Marriages of Mathematics and Physics: A Challenge for Biology

The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the mathematical practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematical analysis of the 19th century, led to the exclusion of “geometric judgments” from the foundations of Mathematics. After the success and the limits of the logico-formal analysis, it is necessary to broaden our foundational tools and re-examine the interactions with natural sciences. In particular, the way the geometric and algebraic approaches organize knowledge is analyzed as a cross-disciplinary and cross-cultural issue and will be examined in Mathematical Physics and Biology. We finally discuss how the current notions of mathematical (phase) “space” should be revisited for the purposes of life sciences

Hybrid Controllers for Path Planning: A Temporal Logic Approach

Robot motion planning algorithms have focused on low-level reachability goals taking into account robot kinematics, or on high level task planning while ignoring low-level dynamics. In this paper, we present an integrated approach to the design of closed–loop hybrid controllers that guarantee by construction that the resulting continuous robot trajectories satisfy sophisticated specifications expressed in the so–called Linear Temporal Logic. In addition, our framework ensures that the temporal logic specification is satisfied even in the presence of an adversary that may instantaneously reposition the robot within the environment a finite number of times. This is achieved by obtaining a Büchi automaton realization of the temporal logic specification, which supervises a finite family of continuous feedback controllers, ensuring consistency between the discrete plan and the continuous execution

Scientific Progress on the Semantic View : An Account of Scientific Progress as Objective Logical and Empirical Strength Increments

The aim of this master thesis is to make a convincing argument that scientific progress can be spoken of in objective terms. In order to make this argument I will propose a philosophical theory of scientific progress. Two concepts will be constructed with this aim in mind, both which are types of strength measures on scientific theories. The first concept, that of logical strength, pertains to the way a theory may exclude, or permit less, model classes compared to another theory. The second concept, that of empirical strength, pertains to an objective measure of the informational content of data models, defined in terms of Kolmogorov complexity. This latter idea stems from communication and computational theory. Scientific progress is then defined as the interaction, or the stepwise increases, of these two strength measures. Central for the conception of a scientific theory is the philosophical framework known as The Semantic View of Scientific Theories. This view can briefly be characterized as an empirical extension of Tarskian model-theory. Another central notion for this theory of scientific progress is the philosophical or metaphysical thesis called structural realism. Both will accordingly be explained and argued for. Finally, as a test on this proposed theory of scientific progress, it will be applied to two examples of theory transition from the history of physical theory. I conclude that the proposed theory handles these two cases well

Logic programming for deliberative robotic task planning

Over the last decade, the use of robots in production and daily life has increased. With increasingly complex tasks and interaction in different environments including humans, robots are required a higher level of autonomy for efficient deliberation. Task planning is a key element of deliberation. It combines elementary operations into a structured plan to satisfy a prescribed goal, given specifications on the robot and the environment. In this manuscript, we present a survey on recent advances in the application of logic programming to the problem of task planning. Logic programming offers several advantages compared to other approaches, including greater expressivity and interpretability which may aid in the development of safe and reliable robots. We analyze different planners and their suitability for specific robotic applications, based on expressivity in domain representation, computational efficiency and software implementation. In this way, we support the robotic designer in choosing the best tool for his application

Causality Analysis and Fault Ascription in Component-Based Systems

This article introduces a general framework for fault ascription, which consists in identifying, within a multi-component system, the components whose faulty behavior has caused the failure of said system. Our framework uses configuration structures as a general semantical model to handle truly concurrent executions, partial and distributed observations in a uniform way. We define a set of expected properties for counterfactual analysis, and present a refined analysis that conforms to our requirements. This contrasts with current practice of evaluating definitions of counterfactual causality a posteriori on a set of toy examples. As an early study of the behavior of our analysis under abstraction we establish its monotony under refinement.Cet article introduit un cadre général pour l’attribution de fautes qui consiste à identifier, dans un système à composants, les composants dont le comportement incorrect a causé le dysfonctionnement du système. Nous définissons un ensemble de propriétés attendues de l’analyse contrefactuelle, et nous présentons une analyse raffinée qui satisfait ces besoins. Ceci contraste avec la pratique courante d’évaluer les définitions de causalité contrefactuelle a posteriori sur un ensemble d’exemples jouets. Nous établissons la monotonie de notre analyse sous différentes notions de raffinement

Examining K-12 Teachers\u27 Affective Job Satisfaction and Perceptions of Blended Instruction

The increasing use of blended models of instruction within the U.S. public school system is transforming the K-12 education. However, few studies have been conducted of the innovation-adoption process involving blended instruction within the K-12 public school sector. In this nonexperimental, quantitative study, Rogers\u27s five perceived attributes of innovations was used as a theoretical lens to explore how teachers\u27 affective job satisfaction might affect the innovation-adoption process at the individual level. Research questions pertained to the relationship, if any, between affective job satisfaction among teachers and their perceptions of the complexity, compatibility, and relative advantage of blended instruction. Surveys were administered to middle school teachers (n = 40) in the core curriculum within southeastern U.S. schools. Data were analyzed for relationships using Spearman\u27s correlation; relationships found to have statistical significance were further explored using ordinal logistic regression. Affective job satisfaction had a moderately positive and statistically significant relationship with how participants perceived the compatibility and relative advantage of blended instruction (rs = .487). However, the relationship was inconsistent among subgroups, varying from rs = .181 (n = 13) to rs = .693 (n = 10). Findings could be used to promote positive social change by providing insight into the role of affective job satisfaction within the innovation-adoption process within the K-12 sector

Modular Verification and Supervisory Controller Design for Discrete-Event Systems Using Abstraction and Incremental Construction.

The subject of this dissertation is modular approaches to the verification and control of discrete-event systems (DES). DES are dynamic systems characterized by discrete states and event-driven evolution. In recent years, a substantial body of work has been built up to provide a theory and framework for the control and verification of DES. Despite all the advancements that have been made in this area, application to real-life systems has been somewhat slow. A significant hurdle to the adoption of these methods is the state-space explosion that occurs in modeling systems of the size most commonly found in industry. A common approach that has been applied to address this complexity problem is to construct a series of smaller modular supervisors, rather than a single monolithic supervisor. The problem with this approach is that the modular supervisors can often conflict with one another. This dissertation develops three new approaches to the supervisory control of DES that adopt a modular aspect to their control, while addressing the potential problem of conflict. The first approach addresses the problem of state-space explosion by offering a procedure for incrementally building modular supervisors that are guaranteed to not conflict with one another by construction. An observer type abstraction is employed to make the procedure more computationally feasible. The second approach of this dissertation constructs traditional modular supervisors, then adds another level of coordinating control to resolve conflict between the supervisors. This work employs a conflict-equivalence preserving abstraction to detect and resolve the conflict. The final approach of this dissertation employs interfaces between different components of the global system. The additional structure of these interfaces allows global properties to be verified through the achievement of local properties. Additionally, these interfaces allow for modular supervisors to be synthesized locally such that the necessary requirements are met by construction. In this work, the correctness of the three approaches is proven. Additionally, application to some manufacturing based examples are employed to illustrate the potential strengths and weaknesses of each of the approaches.Ph.D.Mechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/60669/1/rchill_1.pd