相关论文: Phantom depth and stable phantom exactness

In this work, we present a high-order finite volume framework for the numerical simulation of shallow water flows. The method is designed to accurately capture complex dynamics inherent in shallow water systems, particularly suited for…

The search for a Dark Matter particle is the new grail and hard-sought nirvana of the particle physics community. From the theoretical side, it is the main challenge to provide a consistent and model-independent tool for comparing the…

Let $(R,\mathfrak{m})$ be a Noetherian local ring and $M$ a finitely generated $R$-module. We say $M$ has maximal depth if there is an associated prime $\mathfrak{p}$ of $M$ such that depth $M=\dim R/\mathfrak{p}$. In this paper, we study…

We introduce relative preresolving subcategories and precoresolving subcategories of an abelian category and define homological dimensions and codimensions relative to these subcategories respectively. We study the properties of these…

We present FDM (Fan Duality Model), a linear sequence architecture that resolves the fundamental tension between memory efficiency and associative recall in sequence modeling. FDM separates sequence processing into two components: a wave…

In analogy to the well-known notion of finite--state compressibility of individual sequences, due to Lempel and Ziv, we define a similar notion of "finite-state encryptability" of an individual plaintext sequence, as the minimum asymptotic…

Understanding why Transformers perform so well remains challenging due to their non-convex optimization landscape. In this work, we analyze a shallow Transformer with $m$ independent heads trained by projected gradient descent in the kernel…

We study the so-called Gray filtration on the set of phantom maps between two spaces. Using both its algebraic characterization and the Sullivan completion approach to phantom maps, we generalize some of the recent results of Le, McGibbon…

We analyze the resurgence properties of finite-dimensional exponential integrals which are prototypes for partition functions in quantum field theories. In these simple examples, we demonstrate that perturbation theory, even at arbitrarily…

In this paper, we discuss the black hole complementarity and the firewall proposal at length. Black hole complementarity is inevitable if we assume the following five things: unitarity, entropy-area formula, existence of an information…

The quantum-classical isomorphism for self-consistent field theory, which allows quantum particles in space-time to be represented as classical one-dimensional threads embedded in a five dimensional thermal-space-time, is summarized and…

The density of states, even for a perfectly ordered tight-binding model, can exhibit a tail-like feature at the top of the band, provided the hopping integral falls off in space slowly enough. We apply the coherent potential approximation…

In this paper we give general criteria on tightness and weak convergence of discrete Markov chains to symmetric jump processes on metric measure spaces under mild conditions. As an application, we investigate discrete approximation for a…

We establish an inequality involving colengths of the tight closure of ideals of systems of parameters in local rings with some mild conditions. As an application, we prove and refine a result by Goto and Nakamura, conjectured by Watanabe…

In this article, we investigate the quantum circuit complexity and entanglement entropy in the recently studied black hole gas framework using the two-mode squeezed states formalism written in arbitrary dimensional spatially flat…

We prove a result on approximate recovery, with high probability, of subgroups of a finite nonabelian group $\Gamma$ from their random perturbations. We use this for ad-hoc sequences of $\Gamma_n$ while passing to the continuum limit, in…

Methods for reconstructing the topology of complex networks from time-resolved observations of node dynamics are gaining relevance across scientific disciplines. Of biggest practical interest are methods that make no assumptions about…

Functional depth is the functional data analysis technique that orders a functional data set. Unlike the case of data on the real line, defining this order is non-trivial, and particularly, with functional data, there are a number of…

Cosmological observations of the recent universe suggest that dark energy equation of state parameter $w$ is growing with time, departing from a cosmological constant for which $w=-1$. Standard quintessence models allow for a varying…

Many scientific and engineering applications feature nonsmooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the nonsmooth objective is equipped with…