Related papers: Configuration space of intervals with partially su…
We introduce labelled sequent calculi for the basic normal non-distributive modal logic L and 31 of its axiomatic extensions, where the labels are atomic formulas of a first order language which is interpreted on the canonical extensions of…
Within the framework of finite element systems, we show how spaces of differential forms may be constructed, in such a way that they are equipped with commuting interpolators and contain prescribed functions, and are minimal under these…
We prove that the order of an ordered group is an interval order if and only if it is a semiorder. Next, we prove that every semiorder is isomorphic to a collection $\mathcal J$ of intervals of some totally ordered abelian group, these…
An analogous construction of simplicial homotopy group for Kan complex can be applied to saturated complicial sets to give monoids. In this paper, we investigate how the construction of loop spaces of Kan complexes lifts to the complicial…
We review the problem of finding a general framework within which one can construct quantum theories of non-standard models for space, or space-time. The starting point is the observation that entities of this type can typically be regarded…
The theory of abelian categories proved very useful, providing an axiomatic framework for homology and cohomology of modules over a ring and, in particular, of abelian groups. For many years, a similar categorical framework has been lacking…
We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the…
We connect the homotopy type of simplicial moduli spaces of algebraic structures to the cohomology of their deformation complexes. Then we prove that under several assumptions, mapping spaces of algebras over a monad in an appropriate…
The total homology of the loop space of the configuration space of ordered distinct n points in R^m has a structure of a Hopf algebra defined by the 4-term relations if m>2. We describe a relation of between the cohomology of this loop…
The label ranking problem is a supervised learning scenario in which the learner predicts a total order of the class labels for a given input instance. Recently, research has increasingly focused on the partial label ranking problem, a…
An important problem in multi-label classification is to capture label patterns or underlying structures that have an impact on such patterns. This paper addresses one such problem, namely how to exploit hierarchical structures over labels.…
We introduce and investigate generalizations of interval and proper interval graphs to simplicial complexes, including strong interval, unit interval, and under closed variants. Through equivalent combinatorial and algebraic…
Given labeled points in a high-dimensional vector space, we seek a low-dimensional subspace such that projecting onto this subspace maintains some prescribed distance between points of differing labels. Intended applications include…
Partial label learning deals with the problem where each training instance is assigned a set of candidate labels, only one of which is correct. This paper provides the first attempt to leverage the idea of self-training for dealing with…
We use derived localization of the bar and nerve constructions to provide simple proofs of a number of results in algebraic topology. This includes a recent generalization of Adams' cobar-construction to the non-simply connected case, and a…
We study the problem of recovering the latent ground truth labeling of a structured instance with categorical random variables in the presence of noisy observations. We present a new approximate algorithm for graphs with categorical…
The class of generic structures among those consisting of the measure algebra of a probability space equipped with an automorphism is axiomatizable by positive sentences interpreted using an approximate semantics. The separable generic…
A labeled metric space is intuitively speaking a metric space together with a special set of points to be understood as the geometric boundary of the space. We study basic properties of a recently introduced labeled Gromov-Hausdorff…
We show that for any two homogeneous Cantor sets with sum of Hausdorff dimensions that exceeds 1, one can create an interval in the sumset by applying arbitrary small perturbations (without leaving the class of homogeneous Cantor sets). In…
As a practical foundation for a homotopy theory of abstract spacetime, we extend a category of certain compact partially ordered spaces to a convenient category of locally preordered spaces. In particular, we show that our new category is…