SDPNAL+: A Matlab software for semidefinite programming with bound constraints (version 1.0)

SDPNAL+ is a {\sc Matlab} software package that implements an augmented Lagrangian based method to solve large scale semidefinite programming problems with bound constraints. The implementation was initially based on a majorized semismooth Newton-CG augmented Lagrangian method, here we designed it within an inexact symmetric Gauss-Seidel based semi-proximal ADMM/ALM (alternating direction method of multipliers/augmented Lagrangian method) framework for the purpose of deriving simpler stopping conditions and closing the gap between the practical implementation of the algorithm and the theoretical algorithm. The basic code is written in {\sc Matlab}, but some subroutines in C language are incorporated via Mex files. We also design a convenient interface for users to input their SDP models into the solver. Numerous problems arising from combinatorial optimization and binary integer quadratic programming problems have been tested to evaluate the performance of the solver. Extensive numerical experiments conducted in [Yang, Sun, and Toh, Mathematical Programming Computation, 7 (2015), pp. 331--366] show that the proposed method is quite efficient and robust, in that it is able to solve 98.9\% of the 745 test instances of SDP problems arising from various applications to the accuracy of $10^{-6}$ in the relative KKT residual

FarmTest: Factor-Adjusted Robust Multiple Testing with Approximate False Discovery Control

Large-scale multiple testing with correlated and heavy-tailed data arises in a wide range of research areas from genomics, medical imaging to finance. Conventional methods for estimating the false discovery proportion (FDP) often ignore the effect of heavy-tailedness and the dependence structure among test statistics, and thus may lead to inefficient or even inconsistent estimation. Also, the commonly imposed joint normality assumption is arguably too stringent for many applications. To address these challenges, in this paper we propose a Factor-Adjusted Robust Multiple Testing (FarmTest) procedure for large-scale simultaneous inference with control of the false discovery proportion. We demonstrate that robust factor adjustments are extremely important in both controlling the FDP and improving the power. We identify general conditions under which the proposed method produces consistent estimate of the FDP. As a byproduct that is of independent interest, we establish an exponential-type deviation inequality for a robust $U$-type covariance estimator under the spectral norm. Extensive numerical experiments demonstrate the advantage of the proposed method over several state-of-the-art methods especially when the data are generated from heavy-tailed distributions. The proposed procedures are implemented in the R-package FarmTest.Comment: 52 pages, 9 figure

User-Friendly Covariance Estimation for Heavy-Tailed Distributions

We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we introduce element-wise and spectrum-wise truncation operators, as well as their $M$-estimator counterparts, to robustify the sample covariance matrix. Different from the classical notion of robustness that is characterized by the breakdown property, we focus on the tail robustness which is evidenced by the connection between nonasymptotic deviation and confidence level. The key observation is that the estimators needs to adapt to the sample size, dimensionality of the data and the noise level to achieve optimal tradeoff between bias and robustness. Furthermore, to facilitate their practical use, we propose data-driven procedures that automatically calibrate the tuning parameters. We demonstrate their applications to a series of structured models in high dimensions, including the bandable and low-rank covariance matrices and sparse precision matrices. Numerical studies lend strong support to the proposed methods.Comment: 56 pages, 2 figure

EUCLIA - Exploring the UV/optical continuum lag in active galactic nuclei. I. a model without light echoing

The tight inter-band correlation and the lag-wavelength relation among UV/optical continua of active galactic nuclei have been firmly established. They are usually understood within the widespread reprocessing scenario, however, the implied inter-band lags are generally too small. Furthermore, it is challenged by new evidences, such as the X-ray reprocessing yields too much high frequency UV/optical variations as well as it fails to reproduce the observed timescale-dependent color variations among {\it Swift} lightcurves of NGC 5548. In a different manner, we demonstrate that an upgraded inhomogeneous accretion disk model, whose local {\it independent} temperature fluctuations are subject to a speculated {\it common} large-scale temperature fluctuation, can intrinsically generate the tight inter-band correlation and lag across UV/optical, and be in nice agreement with several observational properties of NGC 5548, including the timescale-dependent color variation. The emergent lag is a result of the {\it differential regression capability} of local temperature fluctuations when responding to the large-scale fluctuation. An average speed of propagations as large as $\gtrsim 15\%$ of the speed of light may be required by this common fluctuation. Several potential physical mechanisms for such propagations are discussed. Our interesting phenomenological scenario may shed new light on comprehending the UV/optical continuum variations of active galactic nuclei.Comment: 18 pages, 8 figures. ApJ accepted. Further comments are very welcome

Multi-wavelength study of the supernova remnant Kes 79 (G33.6+0.1): On its supernova properties and expansion into a molecular environment

Kes 79 (G33.6+0.1) is an aspherical thermal composite supernova remnant (SNR) observed across the electromagnetic spectrum and showing an unusual highly-structured morphology, in addition to harboring a central compact object (CCO). Using the CO J=1-0, J=2-1, and J=3-2 data, we provide the first direct evidence and new morphological evidence to support the physical interaction between the SNR and the molecular cloud at $V_LSR\sim 105$ km s$^{-1}$. We revisit the 380 ks XMM-Newton observations and perform a dedicated spatially resolved X-ray spectroscopic study with careful background subtraction. The overall X-ray-emitting gas is characterized by an under-ionized ($\tau_c \sim 6\times 10^{11}$ cm^${-3}$) cool ($kT_c \approx 0.20$ keV) plasma with solar abundances, plus an under-ionized ($\tau_h\sim 8\times 10^{10}$ cm$^{-3}$) hot ($kT_h\approx 0.80$ keV) plasma with elevated Ne, Mg, Si, S and Ar abundances. Kes 79 appears to have a double-hemisphere morphology viewed along the symmetric axis. Projection effect can explain the multiple shell structures and the thermal composite morphology. The X-ray filaments, spatially correlated with the 24 um IR filaments, are suggested to be due to the SNR shock interaction with dense gas, while the halo forms from SNR breaking out into a tenuous medium. The high-velocity, hot ($kT_h\sim 1.4$--1.6 keV) ejecta patch with high metal abundances, together with the non-uniform metal distribution across the SNR, indicating an asymmetric SN explosion of Kes 79. We refine the Sedov age to 4.4--6.7 kyr and the mean shock velocity to 730 km s$^{-1}$. Our multi-wavelength study suggests a progenitor mass of $\sim 15$--20 solar masses for the core-collapse explosion that formed Kes 79 and its CCO, PSR J1852+0040.Comment: 17 pages, 12 figures, 3 tables, published in Ap

Theoretical and computational advances in nonlinear dynamical systems 2018

Peer reviewedPublisher PD

mmHawkeye: Passive UAV Detection with a COTS mmWave Radar

Small Unmanned Aerial Vehicles (UAVs) are becoming potential threats to security-sensitive areas and personal privacy. A UAV can shoot photos at height, but how to detect such an uninvited intruder is an open problem. This paper presents mmHawkeye, a passive approach for UAV detection with a COTS millimeter wave (mmWave) radar. mmHawkeye doesn't require prior knowledge of the type, motions, and flight trajectory of the UAV, while exploiting the signal feature induced by the UAV's periodic micro-motion (PMM) for long-range accurate detection. The design is therefore effective in dealing with low-SNR and uncertain reflected signals from the UAV. mmHawkeye can further track the UAV's position with dynamic programming and particle filtering, and identify it with a Long Short-Term Memory (LSTM) based detector. We implement mmHawkeye on a commercial mmWave radar and evaluate its performance under varied settings. The experimental results show that mmHawkeye has a detection accuracy of 95.8% and can realize detection at a range up to 80m.Comment: 9 pages, 14 figures, IEEE SECON202

(2′-Amino-4,4′-bi-1,3-thia­zol-2-aminium-κ2 N,N′)aqua­[citrato(4−)-κ3 O,O′,O′′)chromium(III) dihydrate

In the title compound, [Cr(C6H7N4S2)(C6H4O7)(H2O)]·2H2O, the CrIII atom is in a distorted octa­hedral environment, coordinated by one water mol­ecule, two N atoms from a protonated diamino­bithia­zole ligand and three O atoms from a citrate(4−) anion. The complex is zwitterionic, with the H atom from the uncoordinated carboxyl­ate group of the citrate anion transferred to one amino group of the diamino­bithia­zole ligand. O—H⋯O and N—H⋯O hydrogen bonds link the complexes into layers including the two uncoordinated water mol­ecules

Expression of the apoptosis-related genes BCL-2 and BAD in human breast carcinoma and their associated relationship with chemosensitivity

<p>Abstract</p> <p>Objective</p> <p>To evaluate the expression of BCL-2 and BAD genes in tissues of breast carcinoma and investigate the relationship between the expression of BCL-2 and BAD in breast cancer cells with chemosensitivity.</p> <p>Methods</p> <p>Immunohistochemical technique was used to detect the expression of BCL-2, BAD in 10 normal breast tissues, 10 breast fibroadenoma tissues, 40 youth human breast carcinoma tissues, 40 menopause human breast carcinoma tissues. And to detect the expression of ER, PR in 80 human breast carcinoma tissues. 20 Surgical samples of breast cancer, diagnosed by pathology, were obtained from The First Affiliated Hospital of Chongqing Medical University. The cancer sample cells were cultured separately in the incubator at 37°C, 5% CO₂in vitro. The rate of inhibition of cancer cells in 4 kinds of anticancer drugs-- Epirubicin Adriamycin (EADM),5-Fluorouracil (5-Fu), Navelbine(NVB) and Diaminedichloroplatinum (DDP), were assayed by MTT method.</p> <p>Results</p> <p>The expression of BCL-2, BAD genes in young human breast carcinoma tissues were lower than that in menopause human breast carcinoma tissues (<b><it>P </it>< 0.05</b>). There was a negative correlation between the positive expression rate of BCL-2 and histologic grade or the lymph node metastasis (<b><it>P </it>< 0.05</b>). There was a positive correlation between the expression rates of BCL-2 and of ER, PR (<b><it>P </it>< 0.05</b>). The expression of BAD had no relationship with the expression of ER, PR, histologic grade and the lymph node metastasis(<b><it>P </it>= <it>NS</it></b>). Sensitivity rates of 20 breast cancer cells in 0.1 × PPC within 48 h in vitro were 30% EADM,20% 5-Fu,45% NVB and 25% DDP. Respectively, the rate of inhibition of EADM,5- Fu, NVB and DDP were significantly higher in the BCL-2 negative cancer cells than in the BCL-2 positive cancer cells. A negative correlation was found between expression of BCL-2 and chemosensitivity for all the 4 anticancer drugs. The inhibition rates of EADM and NVB were significantly lower in the BAD negative cancer cells than in the BAD positive cancer cells. A positive correlation was found between expression of BAD and chemosensitivity for Epirubicin.</p> <p>Conclusion</p> <p>The expression of BCL-2 and BAD can be used as prognosis factors of breast cancer. Detection of the BCL-2 protein expression level, particularly, combined with the detection of the expression of BCL-2 and BAD as well as ER and PR were helpful in confirming the prognosis of breast carcinoma. The combined detection of BCL-2 and BAD may be markers for predicting the responses to anticancer drugs.</p