2025Preprint
Threshold Circuit Based On Cyclic Codes
René Ndoundam, Syril Corneille Tchio Tchichelia, Hervé Talé Kalachi, Jules Waku
SSRN Electronic Journal
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Chargé de Cours
Scientific activity
Researcher profile
Faculty researcher at the University of Yaoundé I. Grade: Chargé de Cours.
Scientific publications
René Ndoundam, Syril Corneille Tchio Tchichelia, Hervé Talé Kalachi, Jules Waku
SSRN Electronic Journal
Jacques Demongeot, Jules Waku, Olivier Cohen
Mathematical Biosciences & Engineering
<abstract> <sec><title>Background</title><p> The current ribosome has evolved from the primitive stages of life on Earth. Its function is to build proteins and on the basis of this role, we are looking for a universal common ancestor to the ribosome which could: i) present optimal combinatorial properties, and ii) have left vestiges in the current molecules composing the ribosome (rRNA or r-proteins) or helping in its construction and functioning. </p></sec> <sec><title>Methods</title><p> Genomic public databases are used for finding the nucleotide sequences of rRNAs and mRNA of r-proteins and statistical calculations are performed on the occurrence in these genes of some pentamers belonging to the RNA proposed as optimal ribosome ancestor. </p></sec> <sec><title>Results</title><p> After having exhibited a possible solution to the problem of an RNA capable of catalyzing peptide genesis, traces of this RNA are found in many rRNAs and mRNA of r-proteins, as well as in factors contributing to the construction of the current ribosome. </p></sec> <sec><title>Conclusions</title><p> The existence of an optimal primordial RNA whose function is to facilitate the creation of peptide bonds between amino acids may have contributed to accelerate the emergence of the first vital processes. Its traces should be found in many living species inside structures structurally and functionally close to the ribosome, which is already the case in the species studied in this article.</p></sec> </abstract>
Kayode Oshinubi, Sana S. Buhamra, Noriah M. Al-Kandari, Jules Waku, Mustapha Rachdi, Jacques Demongeot
Healthcare
Revisiting the classical model by Ross and Kermack-McKendrick, the Susceptible−Infectious−Recovered (SIR) model used to formalize the COVID-19 epidemic, requires improvements which will be the subject of this article. The heterogeneity in the age of the populations concerned leads to considering models in age groups with specific susceptibilities, which makes the prediction problem more difficult. Basically, there are three age groups of interest which are, respectively, 0−19 years, 20−64 years, and >64 years, but in this article, we only consider two (20−64 years and >64 years) age groups because the group 0−19 years is widely seen as being less infected by the virus since this age group had a low infection rate throughout the pandemic era of this study, especially the countries under consideration. In this article, we proposed a new mathematical age-dependent (Susceptible−Infectious−Goneanewsusceptible−Recovered (SIGR)) model for the COVID-19 outbreak and performed some mathematical analyses by showing the positivity, boundedness, stability, existence, and uniqueness of the solution. We performed numerical simulations of the model with parameters from Kuwait, France, and Cameroon. We discuss the role of these different parameters used in the model; namely, vaccination on the epidemic dynamics. We open a new perspective of improving an age-dependent model and its application to observed data and parameters.
Jacques Demongeot, Kayode Oshinubi, Mustapha Rachdi, Hervé Seligmann, Florence Thuderoz, Jules Waku
Computation
(1) Background: The estimation of daily reproduction numbers throughout the contagiousness period is rarely considered, and only their sum R0 is calculated to quantify the contagiousness level of an infectious disease. (2) Methods: We provide the equation of the discrete dynamics of the epidemic’s growth and obtain an estimation of the daily reproduction numbers by using a deconvolution technique on a series of new COVID-19 cases. (3) Results: We provide both simulation results and estimations for several countries and waves of the COVID-19 outbreak. (4) Discussion: We discuss the role of noise on the stability of the epidemic’s dynamics. (5) Conclusions: We consider the possibility of improving the estimation of the distribution of daily reproduction numbers during the contagiousness period by taking into account the heterogeneity due to several host age classes.
Mustapha Rachdi, Jules Waku, Hana Hazgui, Jacques Demongeot
Entropy
Genetic regulatory networks have evolved by complexifying their control systems with numerous effectors (inhibitors and activators). That is, for example, the case for the double inhibition by microRNAs and circular RNAs, which introduce a ubiquitous double brake control reducing in general the number of attractors of the complex genetic networks (e.g., by destroying positive regulation circuits), in which complexity indices are the number of nodes, their connectivity, the number of strong connected components and the size of their interaction graph. The stability and robustness of the networks correspond to their ability to respectively recover from dynamical and structural disturbances the same asymptotic trajectories, and hence the same number and nature of their attractors. The complexity of the dynamics is quantified here using the notion of attractor entropy: it describes the way the invariant measure of the dynamics is spread over the state space. The stability (robustness) is characterized by the rate at which the system returns to its equilibrium trajectories (invariant measure) after a dynamical (structural) perturbation. The mathematical relationships between the indices of complexity, stability and robustness are presented in case of Markov chains related to threshold Boolean random regulatory networks updated with a Hopfield-like rule. The entropy of the invariant measure of a network as well as the Kolmogorov-Sinaï entropy of the Markov transition matrix ruling its random dynamics can be considered complexity, stability and robustness indices; and it is possible to exploit the links between these notions to characterize the resilience of a biological system with respect to endogenous or exogenous perturbations. The example of the genetic network controlling the kinin-kallikrein system involved in a pathology called angioedema shows the practical interest of the present approach of the complexity and robustness in two cases, its physiological normal and pathological, abnormal, dynamical behaviors.
Jacques Demongeot, Hana Hazgui, Hedi Ben Amor, Jules Waku
Acta Biotheoretica
Jacques Demongeot, Jules Waku
Comptes Rendus Mathématique
This Note deals with the mathematical notions of entropy and stability rate in interaction graphs of genetic networks, in the particular context of the genetic threshold Boolean random regulatory networks (getBrens). It is proved that in certain circumstances of particular connectance, the entropy of the invariant measure of the dynamical system can be considered both as a complexity and a stability index, by exploiting the link between these two notions, fundamental to characterize the resistance of a biological system against endogenous or exogenous perturbations, as in the case of the n -switches. Examples of biological networks are then given showing the practical interest of the mathematical notions of complexity and stability in the case of the control of the morphogenesis.
Jacques Demongeot, Jules Waku
Comptes Rendus Mathématique
Numerous indices of complexity are used in biological regulatory networks like the number of their components, their connectance (or connectivity), or the number of the strong connected components of their interaction graph. Concerning the stability of a biological network, it corresponds to its ability to recover from dynamical or parametric disturbance. Complexity is here quantified by the evolutionary entropy, which describes the way the asymptotic presence distribution of the corresponding dynamical system is spread over the state space and the stability (or robustness) is characterized by the rate at which the system returns to this equilibrium distribution after a perturbation. This article shows the mathematical relationships between entropy and stability rate in the general framework of a Markov chain.
Jean Gaudart, Mohamad Ghassani, J. Mintsa, Jules Waku, Mustapha Rachdi, Ogobara K. Doumbo and 1 more
The classical models by Ross and McKendrick have to be revisited in order to incorporate dynamical elements coming from the demography and from the spatial aspects of epidemics. The classical approach is dealing with populations supposed to be constant during the epidemic wave, but the present pandemics show duration during years imposing now to take into account the population growth as well as the transient or permanent migrations of hosts susceptible or infected, and of vectors and infectious agents. Two examples are studied, concerning malaria in Mali and plague at the middle-age.
Jean Gaudart, Mohamad Ghassani, J. Mintsa, Mustapha Rachdi, Jules Waku, Jacques Demongeot
Acta Biotheoretica
Jacques Demongeot, Jules Waku
Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences
We present here some theoretical and numerical results about interval iterations. We consider first an application of the interval iterations theory to the problem of entrainment in respiratory physiology for which the classical point iterations theory fails. Then, after a brief review of some of the main aspects of point iterations, we explain what is meant by the term 'interval iterations'. It consists essentially in replacing in the point iterations the function to iterate by a set-valued map. We present both theoretical and numerical aspects of this new type of iterations and we observe the dynamical behaviours encountered, such as fixed intervals and interval limit cycles. The comparison between point and interval iterations is carried out with respect to a parameter epsilon, which determines the thickness of a neighbourhood around the function to iterate. We will finally focus our attention on the Verhulst and Ricker functions largely used in population dynamics, which exhibit various asymptotic behaviours.
Jacques Demongeot, Jules Waku
Mathematical Population Studies
For a unimodal growth function f having its maximum at a critical state x c , the interval bounding the population size asymptotically is usually presented as being equal to [f ○2(x c ), f(x c )]. This interval however does not represent the maximum range within which the population size can vary, even asymptotically. The actual invariant interval containing the population size is equal to: [min(x*, f ○2(x c )), f(x c )], where x* denotes the non-zero fixed point, assumed to be unique, of the iteration of f.
Jules Waku, J.-M. Chassery
Deals with the specification of a wavelet for the representation of a discrete contour coded by Freeman chain code. Multiresolution analysis is a functional framework which allows one to build wavelets and to choose which wavelet to use for a given application. The discrete version of data in image processing domain has to be conserved and it needs specific algorithms and tools. The aim is to consider a discrete contour coded by Freeman sequence and to approximate it at several levels of resolution by use of an adapted wavelet. The authors compute the wavelet's coefficients which can be used to reconstruct the original discrete contour. Examples of implementation results with evaluation of entropy and fidelity of reconstruction are presented.>
J.-M. Chassery, Jules Waku
TS. Traitement du signal
Un contour complexe, peut etre approxime a differentes echelles afin d'obtenir une description plus simple contenant moins d'information, mais suffisamment pour le reconnaitre. Nous proposons l'approche multiresolution par ondelettes pour l'approximation d'un contour discret represente par le codage de Freeman. Apres la specification de l'ondelette adaptee a ce probleme, on presente un algorithme d'analyse et de synthese avec une etape de quantification d'un tel contour. Les resultats de l'implementation sont ensuites presentes. Nous calculons l'entropie a chaque niveau de resolution, ainsi que l'erreur quadratique qui permet le calcul du rapport signal sur bruit
Jules Waku, Jean‐Marc Chassery
Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE
In this paper, we are discuss a multiscale analysis of discrete boundary presented by Generalized Chain Code. We briefly review the multiresolution analysis which make possible the construction of wavelets, scaling function and the associated filters. Using the discrete contour generated by Freeman Chain Code, we approximate it at several resolution levels and obtain its wavelet representation. We then reconstruct the original discrete contour from its wavelet representation also generated by Chain Code. Examples of implementation results are presented with the evaluation of entropy and signal to noise ratio to confirm the perfect visual result.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
Syril Corneille Tchio Tchichelia, Hervé Talé Kalachi, Jules Waku, René Ndoundam
SSRN Electronic Journal
Jules Waku, Kayode Oshinubi, Umar Muhammad Adam, Jacques Demongeot
Diseases
OBJECTIVE: The objective of this article is to develop a robust method for forecasting the transition from endemic to epidemic phases in contagious diseases using COVID-19 as a case study. METHODS: Seven indicators are proposed for detecting the endemic/epidemic transition: variation coefficient, entropy, dominant/subdominant spectral ratio, skewness, kurtosis, dispersion index and normality index. Then, principal component analysis (PCA) offers a score built from the seven proposed indicators as the first PCA component, and its forecasting performance is estimated from its ability to predict the entrance in the epidemic exponential growth phase. RESULTS: This score is applied to the retro-prediction of endemic/epidemic transitions of COVID-19 outbreak in seven various countries for which the first PCA component has a good predicting power. CONCLUSION: This research offers a valuable tool for early epidemic detection, aiding in effective public health responses.
Jules Waku, Kayode Oshinubi, Jacques Demongeot
Mathematics and Computers in Simulation
Jacques Demongeot, Kayode Oshinubi, Mustapha Rachdi, Hervé Seligmann, Florence Thuderoz, Jules Waku
Journal of Mathematical and Computational Science
The COVID-19 pandemic continues to spread and already shows a recurrence in many countries, despite several social distancing and vaccination measures implemented all around the world. Epidemiological data are available, and we use the Auto-Regressive Integrated Moving Average (ARIMA) model to analyze incidence pattern and to generate short-term forecasts of cumulative reported cases in Morocco, France, Italy, Spain and USA, using daily reported cumulative cases data from Worldometers, and we report 5-day and 10-day ahead forecasts of cumulative cases and check a posteriori the precision of this forecasting, by confronting it to the real data observed. In the discussion, we propose a link between the ARIMA, elevation and average temperature in several countries’ modelling approaches, for allowing the comparison between their explicative abilities.
Jacques Demongeot, Jules Waku
Comptes Rendus Mathématique
An important example of biological regulatory networks is constituted by the genetic threshold Boolean random regulatory networks (getBren), which are very useful for explaining the precise mechanisms of the genetic control. This article shows the mathematical relationships between parameter sensitivity of the evolutionary entropy and network frustration in the particular context of the getBrens.
Jacques Demongeot, Jules Waku
Comptes Rendus Mathématique
Various indices of complexity are used in biological regulatory networks like the number n of their components and I of the interactions between these components, their connectance (or connectivity) equal to the ratio <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>I</mml:mi> <mml:mo stretchy="false">/</mml:mo> <mml:mi>n</mml:mi> </mml:math> , or the number of the strong connected components of their interaction graph. The stability of a biological network corresponds to its ability to recover from dynamical or parametric disturbance. Complexity is here quantified by the evolutionary entropy, which describes the way the asymptotic presence distribution or equilibrium distribution of the corresponding dynamical system is spread over the state space and the stability (or robustness) is characterized by the rate at which the system returns to its equilibrium distribution after a perturbation. This article applies these notions in the case of genetic networks having a getBren structure ( i.e ., being threshold Boolean random networks) and notably those controlling the cell cycle.
Jacques Demongeot, Jules Waku
On one hand, different indices of complexity have been introduced in biological networks: the number of their components, their connectance (or connectivity) or the number of the strong connected components of their interaction graph. On the other hand, indices of robustness for a biological network characterize its ability to recover from dynamical or parametric disturbance and are linked to the spectrum of the operator defining its dynamics. Here complexity will be quantified by the evolutionary entropy, which describes the way the asymptotic presence distribution of the corresponding dynamical system is spread over the state space and robustness will be characterized by the stability rate at which the system returns to this equilibrium distribution after a perturbation. The paper shows mathematical relationships between entropy and stability rate, in the general framework of Markov chains and in the specific case of Markov chains related to the genetic threshold Boolean random regulatory networks (getBren).
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