Related papers: A local version of Gotzmann's Persistence
We introduce an efficient way, called Newton algorithm, to study arbitrary ideals in C[[x,y]], using a finite succession of Newton polygons. We codify most of the data of the algorithm in a useful combinatorial object, the Newton tree. For…
We describe algorithms for finding the regression of t, a sequence of values, to the closest sequence s by mean squared error, so that s is always increasing (isotonicity) and so the values of two consecutive points do not increase by too…
The local persistence R(t), defined as the proportion of the system still in its initial state at time t, is measured for the Bak--Sneppen model. For 1 and 2 dimensions, it is found that the decay of R(t) depends on one of two classes of…
We consider a class of semilinear parabolic evolution equations subject to a hysteresis operator and a Bochner-Lebesgue integrable source term. The underlying spatial domain is allowed to have a very general boundary. In the first part of…
We study growth rates for strongly continuous semigroups. We prove that a growth rate for the resolvent on imaginary lines implies a corresponding growth rate for the semigroup if either the underlying space is a Hilbert space, or the…
Homo-energetic solutions to the spatially homogeneous Boltzmann equation have been extensively studied, but their global stability in the inhomogeneous setting remains challenging due to unbounded energy growth under self-similar scaling…
We study thermodynamic formalism for topologically transitive partially hyperbolic systems in which the center-stable bundle satisfies a bounded expansion property, and show that every potential function satisfying the Bowen property has a…
Iterative linear solvers have gained recent popularity due to their computational efficiency and low memory footprint for large-scale linear systems. The relaxation method, or Motzkin's method, can be viewed as an iterative method that…
The intersection growth of a group $G$ is the asymptotic behavior of the index of the intersection of all subgroups of $G$ with index at most $n$, and measures the Hausdorff dimension of $G$ in profinite metrics. We study intersection…
We prove an analogue of the Yomdin-Gromov Lemma for $p$-adic definable sets and more broadly in a non-archimedean, definable context. This analogue keeps track of piecewise approximation by Taylor polynomials, a nontrivial aspect in the…
In this paper, we study limiting laws and consistent estimation criteria for the extreme eigenvalues in a spiked covariance model of dimension $p$. Firstly, for fixed $p$, we propose a generalized estimation criterion that can consistently…
Let $F$ be a number field and $p$ an odd prime. We estimate the kernels and cokernels of the codescent maps of the \'etale wild kernels over various $p$-adic Lie extensions. For this, we propose a novel approach of viewing the \'etale wild…
The Grassmann angle improves upon similar angles between subspaces that measure volume contraction in orthogonal projections. It works in real or complex spaces, with important differences, and is asymmetric, what makes it more efficient…
We study a spatially explicit harvesting model in periodic or bounded environments. The model is governed by a parabolic equation with a spatially dependent nonlinearity of Kolmogorov--Petrovsky--Piskunov type, and a negative external…
We present variants of Goodstein's theorem that are equivalent to arithmetical comprehension and to arithmetical transfinite recursion, respectively, over a weak base theory. These variants differ from the usual Goodstein theorem in that…
We give a self-contained treatment of the theory of persistence modules indexed over the real line. We give new proofs of the standard results. Persistence diagrams are constructed using measure theory. Linear algebra lemmas are simplified…
In this paper we develop a Grobner bases theory for ideals of partial difference polynomials with constant or non-constant coefficients. In particular, we introduce a criterion providing the finiteness of such bases when a difference ideal…
The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…
We propose a new deterministic growth model which captures certain features of both the Gompertz and Korf laws. We investigate its main properties, with special attention to the correction factor, the relative growth rate, the inflection…
We propose a simple experimental procedure based on the Elitzur-Vaidman scheme to test the persistence of macroscopic superpositions. We conjecture that its implementation will reveal the persistence of superpositions of macroscopic objects…