Related papers: Resourceful Traces for Commuting Processes
We investigate program equivalence for linear higher-order(sequential) languages endowed with primitives for computational effects. More specifically, we study operationally-based notions of program equivalence for a linear…
Runtime predictive analyses enhance coverage of traditional dynamic analyses based bug detection techniques by identifying a space of feasible reorderings of the observed execution and determining if any of these witnesses the violation of…
This dissertation has two main parts. The first part deals with questions relating to Haghverdi and Scott's notion of partially traced categories. The main result is a representation theorem for such categories: we prove that every…
We introduce proof terms for string rewrite systems and, using these, show that various notions of equivalence on reductions known from the literature can be viewed as different perspectives on the notion of causal equivalence. In…
Fixed effects models are very flexible because they do not make assumptions on the distribution of effects and can also be used if the heterogeneity component is correlated with explanatory variables. A disadvantage is the large number of…
This paper proposes graphical representations of data and rationale provenance in workflows that convert both category labels and associated numeric data between distinct but semantically related taxonomies. We motivate the graphical…
We describe a denotational semantics for an abstract effect system for a higher-order, shared-variable concurrent programming language. We prove the soundness of a number of general effect-based program equivalences, including a…
Partially commutative monoids provide a powerful tool to study graphs, viewingwalks as words whose letters, the edges of the graph, obey a specific commutation rule. A particularclass of traces emerges from this framework, the hikes, whose…
We introduce a type and effect system, for an imperative object calculus, which infers "sharing" possibly introduced by the evaluation of an expression, represented as an equivalence relation among its free variables. This direct…
Given a braided pivotal category $\mathcal C$ and a pivotal module tensor category $\mathcal M$, we define a functor $\mathrm{Tr}_{\mathcal C}:\mathcal M \to \mathcal C$, called the associated categorified trace. By a result of…
Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a…
Premonoidal categories and Freyd categories provide an encompassing framework for the semantics of call-by-value programming languages. Premonoidal categories are a weakening of monoidal categories in which the interchange law for the…
We generalize the notion of a modified trace (or m-trace) to the setting of non-unimodular categories. M-traces are known to play an important role in low-dimensional topology and representation theory, as well as in studying the category…
Within the Geometry of Interaction (GoI) paradigm, we present a setting that enables qualitative differences between classical and quantum processes to be explored. The key construction is the physical interpretation/realization of the…
We use traced monoidal categories to give a precise general version of "geometry of interaction". We give a number of examples of both "particle-style" and "wave-style" instances of this construction. We relate these ideas to semantics of…
We have developed a steady state theory of complex transport networks used to model the flow of commodity, information, viruses, opinions, or traffic. Our approach is based on the use of the Markov chains defined on the graph…
Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a general representation theorem for a wide class of…
Recently there has been significant interest in using causal modelling techniques to understand the structure of physical theories. However, the notion of `causation' is limiting - insisting that a physical theory must involve causal…
Integer-order differential operators were originally used to describe local and isotropic effects, in both space and time. However, in fields like biology, the modelling of complex phenomena with spatial heterogeneity necessitates more…
We continue to develop a new approach to description of charge kinetics in disordered semiconductors. It is based on fractional diffusion equations. This article is devoted to transient processes in structures under dispersive transport…