Graphical Models

This research develops Prisma Project as a governed Tier B structural companion within the Genesis ODE framework. The study focuses on converting a designed geometric source figure into a formal mathematical object through normalized coordinates, a thirteen-node set, a principal segment program, midpoint and symmetry proofs, residual accounting, and solvency-gated evaluation. Its central aim is to show how a visual construct can be translated into a reproducible structural model without being misclassified as canonical runtime evidence or ontology.

Within the Genesis ODE framework, the project is positioned explicitly as governed experimental infrastructure rather than universal metaphysics. The paper therefore distinguishes structural modeling from runtime execution by declaring substrate, observable, evidence tier, and claim boundary in advance. Prisma Project is assigned to Tier B as a structural companion only, while metallurgy-only MVP-A1 runtime work remains restricted to the C_Met substrate and the AmplitudeRampPerturbation family.

The study also addresses governance requirements at the repository level. It incorporates typed telemetry logic, fail-closed validation, branch registration, metadata-dynamics separation, experimental-branch quarantine, and machine-readable schema enforcement. In addition, it documents a deterministic MVP-A1 reference contract containing drift measurement, tether computation, coverage locking, canonical artifact emission, and hash-verified RunManifest control, while preserving the boundary that prevents Tier B structural material from silently entering canonical solver logic.

The result is a tightly scoped research artifact that joins formal geometry, governance architecture, and validation discipline. Rather than treating structural resemblance as proof of shared ontology, the project frames cross-framework translation as informative but non-ontological, establishing a review-ready model for disciplined comparison, serialization, and future empirical extension.

Canonical forms attempt to factor out a non-rigid shape's pose, giving a pose-neutral shape. This opens up the possibility of using methods originally designed for rigid shape retrieval for the task of non-rigid shape retrieval. We extend our recent benchmark for testing canonical form algorithms. Our new benchmark is used to evaluate a greater number of state-of-the-art canonical forms, on five recent non-rigid retrieval datasets, within two different retrieval frameworks. A total of fifteen different canonical form methods are compared. We find that the difference in retrieval accuracy between different canonical form methods is small, but varies significantly across different datasets. We also find that efficiency is the main difference between the methods.

Deformation transfer is an important research problem in geometry processing and computer animation.A fundamental problem for existing deformation transfer methods is to build reliable correspondences. This is challenging, especially when the source and target shapes difer signiicantly and manual labeling is typically used. We propose a novel deformation transfer method that aims at minimizing user efort. We adapt a biharmonic weight deformation framework which is able to produce plausible deformation even with only a few key points. We then develop an automatic algorithm to identify a minimum set of key points on the source model that characterizes the deformation well. While minimal user efort is still needed to specify corresponding points on the target model for the selected key points, our approach avoids the diicult problem of choosing key points. Experimental results demonstrate that our method, despite requiring little user efort, produces better deformation results than alternative solutions.

We propose VoxMorph, a new interactive freeform deformation tool for high resolution voxel grids. Our system exploits cages for high-level deformation control. We tackle the scalability issue by introducing a new 3-scale deformation algorithm composed of a high quality as-rigid-as possible deformation at coarse scale, a quasi-conformal space deformation at mid-scale and a new deformation-adaptive local linear technique at fine scale. The two first scales are applied interactively on a visualization envelope, while the complete full resolution deformation is computed as a post-process after the interactive session, resulting in a high resolution voxel grid containing the deformed model. We tested our system on various real world datasets and demonstrate that our approach offers a good balance between performance and quality.

We present a new curve skeleton model designed for surface modeling and processing. This skeleton is defined as the geometrical integration of a piecewise harmonic parameterization defined over a disk‐cylinder surface decomposition. This decomposition is computed using a progressive Region Graph reduction based on both geometric and topological criteria which can be iteratively optimized to improve region boundaries. The skeleton has an analytical form with regularity inherited from the surface one. Such a form offers well‐defined surface‐skeleton and skeleton‐surface projections. The resulting skeleton satisfies quality criteria which are relevant for skeleton‐based modeling and processing. We propose applications that benefit from our skeleton model, including local thickness editing, inset surface creation for shell mapping, as well as a new mid‐scale feature preserving smoothing.

We devise a novel inference algorithm to effectively solve the cancer progression model reconstruction problem. Our empirical analysis of the accuracy and convergence rate of our algorithm, CAncer PRogression Inference (CAPRI), shows that it outperforms the state-of-the-art algorithms addressing similar problems. Motivation: Several cancer-related genomic data have become available (e.g., The Cancer Genome Atlas, TCGA) typically involving hundreds of patients. At present, most of these data are aggregated in a cross-sectional fashion providing all measurements at the time of diagnosis. Our goal is to infer cancer ?progression? models from such data. These models are represented as directed acyclic graphs (DAGs) of collections of ?selectivity? relations, where a mutation in a gene A ?selects? for a later mutation in a gene B. Gaining insight into the structure of such progressions has the potential to improve both the stratification of patients and personalized therapy choices. Resul...

In molecular analysis, Spatial Distribution Functions (SDF) are fundamental instruments in answering questions related to spatial occurrences and relations of atomic structures over time. Given a molecular trajectory, SDFs can, for example, reveal the occurrence of water in relation to particular structures and hence provide clues of hydrophobic and hydrophilic regions. For the computation of meaningful distribution functions, the definition of molecular reference structures is essential. Therefore we introduce the concept of an internal frame of reference (IFR) for labeled point sets that represent selected molecular structures, and we propose an algorithm for tracking the IFR over time and space using a variant of Kabsch's algorithm. This approach lets us generate a consistent space for the aggregation of the SDF for molecular trajectories and molecular ensembles. We demonstrate the usefulness of the technique by applying it to temporal molecular trajectories as well as ensemble datasets. The examples include different docking scenarios with DNA, insulin, and aspirin.

There are various techniques to design complex free-form shapes with general topology. In contrast to the approaches based on trimmed surfaces and control polyhedra, in curve network-based design feature curves can be directly created and edited in 3D. Multi-sided patches interpolate this curve network with slopes given by associated tangent ribbons. The patches are smoothly connected and yield a natural and predictable surface model. This paper focuses on special design techniques to adjust the interior of transfinite patches when further shape control is needed. While the boundary constraints are retained, additional vertices, curves and even interior control surfaces are supplemented to gain more design freedom. The main idea is to apply different distance-based blending functions with special parameterizations over non-regular, n-sided domains. This concept can be naturally extended to create one-and two-sided patches as well. Shape variations will be demonstrated by a few simple examples.

Transfinite surface interpolation is a classic topic of computer-aided geometric design (CAGD), and many non-quadrilateral schemes are known. Surfaces defined solely by means of their boundary curves and cross-tangent functions are needed, for example, in three-dimensional curve network-based design, and to fill complex irregular holes such as in vertex blending. This paper deals with interpolating so-called tangential ribbons. Former schemes are enhanced and extended in order to minimize shape artifacts and to provide a more natural patch interior. The proposed representation is based on irregular convex domains that correspond to the lengths and orientations of the boundary curves. The mapping of the individual ribbons within the n-sided domain is calculated by focused parameterization methods that ensure a balanced orientation related to the center of the domain and avoid parametric shearing. Distancebased blending functions ensure that modifying or inserting a small edge will have only a local effect over the n-sided patch. Constructions to create one-sided or two-sided patches are also presented. Examples and open research topics conclude the paper.

Palavras-chave: políticos profissionais, comunicação política, plataformas digitais, TikTok, análise de conteúdo. RESUMO Introdução: O artigo explora como políticos brasileiros fazem uso das affordances do TikTok. Investigamos os expedientes interativos e as formas de engajamento com suas audiências. Diferenciamos a apropriação da plataforma por perfis políticos de direita e de esquerda e analisamos os recursos de linguagem empregados pelos políticos, tais como coreografias, dublagens, participação em trends e outros repertórios. Materiais e métodos: A partir de uma base de dados de cerca de 23 mil vídeos publicados no TikTok por um conjunto de 265 perfis ativos mantidos por políticos, foram selecionadas aleatoriamente 378 publicações. Fizemos análise de conteúdo dessa amostra para identificar o uso de recursos de linguagem e de funcionalidades específicas da plataforma, como o enquadramento em formato vertical, filtros, trilha sonora e efeitos visuais, entre outros aspectos. As hipóteses testadas foram que (H1) esses políticos tendem a não incorporar recursos e formatos populares típicos do TikTok; e (H2) eles tendem a não explorar uma linguagem lúdica, de caráter essencialmente apolítico com referências ao entretenimento. Resultados: Os resultados indicaram que a maioria dos conteúdos faz uso de recursos e formatos populares no TikTok, o que contraria a H1. Já a H2 foi confirmada. Na amostra observada, 65% dos vídeos publicados por esses perfis não utilizam qualquer elemento lúdico, nem fazem referência ao entretenimento. Entre os conteúdos com tom apolítico, 63% não possuem essa característica. Além disso, 90,5% dos conteúdos publicados não fazem qualquer esforço de interação com as audiências. Discussão: O uso eficiente do TikTok como ferramenta estratégica passa pelo entendimento da dinâmica do uso da plataforma. O estudo identificou quais estratégias geram mais engajamento na rede e como os atores políticos têm investido seus esforços em algumas dessas formas de engajamento. Conteúdos que trazem ataques e campanhas de difamação rendem muitos comentários, enquanto conteúdos de caráter apolítico, como dancinhas e dublagens, normalmente rendem mais visualizações e curtidas. Os dados podem lançar luz sobre estratégias de produção de conteúdo político para plataformas digitais e indicar discrepâncias entre os usos desses repertórios por parte de políticos de esquerda e de direita.

This paper describes a technology for modelling and rendering heterogeneous objects containing entities of various dimensionalities within a cellular-functional framework based on the implicit complex notion. Implicit complexes make it possible to combine a cellular representation and a constructive function representation. We describe a formal framework for such a hybrid representation and propose a general structure for implicit complexes. Then, we consider how an implicit complex can be described geometrically and topologically along with its associated attributes. Rendering algorithms for implicit complexes using ray-tracing are also discussed. Finally, we present a case study illustrating the proposed methods and algorithms.

Digitization of cuneiform documents is important to boost the research activity on ancient Middle East and some projects have been launched in around 2,000. However, the digitization process is laborious due to the huge scale of the documents and no trustful (semi-)automatic method has established. In this paper, we focused on a cuneiform document digitization task, realization of Optical Character Recognition (OCR) method from the handwritten copies of original materials. Currently, as the first step toward development of such methods, we are constructing a handwritten cuneiform character imageset named with professional assistance. This imageset contains typical stroke patterns for handwriting each frequently appearing cuneiform character and will be able to support the development of handwritten cuneiform OCR system.

The best recovered ordering for the CRC data set. The ordering is plotted against the survival time. The samples in the left part have higher survival times, as expected. The best recovered ordering for the CRC data set. The ordering is plotted against the four CRC histological stages (the first one is the least severe, while the fourth implies cancer metastasis): I (yellow), II (orange), III (pink), IV (red). There are considerably more samples in stage IV in the right half (16 samples) than in the left one (7 samples).

This paper formulates a novel probabilistic graphical model for noisy stimulus-evoked MEG and EEG sensor data obtained in the presence of large background brain activity. The model describes the observed data in terms of unobserved evoked and background factors with additive sensor noise. We present an expectation maximization (EM) algorithm that estimates the model parameters from data. Using the model, the algorithm cleans the stimulus-evoked data by removing interference from background factors and noise artifacts and separates those data into contributions from independent factors. We demonstrate on real and simulated data that the algorithm outperforms benchmark methods for denoising and separation. We also show that the algorithm improves the performance of localization with beamforming algorithms.

Bayesian network structures are usually built using only the data and starting from an empty network or from a naïve Bayes structure. Very often, in some domains, like medicine, a prior structure is already known based on expert knowledge. This structure can be automatically or manually refined in search for better performance models. In this work, we take Bayesian networks built by specialists and show that minor perturbations to this original network can yield better classifiers, while maintaining most of the interpretability of the original network.

Bayesian network structures are usually built using only the data and starting from an empty network or from a naïve Bayes structure. Very often, in some domains, like medicine, a prior structure knowledge is already known. This structure can be automatically or manually refined in search for better performance models. In this work, we take Bayesian networks built by specialists and show that minor perturbations to this original network can yield better classifiers with a very small computational cost, while maintaining most of the intended meaning of the original model.

In this paper, we study the behavior of the vertex-edge Wiener polynomials and their related indices under the disjunctive product of graphs. Results are applied to compute the vertex-edge Wiener indices for the disjunctive product of paths and cycles. 2010 Mathematics Subject Classification: 05C12, 05C76, 05C38.

Gaussian graphical models, where it is assumed that the variables of interest jointly follow a multivariate normal distribution with a sparse precision matrix, have been used to study intrinsic dependence among variables, but the normality assumption may be restrictive in many settings. A nonparanormal graphical model is a semiparametric generalization of a Gaussian graphical model for continuous variables where it is assumed that the variables follow a Gaussian graphical model only after some unknown smooth monotone transformation. We consider a Bayesian approach for the nonparanormal graphical model using a rank likelihood which remains invariant under monotone transformations, thereby avoiding the need to put a prior on the transformation functions. On the underlying precision matrix of the transformed variables, we consider a horseshoe prior on its Cholesky decomposition and use an efficient posterior Gibbs sampling scheme. We present a posterior consistency result on the rank-b...

Networks represent a useful tool to describe relationships among financial firms and network analysis has been extensively used in recent years to study financial connectedness. An aspect, which is often neglected, is that network observations come with errors from different sources, such as estimation and measurement errors, thus a proper statistical treatment of the data is needed before network analysis can be performed. We show that node centrality measures can be heavily affected by random errors and propose a flexible model based on the matrix-variate t distribution and a Bayesian inference procedure to de-noise the data. We provide an application to a network among European financial institutions.

With the elapse of time, financial markets have become more and more correlated. The respective literature presents different channels that have caused these interlinkages. Across financial markets, these mutual dependencies could reflect the similarities in industrial structure, monetary integration, bilateral trade, and geographical proximity. An empirical fact is that there is no unique economic determinant in supporting the integration of financial markets across different countries. However, from empirical observations, it follows that countries in close geographical proximity are more interlinked than countries in different regions The empirical fact is that, after the introduction of the euro, the return correlations among the developed markets as well as European economic and monetary union (EMU) stock markets increased considerably. The empirical observations confirm that these higher dependencies have stabilized since the introduction of the euro. During financial crises, losses tend to spread across financial institutions, thus affecting the financial system as a whole. Systemic risk measures capture the potential losses for the spreading of financial distress across institutions by capturing this increase in tail co-movement. To present this concept, Adrian and Brunnermeier (2011) developed the CoVaR method. To emphasize the systemic nature of their risk measure, they add the measures the prefix Co to the existing risk (which stands for conditional, contagion, or co-movement).

With the elapse of time, financial markets have become more and more correlated. The respective literature presents different channels that have caused these interlinkages. Across financial markets, these mutual dependencies could reflect the similarities in industrial structure, monetary integration, bilateral trade, and geographical proximity. An empirical fact is that there is no unique economic determinant in supporting the integration of financial markets across different countries. However, from empirical observations, it follows that countries in close geographical proximity are more interlinked than countries in different regions The empirical fact is that, after the introduction of the euro, the return correlations among the developed markets as well as European economic and monetary union (EMU) stock markets increased considerably. The empirical observations confirm that these higher dependencies have stabilized since the introduction of the euro. During financial crises, losses tend to spread across financial institutions, thus affecting the financial system as a whole. Systemic risk measures capture the potential losses for the spreading of financial distress across institutions by capturing this increase in tail co-movement. To present this concept, Adrian and Brunnermeier (2011) developed the CoVaR method. To emphasize the systemic nature of their risk measure, they add the measures the prefix Co to the existing risk (which stands for conditional, contagion, or co-movement).

Belief propagation (BP) is a popular method for performing probabilistic inference on graphical models. In this work, we enhance BP and propose self-guided belief propagation (SBP) that incorporates the pairwise potentials only gradually. This homotopy continuation method converges to a unique solution and increases the accuracy without increasing the computational burden. We provide a formal analysis to demonstrate that SBP finds the global optimum of the Bethe approximation for attractive models where all variables favor the same state. Moreover, we apply SBP to various graphs with random potentials and empirically show that: (i) SBP is superior in terms of accuracy whenever BP converges, and (ii) SBP obtains a unique, stable, and accurate solution whenever BP does not converge.

Belief propagation (BP) is a popular method for performing probabilistic inference on graphical models. In this work, we enhance BP and propose self-guided belief propagation (SBP) that incorporates the pairwise potentials only gradually. This homotopy continuation method converges to a unique solution and increases the accuracy without increasing the computational burden. We provide a formal analysis to demonstrate that SBP finds the global optimum of the Bethe approximation for attractive models where all variables favor the same state. Moreover, we apply SBP to various graphs with random potentials and empirically show that: (i) SBP is superior in terms of accuracy whenever BP converges, and (ii) SBP obtains a unique, stable, and accurate solution whenever BP does not converge.

This paper presents new methods for stylising video to produce cartoon motion emphasis cues and modern art. Specifically, we introduce "dynamic cues" as a class of motion emphasis cue, encompassing traditional animation techniques such as anticipation and motion exaggeration. We describe methods for automatically synthesising such cues within video premised upon the recovery of articulated figures, and the subsequent manipulation of the recovered pose trajectories. Additionally, we show how our motion emphasis framework may be applied to emulate artwork in the Futurist style, popularised by Duchamp.

Graphical models (e.g., Bayesian and constraint networks, influence diagrams, and Markov decision processes) have become a central paradigm for knowledge representation and reasoning in both artificial intelligence and computer science in general. These models are used to perform many reasoning tasks, such as scheduling, planning and learning, diagnosis and prediction, design, hardware and software verification, and bioinformatics. These problems can be stated as the formal tasks of constraint satisfaction and satisfiability, combinatorial optimization, and probabilistic inference. It is well known that the tasks are computationally hard, but research during the past three decades has yielded a variety of principles and techniques that significantly advanced the state of the art. This book provides comprehensive coverage of the primary exact algorithms for reasoning with such models. The main feature exploited by the algorithms is the model's graph. We present inference-based, message-passing schemes (e.g., variable-elimination) and search-based, conditioning schemes (e.g., cycle-cutset conditioning and AND/OR search). Each class possesses distinguished characteristics and in particular has different time vs. space behavior. We emphasize the dependence of both schemes on few graph parameters such as the treewidth, cycle-cutset, and (the pseudo-tree) height. The new edition includes the notion of influence diagrams, which focus on sequential decision making under uncertainty. We believe the principles outlined in the book would serve well in moving forward to approximation and anytime-based schemes. The target audience of this book is researchers and students in the artificial intelligence and machine learning area, and beyond.

In this paper we present a cycle-cutset driven stochastic local search algorithm which approximates the optimum of sums of unary and binary potentials, called Stochastic Tree Local Search or ST LS. We study empirically two pure variants of ST LS against the state-of-the art GLS + scheme and against a hybrid.

Graphical models (e.g., Bayesian and constraint networks, influence diagrams, and Markov decision processes) have become a central paradigm for knowledge representation and reasoning in both artificial intelligence and computer science in general. These models are used to perform many reasoning tasks, such as scheduling, planning and learning, diagnosis and prediction, design, hardware and software verification, and bioinformatics. These problems can be stated as the formal tasks of constraint satisfaction and satisfiability, combinatorial optimization, and probabilistic inference. It is well known that the tasks are computationally hard, but research during the past three decades has yielded a variety of principles and techniques that significantly advanced the state of the art. This book provides comprehensive coverage of the primary exact algorithms for reasoning with such models. The main feature exploited by the algorithms is the model's graph. We present inference-based, message-passing schemes (e.g., variable-elimination) and search-based, conditioning schemes (e.g., cycle-cutset conditioning and AND/OR search). Each class possesses distinguished characteristics and in particular has different time vs. space behavior. We emphasize the dependence of both schemes on few graph parameters such as the treewidth, cycle-cutset, and (the pseudo-tree) height. The new edition includes the notion of influence diagrams, which focus on sequential decision making under uncertainty. We believe the principles outlined in the book would serve well in moving forward to approximation and anytime-based schemes. The target audience of this book is researchers and students in the artificial intelligence and machine learning area, and beyond.

This paper is concerned with a multivariate extension of Gaussian message passing applied to pairwise Markov graphs (MGs). Gaussian message passing applied to pairwise MGs is often labeled Gaussian belief propagation (GaBP) and can be used to approximate the marginal of each variable contained in the pairwise MG. We propose a multivariate extension of GaBP (we label this GaBP-m) that can be used to estimate higher-dimensional marginals. Beyond the ability to estimate higher-dimensional marginals, GaBP-m exhibits better convergence behavior than GaBP, and can also provide more accurate univariate marginals. The theoretical results of this paper are based on an extension of the computation tree analysis conducted on univariate nodes to the multivariate case. The main contribution of this paper is the development of a convergence condition for GaBP-m that moves beyond the walk-summability of the precision matrix. Based on this convergence condition, we derived an upper bound for the number of iterations required for convergence of the GaBP-m algorithm. An upper bound on the dissimilarity between the approximate and exact marginal covariance matrices was established. We argue that GaBP-m is robust towards a certain change in variables, a property not shared by iterative solvers of linear systems, such as the conjugate gradient (CG) and preconditioned conjugate gradient (PCG) methods. The advantages of using GaBP-m over GaBP are also illustrated empirically.

This paper is concerned with a multivariate extension of Gaussian message passing applied to pairwise Markov graphs (MGs). Gaussian message passing applied to pairwise MGs is often labeled Gaussian belief propagation (GaBP) and can be used to approximate the marginal of each variable contained in the pairwise MG. We propose a multivariate extension of GaBP (we label this GaBP-m) that can be used to estimate higher-dimensional marginals. Beyond the ability to estimate higher-dimensional marginals, GaBP-m exhibits better convergence behavior than GaBP, and can also provide more accurate univariate marginals. The theoretical results of this paper are based on an extension of the computation tree analysis conducted on univariate nodes to the multivariate case. The main contribution of this paper is the development of a convergence condition for GaBP-m that moves beyond the walk-summability of the precision matrix. Based on this convergence condition, we derived an upper bound for the nu...

This paper analyses the noise present in range data measured by a Konica Minolta Vivid 910 scanner, in order to better characterise real scanner noise. Methods for denoising 3D mesh data have often assumed the noise to be Gaussian, and independently distributed at each mesh point. We show via measurements of an accurately machined almost planar test surface that real scanner data does not have such properties: the errors are not quite Gaussian, and more importantly, exhibit significant short range correlation. We use this to give a simple model for generating noise with similar characteristics. We also consider how noise varies with such factors as laser intensity, orientation of the surface, and distance from the scanner. Finally, we evaluate the performance of three typical mesh denoising algorithms using real and synthetic test data, and suggest that new denoising algorithms are required for effective removal of real noise.

We present a segmentation method for live cell images, using graph cuts and learning methods. The images used here are particularly challenging because of the shared grey-level distributions of cells and background, which only differ by their textures, and the local imprecision around cell borders. We use the P n Potts model recently presented by Kohli et al. [9]: functions on higher-order cliques of pixels are included into the traditional Potts model, allowing us to account for local texture features, and to find the optimal solution efficiently. We use learning methods to define the potential functions used in the P n Potts model. We present the model and the learning methods we used, and compare our segmentation results with similar work in cytometry. While our method performs similarly, it requires little manual tuning and thus is straightforward to adapt to other images.

Dual graph contraction reduces the number of vertices and of edges of a pair of dual image graphs while, at the same time, the topological relations among the 'surviving' components are preserved. Repeated application produces a stack of successively smaller graphs: a pair of dual irregular pyramids. The process is controlled by selected decimation parameters which consist of a subset of surviving vertices and associated contraction kernels. Equivalent contraction kernels (ECKs) combine two or more contraction kernels into one single contraction kernel which generates the same result in one single dual contraction. Decimation parameters of any individual pyramid level can be reconstructed from the ECK of the pyramid's apex if both vertices and edges of this ECK receive labels indicating their annihilation level in the pyramid. This is a labeled spanning tree (LST) of the base graph which allows e cient design and control of di erent types of dual irregular pyramids. Since the LST determines the pyramid, primitive modi cations of the LST transform also pyramids into other pyramids on the same base graph. They open a large variety of possibilities to explore the domain of 'all' pyramids.

An irregular pyramid consists of a stack of successively reduced graphs. Each smaller graph is deduced from the preceding one using contraction or removal kernels. A contraction (resp. removal) kernel defines a forest of the initial (resp. dual ) graph, each tree of this forest being reduced to a single vertex (resp. dual vertex) in the reduced graph. A combinatorial map encodes a planar graph thanks to two permutations encoding the edges and their orientation around the vertices. We present in this article a new definition of contraction and removal kernels which allows to encode the different values attached to a given vertex, dual vertex or edge along the pyramid.

This paper presents a new formalism for irregular pyramids based on combinatorial maps. The combinatorial map formalism allows us to encode a planar graph thanks to two permutations encoding the edges and the vertices of the graph.The combinatorial map formalism encode explicitly the orientation of the planar graph. This last property is useful to describe the partitions of an image which may be considered as a subset of the oriented plane IR 2 . This new constraint allows us to design interesting properties for irregular pyramids. Finally the combinatorial formalism allows us to encode e ciently the graph transformations used in irregular pyramids.

In this paper, we study the behavior of the vertex-edge Wiener polynomials and their related indices under the disjunctive product of graphs. Results are applied to compute the vertex-edge Wiener indices for the disjunctive product of paths and cycles. 2010 Mathematics Subject Classification: 05C12, 05C76, 05C38.

The computational cost of Gaussian process regression grows cubically with respect to the number of variables due to the inversion of the covariance matrix, which is impractical for data sets with more than a few thousand nodes. Furthermore, Gaussian ...

In this paper, we present an analytic-iterative Inverse Kinematics (IK) method, called Sequential IK (SIK), that reconstructs 3D human full-body movements in real time. The input data for the reconstruction is the least possible (i.e., the positions of wrists, ankles, head and pelvis) in order to be usable within a low-cost human motion capture system that would track only these six features. The performance of our approach is compared to other well-known IK methods in reconstruction quality and computation time obtaining satisfactory results for both. The paper first describes how we handle the spine and the clavicles before offering a simple joint limit model for ball-and-socket joints and a method to avoid self-collisions induced by the elbow. The second part focuses on the algorithms comparison study.

In high-dimensional vector autoregressive (VAR) models, it is natural to have large number of predictors relative to the number of observations, and a lack of efficiency in estimation and forecasting. In this context, model selection is a difficult issue and standard procedures may often be inefficient. In this paper we aim to provide a solution to these problems. We introduce sparsity on the structure of temporal dependence of a graphical VAR and develop an efficient model selection approach. We follow a Bayesian approach and introduce prior restrictions to control the maximal number of explanatory variables for VAR models. We discuss the joint inference of the temporal dependence, the maximum lag order and the parameters of the model, and provide an efficient Markov chain Monte Carlo procedure. The efficiency of the proposed approach is showed on simulated experiments and real data to model and forecast selected US macroeconomic variables with many predictors.

In high-dimensional vector autoregressive (VAR) models, it is natural to have large number of predictors relative to the number of observations, and a lack of efficiency in estimation and forecasting. In this context, model selection is a difficult issue and standard procedures may often be inefficient. In this paper we aim to provide a solution to these problems. We introduce sparsity on the structure of temporal dependence of a graphical VAR and develop an efficient model selection approach. We follow a Bayesian approach and introduce prior restrictions to control the maximal number of explanatory variables for VAR models. We discuss the joint inference of the temporal dependence, the maximum lag order and the parameters of the model, and provide an efficient Markov chain Monte Carlo procedure. The efficiency of the proposed approach is showed on simulated experiments and real data to model and forecast selected US macroeconomic variables with many predictors.

1. The concept of model  ………………………..................………………………………….. 2
2. Conceptual foundations and conceptual system ……………………………..…. 2
2.1 Theoretical Relevance ……………………………………...................……………………. 2
2.2   Models in Business Informatics - Subject Relevance ……………………….… 2
2.3   Implementation of Model Thinking - Application and Practical Relevance ....................................................................................................…...2
2.4   Model understanding ………………………..................…………………………………... 3
2.5   Modelling ………………………………………………..........................………………………. 3
2.6   Theory and Model in the Social Sciences ……......………………………………… 4
2.7 System-theoretical interpretation of Models. ………......…………………………. 5
3. Types of models …………………………………………………….....................………….… 6
3.1 Description and Capture Models ……………………….................……………………. 6
3.2 Explanatory Models ……………………………………….........................…………………. 6
3.3 Design models………………………………………...........................………………………… 7
3.4 Meta models and generic models…………….................…………………………….. 7
3.5 Other Models …………………………………………….............................…………………… 7
4. Scientific knowledge process:…………………...............…………………………………… 8
  5. Mentale Modelle ………………………………………....................…………………………… 8
  6. Model freedom for fuzzy inference systems ……...………………………………… 9

In this text, we present a Bayesian framework for active multimodal perception of 3D structure and motion. The design of this framework finds its inspiration in the role of the dorsal perceptual pathway of the human brain. Its composing models build upon a common egocentric spatial configuration that is naturally fitting for the integration of readings from multiple sensors using a Bayesian approach. In the process, we will contribute with efficient and robust probabilistic solutions for cyclopean geometry-based stereovision and auditory perception based only on binaural cues, modelled using a consistent formalisation that allows their hierarchical use as building blocks for the multimodal sensor fusion framework. We will explicitly or implicitly address the most important challenges of sensor fusion using this framework, for vision, audition and vestibular sensing. Moreover, interaction and navigation requires maximal awareness of spatial surroundings, which in turn is obtained through active attentional and behavioural exploration of the environment. The computational models described in this text will support the construction of a simultaneously flexible and powerful robotic implementation of multimodal active perception to be used in real-world applications, such as human-machine interaction or mobile robot navigation.

This paper develops a measure for bounding the performance of AND/OR search algorithms for solving a variety of queries over graphical models. We show how drawing a connection to the recent notion of hypertree decompositions allows to exploit determinism in the problem specification and produce tighter bounds. We demonstrate on a variety of practical problem instances that we are often able to improve upon existing bounds by several orders of magnitude.

The paper investigates the potential of look-ahead in the con-text of AND/OR search in graphical models using the Mini-Bucket heuristic for combinatorial optimization tasks (e.g., MAP/MPE or weighted CSPs). We present and analyze the complexity of computing the residual (a.k.a Bellman update) of the Mini-Bucket heuristic and show how this can be used to identify which parts of the search space are more likely to benefit from look-ahead and how to bound its overhead. We also rephrase the look-ahead computation as a graphical model, to facilitate structure exploiting inference schemes. We demonstrate empirically that augmenting Mini-Bucket heuristics by look-ahead is a cost-effective way of increasing the power of Branch-And-Bound search.

Given two solids A and B with piecewise smooth boundary we discuss the computation of the boundary Γ of the Minkowski sum A + B. This boundary surface Γ is part of the envelope when B is moved by translations defined by vectors a ∈ A, or vice versa. We present an efficient algorithm working for dense point clouds or for triangular meshes. Besides this, the global self intersections of the boundary Γ are detected and resolved. Additionally we point to some relations between Minkowski sums and kinematics, and compute local quadratic approximations of the envelope.