Related papers: State transitions as morphisms for complete lattic…
We present extensions to a continuous-state dependency parsing method that makes it applicable to morphologically rich languages. Starting with a high-performance transition-based parser that uses long short-term memory (LSTM) recurrent…
We provide a definition of enrichment that applies to a wide variety of categorical structures, generalizing Leinster's theory of enriched $T$-multicategories. As a sample of newly enrichable structures, we describe in detail the examples…
A recent proposal of new sets of squeezed states is seen as a particular case of a general context admitting realistic physical Hamiltonians. Such improvements reveal themselves helpful in the study of associated squeezing effects.…
We introduce a theory for encoding and manipulating algebraic data on categories via $\textit{concentration structures}$, which are equivalence relations on morphisms that satisfy certain axioms. For any category with a concentration…
Cofibration categories are a formalization of homotopy theory useful for dealing with homotopy colimits that exist on the level of models as colimits of cofibrant diagrams. In this paper, we deal with their enriched version. Our main result…
We investigate monoidal categories of formal contexts, in which states correspond to formal concepts. In particular we examine the category of bonds or Chu correspondences between contexts, which is known to be equivalent to the…
We present a detailed synthetic overview of the utilisation of categorical techniques in the study of order structures together with their applications in operational quantum theory. First, after reviewing the notion of residuation and its…
This article is an introduction to the basic generalized category theory used in recent work on an extension of the theory of categories and categorical logic, including parts of topos theory. We discuss functors, equivalences, natural…
The entanglement properties of the phase transition in a two dimensional harmonic lattice, similar to the one observed in recent ion trap experiments, are discussed both, for finite number of particles and thermodynamical limit. We show…
Conformal transformations of a Euclidean (complex) plane have some kind of completeness (sufficiency) for the solution of many mathematical and physical-mathematical problems formulated on this plane. There is no such completeness in the…
In this paper we show that classical notions from automata theory such as simulation and bisimulation can be lifted to the context of enriched categories. The usual properties of bisimulation are nearly all preserved in this new context.…
A general class of mass transport models with Q species of conserved mass is considered. The models are defined on a lattice with parallel discrete time update rules. For one-dimensional, totally asymmetric dynamics we derive necessary and…
Interacting systems of particles with generalized statistics are considered on both classical and quantum level. It is shown that all possible quantum states and corresponding processes can be represented in terms of certain specific…
Quantum interfaces between polarized atomic ensembles and coherent states of light, applied recently to manipulate bipartite and multipartite entanglement, are revisited by means of a continuous-variable formalism. The explicit use of the…
Restriction categories were introduced to provide an axiomatic setting for the study of partially defined mappings; they are categories equipped with an operation called restriction which assigns to every morphism an endomorphism of its…
When an entangled state evolves under local unitaries, the entanglement in the state remains fixed. Here we show the dynamical phase acquired by an entangled state in such a scenario can always be understood as the sum of the dynamical…
We develop an alternative view on the concept of connections over a vector bundle map, which consists of a horizontal lift procedure to a prolonged bundle. We further focus on prolongations to an affine bundle and introduce the concept of…
State of the art language models return a natural language text continuation from any piece of input text. This ability to generate coherent text extensions implies significant sophistication, including a knowledge of grammar and semantics.…
We analyze a set of models frequently appearing in quantum optical settings by expressing their Hamiltonians in terms of Fock-state lattices. The few degrees-of-freedom of such models, together with the system symmetries, make the emerging…
We investigate quantum phase transitions (QPTs) in spin chain systems characterized by local Hamiltonians with matrix product ground states. We show how to theoretically engineer such QPT points between states with predetermined properties.…