Related papers: Low upper bounds of ideals
We give a new lower bound for the minimal dispersion of a point set in the unit cube and its inverse function in the high dimension regime. This is done by considering only a very small class of test boxes, which allows us to reduce…
Some monotone increasing sequences of the lower bounds for the minimum eigenvalue of $M$-matrices are given. It is proved that these sequences are convergent and improve some existing results. Numerical examples show that these sequences…
Upper and lower bounds are derived for the quantity in the title, which is tabulated for modest values of $n$ and $k.$ An application to graphs with many cycles is given.
Bounds for the maximum degree of a minimal Gr\"obner basis of simplicial toric ideals with respect to the reverse lexicographic order are given. These bounds are close to the bound stated in Eisenbud-Goto's Conjecture on the…
We study fundamental block-structured integer programs called tree-fold and multi-stage IPs. Tree-fold IPs admit a constraint matrix with independent blocks linked together by few constraints in a recursive pattern; and transposing their…
A fundamental open problem in learning theory is to characterize the best-case teaching dimension $\operatorname{TS}_{\min}$ of a concept class $\mathcal{C}$ with finite VC dimension $d$. Resolving this problem will, in particular, settle…
We introduce a lower bound for the independence number of an arbitrary $k$-uniform hypergraph that only depends on the number of vertices and number of edges of the hypergraph.
We prove two lower bounds for stopping times of sequential tests between general composite nulls and alternatives. The first lower bound is for the setting where the type-1 error level $\alpha$ approaches zero, and equals $\log(1/\alpha)$…
Let A be a commutative ring and I an ideal of A with a reduction Q. In this paper we give an upper bound on the reduction number of I with respect to Q, when a suitable family of ideals in A is given. As a corollary it follows that if some…
The low for random reals are characterized topologically, as well as in terms of domination of Turing functionals on a set of positive measure.
We show that every countable ideal of degrees that are low for isomorphism is contained in a principal ideal of degrees that are low for isomorphism by adapting an exact pair construction. We further show that within the hyperimmune-free…
An ideal is a nonempty collection of subsets closed under heredity and finite additivity. The aim of this paper is to unify some weak separation properties via topological ideals. We concentrate our attention on the separation axioms…
In this work, some combinatorial lower bound for regularity of powers of the edge ideal of a uniform hypergarph is gained. A family of hypergraphs whose regularity of edge ideal attains this bound and has a significant difference from the…
We consider the set of all the ideals of a ring, endowed with the coarse lower topology. The aim of this paper is to study the topological properties of distinguished subspaces of this space and detect the spectrality of some of them.
We derive upper bounds on the tail conditional expectation of binomial and Poisson random variables. Those upper bounds are subsequently employed to the problem of obtaining non-asymptotic lower bounds on the probability that the…
The standard approach to supervised classification involves the minimization of a log-loss as an upper bound to the classification error. While this is a tight bound early on in the optimization, it overemphasizes the influence of…
In this article, we extend the notion of the $F$-thresholds of ideals to the $F$-thresholds for filtrations of ideals. The existence of $F$-thresholds of filtrations are established for various types of filtrations. Moreover, various…
Let $G$ be a finitely generated abelian-by-finite group and $k$ a field of characteristic $p\ge 0$. The Euler class $[k_G]$ of $G$ over $k$ is the class of the trivial $kG$-module in the Grothendieck group $G_0(kG)$. We show that $[k_G]$…
Machine learning models have traditionally been developed under the assumption that the training and test distributions match exactly. However, recent success in few-shot learning and related problems are encouraging signs that these models…
We continue the study of restricted Monte Carlo algorithms in a general setting. Here we show a lower bound for minimal errors in the setting with finite restriction in terms of deterministic minimal errors. This generalizes a result of…