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The evolution of complexity has been a central theme for Biology [2] and Artificial Life research [1]. It is generally agreed that complexity has increased in our universe, giving way to life, multi-cellularity, societies, and systems of…
We propose a rigorous decomposition of predictive error, highlighting that not all 'irreducible' error is genuinely immutable. Many domains stand to benefit from iterative enhancements in measurement, construct validity, and modeling. Our…
Large-scale empirical data, the sample size and the dimension are high, often exhibit various characteristics. For example, the noise term follows unknown distributions or the model is very sparse that the number of critical variables is…
We start by reviewing recent probabilistic results on ergodic sums in a large class of (non-uniformly) hyperbolic dynamical systems. Namely, we describe the central limit theorem, the almost-sure convergence to the gaussian and other stable…
Performance evolution of a number of complex scientific and technical systems demonstrate exponential progress with time exp(+t/C) . The speed of progress C - a measure of difficulty and complexity - is analyzed for high energy elementary…
A list of open problems on global behavior in time of some evolution systems, mainly governed by P.D.E, is given together with some background information explaining the context in which these problems appeared. The common characteristic of…
Dynamics of a social population is analyzed taking into account some physical constraints on individual behavior and decision making abilities. The model, based on Evolutionary Game Theory, predicts that a population has to pass through a…
Complex systems are characterized by specific time-dependent interactions among their many constituents. As a consequence they often manifest rich, non-trivial and unexpected behavior. Examples arise both in the physical and non-physical…
A theoretical analysis of the earthquake prediction problem in space-time is presented. We find an explicit structure of the optimal strategy and its relation to the generalized error diagram. This study is a generalization of the…
Traditionally evolution is seen as a process where from a pool of possible variations of a population (e.g. biological species or industrial goods) a few variations get selected which survive and proliferate, whereas the others vanish.…
Although a system is described by a well-known set of equations leading to a deterministic behavior, in the real world the value of a measurand obtained by an experiment will mostly scatter. Accordingly, an uncertainty is associated with…
The role of the selection pressure and mutation amplitude on the behavior of a single-species population evolving on a two-dimensional lattice, in a periodically changing environment, is studied both analytically and numerically. The…
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in different contexts. Here we propose a generative model to capture the essential dynamics of survival analysis,…
It is shown that, by imposing reparametrization invariance, one may derive a variety of stochastic equations describing the dynamics of surface growth and identify the physical processes responsible for the various terms. This approach…
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…
This paper is to show that most discrete models used for population dynamics in ecology are inherently pathological that their predications cannot be independently verified by experiments because they violate a fundamental principle of…
In this review, I provide an overview of theoretical aspects related to the evolution of galaxies as a function of environment. I discuss the main physical processes at play, their characteristic time-scales and environmental dependency,…
Cosmology contributes a good deal to the investigation of variation of fundamental physical constants. High resolution data is available and allows for detailed analysis over cosmological distances and a multitude of methods were developed.…
1. Theoretical models pertaining to feedbacks between ecological and evolutionary processes are prevalent in multiple biological fields. An integrative overview is currently lacking, due to little crosstalk between the fields and the use of…
Evolutionary algorithms have been frequently applied to constrained continuous optimisation problems. We carry out feature based comparisons of different types of evolutionary algorithms such as evolution strategies, differential evolution…