Existence and Uniqueness of Tri-tronqu\'ee Solutions of the second Painlev\'e hierarchy

The first five classical Painlev\'e equations are known to have solutions described by divergent asymptotic power series near infinity. Here we prove that such solutions also exist for the infinite hierarchy of equations associated with the second Painlev\'e equation. Moreover we prove that these are unique in certain sectors near infinity.Comment: 13 pages, Late

Extending the Lee Carter Model: a Three-way Decomposition

In this paper, we focus on a Multidimensional Data Analysis approach to the Lee-Carter (LC) model of mortality trends . In particular, we extend the bilinear LC model and specify a new model based on a three-way structure, which incorporates a further component in the decomposition of the log-mortality rates. A multi-way component analysis is performed using the Tucker 3 model. The suggested methodology allows us to obtain combined estimates for the three modes: i) time, ii) agegroups and iii) different populations. From the results obtained by the Tucker 3 decomposition, we can jointly compare, in both a numerical and graphical way, the relationships among all three modes and obtain a time series component as a leading indicator of the mortality trend for a group of populations. Further, we carry out a correlation analysis of the estimated trends in order to assess the reliability of the results of the three-way decomposition. The model’s goodness of fit is assessed using an analysis of the residuals. Finally, we discuss how the synthesised mortality index can be used to build concise projected life tables for a group of populations. An application which compares ten European countries is used to illustrate the approach and provide a deeper insight into the model and its implementation

The Synaptic Vesicle SNARE Neuronal Synaptobrevin Promotes Endolysosomal Degradations and Prevents Neurodegeneration

Soluble NSF attachment protein receptors (SNAREs) are the core proteins in membrane fusion. The neuron-specific synaptic v-SNARE n-syb (neuronal Synaptobrevin) plays a key role during synaptic vesicle exocytosis. In this paper, we report that loss of n-syb caused slow neurodegeneration independent of its role in neurotransmitter release in adult Drosophila melanogaster photoreceptor neurons. In addition to synaptic vesicles, n-Syb localized to endosomal vesicles. Loss of n-syb lead to endosomal accumulations, transmembrane protein degradation defects, and a secondary increase in autophagy. Our evidence suggests a primary defect of impaired delivery of vesicles that contain degradation proteins, including the acidification-activated Cathepsin proteases and the neuron-specific proton pump and V0 adenosine triphosphatase component V100. Overexpressing V100 partially rescued n-syb–dependent degeneration through an acidification-independent endosomal sorting mechanism. Collectively, these findings reveal a role for n-Syb in a neuron-specific sort-and-degrade mechanism that protects neurons from degeneration. Our findings further shed light on which intraneuronal compartments exhibit increased or decreased neurotoxicity

Quasi-linear Stokes phenomenon for the Painlev\'e first equation

Using the Riemann-Hilbert approach, the $\Psi$-function corresponding to the solution of the first Painleve equation, $y_{xx}=6y^2+x$, with the asymptotic behavior $y\sim\pm\sqrt{-x/6}$ as $|x|\to\infty$ is constructed. The exponentially small jump in the dominant solution and the coefficient asymptotics in the power-like expansion to the latter are found.Comment: version accepted for publicatio

Statistical Inference in a Directed Network Model with Covariates

Networks are often characterized by node heterogeneity for which nodes exhibit different degrees of interaction and link homophily for which nodes sharing common features tend to associate with each other. In this paper, we propose a new directed network model to capture the former via node-specific parametrization and the latter by incorporating covariates. In particular, this model quantifies the extent of heterogeneity in terms of outgoingness and incomingness of each node by different parameters, thus allowing the number of heterogeneity parameters to be twice the number of nodes. We study the maximum likelihood estimation of the model and establish the uniform consistency and asymptotic normality of the resulting estimators. Numerical studies demonstrate our theoretical findings and a data analysis confirms the usefulness of our model.Comment: 29 pages. minor revisio

Dynamics of defect formation

A dynamic symmetry-breaking transition with noise and inertia is analyzed. Exact solution of the linearized equation that describes the critical region allows precise calculation (exponent and prefactor) of the number of defects produced as a function of the rate of increase of the critical parameter. The procedure is valid in both the overdamped and underdamped limits. In one space dimension, we perform quantitative comparison with numerical simulations of the nonlinear nonautonomous stochastic partial differential equation and report on signatures of underdamped dynamics.Comment: 4 pages, LaTeX, 4 figures. Submitted to Physical Revie

Aging Puerto Ricans’ Experiences of Depression Treatment: A New Ethnographic Exploration

PurposeTo examine aging Puerto Ricans’ experiences with and perceptions of depression treatment.Methodology/approachIn-depth analysis of eight exemplary cases from ethnographic interviews with a subsample of 16 aging Puerto Ricans in the Boston area who are part of the Boston Puerto Rican Health Study.FindingsThe results show that respondents were resistant to accepting pharmacological treatment for their depression, and they often characterized antidepressants as “dope.” Moreover, they claimed that in addition to their health problems, social stressors such as financial strain, lack of jobs, housing problems, and social isolation are triggering or contributing to their depression. Because of this, they express reluctance in accepting clinical treatment only, and suggest that broader social issues and other health needs ought to be addressed as part of an effective treatment. For many, pharmacological treatment is acceptable only in the more severe forms of depression.Research limitations/implicationsThese results have important implications for improving the quality of depression treatment and reducing health disparities for mainland Puerto Ricans.Originality/value of chapterEven though recent studies continue to show a high frequency of depression among Puerto Ricans, issues of treatment quality are still understudied and ethnographic accounts are especially lacking. Our study offers an exploratory investigation of this unresolved research issue

Maxwell Model of Traffic Flows

We investigate traffic flows using the kinetic Boltzmann equations with a Maxwell collision integral. This approach allows analytical determination of the transient behavior and the size distributions. The relaxation of the car and cluster velocity distributions towards steady state is characterized by a wide range of velocity dependent relaxation scales, $R^{1/2}<\tau(v)<R$, with $R$ the ratio of the passing and the collision rates. Furthermore, these relaxation time scales decrease with the velocity, with the smallest scale corresponding to the decay of the overall density. The steady state cluster size distribution follows an unusual scaling form $P_m \sim ^{-4} \Psi(m/< m>^2)$. This distribution is primarily algebraic, $P_m\sim m^{-3/2}$, for $m\ll ^2$, and is exponential otherwise.Comment: revtex, 10 page