Positive approximations of the inverse of fractional powers of SPD M-matrices

This study is motivated by the recent development in the fractional calculus and its applications. During last few years, several different techniques are proposed to localize the nonlocal fractional diffusion operator. They are based on transformation of the original problem to a local elliptic or pseudoparabolic problem, or to an integral representation of the solution, thus increasing the dimension of the computational domain. More recently, an alternative approach aimed at reducing the computational complexity was developed. The linear algebraic system $\cal A^\alpha \bf u=\bf f$, $0< \alpha <1$ is considered, where $\cal A$ is a properly normalized (scalded) symmetric and positive definite matrix obtained from finite element or finite difference approximation of second order elliptic problems in $\Omega\subset\mathbb{R}^d$, $d=1,2,3$. The method is based on best uniform rational approximations (BURA) of the function $t^{\beta-\alpha}$ for $0 < t \le 1$ and natural $\beta$. The maximum principles are among the major qualitative properties of linear elliptic operators/PDEs. In many studies and applications, it is important that such properties are preserved by the selected numerical solution method. In this paper we present and analyze the properties of positive approximations of $\cal A^{-\alpha}$ obtained by the BURA technique. Sufficient conditions for positiveness are proven, complemented by sharp error estimates. The theoretical results are supported by representative numerical tests

Modeling the scaling properties of human mobility

While the fat tailed jump size and the waiting time distributions characterizing individual human trajectories strongly suggest the relevance of the continuous time random walk (CTRW) models of human mobility, no one seriously believes that human traces are truly random. Given the importance of human mobility, from epidemic modeling to traffic prediction and urban planning, we need quantitative models that can account for the statistical characteristics of individual human trajectories. Here we use empirical data on human mobility, captured by mobile phone traces, to show that the predictions of the CTRW models are in systematic conflict with the empirical results. We introduce two principles that govern human trajectories, allowing us to build a statistically self-consistent microscopic model for individual human mobility. The model not only accounts for the empirically observed scaling laws but also allows us to analytically predict most of the pertinent scaling exponents

How Landscape Heterogeneity Frames Optimal Diffusivity in Searching Processes

Theoretical and empirical investigations of search strategies typically have failed to distinguish the distinct roles played by density versus patchiness of resources. It is well known that motility and diffusivity of organisms often increase in environments with low density of resources, but thus far there has been little progress in understanding the specific role of landscape heterogeneity and disorder on random, non-oriented motility. Here we address the general question of how the landscape heterogeneity affects the efficiency of encounter interactions under global constant density of scarce resources. We unveil the key mechanism coupling the landscape structure with optimal search diffusivity. In particular, our main result leads to an empirically testable prediction: enhanced diffusivity (including superdiffusive searches), with shift in the diffusion exponent, favors the success of target encounters in heterogeneous landscapes

Plasticity and rectangularity in survival curves

Living systems inevitably undergo a progressive deterioration of physiological function with age and an increase of vulnerability to disease and death. To maintain health and survival, living systems should optimize survival strategies with adaptive interactions among molecules, cells, organs, individuals, and environments, which arises plasticity in survival curves of living systems. In general, survival dynamics in a population is mathematically depicted by a survival rate, which monotonically changes from 1 to 0 with age. It would be then useful to find an adequate function to describe complicated survival dynamics. Here we describe a flexible survival function, derived from the stretched exponential function by adopting an age-dependent shaping exponent. We note that the exponent is associated with the fractal-like scaling in cumulative mortality rate. The survival function well depicts general features in survival curves; healthy populations exhibit plasticity and evolve towards rectangular-like survival curves, as examples in humans or laboratory animals

Altered patterns of cortical activation in ALS patients during attention and cognitive response inhibition tasks

Since amyotrophic lateral sclerosis (ALS) can be accompanied by executive dysfunction, it is hypothesised that ALS patients will have impaired performance on tests of cognitive inhibition. We predicted that ALS patients would show patterns of abnormal activation in extramotor regions when performing tests requiring the inhibition of prepotent responses (the Stroop effect) and the inhibition of prior negatively primed responses (the negative priming effect) when compared to healthy controls. Functional magnetic resonance imaging was used to measure activation during a sparse sequence block design paradigm investigating the Stroop and negative priming effects in 14 ALS patients and 8 healthy age- and IQ-matched controls. Behavioural measures of performance were collected. Both groups’ reaction times (RTs) reflected the Stroop effect during scanning. The ALS and control groups did not differ significantly for any of the behavioural measures but did show significant differences in cerebral activation during both tasks. The ALS group showed increased activation predominantly in the left middle temporal gyrus (BA 20/21), left superior temporal gyrus (BA 22) and left anterior cingulate gyrus (BA 32). Neither group’s RT data showed clear evidence of a negative priming effect. However the ALS group showed decreased activation, relative to controls, particularly in the left cingulate gyrus (BA 23/24), left precentral gyrus (BA 4/6) and left medial frontal gyrus (BA 6). Greater cerebral activation in the ALS group accompanying the performance of the Stroop effect and areas of decreased activation during the negative priming comparison suggest altered inhibitory processing in ALS, consistent with other evidence of executive dysfunction in ALS. The current findings require further exploration in a larger study

High school drinking mediates the relationship between parental monitoring and college drinking: A longitudinal analysis

<p>Abstract</p> <p>Background</p> <p>College drinking is a significant public health problem. Although parental monitoring and supervision reduces the risk for alcohol consumption among younger adolescents, few studies have investigated the impact of earlier parental monitoring on later college drinking. This study examined whether parental monitoring indirectly exerts a protective effect on college drinking by reducing high school alcohol consumption.</p> <p>Methods</p> <p>A longitudinal cohort of 1,253 male and female students, ages 17 to 19, attending a large, public, mid-Atlantic university was studied at two time points. First, data on high school parental monitoring and alcohol consumption were gathered via questionnaire during the summer prior to college entry. Second, during the first year of college, past-year alcohol consumption was measured via a personal interview. Multiple regression models tested the relationship between parental monitoring and past year alcohol use (i.e., number of drinks per drinking day).</p> <p>Results</p> <p>Holding constant demographics, SAT score, and religiosity, parental monitoring had a significant protective effect on both high school and college drinking level. However, the association between parental monitoring and college drinking level became non-significant once high school drinking level was held constant.</p> <p>Conclusion</p> <p>While parental monitoring did not directly influence college alcohol consumption, evidence for mediation was observed, whereby parental monitoring had an indirect influence on college drinking through reductions in high school drinking. Initiatives that promote effective parenting might be an important strategy to curb high-risk drinking among older adolescents. More research is needed to understand the nature and degree of parent-child communication that is necessary to extend the protective influence of parents into the college years.</p

Diastolic dysfunction in diabetes and the metabolic syndrome: promising potential for diagnosis and prognosis

Cardiac disease in diabetes mellitus and in the metabolic syndrome consists of both vascular and myocardial abnormalities. The latter are characterised predominantly by diastolic dysfunction, which has been difficult to evaluate in spite of its prevalence. While traditional Doppler echocardiographic parameters enable only semiquantitative assessment of diastolic function and cannot reliably distinguish perturbations in loading conditions from altered diastolic functions, new technologies enable detailed quantification of global and regional diastolic function. The most readily available technique for the quantification of subclinical diastolic dysfunction is tissue Doppler imaging, which has been integrated into routine contemporary clinical practice, whereas cine magnetic resonance imaging (CMR) remains a promising complementary research tool for investigating the molecular mechanisms of the disease. Diastolic function is reported to vary linearly with age in normal persons, decreasing by 0.16 cm/s each year. Diastolic function in diabetes and the metabolic syndrome is determined by cardiovascular risk factors that alter myocardial stiffness and myocardial energy availability/bioenergetics. The latter is corroborated by the improvement in diastolic function with improvement in metabolic control of diabetes by specific medical therapy or lifestyle modification. Accordingly, diastolic dysfunction reflects the structural and metabolic milieu in the myocardium, and may allow targeted therapeutic interventions to modulate cardiac metabolism to prevent heart failure in insulin resistance and diabetes

A Preliminary Analysis of the Immunoglobulin Genes in the African Elephant (Loxodonta africana)

The genomic organization of the IgH (Immunoglobulin heavy chain), Igκ (Immunoglobulin kappa chain), and Igλ (Immunoglobulin lambda chain) loci in the African elephant (Loxodonta africana) was annotated using available genome data. The elephant IgH locus on scaffold 57 spans over 2,974 kb, and consists of at least 112 VH gene segments, 87 DH gene segments (the largest number in mammals examined so far), six JH gene segments, a single μ, a δ remnant, and eight γ genes (α and ε genes are missing, most likely due to sequence gaps). The Igκ locus, found on three scaffolds (202, 50 and 86), contains a total of 153 Vκ gene segments, three Jκ segments, and a single Cκ gene. Two different transcriptional orientations were determined for these Vκ gene segments. In contrast, the Igλ locus on scaffold 68 includes 15 Vλ gene segments, all with the same transcriptional polarity as the downstream Jλ-Cλ cluster. These data suggest that the elephant immunoglobulin gene repertoire is highly diverse and complex. Our results provide insights into the immunoglobulin genes in a placental mammal that is evolutionarily distant from humans, mice, and domestic animals