An NNF circuit is a directed acyclic graph (DAG), where each leaf is labelled with either true/false or a literal, and each inner node represents either a conjunction (∧) or a disjunction (∨). A decomposable NNF (DNNF) is an NNF satisfying the decomposabi- lity property for each conjunction node. The C-BDMC language generalizes the DNNF language. In a C-BDMC, the leaves can contain CNF formulae from a given base class C. In this paper, we focus only on renamable Horn formulae. We experimentally compare the sizes of d-BDMC and d-DNNF representations. We describe a new compilation langu- age, called cara DNNF (c-DNNF), that generalizes the DNNF language. A c-DNNF circuit can be considered as a compressed representation of a DNNF circuit. We present a new experimental knowledge compiler, called CaraCompiler, for converting a CNF formula into a d-BDMC or a (c)d-DNNF circuit. CaraCompiler is based on the state-of-the-art compiler D4. Also, we mention some extensions for the compiler D4, such as caching hypergraph cuts that can reduce the compilation times. 1

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This thesis questions the connection between knowledge and finance and advances an account that links both in a two-folded way. The first level departs from what separates the two opposite views or alternative explanations about the value of knowledge. The source and essence of the extra profits in information goods or commodities, such as digital media contents and software, featuring increasing returns to scale owing to their peculiar cost structure manifested by a high fixed cost and very low constant marginal cost, is what separates the two views about the value of knowledge. In light of the near-decomposability/modularity hypothesis, the extra profits in information commodities should arise from &#039 / information hiding,&#039 / which is intrinsic to nearly-decomposable systems or modular architecture because they are built on an ignorance on the parts in regard to the other parts and the whole of system. Such (hidden) design information that gives rise to parts or modules creates, at the same time, the future paths of action or (real) options, according to real-options perspective. When the two perspectives are combined, knowledge production, as distinct from subsequent knowledge commodity production, basically becomes an option creation process. Then, it becomes possible to argue that the concurrence of knowledge and finance is not a coincidence at all because the logics of accumulation is no different but almost identical, which is the second level of the two-folded account attempted in this study. The main contribution of this thesis is to build an account that links financialization to knowledge via the notion of modularity. Such an account sees financialization as a reflection and consequence of a value-driven permanent innovation economy developed under the &#039 / IT paradigm&#039 / in order to exploit a surplus peculiar and intrinsic to the modular structure that makes &#039 / information hiding&#039 / an integral part of such architectures since they are by definition built on an ignorance on the parts in regard to the other parts and the whole of system.

This thesis questions the connection between knowledge and finance and advances an account that links both in a two-folded way. The first level departs from what separates the two opposite views or alternative explanations about the value of knowledge. The source and essence of the extra profits in information goods or commodities, such as digital media contents and software, featuring increasing returns to scale owing to their peculiar cost structure manifested by a high fixed cost and very low constant marginal cost, is what separates the two views about the value of knowledge. In light of the near-decomposability/modularity hypothesis, the extra profits in information commodities should arise from &#039 / information hiding,&#039 / which is intrinsic to nearly-decomposable systems or modular architecture because they are built on an ignorance on the parts in regard to the other parts and the whole of system. Such (hidden) design information that gives rise to parts or modules creates, at the same time, the future paths of action or (real) options, according to real-options perspective. When the two perspectives are combined, knowledge production, as distinct from subsequent knowledge commodity production, basically becomes an option creation process. Then, it becomes possible to argue that the concurrence of knowledge and finance is not a coincidence at all because the logics of accumulation is no different but almost identical, which is the second level of the two-folded account attempted in this study. The main contribution of this thesis is to build an account that links financialization to knowledge via the notion of modularity. Such an account sees financialization as a reflection and consequence of a value-driven permanent innovation economy developed under the &#039 / IT paradigm&#039 / in order to exploit a surplus peculiar and intrinsic to the modular structure that makes &#039 / information hiding&#039 / an integral part of such architectures since they are by definition built on an ignorance on the parts in regard to the other parts and the whole of system.

Soit F ∈ Z[X1, . . . ,Xn] une forme décomposable, c’est-à-dire un polynôme homogène de degré d qui peut être factorisé en formes linéaires sur C. Notons NF (m) le nombre de solutions entières à l’inégalité |F(x)| ≤ m et VF (m) le volume de l’ensemble {x ∈ Rn :|F(x)| ≤ m}. En 2001, Thunder [19] a prouvé une conjecture de W.M. Schmidt, énonçant que, sous des conditions de finitude appropriées, on a NF (m) << m n/d où la constante implicite ne dépend que de n et d. En outre, il a montré une formule asymptotique NF (m) = m n/d V (F) + OF (m n/(d+n−2)) où, cependant, la constante implicite dépend de F. Dans des articles ultérieurs, la préoccupation de Thunder était d’obtenir une formule asymptotique similaire, mais avec la borne supérieure du terme d’erreur |NF (m) −m n/dV (F)| ne dépendant que de n et d. Dans [20] et [22], il a réussi à prouver que si gcd(n, d) = 1, la constante implicite dans le terme d’erreur peut en effet être fonction uniquement de n et d. L’objectif principal de cette thèse est d’étendre les résultats de Thunder au cadre p-adique. `A savoir, nous sommes intéressés par les solutions à l’inégalité |F(x)| · |F(x)|p1 . . . |F(x)|pr ≤ m en x = (x1, x2, . . . ,xn) ∈ Zn avec gcd(x1, x2, . . . ,xn, p1 · · · pr) = 1. (5.4.9) où p1, . . . , pr sont des nombres premiers distincts et |·|p désigne la valeur absolue p-adique habituelle. Le chapitre 1 est consacré au cadre p-adique de ce problème et aux preuves des lemmes auxiliaires. Le chapitre 2 est consacré à l’extension des résultats de Thunder de [19]. Dans le chapitre 3, nous montrons l’effectivité de la condition sous laquelle le nombre de solutions de (5.4.9) est fini. Le chapitre 4 et le chapitre 5 généralisent les résultats de Thunder dans [20], [21] et [22]. / Let F ∈ Z[X1, . . . ,Xn] be a decomposable form, that is, a homogeneous polynomial of degree d which can be factored into linear forms over C. Denote by NF (m) the number of integer solutions to the inequality |F(x)| ≤ m and by VF (m) the volume of the set{x ∈ Rn : |F(x)| ≤ m}. In 2001, Thunder [19] proved a conjecture of W.M. Schmidt, stating that, under suitable finiteness conditions, one has NF (m) << mn/d where the implicit constant depends only on n and d. Further, he showed an asymptotic formula NF (m) = mn/dV (F) + OF (mn/(d+n−2)) where, however, the implicit constant depends on F. In subsequent papers, Thunder’s concern was to obtain a similar asymptotic formula, but with the upper bound of the error term |NF (m)−mn/dV (F)| depending only on n and d. In [20] and [22], hemanaged to prove that if gcd(n, d) = 1, the implicit constant in the error term can indeed be made depending only on n and d.The main objective of this thesis is to extend Thunder’s results to the p-adic setting. Namely, we are interested in solutions to the inequality |F(x)| · |F(x)|p1 . . . |F(x)|pr ≤ m in x = (x1, x2, . . . ,xn) ∈ Zn with gcd(x1, x2, . . . ,xn, p1 · · · pr) = 1. (5.4.3)where p1, . . . , pr are distinct primes and | · |p denotes the usual p-adic absolute value.Chapter 1 is devoted to the p-adic set-up of this problem and to the proofs of the auxiliary lemmas. Chapter 2 is devoted to extending Thunder’s results from [19]. In chapter 3, we show the effectivity of the condition under which the number of solutions of (5.4.3) is finite. Chapter 4 and chapter 5 generalize Thunder’s results from [20], [21] and [22].

This thesis consists of four papers studying structure learning and Bayesian inference in probabilistic graphical models for both undirected and directed acyclic graphs (DAGs). Paper A presents a novel algorithm, called the Christmas tree algorithm (CTA), that incrementally construct junction trees for decomposable graphs by adding one node at a time to the underlying graph. We prove that CTA with positive probability is able to generate all junction trees of any given number of underlying nodes. Importantly for practical applications, we show that the transition probability of the CTA kernel has a computationally tractable expression. Applications of the CTA transition kernel are demonstrated in a sequential Monte Carlo (SMC) setting for counting the number of decomposable graphs. Paper B presents the SMC scheme in a more general setting specifically designed for approximating distributions over decomposable graphs. The transition kernel from CTA from Paper A is incorporated as proposal kernel. To improve the traditional SMC algorithm, a particle Gibbs sampler with a systematic refreshment step is further proposed. A simulation study is performed for approximate graph posterior inference within both log-linear and decomposable Gaussian graphical models showing efficiency of the suggested methodology in both cases. Paper C explores the particle Gibbs sampling scheme of Paper B for approximate posterior computations in the Bayesian predictive classification framework. Specifically, Bayesian model averaging (BMA) based on the posterior exploration of the class-specific model is incorporated into the predictive classifier to take full account of the model uncertainty. For each class, the dependence structure underlying the observed features is represented by a distribution over the space of decomposable graphs. Due to the intractability of explicit expression, averaging over the approximated graph posterior is performed. The proposed BMA classifier reveals superior performance compared to the ordinary Bayesian predictive classifier that does not account for the model uncertainty, as well as to a number of out-of-the-box classifiers. Paper D develops a novel prior distribution over DAGs with the ability to express prior knowledge in terms of graph layerings. In conjunction with the prior, a stochastic optimization algorithm based on the layering property of DAGs is developed for performing structure learning in Bayesian networks. A simulation study shows that the algorithm along with the prior has superior performance compared with existing priors when used for learning graph with a clearly layered structure. / <p>QC 20170915</p>

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The thesis considers a representation of a discrete multidimensional probability distribution using an apparatus of compositional models, and focuses on the theoretical background and structure of search space for structure learning algorithms in the framework of such models and particularly focuses on the subclass of decomposable models. Based on the theoretical results, proposals of basic learning techniques are introduced and compared.

The diploma thesis is focused on possibility of usage biologically decompostable wastes in the biogas plant. The first part of this thesis describes principal production of the manure gas and as well concrete biogas plants, where are shown different approaches and technologies. The main target of the thesis is based on biogas plant design for manipulation with biologically communal wastes from VUT v Brno and chosen parts of Brno. To the proper design of the biogas plant precede evaluation of accesible wastes from choosen localities. Since we consider wastes from households, the way of collection of those wastes is designed. The thesis also consider economic balance and assesment of the biogas plant. Investment costs are predicted, process costs are evaluated and as well profit from selling of the electric energy is consider, profits from charges for manipulation with wastes and profits from selling of compost.

This thesis considers the modulation division based on the concept of uniquely factorable constellation pair (UFCP) and uniquely decodable constellation group (UDCG) in multiuser wireless communication networks. We first consider a two-hop relay network consisting of two single-antenna users and a two-antenna relay node, for which a novel distributed concatenated Alamouti code is devised. This new design allows the source and relay nodes to transmit their own information to the destination node concurrently at the symbol level with the aid of the UFCP generated from both PSK and square QAM constellations as well as by jointly processing the noisy signals received at the relay node. Moreover, an asymptotic symbol error probability (SEP) formula is derived for the ML receiver, showing that the maximum diversity gain function is achieved, which is proportional to $\ln \mathtt{SNR}/\mathtt{SNR}^2$. Then, we concentrate on the point-to-point correlated multiple-input and multiple-output (MIMO) communication systems where full knowledge of channel state information (CSI) is available at the receiver and only the first- and second-order statistics of the channels are available at the transmitter. When the number of antenna elements of both ends goes to infinity while keeping their ratio constant, the asymptotic SEP analysis is carried out for either optimally precoded or uniformly precoded correlated large MIMO fading channels using the zero-forcing (ZF) detector with equally likely PAM, PSK or square QAM constellations. For such systems, we reveal some very nice structures which inspire us to explore two very useful mathematical tools (i.e., the Szego's theorem on large Hermitian Toeplitz matrices and the well-known limit: $\lim_{x\to\infty}(1+1/x)^x=e$), for the systematic study of asymptotic behaviors on their error performance. This new approach enables us to attain a very simple expression for the SEP limit as the number of the available antenna elements goes to infinity. In what follows, the problem of precoder design using a zero-forcing decision-feedback (ZF-DF) detector is also addressed. For such a MIMO system, our principal goal is to efficiently design an optimal precoder that minimizes the asymptotic SEP of the ZF-DF detector under a perfect decision feedback. By fully taking advantage of the product majorization relationship among eigenvalues, singular-values and Cholesky values of the precoded channel matrix parameters, a necessary condition for the optimal solution to satisfy is first developed and then the structure of the optimal solution is characterized. With these results, the original non-convex problem is reformulated into a convex one that can be efficiently solved by using an interior-point method. In addition, by scaling up the antenna array size of both terminals without bound for such a network, we propose a novel method as we did for the ZF receiver scenario to analyze the asymptotic SEP performance of an equal-diagonal QRS precoded large MIMO system when employing an abstract Toeplitz correlation model for the transmitter antenna array. This new approach has a simple expression with a fast convergence rate and thus, is efficient and effective for error performance evaluation. For multiuser communication networks, we first consider a discrete-time multiple-input single-output (MISO) Gaussian broadcast channel (BC) where perfect CSI is available at both the transmitter and all the receivers. We propose a flexible and explicit design of a uniquely decomposable constellation group (UDCG) based on PAM and rectangular QAM constellations. With this new concept, a modulation division (MD) transmission scheme is developed for the considered MISO BC. The proposed MD scheme enables each receiver to uniquely and efficiently recover their desired signals from the superposition of mutually interfering cochannel signals in the absence of noise. Using max-min fairness as a design criterion, the optimal transmitter beamforming problem is solved in a closed-form for two-user MISO BC. Then, for a general case with more than two receivers, a user-grouping based beamforming scheme is developed, where the grouping method, beamforming vector design and power allocation problems are addressed by employing weighted max-min fairness. Then, we consider an uplink massive single-input and multiple-output (SIMO) network consisting of a base station (BS) and several single-antenna users. To recover the transmitted signal matrix of all the users when the antenna array size is large, a novel multi-user space-time modulation (MUSTM) scheme is proposed for the considered network based on the explicit construction of QAM uniquely-decomposable constellation groups (QAM-UDCGs). In addition, we also develop a sub-constellation allocation method at the transmitter side to ensure the signal matrix is always invertible. In the meanwhile, an efficient training correlation receiver (TCR) is proposed which calculates the correlation between the received sum training signal vector and the sum information carrying vector. Moreover, the optimal power allocation problems are addressed by maximizing the coding gain or minimizing the average SEP of the received sum signal under both average and peak power constraints on each user. The proposed transmission scheme not only allows the transmitted signals with strong mutual interference to be decoded by a simple TCR but it also enables the CSI of all the users to be estimated within a minimum number of time slots equal to that of the users. Comprehensive computer simulations are carried out to verify the effectiveness of the proposed uniquely decomposable space-time modulation method in various network topologies and configurations. Our modulation division method will be one of the promising technologies for the fifth generation (5G) communication systems. / Dissertation / Doctor of Philosophy (PhD)