Related papers: Projected distances for multi-parameter persistenc…
Given a filtration of simplicial complexes, one usually applies persistent homology and summarizes the results in barcodes. Then, in order to extract statistical information from these barcodes, one needs to compute statistical indicators…
Structured prediction tasks in machine learning involve the simultaneous prediction of multiple labels. This is typically done by maximizing a score function on the space of labels, which decomposes as a sum of pairwise elements, each…
A construction of Partial Maximum Distance Separable (PMDS) and Sector-Disk (SD) codes extending RAID 5 with two extra parities is given, solving an open problem. Previous constructions relied on computer searches, while our constructions…
We apply the semidefinite programming method to derive bounds for projective codes over a finite field.
Sliced Wasserstein (SW) distances offer an efficient method for comparing high-dimensional probability measures by projecting them onto multiple 1-dimensional probability distributions. However, identifying informative slicing directions…
Multiparameter persistence is a natural extension of the well-known persistent homology, which has attracted a lot of interest. However, there are major theoretical obstacles preventing the full development of this promising theory. In this…
Despite the success of the popular kernelized support vector machines, they have two major limitations: they are restricted to Positive Semi-Definite (PSD) kernels, and their training complexity scales at least quadratically with the size…
A novel uniform circular array (UCA) based near-field (NF) integrated sensing and communication (ISAC) framework is proposed, where the Cylindrical coordinate is invoked to evaluate the joint positioning performance. The joint squared…
Sparsely spread code division multiple access (SCDMA) is a promising non-orthogonal multiple access technique for future wireless communications. In this paper, we propose a novel trainable multiuser detector called sparse trainable…
In this paper, we first propose a spatial-temporal coupled risk assessment paradigm by constructing a three-dimensional spatial-temporal risk field (STRF). Specifically, we introduce spatial-temporal distances to quantify the impact of…
Symbol-pair code is a new coding framework which is proposed to correct errors in the symbol-pair read channel. In particular, maximum distance separable (MDS) symbol-pair codes are a kind of symbol-pair codes with the best possible…
The complex of curves $\mathcal{C}(S_g)$ of a closed orientable surface of genus $g \geq 2$ is the simplicial complex having its vertices, $\mathcal{C}^0(S_g)$, are isotopy classes of essential curves in $S_g$. Two vertices co-bound an edge…
A powerful and flexible approach to structured prediction consists in embedding the structured objects to be predicted into a feature space of possibly infinite dimension by means of output kernels, and then, solving a regression problem in…
We introduce new distance measures for comparing straight-line embedded graphs based on the Fr\'echet distance and the weak Fr\'echet distance. These graph distances are defined using continuous mappings and thus take the combinatorial…
Multidimensional scaling is a statistical process that aims to embed high dimensional data into a lower-dimensional space; this process is often used for the purpose of data visualisation. Common multidimensional scaling algorithms tend to…
As estimators of location parameters, univariate trimmed means are well known for their robustness and efficiency. They can serve as robust alternatives to the sample mean while possessing high efficiencies at normal as well as heavy-tailed…
Diffusion state distance (DSD) is a metric on the vertices of a graph, motivated by bioinformatic modeling. Previous results on the convergence of DSD to a limiting metric relied on the definition being based on symmetric or reversible…
Simulated tempering is popular method of allowing MCMC algorithms to move between modes of a multimodal target density {\pi}. One problem with simulated tempering for multimodal targets is that the weights of the various modes change for…
After recalling the definition of codes as modules over skew polynomial rings, whose multiplication is defined by using an automorphism and a derivation, and some basic facts about them, in the first part of this paper we study some of…
This paper introduces an efficient algorithm for persistence diagram computation, given an input piecewise linear scalar field $f$ defined on a $d$-dimensional simplicial complex $K$, with $d \leq 3$. Our work revisits the seminal algorithm…