Related papers: Order algebras: a quantitative model of interactio…

We survey structures endowed with natural partial orderings and prove their universality. These partial orders include partial orders on sets of words, partial orders formed by geometric objects, grammars, polynomials and homomorphism order…

Classification of ordinal data is one of the most important tasks of relation learning. In this thesis a novel framework for ordered classes is proposed. The technique reduces the problem of classifying ordered classes to the standard…

The purpose of this paper is to give a characterisation of divided power algebras over a reduced operad. Such a characterisation is given in terms of polynomial operations, following the classical example of divided power algebras. We…

Interaction graphs were introduced as a general, uniform, construction of dynamic models of linear logic, encompassing all "Geometry of Interaction" (GoI) constructions introduced so far. This series of work was inspired from Girard's…

It is pointed out that quantum states, in general, contain a new kind of orders that cannot be characterized by symmetry. A concept of quantum order is introduced to describe such orders. As two concrete examples, we discussed quantum…

We study a subclass of POMDPs, called Deterministic POMDPs, that is characterized by deterministic actions and observations. These models do not provide the same generality of POMDPs yet they capture a number of interesting and challenging…

Univariate or multivariate ordinal responses are often assumed to arise from a latent continuous parametric distribution, with covariate effects which enter linearly. We introduce a Bayesian nonparametric modeling approach for univariate…

We use high girth, high chromatic number hypergraphs to show that there are finite models of the equational theory of the semiring of nonnegative integers whose equational theory has no finite axiomatisation, and show this also holds if…

We review the new approach to the theory of nonlinear $W$-algebras which is developed recently and called {\it conformal linearization}. In this approach $W$-algebras are embedded as subalgebras into some {\it linear conformal} algebras…

Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…

Parametric entities appear in many contexts, be it in optimisation, control, modelling of random quantities, or uncertainty quantification. These are all fields where reduced order models (ROMs) have a place to alleviate the computational…

Modeling the structure of coherent texts is a key NLP problem. The task of coherently organizing a given set of sentences has been commonly used to build and evaluate models that understand such structure. We propose an end-to-end…

This paper is devoted to a new approach of the arithmetic of intervals. We present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any…

Motivated by an ongoing project on computer aided derivation of asymptotic models governed by partial differential equations, we introduce a class of term transformations that consists of traversal strategies and insertion of contexts. We…

Substructural logics are formal logical systems that omit familiar structural rules of classical and intuitionistic logic such as contraction, weakening, exchange (commutativity), and associativity. This leads to a resource-sensitive…

A model for statistical ranking is a family of probability distributions whose states are orderings of a fixed finite set of items. We represent the orderings as maximal chains in a graded poset. The most widely used ranking models are…

We continue our study of operator algebras with and contractive approximate identities (cais). In earlier papers we have introduced and studied a new notion of positivity in operator algebras, with an eye to extending certain C*-algebraic…

There are many different models of concurrent processes. The goal of this work is to introduce a common formalized framework for current research in this area and to eliminate shortcomings of existing models of concurrency. Following up the…

Common approaches to concurrent programming begin with languages whose semantics are naturally sequential and add new constructs that provide limited access to concurrency, as exemplified by futures. This approach has been quite successful,…

Language theory, symbolic dynamics, modelisation of viral insertion into the genetic code of a host cell motivate the introduction of new types of bialgebras whose coalgebra parts are not necessarily coassociative. One of the aim of this…