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.

A collaborative approach for incorporating forensic case data into crime investigation using criminal intelligence analysis and visualisation

There is an increasing awareness that the articulation of forensic science and criminal investigation is critical to the resolution of crimes. However, models and methods to support an effective collaboration between these partners are still poorly expressed or even lacking. Three propositions are borrowed from crime intelligence methods in order to bridge this gap: (a) the general intelligence process, (b) the analyses of investigative problems along principal perspectives: entities and their relationships, time and space, quantitative aspects and (c) visualisation methods as a mode of expression of a problem in these dimensions. Indeed, in a collaborative framework, different kinds of visualisations integrating forensic case data can play a central role for supporting decisions. Among them, link-charts are scrutinised for their abilities to structure and ease the analysis of a case by describing how relevant entities are connected. However, designing an informative chart that does not bias the reasoning process is not straightforward. Using visualisation as a catalyser for a collaborative approach integrating forensic data thus calls for better specifications.

Analysis of a finite volume element method for the Stokes problem

In this paper we propose a stabilized conforming finite volume element method for the Stokes equations. On stating the convergence of the method, optimal a priori error estimates in different norms are obtained by establishing the adequate connection between the finite volume and stabilized finite element formulations. A superconvergence result is also derived by using a postprocessing projection method. In particular, the stabilization of the continuous lowest equal order pair finite volume element discretization is achieved by enriching the velocity space with local functions that do not necessarily vanish on the element boundaries. Finally, some numerical experiments that confirm the predicted behavior of the method are provided.

Circulating microRNAs as long-term biomarkers for the detection of erythropoiesis-stimulating agent abuse.

MicroRNAs (miRNAs) are small, non-protein coding transcripts involved in many cellular and physiological mechanisms. Recently, a new class of miRNA called 'circulating miRNAs' was found in cell-free body fluids such as plasma and urine. Circulating miRNAs have been shown to be very stable, specific, and sensitive biomarkers. In this paper, we investigate whether circulating miRNAs can serve as biomarkers for erythropoiesis-stimulating agent abuse. To this end, we analyzed miRNA levels in plasma by miRNA microarrays and quantitative real-time polymerase chain reaction (PCR). Plasma samples are derived from a clinical study with healthy subjects injected with erythropoiesis-stimulating agent (C.E.R.A.). Based on microarray results, we observed a significant difference in the levels of miRNAs in plasma after C.E.R.A. injection. We demonstrated that a specific miRNA, miR-144, exhibit a high increase that lasts 27 days after C.E.R.A. stimulation. Considering the fact that miR-144 is an essential erythropoiesis agent in different organisms, these findings suggest the possibility of using miR-144 as a sensitive and informative biomarker to detect C.E.R.A. abuse. Copyright © 2011 John Wiley & Sons, Ltd.

Artificial Snow Optimization in Winter Sport Destinations Using a Multi-agent Simulation

This paper presents the Juste-Neige system for predicting the snow height on the ski runs of a resort using a multi-agent simulation software. Its aim is to facilitate snow cover management in order to i) reduce the production cost of artificial snow and to improve the profit margin for the companies managing the ski resorts; and ii) to reduce the water and energy consumption, and thus to reduce the environmental impact, by producing only the snow needed for a good skiing experience. The software provides maps with the predicted snow heights for up to 13 days. On these maps, the areas most exposed to snow erosion are highlighted. The software proceeds in three steps: i) interpolation of snow height measurements with a neural network; ii) local meteorological forecasts for every ski resort; iii) simulation of the impact caused by skiers using a multi-agent system. The software has been evaluated in the Swiss ski resort of Verbier and provides useful predictions.

A phase I study of the oral platinum agent satraplatin in sequential combination with capecitabine in the treatment of patients with advanced solid malignancies.

Abstract Background. The broad spectrum of antitumor activity of both the oral platinum analogue satraplatin (S) and capecitabine (C), along with the advantage of their oral administration, prompted a clinical study aimed to define the maximum tolerated dose (MTD) of the combination. Patients and methods. Four dose levels of S (mg/m(2)/day) and C (mg/m(2)/day) were evaluated in adult patients with advanced solid tumors: 60/1650, 80/1650, 60/2000, 70/2000; a course consisted of 28 days with sequential administration of S (days 1-5) and C (days 8-21) followed by one week rest. Results. Thirty-seven patients were treated, 24 in the dose escalation and 13 in the expansion phase; at the MTD, defined at S 70/C 2000, two patients presented dose limiting toxicities: lack of recovery of neutropenia by day 42 and nausea with dose skip of C. Most frequent toxicities were nausea (57%), diarrhea (51%), neutropenia (46%), anorexia, fatigue, vomiting (38% each). Two partial responses were observed in platinum sensitive ovarian cancer and one in prostate cancer. Conclusion. At S 70/C 2000 the combination of sequential S and C is tolerated with manageable toxicities; its evaluation in platinum and fluorouracil sensitive tumor types is worthwhile because of the easier administration and lack of nephro- and neurotoxicity as compared to parent compounds.

Whole-heart coronary vein imaging: a comparison between non-contrast-agent- and contrast-agent-enhanced visualization of the coronary venous system.

The feasibility of three-dimensional (3D) whole-heart imaging of the coronary venous (CV) system was investigated. The hypothesis that coronary magnetic resonance venography (CMRV) can be improved by using an intravascular contrast agent (CA) was tested. A simplified model of the contrast in T(2)-prepared steady-state free precession (SSFP) imaging was applied to calculate optimal T(2)-preparation durations for the various deoxygenation levels expected in venous blood. Non-contrast-agent (nCA)- and CA-enhanced images were compared for the delineation of the coronary sinus (CS) and its main tributaries. A quantitative analysis of the resulting contrast-to-noise ratio (CNR) and signal-to-noise ratio (SNR) in both approaches was performed. Precontrast visualization of the CV system was limited by the poor CNR between large portions of the venous blood and the surrounding tissue. Postcontrast, a significant increase in CNR between the venous blood and the myocardium (Myo) resulted in a clear delineation of the target vessels. The CNR improvement was 347% (P < 0.05) for the CS, 260% (P < 0.01) for the mid cardiac vein (MCV), and 430% (P < 0.05) for the great cardiac vein (GCV). The improvement in SNR was on average 155%, but was not statistically significant for the CS and the MCV. The signal of the Myo could be significantly reduced to about 25% (P < 0.001).

Phenotypic features of carbohydrate sulfotransferase 3 (CHST3) deficiency in 24 patients: congenital dislocations and vertebral changes as principal diagnostic features.

We recently reported on the deficiency of carbohydrate sulfotransferase 3 (CHST3; chondroitin-6-sulfotransferase) in six subjects diagnosed with recessive Larsen syndrome or humero-spinal dysostosis [Hermanns et al. (2008); Am J Hum Genet 82:1368-1374]. Since then, we have identified 17 additional families with CHST3 mutations and we report here on a series of 24 patients in 23 families. The diagnostic hypothesis prior to molecular analysis had been: Larsen syndrome (15 families), humero-spinal dysostosis (four cases), chondrodysplasia with multiple dislocations (CDMD "Megarbane type"; two cases), Desbuquois syndrome (one case), and spondylo-epiphyseal dysplasia (one case). In spite of the different diagnostic labels, the clinical features in these patients were similar and included dislocation of the knees and/or hips at birth, clubfoot, elbow joint dysplasia with subluxation and limited extension, short stature, and progressive kyphosis developing in late childhood. The most useful radiographic clues were the changes of the lumbar vertebrae. Twenty-four different CHST3 mutations were identified; 16 patients had homozygous mutations. We conclude that CHST3 deficiency presents at birth with congenital dislocations of knees, hips, and elbows, and is often diagnosed initially as Larsen syndrome, humero-spinal dysostosis, or chondrodysplasia with dislocations. The incidence of CHST3 deficiency seems to be higher than assumed so far. The clinical and radiographic pattern (joint dislocations, vertebral changes, normal carpal age, lack of facial flattening, and recessive inheritance) is characteristic and distinguishes CHST3 deficiency from other disorders with congenital dislocations such as filamin B-associated dominant Larsen syndrome and Desbuquois syndrome.

Detection of coronary stenoses with contrast enhanced, three-dimensional free breathing coronary MR angiography using the gadolinium-based intravascular contrast agent gadocoletic acid (B-22956).

PURPOSE: To determine the diagnostic value of the intravascular contrast agent gadocoletic acid (B-22956) in three-dimensional, free breathing coronary magnetic resonance angiography (MRA) for stenosis detection in patients with suspected or known coronary artery disease. METHODS: Eighteen patients underwent three-dimensional, free breathing coronary MRA of the left and right coronary system before and after intravenous application of a single dose of gadocoletic acid (B-22956) using three different dose regimens (group A 0.050 mmol/kg; group B 0.075 mmol/kg; group C 0.100 mmol/kg). Precontrast scanning followed a coronary MRA standard non-contrast T2 preparation/turbo-gradient echo sequence (T2Prep); for postcontrast scanning an inversion-recovery gradient echo sequence was used (real-time navigator correction for both scans). In pre- and postcontrast scans quantitative analysis of coronary MRA data was performed to determine the number of visible side branches, vessel length and vessel sharpness of each of the three coronary arteries (LAD, LCX, RCA). The number of assessable coronary artery segments was determined to calculate sensitivity and specificity for detection of stenosis > or = 50% on a segment-to-segment basis (16-segment-model) in pre- and postcontrast scans with x-ray coronary angiography as the standard of reference. RESULTS: Dose group B (0.075 mmol/kg) was preferable with regard to improvement of MR angiographic parameters: in postcontrast scans all MR angiographic parameters increased significantly except for the number of visible side branches of the left circumflex artery. In addition, assessability of coronary artery segments significantly improved postcontrast in this dose group (67 versus 88%, p < 0.01). Diagnostic performance (sensitivity, specificity, accuracy) was 83, 77 and 78% for precontrast and 86, 95 and 94% for postcontrast scans. CONCLUSIONS: The use of gadocoletic acid (B-22956) results in an improvement of MR angiographic parameters, asssessability of coronary segments and detection of coronary stenoses > or = 50%.