相关论文: New examples of $M\setminus L$: intruder sets

Spectrahedra are sets defined by linear matrix inequalities. Projections of spectrahedra are called semidefinitely representable sets. Both kinds of sets are of practical use in polynomial optimization, since they occur as feasible sets in…

The problem of identifying regions of spatially interesting, different or adversarial behavior is inherent to many practical applications involving distributed multisensor systems. In this work, we develop a general framework stemming from…

An integrable polygon is one whose interior angles are fractions of $\pi$; that is to say of the form $\frac \pi n$ for positive integers $n$. We consider the Laplace spectrum on these polygons with the Dirichlet and Neumann boundary…

We show how the traversable wormhole induced by a double-trace deformation of the thermofield double state can be understood as a modular inclusion of the algebras of exterior operators. The effect of this deformation is the creation of a…

Backdoor attacks pose a serious security threat to large language models (LLMs), which are increasingly deployed as general-purpose assistants in safety- and privacy-critical applications. Existing LLM backdoors rely primarily on…

We summarize recent results initiating spectral analysis on pseudo-Riemannian locally symmetric spaces $\Gamma \backslash G/H$, beyond the classical setting where $H$ is compact (e.g. theory of automorphic forms for arithmetic $\Gamma$) or…

Kernel mean embeddings, a widely used technique in machine learning, map probability distributions to elements of a reproducing kernel Hilbert space (RKHS). For supervised learning problems, where input-output pairs are observed, the…

Most finite element methods for solving time-harmonic wave-propagation problems lead to a linear system with a non-normal coefficient matrix. The non-normality is due to boundary conditions and losses. One way to solve these systems is to…

I suggest an extension of the SM by introducing a dark sector with the local $U(1)_{D}$ symmetry. The particles in the dark sector bring about the new physics beyond the SM. In particular the global $B-L$ symmetry is violated just above the…

Federated self-supervised learning (FSSL) has recently emerged as a promising paradigm that enables the exploitation of clients' vast amounts of unlabeled data while preserving data privacy. While FSSL offers advantages, its susceptibility…

Locally Decodable Codes (LDCs) are error-correcting codes for which individual message symbols can be quickly recovered despite errors in the codeword. LDCs for Hamming errors have been studied extensively in the past few decades, where a…

In spite of its many successes, the Standard Model makes many empirical assumptions in the Higgs and fermion sectors for which a deeper theoretical basis is sought. Starting from the usual gauge symmetry $u(1) \times su(2) \times su(3)$…

We are concerned with an harmonic analysis in Hilbert spaces $L^2(\mu)$, where $\mu$ is a probability measure on $\br^n$. The unifying question is the presence of families of orthogonal (complex) exponentials $e_\lambda(x) = \exp(2\pi i…

We introduce local iterated function systems and present some of their basic properties. A new class of local attractors of local iterated function systems, namely local fractal functions, is constructed. We derive formulas so that these…

We describe a new and distinctive interferometry in which a probe particle scatters off a superposition of locations of a single free target particle. In one dimension, probe particles incident on superposed locations of a single "mirror"…

The paper established sufficient conditions of predictability with degeneracy for the spectrum at $M$-periodically located isolated points on the unit circle. It is also shown that $m$-periodic subsequences of these sequences are also…

We study general M-estimators of location on Riemannian manifolds, extending classical notions such as the Frechet mean by replacing the squared loss with a broad class of loss functions. Under minimal regularity conditions on the loss…

Despite being very successful in explaining the wide range of precision experimental results obtained so far, the Standard Model (SM) of elementary particles fails to address two of the greatest observations of the recent decades: tiny but…

Let $X=G/H$ be a reductive homogeneous space with $H$ noncompact, endowed with a $G$-invariant pseudo-Riemannian structure. Let $L$ be a reductive subgroup of $G$ acting properly on $X$ and $\Gamma$ a torsion-free discrete subgroup of $L$.…

We consider a class of functions defined on metric spaces which generalizes the concept of piecewise Lipschitz continuous functions on an interval or on polyhedral structures. The study of such functions requires the investigation of their…