相关论文: Perpendicular Indiscernible Sequences in Real Clos…

I study peer effects that arise from irreversible decisions in the absence of a standard social equilibrium. I model a latent sequence of decisions in continuous time and obtain a closed-form expression for the likelihood, which allows to…

We introduce a fundamental concept -- closed sets of correlations -- for studying non-local correlations. We argue that sets of correlations corresponding to information-theoretic principles, or more generally to consistent physical…

We analyze further the IR singularities that appear in noncommutative field theories on R^d. We argue that all IR singularities in nonplanar one loop diagrams may be interpreted as arising from the tree level exchanges of new light degrees…

Informal lecture notes with examples on sheaf theory and the derived category of sheaves; sheaves and Morse theory; perverse sheaves, and some applications to representation theory. Added Oct 2021: cellular perverse sheaves. Proofs are…

Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…

The article determines the asymptotic shape of the extremal clusters in stationary regularly varying random fields. To deduce this result, we present a general framework for the Poisson approximation of point processes on Polish spaces…

These lecture notes cover basic automata-theoretic concepts and logical formalisms for the modeling and verification of concurrent and distributed systems. Many of these concepts naturally extend the classical automata and logics over…

This paper introduces a novel reachability problem for the scenario involving two agents, where one agent follows another agent using a feedback strategy. The geometry of the reachable set for an agent, termed \emph{dependent reachable…

This series of papers models the dynamics of a large set of interacting neurons within the framework of statistical field theory. The system is described using a two-field model. The first field represents the neuronal activity, while the…

There are two very important subjects in physics: Symmetry of dynamical models and nonlinearity. All really fundamental models are invariant under some particular symmetry groups. There is also no true physics, no our Universe and life at…

This is a non-standard paper, containing some problems, mainly in model theory, which I have, in various degrees, been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me,…

The predictability of a sequence is defined as the asymptotic performance of the best performing predictor in a given class. The value of the predictability of a sequence will in general depend on the choice of this predictor class. The…

Connection between the concept of entanglement and origin of nonlinear phenomena in optics is discussed.

The field of algorithmic randomness studies what it means for infinite binary sequences to be random for some given uncertainty model. Classically, martingale-theoretic notions of such randomness involve precise uncertainty models, and it…

Since early machine learning models, metrics such as accuracy and precision have been the de facto way to evaluate and compare trained models. However, a single metric number doesn't fully capture the similarities and differences between…

As Large Language Models (LLMs) become increasingly widespread, understanding how specific training data shapes their outputs is crucial for transparency, accountability, privacy, and fairness. To explore how LLMs leverage and replicate…

The concept of distance covariance/correlation was introduced recently to characterize dependence among vectors of random variables. We review some statistical aspects of distance covariance/correlation function and we demonstrate its…

This monograph, written for educational purposes, serves as an introduction to the concept of integrability as it applies to systems of differential equations (both ordinary and partial) as well as to vector-valued fields. The general cases…

Large cardinals arising from the existence of arbitrarily long end elementary extension chains over models of set theory are studied here. In particular, we show that the large cardinals obtained that way (`Unfoldable cardinals') behave as…

Decomposable dependency models possess a number of interesting and useful properties. This paper presents new characterizations of decomposable models in terms of independence relationships, which are obtained by adding a single axiom to…