Euclidean geometric invariant of framed knots in manifolds

We present an invariant of a three dimensional manifold with a framed knot in it based on the Reidemeister torsion of an acyclic complex of Euclidean geometric origin. To show its nontriviality, we calculate the invariant for some framed (un)knots in lens spaces. An important feature of our work is that we are not using any nontrivial representation of the manifold fundamental group or knot group.

A computational and geometric approach to phase resetting curves and surfaces

"Vegeu el resum a l'inici del document del fitxer adjunt."

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.

How to improve the formal analytic reasoning and scientific motivation in the intellectual training of medical students

A review article of the The New England Journal of Medicine refers that almost a century ago, Abraham Flexner, a research scholar at the Carnegie Foundation for the Advancement of Teaching, undertook an assessment of medical education in 155 medical schools in operation in the United States and Canada. Flexner’s report emphasized the nonscientific approach of American medical schools to preparation for the profession, which contrasted with the university-based system of medical education in Germany. At the core of Flexner’s view was the notion that formal analytic reasoning, the kind of thinking integral to the natural sciences, should hold pride of place in the intellectual training of physicians. This idea was pioneered at Harvard University, the University of Michigan, and the University of Pennsylvania in the 1880s, but was most fully expressed in the educational program at Johns Hopkins University, which Flexner regarded as the ideal for medical education. (...)

A geometric mechanism of diffusion: Rigorous verification in a priori unstable Hamiltonian systems

In this paper we consider a representative a priori unstable Hamiltonian system with 2+1/2 degrees of freedom, to which we apply the geometric mechanism for diffusion introduced in the paper Delshams et al., Mem.Amer.Math. Soc. 2006, and generalized in Delshams and Huguet, Nonlinearity 2009, and provide explicit, concrete and easily verifiable conditions for the existence of diffusing orbits. The simplification of the hypotheses allows us to perform explicitly the computations along the proof, which contribute to present in an easily understandable way the geometric mechanism of diffusion. In particular, we fully describe the construction of the scattering map and the combination of two types of dynamics on a normally hyperbolic invariant manifold.

Geometric morphometric differences between Panstrongylus geniculatus from field and laboratory

The finding of Panstrongylus geniculatus nymphs inside a house in northeastern Antioquia, Colombia, and the reports related to their increasing presence in homes suggest the need for surveillance methods for monitoring the invasion processes. We analyzed the morphological differences between a wild population and its laboratory descendants, using the techniques of geometric morphometry, with the idea that such differences might parallel those between sylvatic and synanthropic populations. The analyses over five generations showed differences in size but not in shape. Head size and wing size were both reduced from sylvatic to laboratory populations, but the decrease in head size occurred only up to the second generation while the decrease in wing size proceeded up to the fifth generation. In contrast, although a decrease in sexual size dimorphism has been proposed as a marker of colonization in human dwellings, we did not detect any significant loss of dimorphism between sexes of P. geniculatus over the five generations studied. We conclude that size changes may have a physiological origin in response to a change of ecotopes, but more than five generations may be required for the expression of permanent morphological markers of human dwellings colonization.

Response to comment on "the geometric structure of the brain fiber pathways".

In response to Catani et al., we show that corticospinal pathways adhere via sharp turns to two local grid orientations; that our studies have three times the diffusion resolution of those compared; and that the noted technical concerns, including crossing angles, do not challenge the evidence of mathematically specific geometric structure. Thus, the geometric thesis gives the best account of the available evidence.

Diagnosing Patients Combining Principal Components Analysis and Case Based Reasoning

This paper addresses the application of a PCA analysis on categorical data prior to diagnose a patients data set using a Case-Based Reasoning (CBR) system. The particularity is that the standard PCA techniques are designed to deal with numerical attributes, but our medical data set contains many categorical data and alternative methods as RS-PCA are required. Thus, we propose to hybridize RS-PCA (Regular Simplex PCA) and a simple CBR. Results show how the hybrid system produces similar results when diagnosing a medical data set, that the ones obtained when using the original attributes. These results are quite promising since they allow to diagnose with less computation effort and memory storage

Does Reasoning Enhance Learning?

Utilizing the well-known Ultimatum Game, this note presents the following phenomenon. If we start with simple stimulus-response agents, learning through naive reinforcement, and then grant them some introspective capabilities, we get outcomes that are not closer but farther away from the fully introspective game-theoretic approach. The cause of this is the following: there is an asymmetry in the information that agents can deduce from their experience, and this leads to a bias in their learning process.

Clinical reasoning in undergraduate nursing education: a scoping review

Abstract OBJECTIVE This study aimed at analyzing the current state of knowledge on clinical reasoning in undergraduate nursing education. METHODS A systematic scoping review through a search strategy applied to the MEDLINE database, and an analysis of the material recovered by extracting data done by two independent reviewers. The extracted data were analyzed and synthesized in a narrative manner. RESULTS From the 1380 citations retrieved in the search, 23 were kept for review and their contents were summarized into five categories: 1) the experience of developing critical thinking/clinical reasoning/decision-making process; 2) teaching strategies related to the development of critical thinking/clinical reasoning/decision-making process; 3) measurement of variables related to the critical thinking/clinical reasoning/decision-making process; 4) relationship of variables involved in the critical thinking/clinical reasoning/decision-making process; and 5) theoretical development models of critical thinking/clinical reasoning/decision-making process for students. CONCLUSION The biggest challenge for developing knowledge on teaching clinical reasoning seems to be finding consistency between theoretical perspectives on the development of clinical reasoning and methodologies, methods, and procedures in research initiatives in this field.