Self-Similar Blowup Solutions to the 2-Component Camassa-Holm Equations

In this article, we study the self-similar solutions of the 2-component Camassa-Holm equations% \begin{equation} \left\{ \begin{array} [c]{c}% \rho_{t}+u\rho_{x}+\rho u_{x}=0 m_{t}+2u_{x}m+um_{x}+\sigma\rho\rho_{x}=0 \end{array} \right. \end{equation} with \begin{equation} m=u-\alpha^{2}u_{xx}. \end{equation} By the separation method, we can obtain a class of blowup or global solutions for $\sigma=1$ or $-1$. In particular, for the integrable system with $\sigma=1$, we have the global solutions:% \begin{equation} \left\{ \begin{array} [c]{c}% \rho(t,x)=\left\{ \begin{array} [c]{c}% \frac{f\left( \eta\right) }{a(3t)^{1/3}},\text{ for }\eta^{2}<\frac {\alpha^{2}}{\xi} 0,\text{ for }\eta^{2}\geq\frac{\alpha^{2}}{\xi}% \end{array} \right. ,u(t,x)=\frac{\overset{\cdot}{a}(3t)}{a(3t)}x \overset{\cdot\cdot}{a}(s)-\frac{\xi}{3a(s)^{1/3}}=0,\text{ }a(0)=a_{0}% >0,\text{ }\overset{\cdot}{a}(0)=a_{1} f(\eta)=\xi\sqrt{-\frac{1}{\xi}\eta^{2}+\left( \frac{\alpha}{\xi}\right) ^{2}}% \end{array} \right. \end{equation} where $\eta=\frac{x}{a(s)^{1/3}}$ with $s=3t;$ $\xi>0$ and $\alpha\geq0$ are arbitrary constants.\newline Our analytical solutions could provide concrete examples for testing the validation and stabilities of numerical methods for the systems.Comment: 5 more figures can be found in the corresponding journal paper (J. Math. Phys. 51, 093524 (2010) ). Key Words: 2-Component Camassa-Holm Equations, Shallow Water System, Analytical Solutions, Blowup, Global, Self-Similar, Separation Method, Construction of Solutions, Moving Boundar

Promoting post-stroke recovery through focal or whole body vibration: criticisms and prospects from a narrative review

Objective: Several focal muscle vibration (fMV) and whole body vibration (WBV) protocols have been designed to promote brain reorganization processes in patients with stroke. However, whether fMV and WBV should be considered helpful tools to promote post-stroke recovery remains still largely unclear. Methods: We here achieve a comprehensive review of the application of fMV and WBV to promote brain reorganization processes in patients with stroke. By first discussing the putative physiological basis of fMV and WBV and then examining previous observations achieved in recent randomized controlled trials (RCT) in patients with stroke, we critically discuss possible strength and limitations of the currently available data. Results: We provide the first systematic assessment of fMV studies demonstrating some improvement in upper and lower limb functions, in patients with chronic stroke. We also confirm and expand previous considerations about the rather limited rationale for the application of current WBV protocols in patients with chronic stroke. Conclusion: Based on available information, we propose new recommendations for optimal stimulation parameters and strategies for recruitment of specific stroke populations that would more likely benefit from future fMV or WBV application, in terms of speed and amount of post-stroke functional recovery

Amplified biochemical oscillations in cellular systems

We describe a mechanism for pronounced biochemical oscillations, relevant to microscopic systems, such as the intracellular environment. This mechanism operates for reaction schemes which, when modeled using deterministic rate equations, fail to exhibit oscillations for any values of rate constants. The mechanism relies on amplification of the underlying stochasticity of reaction kinetics within a narrow window of frequencies. This amplification allows fluctuations to beat the central limit theorem, having a dominant effect even though the number of molecules in the system is relatively large. The mechanism is quantitatively studied within simple models of self-regulatory gene expression, and glycolytic oscillations.Comment: 35 pages, 6 figure

An anatomy-based lumped parameter model of cerebrospinal venous circulation: can an extracranial anatomical change impact intracranial hemodynamics?

Background The relationship between extracranial venous system abnormalities and central nervous system disorders has been recently theorized. In this paper we delve into this hypothesis by modeling the venous drainage in brain and spinal column areas and simulating the intracranial flow changes due to extracranial morphological stenoses. Methods A lumped parameter model of the cerebro-spinal venous drainage was created based on anatomical knowledge and vessels diameters and lengths taken from literature. Each vein was modeled as a hydraulic resistance, calculated through Poiseuille’s law. The inputs of the model were arterial flow rates of the intracranial, vertebral and lumbar districts. The effects of the obstruction of the main venous outflows were simulated. A database comprising 112 Multiple Sclerosis patients (Male/Female = 42/70; median age ± standard deviation = 43.7 ± 10.5 years) was retrospectively analyzed. Results The flow rate of the main veins estimated with the model was similar to the measures of 21 healthy controls (Male/Female = 10/11; mean age ± standard deviation = 31 ± 11 years), obtained with a 1.5 T Magnetic Resonance scanner. The intracranial reflux topography predicted with the model in cases of internal jugular vein diameter reduction was similar to those observed in the patients with internal jugular vein obstacles. Conclusions The proposed model can predict physiological and pathological behaviors with good fidelity. Despite the simplifications introduced in cerebrospinal venous circulation modeling, the key anatomical feature of the lumped parameter model allowed for a detailed analysis of the consequences of extracranial venous impairments on intracranial pressure and hemodynamics

Computing Cumulative Rewards Using Fast Adaptive Uniformisation

Abstract.The computation of transient probabilities for continuous-time Markov chains often employs uniformisation, also known as the Jensen’s method. The fast adaptive uniformisation method introduced by Mateescu approximates the proba-bility by neglecting insignificant states, and has proven to be effective for quanti-tative analysis of stochastic models arising in chemical and biological applications. However, this method has only been formulated for the analysis of properties at a given point of time t. In this paper, we extend fast adaptive uniformisation to handle expected reward properties which reason about the model behaviour until time t, for example, the expected number of chemical reactions that have occurred until t. To show the feasibility of the approach, we integrate the method into the probabilistic model checker PRISM and apply it to a range of biological models, demonstrating superior performance compared to existing techniques.

Embodied Gesture Processing: Motor-Based Integration of Perception and Action in Social Artificial Agents

A close coupling of perception and action processes is assumed to play an important role in basic capabilities of social interaction, such as guiding attention and observation of others’ behavior, coordinating the form and functions of behavior, or grounding the understanding of others’ behavior in one’s own experiences. In the attempt to endow artificial embodied agents with similar abilities, we present a probabilistic model for the integration of perception and generation of hand-arm gestures via a hierarchy of shared motor representations, allowing for combined bottom-up and top-down processing. Results from human-agent interactions are reported demonstrating the model’s performance in learning, observation, imitation, and generation of gestures

Atypical Social Modulation of Imitation in Autism Spectrum Conditions.

Appropriate modulation of imitation according to social context is important for successful social interaction. In the present study we subliminally primed high-functioning adults with ASC and age- and IQ-matched controls with either a pro- or non- social attitude. Following priming, an automatic imitation paradigm was used to acquire an index of imitation. Whereas imitation levels were higher for pro-socially primed relative to non-socially primed control participants, there was no difference between pro- and non- socially primed individuals with ASC. We conclude that high-functioning adults with ASC demonstrate atypical social modulation of imitation. Given the importance of imitation in social interaction we speculate that difficulties with the modulation of imitation may contribute to the social problems characteristic of ASC

Technology as 'Applied Science': a Serious Misconception that Reinforces Distorted and Impoverished Views of Science

The current consideration of technology as 'applied science', this is to say, as something that comes 'after' science, justifies the lack of attention paid to technology in science education. In our paper we question this simplistic view of the science-technology relationship, historically rooted in the unequal appreciation of intellectual and manual work, and we try to show how the absence of the technological dimension in science education contributes to a na¿ ve and distorted view of science which deeply affects the necessary scientific and technological literacy of all citizens

Some psychosocial and cultural factors in the Arab-Israeli conflict: a review of the literature

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66497/2/10.1177_002200277201600210.pd