Related papers: On Three Alternative Characterizations of Combined…
The analysis of concurrent and reactive systems is based to a large degree on various notions of process equivalence, ranging, on the so-called linear-time/branching-time spectrum, from fine-grained equivalences such as strong bisimilarity…
The (chordal) Loewner differential equation encodes certain curves in the half-plane (aka traces) by continuous real-valued driving functions. Not all curves are traces; the latter can be defined via a geometric condition called the local…
We give an alternate conception of string diagrams as labeled 1-dimensional oriented cobordisms, the operad of which we denote by Cob/O, where O is the set of string labels. The axioms of traced (symmetric monoidal) categories are fully…
We propose a new class of traces motivated by a trace/trace class property discovered by Laurie, Nordgren, Radjavi and Rosenthal concerning products of operators outside the trace class. Spectral traces, traces that depend only on the…
We present tracial analogs of the classical results of Curto and Fialkow on moment matrices. A sequence of real numbers indexed by words in non-commuting variables with values invariant under cyclic permutations of the indexes, is called a…
In the development of operational semantics of concurrent systems, a key decision concerns the adoption of a suitable notion of execution model, which basically amounts to choosing a class of partial orders according to which events are…
In this paper, we define and study the concept of traceable regressions. These are sequences of regressions in joint or single responses for which a corresponding regression graph captures not only an independence structure but represents,…
We combine previous work on coalgebraic logic with the coalgebraic traces semantics of Hasuo, Jacobs, and Sokolova.
In this paper we consider a general system of activities that can, but do not have to, occur. This system is governed by a set containing two types of constraints: precedence and response. A precedence constraint dictates that an activity…
The notion of homomorphism indistinguishability offers a combinatorial framework for characterizing equivalence relations of graphs, in particular equivalences in counting logics within finite model theory. That is, for certain graph…
This paper explores the connection between semantic equivalences and preorders for concrete sequential processes, represented by means of labelled transition systems, and formats of transition system specifications using Plotkin's…
Categorification is a process of lifting structures to a higher categorical level. The original structure can then be recovered by means of the so-called "decategorification" functor. Algebras are typically categorified to additive…
Traces form a coarse notion of semantic equivalence between states of a process, and have been studied coalgebraically for various types of system. We instantiate the finitary coalgebraic trace semantics framework of Hasuo et al. for…
In a multi-modeling based approach, the system under development is described by several models that represent various perspectives and concerns. Obviously, these partial representations are less complex than the global model, but they need…
The notion of a braided chord diagram is introduced and studied. An equivalence relation is given which identifies all braidings of a fixed chord diagram. It is shown that finite-type invariants are stratified by braid index for knots which…
Images of scenes have various objects as well as abundant attributes, and diverse levels of visual categorization are possible. A natural image could be assigned with fine-grained labels that describe major components, coarse-grained labels…
An algebraization of the notion of topology has been proposed more than seventy years ago in a classical paper by McKinsey and Tarski. However, in McKinsey and Tarski's setting the model theoretical notion of homomorphism does not…
Recent progress in multiple object tracking (MOT) has shown that a robust similarity score is key to the success of trackers. A good similarity score is expected to reflect multiple cues, e.g. appearance, location, and topology, over a long…
Path graphs are intersection graphs of paths in a tree. We start from the characterization of path graphs by Monma and Wei [C.L.~Monma,~and~V.K.~Wei, Intersection Graphs of Paths in a Tree, J. Combin. Theory Ser. B, 41:2 (1986) 141--181]…
Transformer architectures, capable of capturing sequential dependencies in the history of user interactions, have become the dominant approach in sequential recommender systems. Despite their success, such models consider sequence elements…