相关论文: Some combinatorial aspects of composition of a set…
We prove a theorem stating that any semantics can be encoded as a compositional semantics, which means that, essentially, the standard definition of compositionality is formally vacuous. We then show that when compositional semantics is…
A survey of properties of a sequence of coefficients appearing in the evaluation of a quartic definite integral is presented. These properties are of analytical, combinatorial and number-theoretical nature.
In this paper we suggest a typed compositional seman-tics for nominal compounds of the form [Adj Noun] that models adjectives as higher-order polymorphic functions, and where types are assumed to represent concepts in an ontology that…
The power of multivariate functions is their ability to model a wide variety of phenomena, but have the disadvantages that they lack an intuitive or interpretable representation, and often require a (very) large number of parameters. We…
We define a canonical form for piecewise defined functions. We show that this has a wider range of application as well as better complexity properties than previous work.
A longstanding question in cognitive science concerns the learning mechanisms underlying compositionality in human cognition. Humans can infer the structured relationships (e.g., grammatical rules) implicit in their sensory observations…
This work explores the tensor and combinatorial constructs underlying the linearised higher-order variational equations of a generic autonomous system along a particular solution. The main result of this paper is a compact yet explicit and…
Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…
We study higher moments of convolutions of the characteristic function of a set, which generalize a classical notion of the additive energy. Such quantities appear in many problems of additive combinatorics as well as in number theory. In…
Well-partial orders, and the ordinal invariants used to measure them, are relevant in set theory, program verification, proof theory and many other areas of computer science and mathematics. In this article we focus on one of the most…
In this paper directional derivative sets and differentials of a given set valued map are studied. Relations between the set valued map and compact subsets of the directional derivative sets of the given map are investigated. Upper and…
A composition of $n\in\NN$ is an ordered collection of one or more positive integers whose sum is $n$. The number of summands is called the number of parts of the composition. A palindromic composition of $n$ is a composition of $n$ in…
A series of physically motivated operations appearing in the study of composite materials are interpreted in terms of elementary continued fraction transforms of matrix valued, rational Stieltjes functions.
Every one knows that an equation is equivalent to a multivariate function. Generally speaking, there are more than one unknown x in this multivariate function and it is not easy to reduce the number of unknown x to one. In this paper we…
In this paper we present algorithmic considerations and theoretical results about the relation between the orders of certain groups associated to the components of a polynomial and the order of the group that corresponds to the polynomial,…
Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide…
We compute two parametric determinants in which rows and columns are indexed by compositions, where in one determinant the entries are products of binomial coefficients, while in the other the entries are products of powers. These results…
We explain how the simplicial higher-order unstable homotopy operations defined in [BBS2] may be composed and inserted one in another, thus forming a coherent if complicated algebraic structure.
The present paper develops two concepts of pointwise differentiability of higher order for arbitrary subsets of Euclidean space defined by comparing their distance functions to those of smooth submanifolds. Results include that…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that appear in imprecise-probabilistic decision…