profil-zyak-2012

Publications

The Arithmetic Geometric Progression Abstract Domain - Jérôme Feret

The Arithmetic Geometric Progression Abstract Domain

Static Analysis of Digital Filters - Jérôme Feret

Static Analysis of Digital Filters

Rule based modelling symmetries refinements - Vincent Danos1

Rule based modelling symmetries refinements

1Compositional Separate Modular Static Analysis of Programs by Abstract Interpretation Patrick Cousot - Patrick Cousot

1Compositional Separate Modular Static Analysis of Programs by Abstract Interpretation Patrick Cousot

Patrick Cousot LIENS École Normale Supérieure - Patrick Cousot

Patrick Cousot LIENS École Normale Supérieure

1Combinatorial complexity and compositional drift in protein interaction networks Eric J Deeds1 Jean Krivine2 Jerome Feret3 Vincent Danos4 Walter Fontana5 -

1Combinatorial complexity and compositional drift in protein interaction networks Eric J Deeds1 Jean Krivine2 Jerome Feret3 Vincent Danos4 Walter Fontana5

Worst Case Analysis of Batch Arrivals with the Increasing Convex Ordering - Jean - Michel Fourneau

Worst Case Analysis of Batch Arrivals with the Increasing Convex Ordering

Jean - Michel Fourneau

BASIC CONCEPTS OF ABSTRACT INTERPRETATION - Patrick Cousot

BASIC CONCEPTS OF ABSTRACT INTERPRETATION

PA IFIC :lTii ffi HEMATI S -

PA IFIC' :lTii ''ffi HEMATI S

INCREASING CONVEX MONOTONE MARKOV CHAINS: THEORY ALGORITHM AND APPLICATIONS - Marin Mersenne

INCREASING CONVEX MONOTONE MARKOV CHAINS: THEORY ALGORITHM AND APPLICATIONS

Programmable Active Memories -

Programmable Active Memories

A Reconfigurable Arithmetic Array for Multimedia Applications - Unknown

A Reconfigurable Arithmetic Array for Multimedia Applications

Digital Algebra and Circuits - Jean Vuillemin

Digital Algebra and Circuits

Reduce Reuse Recycle: Efficiently Solving Multi Label MRFs Karteek Alahari1 Pushmeet Kohli2 Philip H S Torr1 -

Reduce Reuse Recycle: Efficiently Solving Multi Label MRFs Karteek Alahari1 Pushmeet Kohli2 Philip H S Torr1

Learning Mixtures of Offline and Online features for Handwritten Stroke Recognition -

Learning Mixtures of Offline and Online features for Handwritten Stroke Recognition

Mathematical intuition and the cognitive roots of mathematical concepts1 Giuseppe Longo Arnaud Viarouge CNRS et Ecole Normale Superieure Psychology and Human Development Dpt et CREA Ecole Polytechnique Paris Fr Peabody College Vanderbilt University http: www di ens fr users longo Nashville TN USA Abstract The foundation of Mathematics is both a logico formal issue and an epistemological one By the first we mean the explicitation and analysis of formal proof principles which largely a posteriori ground proof on general deduction rules and schemata By the second we mean the investigation of the constitutive genesis of concepts and structures the aim of this paper This genealogy of concepts so dear to Riemann Poincaré and Enriques among others is necessary both in order to enrich the foundational analysis by this too often disregarded aspect the cognitive and historical constitution of mathematical structures and because of the provable incompleteness of proof principles also in the analysis of deduction For the purposes of our investigation we will hint here to the philosophical frame as well as to the some recent advances in Cognition that support our claim the cognitive origin and the constitutive role of mathematical intuition From Logic to Cognition Over the course of the XXth century the relationships between Philosophy and Mathematics have been dominated by Mathematical Logic A most interesting area of Mathematics which from onwards year of one of the major mathematical results of the century Gödelian Incompleteness enjoyed the double status of a discipline that is both technically profound and philosophically fundamental From the foundational point of view Proof Theory constituted its main aspect also on account of other remarkable results Ordinal Analysis after Gentzen Type Theory in the manner of Church Gödel Girard various forms of incompleteness independence in Set Theory and Arithmetics and produced spin offs which are in the course of changing the world: the functions for the computation of proofs ... - Giuseppe Longo

Mathematical intuition and the cognitive roots of mathematical concepts1 Giuseppe Longo Arnaud Viarouge CNRS et Ecole Normale Superieure Psychology and Human Development Dpt et CREA Ecole Polytechnique Paris Fr Peabody College Vanderbilt University http: www di ens fr users longo Nashville TN USA Abstract The foundation of Mathematics is both a logico formal issue and an epistemological one By the first we mean the explicitation and analysis of formal proof principles which largely a posteriori ground proof on general deduction rules and schemata By the second we mean the investigation of the constitutive genesis of concepts and structures the aim of this paper This genealogy of concepts so dear to Riemann Poincaré and Enriques among others is necessary both in order to enrich the foundational analysis by this too often disregarded aspect the cognitive and historical constitution of mathematical structures and because of the provable incompleteness of proof principles also in the analysis of deduction For the purposes of our investigation we will hint here to the philosophical frame as well as to the some recent advances in Cognition that support our claim the cognitive origin and the constitutive role of mathematical intuition From Logic to Cognition Over the course of the XXth century the relationships between Philosophy and Mathematics have been dominated by Mathematical Logic A most interesting area of Mathematics which from onwards year of one of the major mathematical results of the century Gödelian Incompleteness enjoyed the double status of a discipline that is both technically profound and philosophically fundamental From the foundational point of view Proof Theory constituted its main aspect also on account of other remarkable results Ordinal Analysis after Gentzen Type Theory in the manner of Church Gödel Girard various forms of incompleteness independence in Set Theory and Arithmetics and produced spin offs which are in the course of changing the world: the functions for the computation of proofs ...

Discriminative Actions for Recognising Events -

Discriminative Actions for Recognising Events

1Phenomenology of Incompleteness: from Formal Deductions to Mathematics and Physics -

1Phenomenology of Incompleteness: from Formal Deductions to Mathematics and Physics

1Objective and Epistemic Complexity in Biology - Francis Bailly

1Objective and Epistemic Complexity in Biology

From physics to biology by extending criticality and symmetry breakings -

From physics to biology by extending criticality and symmetry breakings

THE MATHEMATICS OF COMPUTING BETWEEN LOGIC AND PHYSICS -

THE MATHEMATICS OF COMPUTING BETWEEN LOGIC AND PHYSICS

CAUSES AND SYMMETRIES IN NATURAL SCIENCES - Francis Bailly

CAUSES AND SYMMETRIES IN NATURAL SCIENCES

Symmetries and symmetry breakings: the fabric of physical interactions and the flow of time1 Giuseppe Longo Dépt d Informatique CNRS Ecole Normale Supérieure et CREA Polytechnique Paris http: www di ens fr users longo Summary This short note develops some ideas along the lines of the stimulating paper by Heylighen Found Sci 2010a It summarizes a theme in several writings with Francis Bailly downloadable from this author s web page The “geometrization” of time and causality is the common ground of the analysis hinted here and in Heylighen s paper Heylighen adds a logical notion consistency in order to understand a possible origin of the selective process that may have originated this organization of natural phenomena We will join our perspectives by hinting to some gnoseological complexes common to mathematics and physics which may shed light on the issues raised by Heylighen Note: Francis Bailly passed away recently: his immense experience in physics has been leading our joint work for many years Historically it is with relativist physics that there occurs a “change of perspective”: we pass from “causal laws” to the structural organization of space and time or even from causal laws to the “legality normativity of geometric structures” This understanding of causal laws by the identification of structural organizations stems essentially from the intrinsic duality existing between the characterization of the geometry of the universe and that of energy momentum within that universe By this duality and the putting into effect of the principle of invariance under the differentiable transformations of space time the “forces” are relativized to the nature of this geometry: they will even appear or disappear according to the geometric nature of the universe chosen a priori to describe physical behaviors Now it is similar for quantum physics in gauge theories Here gauge groups operate upon internal variables such as in the case of relativity where the choice of local gauges and their changes enable to define or ... - Giuseppe Longo

Symmetries and symmetry breakings: the fabric of physical interactions and the flow of time1 Giuseppe Longo Dépt d'Informatique CNRS Ecole Normale Supérieure et CREA Polytechnique Paris http: www di ens fr users longo Summary This short note develops some ideas along the lines of the stimulating paper by Heylighen Found Sci 2010a It summarizes a theme in several writings with Francis Bailly downloadable from this author's web page The “geometrization” of time and causality is the common ground of the analysis hinted here and in Heylighen's paper Heylighen adds a logical notion consistency in order to understand a possible origin of the selective process that may have originated this organization of natural phenomena We will join our perspectives by hinting to some gnoseological complexes common to mathematics and physics which may shed light on the issues raised by Heylighen Note: Francis Bailly passed away recently: his immense experience in physics has been leading our joint work for many years Historically it is with relativist physics that there occurs a “change of perspective”: we pass from “causal laws” to the structural organization of space and time or even from causal laws to the “legality normativity of geometric structures” This understanding of causal laws by the identification of structural organizations stems essentially from the intrinsic duality existing between the characterization of the geometry of the universe and that of energy momentum within that universe By this duality and the putting into effect of the principle of invariance under the differentiable transformations of space time the “forces” are relativized to the nature of this geometry: they will even appear or disappear according to the geometric nature of the universe chosen a priori to describe physical behaviors Now it is similar for quantum physics in gauge theories Here gauge groups operate upon internal variables such as in the case of relativity where the choice of local gauges and their changes enable to define or ...

Some Topologies for Computations - Giuseppe Longo

Some Topologies for Computations

THEOREMS AS CONSTRUCTIVE VISIONS1 Giuseppe Longo CNRS Ecole Normale Supérieure et CREA Ecole Polytechnique Rue D Ulm Paris France http: www di ens fr users longo Abstract This paper briefly reviews some epistemological perspectives on the foundation of mathematical concepts and proofs It provides examples of axioms and proofs from Euclid to recent “concrete incompleteness” theorems In reference to basic cognitive phenomena the paper focuses on order and symmetries as core “construction principles” for mathematical knowledge A distinction is then made between these principles and the “proof principles” of modern Mathemaical Logic The role of the blend of these different forms of founding principles will be stressed both for the purposes of proving and of understanding and communicating the proof THE CONSTRUCTIVE CONTENT OF EUCLID S AXIOMS From the time of Euclid to the age of super computers Western mathematicians have continually tried to develop and refine the foundations of proof and proving Many of these attempts have been based on analyses logically and historically linked to the prevailing philosophical notions of the day However they have all exhibited more or less explcitly some basic cognitive principles for example the notions of symmetry and order Here I trace some of the major steps in the evolution of notion of proof linking them to these cognitive basics For this purpose let s take as a starting point Euclid s Aithemata Requests the minimal constructions required to do geometry: Invited lecture ICMI conference on Proof and Proving Taipei Taiwan May Hanna de Villiers eds Springer - Giuseppe Longo

THEOREMS AS CONSTRUCTIVE VISIONS1 Giuseppe Longo CNRS Ecole Normale Supérieure et CREA Ecole Polytechnique Rue D'Ulm Paris France http: www di ens fr users longo Abstract This paper briefly reviews some epistemological perspectives on the foundation of mathematical concepts and proofs It provides examples of axioms and proofs from Euclid to recent “concrete incompleteness” theorems In reference to basic cognitive phenomena the paper focuses on order and symmetries as core “construction principles” for mathematical knowledge A distinction is then made between these principles and the “proof principles” of modern Mathemaical Logic The role of the blend of these different forms of founding principles will be stressed both for the purposes of proving and of understanding and communicating the proof THE CONSTRUCTIVE CONTENT OF EUCLID'S AXIOMS From the time of Euclid to the age of super computers Western mathematicians have continually tried to develop and refine the foundations of proof and proving Many of these attempts have been based on analyses logically and historically linked to the prevailing philosophical notions of the day However they have all exhibited more or less explcitly some basic cognitive principles for example the notions of symmetry and order Here I trace some of the major steps in the evolution of notion of proof linking them to these cognitive basics For this purpose let's take as a starting point Euclid's Aithemata Requests the minimal constructions required to do geometry: Invited lecture ICMI conference on Proof and Proving Taipei Taiwan May Hanna de Villiers eds Springer

Les mécanismes fondamentaux de l évolution sociale selon Max Weber et Durkheim - Charau@Charau-8gzyirni

Les mécanismes fondamentaux de l'évolution sociale selon Max Weber et Durkheim

Charau@Charau-8gzyirni

On the Relevance of Negative Results1 Giuseppe Longo CNRS et Dépt d Informatique École Normale Supérieure Paris et CREA École Polytechnique http: www di ens fr users longo Abstract The access to scientific knowledge is a construction of objectivity which needs the critical insight of “negative results” These consist in the explicit construction of internal limits to current theories and methods We shall hint to the role of some results which in Logic in Physics or Computing opened up new areas for knowledge by saying “No we cannot compute this we cannot decide that The idea is that both the sciences of life and of cognition in particular in connection to Mathematics and Computing need similar results in order to set limits to the passive transfer of physico mathematical methods into their autonomous construction of knowledge and open the way to new tools and perspectives We will compare this perspective with the requirement both at the national and European levels to finalize most all research activities into foreseeable industrial applications Scientific knowledge and critical insight The analysis of concepts conducted on a comparative level if possible as well as the tentative explanation of the philosophical project should always accompany scientific work In fact critical reflections regarding existing theories are at the core of positive scientific constructions because science is often constructed against the supposed tyranny and autonomy of “facts” which in reality are nothing but “small scale theories” Science is also often constructed by means of an audacious interpretation of “new” and old facts it progresses against the obvious and against common sense le “bon sens” it struggles against the illusions of immediate knowledge and must be capable of escaping from already established theoretical frameworks For example the very high level of mathematical technicity in the geometry of Ptolemaic epicycles constructed from clearly observable facts strongly perplexed numerous Renaissance thinkers such as ... - Giuseppe Longo

On the Relevance of Negative Results1 Giuseppe Longo CNRS et Dépt d'Informatique École Normale Supérieure Paris et CREA École Polytechnique http: www di ens fr users longo Abstract The access to scientific knowledge is a construction of objectivity which needs the critical insight of “negative results” These consist in the explicit construction of internal limits to current theories and methods We shall hint to the role of some results which in Logic in Physics or Computing opened up new areas for knowledge by saying “No we cannot compute this we cannot decide that The idea is that both the sciences of life and of cognition in particular in connection to Mathematics and Computing need similar results in order to set limits to the passive transfer of physico mathematical methods into their autonomous construction of knowledge and open the way to new tools and perspectives We will compare this perspective with the requirement both at the national and European levels to finalize most all research activities into foreseeable industrial applications Scientific knowledge and critical insight The analysis of concepts conducted on a comparative level if possible as well as the tentative explanation of the philosophical project should always accompany scientific work In fact critical reflections regarding existing theories are at the core of positive scientific constructions because science is often constructed against the supposed tyranny and autonomy of “facts” which in reality are nothing but “small scale theories” Science is also often constructed by means of an audacious interpretation of “new” and old facts it progresses against the obvious and against common sense le “bon sens” it struggles against the illusions of immediate knowledge and must be capable of escaping from already established theoretical frameworks For example the very high level of mathematical technicity in the geometry of Ptolemaic epicycles constructed from clearly observable facts strongly perplexed numerous Renaissance thinkers such as ...

1http: www asmp fr Académie des Sciences morales et politiques - Charau@Charau-8gzyirni

1http: www asmp fr Académie des Sciences morales et politiques

Charau@Charau-8gzyirni

Banking Consolidation in Europe - Per Jacobsson

Banking Consolidation in Europe

Financial sector development in transition economies of the next decades -

Financial sector development in transition economies of the next decades

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