Related papers: Uniform Unfolding and Analytic Measurability
We study the class of potential games that are also graphical games with respect to a given graph $G$ of connections between the players. We show that, up to strategic equivalence, this class of games can be identified with the set of…
We study analytic deformations and unfoldings of holomorphic foliations in complex projective plane $\mathbb{C}P(2)$. Let $\{\mathcal{F}_t\}_{t \in \mathbb{D}_{\epsilon}}$ be topological trivial (in $\mathbb{C}^2$) analytic deformation of a…
Finite games in normal form and their mixed extensions are a corner stone of noncooperative game theory. Often generic finite games and their mixed extensions are considered. But the properties which one expects in generic games and the…
We investigate (2,1):1 structures, which consist of a countable set $A$ together with a function $f: A \to A$ such that for every element $x$ in $A$, $f$ maps either exactly one element or exactly two elements of $A$ to $x$. These…
Orbit-finite models of computation generalise the standard models of computation, to allow computation over infinite objects that are finite up to symmetries on atoms, denoted by $\mathbb{A}$. Set theory with atoms is used to reason about…
A complex-analytic structure within the unit disk of the complex plane is presented. It can be used to represent and analyze a large class of real functions. It is shown that any integrable real function can be obtained by means of the…
We consider the notion of the matrix (tensor) distribution of a measurable function of several variables. On the one hand, it is an invariant of this function with respect to a certain group of transformations of variables; on the other…
The unfolding of detector effects is crucial for the comparison of data to theory predictions. While traditional methods are limited to representing the data in a low number of dimensions, machine learning has enabled new unfolding…
Given partial information about a set, we are interested in fully recovering the original set from what is given. If a set encodes itself robustly, any partial information about the set suffices to fully recover the information about the…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that typically arise from applying decision rules…
We introduce the category of b-analytic manifolds, a natural tool to define constructible sheaves and functions up to infinity. We study with some details the operations on these objects and also recall the Radon transform for constructible…
Consider a probability measure supported by a regular geodesic ball in a manifold. For any p larger than or equal to 1 we define a stochastic algorithm which converges almost surely to the p-mean of the measure. Assuming furthermore that…
Building on the work of Avraham, Rubin, and Shelah, we aim to build a variant of the Fra\"iss\'e theory for uncountable models built from finite submodels. With this aim, we generalize the notion of an increasing set of reals to other…
In this paper, we develop a general machinery for finding explicit uniform probability and moment bounds on sub-additive positive functionals of random processes. Using the developed general technique, we derive uniform bounds on the…
In this thesis a connection between the worlds of discrete and continuous conformal geometry is explored. Specifically, a disk pattern production theroem is proved using an energy which measures how ``uniform'' the angle data of a…
We cover some useful techniques in computational aspects of analytic number theory, with specific emphasis on ideas relevant to the evaluation of L-functions. These techniques overlap considerably with basic methods from analytic number…
We investigate the ability of decoder-only transformer models to perform abstract symbolic reasoning; specifically solving propositional logic reasoning problems given in-context. Previous work demonstrated that models fail to generalize to…
The notion of homomorphism indistinguishability offers a combinatorial framework for characterizing equivalence relations of graphs, in particular equivalences in counting logics within finite model theory. That is, for certain graph…
We show pro-definability of spaces of definable types in various classical complete first order theories, including complete o-minimal theories, Presburger arithmetic, $p$-adically closed fields, real closed and algebraically closed valued…
Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…