相关论文: Virial Expansion Bounds Through Tree Partition Sch…

We study the degree landscape of the partition graph $G_n$, whose vertices are the integer partitions of $n$ and whose edges correspond to elementary transfers of one unit between parts, followed by reordering. Using the previously…

We compute explicit upper bounds on the distance between the law of a multivariate Gaussian distribution and the joint law of wavelets/needlets coefficients based on a homogeneous spherical Poisson field. In particular, we develop some…

Phylogenetic trees are leaf-labelled trees used to model the evolution of species. Here we explore the practical impact of kernelization (i.e. data reduction) on the NP-hard problem of computing the TBR distance between two unrooted binary…

In this paper we obtain further improvement of index bounds for character sums of polynomials over finite fields. We present some examples, which show that our new bound is an improved bound compared to both the Weil bound and the index…

Sparse polynomial systems with vertical coefficient dependencies arise naturally when describing the critical points of optimization problems and, when augmented with linear forms, the steady states of chemical reaction networks. Moreover,…

We consider the minimum spanning tree problem on a weighted complete bipartite graph $K_{n_R, n_B}$ whose $n=n_R+n_B$ vertices are random, i.i.d. uniformly distributed points in the unit cube in $d$ dimensions and edge weights are the…

We develop a theoretical framework for the analysis of oblique decision trees, where the splits at each decision node occur at linear combinations of the covariates (as opposed to conventional tree constructions that force axis-aligned…

A tropical expansion is a degeneration of a toroidal embedding, induced by a polyhedral subdivision of its tropicalisation. Each irreducible component of a tropical expansion admits a collapsing map down to a stratum of the original…

Evidence suggests that oblique splits can significantly enhance the performance of decision trees. This paper explores the optimization of high-dimensional oblique splits for decision tree construction, establishing the Sufficient Impurity…

In this paper, we prove a `cut-by-curves criterion' for an overconvergent isocrystal on a smooth variety over a field of characteristic $p>0$ to extend logarithmically to its smooth compactification whose complement is a strict normal…

We present numerical solutions to the extended Doering-Constantin variational principle for upper bounds on the energy dissipation rate in plane Couette flow, bridging the entire range from low to asymptotically high Reynolds numbers. Our…

We introduce a new model of random $d$-dimensional simplicial complexes, for $d\geq 2$, whose $(d-1)$-cells have bounded degrees. We show that with high probability, complexes sampled according to this model are coboundary expanders. The…

In this paper we prove a theorem that provides an upper bound for the density of packings of congruent copies of a given convex body in $\mathbb{R}^n$; this theorem is a generalization of the linear programming bound for sphere packings. We…

We prove complex contraction for zero-free regions of counting weighted set cover problem in which an element can appear in an unbounded number of sets, thus obtaining fully polynomial-time approximation schemes(FPTAS) via Barvinok's…

Constant-dimension codes with the maximum possible minimum distance have been studied under the name of partial spreads in Finite Geometry for several decades. Not surprisingly, for this subclass typically the sharpest bounds on the maximal…

We consider a class of particle systems which appear in various applications such as approximation theory, plasticity, potential theory and space-filling designs. The positions of the particles on the real line are described as a global…

We give a high precision polynomial-time approximation scheme for the supremum of any honest n-variate (n+2)-nomial with a constant term, allowing real exponents as well as real coefficients. Our complexity bounds count field operations and…

This paper investigates one of the most fundamental computer vision problems: image segmentation. We propose a supervised hierarchical approach to object-independent image segmentation. Starting with over-segmenting superpixels, we use a…

Linear fusion is a cornerstone of estimation theory. Implementing optimal linear fusion requires knowledge of the covariance of the vector of errors associated with all the estimators. In distributed or cooperative systems, the…

Extension problems for polynomial valuations on different cones of convex functions are investigated. It is shown that for the classes of functions under consideration, the extension problem reduces to a simple geometric obstruction on the…