Interactive Epistemology and Reasoning: On the Foundations of Game Theory

Game theory describes and analyzes strategic interaction. It is usually distinguished between static games, which are strategic situations in which the players choose only once as well as simultaneously, and dynamic games, which are strategic situations involving sequential choices. In addition, dynamic games can be further classified according to perfect and imperfect information. Indeed, a dynamic game is said to exhibit perfect information, whenever at any point of the game every player has full informational access to all choices that have been conducted so far. However, in the case of imperfect information some players are not fully informed about some choices. Game-theoretic analysis proceeds in two steps. Firstly, games are modelled by so-called form structures which extract and formalize the significant parts of the underlying strategic interaction. The basic and most commonly used models of games are the normal form, which rather sparsely describes a game merely in terms of the players' strategy sets and utilities, and the extensive form, which models a game in a more detailed way as a tree. In fact, it is standard to formalize static games with the normal form and dynamic games with the extensive form. Secondly, solution concepts are developed to solve models of games in the sense of identifying the choices that should be taken by rational players. Indeed, the ultimate objective of the classical approach to game theory, which is of normative character, is the development of a solution concept that is capable of identifying a unique choice for every player in an arbitrary game. However, given the large variety of games, it is not at all certain whether it is possible to device a solution concept with such universal capability. Alternatively, interactive epistemology provides an epistemic approach to game theory of descriptive character. This rather recent discipline analyzes the relation between knowledge, belief and choice of game-playing agents in an epistemic framework. The description of the players' choices in a given game relative to various epistemic assumptions constitutes the fundamental problem addressed by an epistemic approach to game theory. In a general sense, the objective of interactive epistemology consists in characterizing existing game-theoretic solution concepts in terms of epistemic assumptions as well as in proposing novel solution concepts by studying the game-theoretic implications of refined or new epistemic hypotheses. Intuitively, an epistemic model of a game can be interpreted as representing the reasoning of the players. Indeed, before making a decision in a game, the players reason about the game and their respective opponents, given their knowledge and beliefs. Precisely these epistemic mental states on which players base their decisions are explicitly expressible in an epistemic framework. In this PhD thesis, we consider an epistemic approach to game theory from a foundational point of view. In Chapter 1, basic game-theoretic notions as well as Aumann's epistemic framework for games are expounded and illustrated. Also, Aumann's sufficient conditions for backward induction are presented and his conceptual views discussed. In Chapter 2, Aumann's interactive epistemology is conceptually analyzed. In Chapter 3, which is based on joint work with Conrad Heilmann, a three-stage account for dynamic games is introduced and a type-based epistemic model is extended with a notion of agent connectedness. Then, sufficient conditions for backward induction are derived. In Chapter 4, which is based on joint work with Jérémie Cabessa, a topological approach to interactive epistemology is initiated. In particular, the epistemic-topological operator limit knowledge is defined and some implications for games considered. In Chapter 5, which is based on joint work with Jérémie Cabessa and Andrés Perea, Aumann's impossibility theorem on agreeing to disagree is revisited and weakened in the sense that possible contexts are provided in which agents can indeed agree to disagree.

Representing diffusion MRI in 5D for segmentation of white matter tracts with a level set method.

We present a method for segmenting white matter tracts from high angular resolution diffusion MR. images by representing the data in a 5 dimensional space of position and orientation. Whereas crossing fiber tracts cannot be separated in 3D position space, they clearly disentangle in 5D position-orientation space. The segmentation is done using a 5D level set method applied to hyper-surfaces evolving in 5D position-orientation space. In this paper we present a methodology for constructing the position-orientation space. We then show how to implement the standard level set method in such a non-Euclidean high dimensional space. The level set theory is basically defined for N-dimensions but there are several practical implementation details to consider, such as mean curvature. Finally, we will show results from a synthetic model and a few preliminary results on real data of a human brain acquired by high angular resolution diffusion MRI.

Shape complexity based on mutual information

Shape complexity has recently received attention from different fields, such as computer vision and psychology. In this paper, integral geometry and information theory tools are applied to quantify the shape complexity from two different perspectives: from the inside of the object, we evaluate its degree of structure or correlation between its surfaces (inner complexity), and from the outside, we compute its degree of interaction with the circumscribing sphere (outer complexity). Our shape complexity measures are based on the following two facts: uniformly distributed global lines crossing an object define a continuous information channel and the continuous mutual information of this channel is independent of the object discretisation and invariant to translations, rotations, and changes of scale. The measures introduced in this paper can be potentially used as shape descriptors for object recognition, image retrieval, object localisation, tumour analysis, and protein docking, among others

Information-theoretical derivation of an extended thermodynamical description of radiative systems

A radiative equation of the Cattaneo–Vernotte type is derived from information theory and the radiative transfer equation. The equation thus derived is a radiative analog of the equation that is used for the description of hyperbolic heat conduction. It is shown, without recourse to any phenomenological assumption, that radiative transfer may be included in a natural way in the framework of extendedirreversible thermodynamics

Multiuser detection in a dynamic environment — Part II: Joint user identification and parameter estimation

The problem of jointly estimating the number, the identities, and the data of active users in a time-varying multiuser environment was examined in a companion paper (IEEE Trans. Information Theory, vol. 53, no. 9, September 2007), at whose core was the use of the theory of finite random sets on countable spaces. Here we extend that theory to encompass the more general problem of estimating unknown continuous parameters of the active-user signals. This problem is solved here by applying the theory of random finite sets constructed on hybrid spaces. We doso deriving Bayesian recursions that describe the evolution withtime of a posteriori densities of the unknown parameters and data.Unlike in the above cited paper, wherein one could evaluate theexact multiuser set posterior density, here the continuous-parameter Bayesian recursions do not admit closed-form expressions. To circumvent this difficulty, we develop numerical approximationsfor the receivers that are based on Sequential Monte Carlo (SMC)methods (“particle filtering”). Simulation results, referring to acode-divisin multiple-access (CDMA) system, are presented toillustrate the theory.

What is the value of joint processing of pilots and data in block-fading channels?

The spectral efficiency achievable with joint processing of pilot and data symbol observations is compared with that achievable through the conventional (separate) approach of first estimating the channel on the basis of the pilot symbols alone, and subsequently detecting the datasymbols. Studied on the basis of a mutual information lower bound, joint processing is found to provide a non-negligible advantage relative to separate processing, particularly for fast fading. It is shown that, regardless of the fading rate, only a very small number of pilot symbols (at most one per transmit antenna and per channel coherence interval) shouldbe transmitted if joint processing is allowed.

The impact of information on decision-making in palliative care

Résumé Ce travail vise à clarifier les résultats contradictoires de la littérature concernant les besoins des patients d'être informés et de participer à la prise de décision. La littérature insiste sur le contenu de l'information comme base de la prise de décision, bien qu'il existe des preuves que d'autres contenus sont importants pour les patients. La thèse essaie en outre d'identifier des possibilités de mieux répondre aux préférences d'information et de participation des patients. Les travaux ont porté en particulier sur les soins palliatifs. Une analyse de la littérature donne un aperçu sur les soins palliatifs, sur l'information des patients et sur leur participation à la prise de décisions thérapeutiques. Cette analyse résume les résultats d'études précédentes et propose un: modèle théorique d'information, de prise de décision et de relation entre ces deux domaines. Dans le cadre de ce travail, deux études empiriques ont utilisé des questionnaires écrits adressés à des personnes privées et à des professionnels de la santé, couvrant la Suisse et le Royaume Uni, pour identifier d'éventuelles différences entre ces deux pays. Les enquêtes ont été focalisées sur des patients souffrant de cancer du poumon. Les instruments utilisés pour ces études proviennent de la littérature afin de les rendre comparables. Le taux de réponse aux questionnaires était de 30-40%. La majorité des participants aux enquêtes estime que les patients devraient: - collaborer à la prise de décision quant à leur traitement - recevoir autant d'information que possible, positive aussi bien que négative - recevoir toutes les informations mentionnées dans le questionnaire (concernant la maladie, le diagnostic et les traitements), tenant compte de la diversité des priorités des patients - être soutenus par des professionnels de la santé, leur famille, leurs amis et/ou les personnes souffrant de la même maladie En plus, les participants aux enquêtes ont identifié divers contenus de l'information aux patients souffrant d'une maladie grave. Ces contenus comprennent entre autres: - L'aide à la prise de décision concernant le traitement - la possibilité de maintenir le contrôle de la situation - la construction d'une relation entre le patient et le soignant - l'encouragement à faire des projets d'avenir - l'influence de l'état émotionnel - l'aide à la compréhension de la maladie et de son impact - les sources potentielles d'états confusionnels et d'états anxieux La plupart des contenus proposés sont positifs. Les résultats suggèrent la coexistence possible de différents contenus à un moment donné ainsi que leur changement au cours du temps. Un modèle est ensuite développé et commenté pour présenter le diagnostic d'une maladie grave. Ce modèle est basé sur la littérature et intègre les résultats des études empiriques réalisées dans le cadre de ce travail. Ce travail analyse également les sources préférées d'information et de soutien, facteurs qui peuvent influencer ou faire obstacle aux préférences d'information et de participation. Les deux groupes de participants considèrent les médecins spécialistes comme la meilleure source d'information. En ce qui concerne le soutien, les points de vue divergent entre les personnes privées et les professionnels de la santé: généralement, les rôles de soutien semblent peu définis parmi les professionnels. Les barrières à l'information adéquate du patient apparaissent fréquemment liées aux caractéristiques des professionnels et aux problèmes d'organisation. Des progrès dans ce domaine contribueraient à améliorer les soins fournis aux patients. Finalement, les limites des études empiriques sont discutées. Celles-ci comprennent, entre autres, la représentativité restreinte des participants et les objections de certains groupes de participants à quelques détails des questionnaires. Summary The present thesis follows a call from the current body of literature to better understand patient needs for information and for participation in decision-making, as previous research findings had been contradictory. Information so far seems to have been considered essentially as a means to making treatment decisions, despite certain evidence that it may have a number of other values to patients. Furthermore, the thesis aims to identify ways to optimise meeting patient preferences for information and participation in treatment decisions. The current field of interest is palliative care. An extensive literature review depicts the background of current concepts of palliative care, patient information and patient involvement into treatment decisions. It also draws together results from previous studies and develops a theoretical model of information, decision-making, and the relationship between them. This is followed by two empirical studies collecting data from members of the general public and health care professionals by means of postal questionnaires. The professional study covers both Switzerland and the United Kingdom in order to identify possible differences between countries. Both studies focus on newly diagnosed lung cancer patients. The instruments used were taken from the literature to make them comparable. The response rate in both surveys was 30-40%, as expected -sufficient to allow stastical tests to be performed. A third study, addressed to lung cancer patients themselves, turned out to require too much time within the frame available. A majority of both study populations thought that patients should: - have a collaborative role in treatment-related decision-making -receive as much information as possible, good or bad - receive all types of information mentioned in the questionnaire (about illness, tests, and treatment), although priorities varied across the study populations - be supported by health professionals, family members, friends and/or others with the same illness Furthermore they identified various 'meanings' information may have to patients with a serious illness. These included: - being an aid in treatment-related decision-making - allowing control to be maintained over the situation - helping the patient-professional relationship to be constructed - allowing plans to be made - being positive for the patient's emotional state - helping the illness and its impact to be understood - being a source of anxiety - being a potential source of confusion to the patient Meanings were mostly positive. It was suggested that different meanings could co-exist at a given time and that they might change over time. A model of coping with the disclosure of a serious diagnosis is then developped. This model is based on existing models of coping with threatening events, as takeñ from the literature [ref. 77, 78], and integrates findings from the empirical studies. The thesis then analyses the remaining aspects apparent from the two surveys. These range from the identification of preferred information and support providers to factors influencing or impeding information and participation preferences. Specialist doctors were identified by both study populations as the best information providers whilst with regard to support provision views differed between the general public and health professionals. A need for better definition of supportive roles among health care workers seemed apparent. Barriers to information provision often seem related to health professional characteristics or organisational difficulties, and improvements in the latter field could well help optimising patient care. Finally, limitations of the studies are discussed, including questions of representativness of certain results and difficulties with or objections against questionnaire details by some groups of respondents.

Noise and aggregation of information in large markets

We study a novel class of noisy rational expectations equilibria in markets with largenumber of agents. We show that, as long as noise increases with the number of agents inthe economy, the limiting competitive equilibrium is well-defined and leads to non-trivialinformation acquisition, perfect information aggregation, and partially revealing prices,even if per capita noise tends to zero. We find that in such equilibrium risk sharing and price revelation play dierent roles than in the standard limiting economy in which per capita noise is not negligible. We apply our model to study information sales by a monopolist, information acquisition in multi-asset markets, and derivatives trading. Thelimiting equilibria are shown to be perfectly competitive, even when a strategic solutionconcept is used.

Quantum nonlocality in two three-level systems

Recently a new Bell inequality has been introduced by Collins et al. [Phys. Rev. Lett. 88, 040404 (2002)], which is strongly resistant to noise for maximally entangled states of two d-dimensional quantum systems. We prove that a larger violation, or equivalently a stronger resistance to noise, is found for a nonmaximally entangled state. It is shown that the resistance to noise is not a good measure of nonlocality and we introduce some other possible measures. The nonmaximally entangled state turns out to be more robust also for these alternative measures. From these results it follows that two von Neumann measurements per party may be not optimal for detecting nonlocality. For d=3,4, we point out some connections between this inequality and distillability. Indeed, we demonstrate that any state violating it, with the optimal von Neumann settings, is distillable.

Majorization arrow in quantum-algorithm design

We apply majorization theory to study the quantum algorithms known so far and find that there is a majorization principle underlying the way they operate. Grover's algorithm is a neat instance of this principle where majorization works step by step until the optimal target state is found. Extensions of this situation are also found in algorithms based in quantum adiabatic evolution and the family of quantum phase-estimation algorithms, including Shor's algorithm. We state that in quantum algorithms the time arrow is a majorization arrow.

Optimal strategies for sending information through a quantum channel

Quantum states can be used to encode the information contained in a direction, i.e., in a unit vector. We present the best encoding procedure when the quantum state is made up of N spins (qubits). We find that the quality of this optimal procedure, which we quantify in terms of the fidelity, depends solely on the dimension of the encoding space. We also investigate the use of spatial rotations on a quantum state, which provide a natural and less demanding encoding. In this case we prove that the fidelity is directly related to the largest zeros of the Legendre and Jacobi polynomials. We also discuss our results in terms of the information gain.

Light intensity modulates the regulatory network of the shade avoidance response in Arabidopsis.

Plants such as Arabidopsis thaliana respond to foliar shade and neighbors who may become competitors for light resources by elongation growth to secure access to unfiltered sunlight. Challenges faced during this shade avoidance response (SAR) are different under a light-absorbing canopy and during neighbor detection where light remains abundant. In both situations, elongation growth depends on auxin and transcription factors of the phytochrome interacting factor (PIF) class. Using a computational modeling approach to study the SAR regulatory network, we identify and experimentally validate a previously unidentified role for long hypocotyl in far red 1, a negative regulator of the PIFs. Moreover, we find that during neighbor detection, growth is promoted primarily by the production of auxin. In contrast, in true shade, the system operates with less auxin but with an increased sensitivity to the hormonal signal. Our data suggest that this latter signal is less robust, which may reflect a cost-to-robustness tradeoff, a system trait long recognized by engineers and forming the basis of information theory.

Gene Ontology Function prediction in Mollicutes using Protein-Protein Association Networks

Abstract Background: Many complex systems can be represented and analysed as networks. The recent availability of large-scale datasets, has made it possible to elucidate some of the organisational principles and rules that govern their function, robustness and evolution. However, one of the main limitations in using protein-protein interactions for function prediction is the availability of interaction data, especially for Mollicutes. If we could harness predicted interactions, such as those from a Protein-Protein Association Networks (PPAN), combining several protein-protein network function-inference methods with semantic similarity calculations, the use of protein-protein interactions for functional inference in this species would become more potentially useful. Results: In this work we show that using PPAN data combined with other approximations, such as functional module detection, orthology exploitation methods and Gene Ontology (GO)-based information measures helps to predict protein function in Mycoplasma genitalium. Conclusions: To our knowledge, the proposed method is the first that combines functional module detection among species, exploiting an orthology procedure and using information theory-based GO semantic similarity in PPAN of the Mycoplasma species. The results of an evaluation show a higher recall than previously reported methods that focused on only one organism network.

Dissociation between components of spatial memory in rats after recovery from the effects of retrohippocampal lesions

A series of 4 experiments examined the performance of rats with retrohippocampal lesions on a spatial water-maze task. The animals were trained to find and escape onto a hidden platform after swimming in a large pool of opaque water. The platform was invisible and could not be located using olfactory cues. Successful escape performance required the rats to develop strategies of approaching the correct location with reference solely to distal extramaze cues. The lesions encompassed the entire rostro-caudal extent of the lateral and medial entorhinal cortex, and included parts of the pre- and para-subiculum, angular bundle and subiculum. Groups ECR 1 and 2 sustained only partial damage of the subiculum, while Group ECR+S sustained extensive damage. These groups were compared with sham-lesion and unoperated control groups. In Expt 1A, a profound deficit in spatial localisation was found in groups ECR 1 and ECR+S, the rats receiving all training postoperatively. In Expt 1B, these two groups showed hyperactivity in an open-field. In Expt 2, extensive preoperative training caused a transitory saving in performance of the spatial task by group ECR 2, but comparisons with the groups of Expt 1A revealed no sustained improvement, except on one measure of performance in a post-training transfer test. All rats were then given (Expt 3) training on a cueing procedure using a visible platform. The spatial deficit disappeared but, on returning to the normal hidden platform procedure, it reappeared. Nevertheless, a final transfer test, during which the platform was removed from the apparatus, revealed a dissociation between two independent measures of performance: the rats with ECR lesions failed to search for the hidden platform but repeatedly crossed its correct location accurately during traverses of the entire pool. This partial recovery of performance was not (Expt 4) associated with any ability to discriminate between two locations in the pool. The apparently selective recovery of aspects of spatial memory is discussed in relation to O'Keefe and Nadel's (1978) spatial mapping theory of hippocampal function. We propose a modification of the theory in terms of a dissociation between procedural and declarative subcomponents of spatial memory. The declarative component is a flexible access system in which information is stored in a form independent of action. It is permanently lost after the lesion. The procedural component is "unmasked" by the retrohippocampal lesion giving rise to the partial recovery of spatial localisation performance.

Statistical reference criteria for adaptive signal processing in digital communications

A general criterion for the design of adaptive systemsin digital communications called the statistical reference criterionis proposed. The criterion is based on imposition of the probabilitydensity function of the signal of interest at the outputof the adaptive system, with its application to the scenario ofhighly powerful interferers being the main focus of this paper.The knowledge of the pdf of the wanted signal is used as adiscriminator between signals so that interferers with differingdistributions are rejected by the algorithm. Its performance isstudied over a range of scenarios. Equations for gradient-basedcoefficient updates are derived, and the relationship with otherexisting algorithms like the minimum variance and the Wienercriterion are examined.