This thesis introduces a multilinear algebraic framework for computer graphics, computer vision, and machine learning, particularly for the fundamental purposes of image synthesis, analysis, and recognition. Natural images result from the multifactor interaction between the imaging process, the scene illumination, and the scene geometry. We assert that a principled mathematical approach to disentangling and explicitly representing these causal factors, which are essential to image formation, is through numerical multilinear algebra, the algebra of higher-order tensors. Our new image modeling framework is based on(i) a multilinear generalization of principal components analysis (PCA), (ii) a novel multilinear generalization of independent components analysis (ICA), and (iii) a multilinear projection for use in recognition that maps images to the multiple causal factor spaces associated with their formation. Multilinear PCA employs a tensor extension of the conventional matrix singular value decomposition (SVD), known as the M-mode SVD, while our multilinear ICA method involves an analogous M-mode ICA algorithm. As applications of our tensor framework, we tackle important problems in computer graphics, computer vision, and pattern recognition; in particular, (i) image-based rendering, specifically introducing the multilinear synthesis of images of textured surfaces under varying view and illumination conditions, a new technique that we call ``TensorTextures'', as well as (ii) the multilinear analysis and recognition of facial images under variable face shape, view, and illumination conditions, a new technique that we call ``TensorFaces''. In developing these applications, we introduce a multilinear image-based rendering algorithm and a multilinear appearance-based recognition algorithm. As a final, non-image-based application of our framework, we consider the analysis, synthesis and recognition of human motion data using multilinear methods, introducing a new technique that we call ``Human Motion Signatures''.

This thesis introduces a multilinear algebraic framework for computer graphics, computer vision, and machine learning, particularly for the fundamental purposes of image synthesis, analysis, and recognition. Natural images result from the multifactor interaction between the imaging process, the scene illumination, and the scene geometry. We assert that a principled mathematical approach to disentangling and explicitly representing these causal factors, which are essential to image formation, is through numerical multilinear algebra, the algebra of higher-order tensors. Our new image modeling framework is based on(i) a multilinear generalization of principal components analysis (PCA), (ii) a novel multilinear generalization of independent components analysis (ICA), and (iii) a multilinear projection for use in recognition that maps images to the multiple causal factor spaces associated with their formation. Multilinear PCA employs a tensor extension of the conventional matrix singular value decomposition (SVD), known as the M-mode SVD, while our multilinear ICA method involves an analogous M-mode ICA algorithm. As applications of our tensor framework, we tackle important problems in computer graphics, computer vision, and pattern recognition; in particular, (i) image-based rendering, specifically introducing the multilinear synthesis of images of textured surfaces under varying view and illumination conditions, a new technique that we call ``TensorTextures'', as well as (ii) the multilinear analysis and recognition of facial images under variable face shape, view, and illumination conditions, a new technique that we call ``TensorFaces''. In developing these applications, we introduce a multilinear image-based rendering algorithm and a multilinear appearance-based recognition algorithm. As a final, non-image-based application of our framework, we consider the analysis, synthesis and recognition of human motion data using multilinear methods, introducing a new technique that we call ``Human Motion Signatures''.

A substantial number of works have aimed at modeling the receptive field properties of the primary visual cortex (V1). Their evaluation criterion is usually the similarity of the model response properties to the recorded responses from biological organisms. However, as several algorithms were able to demonstrate some degree of similarity to biological data based on the existing criteria, we focus on the robustness against loss of information in the form of occlusions as an additional constraint for better understanding the algorithmic level of early vision in the brain. We try to investigate the influence of competition mechanisms on the robustness. Therefore, we compared four methods employing different competition mechanisms, namely, independent component analysis, non-negative matrix factorization with sparseness constraint, predictive coding/biased competition, and a Hebbian neural network with lateral inhibitory connections. Each of those methods is known to be capable of developing receptive fields comparable to those of V1 simple-cells. Since measuring the robustness of methods having simple-cell like receptive fields against occlusion is difficult, we measure the robustness using the classification accuracy on the MNIST hand written digit dataset. For this we trained all methods on the training set of the MNIST hand written digits dataset and tested them on a MNIST test set with different levels of occlusions. We observe that methods which employ competitive mechanisms have higher robustness against loss of information. Also the kind of the competition mechanisms plays an important role in robustness. Global feedback inhibition as employed in predictive coding/biased competition has an advantage compared to local lateral inhibition learned by an anti-Hebb rule.

Ce travail a porté sur les remaniements corticaux précoces des circuits moteurs et extramoteurs dans la SLA grâce à l’étude des activations IRMf issues de tâches motrices et cognitives. La première partie de nos travaux nous a permis de montrer grâce des tâches simples d’activation motrice en IRMf (1) qu’alors que les patients SLA présentaient un déficit moteur discret, une augmentation des activations corticales est apparue dans les aires sensorimotrices bilatérales du cerveau. (2) Ces modifications précoces de l’activité neuronale étaient corrélées à la latéralisation du déficit moteur du membre ou la prédominance manuelle et surtout, (3) au taux de progression de la maladie à un an et à la survie, suggérant que ce remaniement de l’activité qui correspond probablement à de la plasticité cérébrale a des implications fonctionnelles. Enfin, (4) ce phénomène apparaissait actif puisqu’il s’est poursuivi pendant au moins onze mois. Dans la deuxième partie, nous avons montré lors d’une tâche de fluence verbale silencieuse que (1) les SLA présentaient une suractivation initiale des aires dévolues au processus sémantique avec un renforcement de la connectivité fonctionnelle entre les réseaux (CFR). (2) Au bout de onze mois et alors que l’atteinte des fluences était stable, ce phénomène de compensation s’épuisait avec une diminution conjointe de l’activation des réseaux et de la CFR. La tâche de 2-Back, réalisée alors que les patients ne présentaient pas d’atteinte de la mémoire de travail lors des tests psychométriques, nous a permis de montrer en outre que certains circuits non-moteurs se réorganisaient très précocement chez les patients, alors même qu’ils étaient asymptomatiques / In this work we used motor and cognitive tasks in an fMRI study to explore the early cortical reorganizations of the motor and extra-motor circuits in ALS patients. In a first part, using a simple motor task, we demonstrated (1) that increased cortical BOLD signal changes occurred in specific regions of the brain of ALS patients when their motor deficit was still moderate, and that this early signal changes correlated with (2) the lateralisation of the motor deficit or hand predominance and, more importantly, (3) with the rate of disease progression at one year and survival time, suggesting that modulations of cerebral activity in ALS may have functional implications. Furthermore, (4) this brain plasticity was maintained with time and disease progression during at least eleven months. In a second part, we demonstrated during a silent verbal fluency task (1) that ALS patients presented initially an increased cortical activation of areas devolved to the semantic process with an intensification of the functional network connectivity (FNC). (2) After eleven months and while their performance in tests of verbal fluency was stable, this cerebral compensation ran out with a decrease of the previous cerebral activations and the FNC. A N-back working memory paradigm, realized while the patients did not present any deficit of their working memory, allowed us to show that certain non-motor circuits were reorganized prematurely while patients were still asymptomatic

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Σκοπός της διδακτορικής διατριβής είναι η ανάπτυξη κατάλληλων μεθόδων ψηφιακής επεξεργασίας εικόνας και αναγνώρισης προτύπων με τις οποίες θα προσδιορίζονται βιομετρικές και διαγνωστικές παράμετροι μέσω της αλληλεπίδρασης φωτονίων στο ορατό και υπέρυθρο φάσμα. Πιο συγκεκριμένα επιλύεται ένα αντίστροφο πρόβλημα σκέδασης ΗΜ ακτινοβολίας από ένα ανθρώπινο, υγιές και απαραμόρφωτο ερυθρό αιμοσφαίριο. Παρουσιάζονται μέθοδοι εκτίμησης και αναγνώρισης των γεωμετρικών χαρακτηριστικών απαραμόρφωτων υγιών ερυθρών αιμοσφαιρίων με χρήση εικόνων που προσομοιώνουν φαινόμενα σκέδασης ηλεκτρομαγνητικής ακτινοβολίας που διέρχεται από προσανατολισμένα ερυθρά αιμοσφαίρια. Η διαδικασία της ανάκτησης της πληροφορίας περιλαμβάνει, εξαγωγή χαρακτηριστικών με χρήση δισδιάστατων μετασχηματισμών, κανονικοποίηση των χαρακτηριστικών και την χρήση νευρωνικών δικτύων για την εκτίμηση των γεωμετρικών ιδιοτήτων του ερυθροκυττάρου. Παράλληλα σχεδιάστηκε και αξιολογήθηκε σύστημα αναγνώρισης των γεωμετρικών χαρακτηριστικών των ερυθρών αιμοσφαιρίων. Οι εικόνες σκέδασης δημιουργήθηκαν προσομοιώνοντας το πρόβλημα εμπρόσθιας σκέδασης ενός επίπεδου ηλεκτρομαγνητικού (ΗΜ) κύματος, χρησιμοποιώντας την μέθοδο των συνοριακών στοιχείων, λαμβάνοντας υπόψη τόσο την αξονοσυμμετρική γεωμετρία του ερυθροκυττάρου όσο και τις μη αξονοσυμμετρικές οριακές συνθήκες του προβλήματος. Η επίλυση του εν λόγω προβλήματος πραγματοποιήθηκε στα 632.8 nm και εν συνεχεία επεκτάθηκε σε 12 διακριτά ίσου βήματος μήκη κύματος από 432.8 nm έως 1032.8 nm. Επίσης, προτάθηκε μία νέα πειραματική διάταξη για την απόκτηση πολλαπλών εικόνων σκέδασης και την εκτίμηση των γεωμετρικών χαρακτηριστικών των ερυθρών αιμοσφαιρίων, αποτελούμενη από μία πολυχρωματική πηγή φωτός (Led) και πολλαπλά χρωματικά φίλτρα. Επίσης κατασκευάστηκε μέθοδος επίλυσης του σημαντικού προβλήματος εύρεσης της περιεκτικότητας του διαλύματος σε ερυθρά αιμοσφαίρια διαφορετικών μεγεθών στην περίπτωση απόκτησης πολλαπλών εικόνων σκέδασης από διαφορετικές φωτοδιόδους και πολλαπλά χρωματικά φίλτρα. Στα πειράματα αξιολόγησης της μεθόδου που προτείνεται με εικόνες προσομοίωσης δείχνεται ότι είναι ικανή η εύρεση της αναλογίας των ερυθρών αιμοσφαιρίων με πολύ μεγάλη ακρίβεια ακόμα και στη περίπτωση όπου στις εικόνες έχει προστεθεί λευκός κανονικός θόρυβος. Η βασική μεθοδολογία που παρουσιάζεται στην παρούσα δια-τριβή μπορεί να χρησιμοποιηθεί για την αναγνώριση παθολογικών αιμοσφαιρίων ή να χρησιμοποιηθεί στην αναγνώριση μικροσωματιδίων σε υγρά ή αέρια. / The aim of this PhD thesis is the development of digital image processing and pattern recognition methods to estimate biometric and diagnostic parameters using scattering phenomena in the visible and infrared spectrum. More concretely, several reverse scattering problems of EM radiation from a human, healthy and undistorted Red Blood Cell (RBC) is solved. Methods of estimation and recognition of geometrical characteristics of healthy and undistorted RBCs using simulating images are presented. The information retrieval process includes, features extraction using two-dimensional integral transforms, features normalization, and Neural Networks for estimation of three major RBC geometrical proper-ties. Using the same features set, a recognition system of the geometric characteristics of RBCs was developed and evaluated. The scattering images were created simulating the forward scattering problem of a plane electromagnetic wave using the Boundary Element Method, taking into account both axisymmetric geometry of the scatterer and the non-axisymmetric boundary conditions of the problem. Initially, the problem is solved at 632.8 nm and consequently the same problem was solved at 12 different wavelengths, from 432.8 to 1032.8 nm equally spaced. Also, a new device for acquisition of scattering images from RBCs-flow, consisting of a multi-color light source (Led) was proposed, for RBC size estimation and recognition. Finally, a system for the estimation of different RBCs concentration was developed when scattering images acquired using multiple scattering images acquired from multiple Leds and color filters. The system was evaluated using additive white regular noise.

Abstract Neuropsychiatric illnesses usually become overtly manifest in adolescence and early adulthood. A critical long-term aim is to be able to prevent the development of such illnesses, which requires instruments to identify subjects at high risk of illness and to offer them effective interventions. There is an indisputable need for more sophisticated methods to enable more precise detection of adolescents and young adults who are at high risk of developing psychosis. Abnormal function in brain networks has been reported in people with schizophrenia and other psychotic disorders. Similar abnormalities have been found also in people at risk for developing psychosis, but it is not known whether this applies also to spontaneous resting state activity in young people with a familial risk for psychosis. We conducted resting-state functional MRI (R-fMRI) in 72 (29 male) young adults with a history of psychosis in one or both parents (FR) but without psychosis themselves, and 72 (29 male) similarly healthy control subjects without familial risk for psychosis. Both groups in the Oulu Brain and Mind study were drawn from the Northern Finland Birth Cohort 1986. All volunteers were 20–25 years old. Parental psychosis was established using the Care Register for Health Care. R-fMRI data was pre-processed using independent component analysis (ICA). A dual regression technique was used to detect between-group differences with p < 0.05 threshold corrected for multiple comparisons at voxel level. FR subjects demonstrated significantly decreased activity compared to control subjects in the default mode network and in the central executive network and increased activity in the cerebellum. The findings clarify previously controversial literature on the subject. The finding suggests that abnormal activity in these brain networks in rest may be associated with increased vulnerability to psychosis. The findings maybe helpful in developing more precise methods for detecting young people at highest risk for developing psychosis. / Tiivistelmä Psykoottisiin häiriöihin sairastutaan yleensä nuoruudessa tai varhaisaikuisuudessa. Psykoositutkimuksen tavoitteena on löytää uusia menetelmiä, joiden avulla kyettäisiin tunnistamaan suurimmassa psykoosiriskissä olevat nuoret, jotta heille voitaisiin tarjota sairautta ennaltaehkäiseviä hoitokeinoja. Skitsofreniaan ja muihin psykoottisiin häiriöihin sairastuneilla on havaittu aivotoiminnan poikkeavuuksia. Samankaltaisia aivotoiminnan poikkeavuuksia on havaittu myös nuorilla, jotka ovat vaarassa sairastua psykoosiin. Toistaiseksi on ollut epäselvää, onko psykoosiin sairastuneiden henkilöiden lapsilla aivohermoverkkojen toiminnan poikkeavuuksia lepotilassa. Suoritimme aivojen lepotilan MRI-tutkimuksen (R-fMRI) 72:lle (29 miestä) nuorelle aikuiselle, joiden jompikumpi vanhempi oli sairastunut psykoosin sekä 72:lle (29 miestä) nuorelle aikuiselle, joiden vanhemmat eivät olleet sairastaneet psykoosia. Molemmat tutkimusryhmät tässä Oulu Brain and Mind -tutkimuksessa olivat Pohjois-Suomen 1986 syntymäkohortin jäseniä. Tutkittavat olivat 20–25 vuoden iässä. Lepotilan toiminnallinen magneettikuvaus suoritettiin 1.5 Teslan Siemensin magneettikuvantamislaitteella. Tutkimuskohteiksi valittiin lepotilan toiminnallinen aivohermoverkko, toiminnan ohjauksesta vastaava aivohermoverkko ja pikkuaivot. Kuvantamisdataan sovellettiin itsenäisten komponenttien analyysia aivohermoverkkojen määrittämistä varten. Ryhmien välisen eron havaitsemiseen käytettiin ei-parametristä permutaatiotestiä, joka kynnystettiin tilastollisesti merkitsevään tasoon (p < 0.05). Lepotilan oletushermoverkossa ja toiminnanohjauksesta vastaavassa aivohermoverkoissa havaittiin vähäisempää aktiivisuutta ja pikkuaivoissa kohonnutta aktiivisuutta perinnöllisessä psykoosiriskissä olevilla nuorilla aikuisilla verrattuna verrokkeihin. Tutkimustulokset selkeyttivät aiempaa ristiriitaista kirjallisuutta tutkimusaiheesta. Tutkimuksessa havaittujen aivoalueiden poikkeava toiminta lepotilassa voi liittyä kohonneeseen psykoosin puhkeamisriskiin. Tutkimuslöydösten avulla voidaan todennäköisesti edesauttaa parempien kuvantamismenetelmien kehittämistä suurimmassa psykoosiriskissä olevien nuorten tunnistamiseen.

This thesis is composed of three chapters that propose some novel approaches on tail risk for financial market and forecasting in finance and macroeconomics. The first part of this dissertation focuses on financial market correlations and introduces a simple measure of tail correlation, TailCoR, while the second contribution addresses the issue of identification of non- normal structural shocks in Vector Autoregression which is common on finance. The third part belongs to the vast literature on predictions of economic growth; the problem is tackled using a Bayesian Dynamic Factor model to predict Norwegian GDP.Chapter I: TailCoRThe first chapter introduces a simple measure of tail correlation, TailCoR, which disentangles linear and non linear correlation. The aim is to capture all features of financial market co- movement when extreme events (i.e. financial crises) occur. Indeed, tail correlations may arise because asset prices are either linearly correlated (i.e. the Pearson correlations are different from zero) or non-linearly correlated, meaning that asset prices are dependent at the tail of the distribution.Since it is based on quantiles, TailCoR has three main advantages: i) it is not based on asymptotic arguments, ii) it is very general as it applies with no specific distributional assumption, and iii) it is simple to use. We show that TailCoR also disentangles easily between linear and non-linear correlations. The measure has been successfully tested on simulated data. Several extensions, useful for practitioners, are presented like downside and upside tail correlations.In our empirical analysis, we apply this measure to eight major US banks for the period 2003-2012. For comparison purposes, we compute the upper and lower exceedance correlations and the parametric and non-parametric tail dependence coefficients. On the overall sample, results show that both the linear and non-linear contributions are relevant. The results suggest that co-movement increases during the financial crisis because of both the linear and non- linear correlations. Furthermore, the increase of TailCoR at the end of 2012 is mostly driven by the non-linearity, reflecting the risks of tail events and their spillovers associated with the European sovereign debt crisis. Chapter II: On the identification of non-normal shocks in structural VARThe second chapter deals with the structural interpretation of the VAR using the statistical properties of the innovation terms. In general, financial markets are characterized by non- normal shocks. Under non-Gaussianity, we introduce a methodology based on the reduction of tail dependency to identify the non-normal structural shocks.Borrowing from statistics, the methodology can be summarized in two main steps: i) decor- relate the estimated residuals and ii) the uncorrelated residuals are rotated in order to get a vector of independent shocks using a tail dependency matrix. We do not label the shocks a priori, but post-estimate on the basis of economic judgement.Furthermore, we show how our approach allows to identify all the shocks using a Monte Carlo study. In some cases, the method can turn out to be more significant when the amount of tail events are relevant. Therefore, the frequency of the series and the degree of non-normality are relevant to achieve accurate identification.Finally, we apply our method to two different VAR, all estimated on US data: i) a monthly trivariate model which studies the effects of oil market shocks, and finally ii) a VAR that focuses on the interaction between monetary policy and the stock market. In the first case, we validate the results obtained in the economic literature. In the second case, we cannot confirm the validity of an identification scheme based on combination of short and long run restrictions which is used in part of the empirical literature.Chapter III :Nowcasting NorwayThe third chapter consists in predictions of Norwegian Mainland GDP. Policy institutions have to decide to set their policies without knowledge of the current economic conditions. We estimate a Bayesian dynamic factor model (BDFM) on a panel of macroeconomic variables (all followed by market operators) from 1990 until 2011.First, the BDFM is an extension to the Bayesian framework of the dynamic factor model (DFM). The difference is that, compared with a DFM, there is more dynamics in the BDFM introduced in order to accommodate the dynamic heterogeneity of different variables. How- ever, in order to introduce more dynamics, the BDFM requires to estimate a large number of parameters, which can easily lead to volatile predictions due to estimation uncertainty. This is why the model is estimated with Bayesian methods, which, by shrinking the factor model toward a simple naive prior model, are able to limit estimation uncertainty.The second aspect is the use of a small dataset. A common feature of the literature on DFM is the use of large datasets. However, there is a literature that has shown how, for the purpose of forecasting, DFMs can be estimated on a small number of appropriately selected variables.Finally, through a pseudo real-time exercise, we show that the BDFM performs well both in terms of point forecast, and in terms of density forecasts. Results indicate that our model outperforms standard univariate benchmark models, that it performs as well as the Bloomberg Survey, and that it outperforms the predictions published by the Norges Bank in its monetary policy report. / Doctorat en Sciences économiques et de gestion / info:eu-repo/semantics/nonPublished

Mnoho rozdílných strategií fúze bylo vyvinuto během posledních 15 let výzkumu simultánního EEG-fMRI. Aktuální dizertační práce shrnuje aktuální současný stav v oblasti výzkumu fúze simultánních EEG-fMRI dat a pokládá si za cíl vylepšit vizualizaci úkolem evokovaných mozkových sítí slepou analýzou přímo z nasnímaných dat. Dva rozdílné modely, které by to měly vylepšit, byly navrhnuty v předložené práci (tj. zobecněný spektrální heuristický model a zobecněný prostorovo-frekvenční heuristický model). Zobecněný frekvenční heuristický model využívá fluktuace relativního EEG výkonu v určitých frekvenčních pásmech zprůměrovaných přes elektrody zájmu a srovnává je se zpožděnými fluktuacemi BOLD signálů pomocí obecného lineárního modelu. Získané výsledky ukazují, že model zobrazuje několik na frekvenci závislých rozdílných úkolem evokovaných EEG-fMRI sítí. Model překonává přístup fluktuací absolutního EEG výkonu i klasický (povodní) heuristický přístup. Absolutní výkon vizualizoval s úkolem nesouvisející širokospektrální EEG-fMRI komponentu a klasický heuristický přístup nebyl senzitivní k vizualizaci s úkolem spřažené vizuální sítě, která byla pozorována pro relativní pásmo pro data vizuálního oddball experimentu. Pro EEG-fMRI data s úkolem sémantického rozhodování, frekvenční závislost nebyla ve finálních výsledcích tak evidentní, neboť všechna pásma zobrazily vizuální síť a nezobrazily aktivace v řečových centrech. Tyto výsledky byly pravděpodobně poškozeny artefaktem mrkání v EEG datech. Koeficienty vzájemné informace mezi rozdílnými EEG-fMRI statistickými parametrickými mapami ukázaly, že podobnosti napříč různými frekvenčními pásmy jsou obdobné napříč různými úkoly (tj. vizuální oddball a sémantické rozhodování). Navíc, koeficienty prokázaly, že průměrování napříč různými elektrodami zájmu nepřináší žádnou novou informaci do společné analýzy, tj. signál na jednom svodu je velmi rozmazaný signál z celého skalpu. Z těchto důvodů začalo být třeba lépe zakomponovat informace ze svodů do EEG-fMRI analýzy, a proto jsme navrhli více obecný prostorovo-frekvenční heuristický model a také jak ho odhadnout za pomoci prostorovo-frekvenční skupinové analýzy nezávislých komponent relativního výkonu EEG spektra. Získané výsledky ukazují, že prostorovo-frekvenční heuristický model vizualizuje statisticky nejvíce signifikantní s úkolem spřažené mozkové sítě (srovnáno s výsledky prostorovo-frekvenčních vzorů absolutního výkonu a s výsledky zobecněného frekvenčního heuristického modelu). Prostorovo-frekvenční heuristický model byl jediný, který zaznamenal s úkolem spřažené aktivace v řečových centrech na datech sémantického rozhodování. Mimo fúzi prostorovo-frekvenčních vzorů s fMRI daty, jsme testovali stabilitu odhadů prostorovo-frekvenčních vzorů napříč různými paradigmaty (tj. vizuální oddball, semantické rozhodování a resting-state) za pomoci k-means shlukovacího algoritmu. Dostali jsme 14 stabilních vzorů pro absolutní EEG výkon a 12 stabilních vzorů pro relativní EEG výkon. Ačkoliv 10 z těchto vzorů vypadají podobně napříč výkonovými typy, prostorovo-frekvenční vzory relativního výkonu (tj. vzory prostorovo-frekvenčního heuristického modelu) mají vyšší evidenci k úkolům.

Functional magnetic resonance imaging (fMRI) is recent important method, used in neuroimaging. The aim of this thesis is to develop software tool for comparison of two methods for functional and effective connectivity estimation. In this thesis are described the basics of magnetic resonance imaging, fMRI, basic terms of fMRI experiments and generally are described methods of functional and effective connectivity. Then are more detailed mentioned methods of dynamic causal modeling (DCM), Granger causal modeling (GCM) and independent component analysis (ICA). Practical implementation of DCM in toolbox SMP and ICA in toolbox GIFT is also mentioned. In purpose to describe behavior of DCM and GCM in dependence on several parameters are performed Monte Carlo simulations. Then the concept and realization of software tool for simulating connectivity and comparison of DCM and GCM are described. Finally results of DCM and GCM comparison and results of Monte Carlo simulations are discussed.