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

Autoresonance in a Dissipative System

We study the autoresonant solution of Duffing's equation in the presence of dissipation. This solution is proved to be an attracting set. We evaluate the maximal amplitude of the autoresonant solution and the time of transition from autoresonant growth of the amplitude to the mode of fast oscillations. Analytical results are illustrated by numerical simulations.Comment: 22 pages, 3 figure

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

The Composition of Titan's Lower Atmosphere and Simple Surface Volatiles as Measured by the Cassini-Huygens Probe Gas Chromatograph Mass Spectrometer Experiment

The Cassini-Huygens Probe Gas Chromatograph Mass Spectrometer (GCMS) determined the composition of the Titan atmosphere from ~140km altitude to the surface. After landing, it returned composition data of gases evaporated from the surface. Height profiles of molecular nitrogen (N2), methane (CH4) and molecular hydrogen (H2) were determined. Traces were detected on the surface of evaporating methane, ethane (C2H6), acetylene (C2H2), cyanogen (C2N2) and carbon dioxide (CO2). The methane data showed evidence that methane precipitation occurred recently. The methane mole fraction was (1.48+/-0.09) x 10(exp -2) in the lower stratosphere (139.8 km to 75.5 km) and (5.65+/-0.18) x 10(exp -2) near the surface (6.7 km to the surface). The molecular hydrogen mole fraction was (1.01+/-0.16) x 10(exp -3) in the atmosphere and (9.90+/-0.17) x 10(exp -4) on the surface. Isotope ratios were 167.7+/-0.6 for N-14/N-15 in molecular nitrogen, 91.1+/-1.4 for C-12/C-13 in methane and (1.35+/-0.30) x 10(exp -4) for D/H in molecular hydrogen. The mole fractions of Ar-36 and radiogenic Ar-40 are (2.1+/-0.8) x 10(exp -7) and (3.39 +/-0.12) x 10(exp -5) respectively. Ne-22 has been tentatively identified at a mole fraction of (2.8+/-2.1) x 10(exp -7) Krypton and xenon were below the detection threshold of 1 x 10(exp -8) mole fraction. Science data were not retrieved from the gas chromatograph subsystem as the abundance of the organic trace gases in the atmosphere and on the ground did not reach the detection threshold. Results previously published from the GCMS experiment are superseded by this publication