A unified approach to explain contrary effects of hysteresis and smoothing in nonsmooth systems

Piecewise smooth dynamical systems make use of discontinuities to model switching between regions of smooth evolution. This introduces an ambiguity in prescribing dynamics at the discontinuity: should it be given by a limiting value on one side or other of the discontinuity, or a member of some set containing those values? One way to remove the ambiguity is to regularize the discontinuity, the most common being either to smooth out the discontinuity, or to introduce a hysteresis between switching in one direction or the other across the discontinuity. Here we show that the two can in general lead to qualitatively different dynamical outcomes. We then define a higher dimensional model with both smoothing and hysteresis, and study the competing limits in which hysteretic or smoothing effect dominate the behaviour, only the former of which correspond to Filippov's standard `sliding modes'

A multi-proxy approach to identifying short-lived marine incursions in the Early Carboniferous

This study is a contribution to the TW:eed Project (Tetrapod World: early evolution and diversification), which examines the rebuilding of Carboniferous ecosystems following a mass extinction at the end of the Devonian. The project focuses on the Tournaisian Ballagan Formation of Scotland and the Borders, which contains rare fish and tetrapod material. The Ballagan Formation is characterised by sandstones, dolomitic cementstones, paleosols, siltstones and gypsum deposits. The depositional environment ranges from fluvial, alluvial-plain to marginal-marine environments, with fluvial, floodplain and lacustrine deposition dominant

The Mobilization of China’s Legal System and Religious Bureaucracy as a Means of Combating the Threat of the Falun Gong

In 1992, Li Hongzhi, an obscure man from the northern Chinese province of Jilin, introduced to the world a set of five Qigong exercises which would form the basis of the Falun Gong movement. In the years that followed, the Falun Gong quickly grew to an estimated 100 million practitioners worldwide that expeditiously spread from China to the rest of the world. Though the group was pacifistic in its ideology, the Chinese government was never quite comfortable with the Falun Gong\u27s presence, and in 1999, the government began a widespread effort to discredit the Falun Gong, culminating in the arrest of thousands of Falun Gong members after a government protest held outside of the central government compound, Zhongnanhai in Beijing. Immediately following the arrests, the Falun Gong was officially labeled a seditious cult and its special brand of Qigong was deemed illegal to practice. Today, religion in China remains a tightly managed institution with strict legal controls placed on both its practice and its very existence

The impact of the demographic transition on dengue in Thailand: Insights from a statistical analysis and mathematical modeling

Background: An increase in the average age of dengue hemorrhagic fever (DHF) cases has been reported in Thailand. The cause of this increase is not known. Possible explanations include a reduction in transmission due to declining mosquito populations, declining contact between human and mosquito, and changes in reporting. We propose that a demographic shift toward lower birth and death rates has reduced dengue transmission and lengthened the interval between large epidemics. Methods and Findings: Using data from each of the 72 provinces of Thailand, we looked for associations between force of infection (a measure of hazard, defined as the rate per capita at which susceptible individuals become infected) and demographic and climactic variables. We estimated the force of infection from the age distribution of cases from 1985 to 2005. We find that the force of infection has declined by 2% each year since a peak in the late 1970s and early 1980s. Contrary to recent findings suggesting that the incidence of DHF has increased in Thailand, we find a small but statistically significant decline in DHF incidence since 1985 in a majority of provinces. The strongest predictor of the change in force of infection and the mean force of infection is the median age of the population. Using mathematical simulations of dengue transmission we show that a reduced birth rate and a shift in the population's age structure can explain the shift in the age distribution of cases, reduction of the force of infection, and increase in the periodicity of multiannual oscillations of DHF incidence in the absence of other changes. Conclusions: Lower birth and death rates decrease the flow of susceptible individuals into the population and increase the longevity of immune individuals. The increase in the proportion of the population that is immune increases the likelihood that an infectious mosquito will feed on an immune individual, reducing the force of infection. Though the force of infection has decreased by half, we find that the critical vaccination fraction has not changed significantly, declining from an average of 85% to 80%. Clinical guidelines should consider the impact of continued increases in the age of dengue cases in Thailand. Countries in the region lagging behind Thailand in the demographic transition may experience the same increase as their population ages. The impact of demographic changes on the force of infection has been hypothesized for other diseases, but, to our knowledge, this is the first observation of this phenomenon

Using Domination to Analyze RNA Structures.

Understanding RNA molecules is important to genomics research. Recently researchers at the Courant Institute of Mathematical Sciences used graph theory to model RNA molecules and provided a database of trees representing possible secondary RNA structures. In this thesis we use domination parameters to predict which trees are more likely to exist in nature as RNA structures. This approach appears to have promise in graph theory applications in genomics research

Frequency-preference response in covalent modification cycles under substrate sequestration conditions

Covalent modification cycles (CMCs) are basic units of signaling systems and their properties are well understood. However, their behavior has been mostly characterized in situations where the substrate is in excess over the modifying enzymes. Experimental data on protein abundance suggest that the enzymes and their target proteins are present in comparable concentrations, leading to substrate sequestration by the enzymes. In this enzyme-in-excess regime, CMCs have been shown to exhibit signal termination, the ability of the product to return to a stationary value lower than its peak in response to constant stimulation, while this stimulation is still active, with possible implications for the ability of systems to adapt to environmental inputs. We characterize the conditions leading to signal termination in CMCs in the enzyme-in-excess regime. We also demonstrate that this behavior leads to a preferred frequency response (band-pass filters) when the cycle is subjected to periodic stimulation, whereas the literature reports that CMCs investigated so far behave as low-pass filters. We characterize the relationship between signal termination and the preferred frequency response to periodic inputs and we explore the dynamic mechanism underlying these phenomena. Finally, we describe how the behavior of CMCs is reflected in similar types of responses in the cascades of which they are part. Evidence of protein abundance in vivo shows that enzymes and substrates are present in comparable concentrations, thus suggesting that signal termination and frequency-preference response to periodic inputs are also important dynamic features of cell signaling systems, which have been overlooked.Fil: Reves Szemere, Juliana. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Fisiología, Biología Molecular y Neurociencias. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Fisiología, Biología Molecular y Neurociencias; ArgentinaFil: Rotstein, Horacio. New Jersey Institute of Technology; Estados UnidosFil: Ventura, Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Fisiología, Biología Molecular y Neurociencias. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Fisiología, Biología Molecular y Neurociencias; Argentin

Hongrie : un dispositif innovant

L’objectif pédagogique du lycée français bilingue de Budapest, hautement innovant, est de former de nouvelles générations de professionnels dotés d’une instruction de qualité qui soient en mesure de maîtriser la langue française presque comme une langue maternelle. Ce que propose le lycée français bilingue correspond pleinement aux programmes d’immersion en langue étrangère récemment introduits dans le système éducatif hongrois. La raison d’être implicite de ces programmes est que les élèves ..

A Raman Spectroscopic and Computational Study of the Effects of Halogen Bonding on Pyrimidine Containing Systems

This thesis involves the study of the effects of halogen bonding on pyrimidine containing systems. Halogen bonding is a type of non-covalent interaction that can occur when a Lewis base interacts with an iodine, bromine, or chlorine atom in a second molecule. The phenomenon of halogen bonding is explained by the presence of a localized region of positive electrostatic potential that exists on the halogen. This positive region is referred to as the σ-hole, and gives halogen bonding its other common name, σ-hole bonding. The magnitude of the positive σ-hole depends on both the type of halogen molecule involved in the interaction as well as the characteristics of the molecule to which the halogen is bonded. The strength of the halogen bond tends to increase from chlorine < bromine < iodine. The careful and directed use of this intermolecular interaction has been suggested for use in several areas of supramolecular chemistry. For example, halogen bonding has been employed in crystal engineering as a means of forming new types of crystals. In this work, halogen bonding interactions between a nitrogen-containing heterocyclic biological building block (pyrimidine) and aryl halides are studied both experimentally and theoretically. Experimental Raman spectra of liquid mixtures are compared to the results of electronic structure calculations on halogen bond containing molecular clusters. Mixtures pyrimidine with bromobenzene, iodobenzene, bromopentafluorobenzene, and iodopentafluorobenzene were examined both experimentally and theoretically. Results indicate that the addition of electron withdrawing fluorine atoms strengthen the halogen bond interaction, leading to significant blue shifts in a number of pyrimidine’s normal modes in mixtures of iodopentafluorobenzene and pyrimidine, similar to the shifts induced by hydrogen bonding between pyrimidine and water. Additionally, a co-crystal containing halogen bonds is characterized using micro-Raman spectroscopy and compared to theoretical calculations of the co-crystal complex. Though only small shifts in vibrational modes were observed in the co-crystal, theory and experiment proved to agree very well. An X-Ray crystal structure of the co-crystal, however, confirmed the presence of halogen bonds in the crystal