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The main purpose of this survey is to provide an introduction, algebro-topological in nature, to Hirzebuch-type inequalities for plane curve arrangements in the complex projective plane. These inequalities gain more and more interest due to…
Some basic features of confinement are reviewed, in particular the symmetry patterns of the dual dynamics. Open problems and possible directions of progress are discussed.
The phenomenological implications of a low-energy supersymmetry are surveyed, with particular attention given to unification constraints and the role of a large top quark Yukawa couplings. Generic expectations for sparticle mass spectra are…
Cutting and packing problems are present in many, at first glance unconnected, areas, therefore it's beneficial to have a good understanding of their underlying structure, to select proper techniques for finding solutions. Cutting and…
The so-called algebraic approach to the constraint satisfaction problem (CSP) has been a prevalent method of the study of complexity of these problems since early 2000's. The core of this approach is the notion of polymorphisms which…
Partial descriptions of the Universe are presented in the form of linear equations considered in the free (full, super) Fock space. The universal properties of these equations are discussed. The closure problem caused by computational and…
In this work we propose a novel task framework under which a variety of physical reasoning puzzles can be constructed using very simple rules. Under sparse reward settings, most of these tasks can be very challenging for a reinforcement…
It is argued that the two problems of choosing characterizations and models of complex systems should not be considered independently. A particular criterion for these choices, oriented on the potential usefulness of the results, is…
There are many conceivable possibilities of embedding the MSSM in string theory. These proceedings describe an approach which is based on grand unification in higher dimensions. This allows one to obtain global string-derived models with…
We explore the problem of step-wise explaining how to solve constraint satisfaction problems, with a use case on logic grid puzzles. More specifically, we study the problem of explaining the inference steps that one can take during…
We formulate and analyze the compound information bottleneck programming. In this problem, a Markov chain $ \mathsf{X} \rightarrow \mathsf{Y} \rightarrow \mathsf{Z} $ is assumed with fixed marginal distributions $\mathsf{P}_{\mathsf{X}}$…
An instance of a random constraint satisfaction problem defines a random subset S (the set of solutions) of a large product space (the set of assignments). We consider two prototypical problem ensembles (random k-satisfiability and…
We have a lot of relation to the encoding and the Theory of Information, when considering thinking. This is a natural process and, at once, the complex thing we investigate. This always was a challenge - to understand how our mind works,…
We provide here a proof theoretic account of constraint programming that attempts to capture the essential ingredients of this programming style. We exemplify it by presenting proof rules for linear constraints over interval domains, and…
Ecological systems, as is often noted, are complex. Equally notable is the generalization that complex systems tend to be oscillatory, whether Huygens simple patterns of pendulum entrainment or the twisted chaotic orbits of Lorenz…
This paper draws on diverse areas of computer science to develop a unified view of computation: (1) Optimization in operations research, where a numerical objective function is maximized under constraints, is generalized from the numerical…
We produce a class of $\omega$-categorical structures with finite signature by applying a model-theoretic construction -- a refinement of the Hrushosvki-encoding -- to $\omega$-categorical structures in a possibly infinite signature. We…
We study a popular puzzle game known variously as Clickomania and Same Game. Basically, a rectangular grid of blocks is initially colored with some number of colors, and the player repeatedly removes a chosen connected monochromatic group…
Creating a quantitative theory for the cortex presents challenges and raises questions. What are the significant scales--micro, meso, or macroscopic? What are the interactions--pairwise, higher order, or mean-field? And what control…
Incorporating constraints is a major concern in probabilistic machine learning. A wide variety of problems require predictions to be integrated with reasoning about constraints, from modelling routes on maps to approving loan predictions.…