Related papers: A virtual substitution of Brouwer choice sequence

Let $W$ be an infinite word over finite alphabet $A$. We get combinatorial criteria of existence of interval exchange transformations that generate the word W.

We consider the problem of sequential prediction and provide tools to study the minimax value of the associated game. Classical statistical learning theory provides several useful complexity measures to study learning with i.i.d. data. Our…

Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…

In this project, we will study the Brauer group that was first defined by R. Brauer. The elements of the Brauer group are the equivalence classes of finite dimensional central simple algebra. Therefore understanding the structure of the…

We introduce an infinite family of quantum enhancements of the biquandle counting invariant we call biquandle virtual brackets. Defined in terms of skein invariants of biquandle colored oriented knot and link diagrams with values in a…

This paper describes an alternative method of generating fixed points of certain substitution systems. This method centres on taking infinite words consisting of one repeated letter per word. These infinite words are then interlaced to form…

A new general procedure for a priori selection of more predictable events from a time series of observed variable is proposed. The procedure is applicable to time series which contains different types of events that feature significantly…

In this work we propose a new type of shift spaces, called blur shift spaces, where one can represent with a single symbol an entire set of infinite symbols. Such shift spaces are constructed from classical shift spaces, by choosing some…

We will derive a function that eliminates any sequence of equidistant numbers from the integer numbers, then we will derive its inverse. Then we will use the Sequence elimination function to eliminate the multiples of the prime numbers from…

Classification may not be reliable for several reasons: noise in the data, insufficient input information, overlapping distributions and sharp definition of classes. Faced with several possibilities neural network may in such cases still be…

Transition from Fourier series to Fourier integrals is considered and error introduced by ordinary substitution of integration for summing is estimated. Ambiguity caused by transition from discrete function to continuous one is examined and…

Number sequences defined by a linear recursion relation are studied by means of generating functions. Indices of the terms in the recursion relation have arbitrary differenses. In addition to formulas for the nth term an algorithm is…

From the simplest point of view, transseries are a new kind of expansion for real-valued functions. But transseries constitute much more than that--they have a very rich (algebraic, combinatorial, analytic) structure. The set of transseries…

We show that the closure of the value set of a real linear recurrence sequence is the union of a countable set and a finite collection of intervals. Conversely, any finite collection of closed intervals is the closure of the value set of…

To render a sequence testable, namely capable of identifying and detecting errors, it is necessary to apply a transformation that increases its length by introducing statistical dependence among symbols, as commonly exemplified by the…

Sequential design is a highly active field of research in active learning which provides a general framework for designing computer experiments with limited computational budgets. It aims to create efficient surrogate models to replace…

The theoretical existence of Busy Beaver numbers provides a new notion for decidability and corresponding heuristic for conjectures. The minimum number of states in which a conjecture can be modeled gives a classification of what logic…

Online sequence prediction is the problem of predicting the next element of a sequence given previous elements. This problem has been extensively studied in the context of individual sequence prediction, where no prior assumptions are made…

The sort transform (ST) is a modification of the Burrows-Wheeler transform (BWT). Both transformations map an arbitrary word of length n to a pair consisting of a word of length n and an index between 1 and n. The BWT sorts all rotation…

Near-vector spaces extend linear algebra tools to non-linear algebraic structures, enabling the study of non-linear problems. However, explicit constructions remain rare. This paper introduces a broad computable family of near-vector…