Related papers: Amdahl's and Gustafson-Barsis laws revisited
Evaluating the completion time of a random algorithm or a running stochastic process is a valuable tip not only from a purely theoretical, but also pragmatic point of view. In the formal sense, this kind of a task is specified in terms of…
This paper argues that continued AI scaling requires repeated efficiency doublings. Classical AI scaling laws remain useful because they make progress predictable despite diminishing returns, but the compute variable in those laws is best…
The investigation asymptotic limits on associated data mainly focused on limit theorems of summands of associated data and on the related invariance principles. In a series of papers, we are going to set the general frame of the theory by…
Kramers escape rate in the overdamped systems with the power-law distribution is studied. By using the mean first passage time, we derive the escape rate for the power-law distribution and obtain the Kramers' infinite barrier escape rate in…
We consider an asynchronous system with transitions corresponding to the instructions of a computer system. For each instruction, a runtime is given. We propose a mathematical model, allowing us to construct an algorithm for finding the…
Neural scaling laws define a predictable relationship between a model's parameter count and its performance after training in the form of a power law. However, most research to date has not explicitly investigated whether scaling laws can…
In this paper, we prove two limit laws for functionals of self-intersection symmetric alpha-stable processes with alpha\in(1,2). The results are obtained based on the method of moments, the sample configuration and the chaining argument…
A definition for a class of asynchronous cellular arrays is proposed. An example of such asynchrony would be independent Poisson arrivals of cell iterations. The Ising model in the continuous time formulation of Glauber falls into this…
We introduce the notions of sub Gaussian random variables in sub-linear expectation spaces. To avoid the problem caused by the existence of two different expectations, i.e., the upper expectation and the lower expectation, we divide the…
In this work, the one-dimensional Cellular Automaton is extended to one that involves two sets of symbols and two global rules. As a main result, the Extended Curtis-Hedlund-Lyndon Theorem is demonstrated. Such constructions can be useful…
It is often claimed that the fundamental laws of physics are deterministic and time-symmetric and that therefore our experience of the passage of time is an illusion. This paper will critically discuss these claims and show that they are…
Linear fractional Galton-Watson branching processes in i.i.d.~random environment are, on the quenched level, intimately connected to random difference equations by the evolution of the random parameters of their linear fractional marginals.…
A recent article by Alexopoulos and Leontsinis presented empirical evidence that the first digits of the distances to galaxies are a reasonably good fit to the probabilities predicted by Benford's law, the well known logarithmic statistical…
In the past, efforts were taken to improve the performance of a processor via frequency scaling. However, industry has reached the limits of increasing the frequency and therefore concurrent execution of instructions on multiple cores seems…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
The stochastic properties of variables whose addition leads to $q$-Gaussian distributions $G_q(x)=[1+(q-1)x^2]_+^{1/(1-q)}$ (with $q\in\mathbb{R}$ and where $[f(x)]_+=max\{f(x),0\}$) as limit law for a large number of terms are…
We introduce novel convergence results for asynchronous iterations that appear in the analysis of parallel and distributed optimization algorithms. The results are simple to apply and give explicit estimates for how the degree of asynchrony…
A myriad of applications ranging from engineering and scientific simulations, image and signal processing as well as high-sensitive data retrieval demand high processing power reaching up to teraflops for their efficient execution. While a…
Murphy's Law is $not$ a law in the formal sense yet popular science often compares it with the Second Law of Thermodynamics as both the statements point toward a more disorganized state with time. In this paper, we first construct a…
We consider quantum formalism limited by the classical simulating computer with the fixed memory. The memory is redistributed in the course of modeling by the variation of the set of classical states and the accuracy of the representation…