Estimation of Markov Chain via Rank-Constrained Likelihood

This paper studies the estimation of low-rank Markov chains from empirical trajectories. We propose a non-convex estimator based on rank-constrained likelihood maximization. Statistical upper bounds are provided for the Kullback-Leiber divergence and the $\ell_2$ risk between the estimator and the true transition matrix. The estimator reveals a compressed state space of the Markov chain. We also develop a novel DC (difference of convex function) programming algorithm to tackle the rank-constrained non-smooth optimization problem. Convergence results are established. Experiments show that the proposed estimator achieves better empirical performance than other popular approaches.Comment: Accepted at ICML 201

Exact Clustering in Tensor Block Model: Statistical Optimality and Computational Limit

High-order clustering aims to identify heterogeneous substructures in multiway datasets that arise commonly in neuroimaging, genomics, social network studies, etc. The non-convex and discontinuous nature of this problem pose significant challenges in both statistics and computation. In this paper, we propose a tensor block model and the computationally efficient methods, \emph{high-order Lloyd algorithm} (HLloyd), and \emph{high-order spectral clustering} (HSC), for high-order clustering. The convergence guarantees and statistical optimality are established for the proposed procedure under a mild sub-Gaussian noise assumption. Under the Gaussian tensor block model, we completely characterize the statistical-computational trade-off for achieving high-order exact clustering based on three different signal-to-noise ratio regimes. The analysis relies on new techniques of high-order spectral perturbation analysis and a "singular-value-gap-free" error bound in tensor estimation, which are substantially different from the matrix spectral analyses in the literature. Finally, we show the merits of the proposed procedures via extensive experiments on both synthetic and real datasets.Comment: 65 page

Characterization of fibroblast growth factor 1 in obese children and adolescents

Background: Fibroblast growth factor 1 (FGF1) can regulate glucose and lipid metabolism in obese mice. Serum FGF1 has increased in type 2 diabetes mellitus adults and correlated with BMI. This study aimed to indicate conventional weight loss effects on FGF1 in obese children and adolescents. Materials and methods: Clinical and metabolic parameters of 88 lean and obese individuals (ages 5–15 years) and 39 obese individuals followed with 6 months of lifestyle intervention were collected. Serum FGF1 levels were detected through enzyme-linked immunosorbent assays. Results: FGF1 levels were increased in obese individuals. Serum FGF1 levels were significantly correlated with BMI and waist circumferences (r = 0.377, P = 0.012; r = 0.301, P = 0.047, respectively). Multivariate stepwise linear regression analyses showed that FGF1 levels were significantly correlated with HbA1c and HOMA-IR (β = 0.371, P = 0.008; β = 0.323, P = 0.021, respectively). Weight loss (2.3 ± 0.1 kg) was accompanied by a significant reduction of circulating FGF1 levels (7.2 ± 0.4 pg/mL). Changes in FGF1 were significantly correlated with changes in fasting glucose, HOMA-IR and low-density lipoprotein cholesterol (β = 0.277, P = 0.020; β = 0.474, P < 0.001; β = 0.320, P = 0.008, respectively). Conclusion: FGF1 was related to increased risk of insulin resistance in obese children and adolescents. Serum FGF1 reduced after weight loss in obese individuals and was associated with the improvement of insulin resistance. Changes in serum FGF1 were more correlated with insulin resistance than changes in obesity per se

Population structure and genetic diversity of native and invasive populations of Solanum rostratum (Solanaceae)

Aims: We investigate native and introduced populations of Solanum rostratum, an annual, self-compatible plant that has been introduced around the globe. This study is the first to compare the genetic diversity of Solanum rostratum between native and introduced populations. We aim to (1) determine the level of genetic diversity across the studied regions; (2) explore the likely origins of invasive populations in China; and (3) investigate whether there is the evidence of multiple introductions into China. Methods: We genotyped 329 individuals at 10 microsatellite loci to determine the levels of genetic diversity and to investigate population structure of native and introduced populations of S. rostratum. We studied five populations in each of three regions across two continents: Mexico, the U.S.A. and China. Important Findings: We found the highest genetic diversity among Mexican populations of S. rostratum. Genetic diversity was significantly lower in Chinese and U.S.A. populations, but we found no regional difference in inbreeding coefficients (FIS) or population differentiation (FST). Population structure analyses indicate that Chinese and U.S.A. populations are more closely related to each other than to sampled Mexican populations, revealing that introduced populations in China share an origin with the sampled U.S.A. populations. The distinctiveness between some introduced populations indicates multiple introductions of S. rostratum into China

Design and Analysis of Microchannels for Heat Dissipation of High-Energy VCSELs Based on Laser 3D Printing

For the problem of high waste heat in the active area of high-power VCSEL arrays and the difficulty of heat dissipation, we took advantage of laser 3D printing technology and combined it with the relevant principles of fluid-structure coupling, three kinds of microchannel heat sink with different structures of pin-fin, honeycomb, and double-layer reflow were designed. The heat dissipation capacity of three kinds of heat sinks to the heat flux density 200 W/cm2 VCSEL array and the influence of the key characteristics of the microchannel on the heat dissipation capacity was studied. The results show that the double-layer reflow microchannel heat sink has the strongest heat dissipation capability, with the minimum thermal resistance value of 0.258 °C/W when the microchannel diameter and the cooling mass flow rate were 0.5 mm and 24 L/h, respectively. The inner wall roughness of the pure copper microchannel prepared by 3D printing technology was 7.08 μm, and the heat sink thermal resistance was reduced by 0.7% compared with the smooth channel wall. The deviation of the microchannel diameter from the design size (500 μm) was −10 μm, and the heat sink thermal resistance was reduced by 0.8% compared to the theoretical value, which shows that the surface roughness and size deviation of the 3D printed microchannel had beneficial effect on enhancing heat dissipation. The actual thermal conductivity of the 3D printed pure copper after heat treatment was 310.4 W/m-K, at which point the thermal resistance was 0.306 °C/W, and the maximum temperature was 35.3 °C, which satisfied the operating temperature range of the chip. This study provides a theoretical basis and implementation method for the fabrication of heat sinks for high-energy VCSEL arrays using laser 3D printing technology

On the Use of EBSD and Microhardness to Study the Microstructure Properties of Tungsten Samples Prepared by Selective Laser Melting

Additively manufactured tungsten and its alloys have been widely used for plasma facing components (PFCs) in future nuclear fusion reactors. Under the fusion process, PFCs experience a high-temperature exposure, which will ultimately affect the microstructural features, keeping in mind the importance of microstructures. In this study, microhardness and electron backscatter diffraction (EBSD) techniques were used to study the specimens. Vickers hardness method was used to study tungsten under different parameters. EBSD technique was used to study the microstructure and Kikuchi pattern of samples under different orientations. We mainly focused on selective laser melting (SLM) parameters and the effects of these parameters on the results of different techniques used to study the behavior of samples