Related papers: The Schur Algorithm in Terms of System Realization
The study of factoring relations between subshifts or cellular automata is central in symbolic dynamics. Besides, a notion of intrinsic universality for cellular automata based on an operation of rescaling is receiving more and more…
We consider the set \mathcal{R}_{n} of rational functions of degree at most n\geq1 with no poles on the unit circle \mathbb{T} and its subclass \mathcal{R}_{n,\, r} consisting of rational functions without poles in the annulus \left\{\xi:\;…
A procedure is introduced which allows to represent the dynamics of a non-equilibrium system violating detailed balance by its steady state loop fluxes. It is shown that detailed balance is restored in this representation, such that the…
In the present paper, we construct an algorithm for the evaluation of real Riemann zeta function $\zeta(s)$ for all real $s$, $s>1$, in polynomial time and linear space on Turing machines in Ko-Friedman model. The algorithms is based on a…
To reliably model real robot characteristics, interval linear systems of equations allow to describe families of problems that consider sets of values. This allows to easily account for typical complexities such as sets of joint states and…
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…
Graph embeddings are a ubiquitous tool for machine learning tasks, such as node classification and link prediction, on graph-structured data. However, computing the embeddings for large-scale graphs is prohibitively inefficient even if we…
It is well known that we can use structural proof theory to refine, or generalize, existing paradigmatic computational primitives, or to discover new ones. Under such a point of view we keep developing a programme whose goal is establishing…
Reinforcement learning and classical planning are typically seen as two distinct problems, with differing formulations necessitating different solutions. Yet, when humans are given a task, regardless of the way it is specified, they can…
Operator systems are the unital self-adjoint subspaces of the bounded operators on a Hilbert space. Complex operator systems are an important category containing the C*-algebras and von Neumann algebras, which is increasingly of interest in…
Machine learning models increasingly function as representational systems, yet the philosoph- ical assumptions underlying their internal structures remain largely unexamined. This paper develops a structuralist decision framework for…
With the goal of providing the foundations for a rigorous study of modules of bicomplex holomorphic functions, we develop a general theory of functional analysis with bicomplex scalars. Even though the basic properties of bicomplex number…
This article is devoted to the sharp improvement of the classical Bohr inequality for bounded analytic functions defined on the unit disk. We also prove two other sharp versions of the Bohr inequality by replacing the constant term by the…
It has been shown that a functional interpretation of proofs in mathematical analysis can be given by the product of selection functions, a mode of recursion that has an intuitive reading in terms of the computation of optimal strategies in…
Recent work on recurrence in quantum walks has provided a representation of Schur functions in terms of unitary operators. We propose a generalization of Schur functions by extending this operator representation to arbitrary operators on…
Introduced by Okounkov and Reshetikhin, the Schur process is known to be a determinantal point process, meaning that its correlation functions are minors of a single correlation kernel matrix. Previously, this was derived using…
It is first shown that when the Schr\"{o}dinger equation for a wave function is written in the polar form, complete information about the system's {\em quantum-ness} is separated out in a single term $Q$, the so called `quantum potential'.…
The theory of computational complexity focuses on functions and, hence, studies programs whose interactive behavior is reduced to a simple question/answer pattern. We propose a broader theory whose ultimate goal is expressing and analyzing…
There is a known generalization of the classical Schwarz lemma to holomorphic functions from the polydisk to the disk. In this paper, we characterize those functions which satisfy equality everywhere in this generalized inequality: they are…
We propose an extension of the framework for discussing the computational complexity of problems involving uncountably many objects, such as real numbers, sets and functions, that can be represented only through approximation. The key idea…