相关论文: Sharper Bounds on Four Lattice Constants

In the index coding problem, introduced by Birk and Kol (INFOCOM, 1998), the goal is to broadcast an n bit word to n receivers (one bit per receiver), where the receivers have side information represented by a graph G. The objective is to…

Let $P(z)$ be a polynomial of degree $n$. In $2004$, Aziz and Rather \cite{aziz2004some} investigated the dependence of \[\bigg|P(Rz)-\alpha P(z)+\beta\biggl\{\biggl(\frac{R+1}{2}\biggr)^n-|\alpha|\biggr\}P(z)\bigg|, \ \text{for} \ z \in…

As software systems become more complex, there is an increasing need for new static analyses. Thanks to the declarative style, logic programming is an attractive formalism for specifying them. However, prior work on using logic programming…

In previous work, the second author introduced a topology, for spaces of irreducible representations, that reduces to the classical Zariski topology over commutative rings but provides a proper refinement in various noncommutative settings.…

Perturbative and non-perturbative results are presented on the renormalization constants of the quark field and the vector, axial-vector, pseudoscalar, scalar and tensor currents. The perturbative computation, carried out at one-loop level…

Summations and relations involving the Hurwitz and Riemann zeta-functions are extended first to Barnes zeta-functions and then to zeta-functions of general type. The analysis is motivated by the evaluation of determinants on spheres which…

This article describes a novel optimization solution framework, called alternating gradient descent (GD) and minimization (AltGDmin), that is useful for many problems for which alternating minimization (AltMin) is a popular solution. AltMin…

This paper proposes a frequency-domain system identification method for learning low-order systems. The identification problem is formulated as the minimization of the l2 norm between the identified and measured frequency responses, with…

This paper tackles the problem of Lipschitz regularization of Convolutional Neural Networks. Lipschitz regularity is now established as a key property of modern deep learning with implications in training stability, generalization,…

Kolmogorov-Arnold Networks (KANs) have gained attention for their potential to outperform Multi-Layer Perceptrons (MLPs) in terms of parameter efficiency and interpretability. Unlike traditional MLPs, KANs use learnable non-linear…

Many inverse problems and signal processing problems involve low-rank regularizers based on the nuclear norm. Commonly, proximal gradient methods (PGM) are adopted to solve this type of non-smooth problems as they can offer fast and…

Sum-rank Hamming codes are introduced in this work. They are essentially defined as the longest codes (thus of highest information rate) with minimum sum-rank distance at least $ 3 $ (thus one-error-correcting) for a fixed redundancy $ r $,…

In seminal work, Lov\'asz, Spencer, and Vesztergombi [European J. Combin., 1986] proved a lower bound for the hereditary discrepancy of a matrix $A \in \mathbb{R}^{m \times n}$ in terms of the maximum $|\det(B)|^{1/k}$ over all $k \times k$…

This work is concerned with approximating multivariate functions in unbounded domain by using discrete least-squares projection with random points evaluations. Particular attention are given to functions with random Gaussian or Gamma…

This paper deals with lattices $(L,\Vert~\Vert)$ over polynomial rings, where $L$ is a finitely generated module over $k[t]$, the polynomial ring over the field $k$ in the indeterminate $t$, and $\Vert~\Vert$ is a discrete real-valued…

We propose a non-perturbative method for computing the renormalization constants of generic composite operators. This method is intended to reduce some systematic errors, which are present when one tries to obtain physical predictions from…

In a recent paper (arXiv:0911.2514), one of us (FYW) considered the Potts model and bond and site percolation on two general classes of two-dimensional lattices, the triangular-type and kagome-type lattices, and obtained closed-form…

It has been long--conjectured that the crossing number cr(K_m,n) of the complete bipartite graph K_m,n equals the Zarankiewicz Number Z(m,n):= floor((m-1)/2) floor(m/2) floor((n-1)/2) floor(n/2). Another long--standing conjecture states…

Numerical Stochastic Perturbation Theory was able to get three- (and even four-) loop results for finite Lattice QCD renormalization constants. More recently, a conceptual and technical framework has been devised to tame finite size…

A strong direct product theorem states that, in order to solve k instances of a problem, if we provide less than k times the resource required to compute one instance, then the probability of overall success is exponentially small in k. In…