相关论文: State transitions as morphisms for complete lattic…
In fairly elementary terms this paper presents, and expands upon, a recent result by Garner by which the notion of topologicity of a concrete functor is subsumed under the concept of total cocompleteness of enriched category theory.…
Quantization problems suggest that the category of symplectic manifolds and symplectomorphisms be augmented by the inclusion of canonical relations as morphisms. These relations compose well when a transversality condition is satisfied, but…
Terminological acquisition is an important issue in learning for NLP due to the constant terminological renewal through technological changes. Terms play a key role in several NLP-activities such as machine translation, automatic indexing…
In this paper, we provide a comprehensive analysis of involutive quantales, with a particular focus on quantic frames. We extend the axiomatic foundations of quantale-enriched topological spaces to include closure under the anti-homomorphic…
Let $f \colon X \to Y$ be a morphism of concentrated schemes. We characterize $f$-perfect complexes $\mathcal{E}$ as those such that the functor $\mathcal{E} \otimes^{\mathbf{L}}_X \mathbf{L} f^*-$ preserves bounded complexes. We prove, as…
We consider one-parameter families of quadratic-phase integral transforms which generalize the fractional Fourier transform. Under suitable regularity assumptions, we characterize the one-parameter groups formed by such transforms.…
General hierarchical lattices of coupled maps are considered as dynamical systems. These models may describe many processes occurring in heterogeneous media with tree-like structures. The transition to turbulence via spatiotemporal…
We characterize virtual double categories of enriched categories, functors, and profunctors by introducing a new notion of double-categorical colimits. Our characterization is strict in the sense that it is up to equivalence between virtual…
The aim of this article is to describe a new perspective on functoriality of persistent homology and explain its intrinsic symmetry that is often overlooked. A data set for us is a finite collection of functions, called measurements, with a…
It is common practice in both theoretical computer science and theoretical physics to describe the (static) logic of a system by means of a complete lattice. When formalizing the dynamics of such a system, the updates of that system…
We consider compositions of the transformations of the time variable and canonical transformations of the other coordinates, which map completely integrable system into other completely integrable system. Change of the time gives rise to…
This is a survey about certain "almost homomorphisms" and "almost linear" functionals (called quasi-morphisms and quasi-states) in symplectic topology and their applications to Hamiltonian dynamics, functional-theoretic properties of…
We consider to treat the usual probabilistic cloning, state separation, unambiguous state discrimination, \emph{etc} in a uniform framework. All these transformations can be regarded as special examples of generalized completely positive…
Data integration and migration processes in polystores and multi-model database management systems highly benefit from data and schema transformations. Rigorous modeling of transformations is a complex problem. The data and schema…
The phenomenon of quantum phase transition is considered in the special case in which the evolution laws remain unitary and in which the bound-state energies remain observable. The conventional Hermiticity of observables is lost at the…
Quasi-lattices are introduced in terms of 'join' and 'meet' operations. It is observed that quasi-lattices become lattices when these operations are associative and when these operations satisfy 'modularity' conditions. A fundamental…
We introduce two simple two-dimensional lattice models to study traffic flow in cities. We have found that a few basic elements give rise to the characteristic phase diagram of a first-order phase transition from a freely moving phase to a…
Symmetries are important guiding principle for phase transitions. We systematically construct field theory models with local quantum fields that exhibit the following phase transitions: (1) different symmetry protected topological (SPT)…
Cofunctors are a kind of map between categories which lift morphisms along an object assignment. In this paper, we introduce cofunctors between categories enriched in a distributive monoidal category. We define a double category of enriched…
We introduce two simple two-dimensional lattice models to study traffic flow in cities. We have found that a few basic elements give rise to the characteristic phase diagram of a first-order phase transition from a freely moving phase to a…