Related papers: T-homotopy and refinement of observation (I) : Int…

This work introduces the definition of observation-specific explanations to assign a score to each data point proportional to its importance in the definition of the prediction process. Such explanations involve the identification of the…

An introduction and survey of homotopy type theory in honor of W.W. Tait.

We study the refinement invariance of several intersection (co)homologies existing in the literature. These (co)homologies have been introduced in order to establish the Poincar\'e Duality in variousl contexts. We found the classical…

In this position paper we suggest a possible metric approach to shape comparison that is based on a mathematical formalization of the concept of observer, seen as a collection of suitable operators acting on a metric space of functions.…

This short note introduces a notion of directed homotopy equivalence and of "directed" topological complexity (which elaborates on the notion that can be found in e.g. Farber's book) which have a number of desirable joint properties. In…

Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…

Tate cohomology has been generalised by several authors using different constructions that have applications in group theory, ring theory and homotopical algebra. Therefore, there is a need for a uniform account that explains why their…

The analysis of human motion opens up a wide range of possibilities, such as realistic training simulations or authentic motions in robotics or animation. One of the problems underlying motion analysis is the meaningful comparison of…

We study the coherence and conservativity of extensions of dependent type theories by additional strict equalities. By considering notions of congruences and quotients of models of type theory, we reconstruct Hofmann's proof of the…

In this paper we develop homotopy theoretical methods for studying diagrams. In particular we explain how to construct homotopy colimits and limits in an arbitrary model category. The key concept we introduce is that of a model…

We review the recent progress in the study of cyclic cohomology in the presence of Hopf symmetry.

Capturing the similarities between human language units is crucial for explaining how humans associate different objects, and therefore its computation has received extensive attention, research, and applications. With the ever-increasing…

A refinement of the multinomial distribution is presented where the number of inversions in the sequence of outcomes is tallied. This refinement of the multinomial distribution is its joint distribution with the number of inversions in the…

This note presents an extension to the adaptive control strategy presented in [1] able to counter eventual instability due to disturbances at the input of an otherwise $\mathcal{L}_2$ stable closed-loop system. These disturbances are due to…

Formally capturing the transition from a continuous model to a discrete model is investigated using model based refinement techniques. A very simple model for stopping (eg. of a train) is developed in both the continuous and discrete…

This paper is a compact overview of the heuristic approach to the recently elaborated octonionic binocular mobilevision.

This presentation is the sequel of a paper published in GETCO'00 proceedings where a research program to construct an appropriate algebraic setting for the study of deformations of higher dimensional automata was sketched. This paper…

The monopole map defines an element in an equivariant stable cohomotopy group refining the Seiberg-Witten invariant. This first of two articles presents the details of the definition of the stable cohomotopy invariant and discusses its…

We extend the notion of 'homomorphism-homogeneity' to a wider class of kinds of maps than previously studied, and we investigate the relations between the resulting notions of homomorphism-homogeneity, giving several examples. We also give…

In recent years, with the continuous advancement of deep learning and the emergence of large-scale human motion datasets, human motion prediction technology has gradually gained prominence in various fields such as human-computer…