Related papers: Algorithmic complexity and randomness in elastic s…
Data Science and Machine learning have been growing strong for the past decade. We argue that to make the most of this exciting field we should resist the temptation of assuming that forecasting can be reduced to brute-force data analytics.…
We study the role of connectivity on the linear and nonlinear elastic behavior of amorphous systems using a two-dimensional random network of harmonic springs as a model system. A natural characterization of these systems arises in terms of…
We define the complexity of a continuous-time linear system to be the minimum number of bits required to describe its forward increments to a desired level of fidelity, and compute this quantity using the rate distortion function of a…
We propose an algorithm for optimizations in which the gradients contain stochastic noise. This arises, for example, in structural optimizations when computations of forces and stresses rely on methods involving Monte Carlo sampling, such…
An approach to analyse the properties of a particle system is to compare it with different processes to understand when one of them is larger than other ones. The main technique for that is coupling, which may not be easy to construct. We…
The human nervous system utilizes synaptic plasticity to solve optimization problems. Previous studies have tried to add the plasticity factor to the training process of artificial neural networks, but most of those models require complex…
In recent work, it was shown that elasticity theory can break down in amorphous solids subjected to nonuniform {\em static} loads. The elastic fields are screened by geometric dipoles; these stem from gradients of the quadrupole field…
Random constraint satisfaction problems can display a very rich structure in the space of solutions, with often an ergodicity breaking -- also known as clustering or dynamical -- transition preceding the satisfiability threshold when the…
Many complex systems can spontaneously oscillate under non-periodic forcing. Such self-oscillators are commonplace in biological and technological assemblies where temporal periodicity is needed, such as the beating of a human heart or the…
This is a chapter in the Encyclopedia of Robotics. It is devoted to the study of complexity of complete (or exact) algorithms for robot motion planning. The term ``complete'' indicates that an approach is guaranteed to find the correct…
We propose a test based on the theory of algorithmic complexity and an experimental evaluation of Levin's universal distribution to identify evidence in support of or in contravention of the claim that the world is algorithmic in nature. To…
We discuss a characterization of complexity based on successive approximations of the probability density describing a system by means of maximum entropy methods, thereby quantifying the respective role played by different orders of…
We have developed a simulation technique that uses non-linear finite element analysis and elastic fracture mechanics to compute physically plausible motion for three-dimensional, solid objects as they break, crack, or tear. When these…
Recent experiments have exploited elastic instabilities in membranes to create complex patterns. However, the rational design of such structures poses many challenges, as they are products of nonlinear elastic behavior. We pose a simple…
The stability and ergodicity properties of two adaptive random walk Metropolis algorithms are considered. The both algorithms adjust the scaling of the proposal distribution continuously based on the observed acceptance probability. Unlike…
Numerous soft materials jam into an amorphous solid at high packing fraction. This non-equilibrium phase transition is best understood in the context of a model system in which particles repel elastically when they overlap. Recently,…
This paper will introduce a theory of emergent animal social complexity using various results from computational models and empirical results. These results will be organized into a vertical model of social complexity. This will support the…
In this paper we introduce a new approach for the study of the complex behavior of Minority Game using the tools of algorithmic complexity, physical entropy and information theory. We show that physical complexity and mutual information…
We review the concept of well-posedness in the context of evolutionary problems from mathematical physics for a particular subclass of problems from elasticity theory. The complexity of physical phenomena appears as encoded in so called…
Nowadays the question `what is complexity?' is a challenge to be answered. This question is triggering a great quantity of works in the frontier of physics, biology, mathematics and computer science. Even more when this century has been…