Related papers: Resourceful Traces for Commuting Processes
We investigate causal computations taking sequences of inputs to sequences of outputs where the $n$th output depends on the first $n$ inputs only. We model these in category theory via a construction taking a Cartesian category $C$ to…
We propose a modal logic tailored to describe graph transformations and discuss some of its properties. We focus on a particular class of graphs called termgraphs. They are first-order terms augmented with sharing and cycles. Termgraphs…
Quantum walks are accepted as a generic model for quantum transport. The character of the transport crucially depends on the properties of the walk like its geometry and the driving coin. We demonstrate that increasing transport distance…
An approach is developed which enables one to analyze gravitational effects without usage of any concrete model of geometry (or a class of models of geometry) of space-time and even without any coordinate system. Instead, the formalism of…
We revise our "Physical Traces" paper in the light of the results in "A Categorical Semantics of Quantum Protocols". The key fact is that the notion of a strongly compact closed category allows abstract notions of adjoint, bipartite…
We introduce a new approach to model and analyze \emph{Mobility}. It is fully based on discrete mathematics and yields a class of mobility models, called the \emph{Markov Trace} Model. This model can be seen as the discrete version of the…
We introduce a general categorical framework to reason about quantum theory and other process theories living in spacetimes where Closed Timelike Curves (CTCs) are available, allowing resources to travel back in time and provide…
Analysis of execution traces plays a fundamental role in many program analysis approaches, such as runtime verification, testing, monitoring, and specification mining. Execution traces are frequently parametric, i.e., they contain events…
We consider a family of Markov maps on the unit interval, interpolating between the tent map and the Farey map. The latter map is not uniformly expanding. Each map being composed of two fractional linear transformations, the family…
Computational devices combining two or more different parts, one controlling the operation of the other, for example, derive their power from the interaction, in addition to the capabilities of the parts. Non-classical computation has…
We study the arithmetic Fourier transforms of trace functions on general connected commutative algebraic groups. To do so, we first prove a generic vanishing theorem for twists of perverse sheaves by characters, and using this tool, we…
We generalise the standard constructions of a Cayley graph in terms of a group presentation by allowing some vertices to obey different relators than others. The resulting notion of presentation allows us to represent every vertex…
Execution of concurrent programs implies frequent switching between different thread contexts. This property perplexes analyzing and reasoning about concurrent programs. Trace simplification is a technique that aims at alleviating this…
A rational framework is proposed to explain how we accommodate unbounded sensory input within bounded memory. According to this framework, memory is stored as a statistic-like representation that is repeatedly summarized and compressed to…
We present a probabilistic generative model for inferring a description of coordinated, recursively structured group activities at multiple levels of temporal granularity based on observations of individuals' trajectories. The model…
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…
We explain how categories, and groupoids, can be seen as models for a Lawvere ${\mathfrak Gr}$-theory, where ${\mathfrak Gr}$ is the category of graphs, and show that for Lawvere ${\mathfrak Gr}$-theories finitely presentable models are…
We introduce a representation learning framework for spatial trajectories. We represent partial observations of trajectories as probability distributions in a learned latent space, which characterize the uncertainty about unobserved parts…
Trace Dynamics is a classical dynamical theory of noncommuting matrices in which cyclic permutation inside a trace is used to define the derivative with respect to an operator. We use the methods of Trace Dynamics to construct a…
We introduce a cyclic proof system for the two-way alternation-free modal $\mu$-calculus. The system manipulates one-sided Gentzen sequents and locally deals with the backwards modalities by allowing analytic applications of the cut rule.…