Computational Complexity

The Vassiliev conjecture states that the Vassiliev invariants are dense in the space of all numerical link invariants in the sense that any link invariant is a pointwise limit of Vassiliev invariants. In this article, we prove that the Vassiliev conjecture holds in the case of the coefficients of the HOMFLY and the Kauffman polynomials. Contents 1 Reducing the problem: the weak Vassiliev conjecture 2 2 Approximation of the coefficients of the HOMFLYPT polynomial by Vassiliev invariants 3 2.1 Notations .

In this paper, a uniform approach to maximal permissiveness in modular control of discrete-event systems is proposed. It is based on three important concepts of modular closed-loops: monotonicity, distributivity, and exchangeability. Monotonicity of various closed-loops satisfying a given property considered in this paper holds whenever the underlying property is preserved under language unions. Distributivity holds if the inverse projections of local plants satisfy the given property with respect to each other. Among new results, sufficient conditions are proposed for distributed computation of supremal relatively observable sublanguages.

For supervisory control of large-scale modular DES the possibility of performing control-related computation locally (in components) is of utmost importance to computational complexity. Unlike our previous results, where the specification language is decomposable into local specification languages, this paper concerns the case of general specification languages that are neither necessarily decomposable nor contained in the global plant language. Still the conditions are found under which building of the global plant is avoided for the computation of the supremal normal sublanguages of the (global) specification language.

Modular supervisory control of discrete-event systems (DES), where the global DES is composed of local components that run concurrently, is considered. For supervisory control of large-scale modular DES the possibility of performing control-related computations locally (in components) is of utmost importance to computational complexity. Recently we have treated the case, where the specification language is decomposable into local specification languages and is included in the (global) plant language. In this paper the case of general specification languages that are neither necessarily decomposable nor contained in the global plant language is studied. Sufficient conditions are found under which any manipulation with the global plant is avoided for the computation of supremal controllable sublanguages of (global) indecomposable specification languages.

Control of modular and distributed discrete-event systems appears as an approach to handle computational complexity of synthesizing supervisory controllers for large scale systems. For both modular and distributed discrete-event systems sufficient and necessary conditions are derived for modular control synthesis to equal global control synthesis for the supremal controllable sublanguage, for the supremal normal sublanguage, and for the supremal controllalble and normal sublanguage. The modular control synthesis has a much lower computational complexity than the corresponding global control synthesis for the respective sublanguages.

A design procedure for frequency-response masking (FRM) prototype filters of cosine-modulated filter banks (CMFBs) is proposed. In the given method, we perform minimization of the maximum attenuation level in the filter's stopband, subject to intersymbol interference (ISI) and intercarrier interference (ICI) constraints. For optimization, a quasi-Newton algorithm with line search is used, and we provide simplified analytical expressions to impose the interference constraints, which greatly reduce the computational complexity of the optimization procedure. The result is lower levels of ISI and ICI for a predetermined filter order, or a reduced filter complexity for given levels of interferences. It is then illustrated how the FRM-CMFB structure is suitable for implementing filter banks with a large number of bands, yielding sharp transition bands and small roll-off factors, which is an attractive feature for a wide range of practical applications.

This paper presents an extension of Observer Theory within the context of the Ruliad, using a mathematically rigorous formalization with category theory as the unifying framework.

This paper demonstrates how the interaction between Observers and the Ruliad can give rise to hierarchical domains of reality through sampling constraints, information integration, and entropy reduction.

By formalizing the Observer as an active agent that samples and integrates information across different domains, we provide a novel approach to understanding consciousness, causation, and the nature of reality within a computational framework.

The framework reconciles discrete computational structures with apparently continuous Observer experiences, addresses the causal relationship between different domains of reality, and provides a foundation for understanding qualia through information integration within the Ruliad.

We conclude with empirical predictions and applications across physics, cognitive science, and artificial intelligence.

This is a philosophical paper. It claims that there is a gap to be filled in the relationship between complexity theory (CT) and quantum theory (QT). This gap concerns two very distinct understandings of time. The paper provides the ground for filling up such gap. Indeed, most works on complexity at large focus on the macroscopic world, leaving behind the importance of the microscopic world. This paper specifies what both worlds consist of, and argues that a solid account of the world, i.e. complexity, must necessarily take into account both dimensions of reality. Celui-ci c'est un article philosophique. Il soutient qu'il y a un gap qui doit être rempli dans la relation entre la théorie de la complexité (TC) et la théorie quantique (TQ). Ce gap consiste en ceci qu'on trouve deux compréhensions parfaitement différentes vis-à-vis le temps. Cet article fourni les bases pour remplir le gap. Il est certain, la plupart des travaux concernant la complexité se concentrent sur le monde macroscopique, et laissent de côté l'importance du monde microscopique. Ce texte rend explicite en quoi consiste chacun des deux mondes et affirme qu'un compte-rendu solide du monde, voire de la complexité doit nécessairement tenir compte des deux dimensions de la réalité.

As ecologists and foresters produce an increasing range of probabilistic data, mathematical techniques that address the fundamental interactions between stochastic events and spatial landscape features have the potential to provide valuable decision support in the sustainable management of natural resources. The heart of this thesis explores two models motivated by pressing environmental issues: limiting the spread of wildfire and invasive species containment. We formulate stochastic spatial models in graphs that capture key tradeoffs, and prove a number of original optimization results. Since even deterministic cases in highly-restricted graph classes are NP-Hard (that is, they can not efficiently be solved to optimality), our studies focus on approximation algorithms that efficiently produce solutions which are provably near-optimal. Our models also represent natural generalizations of ideas in the optimization and computer science literature. In particular, while much recent attention has been devoted to questions about connecting stochastically chosen sets, our applications in sustainable planning suggest extensions of deterministic graphcutting models; we explore novel problems in stochastic disconnection. Morgan Spencer was born on May 2, 1983 in Redmond, Washington. Gwen attended public schools in Washington State for elementary, middle, and high school, graduating from Mount Rainier High School in Des Moines, WA in 2001. From 4th through 12th grade Gwen's love of mathematics grew through involvement in her schools' math teams which were generously organized by volunteer parents and teachers. At Harvey Mudd College (Claremont, CA), Gwen chose a major in Mathematics, graduating with high distinction in 2005. Next, Gwen spent a year independently traveling the world interviewing women scientists as a Watson Fellow. Returning from this great adventure, Gwen came to Cornell University to learn about something called "Operations Research." As it turns out, this new thing involved plenty of mathematics, and a beautiful new set of ideas about algorithms. Six years after her arrival, in May 2012, Gwen expects to receive her Ph.D. in Operations Research from Cornell University, following the M.S. in Operations Research she earned in May 2010.

Cost control for the Internet access providers (AP) influences not only the nominal speeds offered to the customers, but also other, more controversial, policies related to traffic shaping and discrimination. Given that the cost for the AP is determined by the peak-hour traffic (e.g. through the 95th-percentile), the individual user contribution towards the aggregate cost is not a linear function of its byte usage. In this paper we propose a metric for evaluating the contribution each individual user has on the peak demand, that is based on Shapley value, a well known game-theoretic concept. Given the computational complexity of calculating the Shapley value, we use a Monte Carlo method for approximating it with reasonable accuracy. We employ our methodology to study a dataset that logs per-subscriber temporal usage patterns over one month period for 10K broadband subscribers of a European AP and report observed results.

Smart antenna is recognized as promising technologies for higher user capacity in 3G wireless networks by effectively reducing multipath and co-channel interference. Advent of powerful, low-cost, digital processing components and the development of software-based techniques has made smart antenna systems a practical reality for both base station and mobile station of a cellular communications systems in the next generation. The core of smart antenna is the selection of smart algorithms in adaptive array. Using beam forming algorithms the weight of antenna arrays can be adjusted to form certain amount of adaptive beam to track corresponding users automatically and at the same time to minimize interference arising from other users by introducing nulls in their directions. Thus interferences can be suppressed and the desired signals can be extracted. This research work provides description, comparative analysis and utility of various reference signal based algorithms as well as blind adaptive algorithms. Exhaustive simulation study of beam patterns and learning characteristics have proved the efficacies of the proposed work from application point of view.

This paper investigates the computational complexity of approximating several NPoptimization problems using the number of queries to an NP oracle as a complexity measure. The results show a trade-off between the closeness of the approximation and the number of queries required. For an approximation factor k(n), log log k(n) n queries to an NP oracle can be used to approximate the maximum clique size of a graph within a factor of k(n). However, this approximation cannot be achieved using fewer than log log k(n) n -c queries to any oracle unless P = NP, where c is a constant that does not depend on k. These results hold for approximation factors k(n) ≥ 2 that belong to a class of functions which includes any integer constant function, log n, log a n and n 1/a . Similar results are obtained for graph coloring, set cover and other NP-optimization problems.

We show that any 1-round 2-server Private Information Retrieval Protocol where the answers are 1-bit long must ask questions that are at least n -2 bits long, which is nearly equal to the known n -1 upper bound. This improves upon the approximately 0.25n lower bound of Kerenidis and de Wolf while avoiding their use of quantum techniques.

The paper considers scheduling problems for parallel dedicated machines subject to resource constraints. A fairly complete computational complexity classiÿcation is obtained, a number of polynomial-time algorithms are designed. For the problem with a ÿxed number of machines in which a job uses at most one resource of unit size a polynomial-time approximation scheme is o ered.

Green manufacturing is the process of producing product by minimizing natural resource use, reducing environmental pollution or wastes. Garment industry in Bangladesh plays a vital role in the country's economy. But most of these industries are indifferent to environmental regulation. A huge amount of river water is being polluted daily by the dyeing sections. So it is necessary to treat the water to a standard level before discharge. The purpose of this research is to establish an approach for the modification of dyeing section of textile industries. Before going to the approach a survey with some questionnaire was performed to identify drivers and barriers regarding green manufacturing implementation. Then these drivers and barriers were ranked with fuzzy TOPSIS tool. A system model was followed for making an approach of green manufacturing. ETP (Effluent Treatment plant) plant is suggested along with an existing dyeing process for treating waste water.

In this paper a government form is modeled as an effectivity function scheme (EFS) i.e. a parameterized family of effectivity functions having admissible (strong) weight-profiles as the relevant parameters. Working in a 2-jurisdiction outcome space we show that the existence of umpires is consistent with strong core-stability of a neo-parliamentary or mixed semi-presidential government form provided that the majority formation rule is collegial.

Owing to numerous potential applications, wireless sensor networks have been attracting significant research effort recently. The critical challenge that wireless sensor networks often face is to sustain long-term operation on limited battery energy. Coverage maintenance schemes can effectively prolong network lifetime by selecting and employing a subset of sensors in the network to provide sufficient sensing coverage over a target region. We envision future wireless sensor networks composed of a vast number of miniaturized sensors in exceedingly high density. Therefore, the key issue of coverage maintenance for future sensor networks is the scalability to sensor deployment density. In this paper, we propose a novel coverage maintenance scheme, scalable coverage maintenance (SCOM), which is scalable to sensor deployment density in terms of communication overhead (i.e., number of transmitted and received beacons) and computational complexity (i.e., time and space complexity). In addition, SCOM achieves high energy efficiency and load balancing over different sensors. We have validated our claims through both analysis and simulations.

Viewing Dehn's algorithm as a rewriting system, we generalise to allow an alphabet containing letters which do not necessarily represent group elements. This extends the class of groups for which the algorithm solves the word problem to include nilpotent groups, geometrically finite groups and fundamental groups of certain geometrically decomposable manifolds. The class has several nice closure properties. We also show that if a group has an infinite subgroup and one of exponential growth, and they commute, then it does not admit such an algorithm.

Viewing Dehn's algorithm as a rewriting system, we generalise to allow an alphabet containing letters which do not necessarily represent group elements. This extends the class of groups for which the algorithm solves the word problem to include nilpotent groups, geometrically finite groups and fundamental groups of certain geometrically decomposable manifolds. The class has several nice closure properties. We also show that if a group has an infinite subgroup and one of exponential growth, and they commute, then it does not admit such an algorithm.

This paper presents a unified theoretical framework that derives classical, quantum, and relativistic physics from the first principles of conscious observation and resonance coherence, formally integrating these into the Omniological Resonance Theory (ORT) [Schepis, 2025]. Utilizing a prime-encoded Hilbert space H p as the foundational geometry of spacetime, we introduce a model wherein physical laws emerge from the entropy-mediated collapse of symbolic phase states. These states evolve within a resonance field R(x, t) governed by the observer principle-consciousness as the primary tuning agent of physical law, formalized through the relation O • S → R. We demonstrate that the maximization of resonance coherence along geodesics directly corresponds to the classical principle of least action, reinterpreted here as the path of maximal informational congruence between observer and observed, expressed mathematically as δ

We present a stochastic approach for solving the quantumkinetic equation introduced in Part I. A Monte Carlo method based on backward time evolution of the numerical trajectories is developed. The computational complexity and the stochastic error are investigated numerically. Variance reduction techniques are applied, which demonstrate a clear advantage with respect to the approaches based on symmetry transformation. Parallel implementation is realized on a GRID infrastructure.

The in ation GI of a graph G is the line graph of the subdivision of G. If G is a complete graph the equality ir(GI) = (GI) was proved by Favaron in 1998. We conjectured that the equality holds when G is any graph of radius 1. But it turned out that it is not true. Moreover, we proved that for the class of radius 1 graphs there does not exist a better upper bound for the relation (GI)=ir(GI) then 3 2 . We found also a su cient condition for the equality (GI) = ir(GI).

We investigate the computational complexity of deciding the occurrence of many different dynamical behaviours in reaction systems, with an emphasis on biologically relevant problems (i.e., existence of fixed points and fixed point attractors). We show that the decision problems of recognising these dynamical behaviours span a number of complexity classes ranging from FO-uniform AC 0 to Π P 2 -completeness with several intermediate problems being either NP or coNP-complete.

on computers. Indeed, computer simulations and practical applications of CA usually take place in these subspaces. The second origin is connected to the question of suitability of the classical Cantor topology for the study of chaotic behavior of CA and of symbolic systems in general. We briefly recall the motivations. Consider sensitivity to initial conditions for a CA in the Cantor topology. The shift map σ, which is a very simple CA, is sensitive to initial conditions since small perturbations far from the central region are eventually brought to the central part. However, from an algorithmic point of view, the shift map is very simple. We are inclined to regard a system as chaotic if its behavior cannot easily be reconstructed. This is not the case of the shift map whose chaoticity is more an artifact of the Cantor metric, rather than an intrinsic property of the system. Therefore, one may want to define another metric in which sensitive CA not only transport information (like the shift map) but also build/destroy new information at each time step. This basic requirement stimulated the quest for alternative topologies to the classical Cantor space. This lead first to the Besicovitch topology and then to the Weyl topology in Cattaneo et al [4]. used to investigate almost periodic real functions (see Besicovitch [1] or Iwanik ). Both these pseudometrics can be defined starting from suitable semi-measures on the set Z of integers. This way of construction had a Pandora effect opening the way to many new interesting topological spaces. Some of them are reported in this paper; others can be found in Cervelle and Formenti . Each topology focuses on some peculiar aspects of the dynamics under study but all of them have a common denominator, namely non-compactness.

This paper presents a novel approach to data classification using polymorphic graph computing, which self-organizes at runtime during both training and inference. Inspired by biological neural networks, the proposed class of classifiers leverages dynamically formed computational graphs with data transformation nodes. This innovative architecture enables highly adaptable and versatile classifiers suitable for a wide range of applications, including generative tasks in natural language processing. The ability to self-organize and evolve at runtime makes these classifiers particularly well-suited for complex and dynamic data analysis tasks.

In this paper we are proposing an interleaver design i.e. power rotational interleaver. The basic purpose of this design is to reduce the bandwidth occupied by the interleaver. This approach provides an efficient result for multiple users. The complexity of this design is same as that of master random interleaver while the bandwidth requirement is reduced up to a great extent. On the basis of simulation results it is concluded that the performance of power rotational interleaver is as good as that is of random interleaver.

Web spam is a big challenge for quality of search engine results. It is very important for search engines to detect web spam accurately. In this paper we present 32 low cost quality factors to classify spam and ham pages on real time basis. These features can be divided in to three categories: (i) URL features, (ii) Content features, and (iii) Link features. We developed a classifier using Resilient Back-propagation learning algorithm of neural network and obtained good accuracy. This classifier can be applied to search engine results on real time because calculation of these features require very little CPU resources.

The Stop Number Problem arises in the management of a dial-a-ride system served by a fleet of autonomous electric vehicles. In such a system, clients request for a ride from an origin station to a destination station, and a fleet of capacitated vehicles must satisfy all requests. The goal is to minimize the number of pick-up/drop-off operations. In this paper we focus on a special case of this problem that was recently conjectured to be NP-Hard. In this regard, we show how such special case relates to other problems known in the literature in order to derive some polynomial-time solvable variants. Moreover, we provide a positive answer to the conjecture by showing that the problem is NP-Hard for any fixed capacity greater than or equal to 2, even for the case where the graph of requests is restricted to the class of planar bipartite graphs. Our proof of NP-Hardness also improves the complexity results known in the literature for the related problems identified.

We give the basic properties of discrete convolution in the space of complexity functions and its dual space. Two inequalities are identified, and defined in the general context of an arbitrary binary operation in any weighted quasi-metric space. In that setting, some quasi-metric and convergence consequences of those inequalities are proven. Using convolution, we show a method for building improver functionals in the complexity space. We also consider convolution in three topologies within the dual space, obtaining two topological monoids.

In this paper, the problem of maximizing the number of active users satisfying a required quality of service (QoS) in n-user interference channels is investigated. This problem is known as an NP-complete problem. We introduce an efficient suboptimal algorithm, relying on the ...

This paper proposes a traffic model and a parameter fitting procedure that are capable of achieving accurate prediction of the queuing behavior for IP traffic exhibiting long-range dependence. The modeling process is a discrete-time batch Markovian arrival process (dBMAP) that jointly characterizes the packet arrival process and the packet size distribution. In the proposed dBMAP, packet arrivals occur according to a discrete-time Markov modulated Poisson process (dMMPP) and each arrival is characterized by a packet size with a general distribution that may depend on the phase of the dMMPP. The fitting procedure is designed to provide a close match of both the autocovariance and the marginal distribution of the packet arrival process, using a dMMPP; a packet size distribution is fitted individually to each state of the dMMPP. A major feature of the procedure is that the number of states of the fitted dBMAP is not fixed a priori; it is determined as part of the procedure itself. In this way, the procedure allows establishing a compromise between the accuracy of the fitting and the number of parameters, while maintaining a low computational complexity. We apply the inference procedure to several traffic traces exhibiting long-range dependence. Very good results were obtained since the fitted dBMAPs match closely the autocovariance, the marginal distribution and the queuing behavior of the measured traces. Our results also show that ignoring the packet size distribution and its correlation with the packet arrival process can lead to large errors in terms of queuing behavior.

Brain Computer Interface (BCI) systems translate brain rhythms into signals comprehensible by computers. BCI has numerous applications in the clinical domain, the computer gaming, and the military. Real-time analysis of single trial brain signals is a challenging task, due to the low SNR of the incoming signals, added noise due to muscle artifacts, and trial-to-trial variability. In this work we present a computationally lightweight classification method based on several time and frequency domain features. After preprocessing and filtering, wavelet transform and Short Time Fourier Transform (STFT) are used for feature extraction. Feature vectors which are extracted from θ and α frequency bands are classified using a Support Vector Machine (SVM) classifier. EEG data were recorded from 64 electrodes during three different Go/NoGo tasks. We achieved 91% classification accuracy for two-class discrimination. The high recognition rate and low computational complexity makes this approach a...

Context-based Adaptive Binary Arithmetic Coder (CABAC) is the advanced entropy coding tool employed by main and higher profiles of H.264/AVC. In these applications, hardware acceleration is needed as the computational load of CABAC is high. To improve the implementation time, Graphical Processing Unit (GPU) NVIDIA GeForce 820M has been used. This paper describes the design and GPU implementation of CABAC and comparative study of Discrete Wavelet Transform (DWT) and without DWT for threedimensional (3-D) medical image compression systems. The proposed system architectures were simulated in MATLAB. Implementation results on Magnetic Resonance Image (MRI) and Computed Tomography (CT) images with GPU and Central Processing Unit (CPU) are presented, showing GPU significantly outperformed with respect to a single-threaded CPU implementation. These results revealed that GPU is the best candidate for image compression application. In overall, CT and MRI modalities with DWT outperform in ter...

Abstract—The search for lightweight authentication protocols suitable for low-cost RFID tags constitutes an active and challenging research area. In this context, a family of protocols based on the LPN problem has been proposed: the so-called HB-family. Despite the rich literature regarding the cryptanalysis of these protocols, there are no published results about the impact of fault analysis over them. The purpose of this paper is to fill this gap by presenting a fault analytic method against a prominent member of the HB-family: HB + protocol. We demonstrate that the fault analysis model can lead to a flexible and effective attack against HB-like protocols, posing a serious threat over them. Index Terms—Fault analysis, authentication protocols, HB + protocol, RFID systems. I.

When numerical simulations are time consuming, the simulator is replaced by a simple (meta-)model which approximates its behavior. This surrogate model is adjusted on a set of carefully chosen computer experiments, or Design of Experiments (DoE), with the objective of obtaining the best possible approximation with available computational budget. For the widely used Gaussian process models, Mutual Information (MI) is a particularly attractive DoE quality measure. Finding the set of configurations that optimise the MI criterion is a NP-hard problem, and in this paper we concentrate on the sequential construction of designs by greedily maximising MI. Unfortunately, even this much simpler problem is still computationally demanding, still involving prohibitively large running times. We propose a new algorithm for the sequential construction of MI-optimal designs that shares computational costs across several candidate points, enabling a significant reduction of computing time. In particu...

Justification Logic is an emerging field that studies provability, knowledge, and belief via explicit proofs or justifications that are part of the language. There exist many justification logics closely related to modal epistemic logics of knowledge and belief. Instead of modality in pure justification logics, or in addition to modality in hybrid logics, which has an existential epistemic reading 'there exists a proof of F ,' all justification logics use constructs t : F , where a justification term t represents a blueprint of a Hilbert-style proof of F . The first justification logic, LP, introduced by Sergei Artemov, was shown to be a justification counterpart of modal logic S4 and serves as a missing link between S4 and Peano arithmetic, thereby solving a long-standing problem of provability semantics for S4 and Int. The machinery of explicit justifications can be used to analyze well-known v epistemic paradoxes, e.g. Gettier's examples of justified true belief that can hardly be considered knowledge, and to find new approaches to the concept of common knowledge. Yet another possible application is the Logical Omniscience Problem, which reflects an undesirable property of knowledge as described by modality when an agent knows all the logical consequences of his/her knowledge. The language of justification logic opens new ways to tackle this problem. This thesis focuses on quantitative analysis of justification logics. We explore their decidability and complexity of Validity Problem for them. A closer analysis of the realization phenomenon in general and of one procedure in particular enables us to deduce interesting corollaries about selfreferentiality for several modal logics. A framework for proving decidability of various justification logics is developed by generalizing the Finite Model Property. Limitations of the method are demonstrated through an example of an undecidable justification logic. We study reflected fragments of justification logics and provide them with an axiomatization and a decision procedure whose complexity (the upper bound) turns out to be uniform for all justification logics, both pure and hybrid. For many justification logics, we also present lower and upper complexity bounds. vii I would also like to mention Vladimir Uspensky, who inspired me to go into Mathematical Logic, and Tatiana Yavorskaya (Sidon), who helped me make the first logical steps. My mathematical consciousness was shaped by my high-school teacher Vera Petrovna Filinova. It all really started with her relentless devotion to the purity and rigor of mathematics. I have been fortunate to work alongside colleagues and friends whose suggestions and personalities have had a profound effect on my work and on how I feel about it: Eva Antonakos, Amotz Bar-Noy, Walter Dean, Evan Goris, Eric Pacuit, Bryan Renne, Stathis Zachos. I also thank Arnon Avron, Balder ten Cate, Paul Égré, Valentin Goranko, Wojtek Jamroga, Natalia Rubtsova for suggestions provided at various conferences. I thank CUNY Graduate Center and the Research Foundation of CUNY for their financial support. Needless to say, nothing would have happened in the first place without my family and their ever-lasting support: my musician mother, who has had to put up with her math-inclined son; my father; my grandfather, who have taught me to be strong; my late grandmother, who has taught me to be kind; my uncle, who has helped me to combine these two and still tries to teach viii me to restrict the use of binary logic to math only; Stas and Noemi, who have taught me how to be a New Yorker; my little niece, who is an eternal source of joy and happiness for everybody around her. And of course I could not have made it this far without Galina, who has made my life sound and complete and dramatically increased my personal complexity by means of duality, at the same time simplifying all decision procedures.

We first show that the optimal and undominated outcomes of an unconstrained (and possibly cyclic) CP-net are the solutions of a set of hard constraints. We then propose a new algorithm for finding the optimal outcomes of a constrained CPnet which makes use of hard constraint solving. Unlike previous algorithms, this new algorithm works even with cyclic CP-nets. In addition, the algorithm is not tied to CP-nets, but can work with any preference formalism which produces a preorder over the outcomes. We also propose an approximation method which weakens the preference ordering induced by the CP-net, returning a larger set of outcomes, but provides a significant computational advantage. Finally, we describe a weighted constraint approach that allows to find good solutions even when optimals do not exist.

We show that any two pseudoconfigurations of n points in general position in the plane are transformable into each other by a finite sequence of elementary transformations of two types, generalizing a theorem of Ringel. This result is used to prove Tverberg-type theorems for pseudoconfigurations and the Partition Conjecture is shown to be true for a new class of convexity spaces.

We show that any two pseudoconfigurations of n points in general position in the plane are transformable into each other by a finite sequence of elementary transformations of two types, generalizing a theorem of Ringel. This result is used to prove Tverberg-type theorems for pseudoconfigurations and the Partition Conjecture is shown to be true for a new class of convexity spaces.

Game boards are described in the Ludii general game system by their underlying graphs, based on tiling, shape and graph operators, with the automatic detection of important properties such as topological relationships between graph elements, directions and radial step sequences. This approach allows most conceivable game boards to be described simply and succinctly.

Clustering techniques are very attractive for identifying and extracting patterns of interests from datasets. However, their application to very large spatial datasets presents numerous challenges such as high-dimensionality, heterogeneity, and high complexity of some algorithms. Distributed clustering techniques constitute a very good alternative to the Big Data challenges (e.g., Volume, Variety, Veracity, and Velocity). In this paper, we developed and implemented a Dynamic Parallel and Distributed clustering (DPDC) approach that can analyse Big Data within a reasonable response time and produce accurate results, by using existing and current computing and storage infrastructure, such as cloud computing. The DPDC approach consists of two phases. The first phase is fully parallel and it generates local clusters and the second phase aggregates the local results to obtain global clusters. The aggregation phase is designed in such a way that the final clusters are compact and accurate while the overall process is efficient in time and memory allocation. DPDC was thoroughly tested and compared to wellknown clustering algorithms BIRCH and CURE. The results show that the approach not only produces high-quality results but also scales up very well by taking advantage of the Hadoop MapReduce paradigm or any distributed system.

We propose a unified formalism that identifies the event horizon, the Riemann Hypothesis critical line, and symbolic resonance collapse as structurally equivalent phenomena marking the transition from quantized identity to continuous gravitational integration. Through the symbolic resonance framework developed for both computational complexity and quantum number theory, we demonstrate that the boundary where symbolic identity collapses into field coherence is the very fabric of gravitational manifestation. The loss of symbolic distinction within an attractor is not a metaphor-it is the act of observation, the genesis of gravity, and the dimensional reduction that defines spacetime curvature. This approach builds upon established results in quantum decoherence theory [Zurek, 2003], holographic encoding of spacetime [Susskind, 1995], and recent formulations of gravity as entropic force [Verlinde, 2011].

The problem addressed in this work is that of enhancing speech signals corrupted by additive noise and improving the performance of automatic speech recognizers in noisy conditions. The enhanced speech signals can also improve the intelligibility of speech in noisy conditions for human listeners with hearing impairment as well as for normal listeners. The original Phase Opponency (PO) model, proposed to detect tones in noise, simulates the processing of the information in neural discharge times and exploits the frequency-dependent phase properties of the tuned filters in the auditory periphery along with the cross-auditory-nerve-fiber coincidence detection to extract temporal cues. The Modified Phase Opponency (MPO) proposed here alters the components of the PO model in such a way that the basic functionality of the PO model is maintained but the various properties of the model can be analyzed and modified independently of each other. This work presents a detailed mathematical formulation of the MPO model and the relation between the properties of the narrowband signal that needs to be detected and the properties of the MPO model. vi LIST OF TABLES 1.1 Comparison of performance of human speech perception and ASR in speech-shaped noise conditions. Numbers indicate accuracies in percentage.

We present a formal synthesis between Möbius Collapse Logic (MCL) and the Entropic Resonance framework. While MCL models computation as a topological field collapse structured by resonance weight hierarchies and Möbius self-transformations, Entropic Resonance grounds computational and physical reality in prime-number Hilbert spaces, entropy-driven resonance collapse, and consciousness-derived symbolic phase fields. We demonstrate that MCL's constructs naturally embed within Entropic Resonance as specific topological manifestations of prime-resonance symbolic dynamics. This unification reveals profound connections between computational field theory, number-theoretic resonance structures, and quantum consciousness models. Our framework provides testable predictions at the intersection of topological computation and quantum information theory, suggesting that computational collapse processes may exhibit prime-structured resonance patterns detectable through phase coherence measurements. The synthesis not only elucidates deeper relationships between computation, entropy, quantum mechanics, and consciousness, but also offers a complete ontology linking field topology, number theory, and semantic resonance with implications for quantum gravity, non-local computation, and the mathematics of consciousness.