Détails

Affichages : 7722

A. PERSONAL DETAILS

• Name: Chaskalovic
• Surname: Joel
• Grade: Qualified Full Professor in Applied Mathematics (CNU 24).
• Workplace: University Pierre and Marie Curie, 4 Place Jussieu 75252 Paris Cedex 5, France.
• Laboratory: UMR 7190 - Institut Jean le Rond d’Alembert.

B. EDUCATION

2001: State Doctorat (Habilitation à Diriger des Recherches), (UPMC – Paris 6).

Specialty: Mechanics.
Title: Nonlinearity in Mechanics: Modelling and mathematical analysis.
Subject 1: Contribution to the mathematical modelling applied to tornadoes.
Subject 2: Bifurcation theory applied to buckling states of a cylindrical shell.

1991: PhD (Doctorat de l’Université), (UPMC – Paris 6).

Specialty: Mechanics.
Thesis entitled: Mathematical modelling applied to tornadoes genesis.
Distinction: With very high honors.

1986: Engineer of « Ecole Nationale des Ponts et Chaussées ».

M.Sc. of Numerical Analysis (DEA), (UPMC – Paris 6)
Distinction: With honors.

1984: Maîtrise of Mechanics- Option « Scientific Computation », (UPMC – Paris 6).

Rank: 1st.
Distinction: With high honors.
Admission to « Ecole Nationale des Ponts et Chaussées ».

1983: B.Sc. of Mechanics - Option « Scientific Computation» (Licence), (UPMC – Paris 6).

Rank: 1st.
Distinction: With high honors.

C. DELEGATION - INVITATION ABROAD

1. 01/09/2007 - 01/09/2009: Visiting Professor in the Department of Mathematics at Ariel University, Israel.
2. 21/07/1996 - 11/08/1996: Invitation to the Mathematics Department of Bar-Ilan University, Israel.
3. 15/12/2002 - 09/01/2003: Invitation to the Engineering Faculty of Technion University, Haifa - Israel.

D. INTERNATIONAL CONFERENCES

D.I) Probabilistic model and functional analysis applied to relative accuracy of Lagrange finite elements approximations 

1. J. Chaskalovic and F. Assous, 2018, From a geometrical interpretation of Bramble-Hilbert lemma to a probability distribution for finite element accuracy, Proceeding of the 7^th Conference on Finite Difference Methods: Theory and Applications, (2018) published in LNCS, Springer. 

D.II) Mathematical modelling and data mining applied to particle physics

1. F. Assous and J. Chaskalovic, 2010,Data mining techniques for numerical approximations of asymptotic solutions to the Vlasov–Maxwell equations, Research Workshop of the Israel Science Foundation: Functional Differential Equations and Applications.
2. F. Assous and J. Chaskalovic, 2011,Data mining methods for performance evaluations to asymptotic numerical models, International Conference on Computational Science, ICCS 2011, Procedia Computer Science, Vol. 4 , pp. 518–527.
3. F. Assous and J. Chaskalovic, 2011,Data mining techniques for numerical approximations of asymptotic solutions to the Vlasov–Maxwell equations, Int. Conf. Dynam. Syst. Appl., Atlanta -USA.
4. F. Assous and J. Chaskalovic, 2012,Data Mining Methods Applied to Numerical Approximations for Pde’s, Annual SIAM, Minneapolis, USA.
5. J. Chaskalovic and F. Assous, 2013,A posteriori Error Analysis in Numerical Approximations of Pde’s: A Pilot Study Using Data Mining Techniques, FEMTEC 2013, Las Vegas, USA.
6. F. Assous and J. Chaskalovic, 2013,A Paraxial Asymptotic Model for the Coupled Vlasov-Maxwell Problem in Electromagnetic, FEMTEC 2013, Las Vegas, USA.
7. J. Chaskalovic and F. Assous, 2015, Sensitivity analysis of asymptotic Vlasov-Maxwell models using data mining techniques for uncertainty quantification, 2^nd Frontiers in Computational Physics conference, Zurich, Suisse.
8. J. Chaskalovic and F. Assous, 2015, Data mining and probabilistic models for error estimate analysis of finite element method, AMMCS-CAIMS, Waterloo, Canada.
9. F. Assous and J. Chaskalovic, 2015, New accurate reduced mathematical model particle beam simulation, AMMCS-CAIMS, Waterloo, Canada.    

D.III) Mathematical modelling applied to Mechanics

1. J. Chaskalovic, 1988,Un résultat d'unicité des solutions de Navier-Stokes modélisant une tornade, Congrès National d'Analyse Numérique d'Evian.
2. J. Chaskalovic, 1992, A new mathematical model applied to tornado's genesis, 18^th International Congress of Theoretical and Applied Mechanics (Haïfa, Israël).
3. J. Chaskalovic et A. Chauvière, 1999, Convection thermique dans une ligne de puits ou de sources tourbillonnaire, 14^ème Congrès Français de Mécanique, Toulouse.
4. A. Chauvière and J. Chaskalovic, 2002, Modélisation mathématique appliquée aux tornades atmosphériques en régime développé, Proc. 5^èmeRencontre du non linéaire de l’Institut Henri Poincaré, Paris.
5. J. Ratsaby and J. Chaskalovic, 2009, Random patterns and complexity in static structures, International Conference on Artificial Intelligence and Pattern Recognition (AIPR, Orlando - USA).

D.IV) Mathematical modelling and data mining applied to Medicine

1. O. Kulski, J. Chaskalovic, et al., 2004, Facteurs explicatifs des pronostics des IIU : analyse exploratoire de 2089 cycles à l’aide d’outils statistiques de Data Mining, Actes du Congrès de la 9^ème journée de la Fédération Française d’Etude de la Reproduction, (Paris).

2. X. Nguyen, J. Chaskalovic and al., 2008, OSAS, CPAP and Insomnia explored by data mining Methods, European Respiratory Society,   Sleep Medicine: Berlin, Allemagne.

3. Xuân-Lan Nguyen, B. Fleury, Joël Chaskalovic et al, 2010,SAOS et Insomnie : Influence réciproque de l’Insomnie et de la ventilation en pression positive continue (PPC), Le Congrès  du Sommeil, Tour - France.

D.V) Probabilist and mathematical modelling applied to Media Research

1. J. Chaskalovic, 1993, National Congress of IREP, For a new birth of the media-planning, Paris.
2. J. Chaskalovic, 1994, Congress of GRP, On a new mathematical model of evaluation of the coverage rates, Brussels.
3. J. Chaskalovic, 1995, National Congress of IREP, Reflexions on the description of the real behaviours for media exposures, Paris.
4. J. Chaskalovic, 2005, National Congress of IREP, A new mathematical law of the advertising remembering, Paris.
5. J. Chaskalovic, 2006, Gravitation theory applied to mathematical modelling in geo-marketing,The 5^th International Conference on Mathematical Modelling and Computer Simulations of Materials Technologies, Ariel, (Israel).
6. A. Vanheuverzwyn and J. Chaskalovic, 2007, Innovation in estimation - A reliable approach for radio audience indicators, Esomar WM3, Dublin.
7. J. Chaskalovic, 2008, Individual probabilities of media exposure as solutions of a Volterra Integro equation,The 5^th International Conference on Mathematical Modelling and Computer Simulations of Materials Technologies, Ariel, (Israel).

E. NATIONAL AND INTERNATIONAL INFLUENCE

Invitations abroad

1. 01/09/2007 - 01/09/2009: Invited Professor in the Department of Mathematics at Ariel University - Israel, (Delegation and CRCT).
2. 21/07/1996 - 11/08/1996: Invitation in the Department of Mathematics of Bar-Ilan University, (Israel).
3.  15/12/2002 - 09/01/2003: Invitation in the Engineering Faculty of the Technion University, Haifa, (Israel).

Invited talks and graduate courses given abroad (Out of Congresses)

1. Mathematical modeling applied to tornadoes , Faculty of Mechanical Engineering, Technion of Haifa, (Israel), (2002).
2. Data Mining and Real Systems Modeling: Media Marketing and Physical Applications , Faculty of Mechanical Engineering, Technion of Haifa (Israel), (2002).
3. Advanced Calculus , Mathematical and Engineering Departments, Ariel University (Israel), (2007-2009).
4. Numerical methods for partial differential equations , Mathematical and Engineering Departments, Ariel University (Israel), (2007-2009).
5. Functional analysis for partial differential equations , Mathematical and Engineering Departments, Ariel University (Israel), (2007-2009).

National and international seminars

1. Seminar of the Mathematics Department at Sorbonne University (Paris 5). Data Mining Techniques for Numerical approximations analysis, (2011).
2. Seminar of the Mathematics Department at Bar Ilan University (Israel). A new mathod to evaluate asymptotic numerical models by data mining techniques, (2012).
3. Seminar of LMM – UPMC (Paris 6). Exact solutions of Navier-Stokes equations with thermal coupling, (1997).
4.  Seminar of LMM – UPMC (Paris 6). Exact solutions of Navier-Stokes equations modelling atmospherical tornadoes, (2001).
5.  Seminar of the Faculty de Mechanics at Technion – (Haifa, Israël). Mathematical modelling applied to tornadoes, (2002).
6. Seminar of the Faculty de Mechanics at Technion – (Haïfa, Israël). Data mining and real systems modelling: Media Marketing and Physical applications, (2002).
7.  Seminar of LMM – UPMC (Paris 6). Data Mining process and probabilistic models applied to engineering sciences, (2005).
8.  Seminar of the Academic College of Engineering at Afeka - Tel Aviv, (Israël). On principles of gravitation theory applied to Geo-Marketing, (2006).
9. Seminar of the Mathematics Department at Bar Ilan University (Israel). Mathematical models applied to mdeia exposure, (2008).

Editorial responsabilities

• 2013-2014: Invited Editor in Chief of Comptes Rendus Mécanique of the Scienc es Academy: Responsible of a special number entitled « Theoretical and Numerical Approaches for Vlasov-Maxwell Equations ».

Member of scientific council

• 2002-2008 :   Member of IREP scientific council (Institut de la Recherche et d’Etude Publicitaire).

Détails

Affichages : 3628

• Probabilistic approach for a priori and error estimate of solution and approximation to determinist partial differential equations.

1. Mixed geometrical-probabilisitic interpretation of error estimate derived form Bramble-Hilbert lemma: Application to the relative accuracy between two Lagrange finite elements.

2. On generalized binomial laws to evaluate finite element accuracy:On generalized binomial laws to evaluate finite element accuracy:toward applications for adaptive mesh refinement.

3. Relative accuracy for high order finite element by a mixed functional-probabilistic approach.

4. Explicit k−dependency for P_k finite elements in W^m,p error estimates: application to probabilistic laws for accuracy analysis.

5. Continuous probability distribution to compare the approximation error between two Lagrange finite elements.

• Mathematical modelling and data mining applied to Particle Physics.

1. Analysis of numerical approximations of asymptotic solutions of the Vlasov-Maxwell equations modeling a beam of ultra-relativistic particles, (Collaboration with Prof. F. Assous, Ariel University, Israel).

We propose a new approach that consists in using data mining techniques for scientific computing. Indeed, data mining has proved to be efficient in other contexts which deal with huge data like in biology, medicine, marketing, advertising and communications.

Our aim, here, is to deal with the important problem of the exploitation of the results produced by any numerical method. Indeed, more and more data are created today by numerical simulations. Thus, it seems necessary to look at efficient tools to analyze them. In this work, we focus our presentation to a test case dedicated to an asymptotic paraxial approximation to model ultrarelativistic particles. Our method directly deals with numerical results of simulations and try to understand what each order of the asymptotic expansion brings to the simulation results over what could be obtained by other lower-order or less accurate means. This new heuristic approach offers new potential applications to treat numerical solutions to mathematical models.

2. Error Analysis in Numerical Approximations of PDE's: A Pilot Study Using Data Mining Techniques Data Mining applied to Engineering Sciences, (Collaboration with A. Lombardi, CERN, Geneva, Swisserland and Prof. F. Assous, Ariel University, Israel).

We introduced in 1. a new methodology based on data mining techniques for numerical approximation analysis. Our aim is to extend this methodology to a posteriori error analysis in numerical approximations of partial differential equations. It concerns the treatment of the sources of errors involved in any process of approximation, which describes a given real system by a mathematical model, solved by numerical approximation methods, and whose exploitation, in ne, will provide the understanding, the control and the forecast of this system.

Let us consider a real system (S) modeled by a set of partial differential equations (E). Generally, the solution of such a system is carried out by numerical approximations methods, as finite elements, finite volumes, finite differences, or any other appropriate numerical method. Regarding the production of these approximations, it is essential to consider the sources of errors which spoil the accuracy of the description and the understanding of the real system (S). In this work, we define four types of errors : the modeling error, the approximation error, the parametrization error and the discretization error. In this work, we focus our attention to a test case devoted to the discretization error defined as follow: For a given family of approximations methods - for instance the Pk finite elements, k = 1,2... - we consider two numerical methods of this family, says (MN1) and (MN2). The discretization error is defined as the error due to the difference of order between (MN1) and (MN2).

As an example, we considered numerical solutions to Vlasov Maxwell equations, computed by an asymptotic model, and numerically discretized by P1 and P2 finite elements. A priori, the Bramble-Hilbert theorem claims that, under certain conditions of regularity of the mesh and of the solution, the results obtained by the finite elements P2 (of order 2) will be more precise than those computed by finite elements P1 (of order 1).

However, the estimations of the approximation error contain multiplicative constants, unknown or difficult to estimate. As a consequence, we looked for circumstances for which the finite element method P1 would be locally ”equivalent” or more ”accurate” than the finite element method P2.

Then, we sought to identify and to qualify such situations by exploratory data mining techniques. Typically, the segmentation by decision trees was effective in this perspective. Indeed, the algorithm of segmentation allowed us to identify and to characterize the rows of a suitable database that correspond to an equivalent precision between P1 and P2. Particularly, we showed that it may sometimes be possible to euristically precise the classical Bramble Hilbert’s theorem, that gives a global error estimate, whereas our approach may give an local error estimate.

• Mathematical modeling and data mining tehcniques applied to Engineering Sciences.

1. Characterization by Data Mining methods of solutions to Pareto optimal front: application to the identification of optimal trajectories aerodynamic micro-UAVs (Collaboration with M. Hamdaoui and P. Sagaut the IJLRDA-UPMC and S. Doncieux of ISIR-UPMC).

The aim of this work is to present a method to find and analyze maximum propulsive efficiency kinematics for a birdlike flapping-wing unmanned aerial vehicle using multiobjective evolutionary optimization and data-mining tools.

For the sake of clarity and simplicity, simple geometry (rectangular wings with the same profile along the span) and simple kinematics (symmetrical harmonic dihedral motion) are used. In addition, it is assumed that the birdlike aerial vehicle (for which the span and surface area are, respectively, 1m and 0:15 m2) is in horizontal motion at low cruise speed (6 m=s).

The aerodynamic performances of the flapping-wing vehicle are evaluated with a semiempirical flight physics model and the problem is solved using an efficient multiobjective evolutionary algorithm called
-MOEA. Groups of attractive solutions are defined on the Pareto surface, and the most efficient solutions within these groups are characterized. Given the high dimensionality of the Pareto surface in the kinematic parameters space, data-mining techniques are used to conduct the study.

First, it is shown that these groups can be qualified versus the whole Pareto surface by accurate mathematical relations on the kinematic parameters. Second, the inner structure of each group is studied and highly accurate mathematical relations are found on the optimized parameters describing the most efficient solutions.

• Mathematical modelling Data Mining explorations for medical applications.

1. Data Mining method applied to "Sleep Apnea Syndrom": Modelling the interaction of treatment of sleep apnea problems and Insomnia, (Collaboration with Dr. B. Fleury and XL Nguyen Sleep from the Unit of the Pneumology Service at the Hospital Saint Antoine in Paris (CETTSSA), Paris).

Obstructive Sleep Apnoea Syndrome (OSAS) and insomnia are common pathologies sharing a high comorbidity. CPAP is a cumbersome treatment. Yet, CPAP compliance must remain optimal in order to reverse excessive daytime sleepiness and prevent the cardiovascular consequences of OSAS. 

But chronic insomnia could negatively affect CPAP compliance. To assess the consequences of insomnia symptoms on long-term CPAP we explore a prospective study which was conducted on 148 OSAS patients (RDI = 39.0 ± 21.3/h), age = 54.8 ± 11.8 years, BMI = 29.1 ± 6.3 kg/m2, Epworth Score = 12.2 ± 5.4, on CPAP.

Using the Insomnia Severity Index (ISI) as an indicator of insomnia (ISI P14 = moderate to severe insomnia) and baseline data (anthropometric data, sleeping medication intakes, CPAP compliance, Epworth, Pittsburgh Sleep Quality and ISI scores, polygraphic recording data), Data Mining techniques (mainly, decision trees) identified the major rules explaining the features ‘‘High” or ‘‘Low ISI” and ‘‘High” or ‘‘Low Use” in the groups defined, according to the median values of the ISI and the 6th month-compliance, respectively. 

The main results we found are: Median ISI was 15 and median 6th month-compliance was 4.38 h/night. Moderate to severe insomnia complaint was found in 50% of patients. In the ‘‘High” and ‘‘Low ISI,” the 6th month-compliance was not significantly different (3.7 ± 2.3 vs 4.2 ± 2.3 h/night). In the classification models of compliance, the ISI was not a predictor of CPAP rejection or of long-term use, the predictor for explaining CPAP abandonment being the RDI, and the predictor of the 6th month-compliance being the one month-compliance. 

As a conclusion, insomnia symptoms were highly prevalent in OSAS patients, but had no impact on CPAP rejection or on long-term compliance.

2. Evolution of health-related quality of life two to seven years after retropubic radical prostatectomy: evaluation by UCLA prostate cancer index.  (Collaboration with Prof. M. Zerbib Head of Urology - Cancerology Department of the Hospital Cochin in Paris).

To determine changes in health-related quality of life (HRQOL) in patients treated with retropubic radical prostatectomy (RP) between two and seven years after surgery, a questionnaire from the University of California Los Angeles was sent to 142 patients previously treated with retropubic RP as mono-therapy for clinically localized prostate cancer.

Patients were divided into five groups according to time from surgery. Demographics, clinical and pathological characteristics of patients were compared between these groups. Correlation coefficients controlled for age at the time of questionnaire between HRQOL scores and time from RP were assessed. A total of 105 patients (74%) returned the questionnaire. The mean time from surgery was 48 months (range 25-84). Demographics, clinical and pathological characteristics of patients were not statistically different between time groups.

Several recoding items were found to decrease significantly with the time from RP including physical functioning, role limitations due to physical health problem, vitality, and general health. In contrary, urinary, bowel and sexual scores were not significantly correlated to time from RP. Although sexual, urinary and bowel scores seem to remain stable from 2 to 7 years following RP, general health appears to significantly deteriorate with time after RP, independent of the patient's age at the time of the questionnaire.

3. Mathematical modeling of the immune system during injections combined BCG and interleukin-2 in the treatment of Superficial Bladder Cancer (Collaboration with Prof. J. Gluckman, Head of Immunology Department of the Hospital Saint -Louis in Paris and Dr. S. Bunimovich from University of Tel-Aviv).

We developed a mathematical model that describes the growth of superficial bladder cancer and the effect thereupon of immunotherapy based on the administration of Bacillus Calmette-Guerin (BCG) combined or not with interleukin-2 (IL-2). Intravesical instillations of BCG performed after surgical removal of tumors represents an established treatment with approximately 50% success rate. So far, attempts to improve this efficiency have not led to essential changes. However, convincing clinical results have been reported on the combination of IL-2 to BCG, even though this is still not applied in current practice.

The present model provides insights into the dynamical outcomes arising in the bladder from the interactions of immune cells with tumor cells in the course of BCG therapy associated or not with IL-2. Specifically, from the simulations performed using seven ordinary and non-linear differential
equations we obtained indications on the conditions that would result in successful bladder cancer treatment.

We show that immune cells–effector lymphocytes and antigen-presenting cells–expand and reach a sustainable plateau under BCG treatment, which may account for its beneficial effect, resulting from inflammatory ‘‘side-effects’’ which eliminate residual or eventual newly arising tumor cells, providing thus protection from further cancer development.

We find, however, that IL-2 does not actually potentiate the effect of BCG as regards tumor cell eradication. Hence, associating both under the conditions simulated should not result in more efficient treatment of bladder cancer patients.

4. Statistical techniques applied to the modification of the breathing pattern due to repetitive trnascanial magnetic stimulation (Collaboration with Prof. T. Similovski - Head of Pneumology Department of Pitié-Salepétrière Hospital in Paris).

In awake humans, breathing depends on automatic brainstem pattern generators. It is also heavily influenced by cortical networks. For example, functional magnetic resonance imaging and electroencephalographic data show that the supplementary motor area becomes active when breathing is made difficult by inspiratory mechanical loads like resistances or threshold valves. This is associated with perceived respiratory discomfort.

We hypothesized that manipulating the excitability of the supplementary motor area with repetitive transcranial magnetic stimulation would modify the breathing pattern response to an experimental inspiratory load possibly respiratory discomfort. Seven subjects (3 men, age 25±4) were studied. Breathing pattern and respiratory discomfort during inspiratory loading were described before and after conditioning the supplementary motor area with repetitive stimulation, using an excitatory paradigm (5Hz stimulation), an inhibitory paradigm, or sham stimulation.

No significant change in breathing pattern during loading was observed after sham conditioning. Excitatory conditioning shortened inspiratory time (p=0.001), decreased tidal volume (p=0.016), and decreased ventilation (p=0.003), as corroborated by an increased end-tidal expired carbon dioxide (p=0.013). Inhibitory conditioning did not affect ventilation, but lengthened expiratory time (p=0.031).

Respiratory discomfort was mild under baseline conditions, and unchanged after conditioning of the supplementary motor area. This is the first study to show that repetitive transcranial magnetic stimulation conditioning of the cerebral cortex can alter breathing pattern. A 5 Hz conditioning protocol, known to enhance corticophrenic excitability, can reduce the amount of hyperventilation induced by inspiratory threshold loading. Further studies are needed to determine whether and under what circumstances rTMS can have an effect on dyspnoea.

Détails

Affichages : 5282

2013 – 2016 : Faculté de Mathématiques, UPMC – Paris 6: 

- B.Sc. Mathematics (L2), Responsible of the course « Series and generalised intergrals (advanced) ».

- B.Sc. Mathematics (L2), Responsible of the course « Series of Functions and integrals ».

- B.Sc. Mathematics (L2), Responsible of the course « Vector calculus and multiple integrals ».

- M.Sc. in Physics (M1), Research project managment

  Project title : « Physical interpretation of the correction to Newton's law by the Schwarzschild metric ».

2009 – 2012: Faculty of Engineering, UPMC – Paris 6. ».

  - B.Sc. (L2 Pro): Responsible of the course « Mathematical tools 2 ».

  - B.Sc. (L3): Co-responsible of the course « Pde’s for Mechanics ».

2009 – 2012: Polytechnic Engineering Schools (EPU, GM3), UPMC – Paris 6: ».

   - 2^nd year of Engineer cycle : Responsible of the course « Mathematical tools for Engineer 2 ».

2004 – 2007: Faculty of Engineering, UPMC – Paris 6. ».

   - M.Sc. of Fluid Mechanics (SDI-MFE, M1): Responsible of the course « Mathematics and Numerical Methods for Mechanics ».

   - M.Sc. of Fluid Mechanics (SDI-MFE, M1): Responsible of the course « Numerical Methods applied to nonlinear hyperbolic Pde’s ».

   - M.Sc. of Fluid Mechanics (SDI-MFE, M2): Responsible of the course «Data Mining applied to engineering sciences »

1988 – 2003: : Faculty of Mechanics 923, UPMC – Paris 6. ».

- M.Sc. of Mechanics (SDI-MFE, M1): Responsible of the course « Numerical Methods for Mechanics ».

- M.Sc. of Mechanics (SDI-MFE, M1): « Solid Mechanics». Participation in tutorials.

Détails

Affichages : 17871

Phone/ Fax: 01.44.27.87.18/ 52.59
email: Cette adresse e-mail est protégée contre les robots spammeurs. Vous devez activer le JavaScript pour la visualiser.
Address: Campus de Jussieu, Tour 55-65, bureau 512 (5th floor)
Mailing Address: Institut Jean le Rond d'Alembert Université Pierre et Marie Curie
Boîte 162, Tour 55-65, Tour 55-65, 4 place Jussieu, 75252 Paris Cedex 05.

Qualified Full Professor in Applied Mathematics (CNU 26)

Nouveau ! Le Chaine sur Youtube "Mathematics Academy" est ouverte à l'adresse : https://www.youtube.com/channel/UC0awSYDxX0eqJbugrdWDjWg

International Academic Lecture at CERN (Geneva) - 13/12/2016:

Data Mining and Real Systems Modeling 

LAST INVITED INTERNATIONAL PLENARY CONFERENCES

1. 2023, On a new Taylor-like theorem: Application for error estimates of numerical approximations, 15^th International Conference on Pure and Applied Mathematics, (Rhodes, Greece).

2. 2022, A new probabilistic approach applied to error estimates of numerical approximations, 8^th International Conference on Mathematics and Computers in Sciences and Industry, (Athens, Greece).

3. 2022, Revisited finite element error estimate by a new probabilistic approach, 8^th Ariel University Conference on Functional Differential Equations and Applications, (Ariel, Israel).

4. 2019, From a geometrical interpretation of Bramble Hilbert lemma to a probabilistic distribution for relative finite elements accuracy, International Academic Conference at CERN, (Geneva, Switzerland).

5. 2018, From a geometrical interpretation of Bramble Hilbert lemma to a probabilistic distribution for finite elements accuracy, 7^th International Conference of Finite Difference Methods. Theory and Applications, (Lozenetz, Bulgaria).

6. 2016, Data Mining and Real Systems Modeling, International Academic Conference at CERN, (Geneva, Switzerland).

Research topics:

1. Probabilistic approach for a priori and error estimate of solution and approximation to determinist partial differential equations

• Mixed geometrical-probabilisitic interpretation of error estimate derived form Bramble-Hilbert lemma: Application to the relative accuracy between two Lagrange finite elements.

• On generalized binomial laws to evaluate finite element accuracy:On generalized binomial laws to evaluate finite element accuracy:toward applications for adaptive mesh refinement.

• Relative accuracy for high order finite element by a mixed functional-probabilistic approach.

• Explicit k−dependency for P_k finite elements in W^m,p error estimates: application to probabilistic laws for accuracy analysis.

• Continuous probability distribution to compare the approximation error between two Lagrange finite elements.

 2. Mathematical Modeling and Data Mining for Particle Physics

• Probabilist models and Data Mining methods for error estimate of finite element method.

• Asymptotic solutions of Vlasov-Maxwell equations applied to relativist paraxial beams.

3. Mathematical modeling and Data Mining applied to Mechanics

• Bifurcation analysis of Navier Stokes solutions which model atmospheric tornadoes genesis.

• Data Mining methods applied to aerodynamic optimization strategies for unmanned flight.

• The complexity, randomness and chaos in elastic vibration systems.

4. Mathematical Modeling andData Mining for Medicine

• Treatment of Sleep Apnea: Model predictive and characterization protocols "success" and "failure." Exploratory analysis of the relationship between insomnia and Disease Sleep Apnea by data mining methods.

• Statistical and Data Mining techniques applied to the relationship between the excitability of the supplementary motor area with repetitive transcranial magnetic stimulation and the breathing pattern response caused by an experimental inspiratory load possibly respiratory discomfort.

• Evolution of health-related quality of life two to seven years after retropubic radical prostatectomy: evaluation by UCLA prostate cancer index.

• Mathematical methods applied to model the human immune system for the treatment of bladder cancer by injecting the bacteria BCG and interleukin-2.

• Explicative factors of intrauterine insemination success based on exploratory analysis of 2089 cycles done with statistical and Data Mining tools.

5. Probabilistic modeling for media and marketing

• Volterra integro differential equation model applied to marketing and media behavior.

• Unsteady Markov process applied to media exposure.

• General relativity models applied to geomarking.