Papers by Daniel M Dubois
Bulletin de la Classe des sciences. Académie royale de Belgique, 1993
This paper deals with the foundation of a Non-linear Threshold Logic as a significative extension... more This paper deals with the foundation of a Non-linear Threshold Logic as a significative extension of the classical Threshold Logic initiated by McCulloch and Pitts 50 years ago. The mathematical theory of this new logic is based on Heaviside a Non-linear argument of the Function. The determination of the parameters is made by an algebraic learning. For the first time, we introduced the so-called Heaviside Fixed Function. The models of the Dubois' Fractal Neural Network and the Fukushima et al Neocognitron give the original framework of the new Non-linear Threshold Logic. The Threshold Logic, using linear argument of the Heaviside function, is not capable of resolving all Boolean functions with only one neuron. It is demonstrated that our Non-linear Threshold Logic resolved all the Boolean functions with one single neuron for any number of inputs, ie even the XOR problem. This is a good test for our method. Moreover it is shown that the very difficult Parity problem has also a very elegant solution for obtaining the parity of any Boolean patterns from one single neuron with any number of inputs. In the technology of neural networks, the back-propagation methods are based on hidden neurons to resolve the Boolean functions. There are some difficulties to obtain the global minimum as the number of neurons increases and the combinatorial explosion gives many problems for practical applications. The Non-linear Threshold Logic will permit to diminish a great quantity of neurons in the neural networks with the back-propagation. The possibilities of bigger practical applications are so given by this Non-linear Threshold Logic in the technology of neural machines due to the diminution of the necessary number of neurons and so to avoid some combinatorial explosion problems. Turbo Brain 1.0, a package for Personal Computers, has been developped from this Non-linear Threshold Logic with a Symbolic software.
After major organizational problems in creating such a conference (the symposium on "Science and ... more After major organizational problems in creating such a conference (the symposium on "Science and the future of Planet Earth"), we planned to continue to work on the hard scientific foundations of the project during the CASYS'03 conference in Liege. In the meantime, Michel passed away. In order to expose this Manifesto (which was written beautifully and categorically-characteristic of all Michel's works), to the scientific and intellectual community, we decided to present it on CASYS'05 with the last review we have. Because Michel was actually the key person of preparing this documents and put coauthors in inverse alphabetic order, we decided to put him on the first place. All others should remain the same. We hope that this would not have annoyed Michel. In such a way this document will stay as a spiritual monument to Michel in memory of his unfinished project (see www.globalprojectmb.org for more). Michel and his Manifesto are worth that. With this, we hope that all his ideas shared with the coauthors will rest in peace but not in vain...
Nucleation and Atmospheric Aerosols, 2002
ABSTRACT
Journal of physics, Mar 1, 2022
Although the question of negative energy solutions of the Dirac equation did not receive any rele... more Although the question of negative energy solutions of the Dirac equation did not receive any relevant answer, it has been incorrectly said that the Dirac Sea Hole theory predicted the existence of the positron. Now several authors have considered the possible existence of negative mass particles. us We show that the concept and the definition of the antielectron should be re-examined, and should be understand in a way which is fully compatible with Dirac negative energy states of electrons, i.e. with negative masses. The symmetry between positive and negative energy states in the Dirac equation leads to add the mass inversion M as a new symmetry to the CPT group, giving the MCPT group. We discuss the completeness of the Wigner theorem and the definitions of time reversal. Furthermore negative masses have been recently applied to Cosmology.
This book constitutes the proceedings of the Seventh International Conference on Computing Antici... more This book constitutes the proceedings of the Seventh International Conference on Computing Anticipatory Systems, CASYS'05. The volume includes all invited papers as well as those papers that received a best paper award. Also included is a lecture on 'General Principles for Brain Design', presented by Brian D. Josephson, Nobel Laureate in Physics. The papers discuss recent research and development in the modeling and computing of anticipatory systems in fields of natural and artificial systems.
Bulletin de la Classe des sciences, 1993
This paper deals with the foundation of a Non-linear Threshold Logic as a significative extension... more This paper deals with the foundation of a Non-linear Threshold Logic as a significative extension of the classical Threshold Logic initiated by McCulloch and Pitts 50 years ago. The mathematical theory of this new logic is based on Heaviside a Non-linear argument of the Function. The determination of the parameters is made by an algebraic learning. For the first time, we introduced the so-called Heaviside Fixed Function. The models of the Dubois' Fractal Neural Network and the Fukushima et al Neocognitron give the original framework of the new Non-linear Threshold Logic. The Threshold Logic, using linear argument of the Heaviside function, is not capable of resolving all Boolean functions with only one neuron. It is demonstrated that our Non-linear Threshold Logic resolved all the Boolean functions with one single neuron for any number of inputs, ie even the XOR problem. This is a good test for our method. Moreover it is shown that the very difficult Parity problem has also a ve...
AIP Conference Proceedings, 1998
This paper deals with a discrete mathematical model of epidemiological systems based on the SIRS ... more This paper deals with a discrete mathematical model of epidemiological systems based on the SIRS model. A population of susceptible individuals can be infected by contact to infective individuals which recover. The first part of this paper deals with temporal discrete models. Three threshold values of a control parameter depending on the transmission rate and the total population share the behaviour of the epidemic in four zones: no infection, increase of infection, bifurcation and then chaos. It is shown that for the same transmission rate, a critical total population shares the dynamics of the infection: for low population, infection disappears and for high population, the infection increases but the number of susceptible individuals remains at a positive constant value. In the second part of this paper, the SIRS model is generalised in taking into account the spatial diffusion of the populations. Classically space-time models are based on the reaction-diffusion equation. There is a problem with such a ...
Nucleation and Atmospheric Aerosols, 2006
ABSTRACT
Cette communication traite de la question de savoir si cela est possible de programmer un système... more Cette communication traite de la question de savoir si cela est possible de programmer un système de neurones avec une langue et une conscience. Il existe plusieurs niveaux et catégories de langages, par exemple, le langage verbal et le langage non-verbal, le langage des signes, etc. Il y a aussi plusieurs niveaux et catégories de conscience, par exemple, la conscience verbale, l’autoconscience non verbale et l'absence de conscience avec l’a-conscience. Par une approche systémique, nous étendons le rôle du cerveau à l'ensemble des neurones de l’ectoderme, dont les systèmes nerveux, le tronc cérébral, le cerveau et la peau qui est l'enveloppe réelle du cerveau avec l'environnement. Cet article montrera qu’un tel système neuronal peut être programmé, en se basant sur la recherche scientifique en neurosciences expérimentales et en intelligence artificielle, étendant de facto toutes les possibilités d'apprentissage des réseaux de neurones classiques.This communicatio...
Simulation for Cyber-Physical Systems Engineering, 2020
This chapter will present algorithms for simulation of discrete space-time partial differential e... more This chapter will present algorithms for simulation of discrete space-time partial differential equations in classical physics and relativistic quantum mechanics. In simulation-based cyber-physical system studies, the main properties of the algorithms must meet the following conditions. The algorithms must be numerically stable and must be as compact as possible to be embedded in cyber-physical systems. Moreover the algorithms must be executed in real-time as quickly as possible without too much access to the memory. The presented algorithms in this paper meet these constraints. As a first example, we present the second-order hyperincursive discrete harmonic oscillator that shows the conservation of energy. This recursive discrete harmonic oscillator is separable to two incursive discrete oscillators with the conservation of the constant of motion. The incursive discrete oscillators are related to forward and backward time derivatives and show anticipative properties. The incursive discrete oscillators are not recursive but time inverse of each other and are executed in series without the need of a work memory. Then, we present the secondorder hyperincursive discrete Klein-Gordon equation given by space-time secondorder partial differential equations for the simulation of the quantum Majorana real 4-spinors equations and of the relativistic quantum Dirac complex 4-spinors equations. One very important characteristic of these algorithms is the fact that they are space-time symmetric, so the algorithms are fully invertible (reversible) in time and space. The development of simulation-based cyber-physical systems indeed evolves to quantum computing. So the presented computing tools are well adapted to these future requirements.
This communication deals with the question to know if this is possible to program a neural system... more This communication deals with the question to know if this is possible to program a neural system with a language and a consciousness. There are several levels and categories of language, by example, verbal and non-verbal languages, signs language, etc. There are also several levels and categories of consciousness, by example, verbal consciousness, non-verbal selfconsciousness, and absence of consciousness with the a-consciousness. By a systemic approach, we extend the role of the brain to the whole neural ectoderm, including the nervous systems, the brainstem, the brain, and the skin that is the actual envelope of the brain to the environment. This paper will demonstrate that such a neural system can be programmed, on the basis of scientific research in experimental neurosciences and in artificial intelligence, extending de facto all the possibilities of learning of classical neural networks.
Even in inter regional risk management phenomena of retardation and adaptation play an important ... more Even in inter regional risk management phenomena of retardation and adaptation play an important role in the interplay between different logical management levels. In this paper it is demonstrated that an System Dynamics (SD) approach may be very suitable for modeling and simulating such phenomena. In some situations, however, SD approaches and modeling tools may pose some unnecessary restrictions on the procedure. Hence, the authors recommend a pragmatic and flexible attitude towards the choice of approach and tools.
Journal of Physics: Conference Series, 2019
In cybernetics, the Shannon formula is a positive function that measures the entropy of discrete ... more In cybernetics, the Shannon formula is a positive function that measures the entropy of discrete probability distributions. The conversion of this formula to continuous probability distributions gives the infinity and negativity catastrophes, similar to the problem of renormalisation in physics. This paper suggests a solution to these two open problems, in starting from the derivation of positive definite functions from the Shannon entropy. These definite positive functions are related to the constant of motion of the non-linear Lotka-Volterra system. Then these positive definite functions are generalized for exchange of information with both discrete and continuous probability distributions. These functions generalized the Kullback-Leibler and Wiener information gain. A practical example is presented which shows a remarkable result with a scale invariance of the information gain. Then in this paper, we recall the properties of the differential equations of the non-linear Volterra p...
Journal of Physics: Conference Series, 2019
This paper presents the second order hyperincursive discrete Klein-Gordon equation in three spati... more This paper presents the second order hyperincursive discrete Klein-Gordon equation in three spatial dimensions. This discrete Klein-Gordon equation bifurcates to 4 incursive discrete equations. We present the 4 incursive discrete Dubois-Ord-Mann real equations and the corresponding first order partial differential equations. In three spatial dimensions, the two oscillators given by these equations are now entangled with one spatial dimension, so the 4 equations form a whole. Then, we deduce the 4 incursive discrete Dubois-Majorana real equations and the corresponding first order partial differential equations. Next, these Dubois-Majorana real equations are presented in the generic form of the Dirac 4-spinors equation. In making a change in the indexes of the 4 functions in the Dubois-Majorana equations, the 4 first order partial differential equations become identical to the Majorana real 4-spinors equations. Then, we demonstrate that the Majorana equations bifurcate to the 8 real D...
Journal of Physics: Conference Series, 2019
This paper begins with the formalization of the second order hyperincursive discrete Klein-Gordon... more This paper begins with the formalization of the second order hyperincursive discrete Klein-Gordon equation. The temporal second order hyperincursive discrete Klein-Gordon equation is similar to the time-symmetric hyperincursive discrete harmonic oscillator and so bifurcates into a group of 4 incursive discrete real equations of first order. In this group, two equations are the discrete time reverse of the two other equations, giving an oscillator and an anti-oscillator. Firstly, the discrete Klein-Gordon equation, with one space dimension (1D), bifurcates to 4 first order incursive discrete equations that we called the Dubois-Ord-Mann real 4-spinors equations because Ord and Mann obtained the same equations from a stochastic method. Secondly, we generalize to three spatial dimensions (3D) these discrete Dubois-Ord-Mann equations. These 4 discrete equations are then transformed to real partial differential equations which can be written under the generic form of the Dirac quantum 4-s...
Journal of Physics: Conference Series, 2019
This paper deals with a review of the properties of the hyperincursive discrete harmonic oscillat... more This paper deals with a review of the properties of the hyperincursive discrete harmonic oscillator separable into two incursive discrete harmonic oscillators. We begin with a presentation step by step of the second order discrete harmonic oscillator. Then the 4 incursive discrete equations of the hyperincursive discrete harmonic oscillator are presented. The constants of motion of the two incursive discrete harmonic oscillators are analyzed. After that, we give a numerical simulation of the incursive discrete harmonic oscillator. The numerical values correspond exactly to the analytical solutions. Then we present the hyperincursive discrete harmonic oscillator. And we give also a numerical simulation of the hyperincursive discrete harmonic oscillator. The numerical values correspond also to the analytical solutions. Finally, we demonstrate that a rotation on the position and velocity variables of the incursive discrete harmonic oscillators gives rise to a pure quadratic expression ...
Acta Systemica, 2010
This paper deals with a breakthrough in the concept of free will in the human decision making. It... more This paper deals with a breakthrough in the concept of free will in the human decision making. It is assumed that the consciousness and unconsciousness show the same mind processes in the human brain. The decision making initiates unconsciously in the human brain, and, eventually, becomes a conscious decision. So the free will is unconsciously prepared in the human brain. Then I conjecture that what is called the conscious human brain is just the enlightening of some parts of the unconscious human brain.
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Papers by Daniel M Dubois