相关论文: Generating Compatibility Conditions in Mathematica…

The construction of frames for a Hilbert space H can be equated to the decomposition of the frame operator as a sum of positive operators having rank one. This realization provides a different approach to questions regarding frames with…

Compositional generalization is a crucial property in artificial intelligence, enabling models to handle novel combinations of known components. While most deep learning models lack this capability, certain models succeed in specific tasks,…

We conduct the first detailed analysis in quantum information of recently derived operator relations from the study of quantum one-way local operations and classical communications (LOCC). We show how operator structures such as operator…

Coherence is an essential property of well-written texts, that refers to the way textual units relate to one another. In the era of generative AI, coherence assessment is essential for many NLP tasks; summarization, generation, long-form…

The problem of matching a query string to a directed graph, whose vertices are labeled by strings, has application in different fields, from data mining to computational biology. Several variants of the problem have been considered,…

Quantum coherence has received significant attention in recent years, but its study is mostly conducted in single party settings. In this paper, we generalize important results in multipartite entanglement theory to their counterparts in…

We explore higher-dimensional conformal field theories (CFTs) in the presence of a conformal defect that itself hosts another sub-dimensional defect. We refer to this new kind of conformal defect as the composite defect. We elaborate on the…

Conformal field theories with correlation functions which have logarithmic singularities are considered. It is shown that those singularities imply the existence of additional operators in the theory which together with ordinary primary…

We consider the issue of vacuum misalignment induced by four-Fermi couplings in a generic strongly coupled four-dimensional gauge theory. After briefly reviewing the general formalism, we focus on the case of partial compositness-like…

We study intrinsic simulations between cellular automata and introduce a new necessary condition for a CA to simulate another one. Although expressed for general CA, this condition is targeted towards surjective CA and especially linear…

Perfect phylogeny consisting of determining the compatibility of a set of characters is known to be NP-complete. We propose in this article a conjecture on the necessary and sufficient conditions of compatibility: Given a set $\mathcal{C}$…

We study the behavior of infinite systems of coupled harmonic oscillators as t->infinity, and generalize the Central Limit Theorem (CLT) to show that their reduced Wigner distributions become Gaussian under quite general conditions. This…

We consider the equivalence problem of four-dimensional semi-Riemannian metrics with the $2$-dimensional Abelian Killing algebra. In the generic case we determine a semi-invariant frame and a fundamental set of first-order scalar…

We construct explicit generators for the higher scissors congruence K-theory of the line. We use this to derive an explicit generating set for the homology of the group of interval exchange transformations. Our proof makes use of an…

In the classical synthesis problem, we are given an LTL formula \psi over sets of input and output signals, and we synthesize a system T that realizes \psi: with every input sequences x, the system associates an output sequence T(x) such…

We consider Galerkin approximations of holomorphic Fredholm operator eigenvalue problems for which the operator values don't have the structure "coercive+compact". In this case the regularity (in sense of [O. Karma, Numer. Funct. Anal.…

Operator learning has emerged as a new paradigm for the data-driven approximation of nonlinear operators. Despite its empirical success, the theoretical underpinnings governing the conditions for efficient operator learning remain…

Using first principles from inference, we design a set of functionals for the purposes of \textit{ranking} joint probability distributions with respect to their correlations. Starting with a general functional, we impose its desired…

For iterative learning control (ILC), one of the basic problems left to address is how to solve the contradiction between convergence conditions for the output tracking error and for the input signal (or error). This problem is considered…

Neural sequence-to-sequence models are currently the predominant choice for language generation tasks. Yet, on word-level tasks, exact inference of these models reveals the empty string is often the global optimum. Prior works have…