相关论文: An Algorithmic Proof of Suslin's Stability Theorem…
The families of bijective transformations $G_n$ of affine space $K^n$ over general commutative ring $K$ of increasing order with the property of stability will be constructed. Stability means that maximal degree of elements of cyclic…
Based on the Suzuki product-formula approach, we construct a family of unconditionally stable algorithms to solve the time-dependent Maxwell equations. We describe a practical implementation of these algorithms for one-, two-, and…
This paper is purely expository. We present short elementary proofs of * the Gauss Theorem on constructibility of regular polygons; * the existence of a cubic equation unsolvable in real radicals; * the existence of a quintic equation…
Bagging is an important technique for stabilizing machine learning models. In this paper, we derive a finite-sample guarantee on the stability of bagging for any model. Our result places no assumptions on the distribution of the data, on…
In this paper, we study the arithmetics of skew polynomial rings over finite fields, mostly from an algorithmic point of view. We give various algorithms for fast multiplication, division and extended Euclidean division. We give a precise…
We give an effective uniform bound on the multigraded regularity of a subscheme of a smooth projective toric variety X with a given multigraded Hilbert polynomial. To establish this bound, we introduce a new combinatorial tool, called a…
We study multivariate polynomials over `structured' grids. We begin by proposing an interpretation as to what it means for a finite subset of a field to be structured; we do so by means of a numerical parameter, the nullity. We then extend…
Given a rational monomial map, we consider the question of finding a toric variety on which it is algebraically stable. We give conditions for when such variety does or does not exist. We also obtain several precise estimates of the degree…
In this note, we show various minimality results for a geometric theory of fields $T$: $T$ is stable if and only if it is strongly minimal, $T$ is simple if and only if it has SU-rank 1, and $T$ is rosy if and only if $T$ is surgical.…
Super-stability and strong stability are properties of a matching in the stable matching problem with ties. In this paper, we introduce a common generalization of super-stability and strong stability, which we call non-uniform stability.…
Polynomial system solving is a classical problem in mathematics with a wide range of applications. This makes its complexity a fundamental problem in computer science. Depending on the context, solving has different meanings. In order to…
We prove the non-linear stability of a large class of spherically symmetric equilibrium solutions of both the collisonless Boltzmann equation and of the Euler equations in MOND. This is the first such stability result that is proven with…
In this paper, we prove that Dedekind-Mertens lemma holds only for those semimodules whose subsemimodules are subtractive. We introduce Gaussian semirings and prove that bounded distributive lattices are Gaussian semirings. Then we…
We consider mixtures of $k\geq 2$ Gaussian components with unknown means and unknown covariance (identical for all components) that are well-separated, i.e., distinct components have statistical overlap at most $k^{-C}$ for a large enough…
It is well known that the vertices of any Euclidean simplicial regular polytope determine an optimal packing of equal spherical balls. We prove a stability version of optimal order of this result.
This paper studies the unitary diagonalization of matrices over formal power series rings. Our main result shows that a normal matrix is unitarily diagonalizable if and only if its minimal polynomial completely splits over the ring and the…
In this paper, we see several basic properties of graded linear series. We firstly see that, if a graded linear series contains an ample series, then so are the pullbacks of the system under birational morphisms. Using this proposition, we…
We study the problem of factoring univariate polynomials over finite fields. Under the assumption of the Extended Riemann Hypothesis (ERH), (Gao, 2001) designed a polynomial time algorithm that fails to factor only if the input polynomial…
We show an algorithm for computing the permanent of a random matrix with vanishing mean in quasi-polynomial time. Among special cases are the Gaussian, and biased-Bernoulli random matrices with mean 1/lnln(n)^{1/8}. In addition, we can…
In this paper, we explore the merits of various algorithms for polynomial optimization problems, focusing on alternatives to sum of squares programming. While we refer to advantages and disadvantages of Quantifier Elimination, Reformulation…