?aJnE H C JOoKoZ?AE=k%c C JnP � � ~�� =@= ~}|]HKUhE FDJ� � = M�� L@L}|fH=UhE�MOEKH�F@:K< LmJ C C <�>Do.JnEKHK?AEKk;>Do.<N<�H�H C JOox>dc C JnP � A �}~yLNP�> � FDJ � A � > LNP�>� � �9:=< � MOTAS=<yJOc�c C ?ALmF@?AJnE'Lz:KMOE=kO<�>;c C JnP ��� � : |n~ > ��H=UlE LNP

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F@:=< FD<�P�o.< C M}F@S C <-k C MOHK?a<�EbF�?AE4F@:=< c C <N<�>@oxMOE�F@:=< ` W < C c S C F@:=< C SKEKTaJnMOHK>rFDJ � � A | = : > | H=UlE W <Nc J C <TaJnMOHK?_E=k S=oQM}knMO?AE�FDJ�� � = M@LO~@M}|4H=UlE�F@:K?A>�?A> W <�LNMOSK>@<F@:=< FD<�P�o.< C M}F@S C <k C MOHK?a<�EbF�L :xMOE=kO<�>"> ?aknEK> �;yE F@:=<tH C M � ox?_E F@:=< ` W < C FD<�EK>@?AJnE ?AEKL C <�MO>D<�> � �"L > L >@= | H=UlE �%^ E F@:=< C <�P MO?_EK?AE=k c C <N<�>@oxMOEc JnTATaJ � ?AE=k F@:=<tH C M � ox?AE F@:=< ` W < C SKEKTAJnMOHK>�M}knMO?AE q F@:K?A>�F@?AP�< FDJ%M � MOTAS=< JOc � � � : | � = : H=UlE qF@:=<tc C ?ALmF@?AJnEKMOT ciJ C Lm< C <�>Do.JnEK> ? W Ta<'ciJ C F@:K?A> >@:KJ � > MOE ?AEKL C <�MO>@<tc C JnP � � > ��� | � H=UhE]LNP � FDJ� � = {@L}|O| H=UlE LNP � � 9:K<'` W < C TA<�M � <�> F@:K< H C M � oZ?AE MOEKH P MO?AEbF@MO?AEK>�F@:=<t> MOP�<t>Do.<N<�H MOEKHFD<�EK>@?AJnE c J C F@:=< C <�>DFyJOc"F@:=<�FDJ � SKEbF@?ATdF@:=<�o.Jn?AEbF�JOc"<msl?aFyc C JnP F@:=<�F@:K? C H C JnT_Ta< C � � JOFD<�F@:KM}F F@:=<SKEKTAJnMOHK?AE=k MO>4>@:=J � E%?AE F@:=< � � � � � > � � � � ?AE = : ?AEKHK?ALNM}FD<�>fMt>DF C MO?akn:bFD<�EK?AEKktJOc F@:=<QSKExTaJnMOHK?AE=kLNS C � < q F@:K?_>�?A> W <�LNMOSK>D<4F@:=<4oxTaJOFy>@:=J � >;F@:K<�> ?AH=< � ?a< � JOc�F@:K<4o C JOk C <�>@>�JOc5F@:=<�H C M � o.Jn?AEbF;JnE F@:=<

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Page 134: Vohra - PhD (GaTech, 2006)

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Page 138: Vohra - PhD (GaTech, 2006)

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Page 139: Vohra - PhD (GaTech, 2006)

FD<�EK>@?AJnE�� � � � q � <�TaJhLN?AFVU� � � � MOEKH FD<�P o7< C M}F@S C < � � � �->@S C c MOLm< �9:K< FD<�P�o.< C M}F@S C < o C JO`xTa< ciJ C M $&� �!� � � ��$ � � � � "���� ���1?_>�>@:KJ � E ?AE Rd?AknS C < = { q F@:=< C JnTATa< C FD<�P �

o.< C M}F@S C < ?_> P MO?AEbF@MO?AE=<�H M}F = : > � � :K?ATa< C <�>DF;JOcrF@:=< H C M � TA?AE=<y?A> O<NoKF;M}F1{@M > � � � ?aF@: M $&� �!� � ���$ ��� �� "���� ��� F@:=< FD<�EK>@?aJnE o C JO`xTA< ?A>f?AHK<�EGF@?ALNMOT�FDJ F@:=<'?A>DJOF@:=< C P MOT�LNMO>D< C ?akn:bFfS=o FDJIF@:=< o7Jn?_EGF JOcM}FDF@MOL :xP�<�EGFyFDJ'F@:=<fF@:x? C H C JnTATA< C � ;yEtF@:=< F@:K? C H C JnTATa< C�q HxS=< FDJ :=<�M}F@?AE=k q F@:=<f` W < C FD<�Ex>@?aJnEIH C JOox>c C JnP � �0L > L >@= { H=UhE FDJ�� � = LO~ : L@M H=UhE � p ?AEKLm<QF@:=< ` W < C ?A>f:K<�M}F@>4SKo J � < C > P MOTAT C <Nkn?aJnEH=J � EK>DF C <�MOP c C JnP F@:K<fo.Jn?AEbFJOc�M}FDF@MOL :KP <�EGFyFDJ'F@:=< C JnT_Ta< C MQF@:=< C P MOTrk C MOHK?a<�EbF;<ms=?aF@> � 9;:=<fc C ?AL �F@?aJnEKMOTrc J C Lm< F@:hSK>�kO<�E=< C M}FD<�H FDJ >@M}F@?A>Dc U <�gbSx?ATA? W C ?ASKP ?AEKL C <�MO>@<�>;c C JnP � � � : { : > L'H=UlEILNP

� M}FF@:=< o.Jn?AEbF JOcdM}FDF@MOLz:KP�<�EbF�FDJQF@:=< F@:K? C H C JnTATa< C FDJ��N< C J'M}FF@:=< <�EKHtJOcdF@:K< LmJbJnTAHKJ � E��NJnEK< �9:K<1LmJnP W ?AEKM}F@?AJnEQJOcrF@:=<1T_MO>DF"F � J�FD<�P o7< C M}F@S C <1o C JO`xTa<�>"kn? � <�> M $&� � � � � � � � ���#&�!� ��� ��$&� �!� � �

��$ ��� � � "���� ��� q > :=J � E ?_E Ru?aknS C < = � � � ?AF@: M $ � �!� � � � � � �� #&��� ��� � $&� �!� � � � "�� � ���1F@:=< C <�>@o7JnEx>D< JOcF@:=<'` W < C ?A>4>@:=J � E ?AE Ru?aknS C <�> = LIFDJ%~ : � :x?AL : ?A> M TA?AEK<�M C LmJnP W ?AEKM}F@?aJnE JOcF@:=< o C < � ?aJnSK> F � Jo C JO`ZTa<�> �^ E Rd?AknS C < ~O{4?A>-F@:=<yFD<�P�o.< C M}F@S C <yo C JO`ZTa<�c J C M $&� � � � � ��� ����# ��� M}F = : > � F@:=<y` W < C :=<�M}F@> S=o

TA?AEK<�M C TaU�c C JnP){@M >�� FDJ = : > � MO> ?aF >@TA?AH=<�>5JnE'F@:=<1H C M � oZ?AEQMOEKH F@:=<�E'M}ciFD< C <ms=?aF@?AEKkfF@:=<yH C M � ox?AE?aF�LmJhJnTA> H=J � E FDJ {@M > � ?AE F@:=< c C <N<�>DoZMOE � � :=<�E M $&� �!� � � ��� ����# ��� ?A>�SK>D<�H q ` W < C�C <�>Do.JnEKHK>MO> >@:KJ � E ?_E Rd?AknS C <�> ~ > FDJ ~O~ q F@:=<t` W < C FD<�EK> ?aJnE H C JOox>�PQM C kn?AEKMOTATAU%c C JnP � ��~�� =@= ~ A H=UlEFDJ � � ~O~ = ~O~��IH=UlE JnE F@:=< >D<�LmJnEKH C JnTATa< C � J � < � < C JnE M}FDF@MOLz:K?AE=ktFDJIF@:=< H C M � ox?AE F@:=<�` W < CSKEKTAJnMOHK>*c C JnP � � ~O~ = ~O~��1H=UlEfFDJ � � A � = | : |fH=UhE MOEKH F@:=<�E TAJnMOHK> W MOL fSKofFDJ � � = ~@L@L A | H=UlEMOEKH F@:=<�E <msl?aF@>"F@:=<yH C M � ox?AE q E=JOFD<�F@:K<�F@:KM}F-F@:=<1` W < C TaJnMOHx>"S=o JnEQF@:K<1H C M � ox?_E LNMOE W < W <�LNMOSK>D<F@:=<'>DF@? E=<�>@> F C MOEx>@?aF@?aJnEK>f?AEGFDJIF@:=< `xEKMOT5>DF@? oxM C Ff?_E F@:=< LmJnEx>DF@?aF@S=F@? � <Q<�gbSKM}F@?AJnE � 8�>fF@:=< ` W < CLmJhJnTA>?AE F@:K< C <�P MO?AEx?AE=k4oxM C FJOcdF@:=< c C <N<�>DoxMOE q HKS=< FDJ F@:K< FD<�P�o.< C M}F@S C < k C MOHK?a<�EbF q ?aFTaJnMOHK> W MOL S=o FDJ%M `xEKMOT � MOTAS=< JOc � �"L > L >@= | H=UlE W <NciJ C < M}FDF@MOLz:K?AE=k%FDJ F@:K<'`ZEKMOT C JnTATa< C � 9:=<'c C ?ALmF@?aJnEc J C Lm<QJnE F@:=<Q` W < C � :=<�E ?aF@> JnE F@:=< H C M � ox?AE ` C >DFfH=<�L C <�MO>@<�>fc C JnP � � {}| M = |O| HKUhE%LNP � FDJ: A M = ~O~ H=UhE LNP� � HxS=<yFDJ F@:=< FD<�P�o.< C M}F@S C < k C MOHK?a<�EbFMOEKH F@:=<�E ?_EKL C <�MO>D<�> FDJ : � M :@: ~QH=UlE LNP �

FDJ PQMO?AEGF@MO?_E <�gbSx?ATA? W C ?ASKP � ?aF@: F@:=<Q?_EKL C <�MO>D<�H ` W < C >DF@? E=<�>@> MO>fF@:=< ` W < C F C MOEK>@?aF@?aJnEx> ?AEbFDJtF@:=<`xEKMOTZ>DF@? o.J C F@?aJnE JOc*F@:=<�LmJnEx>DF@?aF@S=F@? � <1LNS C � < � 9:K<;FD<�EK>@?AJnE H C JOox>5MO>"F@:=< � <�TaJhLN?AFVU ?AEKL C <�MO>D<�> q F@:K?A>?A> HxS=<�FDJtF@:=<Q?_EKL C <�MO>@?AEKk FD<�P�o.< C M}F@S C < MOTaJnEKktF@:=<QH C M � TA?_E=< � 9:=< >@SxHKH=<�E HK?ao%>@<N<�E ?AE FD<�Ex>@?aJnEMO>�F@:=< � <�TaJlLN?aF U ?AEKL C <�MO>D<�>�?A>�HKS=<'FDJ F@:=< L :KMOEKkO< JOc1>DF@? E=<�> > JOc�F@:=< ` W < C � 9:=< FD<�EK> ?aJnE F@:=<�E

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Page 140: Vohra - PhD (GaTech, 2006)

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Page 141: Vohra - PhD (GaTech, 2006)

��������� � � � Ru? W < C FD<�EK>@?aJnE � � � � � < C >@SK>M C LNTA<�E=kOF@: � HKS=< FDJQM�:=<�M}FD<�HIc C <N<�>DoxMOE W <NF � <N<�EI>@<�LmJnEKHC JnTATA< C MOEKHtH C M � ox?AE �

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Page 142: Vohra - PhD (GaTech, 2006)

��������� � � � R C ?ALmF@?aJnEIciJ C Lm< � � � � � < C >@SK>M C LNTA<�E=kOF@: � HKS=< FDJ MQ:=<�M}FD<�HIc C <N<�>@oxMOE W <NF � <N<�E >@<�LmJnEKHC JnTATA< C MOEKHtH C M � ox?AE �

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Page 143: Vohra - PhD (GaTech, 2006)

��������� � � Ru? W < C FD<�EK>@?aJnE � � � � � < C >@SK> � <�TaJhLN?AFVU � � ��HxS=<FDJ Mf:=<�M}FD<�HQc C <N<�>DoZMOE W <NF � <N<�E >@<�LmJnEKHC JnTATA< C MOEKHtH C M � ox?AE �

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Page 144: Vohra - PhD (GaTech, 2006)

# � � � ��� � J � 9:K< FD<�P�o.< C M}F@S C < o C JO`xTa<yJOcuF@:=< H C M � TA?AE=< � ?AF@: M :=<�M}FD<�Ht`ZEKMOT.F@M O<�S=o C JnTATa< C �

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Page 145: Vohra - PhD (GaTech, 2006)

# � � � ��� �KX � Ru? W < C � <�TaJlLN?aFVU� � � � � < C > SK>M C LNTa<�EKkOF@: � HKS=<yFDJ F@:=<f:K<�M}FD<�HtF@:K? C H C JnTATa< C �

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Page 146: Vohra - PhD (GaTech, 2006)

# � ������� ����� Rd? W < C FD<�Ex>@?aJnE�� � � � � < C >@Sx>M C LNTa<�E=kOF@: � HKSK<1FDJ F@:=< :=<�M}FD<�HIF@:K? C H C JnT_Ta< C �

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Page 147: Vohra - PhD (GaTech, 2006)

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Page 148: Vohra - PhD (GaTech, 2006)

# � � � � � ����� Ru? W < C FD<�EK>@?aJnE � � � � � < C >@SK> � <�TaJlLN?aF U� � � � HKS=< FDJ F@:=< :K<�M}FD<�HtF@:K? C H C JnTATa< C �

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Page 149: Vohra - PhD (GaTech, 2006)

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Page 150: Vohra - PhD (GaTech, 2006)

��������� � � � Ru? W < C � <�TaJlLN?aFVU� � � � � < C >@SK> M C LNTA<�E=kOF@: � c J C Mt:=<�M}FD<�H c C <N<�>DoxMOE MOExH%:=<�M}FD<�H F@:K? C HC JnTATA< C �

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Page 151: Vohra - PhD (GaTech, 2006)

��������� � � � Ru? W < C FD<�EK>@?AJnE�� � � � � < C >@Sx> M C LNTa<�E=kOF@: � ciJ C MI:=<�M}FD<�H c C <N<�>DoxMOE%MOEKH :=<�M}FD<�H F@:K? C HC JnTATA< C �

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Page 152: Vohra - PhD (GaTech, 2006)

��������� � � � R C ?ALmF@?aJnE ciJ C Lm< � � � � � < C >@SK>4M C LNTa<�EKkOF@: � c J C MI:K<�M}FD<�H c C <N<�>DoZMOE MOEKH :=<�M}FD<�H F@:K? C HC JnTATA< C �

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Page 153: Vohra - PhD (GaTech, 2006)

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Page 154: Vohra - PhD (GaTech, 2006)

��������� � � � 9:K< FD<�P�o.< C M}F@S C < o C JO`ZTa< JOcxF@:=<H C M � TA?_E=< � ?aF@:�M :=<�M}FD<�H H C M � ox?_E4M}F�MyFD<�P o7< C M}F@S C <JOc = : > � �

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Page 155: Vohra - PhD (GaTech, 2006)

?AEKL C <�MO>D<�>MO>F@:K< ` W < C LmJbJnTA>;?AE F@:=< c C <N<�>DoxMOE �p :KJ � E FDJOkO<NF@:K< C ?_E Ru?aknS C <I~��%M C < MOTATF@:=<tFD<�EK>@?AJnE o C JO`ZTa<�>�J W F@MO?AE=<�H]<�M C TA?a< C � 9:=< C <IM C <

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Page 157: Vohra - PhD (GaTech, 2006)

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Page 158: Vohra - PhD (GaTech, 2006)

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Page 159: Vohra - PhD (GaTech, 2006)

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Page 160: Vohra - PhD (GaTech, 2006)

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Page 161: Vohra - PhD (GaTech, 2006)

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Page 162: Vohra - PhD (GaTech, 2006)

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` W < C TaJnMOHK>�S=o JnE F@:=< >D<�LmJnEKH C JnTATA< C c C JnP � � ~�� =@= ~}|%H=UlE FDJ � � � M@M > {}| H=UhE LmJnP�oZM C <�HFDJ F@:=<tLNMO>D< � :=< C < F@:=<tH C M � ox?_E ?_>�M}F � � > |%LNP ?AE � :K?_L : LNMO>D<tF@:=< ` W < C SKExTaJnMOHK> � p J W UTaJ � < C ?_E=k F@:=<�H C M � ox?AE SKEKTaJnMOHK?_E=k LNMOE W <�?AEKHKSxLm<�HIJnE F@:=< >@<�LmJnEKH C JnTATa< C MOEKH W U C MO?_>@?AE=k ?aFyF@:=<MOP�JnSKEbF;SKExTaJnMOHK?AE=k C <�HxSKLm<�>MOEKH C < � < C >D<�>FDJ'TaJnMOHK?AEKk W <NUOJnEKHIM L C ?aF@?ALNMOT�:=<�?akn:bF JOcdF@:K<fH C M � ox?AE �e<�P <�P W < C F@:KM}F;JnE F@:=<fH C M � ox?_E'?AF@>D<�Tac�F@:K< ` W < C MOT � M�Ul>;TaJnMOHK> SKo �9:K< C <�>Do.JnEK>D< c C JnP SK>@?AE=k M $&� �!� � � �� � "�� � � � � � �# ��� ?A> >@:=J � E ?AE]Rd?AknS C < � | q � :K<�E F@:=<

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� ?aF@:4M $&� �!� � � ��$ ��� � � "���� ��� q F@:=< C <�>Do.JnEK>@<"?A>r>@:=J � E ?AE4Ru?aknS C < � : q F@:=<-FD<�EK>@?aJnE o C JO`xTA<5P M}F@L :K<�>F@:=<;?_>DJOF@:=< C P MOTKo C JO`xTa< FDJ F@:=<o.Jn?AEbF�JOc.M}FDF@MOLz:KP�<�EbF"FDJ F@:=<F@:K? C H C JnTATa< C q M}F � :K?_L :�o.Jn?AEbFuF@:=<` W < C?A>1>@S W �D<�LmFD<�H FDJ MQF@:=< C P MOTdk C MOHK?a<�EbF1HxS=<fFDJ M >@:=J C Fy:=<�M}FyS=o �NJnE=< � > {@M LNP FDJ >@> { LNP � � :K?_L :F@M O<�>dF@:=<-` W < C FD<�P�o.< C M}F@S C <"FDJ = : > � � j1SK<5FDJ;F@:K<-:K?Akn: FD<�P�o.< C M}F@S C <"k C MOHK?a<�EbF�F@:K<5` W < C SKExTaJnMOHK>FDJQM�FD<�EK> ?aJnE JOc � � = LO~ : M}|'H=UhE MOExH >DF@M�Ul>;M}FF@:x?A> � MOT_S=<�H SKEbF@?AT.?aF <msl?AF@> c C JnP F@:=< F@:K? C H C JnTATa< C �� JnP�oZM C <�H FDJ F@:=< LNMO>D< JOc � � > |ILNP F@:=<�FD<�EK>@?aJnE ` C >DF H C JOox>1JnE F@:K<�>@<�LmJnEKH C JnTATA< C MOExH F@:=<�ELmJnEbF@?AEbSKJn>@TaUt?AEKL C <�MO>D<�>;FDJ'F@:=< `xEKMOT � MOTAS=< JnEIF@:K< H C M � ox?AE W <NciJ C < H C JOoKox?_E=k H=J � EIJnE F@:=<4F@:K? C HC JnTATA< C �9:K<4c JnS C F@: LNMO>D< q >@:=J � E ?AE Rd?AknS C < �}{ q ?A> � ?aF@: M $&� �!� � � � � � ���# ��� ��� � $&� �!� � � ��$ � � � � "���� ��� �

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Page 163: Vohra - PhD (GaTech, 2006)

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Page 164: Vohra - PhD (GaTech, 2006)

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Page 165: Vohra - PhD (GaTech, 2006)

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Page 166: Vohra - PhD (GaTech, 2006)

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Page 167: Vohra - PhD (GaTech, 2006)

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Page 168: Vohra - PhD (GaTech, 2006)

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Page 169: Vohra - PhD (GaTech, 2006)

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Page 170: Vohra - PhD (GaTech, 2006)

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Page 171: Vohra - PhD (GaTech, 2006)

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Page 172: Vohra - PhD (GaTech, 2006)

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Page 173: Vohra - PhD (GaTech, 2006)

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Page 174: Vohra - PhD (GaTech, 2006)

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Page 191: Vohra - PhD (GaTech, 2006)

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Page 193: Vohra - PhD (GaTech, 2006)

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Page 194: Vohra - PhD (GaTech, 2006)

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Page 195: Vohra - PhD (GaTech, 2006)

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Page 208: Vohra - PhD (GaTech, 2006)

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Page 209: Vohra - PhD (GaTech, 2006)

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Page 210: Vohra - PhD (GaTech, 2006)

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