Related papers: A Monadic Calculus with Episodic Flows
Monads can be interpreted as encoding formal expressions, or formal operations in the sense of universal algebra. We give a construction which formalizes the idea of "evaluating an expression partially": for example, "2+3" can be obtained…
An algorithm, based on numerical description of the terms of many-body perturbation theory (Goldstone diagrams), is presented. The algorithm allows the use of the same piece of computer code to evaluate any particular diagram in any…
In large-scale computation of physics problems, one often encounters the problem of determining a multi-dimensional function, which can be time-consuming when computing each point in this multi-dimensional space is already time-demanding.…
Complex algebraic calculations can be performed by reconstructing analytic results from numerical evaluations over finite fields. We describe FiniteFlow, a framework for defining and executing numerical algorithms over finite fields and…
We define a broad class of deterministic stream functions and show they can be implemented as homomorphisms into a "state" monoid. The homomorphism laws are simpler than the conditions of previous semantic frameworks for stream program…
Many planning formalisms allow for mixing numeric with Boolean effects. However, most of these formalisms are undecidable. In this paper, we will analyze possible causes for this undecidability by studying the number of different…
A diagrammatic technique is derived for calculating processes involving the production of large numbers of particles. As an example, the amplitude of three particles scattering into $n$ particles at the kinematical threshold in…
We describe quantizations on monoidal categories of modules over finite groups. They are given by quantizers which are elements of a group algebra. Over the complex numbers we find these explicitly. For modules over S3 and A4 we are given…
The operad of moulds is realized in terms of an operational calculus of formal integrals (continuous formal power series). This leads to many simplifications and to the discovery of various suboperads. In particular, we prove a conjecture…
In this paper, a monad-based denotational model is introduced and shown adequate for the Proto-Quipper family of calculi, themselves being idealized versions of the Quipper programming language. The use of a monadic approach allows us to…
It is well known that the action functional can be used to define classical, quantum, closed, and open dynamics in a generalization of the variational principle and in the path integral formalism in classical and quantum dynamics,…
We propose a model for deterministic distributed function computation by a network of identical and anonymous nodes, with bounded computation and storage capabilities that do not scale with the network size. Our goal is to characterize the…
In many massively parallel data management platforms, programs are represented as small imperative pieces of code connected in a data flow. This popular abstraction makes it hard to apply algebraic reordering techniques employed by…
First principles based exploration of chemical space deepens our understanding of chemistry, and might help with the design of new materials or experiments. Due to the computational cost of quantum chemistry methods and the immens number of…
Classical AI planners provide solutions to planning problems in the form of long and opaque text outputs. To aid in the understanding transferability of planning solutions, it is necessary to have a rich and comprehensible representation…
In this work, we study the problem of actively classifying the attributes of dynamical systems characterized as a finite set of Markov decision process (MDP) models. We are interested in finding strategies that actively interact with the…
Computational mechanics quantifies structure in a stochastic process via its causal states, leading to the process's minimal, optimal predictor---the $\epsilon$-machine. We extend computational mechanics to communication channels between…
Wall-crossing phenomena are ubiquitous in many problems of algebraic geometry and theoretical physics. Various ways to encode the relevant information and the need to track the changes under the variation of parameters lead to rather…
Many natural systems exhibit dynamics characterized by alternating phases or recurring sets of states. Describing the fluctuations of such systems over stochastic trajectories is necessary across diverse fields, from biological motors to…
We revisit once again the connection between three notions of computation: monads, arrows and idioms (also called applicative functors). We employ monoidal categories of finitary functors and profunctors on finite sets as models of these…