Optimized Dimensionality Reduction for Moment-based Distributionally Robust Optimization

Moment-based distributionally robust optimization (DRO) provides an optimization framework to integrate statistical information with traditional optimization approaches. Under this framework, one assumes that the underlying joint distribution of random parameters runs in a distributional ambiguity set constructed by moment information and makes decisions against the worst-case distribution within the set. Although most moment-based DRO problems can be reformulated as semidefinite programming (SDP) problems that can be solved in polynomial time, solving high-dimensional SDPs is still time-consuming. Unlike existing approximation approaches that first reduce the dimensionality of random parameters and then solve the approximated SDPs, we propose an optimized dimensionality reduction (ODR) approach. We first show that the ranks of the matrices in the SDP reformulations are small, by which we are then motivated to integrate the dimensionality reduction of random parameters with the subsequent optimization problems. Such integration enables two outer and one inner approximations of the original problem, all of which are low-dimensional SDPs that can be solved efficiently. More importantly, these approximations can theoretically achieve the optimal value of the original high-dimensional SDPs. As these approximations are nonconvex SDPs, we develop modified Alternating Direction Method of Multipliers (ADMM) algorithms to solve them efficiently. We demonstrate the effectiveness of our proposed ODR approach and algorithm in solving two practical problems. Numerical results show significant advantages of our approach on the computational time and solution quality over the three best possible benchmark approaches. Our approach can obtain an optimal or near-optimal (mostly within 0.1%) solution and reduce the computational time by up to three orders of magnitude

The Mesozoic magmatic, metamorphic, and tectonic evolution of the eastern Gangdese magmatic arc, southern Tibet

Magmatic arcs are natural laboratories for studying the growth of continental crusts. The Gangdese arc, southern Tibet, is an archetypal continental magmatic arc that formed due to Mesozoic subduction of the Neo-Tethyan oceanic lithosphere; however, its formation and evolution remain controversial. In this contribution, we combine newly reported and previously published geochemical and geochronological data for Mesozoic magmatic rocks in the eastern Gangdese arc to reveal its magmatic and metamorphic histories and review its growth, thickening, and fractionation and mineralization processes. Our results show that: (1) the Gangdese arc consists of multiple Mesozoic arc-type magmatic rocks and records voluminous juvenile crustal growth. (2) The Mesozoic magmatic rocks experienced Late Cretaceous granulite-facies metamorphism and partial melting, thus producing hydrous and metallogenic element-rich migmatites that form a major component of the lower arc crust and are a potential source for the Miocene ore-hosting porphyries. (3) The Gangdese arc witnessed crustal thickening and reworking during the Middle to Late Jurassic and Late Cretaceous. (4) Crystallization-fractionation of mantle-derived magmas and partial melting of thickened juvenile lower crust induced intracrustal chemical differentiation during subduction. We suggest that the Gangdese arc underwent the following main tectonic, magmatic, and metamorphic evolution processes: normal subduction and associated mantle-derived magmatism during the Late Triassic to Jurassic; shallow subduction during the Early Cretaceous and an associated magmatic lull; and mid-oceanic ridge subduction, high-temperature metamorphism and an associated magmatic flare-up during the early Late Cretaceous, and flat subduction, high-temperature and high-pressure metamorphism, partial melting, and associated crust-derived magmatism during the late Late Cretaceous. Key issues for further research include the temporal and spatial distributions of Mesozoic magmatic rocks, the evolution of the components and compositions of arc crust over time, and the metallogenic processes that occur in such environments during subduction

Epitaxial growth of Cu on Cu(001): experiments and simulations

A quantitative comparison between experimental and Monte Carlo simulation results for the epitaxial growth of Cu/Cu(001) in the submonolayer regime is presented. The simulations take into account a complete set of hopping processes whose activation energies are derived from semi-empirical calculations using the embedded-atom method. The island separation is measured as a function of the incoming flux and the temperature. A good quantitative agreement between the experiment and simulation is found for the island separation, the activation energies for the dominant processes, and the exponents that characterize the growth. The simulation results are then analyzed at lower coverages, which are not accessible experimentally, providing good agreement with theoretical predictions as well.Comment: Latex document. 7 pages. 3 embedded figures in separate PS files. One bbl fil

Common susceptibility variants are shared between schizophrenia and psoriasis in the Han Chinese population

Previous studies have shown that individuals with schizophrenia have a greater risk for psoriasis than a typical person. This suggests that there might be a shared genetic etiology between the 2 conditions. We aimed to characterize the potential shared genetic susceptibility between schizophrenia and psoriasis using genome-wide marker genotype data

The application of radiomics in esophageal cancer: Predicting the response after neoadjuvant therapy

Esophageal cancer (EC) is one of the fatal malignant neoplasms worldwide. Neoadjuvant therapy (NAT) combined with surgery has become the standard treatment for locally advanced EC. However, the treatment efficacy for patients with EC who received NAT varies from patient to patient. Currently, the evaluation of efficacy after NAT for EC lacks accurate and uniform criteria. Radiomics is a multi-parameter quantitative approach for developing medical imaging in the era of precision medicine and has provided a novel view of medical images. As a non-invasive image analysis method, radiomics is an inevitable trend in NAT efficacy prediction and prognosis classification of EC by analyzing the high-throughput imaging features of lesions extracted from medical images. In this literature review, we discuss the definition and workflow of radiomics, the advances in efficacy prediction after NAT, and the current application of radiomics for predicting efficacy after NAT

Study of J/ψ→ppˉJ/\psi\to p\bar{p} and J/ψ→nnˉJ/\psi\to n\bar{n}

The decays $J/\psi\to p\bar{p}$ and $J/\psi\to n\bar{n}$ have been investigated with a sample of 225.2 million $J/\psi$ events collected with the BESIII detector at the BEPCII $e^+e^-$ collider. The branching fractions are determined to be $\mathcal{B}(J/\psi\to p\bar{p})=(2.112\pm0.004\pm0.031)\times10^{-3}$ and $\mathcal{B}(J/\psi\to n\bar{n})=(2.07\pm0.01\pm0.17)\times10^{-3}$. Distributions of the angle $\theta$ between the proton or anti-neutron and the beam direction are well described by the form $1+\alpha\cos^2\theta$, and we find $\alpha=0.595\pm0.012\pm0.015$ for $J/\psi\to p\bar{p}$ and $\alpha=0.50\pm0.04\pm0.21$ for $J/\psi\to n\bar{n}$. Our branching-fraction results suggest a large phase angle between the strong and electromagnetic amplitudes describing the $J/\psi\to N\bar{N}$ decay.Comment: 16 pages, 13 figures, the 2nd version, submitted to PR

First observation of the M1 transition ψ(3686)→γηc(2S)\psi(3686)\to \gamma\eta_c(2S)

Using a sample of 106 million \psi(3686) events collected with the BESIII detector at the BEPCII storage ring, we have made the first measurement of the M1 transition between the radially excited charmonium S-wave spin-triplet and the radially excited S-wave spin-singlet states: \psi(3686)\to\gamma\eta_c(2S). Analyses of the processes \psi(2S)\to \gamma\eta_c(2S) with \eta_c(2S)\to \K_S^0 K\pi and K^+K^-\pi^0 gave an \eta_c(2S) signal with a statistical significance of greater than 10 standard deviations under a wide range of assumptions about the signal and background properties. The data are used to obtain measurements of the \eta_c(2S) mass (M(\eta_c(2S))=3637.6\pm 2.9_\mathrm{stat}\pm 1.6_\mathrm{sys} MeV/c^2), width (\Gamma(\eta_c(2S))=16.9\pm 6.4_\mathrm{stat}\pm 4.8_\mathrm{sys} MeV), and the product branching fraction (\BR(\psi(3686)\to \gamma\eta_c(2S))\times \BR(\eta_c(2S)\to K\bar K\pi) = (1.30\pm 0.20_\mathrm{stat}\pm 0.30_\mathrm{sys})\times 10^{-5}). Combining our result with a BaBar measurement of \BR(\eta_c(2S)\to K\bar K \pi), we find the branching fraction of the M1 transition to be \BR(\psi(3686)\to\gamma\eta_c(2S)) = (6.8\pm 1.1_\mathrm{stat}\pm 4.5_\mathrm{sys})\times 10^{-4}.Comment: 7 pages, 1 figure, 1 tabl

Two-photon widths of the χc0,2\chi_{c0, 2} states and helicity analysis for \chi_{c2}\ar\gamma\gamma}

Based on a data sample of 106 M $\psi^{\prime}$ events collected with the BESIII detector, the decays \psi^{\prime}\ar\gamma\chi_{c0, 2},\chi_{c0, 2}\ar\gamma\gamma are studied to determine the two-photon widths of the $\chi_{c0, 2}$ states. The two-photon decay branching fractions are determined to be {\cal B}(\chi_{c0}\ar\gamma\gamma) = (2.24\pm 0.19\pm 0.12\pm 0.08)\times 10^{-4} and {\cal B}(\chi_{c2}\ar\gamma\gamma) = (3.21\pm 0.18\pm 0.17\pm 0.13)\times 10^{-4}. From these, the two-photon widths are determined to be $\Gamma_{\gamma \gamma}(\chi_{c0}) = (2.33\pm0.20\pm0.13\pm0.17)$ keV, $\Gamma_{\gamma \gamma}(\chi_{c2}) = (0.63\pm0.04\pm0.04\pm0.04)$ keV, and $\cal R$ $=\Gamma_{\gamma \gamma}(\chi_{c2})/\Gamma_{\gamma \gamma}(\chi_{c0})=0.271\pm 0.029\pm 0.013\pm 0.027$, where the uncertainties are statistical, systematic, and those from the PDG {\cal B}(\psi^{\prime}\ar\gamma\chi_{c0,2}) and $\Gamma(\chi_{c0,2})$ errors, respectively. The ratio of the two-photon widths for helicity $\lambda=0$ and helicity $\lambda=2$ components in the decay \chi_{c2}\ar\gamma\gamma is measured for the first time to be $f_{0/2} =\Gamma^{\lambda=0}_{\gamma\gamma}(\chi_{c2})/\Gamma^{\lambda=2}_{\gamma\gamma}(\chi_{c2}) = 0.00\pm0.02\pm0.02$.Comment: 10 pages, 4 figure

Common susceptibility variants are shared between schizophrenia and psoriasis in the Han Chinese population

Background Previous studies have shown that individuals with schizophrenia have a greater risk for psoriasis than a typical person. This suggests that there might be a shared genetic etiology between the 2 conditions. We aimed to characterize the potential shared genetic susceptibility between schizophrenia and psoriasis using genome-wide marker genotype data. Methods We obtained genetic data on individuals with psoriasis, schizophrenia and control individuals. We applied a marker-based coheritability estimation procedure, polygenic score analysis, a gene set enrichment test and a least absolute shrinkage and selection operator regression model to estimate the potential shared genetic etiology between the 2 diseases. We validated the results in independent schizophrenia and psoriasis cohorts from Singapore. Results We included 1139 individuals with psoriasis, 744 with schizophrenia and 1678 controls in our analysis, and we validated the results in independent cohorts, including 441 individuals with psoriasis (and 2420 controls) and 1630 with schizophrenia (and 1860 controls). We estimated that a large fraction of schizophrenia and psoriasis risk could be attributed to common variants (h(SNP)(2) = 29% 5.0%, p = 2.00 x 10(-8)), with a coheritability estimate between the traits of 21%. We identified 5 variants within the human leukocyte antigen (HLA) gene region, which were most likely to be associated with both diseases and collectively conferred a significant risk effect (odds ratio of highest risk quartile = 6.03, p < 2.00 x 10(-16)). We discovered that variants contributing most to the shared heritable component between psoriasis and schizophrenia were enriched in antigen processing and cell endoplasmic reticulum. Limitations Our sample size was relatively small. The findings of 5 HLA gene variants were complicated by the complex structure in the HLA region. Conclusion We found evidence for a shared genetic etiology between schizophrenia and psoriasis. The mechanism for this shared genetic basis likely involves immune and calcium signalling pathways.National Natural Science Foundation of China [81370044, 81000692, 81273301, 81072461, 81130031, 81222022, 81222017]; China Council of Scholarship [201208340003]; Youth Project of the Outstanding Talents of Organization Department of the CPC Central Committee Program [31200939]; Pre-National Basic Research Program of China (973 Plan) [2012CB722404]; Anhui Province Natural Science Foundation [1208085QH145]; Anhui High Education Young Talent; Anhui Medical University [XJ201429]; NIH [1UL1TR001114, U19 AG023122-09, R01 DA030976-05, R01 MH094483-03, R01 AG035020-05, R01 MH100351-02, R21 AG045789-01A1]; Human Longevity, Inc.; Johnson and Johnson; Tanner Foundation; Stand-Up-to-Cancer organization; National Research Foundation Singapore under the National Medical Research Council Translational and Clinical Research Flagship Program [NMRC/TCR/003/2008]SCI(E)[email protected]; [email protected]