Related papers: A new version of Toom's proof
We prove that generically, both in a topological and measure-theoretical sense, an invariant Lagrangian Diophantine torus of a Hamiltonian system is doubly exponentially stable in the sense that nearby solutions remain close to the torus…
We characterise subcategories of semistable modules for noncommutative minimal models of compound Du Val singularities, including the non-isolated case. We find that the stability is controlled by an infinite polyhedral fan that stems from…
The paper presents a new control algorithm for unstable linear systems with input delay. In comparison with known analogues, the control law has been designed, which is a modification of the Smith predictor, and is the simplest one to…
In this paper, we prove several stability theorems for multiplicities of naturally defined representations of symmetric groups. The first such theorem states that if we consider the diagonal action of the symmetric group $S_{m+r}$ on $k$…
We establish existence and stabilty results for solitons in noncommutative scalar field theories in even space dimension $2d$. In particular, for any finite rank spectral projection $P$ of the number operator ${\mathcal N}$ of the…
We provide a simplified approach to the the stable Hopf invariant. We provide short elementary proofs of the Cartan Formula, the Composition Formula, and the Transfer formula. In addition, when $\pi$ is a discrete group, we show how to…
A stable soliton configuration for a nucleon emerges when the nucleon stability and $\Sigma_N$ term discrepancy problems are studied semi-quantitatively within a local theory developed recently. The approach developed here goes beyond the…
Stable distributions provide a flexible framework for modeling heavy-tailed and skewed data, with the stability index $\alpha$ quantifying tail heaviness. We propose a new semiparametric estimator for $\alpha$ that leverages the two-sum…
It is, by now, classical that lattices in higher rank semisimple groups have various rigidity properties. In this work, we add another such rigidity property to the list: uniform stability with respect to the family of unitary operators on…
We give a simple Sch\"onhage Storage Modification Machine that simulates one iteration of the Rule 110 cellular automaton. This provides an alternative construction to Sch\"onhage's original proof of the Turing completeness of the eponymous…
To foster trust in machine learning models, explanations must be faithful and stable for consistent insights. Existing relevant works rely on the $\ell_p$ distance for stability assessment, which diverges from human perception. Besides,…
In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The…
In various supersymmetric extensions of the Standard Model there appear non-topological solitons due to the existence of U(1) global symmetries associated with Baryon and/or Lepton quantum numbers. Trilinear couplings (A-terms) in the…
We investigate the low-noise regime of a large class of probabilistic cellular automata, including the North-East-Center model of A. Toom. They are defined as stochastic perturbations of cellular automata with a binary state space and a…
We prove homological stability for both general linear groups of modules over a ring with finite stable rank and unitary groups of quadratic modules over a ring with finite unitary stable rank. In particular, we do not assume the modules…
In this paper, we study properties and patterns on permutations of multisets whose multivariate generating functions are symmetric. We interpret this phenomenon through the lens of group actions and define such a property or pattern as…
This paper has been withdrawn by the authors due to an error in the proof of Lemma 3.9. The correct proof of global stability is given in arXiv:1101.5177
The rich non-linear dynamics of the coupled oscillators (under second harmonic injection) can be leveraged to solve computationally hard problems in combinatorial optimization such as finding the ground state of the Ising Hamiltonian. While…
In this work, we propose the design and analysis of a novel continuous robust controller for a class of multi--input multi--output (MIMO) nonlinear uncertain systems. The systems under consideration contains unstructured uncertainties in…
This essay examines how automation has reconfigured mathematical proof and labor, and what might happen in the future. It discusses practical standards of proof, distinguishes between prominent forms of automation in research, provides…