Related papers: Algorithmic Proof of the Epsilon Constant Conjectu…

We describe a rigorous construction, using matched asymptotic expansions, which establishes under very general conditions that local terrestrial and solar-system experiments will measure the effects of varying `constants' of Nature…

The arrival of AI techniques in computations, with the potential for hallucinations and non-robustness, has made trustworthiness of algorithms a focal point. However, trustworthiness of the many classical approaches are not well understood.…

We prove the formal degree conjecture for simple supercuspidal representations of symplectic groups and quasi-split even special orthogonal groups over a p-adic field, under the assumption that p is odd. The essential part is to compute the…

The Local Converse Problem is to determine how the family of the local gamma factors $\gamma(s,\pi\times\tau,\psi)$ characterizes the isomorphism class of an irreducible admissible generic representation $\pi$ of $\mathrm{GL}_n(F)$, with…

Raghavendra (STOC 2008) gave an elegant and surprising result: if Khot's Unique Games Conjecture (STOC 2002) is true, then for every constraint satisfaction problem (CSP), the best approximation ratio is attained by a certain simple…

We suspect that the ``genus part'' of the class number of a number field K may be an obstruction for an ``easy proof'' of the classical p-rank epsilon-conjecture for p-class groups and, a fortiori, for a proof of the ``strong…

For nonconvex optimization in machine learning, this article proves that every local minimum achieves the globally optimal value of the perturbable gradient basis model at any differentiable point. As a result, nonconvex machine learning is…

Under certain general conditions, an explicit formula to compute the greatest delta-epsilon function of a continuous function is given. From this formula, a new way to analyze the uniform continuity of a continuous function is given.…

Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that,…

We give a constant factor polynomial time pseudo-approximation algorithm for min-sum clustering with or without outliers. The algorithm is allowed to exclude an arbitrarily small constant fraction of the points. For instance, we show how to…

This paper considers the finite element solution of the boundary value problem of Poisson's equation and proposes a guaranteed em a posteriori local error estimation based on the hypercircle method. Compared to the existing literature on…

We propose a new gradient descent algorithm with added stochastic terms for finding the global optimizers of nonconvex optimization problems. A key component in the algorithm is the adaptive tuning of the randomness based on the value of…

Any Littlestone class, or stable graph, has finite sets which function as ``virtual elements'': these can be seen from the learning side as representing hypotheses which are expressible as weighted majority opinions of hypotheses in the…

The efficient simulation of quantum dynamics and ground states is a central challenge in physics and a key frontier for quantum advantage. While short-time evolution in one-dimensional systems can often be simulated classically, extending…

Many beautiful experiments have been addressed to test standard quantum mechanics against local realistic models. Even if a strong evidence favouring standard quantum mechanics is emerged, a conclusive experiment is still lacking, because…

We present a simple deterministic distributed $(2+\epsilon)$-approximation algorithm for minimum weight vertex cover, which completes in $O(\log{\Delta}/\epsilon\log\log{\Delta})$ rounds, where $\Delta$ is the maximum degree in the graph,…

We study the problem of {\sl certification}: given queries to a function $f : \{0,1\}^n \to \{0,1\}$ with certificate complexity $\le k$ and an input $x^\star$, output a size-$k$ certificate for $f$'s value on $x^\star$. This abstractly…

Anthropic models can give testable predictions, which can be confirmed or falsified at a specified confidence level. This is illustrated using the successful prediction of the cosmological constant as an example. The history and the nature…

Recently, a new conjecture on the degrees of the irreducible Brauer characters of a finite group was presented by the second author. In this paper we propose a 'local' version of this conjecture for blocks B of finite groups, giving a lower…

We give a new proof of the epsilon dichotomy conjecture, stated by Prasad and Takloo-Bighash, for non Archimedean local fields of characteristic zero, when the twisting character is trivial. Our method relies on the functional equation and…