相关论文: Classifying topoi in synthetic guarded domain theo…

The language of homotopy type theory has proved to be appropriate as an internal language for various higher toposes, for example with Synthetic Algebraic Geometry for the Zariski topos. In this paper we apply such techniques to the higher…

We present an abstract unifying framework for interpreting Stone-type dualities; several known dualities are seen to be instances of just one topos-theoretic phenomenon, and new dualities are introduced. In fact, infinitely many new…

The ALEA Coq library formalizes measure theory based on a variant of the Giry monad on the category of sets. This enables the interpretation of a probabilistic programming language with primitives for sampling from discrete distributions.…

Gradually typed languages are designed to support both dynamically typed and statically typed programming styles while preserving the benefits of each. While existing gradual type soundness theorems for these languages aim to show that…

This review is an extended version of the Seoul ICM 2014 proceedings.It is a short overview of the "topological recursion", a relation appearing in the asymptotic expansion of many integrable systems and in enumerative problems. We recall…

We introduce a class of codes with overlapping code words, that we call SPO-codes. The SPO-codes are related to the Markov codes that were introduced in: G. Keller, J. Combinatorial Theory 56, (1991),pp.\ 75--83. The process of generating a…

Autoregressive models, such as the GPT family, use a fixed order, usually left-to-right, to generate sequences. However, this is not a necessity. In this paper, we challenge this assumption and show that by simply adding a positional…

Continuous time (CT) and discrete time (DT) linear time invariant (LTI) systems are commonly introduced through distinct mathematical formalisms, which can obscure their underlying dynamical equivalence. This tutorial presents a unified…

Network experiments are essential to network-related scientific research (e.g., congestion control, QoS, network topology design, and traffic engineering). However, (re)configuring various topologies on a real testbed is expensive,…

We investigate the physics of one-dimensional symmetry protected topological (SPT) phases protected by symmetries whose symmetry generators exhibit spatial modulation. We focus in particular on phases protected by symmetries with linear…

It was recently established that the formalism of the generalized transfer operator (GTO) of dynamical systems (DS) theory, applied to stochastic differential equations (SDEs) of arbitrary form, belongs to the family of cohomological…

Chain-of-Thought (CoT) has been shown to significantly improve the reasoning accuracy of large language models (LLMs) on complex tasks. However, due to the autoregressive, step-by-step generation paradigm, existing CoT methods suffer from…

This paper develops a Multiset Rewriting language with explicit time for the specification and analysis of Time-Sensitive Distributed Systems (TSDS). Goals are often specified using explicit time constraints. A good trace is an infinite…

Notions of guardedness serve to delineate admissible recursive definitions in various settings in a compositional manner. In recent work, we have introduced an axiomatic notion of guardedness in symmetric monoidal categories, which serves…

In the companion paper of the authors, a general synchronization framework was developed in the paradigmatic context of the 2D Navier-Stokes equations that allows one to precisely study the relation between the determining modes property of…

We study a cost-aware programming language for higher-order recursion dubbed $\textbf{PCF}_\mathsf{cost}$ in the setting of synthetic domain theory (SDT). Our main contribution relates the denotational cost semantics of…

Models of iterated computation, such as (completely) iterative monads, often depend on a notion of guardedness, which guarantees unique solvability of recursive equations and requires roughly that recursive calls happen only under certain…

The symplectic geometry mode decomposition (SGMD) is a powerful method for analyzing time sequences. The SGMD is based on the upper conversion via embedding and down conversion via diagonal averaging principle (DAP) inherited from the…

Human mobility modeling from GPS-trajectories and synthetic trajectory generation are crucial for various applications, such as urban planning, disaster management and epidemiology. Both of these tasks often require filling gaps in a…

This paper presents a new theory, known as robust dynamic pro- gramming, for a class of continuous-time dynamical systems. Different from traditional dynamic programming (DP) methods, this new theory serves as a fundamental tool to analyze…