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This paper studies recurrence phenomena in iterative holomorphic dynamics of certain multi-valued maps. In particular, we prove an analogue of the Poincar\'e recurrence theorem for meromorphic correspondences with respect to certain…
Symbolic models are abstract descriptions of continuous systems in which symbols represent aggregates of continuous states. In the last few years there has been a growing interest in the use of symbolic models as a tool for mitigating…
A new approach to the phenomenon of large numbers coincidence leads to unexpected results. No matter how strange it might sound, the exact value of cosmological parameters and their analytical expression through fundamental constants have…
Let X be a subshift satisfy non-uniform structure. In this paper, we give quantitative estimate of the recurrence sets. These results can be applied to a large class of symbolic systems, including beta-shifts, S-gap shifts and their…
Recent progress of symbolic dynamics of one- and especially two-dimensional maps has enabled us to construct symbolic dynamics for systems of ordinary differential equations (ODEs). Numerical study under the guidance of symbolic dynamics is…
We present a certain generalization of a recent result of M. I. Cirnu on linear recurrence relations with coefficient in progressions [2]. We provide some interesting examples related to some well-known integer sequences, such as Fibonacci…
We develop a theory of limits of finite posets in close analogy to the recent theory of graph limits. In particular, we study representations of the limits by functions of two variables on a probability space, and connections to…
We introduce the idea of *representation stability* (and several variations) for a sequence of representations V_n of groups G_n. A central application of the new viewpoint we introduce here is the importation of representation theory into…
Building on the theory of symbolic extensions and uniform generators for discrete transformations we develop a similar theory for topological regular flows. In this context a symbolic extension is given by a suspension flow over a subshift.
Quantum mechanics led to spectacular technological developments, discovery of new constituents of matter and new materials. However there is still no consensus on its interpretation and limitations. Some scientists and scientific writers…
The known fundamental symmetries and interactions are well described by the Standard Model. Features of this powerful theory, which are described but not deeper explained, are addressed in a variety of speculative models. Experimental tests…
Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results…
This work shows that the recently discovered operator contraction identity for solving the discreet Path Integral of the harmonic oscillator can be applied equally to fermions in any dimension. This then yields an exactly solvable model for…
The compactness phenomenon is one of the featured aspects of structuralism in mathematics. In simple and broad words, a compactness property holds in a structure if a related property is satisfied by sufficiently many substructures of that…
The different notions of matings of pairs of equal degree polynomials are introduced and are related to each other as well as known results on matings. The possible obstructions to matings are identified and related. Moreover the relations…
Over the past 50 years many have debated what representation should be used to capture the meaning of natural language utterances. Recently new needs of such representations have been raised in research. Here I survey some of the…
We introduce the notion of strong regular embeddings of Deligne-Mumford stacks. These morphisms naturally arise in the related contexts of generalized Euler sequences and hypertoric geometry.
Inspired by empirical work in neuroscience for Bayesian approaches to brain function, we give a unified probabilistic account of various types of symbolic reasoning from data. We characterise them in terms of formal logic using the…
We consider the question of continuity of limit sets for sequences of geometrically finite subgroups of isometry groups of rank-one symmetric spaces, and prove analogues of classical (Kleinian) theorems in this context. In particular we…
Research on integrated neural-symbolic systems has made significant progress in the recent past. In particular the understanding of ways to deal with symbolic knowledge within connectionist systems (also called artificial neural networks)…