Related papers: Exploring the Boundaries of Monad Tensorability on…
Operads are algebraic devices offering a formalization of the concept of operations with several inputs and one output. Such operations can be naturally composed to form bigger and more complex ones. Coming historically from algebraic…
The development of compositional distributional models of semantics reconciling the empirical aspects of distributional semantics with the compositional aspects of formal semantics is a popular topic in the contemporary literature. This…
A central problem in the study of resource theories is to find functions that are nonincreasing under resource conversions - termed monotones - in order to quantify resourcefulness. Various constructions of monotones appear in many…
We study the existence and left properness of transferred model structures for "monoid-like" objects in monoidal model categories. These include genuine monoids, but also all kinds of operads as for instance symmetric, cyclic, modular,…
A new and extensive formalism is developed for monads and galaxies in non-standard enlargements. It is shown that monads and galaxies can be manipulated using order-preserving and order-reversing set-to-set maps, and that set properties…
We find a necessary and sufficient condition for the existence of the tensor product of modules over a Lie conformal algebra. We provide two algebraic constructions of the tensor product. We show the relation between tensor product and…
Word embedding is a powerful tool in natural language processing. In this paper we consider the problem of word embedding composition \--- given vector representations of two words, compute a vector for the entire phrase. We give a…
When given a class of functions and a finite collection of sets, one might be interested whether the class in question contains any function whose domain is a subset of the union of the sets of the given collection and whose restrictions to…
Free tensors are tensors which, after a change of bases, have free support: any two distinct elements of its support differ in at least two coordinates. They play a distinguished role in the theory of bilinear complexity, in particular in…
In this thesis we study three problems. The first is the superposition of the operators and their proprities, such as boundedness,continuity,regularity and the inequalities of the norms of the composition of functions in some functional…
Two successive generalizations of the usual tensor products are given. One can be constructed for arbitrary binary operations, and not only for semigroups, groups or vector spaces. The second one, still more general, is constructed for…
In this paper, we introduce semi-infinite tensor complementarity problem to provide an approach for considering a more realistic situation of the problem. We prove the necessary and sufficient conditions for the existence of the solution…
Restriction is a natural quasi-order on $d$-way tensors. We establish a remarkable aspect of this quasi-order in the case of tensors over a fixed finite field -- namely, that it is a well-quasi-order: it admits no infinite antichains and no…
It is well known that tensor models for a tensor with no symmetry admit a $1/N$ expansion dominated by melonic graphs. This result relies crucially on identifying \emph{jackets} which are globally defined ribbon graphs embedded in the…
We study monads resulting from the combination of nondeterministic and probabilistic behaviour with the possibility of termination, which is essential in program semantics. Our main contributions are presentation results for the monads,…
The tensor complementarity problem is a specially structured nonlinear complementarity problem, then it has its particular and nice properties other than ones of the classical nonlinear complementarity problem. In this paper, it is proved…
The coalgebraic modelling of alternating automata and of probabilistic automata has long been obstructed by the absence of distributive laws of the powerset monad over itself, respectively of the powerset monad over the finite distribution…
We consider colored compositions where only some parts are allowed different colors, depending on their locations in the composition. The counting sequences are obtained through generating functions. Connections to many other combinatorial…
A well-known challenge in the semantics of programming languages is how to combine non-determinism and probability. At a technical level, the problem arises from the fact that there is a no distributive law between the powerset monad and…
We investigate a class of supersymmetric quantum mechanical theories (with two supercharges) having tensor-valued degrees of freedom which are dominated by melon diagrams in the large $N$ limit. One motivation was to examine the interplay…