A kinematic calibration of the O-rich Mira variable period–age relation from Gaia

Empirical and theoretical studies have demonstrated that the periods of Mira variable stars are related to their ages. This, together with their brightness in the infrared, makes them powerful probes of the formation and evolution of highly-extincted or distant parts of the Local Group. Here we utilize the Gaia DR3 catalogue of long-period variable candidates to calibrate the period–age relation of the Mira variables. Dynamical models are fitted to the O-rich Mira variable population across the extended solar neighbourhood and then the resulting solar neighbourhood period–kinematic relations are compared to external calibrations of the age–kinematic relations to derive a Mira variable period–age relation of $\tau \approx (6.9\pm 0.3)\, \mathrm{Gyr}(1+\tanh ((330\, \mathrm{d}-P)/(400\pm 90)\mathrm{d})$. Our results compare well with previous calibrations using smaller data sets as well as the period–age properties of Local Group cluster members. This calibration opens the possibility of accurately characterizing the star formation and the impact of different evolutionary processes throughout the Local Group

Matrix Infinitely Divisible Series: Tail Inequalities and Applications in Optimization

In this paper, we study tail inequalities of the largest eigenvalue of a matrix infinitely divisible (i.d.) series, which is a finite sum of fixed matrices weighted by i.d. random variables. We obtain several types of tail inequalities, including Bennett-type and Bernstein-type inequalities. This allows us to further bound the expectation of the spectral norm of a matrix i.d. series. Moreover, by developing a new lower-bound function for $Q(s)=(s+1)\log(s+1)-s$ that appears in the Bennett-type inequality, we derive a tighter tail inequality of the largest eigenvalue of the matrix i.d. series than the Bernstein-type inequality when the matrix dimension is high. The resulting lower-bound function is of independent interest and can improve any Bennett-type concentration inequality that involves the function $Q(s)$. The class of i.d. probability distributions is large and includes Gaussian and Poisson distributions, among many others. Therefore, our results encompass the existing work \cite{tropp2012user} on matrix Gaussian series as a special case. Lastly, we show that the tail inequalities of a matrix i.d. series have applications in several optimization problems including the chance constrained optimization problem and the quadratic optimization problem with orthogonality constraints.Comment: Comments Welcome

RNTrajRec: Road Network Enhanced Trajectory Recovery with Spatial-Temporal Transformer

GPS trajectories are the essential foundations for many trajectory-based applications, such as travel time estimation, traffic prediction and trajectory similarity measurement. Most applications require a large amount of high sample rate trajectories to achieve a good performance. However, many real-life trajectories are collected with low sample rate due to energy concern or other constraints.We study the task of trajectory recovery in this paper as a means for increasing the sample rate of low sample trajectories. Currently, most existing works on trajectory recovery follow a sequence-to-sequence diagram, with an encoder to encode a trajectory and a decoder to recover real GPS points in the trajectory. However, these works ignore the topology of road network and only use grid information or raw GPS points as input. Therefore, the encoder model is not able to capture rich spatial information of the GPS points along the trajectory, making the prediction less accurate and lack spatial consistency. In this paper, we propose a road network enhanced transformer-based framework, namely RNTrajRec, for trajectory recovery. RNTrajRec first uses a graph model, namely GridGNN, to learn the embedding features of each road segment. It next develops a spatial-temporal transformer model, namely GPSFormer, to learn rich spatial and temporal features along with a Sub-Graph Generation module to capture the spatial features for each GPS point in the trajectory. It finally forwards the outputs of encoder model into a multi-task decoder model to recover the missing GPS points. Extensive experiments based on three large-scale real-life trajectory datasets confirm the effectiveness of our approach

miRDis: a Web tool for endogenous and exogenous microRNA discovery based on deep-sequencing data analysis

Small RNA sequencing is the most widely used tool for microRNA (miRNA) discovery, and shows great potential for the efficient study of miRNA cross-species transport, i.e., by detecting the presence of exogenous miRNA sequences in the host species. Because of the increased appreciation of dietary miRNAs and their far-reaching implication in human health, research interests are currently growing with regard to exogenous miRNAs bioavailability, mechanisms of cross-species transport and miRNA function in cellular biological processes. In this article, we present microRNA Discovery (miRDis), a new small RNA sequencing data analysis pipeline for both endogenous and exogenous miRNA detection. Specifically, we developed and deployed a Web service that supports the annotation and expression profiling data of known host miRNAs and the detection of novel miRNAs, other noncoding RNAs, and the exogenous miRNAs from dietary species. As a proofof- concept, we analyzed a set of human plasma sequencing data from a milk-feeding study where 225 human miRNAs were detected in the plasma samples and 44 show elevated expression after milk intake. By examining the bovine-specific sequences, data indicate that three bovine miRNAs (bta-miR-378, -181* and -150) are present in human plasma possibly because of the dietary uptake. Further evaluation based on different sets of public data demonstrates that miRDis outperforms other state-of-the-art tools in both detection and quantification of miRNA from either animal or plant sources. The miRDis Web server is available at: http://sbbi.unl.edu/miRDis/index.php

Trajectory similarity learning with auxiliary supervision and optimal matching

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