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1,183 results on '"Aubin, Jean-Pierre"'

3. Coviability, Through the Lens of the Mathematical Theory of Viability

Author

Aubin, Jean-Pierre, Durand, Marie-Hélène, Barrière, Olivier, editor, Behnassi, Mohamed, editor, David, Gilbert, editor, Douzal, Vincent, editor, Fargette, Mireille, editor, Libourel, Thérèse, editor, Loireau, Maud, editor, Pascal, Laurence, editor, Prost, Catherine, editor, Ravena-Cañete, Voyner, editor, Seyler, Frédérique, editor, and Morand, Serge, editor

Published
2019
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4. Introductory Chapter: An Interweaving to Be Formalized, the Biosphere Faced with the Relationship Between the Human and the Non-human

Author

Barrière, Olivier, Prost, Catherine, Ravena-Cañete, Voyner, Douzal, Vincent, Fargette, Mireille, Aubin, Jean-Pierre, Barrière, Olivier, editor, Behnassi, Mohamed, editor, David, Gilbert, editor, Douzal, Vincent, editor, Fargette, Mireille, editor, Libourel, Thérèse, editor, Loireau, Maud, editor, Pascal, Laurence, editor, Prost, Catherine, editor, Ravena-Cañete, Voyner, editor, Seyler, Frédérique, editor, and Morand, Serge, editor

Published
2019
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5. Cournot Maps for Intercepting Evader Evolutions by a Pursuer

Author

Aubin, Jean-Pierre and Luxi, Chen

Subjects
Mathematics - Optimization and Control
Abstract

Instead of studying evolutions governed by an evolutionary system starting at a given initial state on a prescribed future time interval, finite or infinite, we tackle the problem of looking both for a past interval [T-D,T] of aperture (or length, duration) D and for the viable evolutions arriving at a prescribed terminal state at the end of the temporal window (and thus telescoping if more than one such evolutions exist). Hence, given time and duration dependent evolutionary system and viability constraints, as well as time dependent departure constraints, the Cournot map associates with any terminal time T and state x the apertures D(T,x) of the intervals [T-D(T,x),T], the starting (or initial) states at the beginning of the temporal window from which at least one viable evolution will reach the given terminal state x at T. Cournot maps can be used by a pursuer to intercept an evader's evolution in dynamic game theory. After providing some properties of Cournot maps are next investigated, above all, the regulation map piloting the viables evolutions at each time and for each duration from the beginning of the temporal window up to terminal time. The next question investigated is the selection of controls or regulons in the regulation map whenever several of them exist. Selection processes are either time dependent, when the selection operates at each time, duration and state for selecting a regulon satisfying required properties (for instance, minimal norm, minimal speed), or intertemporal. In this case, viable evolutions are required to optimize some prescribed intertemporal functional, as in optimal control. This generates value functions, the topics of the second part of this study

Published
2013

6. Transports Regulators of Networks with Junctions Detected by Durations Functions

Author

Aubin, Jean-Pierre

Subjects
Mathematics - Optimization and Control
Abstract

This study advocates a mathematical framework of ''transport relations'' on a network. They single out a subset of ''traffic states'' described by time, duration, position and other traffic attributes (called ''monads'' for short). Duration evolutions are non-negative, decreasing toward zero for incoming durations, increasing from zero for outgoing durations, allowing the detection of ''junction states'' defined as traffic states with ''zero duration''. A ''junction relation'' (crossroads, synapses, clearing houses, etc.) Is a subset of the transport relation made of junction states? The objective is to construct a ''transport regulator'' associating with traffic states a set of ''celerities'' that mobiles circulating in the network can use as velocities. In other word, a network is regarded as a ''provider of velocity information'' to the mobiles for travelling from one departure state to an arrival state across a junction relation (a kind of geodesic problem). This investigation assumes that a system governs the evolution of monads in function of time, duration and position using celerities as controls and provides the transport regulator, a feedback from transport states to celerities. The proposed mathematical framework can acclimate road or aerial networks, endocrine (hormonal) or synaptic (neurotransmitters) networks, financial or economic networks, which motivated this investigation. This framework could probably accommodate computer and even social networks. This investigation is restricted to junctions between two routes., Comment: 26 pages

Published
2013

7. Retro-Prospective Differential Inclusions and their Control by the Differential Connection Tensors of their Evolutions: The trendometer

Author

Aubin, Jean-Pierre

Subjects
Mathematics - Optimization and Control
Abstract

This study is motivated by two different, yet, connected, motivations. The first one follows the observation that the classical definition of derivatives involves prospective (or forward) difference quotients, not known whenever the time is directed, at least at the macroscopic level. Actually, the available and known derivatives are retrospective (or backward). They co\"incide whenever the functions are differentiable in the classical sense, but not in the case of non smooth maps, single-valued or set-valued. The later ones are used in differential inclusions (and thus, in uncertain control systems) governing evolutions in function of time and state. We follow the plea of some physicists for taking also into account the retrospective derivatives to study prospective evolutions in function of time, state and retrospective derivatives, a particular, but specific, example of historical of ''path dependent'' evolutionary systems. This is even more crucial in life sciences, in the absence of experimentation of uncertain evolutionary systems. The second motivation emerged from the study of networks with junctions (cross-roads in traffic networks, synapses in neural networks, banks in financial networks, etc.), an important feature of ''complex systems''. At each junction, the velocities of the incoming (retrospective) and outgoing (prospective) evolutions are confronted. One measure of this confrontation (''jerkiness'') is provided by the product of the retrospective and prospective velocities, negative in ''inhibitory'' junctions, positive for ''excitatory'' ones, for instance. This leads to the introduction of the ''differential connection tensor'' of two evolutions, defined as the tensor product of retrospective and prospective derivatives, which can be used for controlling evolutionary systems governing the evolutions through networks with junctions., Comment: 24 pages

Published
2013

8. Traffic Specifications

Author

Aubin, Jean-Pierre, Désilles, Anya, Schröder, Jörg, Series editor, Weigand, Bernhard, Series editor, Aubin, Jean-Pierre, and Désilles, Anya

Published
2017
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11. Mathematical Appendixes

Author

Aubin, Jean-Pierre, Désilles, Anya, Schröder, Jörg, Series editor, Weigand, Bernhard, Series editor, Aubin, Jean-Pierre, and Désilles, Anya

Published
2017
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14. Traveling on the Network

Author

Aubin, Jean-Pierre, Désilles, Anya, Schröder, Jörg, Series editor, Weigand, Bernhard, Series editor, Aubin, Jean-Pierre, and Désilles, Anya

Published
2017
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15. Introduction

Author

Aubin, Jean-Pierre, Désilles, Anya, Schröder, Jörg, Series editor, Weigand, Bernhard, Series editor, Aubin, Jean-Pierre, and Désilles, Anya

Published
2017
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16. Constructing and exploring wells of energy landscapes

Author

Aubin, Jean-Pierre and Lesne, Annick

Subjects
Condensed Matter - Statistical Mechanics
Abstract

Landscape paradigm is ubiquitous in physics and other natural sciences, but it has to be supplemented with both quantitative and qualitatively meaningful tools for analyzing the topography of a given landscape. We here consider dynamic explorations of the relief and introduce as basic topographic features ``wells of duration $T$ and altitude $y$''. We determine an intrinsic exploration mechanism governing the evolutions from an initial state in the well up to its rim in a prescribed time, whose finite-difference approximations on finite grids yield a constructive algorithm for determining the wells. Our main results are thus (i) a quantitative characterization of landscape topography rooted in a dynamic exploration of the landscape, (ii) an alternative to stochastic gradient dynamics for performing such an exploration, (iii) a constructive access to the wells and (iv) the determination of some bare dynamic features inherent to the landscape. The mathematical tools used here are not familiar in physics: They come from set-valued analysis (differential calculus of set-valued maps and differential inclusions) and viability theory (capture basins of targets under evolutionary systems) which have been developed during the last two decades; we therefore propose a minimal appendix exposing them at the end of this paper to bridge the possible gap., Comment: 28 pages, submitted to J. Math. Phys --

Published
2004
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17. The method of characteristics revisited. A viability approach

Author

Aubin, Jean-Pierre

Subjects
Mathematics - Dynamical Systems, 34K35, 34C35, 49L05, 49L25, 70H20
Abstract

This mini-course provides a presentation of the method of characteristics to initial/boundary-value problems for systems of first-order partial differential equations and to Hamilton-Jacobi variational inequalities. In particular, these results are indeed useful for the treatment of hybrid systems of control theory. We rely on tools forged by set-valued analysis and viability theory, which happen to be both efficient and versatile to cover many problems. They find here unexpected relevance.

Published
1999

18. Endowing Exchange Values: Adam Smith’s Invisible Man

Author

Aubin, Jean-Pierre, Fandel, Günter, Editor-in-chief, Trockel, Walter, Editor-in-chief, Dawid, Herbert, Series editor, Dimitrov, Dinko, Series editor, Gerber, Anke, Series editor, Haake, Claus-Jochen, Series editor, Hofmann, Christian, Series editor, Pfeiffer, Thomas, Series editor, Slowiński, Roman, Series editor, Zijm, W.H.M., Series editor, and Aubin, Jean-Pierre

Published
2014
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19. Endowing Fundamental Values: Willingness to Pay

Author

Aubin, Jean-Pierre, Fandel, Günter, Editor-in-chief, Trockel, Walter, Editor-in-chief, Dawid, Herbert, Series editor, Dimitrov, Dinko, Series editor, Gerber, Anke, Series editor, Haake, Claus-Jochen, Series editor, Hofmann, Christian, Series editor, Pfeiffer, Thomas, Series editor, Slowiński, Roman, Series editor, Zijm, W.H.M., Series editor, and Aubin, Jean-Pierre

Published
2014
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20. Why Viability Theory?

Author

Aubin, Jean-Pierre, Fandel, Günter, Editor-in-chief, Trockel, Walter, Editor-in-chief, Dawid, Herbert, Series editor, Dimitrov, Dinko, Series editor, Gerber, Anke, Series editor, Haake, Claus-Jochen, Series editor, Hofmann, Christian, Series editor, Pfeiffer, Thomas, Series editor, Slowiński, Roman, Series editor, Zijm, W.H.M., Series editor, and Aubin, Jean-Pierre

Published
2014
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21. Keeping the Endowment Above a Viability Threshold

Author

Aubin, Jean-Pierre, Fandel, Günter, Editor-in-chief, Trockel, Walter, Editor-in-chief, Dawid, Herbert, Series editor, Dimitrov, Dinko, Series editor, Gerber, Anke, Series editor, Haake, Claus-Jochen, Series editor, Hofmann, Christian, Series editor, Pfeiffer, Thomas, Series editor, Slowiński, Roman, Series editor, Zijm, W.H.M., Series editor, and Aubin, Jean-Pierre

Published
2014
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22. What Is to Be Done?

Author

Aubin, Jean-Pierre, Fandel, Günter, Editor-in-chief, Trockel, Walter, Editor-in-chief, Dawid, Herbert, Series editor, Dimitrov, Dinko, Series editor, Gerber, Anke, Series editor, Haake, Claus-Jochen, Series editor, Hofmann, Christian, Series editor, Pfeiffer, Thomas, Series editor, Slowiński, Roman, Series editor, Zijm, W.H.M., Series editor, and Aubin, Jean-Pierre

Published
2014
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23. Evolutions and Their Temporal Windows

Author

Aubin, Jean-Pierre, Fandel, Günter, Editor-in-chief, Trockel, Walter, Editor-in-chief, Dawid, Herbert, Series editor, Dimitrov, Dinko, Series editor, Gerber, Anke, Series editor, Haake, Claus-Jochen, Series editor, Hofmann, Christian, Series editor, Pfeiffer, Thomas, Series editor, Slowiński, Roman, Series editor, Zijm, W.H.M., Series editor, and Aubin, Jean-Pierre

Published
2014
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24. Uncertain Endowments and Economic Cycles

Author

Aubin, Jean-Pierre, Fandel, Günter, Editor-in-chief, Trockel, Walter, Editor-in-chief, Dawid, Herbert, Series editor, Dimitrov, Dinko, Series editor, Gerber, Anke, Series editor, Haake, Claus-Jochen, Series editor, Hofmann, Christian, Series editor, Pfeiffer, Thomas, Series editor, Slowiński, Roman, Series editor, Zijm, W.H.M., Series editor, and Aubin, Jean-Pierre

Published
2014
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25. The Underlying Thesis

Author

Aubin, Jean-Pierre, Fandel, Günter, Editor-in-chief, Trockel, Walter, Editor-in-chief, Dawid, Herbert, Series editor, Dimitrov, Dinko, Series editor, Gerber, Anke, Series editor, Haake, Claus-Jochen, Series editor, Hofmann, Christian, Series editor, Pfeiffer, Thomas, Series editor, Slowiński, Roman, Series editor, Zijm, W.H.M., Series editor, and Aubin, Jean-Pierre

Published
2014
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26. How Long and How Much Endowing One Commodity

Author

Aubin, Jean-Pierre, Fandel, Günter, Editor-in-chief, Trockel, Walter, Editor-in-chief, Dawid, Herbert, Series editor, Dimitrov, Dinko, Series editor, Gerber, Anke, Series editor, Haake, Claus-Jochen, Series editor, Hofmann, Christian, Series editor, Pfeiffer, Thomas, Series editor, Slowiński, Roman, Series editor, Zijm, W.H.M., Series editor, and Aubin, Jean-Pierre

Published
2014
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32. Rainbow Options in Discrete Time, II

Author

Bernhard, Pierre, Engwerda, Jacob C., Roorda, Berend, Schumacher, J. M., Kolokoltsov, Vassili, Saint-Pierre, Patrick, Aubin, Jean-Pierre, Bernhard, Pierre, Engwerda, Jacob C., Roorda, Berend, Schumacher, J.M., Kolokoltsov, Vassili, Saint-Pierre, Patrick, and Aubin, Jean-Pierre

Published
2013
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33. Continuous-Time Limits

Author

Bernhard, Pierre, Engwerda, Jacob C., Roorda, Berend, Schumacher, J. M., Kolokoltsov, Vassili, Saint-Pierre, Patrick, Aubin, Jean-Pierre, Bernhard, Pierre, Engwerda, Jacob C., Roorda, Berend, Schumacher, J.M., Kolokoltsov, Vassili, Saint-Pierre, Patrick, and Aubin, Jean-Pierre

Published
2013
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35. Credit Derivatives

Author

Bernhard, Pierre, Engwerda, Jacob C., Roorda, Berend, Schumacher, J. M., Kolokoltsov, Vassili, Saint-Pierre, Patrick, Aubin, Jean-Pierre, Bernhard, Pierre, Engwerda, Jacob C., Roorda, Berend, Schumacher, J.M., Kolokoltsov, Vassili, Saint-Pierre, Patrick, and Aubin, Jean-Pierre

Published
2013
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38. Digital Options

Author

Bernhard, Pierre, Engwerda, Jacob C., Roorda, Berend, Schumacher, J. M., Kolokoltsov, Vassili, Saint-Pierre, Patrick, Aubin, Jean-Pierre, Bernhard, Pierre, Engwerda, Jacob C., Roorda, Berend, Schumacher, J.M., Kolokoltsov, Vassili, Saint-Pierre, Patrick, and Aubin, Jean-Pierre

Published
2013
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39. Vanilla Options

Author

Bernhard, Pierre, Engwerda, Jacob C., Roorda, Berend, Schumacher, J. M., Kolokoltsov, Vassili, Saint-Pierre, Patrick, Aubin, Jean-Pierre, Bernhard, Pierre, Engwerda, Jacob C., Roorda, Berend, Schumacher, J.M., Kolokoltsov, Vassili, Saint-Pierre, Patrick, and Aubin, Jean-Pierre

Published
2013
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41. Validation

Author

Bernhard, Pierre, Engwerda, Jacob C., Roorda, Berend, Schumacher, J. M., Kolokoltsov, Vassili, Saint-Pierre, Patrick, Aubin, Jean-Pierre, Bernhard, Pierre, Engwerda, Jacob C., Roorda, Berend, Schumacher, J.M., Kolokoltsov, Vassili, Saint-Pierre, Patrick, and Aubin, Jean-Pierre

Published
2013
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42. Appendix: Proofs

Author

Bernhard, Pierre, Engwerda, Jacob C., Roorda, Berend, Schumacher, J. M., Kolokoltsov, Vassili, Saint-Pierre, Patrick, Aubin, Jean-Pierre, Bernhard, Pierre, Engwerda, Jacob C., Roorda, Berend, Schumacher, J.M., Kolokoltsov, Vassili, Saint-Pierre, Patrick, and Aubin, Jean-Pierre

Published
2013
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43. Introduction

Author

Bernhard, Pierre, Engwerda, Jacob C., Roorda, Berend, Schumacher, J. M., Kolokoltsov, Vassili, Saint-Pierre, Patrick, Aubin, Jean-Pierre, Bernhard, Pierre, Engwerda, Jacob C., Roorda, Berend, Schumacher, J.M., Kolokoltsov, Vassili, Saint-Pierre, Patrick, and Aubin, Jean-Pierre

Published
2013
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44. Optimal Hedging Under Robust-Cost Constraints

Author

Bernhard, Pierre, Engwerda, Jacob C., Roorda, Berend, Schumacher, J. M., Kolokoltsov, Vassili, Saint-Pierre, Patrick, Aubin, Jean-Pierre, Bernhard, Pierre, Engwerda, Jacob C., Roorda, Berend, Schumacher, J.M., Kolokoltsov, Vassili, Saint-Pierre, Patrick, and Aubin, Jean-Pierre

Published
2013
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45. Fair Price Intervals

Author

Bernhard, Pierre, Engwerda, Jacob C., Roorda, Berend, Schumacher, J. M., Kolokoltsov, Vassili, Saint-Pierre, Patrick, Aubin, Jean-Pierre, Bernhard, Pierre, Engwerda, Jacob C., Roorda, Berend, Schumacher, J.M., Kolokoltsov, Vassili, Saint-Pierre, Patrick, and Aubin, Jean-Pierre

Published
2013
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46. Merton’s Optimal Dynamic Portfolio Revisited

Author

Bernhard, Pierre, Engwerda, Jacob C., Roorda, Berend, Schumacher, J. M., Kolokoltsov, Vassili, Saint-Pierre, Patrick, Aubin, Jean-Pierre, Bernhard, Pierre, Engwerda, Jacob C., Roorda, Berend, Schumacher, J.M., Kolokoltsov, Vassili, Saint-Pierre, Patrick, and Aubin, Jean-Pierre

Published
2013
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47. Option Pricing: Classic Results

Author

Bernhard, Pierre, Engwerda, Jacob C., Roorda, Berend, Schumacher, J. M., Kolokoltsov, Vassili, Saint-Pierre, Patrick, Aubin, Jean-Pierre, Bernhard, Pierre, Engwerda, Jacob C., Roorda, Berend, Schumacher, J.M., Kolokoltsov, Vassili, Saint-Pierre, Patrick, and Aubin, Jean-Pierre

Published
2013
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48. Generalized Lax-Hopf Formulas for Cournot Maps and Hamilton-Jacobi-McKendrick Equations

Author

Aubin, Jean-Pierre, Chen, Luxi, Ancona, Vincenzo, Editor-in-chief, Cannarsa, Piermarco, Series editor, Canuto, Claudio, Series editor, Coletti, Giulianella, Series editor, Marcellini, Paolo, Series editor, Patrizio, Giorgio, Series editor, Ruggeri, Tommaso, Series editor, Strickland, Elisabetta, Series editor, Verra, Alessandro, Series editor, Bettiol, Piernicola, editor, Colombo, Giovanni, editor, Motta, Monica, editor, and Rampazzo, Franco, editor

Published
2015
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50. Restoring Viability

Author

Aubin, Jean-Pierre, Bayen, Alexandre M., Saint-Pierre, Patrick, Aubin, Jean-Pierre, Bayen, Alexandre M., and Saint-Pierre, Patrick

Published
2011
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