Related papers: Amdahl's and Gustafson-Barsis laws revisited
In this article, we update the reference [14] in two aspects. First, we note that in order for the control law (12) in [14] to be equivalent to the control law (3) in [14], we need to assume that the samplings for all subsystems must be…
This note argues for more use of simple models beyond Amdahl's Law: Bottleneck Analysis, Little's Law, and a M/M/1 Queue.
Speedable numbers are real numbers which are algorithmically approximable from below and whose approximations can be accelerated nonuniformly. We begin this article by answering a question of Barmpalias by separating a strict subclass that…
Statistical laws describe regular patterns observed in diverse scientific domains, ranging from the magnitude of earthquakes (Gutenberg-Richter law) and metabolic rates in organisms (Kleiber's law), to the frequency distribution of words in…
Repeated recursion unfolding is a new approach that repeatedly unfolds a recursion with itself and simplifies it while keeping all unfolded rules. Each unfolding doubles the number of recursive steps covered. This reduces the number of…
We extend the speed limit of a distance between two states evolving by different generators for quantum systems [K. Suzuki and K. Takahashi, Phys. Rev. Res. 2, 032016(R) (2020)] to the classical stochastic processes described by the master…
The universal scalability law of computational capacity is a rational function C_p = P(p)/Q(p) with P(p) a linear polynomial and Q(p) a second-degree polynomial in the number of physical processors p, that has been long used for statistical…
High-speed disperse multiphase flows are present in numerous environmental and engineering applications with complex interactions between turbulence, shock waves, and particles. Compared to its incompressible counterpart, compressible…
Parallel replica dynamics is a method for accelerating the computation of processes characterized by a sequence of infrequent events. In this work, the processes are governed by the overdamped Langevin equation. Such processes spend much of…
Central to the power of quantum computing is the concept of quantum parallelism: quantum systems can explore and process multiple computational paths simultaneously. In this paper, we discuss the elusive nature of quantum parallelism,…
We prove the well-posedness of a system of balance laws inspired by [8], describing macro-scopically the traffic flow on a multi-lane road network. Motivated by real applications, we allow for the the presence of space discontinuities both…
We have defined a slowness, s, as the reciprocal conjugate of velocity, v. s = -ih/v. We have shown that Einstein's postulate (v has an upper limit) implies that s is discrete. A velocity operator is defined as the derivative with respect…
For the stochastic six-vertex model on the quadrant $\mathbb{Z}_{\geq0}\times\mathbb{Z}_{\geq0}$ with step initial conditions and a single second-class particle at the origin, we show almost sure convergence of the speed of the second-class…
The standard small-time functional central limit theorem of semimartingales has been established in (Gerhold, S., Kleinert, M., Porkert, P., and Shkolnikov, M. (2015). Small time central limit theorems for semimartingales with applications.…
We discuss the computational performance of the adaptive resolution technique in molecular simulation when it is compared with equivalent full coarse-grained and full atomistic simulations. We show that an estimate of its efficiency, within…
This paper revisits Menzerath's Law, also known as the Menzerath-Altmann Law, which models a relationship between the length of a linguistic construct and the average length of its constituents. Recent findings indicate that simple…
Complex systems are often characterized by the interplay of multiple interconnected dynamical processes operating across a range of temporal scales. This phenomenon is widespread in both biological and artificial scenarios, making it…
Particle flows injected as beams and scattered by an intruder are numerically studied. We find a crossover of the drag force from Epstein's law to Newton's law, depending on the ratio of the speed to the thermal speed. These laws can be…
The experience shows that cooperating and communicating computing systems, comprising segregated single processors, have severe performance limitations. In his classic "First Draft" von Neumann warned that using a "too fast processor"…
A finite element approach to the elastic flow of a curve coupled with a diffusion equation on the curve is analysed. Considering the graph case, the problem is weakly formulated and approximated with continuous linear finite elements, which…