Related papers: On the algorithmic behaviour of complex physical s…
So far, following the works of A.M. Turing, the algorithms were considered as the mathematical abstraction from which we could write programs for computers whose principle was based on the theoretical concept of Turing machine. We start…
Nature-inspired algorithms are among the most powerful algorithms for optimization. This paper intends to provide a detailed description of a new Firefly Algorithm (FA) for multimodal optimization applications. We will compare the proposed…
A model of an organism as an autonomous intelligent system has been proposed. This model was used to analyze learning of an organism in various environmental conditions. Processes of learning were divided into two types: strong and weak…
This manuscript portrays optimization as a process. In many practical applications the environment is so complex that it is infeasible to lay out a comprehensive theoretical model and use classical algorithmic theory and mathematical…
Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…
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.…
A primary motivation for our research in Digital Ecosystems is the desire to exploit the self-organising properties of biological ecosystems. Ecosystems are thought to be robust, scalable architectures that can automatically solve complex,…
Every organism in an environment, whether biological, robotic or virtual, must be able to predict certain aspects of its environment in order to survive or perform whatever task is intended. It needs a model that is capable of estimating…
Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an…
The vision of Organic Computing addresses challenges that arise in the design of future information systems that are comprised of numerous, heterogeneous, resource-constrained and error-prone components or devices. Here, the notion organic…
A primary motivation for our research in Digital Ecosystems is the desire to exploit the self-organising properties of biological ecosystems. Ecosystems are thought to be robust, scalable architectures that can automatically solve complex,…
An overview of some methods of statistical physics applied to the analysis of algorithms for optimization problems (satisfiability of Boolean constraints, vertex cover of graphs, decoding, ...) with distributions of random inputs is…
Understanding the geometric properties of gradient descent dynamics is a key ingredient in deciphering the recent success of very large machine learning models. A striking observation is that trained over-parameterized models retain some…
To analyze the evolutionary emergence of structural complexity in physical processes we introduce a general, but tractable, model of objects that interact to produce new objects. Since the objects--\emph{$epsilon$-machines}--have well…
Decisions in organizations are about evaluating alternatives and choosing the one that would best serve organizational goals. To the extent that the evaluation of alternatives could be formulated as a predictive task with appropriate…
Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…
This text presents the proofs of the technical facts underlying theoretical justification of the convergence and performance of the novel algorithm for reactive navigation of differential drive wheeled robots in dynamic uncertain…
Based on Darwin's natural selection, we developed "machine scientists" to discover the laws of nature by learning from raw data. "Machine scientists" construct physical theories by applying a logic tree (state Decision Tree) and a value…
People solve different problems and know that some of them are simple, some are complex and some insoluble. The main goal of this work is to develop a mathematical theory of algorithmic complexity for problems. This theory is aimed at…
Forgetfulness is a common feature of nature. Moreover, without forgetfulness, repeatability would be impossible. Despite this, small systems constantly leak information about their state to their surroundings, and quantum mechanics tells us…