Related papers: Rotational component spaces for infinite-type tran…

This paper focuses on the equivalent expression of fractional integrals/derivatives with an infinite series. A universal framework for fractional Taylor series is developed by expanding an analytic function at the initial instant or the…

Several recent works have developed a new, probabilistic interpretation for numerical algorithms solving linear systems in which the solution is inferred in a Bayesian framework, either directly or by inferring the unknown action of the…

We study unirational algebraic varieties and the fields of rational functions on them. We show that after adding a finite number of variables some of these fields admit an infinitely transitive model. The latter is an algebraic variety with…

Compositional generalization, the ability to recognize familiar parts in novel contexts, is a defining property of intelligent systems. Although modern models are trained on massive datasets, they still cover only a tiny fraction of the…

As countless examples show, it can be fruitful to study a sequence of complicated objects all at once via the formalism of generating functions. We apply this point of view to the homology and combinatorics of orbit configuration spaces:…

We derive exact matrix integral representations for different sums over partitions. The characteristic feature of all obtained matrix models is the presence of logarithmic (or, vice versa, exponential) terms in the potential. Our derivation…

We construct the first examples of rationally convex surfaces in the complex plane with hyperbolic complex tangencies. In fact, we give two very different types of rationally convex surfaces: those that admit analytic fillings by…

In translation surfaces of finite area (corresponding to holomorphic differentials), directions of saddle connections are dense in the unit circle. On the contrary, saddle connections are fewer in translation surfaces with poles…

We compute the higher topological complexity of ordered configuration spaces of orientable surfaces, thus extending Cohen-Farber's description of the ordinary topological complexity of those spaces.

A momentum-space approach to conformal field theory offers a new perspective on cosmological correlators and better reveals the underlying connections to scattering amplitudes. This thesis explores the interplay between integral…

We classify irreducible unitary representations of the group of all infinite matrices over a $p$-adic field ($p\ne 2$) with integer elements equipped with a natural topology. Any irreducible representation passes through a group $GL$ of…

We analyze the possibility of defining infinite-dimensional manifolds as ringed spaces. More precisely, we consider three definitions of manifolds modeled on locally convex spaces: in terms of charts and atlases, in terms of ringed spaces,…

We define a notion of (one-sided) shift spaces over infinite alphabets. Unlike many previous approaches to shift spaces over countable alphabets, our shift spaces are compact Hausdorff spaces. We examine shift morphisms between these shift…

The concept of permutograph is introduced and properties of integral functions on permutographs are established. The central result characterizes the class of integral functions that are representable as lattice polynomials. This result is…

We analyze here Hamiltonian stationary surfaces in the complex projective plane as (local) solutions to an integrable system, formulated as a zero curvature on a loop group. As an application, we show in details why such tori are finite…

There are three types of results in this paper. The first, extending a representation theorem on a conformal mapping that omits two values of equal modulus. This was due to Brickman and Wilken. They constructed a representation as a convex…

We study the computational and structural aspects of countable two-dimensional SFTs and other subshifts. Our main focus is on the topological derivatives and subpattern posets of these objects, and our main results are constructions of…

We present a new approach to termination analysis of logic programs. The essence of the approach is that we make use of general orderings (instead of level mappings), like it is done in transformational approaches to logic program…

A surface in a Riemannian space is called of constant astigmatism if the difference between the principal radii of curvatures at each point is a constant function. In this paper we give a classification of all rotational surfaces of…

Syntactic theory has traditionally adopted a constructivist approach, in which a set of atomic elements are manipulated by combinatory operations to yield derived, complex elements. Syntactic structure is thus seen as the result or discrete…