Communication in networks with hierarchical branching

We present a simple model of communication in networks with hierarchical branching. We analyze the behavior of the model from the viewpoint of critical systems under different situations. For certain values of the parameters, a continuous phase transition between a sparse and a congested regime is observed and accurately described by an order parameter and the power spectra. At the critical point the behavior of the model is totally independent of the number of hierarchical levels. Also scaling properties are observed when the size of the system varies. The presence of noise in the communication is shown to break the transition. The analytical results are a useful guide to forecasting the main features of real networks.

Identifying financial crises in real time

Following the thermodynamic formulation of a multifractal measure that was shown to enable the detection of large fluctuations at an early stage, here we propose a new index which permits us to distinguish events like financial crises in real time. We calculate the partition function from which we can obtain thermodynamic quantities analogous to the free energy and specific heat. The index is defined as the normalized energy variation and it can be used to study the behavior of stochastic time series, such as financial market daily data. Famous financial market crashes-Black Thursday (1929), Black Monday (1987) and the subprime crisis (2008)-are identified with clear and robust results. The method is also applied to the market fluctuations of 2011. From these results it appears as if the apparent crisis of 2011 is of a different nature to the other three. We also show that the analysis has forecasting capabilities. © 2012 Elsevier B.V. All rights reserved.

How Plankton Swim: An Interdisciplinary Approach for Using Mathematics & Physics to Understand the Biology of the Natural World

The authors have developed and field-tested high school-level curricular materials that guide students to use biology, mathematics, and physics to understand plankton and how these tiny organisms move in a world where their intuition does not apply. The authors chose plankton as the focus of their materials primarily because the challenges faced by plankton are novel problems to most students, forcing adoption of new perspectives and making the study of plankton exciting. Additional reasons that they chose plankton to focus on include their ecological importance, their availability to most teachers and students, the ease with which they can be collected and observed, and the current focus of some scientific researchers on their movement and behavior. These curricular materials include a series of inquiry-based, hands-on exercises designed to be accessible to students with a range of backgrounds. Many of these materials could be adapted for use by middle-school, and/or college-level students. In this article, the authors describe sample lessons, summarize what worked well, and flag obstacles they encountered while integrating mathematics and physics into the biology classroom.

The “FRA wheel” as a teaching tool to elaborate on the identity aspects of physics and mathematics as disciplines in interdisciplinary contexts

This thesis project is framed in the research field of Physics Education and aims to contribute to the reflection on the importance of disciplinary identities in addressing interdisciplinarity through the lens of the Nature of Science (NOS). In particular, the study focuses on the module on the parabola and parabolic motion, which was designed within the EU project IDENTITIES. The project aims to design modules to innovate pre-service teacher education according to contemporary challenges, focusing on interdisciplinarity in curricular and STEM topics (especially between physics, mathematics and computer science). The modules are designed according to a model of disciplines and interdisciplinarity that the project IDENTITIES has been elaborating on two main theoretical frameworks: the Family Resemblance Approach (FRA), reconceptualized for the Nature of science (Erduran & Dagher, 2014), and the boundary crossing and boundary objects framework by Akkerman and Bakker (2011). The main aim of the thesis is to explore the impact of this interdisciplinary model in the specific case of the implementation of the parabola and parabolic motion module in a context of preservice teacher education. To reach this purpose, we have analyzed some data collected during the implementation in order to investigate, in particular, the role of the FRA as a learning tool to: a) elaborate on the concept of “discipline”, within the broader problem to define interdisciplinarity; b) compare the epistemic core of physics and mathematics; c) develop epistemic skills and interdisciplinary competences in student-teachers. The analysis of the data led us to recognize three different roles played by the FRA: FRA as epistemological activator, FRA as scaffolding for reasoning and navigating (inhabiting) the complexity, and FRA as lens to investigate the relationship between physics and mathematics in the historical case.

Introduction to engineering : a case study of an interdisciplinary course in Mathematics, Science and Technology

This thesis research was a qualitative case study of a single class of Interdisciplinary Studies: Introduction to Engineering taught in a secondary school. The study endeavoured to explore students' experiences in and perceptions of the course, and to investigate the viability of engineering as an interdisciplinary theme at the secondary school level. Data were collected in the form of student questionnaires, the researcher's observations and reflections, and artefacts representative of students' work. Data analysis was performed by coding textual data and classifying text segments into common themes. The themes that emerged from the data were aligned with facets of interdisciplinary study, including making connections, project-based learning, and student engagement and affective outcomes. The findings of the study showed that students were positive about their experiences in the course, and enjoyed its project-driven nature. Content from mathematics, physics, and technological design was easily integrated under the umbrella of engineering. Students felt that the opportunity to develop problem solving and teamwork skills were two of the most important aspects of the course and could be relevant not only for engineering, but for other disciplines or their day-to-day lives after secondary school. The study concluded that engineering education in secondary school can be a worthwhile experience for a variety of students and not just those intending postsecondary study in engineering. This has implications for the inclusion of engineering in the secondary school curriculum and can inform the practice of curriculum planners at the school, school board, and provincial levels. Suggested directions for further research include classroom-based action research in the areas of technological education, engineering education in secondary school, and interdisciplinary education.

A critical analysis on "Active Learning" in the light of Cultural-Historical Activity Theory (CHAT): Implications to Physics Education and to experimental activities as a particular case.

This is a research paper in which we discuss “active learning” in the light of Cultural-Historical Activity Theory (CHAT), a powerful framework to analyze human activity, including teaching and learning process and the relations between education and wider human dimensions as politics, development, emancipation etc. This framework has its origin in Vygotsky's works in the psychology, supported by a Marxist perspective, but nowadays is a interdisciplinary field encompassing History, Anthropology, Psychology, Education for example.

The lattice solid model to simulate the physics of rocks and earthquakes: Incorporation of friction

The particle-based lattice solid model developed to study the physics of rocks and the nonlinear dynamics of earthquakes is refined by incorporating intrinsic friction between particles. The model provides a means for studying the causes of seismic wave attenuation, as well as frictional heat generation, fault zone evolution, and localisation phenomena. A modified velocity-Verlat scheme that allows friction to be precisely modelled is developed. This is a difficult computational problem given that a discontinuity must be accurately simulated by the numerical approach (i.e., the transition from static to dynamical frictional behaviour). This is achieved using a half time step integration scheme. At each half time step, a nonlinear system is solved to compute the static frictional forces and states of touching particle-pairs. Improved efficiency is achieved by adaptively adjusting the time step increment, depending on the particle velocities in the system. The total energy is calculated and verified to remain constant to a high precision during simulations. Numerical experiments show that the model can be applied to the study of earthquake dynamics, the stick-slip instability, heat generation, and fault zone evolution. Such experiments may lead to a conclusive resolution of the heat flow paradox and improved understanding of earthquake precursory phenomena and dynamics. (C) 1999 Academic Press.

Problems in physics and mathematics contexts with middle and high school classes: vertical and horizontal comparison

My thesis falls within the framework of physics education and teaching of mathematics. The objective of this report was made possible by using geometrical (in mathematics) and qualitative (in physics) problems. We have prepared four (resp. three) open answer exercises for mathematics (resp. physics). The test batch has been selected across two different school phases: end of the middle school (third year, 8\textsuperscript{th} grade) and beginning of high school (second and third year, 10\textsuperscript{th} and 11\textsuperscript{th} grades respectively). High school students achieved the best results in almost every problem, but 10\textsuperscript{th} grade students got the best overall results. Moreover, a clear tendency to not even try qualitative problems resolution has emerged from the first collection of graphs, regardless of subject and grade. In order to improve students' problem-solving skills, it is worth to invest on vertical learning and spiral curricula. It would make sense to establish a stronger and clearer connection between physics and mathematical knowledge through an interdisciplinary approach.

Qualitative Analysis of the Interdisciplinary Interaction between Data Analysis Specialists and Novice Clinical Researchers

Background: The inherent complexity of statistical methods and clinical phenomena compel researchers with diverse domains of expertise to work in interdisciplinary teams, where none of them have a complete knowledge in their counterpart's field. As a result, knowledge exchange may often be characterized by miscommunication leading to misinterpretation, ultimately resulting in errors in research and even clinical practice. Though communication has a central role in interdisciplinary collaboration and since miscommunication can have a negative impact on research processes, to the best of our knowledge, no study has yet explored how data analysis specialists and clinical researchers communicate over time. Methods/Principal Findings: We conducted qualitative analysis of encounters between clinical researchers and data analysis specialists (epidemiologist, clinical epidemiologist, and data mining specialist). These encounters were recorded and systematically analyzed using a grounded theory methodology for extraction of emerging themes, followed by data triangulation and analysis of negative cases for validation. A policy analysis was then performed using a system dynamics methodology looking for potential interventions to improve this process. Four major emerging themes were found. Definitions using lay language were frequently employed as a way to bridge the language gap between the specialties. Thought experiments presented a series of ""what if'' situations that helped clarify how the method or information from the other field would behave, if exposed to alternative situations, ultimately aiding in explaining their main objective. Metaphors and analogies were used to translate concepts across fields, from the unfamiliar to the familiar. Prolepsis was used to anticipate study outcomes, thus helping specialists understand the current context based on an understanding of their final goal. Conclusion/Significance: The communication between clinical researchers and data analysis specialists presents multiple challenges that can lead to errors.

PARTITIONED ANALYSIS FOR DIMENSIONALLY-HETEROGENEOUS HYDRAULIC NETWORKS

In this work an iterative strategy is developed to tackle the problem of coupling dimensionally-heterogeneous models in the context of fluid mechanics. The procedure proposed here makes use of a reinterpretation of the original problem as a nonlinear interface problem for which classical nonlinear solvers can be applied. Strong coupling of the partitions is achieved while dealing with different codes for each partition, each code in black-box mode. The main application for which this procedure is envisaged arises when modeling hydraulic networks in which complex and simple subsystems are treated using detailed and simplified models, correspondingly. The potentialities and the performance of the strategy are assessed through several examples involving transient flows and complex network configurations.

Transition amplitude for two-time physics

We present the transition amplitude for a particle moving in a space with two times and D space dimensions having an Sp(2, R) local symmetry and an SO(D, 2) rigid symmetry. It was obtained from the BRST-BFV quantization with a unique gauge choice. We show that by constraining the initial and final points of this amplitude to lie on some hypersurface of the D + 2 space the resulting amplitude reproduces well-known systems in lower dimensions. This work provides an alternative way to derive the effects of two-time physics where all the results come from a single transition amplitude.

Reverse engineering in many-body quantum physics: Correspondence between many-body systems and effective single-particle equations

The mapping, exact or approximate, of a many-body problem onto an effective single-body problem is one of the most widely used conceptual and computational tools of physics. Here, we propose and investigate the inverse map of effective approximate single-particle equations onto the corresponding many-particle system. This approach allows us to understand which interacting system a given single-particle approximation is actually describing, and how far this is from the original physical many-body system. We illustrate the resulting reverse engineering process by means of the Kohn-Sham equations of density-functional theory. In this application, our procedure sheds light on the nonlocality of the density-potential mapping of density-functional theory, and on the self-interaction error inherent in approximate density functionals.

Multifractal regime transition in a modified minority game model

The search for more realistic modeling of financial time series reveals several stylized facts of real markets. In this work we focus on the multifractal properties found in price and index signals. Although the usual minority game (MG) models do not exhibit multifractality, we study here one of its variants that does. We show that the nonsynchronous MG models in the nonergodic phase is multifractal and in this sense, together with other stylized facts, constitute a better modeling tool. Using the structure function (SF) approach we detected the stationary and the scaling range of the time series generated by the MG model and, from the linear (non-linear) behavior of the SF we identified the fractal (multifractal) regimes. Finally, using the wavelet transform modulus maxima (WTMM) technique we obtained its multifractal spectrum width for different dynamical regimes. (C) 2009 Elsevier Ltd. All rights reserved.

Low dimensional behavior in three-dimensional coupled map lattices

The analysis of one-, two-, and three-dimensional coupled map lattices is here developed under a statistical and dynamical perspective. We show that the three-dimensional CML exhibits low dimensional behavior with long range correlation and the power spectrum follows 1/f noise. This approach leads to an integrated understanding of the most important properties of these universal models of spatiotemporal chaos. We perform a complete time series analysis of the model and investigate the dependence of the signal properties by change of dimension. (c) 2008 Elsevier Ltd. All rights reserved.

Continuous opinions and discrete actions in opinion dynamics problems

A model where agents show discrete behavior regarding their actions, but have continuous opinions that are updated by interacting with other agents is presented. This new updating rule is applied to both the voter and Sznajd models for interaction between neighbors, and its consequences are discussed. The appearance of extremists is naturally observed and it seems to be a characteristic of this model.