Inclusive fitness maximization: an axiomatic approach

Kin selection theorists argue that evolution in social contexts will lead organisms to behave as if maximizing their inclusive, as opposed to personal, fitness. The inclusive fitness concept allows biologists to treat organisms as akin to rational agents seeking to maximize a utility function. Here we develop this idea and place it on a firm footing by employing a standard decision-theoretic methodology. We show how the principle of inclusive fitness maximization and a related principle of quasi-inclusive fitness maximization can be derived from axioms on an individual’s ‘as if preferences’ (binary choices). Our results help integrate evolutionary theory and rational choice theory, help draw out the behavioural implications of inclusive fitness maximization, and point to a possible way in which evolution could lead organisms to implement it.

Bayesian inference and model comparison for random choice structures

We complete the development of a testing ground for axioms of discrete stochastic choice. Our contribution here is to develop new posterior simulation methods for Bayesian inference, suitable for a class of prior distributions introduced by McCausland and Marley (2013). These prior distributions are joint distributions over various choice distributions over choice sets of di fferent sizes. Since choice distributions over di fferent choice sets can be mutually dependent, previous methods relying on conjugate prior distributions do not apply. We demonstrate by analyzing data from a previously reported experiment and report evidence for and against various axioms.

Expected utility without full transitivity

We generalize the classical expected-utility criterion by weakening transitivity to Suzumura consistency. In the absence of full transitivity, reflexivity and completeness no longer follow as a consequence of the system of axioms employed and a richer class of rankings of probability distributions results. This class is characterized by means of standard expected-utility axioms in addition to Suzumura consistency. An important feature of some members of our new class is that they allow us to soften the negative impact of wellknown paradoxes without abandoning the expected-utility framework altogether.

Welfare criteria from choice: the sequential solution

We study the problem of deriving a complete welfare ordering from a choice function. Under the sequential solution, the best alternative is the alternative chosen from the universal set; the second best is the one chosen when the best alternative is removed; and so on. We show that this is the only completion of Bernheim and Rangel's (2009) welfare relation that satisfies two natural axioms: neutrality, which ensures that the names of the alternatives are welfare-irrelevant; and persistence, which stipulates that every choice function between two welfare-identical choice functions must exhibit the same welfare ordering.

Population Ethics, Social Choice Theory, and Two problems in the Measurement of Economic Poverty

Full Text / Article complet

L’univers dans un point noir : esthétique et matérialité dans l’oeuvre de Jack Kirby

Notre recherche étudie les particularités esthétiques et matérialistes de l’oeuvre du bédéiste américain Jack Kirby (1917-1994) et la manière dont elles répondent d’agencements qui visent à déconstruire et reconstruire les formes sur la page. Contemporain de Will Eisner, Kirby est largement considéré comme l'auteur et dessinateur le plus influent de son époque, co-signant les premières aventures de certains des super-héros qui perdurent et qui sont aujourd’hui la manne de l’industrie hollywoodienne (Captain America, les Fantastic Four, Hulk, etc.). Son oeuvre protéiforme est composée de superpositions de textures, d’objets récupérés, de figures déviées et trouve dans son rapport à la matière les principaux axiomes qui la définissent. Cherchant dans son travail à cerner les fonctions des nombreux amoncellements de points noirs (baptisés kirby dots par la critique et l’industrie), nous nous écartons des modèles d’analyse sémiologiques pour constituer une approche écosophique de la bande dessinée. Dans cette dernière, nous avons recours à la schizo-analyse théorisée par Gilles Deleuze et Félix Guattari dans leur ouvrage L’Anti-OEdipe (1972) afin de cerner les conditions de la production de sens et de non-sens du point kirbyen. Pour ce faire, nous proposons de reconsidérer la BD comme une écologie séquentialisée, composée de cases sans icônes, c’est-à-dire d’un espace pris au plus près de la planche, pour soi et en soi, sans rapport de causalité fixe ou de structure prédéterminée. Nous envisageons ensuite les territorialités archaïques de la bande dessinée pour mieux définir son ontogénie, puis pour étudier les rapports machiniques et schizos qu’entretiennent entre eux les différents espaces (que nous distinguons en espaces striés et en espaces lisses) ainsi que les différents traits de la planche. Finalement, nous expliquerons en quoi le point kirbyen apparaît comme une machine abstraite, c’est-à-dire une instance capable d’auto-générer, d’auto-poïétiser, son propre mystère représentationnel.

On Some Infinite Convex Invariants

The present study on some infinite convex invariants. The origin of convexity can be traced back to the period of Archimedes and Euclid. At the turn of the nineteenth centaury , convexicity became an independent branch of mathematics with its own problems, methods and theories. The convexity can be sorted out into two kinds, the first type deals with generalization of particular problems such as separation of convex sets[EL], extremality[FA], [DAV] or continuous selection Michael[M1] and the second type involved with a multi- purpose system of axioms. The theory of convex invariants has grown out of the classical results of Helly, Radon and Caratheodory in Euclidean spaces. Levi gave the first general definition of the invariants Helly number and Radon number. The notation of a convex structure was introduced by Jamison[JA4] and that of generating degree was introduced by Van de Vel[VAD8]. We also prove that for a non-coarse convex structure, rank is less than or equal to the generating degree, and also generalize Tverberg’s theorem using infinite partition numbers. Compare the transfinite topological and transfinite convex dimensions

Some aspects of history of Indian mathematics in 18th and early 19th century

This thesis is an attempt to throw light on the works of some Indian Mathematicians who wrote in Arabic or persian In the Introductory Chapter on outline of general history of Mathematics during the eighteenth Bnd nineteenth century has been sketched. During that period there were two streams of Mathematical activity. On one side many eminent scholers, who wrote in Sanskrit, .he l d the field as before without being much influenced by other sources. On the other side there were scholars whose writings were based on Arabic and Persian text but who occasionally drew upon other sources also.

Axiomatic Characterization of the Antimedian Function on Paths and Hypercubes

An antimedian of a pro le = (x1; x2; : : : ; xk) of vertices of a graph G is a vertex maximizing the sum of the distances to the elements of the pro le. The antimedian function is de ned on the set of all pro les on G and has as output the set of antimedians of a pro le. It is a typical location function for nding a location for an obnoxious facility. The `converse' of the antimedian function is the median function, where the distance sum is minimized. The median function is well studied. For instance it has been characterized axiomatically by three simple axioms on median graphs. The median function behaves nicely on many classes of graphs. In contrast the antimedian function does not have a nice behavior on most classes. So a nice axiomatic characterization may not be expected. In this paper such a characterization is obtained for the two classes of graphs on which the antimedian is well-behaved: paths and hypercubes.

Fourier-Matrizen und Ringe mit Basis

Bei der Bestimmung der irreduziblen Charaktere einer Gruppe vom Lie-Typ entwickelte Lusztig eine Theorie, in der eine sogenannte Fourier-Transformation auftaucht. Dies ist eine Matrix, die nur von der Weylgruppe der Gruppe vom Lie-Typ abhängt. Anhand der Eigenschaften, die eine solche Fourier- Matrix erfüllen muß, haben Geck und Malle ein Axiomensystem aufgestellt. Dieses ermöglichte es Broue, Malle und Michel füur die Spetses, über die noch vieles unbekannt ist, Fourier-Matrizen zu bestimmen. Das Ziel dieser Arbeit ist eine Untersuchung und neue Interpretation dieser Fourier-Matrizen, die hoffentlich weitere Informationen zu den Spetses liefert. Die Werkzeuge, die dabei entstehen, sind sehr vielseitig verwendbar, denn diese Matrizen entsprechen gewissen Z-Algebren, die im Wesentlichen die Eigenschaften von Tafelalgebren besitzen. Diese spielen in der Darstellungstheorie eine wichtige Rolle, weil z.B. Darstellungsringe Tafelalgebren sind. In der Theorie der Kac-Moody-Algebren gibt es die sogenannte Kac-Peterson-Matrix, die auch die Eigenschaften unserer Fourier-Matrizen besitzt. Ein wichtiges Resultat dieser Arbeit ist, daß die Fourier-Matrizen, die G. Malle zu den imprimitiven komplexen Spiegelungsgruppen definiert, die Eigenschaft besitzen, daß die Strukturkonstanten der zugehörigen Algebren ganze Zahlen sind. Dazu müssen äußere Produkte von Gruppenringen von zyklischen Gruppen untersucht werden. Außerdem gibt es einen Zusammenhang zu den Kac-Peterson-Matrizen: Wir beweisen, daß wir durch Bildung äußerer Produkte von den Matrizen vom Typ A(1)1 zu denen vom Typ C(1) l gelangen. Lusztig erkannte, daß manche seiner Fourier-Matrizen zum Darstellungsring des Quantendoppels einer endlichen Gruppe gehören. Deswegen ist es naheliegend zu versuchen, die noch ungeklärten Matrizen als solche zu identifizieren. Coste, Gannon und Ruelle untersuchen diesen Darstellungsring. Sie stellen eine Reihe von wichtigen Fragen. Eine dieser Fragen beantworten wir, nämlich inwieweit rekonstruiert werden kann, zu welcher endlichen Gruppe gegebene Matrizen gehören. Den Darstellungsring des getwisteten Quantendoppels berechnen wir für viele Beispiele am Computer. Dazu müssen unter anderem Elemente aus der dritten Kohomologie-Gruppe H3(G,C×) explizit berechnet werden, was bisher anscheinend in noch keinem Computeralgebra-System implementiert wurde. Leider ergibt sich hierbei kein Zusammenhang zu den von Spetses herrührenden Matrizen. Die Werkzeuge, die in der Arbeit entwickelt werden, ermöglichen eine strukturelle Zerlegung der Z-Ringe mit Basis in bekannte Anteile. So können wir für die meisten Matrizen der Spetses Konstruktionen angeben: Die zugehörigen Z-Algebren sind Faktorringe von Tensorprodukten von affinen Ringe Charakterringen und von Darstellungsringen von Quantendoppeln.

ONTIC: A Knowledge Representation System for Mathematics

Ontic is an interactive system for developing and verifying mathematics. Ontic's verification mechanism is capable of automatically finding and applying information from a library containing hundreds of mathematical facts. Starting with only the axioms of Zermelo-Fraenkel set theory, the Ontic system has been used to build a data base of definitions and lemmas leading to a proof of the Stone representation theorem for Boolean lattices. The Ontic system has been used to explore issues in knowledge representation, automated deduction, and the automatic use of large data bases.

Programmable Self-Assembly: Constructing Global Shape using Biologically-inspire

In this thesis I present a language for instructing a sheet of identically-programmed, flexible, autonomous agents (``cells'') to assemble themselves into a predetermined global shape, using local interactions. The global shape is described as a folding construction on a continuous sheet, using a set of axioms from paper-folding (origami). I provide a means of automatically deriving the cell program, executed by all cells, from the global shape description. With this language, a wide variety of global shapes and patterns can be synthesized, using only local interactions between identically-programmed cells. Examples include flat layered shapes, all plane Euclidean constructions, and a variety of tessellation patterns. In contrast to approaches based on cellular automata or evolution, the cell program is directly derived from the global shape description and is composed from a small number of biologically-inspired primitives: gradients, neighborhood query, polarity inversion, cell-to-cell contact and flexible folding. The cell programs are robust, without relying on regular cell placement, global coordinates, or synchronous operation and can tolerate a small amount of random cell death. I show that an average cell neighborhood of 15 is sufficient to reliably self-assemble complex shapes and geometric patterns on randomly distributed cells. The language provides many insights into the relationship between local and global descriptions of behavior, such as the advantage of constructive languages, mechanisms for achieving global robustness, and mechanisms for achieving scale-independent shapes from a single cell program. The language suggests a mechanism by which many related shapes can be created by the same cell program, in the manner of D'Arcy Thompson's famous coordinate transformations. The thesis illuminates how complex morphology and pattern can emerge from local interactions, and how one can engineer robust self-assembly.

Exam 2001 pdf

Exam questions and solutions in PDF

Exam 2001

Exam questions and solutions in LaTex

Análisis del Ejército Zapatista de Liberación Nacional como modelo de guerrilla estética, a la luz de la teoría de la resistencia planteada por Jacques Rancière

Justo ahora, cuando parece haberse agotado el entendimiento del zapatismo como movimiento revolucionario tradicional, esta monografía propone dar un doble salto mortal para destruir las barreras obsoletas de las teorías revolucionarias y aterrizar en lo que Rancière llama la Resistencia de los Sin Parte. El alarido bestial se transforma en palabra para sacudir las estructuras más íntimas del orden y actualizar la pésima partición de los lugares y las funciones comunes en la comunidad. Las partes mal contadas acceden a la palabra para reclamar una partición justa de lo común, e inscribir así las libertades como axiomas para el todo comunitario. Lo descolorido toma color, lo oculto es visto, lo incontado entra en el conteo de las partes, lo que no tiene rostro ni voz es ahora escuchado, las sombras adquieren cuerpos y los cuerpos adquieren vida. La resistencia por la incorporación cambió para siempre la política tradicional mexicana, al punto de que ésta ha dejado de llamarse como tal para quien escribió esta investigación. La palabra común, la imagen del líder Marcos, y los símbolos como el pasamontañas, hacen que la rebelión zapatista sea una rebelión desde y para los sin parte, una voz para incorporar a los sin voz: el rostro indefinido de una máscara que defiende con enjundia a los olvidados y los devuelve a la arena de los vistos. Chiapas habla, los fantasmas resucitan, las partes mal contadas reclaman una justa partición de lo visible en la comunidad. Marcos y los suyo se han salido con la suya.