Kinematic Equations for Front Motion and Spiral-Wave Nucleation

We present a new set of kinematic equations for front motion in bistable media. The equations extend earlier kinematic approaches by coupling the front curvature with the order parameter associated with a parity breaking front bifurcation. In addition to naturally describing the core region of rotating spiral waves the equations can be be used to study the nucleation of spiral-wave pairs along uniformly propagating fronts. The analysis of spiral-wave nucleation reduces to the simpler problem of droplet, or domain, nucleation in one space dimension.Comment: 8 pages. Aric Hagberg: http://cnls.lanl.gov/~aric; Ehud Meron: http://www.bgu.ac.il/BIDR/research/staff/meron.htm

Singularity Structure, Symmetries and Integrability of Generalized Fisher Type Nonlinear Diffusion Equation

In this letter, the integrability aspects of a generalized Fisher type equation with modified diffusion in (1+1) and (2+1) dimensions are studied by carrying out a singularity structure and symmetry analysis. It is shown that the Painlev\'e property exists only for a special choice of the parameter ($m=2$). A B\"acklund transformation is shown to give rise to the linearizing transformation to the linear heat equation for this case ($m=2$). A Lie symmetry analysis also picks out the same case ($m=2$) as the only system among this class as having nontrivial infinite dimensional Lie algebra of symmetries and that the similarity variables and similarity reductions lead in a natural way to the linearizing transformation and physically important classes of solutions (including known ones in the literature), thereby giving a group theoretical understanding of the system. For nonintegrable cases in (2+1) dimensions, associated Lie symmetries and similarity reductions are indicated.Comment: 8 page

Relatório de estágio

I (Prática Pedagógica)- No que se refere à secção da tese dedicada ao estágio, esta pretende desenvolver uma síntese do que se passou ao longo deste ano lectivo. Durante o ano lectivo 2012/2013, tive a oportunidade de assistir a aulas ministradas pela professora Ana Valente. A tese procura focar variados aspectos das aulas a que assisti. De uma forma geral, o relatório do estágio evidencia vários aspectos: metodologias de ensino, questões motivacionais, relação aluno/professor, questões de disciplina, entre outras. No decorrer das aulas, foi possível constatar muitas dessas questões na prática. Tentei registar as actividades desenvolvidas nas aulas relativas a várias questões, nomeadamente questões relacionadas com a prática do instrumento, assim como outras relacionadas com a noção de musicalidade. Como resultado, esta secção apresenta diversos tipos de estratégias de ensino, ilustrando exemplos práticos que efectivamente se passaram nas aulas. É essencialmente, uma secção dedicada à reflexão sobre metodologias de ensino e estudo. A segunda parte desta secção é relativa à análise das gravações das aulas dadas por mim e pretende sobretudo focar-se na crítica pessoal. É uma parte importante do estágio, em que tenho a oportunidade de observar a minha forma pedagógica de lidar com os alunos. Por fim, a terceira parte do relatório refere-se à observação crítica da abordagem da professora tendo por base o meu ponto de vista. Esta parte pretende essencialmente descrever e analisar a forma como a professora dá as aulas. Com base no que disse anteriormente, esta parte do trabalho mostra mais em detalhe as metodologias e estratégias de ensino utilizadas pela professora em questão. De um modo geral, esta secção pretende descrever as três vertentes que mencionei anteriormente (relatório das aulas, análise das gravações, observação crítica ao método pedagógico da professora).II (Investigação) - A investigação que realizei ao longo do mestrado, teve por objectivo juntar o máximo de informação disponível acerca do tema central desta tese. Depois de muito reflectir sobre qual deveria ser o tema central do trabalho, decidi basear a minha investigação na área do raciocínio. Irei ao longo do trabalho aprofundar várias questões relacionadas com a actividade cognitiva, assim como diversos assuntos relevantes para este tema. Uma das razões que me levou a optar por este tema (padrões de raciocínio) deve-se ao facto do Mestrado em Ensino da Música que frequento, despertar em mim uma enorme curiosidade sobre os vários mecanismos cognitivos que ocorrem ao longo do processo de aprendizagem. Rapidamente percebi que se tratava de algo complexo de analisar porque de acordo com a investigação que realizei, verifiquei que todas as formas de raciocínio e aquisição de conhecimento são muito diferentes e variam muito de pessoa para pessoa. Ao longo da investigação irei mencionar as mais variadas questões associadas ao raciocínio, irei focar-me essencialmente nas diferentes formas de raciocinar no contexto da leitura à primeira vista e memorização das obras musicais (raciocínio intervalar, memória auditiva, etc.). Para além do que referi anteriormente, também irei comparar várias estratégias de ensino com a minha própria experiência pessoal. Para isso, irei apresentar imagens bastante acessíveis que sugerem ao leitor diferentes formas de raciocinar musicalmente. A maior parte dessas imagens explicam formas intuitivas que facilitam a compreensão das mais variadas questões musicais, tais como: ritmo, harmonia, cálculo intervalar, leitura, improvisação. O conceito mais importante presente nesta investigação, é o conceito de “Padrões”, isso deve-se ao facto do cérebro humano, funcionar de um modo muito lógico e precisar quase sempre de organizar a informação adquirida mediante certas sequências (padrões). Esta é uma questão essencial para que uma pessoa aprenda e relacione informação adquirida de uma forma consistente e sustentável, como iremos ver ao longo da parte da investigação.ABSTRACT I (Teaching)- With regard to the section devoted to the thesis internship, it aims to develop a resume of what happened during this school year. During the academic year 2012/2013, I had the opportunity to attend classes taught by Professor Ana Valente. The thesis tries to focus on various aspects of the classes I attended. Overall, the report highlights various aspects of the stage: teaching methodologies, motivational issues, relationship student / teacher, discipline issues, among others. During the classes, it was possible to see many of these issues in real time. I tried as much as possible, record the activities in class regarding various issues, including issues related to the practice of the instrument, as well as others related to the notion of musicality. As a result, this section presents various types of teaching strategies, illustrating practical examples that occurred in class. It is essentially a section dedicated to reflection on teaching methodologies and study. The second part of this section is relative to analysis of recordings of lectures given by me about everything and want to focus on personal criticism. It is an important part of the stage, where I have the opportunity to observe my way of dealing with students and teaching. Finally, the third part of the report refers to the criticism of the teacher based on my point of view. This part essentially describe and analyze how the teacher gives lessons. Based on what I said earlier, this part of the work shows more detail about methodologies and teaching strategies used by the teacher. In general, this section main goal is to describe the three components I mentioned earlier (school report, analysis of the recordings, criticism of the teacher's pedagogical method).ABSTRATC II (Research)- The research that I realized during the masters, the main goal was to gather the maximum of information available relative to the main subject. After a long period of reflection about what should be the main subject of this work, I decided to make my investigation around cognitive patterns and brain function in general. During the thesis I will deepen various issues related to cognitive activity, as well as various issues relevant to this topic. One of the reasons that led me to choose this topic (cognitive patterns), is because the Master in Teaching Music I attend, aroused in me a strong curiosity about the various cognitive mechanisms that occur during the learning process. I quickly realized that this was something complex to analyze because according to research I did, I found that all forms of reasoning and acquiring knowledge are very different and it's quite different from person to person. Throughout the investigation I will mention a wide range of issues associated with reasoning, I will focus primarily on many different ways of thinking in the context of sight-reading and memorization of musical works (interval reasoning, auditory memory, etc ...). In addition to what I mentioned earlier, I will also compare various teaching strategies with my own personal experience. For this, I will present quite affordable images that suggest the reader to different ways of thinking musically. Most of these pictures explain intuitive ways that help to understand various musical issues such as rhythm, harmony, interval calculation, reading, improvisation. The most relevant concept in this present research is the concept of "patterns", this is due to the fact that the human brain to function in a very logical and almost always need to organize the information acquired through certain sequences (patterns). This is a critical issue for a person to learn and relate information acquired from a consistent and sustainable, as we will see along the part of the investigation

Quantum Cellular Neural Networks

We have previously proposed a way of using coupled quantum dots to construct digital computing elements - quantum-dot cellular automata (QCA). Here we consider a different approach to using coupled quantum-dot cells in an architecture which, rather that reproducing Boolean logic, uses a physical near-neighbor connectivity to construct an analog Cellular Neural Network (CNN).Comment: 7 pages including 3 figure

A Quantitative Study of the Division Cycle of Caulobacter crescentus Stalked Cells

Progression of a cell through the division cycle is tightly controlled at different steps to ensure the integrity of genome replication and partitioning to daughter cells. From published experimental evidence, we propose a molecular mechanism for control of the cell division cycle in Caulobacter crescentus. The mechanism, which is based on the synthesis and degradation of three “master regulator” proteins (CtrA, GcrA, and DnaA), is converted into a quantitative model, in order to study the temporal dynamics of these and other cell cycle proteins. The model accounts for important details of the physiology, biochemistry, and genetics of cell cycle control in stalked C. crescentus cell. It reproduces protein time courses in wild-type cells, mimics correctly the phenotypes of many mutant strains, and predicts the phenotypes of currently uncharacterized mutants. Since many of the proteins involved in regulating the cell cycle of C. crescentus are conserved among many genera of α-proteobacteria, the proposed mechanism may be applicable to other species of importance in agriculture and medicine

Control of scroll wave turbulence using resonant perturbations

Turbulence of scroll waves is a sort of spatio-temporal chaos that exists in three-dimensional excitable media. Cardiac tissue and the Belousov-Zhabotinsky reaction are examples of such media. In cardiac tissue, chaotic behaviour is believed to underlie fibrillation which, without intervention, precedes cardiac death. In this study we investigate suppression of the turbulence using stimulation of two different types, "modulation of excitability" and "extra transmembrane current". With cardiac defibrillation in mind, we used a single pulse as well as repetitive extra current with both constant and feedback controlled frequency. We show that turbulence can be terminated using either a resonant modulation of excitability or a resonant extra current. The turbulence is terminated with much higher probability using a resonant frequency perturbation than a non-resonant one. Suppression of the turbulence using a resonant frequency is up to fifty times faster than using a non-resonant frequency, in both the modulation of excitability and the extra current modes. We also demonstrate that resonant perturbation requires strength one order of magnitude lower than that of a single pulse, which is currently used in clinical practice to terminate cardiac fibrillation. Our results provide a robust method of controlling complex chaotic spatio-temporal processes. Resonant drift of spiral waves has been studied extensively in two dimensions, however, these results show for the first time that it also works in three dimensions, despite the complex nature of the scroll wave turbulence.Comment: 13 pages, 12 figures, submitted to Phys Rev E 2008/06/13. Last version: 2008/09/18, after revie

Elucidation of Directionality for Co-Expressed Genes: Predicting Intra-Operon Termination Sites

We present a novel framework for inferring regulatory and sequence-level information from gene co-expression networks. The key idea of our methodology is the systematic integration of network inference and network topological analysis approaches for uncovering biological insights. We determine the gene co-expression network of Bacillus subtilis using Affymetrix GeneChip time series data and show how the inferred network topology can be linked to sequence-level information hard-wired in the organism's genome. We propose a systematic way for determining the correlation threshold at which two genes are assessed to be co-expressed by using the clustering coefficient and we expand the scope of the gene co-expression network by proposing the slope ratio metric as a means for incorporating directionality on the edges. We show through specific examples for B. subtilis that by incorporating expression level information in addition to the temporal expression patterns, we can uncover sequence-level biological insights. In particular, we are able to identify a number of cases where (i) the co-expressed genes are part of a single transcriptional unit or operon and (ii) the inferred directionality arises due to the presence of intra-operon transcription termination sites.Comment: 7 pages, 8 figures, accepted in Bioinformatic

Social representations of Russian and Byelorussians about man's roles depending on communication with psychological measurements of culture

Given article is devoted the analysis of social representations of young men about man's roles. On sample of Russian and Byelorussians (334 persons) by means of a scale of cultural values (G.Hofstede) and the modified variant of a technique «Semantic differential» directed on studying of representations of young men about traditional man's roles (the getter, the defender, the professional figure, the head of the family, the husband, the father), social representations about man's roles depending on psychological measurements of culture on G.Hovstede are considered. As a result the personal characteristics attributed traditional man's roles in Russian and Belarus cultures are allocated. Are revealed as cultural – specific, and the general social representations of Russian and Byelorussians about the maintenance of man's roles. The received results can be used at carrying out of psychotherapy and the personal consultations connected with questions of mutual relation of floors, gender and family conflicts, crises masculinity, and as for working out training programs in the field of intercultural interaction

On the Integrability, B\"Acklund Transformation and Symmetry Aspects of a Generalized Fisher Type Nonlinear Reaction-Diffusion Equation

The dynamics of nonlinear reaction-diffusion systems is dominated by the onset of patterns and Fisher equation is considered to be a prototype of such diffusive equations. Here we investigate the integrability properties of a generalized Fisher equation in both (1+1) and (2+1) dimensions. A Painlev\'e singularity structure analysis singles out a special case ($m=2$) as integrable. More interestingly, a B\"acklund transformation is shown to give rise to a linearizing transformation for the integrable case. A Lie symmetry analysis again separates out the same $m=2$ case as the integrable one and hence we report several physically interesting solutions via similarity reductions. Thus we give a group theoretical interpretation for the system under study. Explicit and numerical solutions for specific cases of nonintegrable systems are also given. In particular, the system is found to exhibit different types of travelling wave solutions and patterns, static structures and localized structures. Besides the Lie symmetry analysis, nonclassical and generalized conditional symmetry analysis are also carried out.Comment: 30 pages, 10 figures, to appear in Int. J. Bifur. Chaos (2004