Related papers: sp-Homogeneous Linear Orderings
Agglomerative hierarchical clustering can be implemented with several strategies that differ in the way elements of a collection are grouped together to build a hierarchy of clusters. Here we introduce versatile linkage, a new infinite…
Representations in the form of Symmetric Positive Definite (SPD) matrices have been popularized in a variety of visual learning applications due to their demonstrated ability to capture rich second-order statistics of visual data. There…
Consider a sequence of real-valued functions of a real variable given by a homogeneous linear recursion with differentiable coefficients. We show that if the functions in the sequence are differentiable, then the sequence of derivatives…
A linear operator $T$ between two lattice-normed spaces is said to be $p$-compact if, for any $p$-bounded net $x_\alpha$, the net $Tx_\alpha$ has a $p$-convergent subnet. $p$-Compact operators generalize several known classes of operators…
For a sequence of uniformly bounded, degenerate semigroups on a Hilbert space, we compare various types of convergences to a limit semigroup. Among others, we show that convergence of the semigroups, or of the resolvents of the generators,…
It is studied that pointwise estimates and continuities on Hardy spaces of pseudo-differential operators (PDOs for short) with the symbol in general H\"{o}rmander's classes. We get weighted weak-type $(1,1)$ estimate, weighted normal…
This paper is devoted to second-order variational analysis of a rather broad class of extended-real-valued piecewise liner functions and their applications to various issues of optimization and stability. Based on our recent explicit…
Many classification problems consider classes that form a hierarchy. Classifiers that are aware of this hierarchy may be able to make confident predictions at a coarse level despite being uncertain at the fine-grained level. While it is…
In this work we study a weak order ideal associated with the coset leaders of a non-binary linear code. This set allows the incrementally computation of the coset leaders and the definitions of the set of leader codewords. This set of…
Existing deep multitask learning (MTL) approaches align layers shared between tasks in a parallel ordering. Such an organization significantly constricts the types of shared structure that can be learned. The necessity of parallel ordering…
We show that the order dimension of the weak order on a Coxeter group of type A, B or D is equal to the rank of the Coxeter group, and give bounds on the order dimensions for the other finite types. This result arises from a unified…
We introduce and study weak o-minimality in the context of complete types in an arbitrary first-order theory. A type $p\in S(A)$ is weakly o-minimal if for some relatively $A$-definable linear order, $<$, on $p(\mathfrak{C})$ every…
The design of robust learning systems that offer stable performance under a wide range of supervision degrees is investigated in this work. We choose the image classification problem as an illustrative example and focus on the design of…
Rank aggregation problems aim to combine multiple individual orderings of a common set of items into a consensus ranking that best reflects the collective preferences. This paper introduces a general Integer Linear Programming (ILP)…
This paper proposes basic definitions of similarity and similarity indexes between heterogeneous linear systems and presents a similarity-based learning control strategy. By exploring geometric properties of admissible behaviors of linear…
With the dramatic increase in the amount of the text-based data which commonly contains misspellings and other errors, querying such data with flexible search patterns becomes more and more commonplace. Relational databases support the LIKE…
We study the degree spectra and reverse-mathematical applications of computably enumerable and co-computably enumerable partial orders. We formulate versions of the chain/antichain principle and ascending/descending sequence principle for…
A simple MATLAB implementation of hierarchical shape functions on 2D rectangles is explained and available for download. Global shape functions are ordered for a given polynomial degree according to the indices of the nodes, edges, or…
Topological techniques have become a popular tool for studying information flows in neural networks. In particular, simplicial homology theory is used to analyze how cognitive representations of space emerge from large conglomerates of…
This is the first contribution of a sequence of papers introducing the notions of $s$-weak order and $s$-permutahedra, certain discrete objects that are indexed by a sequence of non-negative integers $s$. In this first paper, we concentrate…