Related papers: Amdahl's and Gustafson-Barsis laws revisited
We establish a strong law of large numbers for one-dimensional continuous-time random walks in dynamic random environments under two main assumptions: the environment is required to satisfy a decoupling inequality that can be interpreted as…
A behavioural theory consists of machine-independent postulates characterizing a particular class of algorithms or systems, an abstract machine model that provably satisfies these postulates, and a rigorous proof that any algorithm or…
Gradient descent, and coordinate descent in particular, are core tools in machine learning and elsewhere. Large problem instances are common. To help solve them, two orthogonal approaches are known: acceleration and parallelism. In this…
We seek tight bounds on the viable parallelism in asynchronous implementations of coordinate descent that achieves linear speedup. We focus on asynchronous coordinate descent (ACD) algorithms on convex functions which consist of the sum of…
A continuous approximation for the results of [1] is obtained. In this approximation the energy distribution is represented in the form of the product of the Gibbs factor and superstatistics factor. The mutual weights of the factors are…
Quantum computation is frequently mischaracterized as the simultaneous execution of exponentially many classical computations. This article offers a conceptual clarification of why this ``branchwise parallelism'' picture is misleading,…
Today we live in the age of artificial intelligence and machine learning; from small startups to HW or SW giants, everyone wants to build machine intelligence chips, applications. The task, however, is hard: not only because of the size of…
A finite point process is characterized by the distribution of the number of points (the size) of the process. In some applications, for example, in the context of packet flows in modern communication networks, it is of interest to infer…
We are given a set of jobs, each one specified by its release date, its deadline and its processing volume (work), and a single (or a set of) speed-scalable processor(s). We adopt the standard model in speed-scaling in which if a processor…
In competitive parallel computing, the identical copies of a code in a phase of a sequential program are assigned to processor cores and the result of the fastest core is adopted. In the literature, it is reported that a superlinear speedup…
The escape of the randomly accelerated undamped particle from the finite interval under action of stochastic resetting is studied. The motion of such a particle is described by the full Langevin equation and the particle is characterized by…
In the world of supercomputers, the large number of processors requires to minimize the inefficiencies of parallelization, which appear as a sequential part of the program from the point of view of Amdahl's law. The recently suggested new…
An excited random walk is a non-Markovian extension of the simple random walk, in which the walk's behavior at time $n$ is impacted by the path it has taken up to time $n$. The properties of an excited random walk are more difficult to…
Pre-exascale High Performance Computers (HPC) can reach more than 400 Pflop/s real perfor-mance according the HPLinpack benchmarks. For nanoscience and quantum biology there are requirements for those program codes based on quantum physics…
Real-time systems applications usually consist of a set of concurrent activities with timing-related properties. Developing these applications requires programming paradigms that can effectively handle the specification of concurrent…
Within the mode-coupling theory for structural relaxation in simple systems the asymptotic laws and their leading-asymptotic correction formulas are derived for the motion of a tagged particle near a glass-transition singularity. These…
This paper introduces a novel, fast atomic-snapshot protocol for asynchronous message-passing systems. In the process of defining what ``fast'' means exactly, we spot a few interesting issues that arise when conventional time metrics are…
We study non-terminating graph rewriting models, whose local rules are applied non-deterministically -- and yet enjoy a strong form of determinism, namely space-time determinism. Of course in the case of terminating computation it is…
A general class of non-Markov, supercritical Gaussian branching particle systems is introduced and its long-time asymptotics is studied. Both weak and strong laws of large numbers are developed with the limit object being characterized in…
We present a simplified model of data flow on processors in a high performance computing framework involving computations necessitating inter-processor communications. From this ordinary differential model, we take its asymptotic limit,…