Related papers: The strength of the Inner Model Hypothesis
Computational simulations are a popular method for testing hypotheses about the emergence of communication. This kind of research is performed in a variety of traditions including language evolution, developmental psychology, cognitive…
We prove the two theorems of the title, settling two long standing questions in the local theory of singular minimal hypersurfaces. The sharpness of either result is with respect to its hypothesis on the size of the allowable singular sets.…
This is an introduction of a book called "strong regularity", to appear at Ast\'erisque, containing: 1) Yoccoz' proof of Jakobson theorem www.college-de-france.fr/media/jean-christophe-yoccoz/UPL7416254474776698194_Jakobson_jcy.pdf 2)…
The goal of this article is to initiate a discussion on what it takes to claim "there is no new physics at the weak scale," namely that the Standard Model (SM) is "isolated." The lack of discovery of beyond the SM (BSM) physics suggests…
As large language models (LLMs) are overwhelmingly more and more integrated into various applications, ensuring they generate safe responses is a pressing need. Previous studies on alignment have largely focused on general…
For interval polynomial matrices, we identify the minimal testing set, whose stability can guarantee that of the whole uncertain set. Our results improve the conclusions given by Kamal and Dahleh.
The aim of this article is to simplify Pfanzagl's proof of consistency for asymptotic maximum likelihood estimators, and to extend it to more general asymptotic M-estimators. The method relies on the existence of a sort of contraction of…
This paper investigates the robust stability and stabilization analysis of interval fractional-order systems with time-varying delay. The stability problem of such systems is solved first, and then using the proposed results a stabilization…
When M is a finitely generated graded module over a standard graded algebra S and I is an ideal of S, it is known from work of Cutkosky, Herzog, Kodiyalam, R\"omer, Trung and Wang that the Castelnuovo-Mumford regularity of I^mM has the form…
Discussion of "On the Birnbaum Argument for the Strong Likelihood Principle" by Deborah G. Mayo [arXiv:1302.7021].
This study develops a framework for testing hypotheses on structural parameters in incomplete models. Such models make set-valued predictions and hence do not generally yield a unique likelihood function. The model structure, however,…
A robust minimax test for two composite hypotheses, which are determined by the neighborhoods of two nominal distributions with respect to a set of distances - called $\alpha-$divergence distances, is proposed. Sion's minimax theorem is…
Critical Infrastructures like power and communication networks are highly interdependent on each other for their full functionality. Many significant research have been pursued to model the interdependency and failure analysis of these…
The Uniform Information Density (UID) hypothesis proposes that effective communication is achieved by maintaining a stable flow of information. In this work, we revisit this principle in the context of Large Language Model (LLM) reasoning,…
This paper consists of two related parts. In the first part we give a self-contained proof of homological stability for the spaces C_n(M;X) of configurations of n unordered points in a connected open manifold M with labels in a…
This is a preliminary version of a monograph on homogeneous dynamics and application to some problems of unlikely intersections in Shimura varieties. It consists of four articles, which can be read independently. The first one, by the two…
The Maximal Information Coefficient (MIC) of Reshef et al. (Science, 2011) is a statistic for measuring dependence between variable pairs in large datasets. In this note, we prove that MIC is a consistent estimator of the corresponding…
In this article we present three robust instability mechanisms for linear and nonlinear inverse problems. All of these are based on strong compression properties (in the sense of singular value or entropy number bounds) which we deduce…
The h-index (Hirsch, 2005) is robust, remaining relatively unaffected by errors in the long tails of the citations-rank distribution, such as typographic errors that short-change frequently-cited papers and create bogus additional records.…
We introduce varying spin strengths to the Ising model, a central pillar of statistical physics. With inhomogeneous physical systems in mind, but also anticipating interdisciplinary applications, we present the model on network structures…