Institute of Computer Science

8/14/2019 Institute of Computer Science

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Institute of Computer ScienceAcademy of Sciences of the Czech Republic

Fuzzy Class Theory: A Primer v1.0Libor Behounek and Petr Cintula1

Technical report No. 939

December 2006

Abstract:

Fuzzy Class Theory was proposed as a formal background of an axiomatic approach to fuzzy mathematics

built inside a sufficiently strong formal fuzzy logic. The goal of this text is to provide a thorough introduction

to this theory for non-specialists in formal fuzzy logic. First, we give an informal exposition of the apparatus

of the theory and explain how its results can be interpreted from the point of view of traditional fuzzy

mathematics. Secondly, we address notable features of this theory, starting with the importance of graded

theories, continuing through natural embedding and then fuzzifying of classical mathematical theories,

ending with basic methodological guidelines regarding the latter. Finally, we show how to prove the results

in Fuzzy Class Theory, by employing not only proof methods for particular first-order logic but also new

strong methods which heavily utilize the advantages of formal build-up of the Fuzzy Class Theory.

This is version 1.0 of the Primer. A newer version may be downloadable from www.cs.cas.cz/hp.

Keywords:

Fuzzy Class Theory, graded properties, proof methods

1Institute of Computer Science, Academy of Sciences of the Czech Republic, P. O. Box 5, 182 07 Prague 8, Czech

Republic, {behounek,cintula}@cs.cas.cz. The work of Libor Behounek was supported by the grant No. B100300502of the Grant Agency of the Academy of Sciences of the Czech Republic. The work of Petr Cintula was partly supported

by the grant No. B100300502 of the Grant Agency of the Academy of Sciences of the Czech Republic and partly by by

the Institutional Research Plan AV0Z10300504.


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2

Institute of Computer Science

Academy of Sciences of the Czech Republic

Correlation Dimension-Based Classifier

Marcel Jiina and Marcel Jiina, jr.

Technical Report No. V-945

January 2006

Abstract

An innovative approach that utilizes the correlation dimension (CD) both for probability density estimateof data and consequently for classification is suggested. The idea of correlation dimension classifierdirectly follows the principle of classifier, which uses the distribution mapping exponent (DME). Thebasic difference between these two approaches is that DME is a local feature while CD is globalfeature. A new "hyperbolic" approximation of the correlation integral for the correlation dimensionestimation is suggested. It is shown that CD-based classifier outperforms DME classifier and manyother classifiers published on Machine Learning Repository pages.

Keywords:

Multivariate data; Correlation dimension; Nearest neighbors; Distribution mapping exponent; Powerapproximation, Classification, ML Repository.

Pod Vodrenskou v 2, 182 07 Prague 8, phone: +420 266 051 111, fax: +420 286 585 789

e-mail: [email protected]


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European Summer School inInformation Retrieval ESSIR 2005

Zdenka Linkova1


February 2006

Abstract:

Information Retrieval (IR) as a process of searching relevant information is a significant discipline of a dataprocessing field. European Summer School in Information Retrieval ESSIR provides students, academicand industrial researchers and developers a grounding in the core objects of IR (models, architectures,algorithms), as well as covering some current topics, e.g. information retrieval from the Web. We haveparticipated its 5th year that was held at Dublin City University in Dublin, Ireland.

Keywords:Summer school, Information Retrieval.

1Institute of Computer Science, Academy of Sciences of the Czech Republic,182 07 Prague 8, Czech Republic


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Reasoning about Bang3multi-agent systems in KR-Hyper

Gerd Beuster, Roman Neruda, Bjorn Pelzer


January 2006

Abstract:

Bang3 is a Multi-Agent-System platform focusing on soft computing. KR-Hyper is an automatic

theorem proofer for First Order Logic. In this paper, we describe how KR-HYPER can be connected to

Bang3 in order to allow reasoning about Multi-Agent-Systems.

Keywords:

MAS, Bang, KR-HYPER, Logic, Deduction, Description Logics, First Order Logic, Agents


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Navrh totaln nahrady kolennhokloubu s rotacn polyetylenovouvlozkou

Jir Stehlk, Jir Nedoma


May 2006

Abstrakt:

In the paper the analyses of effect of axial changes on the weight-bearing total knee replacenets (TKRs)in frontal and sagital planes are shortly discussed. On the basis of obtained numerical results two rotarytypes of TKRs are presented and discussed.

Keywords:Total knee replacement (TKR), axial changes, rotary TKR.


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Biomechanical analysis of the effectof axial angle changes on the

weight-bearing total kneereplacements

J. Stehlk1, P. Vavrk2, J. Danek3, J. Nedoma4,

I. Hlavacek5, F. Denk6


May 2006

Abstrakt:

The aim of this paper is to compare of the biomechanical influences of different grades of valgus deformityafter the total knee replacement (TKR) based on the contact model problem with friction, the finite elementmethod and the nonoverlapping domain decomposition method.

Keywords:Biomechanics, knee, total replacement, valgus deformity

1Orthopaedic Department, The Hospital Ceske Budejovice, B. Nemcova Str. 585/54, 370 01 Ceske Budejovice, CzechRepublic, e-mail: [email protected]

21st Ortopaedical Department, 1st Medical Faculty of the Charles University Prague, V uvalu 84, 150 00 Prague 5- Motol, Czech Republic, e-mail: [email protected]

3Centre of Applied Mathematics, University of West Bohemia, Univerzitn 8, 306 14 Pilsen, Czech Republic andInstitute of Computer Science, Academy of Sciences of the Czech Republic, Pod vod arenskou vez 2, 182 07 Prague 8,Czech Republic e-mail: [email protected]

4Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vod arenskou vez 2, 182 07 Prague 8,Czech Republic, e-mail: [email protected]

5Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vod arenskou vez 2, 182 07 Prague 8,Czech Republic and Mathematical Institute, Academy of Sciences of the Czech Republic, Zitna 25, 115 67 Prague 1,Czech Republic, e-mail: [email protected]

6WALTER a.s., Jinonicka 329, 158 01 Prague 5 - Jinonice, Czech Republic, e-mail: [email protected]


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Analysis of axial angle changes onthe weight-bearing total kneereplacements

J. Stehlk1, P. Vavrk2, J. Danek3, J. Nedoma4,

I. Hlavacek5, F. Denk6


May 2006

Abstrakt:

Background. The analysis of the effect of axial angle changes on the weight-bearing total knee replacements(TKR) was investigated and discussed.

Methods. A two dimensional finite element models of the femorotibial joint in the frontal and the sagitalplanes were developed from CT images. For computation the nonoverlapping finite element techniquedevelped in our institute was used.Results. The effect of axial angle changes on the weight-bearing total knee replacements is analysedin frontal and sagital planes. It is shown that optimal distribution of forces operated on the TKR inanteroposterior direction and well-balanced transition of forces in anteroposterior direction will correspondto the 7 deg. case. The results show a good agreement between theoretical and orthopadic observations.

Keywords:Biomechanics, Knee, Total replacement, Axial changes

1Orthopaedic Department, The Hospital Ceske Budejovice, B. Nemcova Str. 585/54, 370 01 Ceske Budejovice, CzechRepublic, e-mail: [email protected]

21st Ortopaedical Department, 1st Medical Faculty of the Charles University Prague, V uvalu 84, 150 00 Prague 5- Motol, Czech Republic, e-mail: [email protected]

3Centre of Applied Mathematics, University of West Bohemia, Univerzitn 8, 306 14 Pilsen, Czech Republic andInstitute of Computer Science, Academy of Sciences of the Czech Republic, Pod vod arenskou vez 2, 182 07 Prague 8,Czech Republic e-mail: [email protected]

4Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vod arenskou vez 2, 182 07 Prague 8,Czech Republic, e-mail: [email protected]

5Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vod arenskou vez 2, 182 07 Prague 8,Czech Republic and Mathematical Institute, Academy of Sciences of the Czech Republic, Zitna 25, 115 67 Prague 1,Czech Republic, e-mail: [email protected]

6WALTER a.s., Jinonicka 329, 158 01 Prague 5 - Jinonice, Czech Republic, e-mail: [email protected]


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Boolean factor analysis byHopfield-like autoassociativememory 1

A. A. Frolov2

and D. Husek3

and I. P. Muraviev4

and P.A. Polyakov5


February 2006

Abstract:

The feature space transformation is a widely used method for data compression. Due to this transfor-mation the original patterns are mapped into the space of features or factors of reduced dimensionality.In this paper we demonstrate that Hebbian learning in Hopfield-like neural network is a natural procedure

for Boolean factor analysis. Due to this learning, neurons that tend to fire together (represent one com-mon factor) are more correlated and thus create an attractor of the network dynamics. If the attractionbasins around factors are large enough, the factors could be revealed by random search. This paper isdedicated to estimation of the size of attraction basins around factors. Two global spurious attractors areshown to prevent convergence of the network activity to the factors invalidating any procedure of theirsearch. These global attractors can be completely deleted from network dynamics by introducing a singleinhibitory neuron with bi-directional Hebbian synapses. Due to additional inhibition, the size of attractionbasins around factors becomes the same as around the stored patterns in usual Hopfield network. Theprocedure of factors search is described in the accompanying paper.

Keywords:

Boolean factor analysis, Hopfield neural network, unsupervised learning

1The work was partly supported by the Institutional Research Plan AV0Z10300504 Computer Science for theInformation Society: Models, Algorithms, Appplications and by grant Intelligent methods for increasing of reliabilityof electrical networks 1ET100300414 granted by GA AS CR

2Institute of Higher Nervous Activity and Neurophysiology of the Russian Academy of Sciences, Butlerova 5a, 117 485Moscow, Russia; e-mail: [email protected]

3Institute of Computer Science Academy of Science of the Czech Republic, Pod Vodarenskou vez 2, 182 07 Prague 8,Czech Republic; tel. (+420)26605 3230, Fax: (+420) 28658 5789, e-mail: [email protected]

4Institute of Higher Nervous Activity and Neurophysiology of the Russian Academy of Sciences, Butlerova 5a, 117 485Moscow, Russia;e-mail: [email protected]

5Institute of Optical Neural Technologies of the Russian Academy of Sciences, Vavilova 44, 119 333 Moscow, Russia;

e-mail: [email protected]


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Boolean factor analysis byHopfield-like autoassociativememory: factors search1

A. A. Frolov2, D. Husek3, P. Y. Polyakov4, I. P. Muraviev5


February 2006

Abstract:

In our previous paper [6] we have shown that Hebbian learning in Hopfield-like neural network is anatural procedure for Boolean factor analysis. Hebbian learning forms a connection matrix of the networkas a co-variation matrix of input signal space. Neurons that represent one common factor are morecorrelated and thus create attractor of the network dynamics. In this paper we describe a procedure offactors retrieval. According to this procedure, network dynamics evolve forward starting from a randominitial state and stabilize in the attractor which corresponds to one of the factors (a true attractor) orone of the spurious attractors. Separation of true and spurious attractors is based on calculation of theirLyapunov function and activation threshold. We studied efficiency of the retrieval procedure by computersimulation.

Keywords:Boolean factor analysis, Hopfield neural network, unsupervised learning, recall procedure, data mining.

1This work was supported by grant from Grant Agency of Czech Republic, Prague No.201/05/0079 and by grant1ET100300414 of the research program Information Society granted by GA AS CR.

2Institute of Higher Nervous Activity and Neurophysiology of the Russian Academy of Sciences; e-mail:[email protected]

3Institute of Computer Science Academy of Science of the Czech Republice; E-mail: [email protected] of Optical Neural Technologies of the Russian Academy of Sciences; e-mail: [email protected] of Higher Nervous Activity and Neurophysiology of the Russian Academy of Sciences; E-mail: mu-

[email protected]


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Johnson score and characteristics ofdistributions 1

Zdenek Fabian


February 2006

Abstract:

New measures of central tendency and dispersion of continuous probability distributions are introduced.

They exist for common distributions and their estimates have necessary statistical properties. Their meaning

is explained by means of instructive examples.

Keywords:

basic characteristics, variance, Johnson transform

1The work was supported by Grant Agency AS CR under grant IAA1075403.


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The minC Combination of BeliefFunctions: derivation andformulas.1

Milan Daniel2


June 2006

Abstract:

Principal ideas of the minC combination are recalled. A mathematical structure of generalized frames of

discernment is analysed and formalized. A generalized schema for a computation of the minC combination

is presented. Conflicting belief masses redistribution among non-conflicting focal elements is overviewed.

Final general formulas for computation of the minC combination are presented.

Some examples of computation of the minC combination follow. A brief comparison of the minC

combination with other combination rules is presented. Related works and approaches and some open

problems for a future research are referred in the end.

Keywords:

Belief function, Combination of belief functions, Dempster-Shafer theory, Conflict, Potential conflict,

Contradiction, minC combination.

1The support of the grant 1ET100300419 GA AV CR is kindly announced.

The work was partly supported by the Institutional Research Plan AV0Z10300504 Computer Science for the Information

Society: Mo dels, Algorithms, Applications.

[email protected]


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Primarne dualn metoda aktivnchmnozin pro jednostranny kontaktpruznych teles s danym trenm

I.Hlavacek


March 2006

Abstrakt:

Uvazujeme jednostranny kontakt dvou pruznych rovinnych nebo prostorovych teles. Smsena variacn for-mulace vede na problem sedloveho bodu, ktery diskretizujeme metodou konecnych prvku. K nalezen sed-loveho b odu aplikujeme novou metodu tzv. primarne dualn strategie aktivnch mnozin (PDAS), ktera seda ztotoznit se zobecnenou Newtonovou iteracn metodou.

V 1. kapitole je analyzovano resen koercivnch i semi-koercivnch uloh bez tren. 2. resp. 3. kapitolaje venovana kontaktu s danym trenm podle Trescova modelu ve 2D-, resp. 3D-formulaci. K nalezenprslusneho sedloveho bodu je navrzen iteracn algoritmus, ktery kombinuje projekce z metody Uzawovys metodou PDAS v kazdem iteracnm kroku.

Keywords:Jednostranny kontakt, dane tren, metoda konecnych prvku, sedlovy bod, zobecnena Newtonova metoda


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HUGO: A Cognitive Architecture

with an Incorporated World Model1

Jir Wiedermann


April 2006

Abstract:

We present a design of cognitive system architecture with an internal world model. The internal world

model is realized with the help of artificial mirror neurons. We consider generalized artificial mirror neurons

acting both as a mechanism for assembling and learning multimodal sensorimotor information and as as-

sociative memory for invoking multimodal information given only some of its components. We show that

within an artificial cognitive system a network of generalized mirror neurons can simultaneously serve as

an internal world model recognized by the agent and as that of the agents position within this world. We

also specify a self-organizing control mechanism, which is based on the basic operations over concepts that

were essentially identified by the British 18th century philosopher David Hume. This control mechanism

makes use of the internal world model constructed in agents interaction with real world and straightfor-

wardly supports imitation learning. Building heavily on the properties of the generalized mirror net and

on automatic abstract concept creation, we offer an algorithmic explanation of computational language

acquisition, thinking and consciousness in our model. Rather than describing an implementation of the

respective mechanisms, the aim of the paper is to establish a proof of the principle of algorithmic nature

of higher cognitive functions.

Keywords:

cognitive systems; embodied cognition; internal world model; mirror neurons; thinking; consciousness

1This work was done within the Institutional Research Plan AV0Z10300504 and was partially supported by grant

No. 1ET100300419


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Chtli byste bt mozkem v bace?

Ji Wiedermann1


duben 2006

Abstrakt:

Modern teorie kognitivnch systm pohl na tyto systmy jako na autonomn vtlen vpoetn systmy,kter se situuj v okol prostednictvm svch senzomotorickch jednotek. Pesto zejmna v kruzch po-

taovch teoretik je opakovan slyet nzory, e na kognici lze pod mon pohlet i klasicky, jako

na problm specifickho zpracovn dat a e tud vtlen nen nezbytn pro zachycen podstaty kognice.

Ukeme, e takto zjednoduen pohled opomj podstatnou vlastnost kognitivnch systm - a sice jejich

aktivn vliv na vbr i dokonce vznik vstupnch dat. Bez tto zptn vazby si systm neme vytvoit svj

vnitn model svta poznan prostednictvm svch akc. Pro vysvtlen povahy zmnnho problmu poui-

jeme vpoetn model kognitivnch systm zaveden autorem v pedchozch pracch. Tento model umon

na principieln rovni pemlet o fungovn algoritmickch mechanizm imitace, komunikace, vzniku ei,

mylen a vdom a tm pispt i k jejich pochopen v ivch systmech.

Keywords:

kognitivn systmy; vtlenost; situovanost; vnitn model svta

1Tato prce vznikla v rmci vzkumnho zmru AV0Z10300504 s stenou podporou grantu 1ET100300419


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Integral combinations ofHeavisides1

Paul C. Kainen2, Vera Kurkova3, Andrew Vogt4


May 2006

Abstract:

A sufficiently smooth function ofd variables that decays fast enough at infinity can be represented pointwiseby an integral combination of Heaviside plane waves (i.e., characteristic functions of closed half-spaces).The weight function in such a representation depends on the derivatives of the represented function. Therepresentation is proved here by elementary techniques with separate arguments for even and odd d, andunifies and extends various results in the literature.

Keywords:Feedforward neural network, perceptron, Heaviside function, plane wave, integral formula, Radontransform, Greens function for iterated Laplacians, order of vanishing, function of controlled decay.

1V. K. was partially supported by GA CR grant number 201/05/0557 and the Institutional Research PlanAV0Z10300504. Collaboration of the three authors was also supported by NAS COBASE grants and the GeorgetownUniversity International Affairs Office.

2Department of Mathematics, Georgetown University, Washington, D.C. 20057-12333Institute of Computer Science, Acad. of Sci. of the Czech Republic, P.O. Box 5, 182 07 Prague 8, Czech Republic4Department of Mathematics, Georgetown University, Washington, D.C. 20057-1233


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Johnson system of parametricfamilies1

Zdenek Fabian


July 2006

Abstract:

We present a system of parametric unimodal continuous distributions, containing all possible types of

score functions of prototypes. We call it a Johnson system since Johnson transformation is used for its

construction. The system contains many used probability distributions, some of them in reparametrized

forms, with unified meaning of parameters. Three non-Johnson systems are mentioned as well.

2000 Mahematics Subject Classification codes: 62A01, 62F01

Keywords:

systems of distributions, transformation, core function

1The work was supported by the Grant Agency AS CR under grant IS 1ET400300513.


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A Model of an Amorphous

Computer and its CommunicationProtocol1

Lukas Petru2

and Jir Wiedermann3


August 2006

Abstract:

We design a formal model of an amorphous computer suitable for theoretical investigation of its compu-tational properties. The model consists of a finite set of nodes created by RAMs with restricted memory,

which are dispersed uniformly in a given area. Within a limited radius the nodes can communicate with their

neighbors via a single-channel radio. The assumptions on low-level communication abilities are among the

weakest possible: the nodes work asynchronously, there is no broadcasting collision detection mechanism

and no network addresses. For the underlying network we design a randomized communication protocol

and analyze its efficiency. The subsequent experiments and combinatorial analysis of random networks

show that the expectations under which our protocol was designed are met by the vast majority of the

instances of our amorphous computer model.

Keywords:

amorphous computing; networks; communication protocols; random graphs; complexity;

1This research was carried out within the institutional research plan AV0Z10300504 and partially supported by theGA CR grant No. 1ET100300419 and GD201/05/H014.

2Faculty of Mathematics and Physics, Charles University, Malostranske namest 25, 118 00 Prague 1, Czech Republic,email:[email protected]

3Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vod arenskou vez 2, 182 07 Prague

8, Czech Republic


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Johnson point and Johnsonvariance

Zdenek Fabian


July 2006

Abstract:

New measures of central tendency and dispersion of continuous probability distributions were introducedin [1]. In this paper we show that they offer a simple and suitable description of heavy-tailed distributions,i.e., the distributions which may not have the mean and/or variance.

MSC: 62A01, 62F01

Keywords:basic characteristics, Johnson transform, parametric estimates

The author is indebted to I. Vajda for valuable critical remarks and suggestions. The work was supported by Grant

Agency AS CR under grant number IAA1075403.


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A strong nonrandom pattern in

Matlab default random numbergenerator

Petr Savicky1


September 2006

Abstract:

The default random number generator in Matlab versions between 5 and at least 7.3 (R2006b) has astrong dependence between the numbers zi+1, zi+16, zi+28 in the generated sequence. In particular, thereis no index i such that the inequalities zi+1 < 1/4, 1/4 zi+16 < 1/2, and 1/2 zi+28 are satisfiedsimultaneously. This fact is proved as a consequence of the recurrence relation defining the generator.A random sequence satisfies the inequalities with probability 1/32. Another example demonstrating thedependence is a simple function f with values 1 and 1, such that the correlation between f(zi+1, zi+16)and sign(zi+28 1/2) is at least 0.416, while it should be zero.

A simple distribution on three variables that closely approximates the joint distribution ofzi+1, zi+16, zi+28is described. The region of zero density in the approximating distribution has volume 4/21 in the threedimensional unit cube. For every integer 1 k 10, there is a parallelepiped with edges 1/2k+1, 1/2k and1/2k+1, where the density of the distribution is 2k. Numerical simulation confirms that the distribution ofthe original generator matches the approximation within small random error corresponding to the sample

size.

Keywords:pseudorandom number generator, Matlab, dependence

1Institute of Computer Science, Academy of Sciences of CR, Czech Republic, [email protected]


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New class of limited-memoryvariationally-derived variable metricmethods

J. Vlcek, L. Luksan1

Technical report No. V 973

December 2006

Abstract:

A new family of limited-memory variationally-derived variable metric or quasi-Newton meth-

ods for unconstrained minimization is given. The methods have quadratic termination prop-

erty and use updates, invariant under linear transformations. Some encouraging numericalexperience is reported.

Keywords:

Unconstrained minimization, variable metric methods, limited-memory methods, quadratic

termination property, invariance property, numerical results

1This work was supported by the Grant Agency of the Czech Academy of Sciences, project No.

IAA1030405 and the Institutional research plan No. AV0Z10300504, L. Luksan is also from Technical

University of Liberec, Halkova 6, 461 17 Liberec


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Web Search Engines and LinearAlgebra1

Roman Spanek2


September 2006

Abstract:

The technical report presents a brief overview on web search engines with deeper insight into their linearalgebra background. The linear algebra plays very important rule in modern web search algorithms (e.g.Google). The report presents two algorithms, particularly HITS and PageRank. The algorithms are dis-cussed on their convergence problems and also some improvements to their personalization abilities. Thecomputation complexity is also mentioned and briefly sketched.

Keywords:Web searching engines, PapeRank, HITS, Power Method

1The work was supported by the project 1ET100300419 of the Program Information Society (of the ThematicProgram II of the National Research Program of the Czech Republic) Intelligent Models, Algorithms, Methods andTools for the Semantic Web Realization, partly by the Institutional Research Plan AV0Z10300504 Computer Sciencefor the Information Society: Models, Algorithms, Applications and by Ministry of Education, Youth and Sports of theCzech Republic, project No. 1M4674788502 Advanced Remedial Technology and Processes.

2Institute of Computer Science, Acad. of Sci. of the Czech Republic, P.O. Box 5, 182 07 Prague 8, Czech Republic


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Computing by Broadcasting:

Alternation in Disguise(Extended Version)12

Jir Wiedermann3

and Dana Pardubska4


September 2006

Abstract:

Wireless parallel Turing machine (WPTM) is a new computational model introduced recently by the authors.Its design has been inspired by wireless mobile networking. The WPTM is an entirely deterministic modelof parallel computations where the processes communicate wirelessly via dynamically tuned broadcastingchannels. We show a tight connection between the computations of WPTMs and those of the classicalalternating Turing machines. Namely, we prove that time-space simultaneously bounded computations onWPTMs correspond exactly to similarly bounded computations of alternating Turing machines. This resultleads not only to an alternate characterization of alternation, but it also offers an alternate view of boundeduniform circuit families, such as NCi and NC.

Keywords:wireless parallel Turing machine; alternating Turing machine; time and space complexity; circuitcomplexity

1The research was carried out within the institutional research plan AV0Z10300504 and partially supported by grantNo. 1ET100300517

2The research was partially supported by grant VEGA 1/3106/063Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vod arenskou vez 2, 182 07 Prague

8, Czech Republic4Department of Computer Science, Comenius University, Mlynska dolina, 842 48 Bratislava, Slovakia, pardub-

[email protected]


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Rates of approximation of smoothfunctions by Gaussian radial-basisnetworks

Paul C. Kainen1, Vera Kurkova2, Marcello Sanguineti3


October 2006

Abstract:

Complexity of Gaussian radial-basis-function networks, with varying widths, is bounded above in terms ofthe rate of decrease of approximation error with increasing number of hidden units. Bounds are explicitlygiven in terms of norms measuring smoothness (Bessel and Sobolev norms). Estimates are proven usingsuitable integral representations in the form of networks with continua of hidden units computing scaledGaussians and translated Bessel potentials.

Keywords:Gaussian radial-basis functions, rates of approximation, Bessels potencials.

1Department of Mathematics, Georgetown University, Washington, D. C. 20057-1233, USA, [email protected] of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodarenskou vez 2, Prague 8,

Czech Republic, [email protected] of Communications, Computer, and System Sciences (DIST), University of Genoa, Via Opera Pia 13,

16145 Genova, Italy, [email protected]


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UFO 2006Interactive System for Universal FunctionalOptimization

L.Luksan, M.Tuma, J.Hartman, J.Vlcek, N.Ramesova,

M.Siska, C.Matonoha 1


December 2006

Abstract:

This report contains a description of the interactive system for universal functional optimization UFO, version

2006.

Keywords:

Numerical optimization, nonlinear programming, nonlinear approximation, algorithms, software systems.

1This work was supported by the Grant Agency of the Czech Academy of Sciences, project code IAA1030405, L.Luksan,

and M.Tuma are also from Technical University of Liberec, Halkova 6, 461 17 Liberec.


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New measures of central tendencyand variability of continuousdistributions

Zdenek Fabian


October 2006

Abstract:

A scalar inference function introduced in Fabian (2001) is generalized for a larger class of continuousdistributions. Its first two moments are used for introduction of measures of the central tendency andthe variability of the distribution. The number of examples shows that the new measures are plausible forcontinuous distribution, even for such for which the mean and/or the variance do not exist. They can beestimated from the data through the maximum likelihood estimates of the parameters; the estimates areexpressed in particular cases by algebraic formulas without need to estimate the parameters.

Mathematics Subject Classification Primary 62A01; Secondary 62F01.

Keywords:Description of distributions; Basic statistics; Score function; Core function; Point estimates


27/35


A lower bound technique forrestricted branching programs(version F)1

Stanislav Zak2


November 2006

Abstract:

We attempt to create a new lower bound technique based on a tight observation concerning separation

of positive and negative input strings. This technique gives a superpolynomial lower bound for restricted

branching programs computing a special Boolean function.

Keywords:

branching programs, lower bounds

1Research partially supported by the Information Society project 1ET100300517 and the Institutional Research

Plan AV0Z10300504.2Institute of Computer Science, Academy of Sciences of the Czech Republic, P. O. Box 5, 18207 Prague 8, Czech

Republic, [email protected]


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29/35


Matematicky model zatezovan

kloubnho systemu casovepromennymi silami

Jir Nedoma


November 2006

Abstract:

This paper represents the Technical Report of the Project of the Ministry of Industry and Trade of the CzechRepublic No. FT-TA/087 and deals with constructions of quasi-static and dynamic models of human jointsand their total replacements. Moreover, this paper deals with the numerical analyses of the quasi-static andthe dynamic non-linear contact problems with Coulombian friction in linear elasticity in the quasi-staticcase and/or in visco-elasticity with short memory. The human skeletal systems are modelled by elasticor visco-elastic bodies of arbitrary shapes being in mutual contacts. The Coulombian law of friction oncontact boundaries is assumed. In the quasi-static model the finite element technique and the semi-discretescheme are assumed and in the dynamic case the semi-implicit scheme in time and the FE approximationin space are used. The error estimates, the convergences of the numerical approximations and the optimalerror estimates are developed and discussed. Numerical simulation of Coulombian frictions are based onthe Tresca models of friction. The problems of contact problems of Tresca type are formulated as mixedvariational problems with Lagrange multipliers in 2D and 3D and the algorithms of finding the saddle pointare based on the primal-dual active set strategies and/or on the Uzawa algorithm and conjugate gradientmethod with constrains in every step of Uzawa algorithm.

Keywords:Biomechanics, human joints, total joint replacements, linear elasticity, visco-elasticity with short memory,Coulomb and Tresca models of friction, FEM, semi-discrete scheme, semi-implicit scheme


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Problematika prpravy 3D stepro metodu konecnych prvkus vyuzitm medicnskych obrazovychdat a nasledne mozne zpusoby

vizualizace vysledku

Josef Danek


December 2006

Abstrakt:

Predlozena studie je vyzkumnou zpravou Projektu MPO CR c. FT-TA/087

Komplexn vyzkum bi-

omechanickych podmnek aplikace umelych skeletalnch nahrad, interakce nahrad s or-ganismem, vyho dnocen prcin selhan a navrh podmnek pro zvysen jejich stability zarok 2006 a ukoly:

B. Mechanicke a biomechanicke hodnocen

B.3.3. Numericke resen 2D a 3D matematickych modelu metodou konecnych prvku, vcetne vyvojevhodnych algoritmu, aplikace metod vyuzvajcch i vceprocesorovych poctacu (tzv. domain decompositionmethods).

aC. Stanoven po dmnek pro zvysen stability umelych nahrad v lidskem organismu

C.3.3 Aplikace algoritmu umoznujcch numerickou analyzu umelych nahrad kloubu(i) ve vazbe na CT snmkovan,(ii) ve vazbe na navigovanou operacn techniku.

Ve studii je diskutovan problem zskavan 3D konecneprvkove ste pro modely lidskych kloubu a jejichnahrad. Pri generovan ste se vychaz obrazovych dat zskanych pomoc poctacove tomografie (CT) nebomagneticke rezonance (MRI). Ke zpracovan snmku je nutne vyuzit softwaru zamereneho na vizualizacia 3D rekonstrukci objektu. Podobne pro postprocessing je vhodne pouzt software, ktery umoznuje vizua-lizaci vypoctenych dat na konecneprvkove sti.

Keywords:Biomechanika, geometrie, metoda konecnych prvku, poctacova tomografie (CT), magneticka rezonance(MRI)


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Vysledky numerickeho modelovanzatzeneho kolennho kloubu a jeho

nahrady s uvazovanm kloubnhopouzdra

J. Danek, J. Stehlk, J. Nedoma, I. Hlavacek


December 2006

Abstrakt:

Predlozena studie je vyzkumnou zpravou Projektu MPO CR c. FT-TA/087 Komplexn vyzkum bi-omechanickych podmnek aplikace umelych skeletalnch nahrad, interakce nahrad s or-

ganismem, vyho dnocen prcin selhan a navrh podmnek pro zvysen jejich stability zarok 2006 a ukoly:

B. Mechanicke a biomechanicke hodnocen

B.3.3. Numericke resen 2D a 3D matematickych modelu metodou konecnych prvku, vcetne vyvojevhodnych algoritmu, aplikace metod vyuzvajcch i vceprocesorovych poctacu (tzv. domain decompositionmethods).

aC. Stanoven po dmnek pro zvysen stability umelych nahrad v lidskem organismu

C.3.3 Aplikace algoritmu umoznujcch numerickou analyzu umelych nahrad kloubu(i) ve vazbe na CT snmkovan,(ii) ve vazbe na navigovanou operacn techniku.

Vyzkumna zprava obsahuje numericke vysledky pro modely kolennho kloubu bez totaln nahrady (Model I)a dale pak vysledky pro modely kolennho kloubu s aplikovanou totaln nahradou pro ruzne stupne valgozity(Modely II az VI). Modely jsou uvazovany ve frontalnm rezu a jejich soucast je i kloubn pouzdro.

Keywords:Biomechanika, kolenn kloub, totaln nahrada kolennho kloubu, metoda konecnych prvku


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Generalizations and Extensions ofLattice-Valued PossibilisticMeasures, Part II1

Ivan Kramosil


December 2006

Abstract:

In this technical report, the systematic investigation of lattice-valued p ossibilistic measures, opened in the

first part of this report (cf. Technical Report No. 952, ICS AS CR, December 2005) is pursued and focusedtowards possibilistic variants of the notions of outer (upper) and lower (inner) possibilistic measures inducedby a given partial possibilistic measure. The notion of Lebesgue measurability for possibilistic measuresis defined and it is generalized to the notion of almost-measurability in the sense that the values of innerand outer measure ascribed to a set are not identical, as demanded in the case of Lebesgue measurability,but these two values do not differ too much from each other in the sense definable within the latticestructure. In the rest of this report, the probabilistic model of decision making under uncertainty is modifiedto the case of lattice-valued possibilistic measures, so arriving at the notion of possibilistic decision function.The Bayesian and the minimax principles when quantifying the qualities of particular possibilistic decisionfunctions are also analyzed and applied to some cases, e.g., to the case of possibilistic decision functionsfor state identification.

Keywords:Lattice-valued possibilistic measures, inner (lower) and outer (upper) possibilistic measures,approximation and completion of partial lattice-valued possibilistic measures, decision making underuncertainty, possibilistic decision function, possibilistic loss function.

1This research was partially supported by the grant No. IAA100300503 of GA AS CR and by the Institutional

Research Plan AV0Z10300504 Computer Science for the Information Society: Models, Algorithms, Application


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Evolving neural networks which

control a simple robotic agent

Roman Neruda, Stanislav Slusny1


December 2006

Abstract:

The design of intelligent embodied agents represents one of the key research topicsof todays artificial intelligence. These agents should be able to adopt to changes

of the environment and to modify their behaviour according to acquired knowledge.The goal of this work is the study of emergence of intelligent behaviour within a

simple intelligent agent. Cognitive agent functions will be realized by mechanismsbased on neural networks and evolutionary algorithms, where the evolutionary al-

gorithm will be responsible for the adaptation of a neural network in a simulatedenvironment.

Keywords:Evolutionary algorithms, neural networks, robotic agent.

1Acknowledgment This work was supported by the Ministry of Education of the Czech Republic under the

project Center of Applied Cybernetics No. 1M684077004 (1M0567).


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Interior point methods for minimization ofcomposite nonsmooth functions

L.Luksan, C.Matonoha, J.Vlcek 1


December 2006

Abstrakt:

In this report, we propose a class of primal interior point methods for minimization of

composite nonsmooth functions. After a short introduction where composite nonsmooth

functions are defined, we describe two algorithms based on iterative and direct determination

of the minimax vector respectively. Finally, we investigate most important special cases a

give results of numerical experiments, which demonstrate high efficiency of primal interiorpoint methods for composite nonsmooth functions.

Keywords:

Numerical optimization, nonlinear programming, nonlinear approximation, algorithms,

software systems.

1This work was supported by the Grant Agency of the Czech Academy of Sciences, project code

IAA1030405, L.Luksan is also from Technical University of Liberec, Halkova 6, 461 17 Liberec.


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Programy pro resen rovnic chemickekinetiky

L.Luksan, M.Rozloznk, M.Tuma 1

Technical report No. V988

Prosinec 2006

Abstrakt:

V praci jsou analyzovany rovnice popisujc chemickou kinetiku a vyvinuty efektivn metody

pro jejich resen. Jsou studovany a implementovany metody pro resen tuhych systemu

nelinearnch diferencialnch rovnic s pocatecnmi podmnkami. Jsou tez popsany prslusne

programy napsane v jazyce Fortran a uvedeny jejich vypisy. Prilozeny jsou ukazky vypoctu

a vysledky vzoroveho problemu.

Keywords:

Chemicka kinetika, nelinearn diferencialn rovnice, tuhe systemy, implicitn metody typu

Runge-Kutta, softwarova realizace.

1Tato prace byla podporena Ministerstvem prumyslu a obchodu CR, grant TANDEM: FT-TA/066,a vyzkumnym zamerem AV0Z10300504 Akademie ved CR.

Documents

Institute of Computer Science