Related papers: Bounds for D-finite closure properties
In communication field, an important issue is to group users and base stations to as many as possible subnetworks satisfying certain interference constraints. These problems are usually formulated as a graph partition problems which…
We present deterministic techniques for computing upper and lower bounds on marginal probabilities in sigmoid and noisy-OR networks. These techniques become useful when the size of the network (or clique size) precludes exact computations.…
In this paper we establish sharp weighted bounds (Buckley type theorems) for one{sided maximal and fractional integral operators in terms of one{sided $A_p$ characteristics. Appropriate sharp bounds for strong maximal functions, multiple…
Matrix product operators allow efficient descriptions (or realizations) of states on a 1D lattice. We consider the task of learning a realization of minimal dimension from copies of an unknown state, such that the resulting operator is…
The `linear orbit' of a plane curve of degree d is its orbit in P^{d(d+3)/2} under the natural action of PGL(3). We classify curves with positive dimensional stabilizer, and we compute the degree of the closure of the linear orbits of…
An approach for the computation of upper bounds on the size of large complete arcs is presented. We obtain in particular geometrical properties of irreducible envelopes associated to a second largest complete arc provided that the order of…
The question of self-adjoint realizations of sign-indefinite second order differential operators is discussed in terms of a model problem. Operators of the type $-\frac{d}{dx} \sgn (x) \frac{d}{dx}$ are generalized to finite, not…
We consider the number of linear extensions of an N-free order P. We give upper and lower bounds on this number in terms of parameters of the corresponding arc diagram. We propose a dynamic programming algorithm to calculate the number. The…
We consider the resolvent estimates and properties of virtual states of the higher order derivatives in one dimension, focusing on Schroedinger-type operators of degree $N=3$ (the approach applies to higher orders). The derivation is based…
We obtain approximation results for general positive linear operators satisfying mild conditions, when acting on discontinuous functions and absolutely continuous functions having discontinuous derivatives. The upper bounds, given in terms…
For a class of non-selfadjoint semiclassical operators in dimension one, we get a complete asymptotic description of all eigenvalues near a critical value of the leading symbol of the operator on the boundary of the pseudospectrum.
We provide an index bound for character sums of polynomials over finite fields. This improves the Weil bound for high degree polynomials with small indices, as well as polynomials with large indices that are generated by cyclotomic mappings…
Let $F$ be a univariate polynomial or rational fraction of degree $d$ defined over a number field. We give bounds from above on the absolute logarithmic Weil height of $F$ in terms of the heights of its values at small integers: we review…
We study properties of pseudodifferential operators which arise in their use in boundary value problems. Smooth domains as well as intersections of smooth domains are considered.
We present some variations on some of the main open problems on character degrees. We collect some of the methods that have proven to be very useful to work on these problems. These methods are also useful to solve certain problems on zeros…
When an eigenvector of a semi-bounded operator is positive, we show that a remarkably simple argument allows to obtain upper and lower bounds for its associated eigenvalue. This theorem is a substantial generalization of Barta-like…
This paper provides statistical guarantees on the accuracy of dynamical models learned from dependent data sequences. Specifically, we develop uniform error bounds that apply to quantized models and imperfect optimization algorithms…
In this paper, we study the $L^{p}$-improving property for the maximal operators along a large class of curves of finite type in the plane with dilation set $E \subset [1,2]$. The $L^{p}$-improving region depends on the order of finite type…
The structure of data organization is widely recognized as having a substantial influence on the efficacy of machine learning algorithms, particularly in binary classification tasks. Our research provides a theoretical framework suggesting…
We investigate elliptic boundary-value problems for which the maximum of the orders of the boundary operators is equal to or greater than the order of the elliptic differential equation. We prove that the operator corresponding to an…