Related papers: Amdahl's and Gustafson-Barsis laws revisited
We study the asymptotic speed of a second class particle in the two-species asymmetric simple exclusion process (ASEP) on $\mathbb{Z}$ with each particle belonging either to the first class or the second class. For any fixed non-negative…
This paper performs the analysis necessary to bound the running time of known, efficient algorithms for generating all longest common subsequences. That is, we bound the running time as a function of input size for algorithms with time…
Nonequilibrium thermodynamics of a general second-order stochastic system is investigated. We prove that at steady state, under inversion of velocities, the condition of time-reversibility over the phase space is equivalent to the…
It is generally believed that a generic system can be reversibly transformed from one state into another by sufficiently slow change of parameters. A standard argument favoring this assertion is based on a possibility to expand the energy…
The problem of guessing a random string is revisited. A close relation between guessing and compression is first established. Then it is shown that if the sequence of distributions of the information spectrum satisfies the large deviation…
The law of large numbers is one of the fundamental properties which algorithmically random infinite sequences ought to satisfy. In this paper, we show that the law of large numbers can be effectivized for an arbitrary Schnorr random…
In this paper, we consider the problem of scheduling an application on a parallel computational platform. The application is a particular task graph, either a linear chain of tasks, or a set of independent tasks. The platform is made of…
In the random acceleration process, a point particle is accelerated according to $\ddot{x}=\eta(t)$, where the right hand side represents Gaussian white noise with zero mean. We begin with the case of a particle with initial position $x_0$…
We discuss Pitman's representation of a Markov process, which serves as a discrete analog to the Bessel 3D process starting at time 0 from an arbitrary initial law. This representation involves maxima of lazy simple random walks and an…
In this short presentation, we address two somewhat separate issues. The first one deals with the establishment (vs discovery) of what we call "physical laws". The discussion runs on a "successive approximations" approach, suited to our own…
Galaxies obey a set of strict dynamical laws, which imply a close coupling between the visible matter (stars and gas) and the observed dynamics (set by dark matter in the standard cosmological context). Here we review recent results from…
In order to define graph transformations by the simultaneous application of concurrent rules, we have adopted in previous work a structure of attributed graphs stable by unions. We analyze the consequences on parallel independence, a…
There are enormous amount of examples of Computation in nature, exemplified across multiple species in biology. One crucial aim for these computations across all life forms their ability to learn and thereby increase the chance of their…
Cellular automata are often used to model systems in physics, social sciences, biology that are inherently asynchronous. Over the past 20 years, studies have demonstrated that the behavior of cellular automata drastically changed under…
The special relativity laws emerge as one-parameter (light speed) generalizations of the corresponding laws of classical physics. These generalizations, imposed by the Lorentz transformations, affect both the definition of the various…
Behavior of condensed matter systems deviating from the standard equilibrium conditions is discussed. Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the…
We show for several computational problems how classical greedy algorithms for special cases can be derived in a simple way from dynamic programs for the general case: interval scheduling (restricted to unit weights), knapsack (restricted…
The design of guidance law can be considered a kind of finite-time error-tracking problem. A unified free-time convergent guidance law design approach based on the error dynamics and the free-time convergence method is proposed in this…
We study the stochastic motion of a particle subject to spatially varying Lorentz force in the small-mass limit. The limiting procedure yields an additional drift term in the overdamped equation that cannot be obtained by simply setting…
In this short paper, we study the simulation of a large system of stochastic processes subject to a common driving noise and fast mean-reverting stochastic volatilities. This model may be used to describe the firm values of a large pool of…