Related papers: Computational Flows in Arithmetic
Traffic flows in a distributed computing network require both transmission and processing, and can be interdicted by removing either communication or computation resources. We study the robustness of a distributed computing network under…
An extended formulation of a polytope is a linear description of this polytope using extra variables besides the variables in which the polytope is defined. The interest of extended formulations is due to the fact that many interesting…
The Max-Flow Min-Cut theorem is the classical duality result for the Max-Flow problem, which considers flow of a single commodity. We study a multiple commodity generalization of Max-Flow in which flows are composed of real-valued k-vectors…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
We present a light formalism for proofs that encodes their inferential structure, along with a system that transforms these representations into flow-chart diagrams. Such diagrams should improve the comprehensibility of proofs. We discuss…
Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…
The applications and impact of high fidelity simulation of fluid flows are far-reaching. They include settling some long-standing and fundamental questions in turbulence. However, the computational resources required for such efforts are…
Robust network flows are a concept for dealing with uncertainty and unforeseen failures in the network infrastructure. They and their dual counterpart, network flow interdiction, have received steady attention within the operations research…
Flow networks have attracted a lot of research in computer science. Indeed, many questions in numerous application areas can be reduced to questions about flow networks. Many of these applications would benefit from a framework in which one…
Temporal interaction networks capture the history of activities between entities along a timeline. At each interaction, some quantity of data (money, information, kbytes, etc.) flows from one vertex of the network to another. Flow-based…
Fluid flows are omnipresent in nature and engineering disciplines. The reliable computation of fluids has been a long-lasting challenge due to nonlinear interactions over multiple spatio-temporal scales. The compressible Navier-Stokes…
We study rational streams (over a field) from a coalgebraic perspective. Exploiting the finality of the set of streams, we present an elementary and uniform proof of the equivalence of four notions of representability of rational streams:…
We consider fixed boundary flow with canonical interpretability as principal components extended on non-linear Riemannian manifolds. We aim to find a flow with fixed starting and ending points for noisy multivariate data sets lying on an…
We introduce and prove basic results about several graph-theoretic notions relevant to the multiresolution analysis of flow graphs that represent the transfer of control in computer programs. We take a category-theoretical viewpoint to…
We consider two classes of stream-based computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. The dataflow architecture is a natural platform for programming with streams.…
Neural networks have been successfully applied in various resource-constrained edge devices, where usually central processing units (CPUs) instead of graphics processing units exist due to limited power availability. State-of-the-art…
In network function computation is as a means to reduce the required communication flow in terms of number of bits transmitted per source symbol. However, the rate region for the function computation problem in general topologies is an open…
Motivated by the challenge of analyzing data sets with periodic boundary conditions to investigate transportation properties, we introduce a concept of circular max-flow for graphs mapped onto the circle. Unlike classical max-flow…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
In three-dimensional computational topology, the theory of normal surfaces is a tool of great theoretical and practical significance. Although this theory typically leads to exponential time algorithms, very little is known about how these…