Optimality of Graphlet Screening in High Dimensional Variable Selection

Consider a linear regression model where the design matrix X has n rows and p columns. We assume (a) p is much large than n, (b) the coefficient vector beta is sparse in the sense that only a small fraction of its coordinates is nonzero, and (c) the Gram matrix G = X'X is sparse in the sense that each row has relatively few large coordinates (diagonals of G are normalized to 1). The sparsity in G naturally induces the sparsity of the so-called graph of strong dependence (GOSD). We find an interesting interplay between the signal sparsity and the graph sparsity, which ensures that in a broad context, the set of true signals decompose into many different small-size components of GOSD, where different components are disconnected. We propose Graphlet Screening (GS) as a new approach to variable selection, which is a two-stage Screen and Clean method. The key methodological innovation of GS is to use GOSD to guide both the screening and cleaning. Compared to m-variate brute-forth screening that has a computational cost of p^m, the GS only has a computational cost of p (up to some multi-log(p) factors) in screening. We measure the performance of any variable selection procedure by the minimax Hamming distance. We show that in a very broad class of situations, GS achieves the optimal rate of convergence in terms of the Hamming distance. Somewhat surprisingly, the well-known procedures subset selection and the lasso are rate non-optimal, even in very simple settings and even when their tuning parameters are ideally set

Functional renormalization group study of the Quark-Meson model with ω\omega meson

We study the phase diagram of two-flavor massless QCD at finite baryon density by applying the functional renormalization group (FRG) for a quark-meson model with $\sigma, \pi$, and $\omega$ mesons. The dynamical fluctuations of quarks, $\sigma$, and $\pi$ are included into the flow equations, while the amplitudes of $\omega$-fields are also allowed to fluctuate. At high temperature the effects of the $\omega$-field on the phase boundary are qualitatively similar to the mean-field calculations; the phase boundary is shifted to the higher chemical potential region. As the temperature is lowered, however, the transition line bends back to the lower chemical potential region, irrespective to the strength of the vector coupling. In our FRG calculations, the driving force of the low temperature first order line is the fluctuations rather the quark density, and the effects of $\omega$-fields have little impact. At low temperature, the effective potential at small $\sigma$ field is very sensitive to the infrared cutoff scale, and this significantly affects our determination of the phase boundaries. The critical chemical potential at the tricritical point is affected by the $\omega$-field effects but its critical temperature stays around the similar value. Some caveats are given in interpreting our model results.Comment: 10 pages, 11 figure

Lasso adjustments of treatment effect estimates in randomized experiments

We provide a principled way for investigators to analyze randomized experiments when the number of covariates is large. Investigators often use linear multivariate regression to analyze randomized experiments instead of simply reporting the difference of means between treatment and control groups. Their aim is to reduce the variance of the estimated treatment effect by adjusting for covariates. If there are a large number of covariates relative to the number of observations, regression may perform poorly because of overfitting. In such cases, the Lasso may be helpful. We study the resulting Lasso-based treatment effect estimator under the Neyman-Rubin model of randomized experiments. We present theoretical conditions that guarantee that the estimator is more efficient than the simple difference-of-means estimator, and we provide a conservative estimator of the asymptotic variance, which can yield tighter confidence intervals than the difference-of-means estimator. Simulation and data examples show that Lasso-based adjustment can be advantageous even when the number of covariates is less than the number of observations. Specifically, a variant using Lasso for selection and OLS for estimation performs particularly well, and it chooses a smoothing parameter based on combined performance of Lasso and OLS

Iterative detection and decoding for SCMA systems with LDPC codes

Sparse code multiple access (SCMA) is a promising multiplexing approach to achieve high system capacity. In this paper, we develop a novel iterative detection and decoding scheme for SCMA systems combined with Low-density Parity-check (LDPC) decoding. In particular, we decompose the output of the message passing algorithm (MPA) based SCMA multiuser detection into intrinsic part and prior part. Then we design a joint detection and decoding scheme which iteratively exchanges the intrinsic information between the detector and the decoder, yielding a satisfied performance gain. Moreover, the proposed scheme has almost the same complexity compared to the traditional receiver for LDPC-coded SCMA systems. As numerical results demonstrate, the proposed scheme has a substantial gain over the traditional SCMA receiver on AWGN channels and Rayleigh fading channels

Enhanced optical Kerr nonlinearity of graphene/Si hybrid waveguide

In this work, we experimentally study the optical kerr nonlinearities of graphene/Si hybrid waveguides with enhanced self-phase modulation. In the case of CMOS compatible materials for nonlinear optical signal processing, Si and silicon nitride waveguides have been extensively investigated over the past decade. However, Si waveguides exhibit strong two-photon absorption (TPA) at telecommunication wavelengths, which lead to a significant reduction of nonlinear figure of merit. In contrast, silicon nitride based material system usually suppress the TPA, but simultaneously leads to the reduction of the Kerr nonlinearity by two orders of magnitude. Here, we introduce a graphene/Si hybrid waveguide, which remain the optical properties and CMOS compatibility of Si waveguides, while enhance the Kerr nonlinearity by transferring patterned graphene over the top of the waveguides. The graphene/Si waveguides are measured with a nonlinear parameter of 510 W-1m-1. Enhanced nonlinear figure-of-merit (FOM) of 2.48 has been achieved, which is three times higher than that of the Si waveguide. This work reveals the potential application of graphene/Si hybrid photonic waveguides with high Kerr nonlinearity and FOM for nonlinear all-optical signal processing.Comment: 11pages, 6 figures, journal articl

Anomalous gauge couplings of the Higgs boson at the CERN LHC: Semileptonic mode in WW scatterings

We make a full tree level study of the signatures of anomalous gauge couplings of the Higgs boson at the CERN LHC via the semileptonic decay mode in WW scatterings. Both signals and backgrounds are studied at the hadron level for the Higgs mass in the range 115 GeV to 200 GeV. We carefully impose suitable kinematical cuts for suppressing the backgrounds. To the same sensitivity as in the pure leptonic mode, our result shows that the semileptonic mode can reduce the required integrated luminosity by a factor of 3. If the anomalous couplings in nature are actually larger than the sensitivity bounds shown in the text, the experiment can start the test for an integrated luminosity of 50 inverse fb.Comment: PACS numbers updated. Version published in Phys.Rev.D79,055010(2009

Traffic-Aware Transmission Mode Selection in D2D-enabled Cellular Networks with Token System

We consider a D2D-enabled cellular network where user equipments (UEs) owned by rational users are incentivized to form D2D pairs using tokens. They exchange tokens electronically to "buy" and "sell" D2D services. Meanwhile the devices have the ability to choose the transmission mode, i.e. receiving data via cellular links or D2D links. Thus taking the different benefits brought by diverse traffic types as a prior, the UEs can utilize their tokens more efficiently via transmission mode selection. In this paper, the optimal transmission mode selection strategy as well as token collection policy are investigated to maximize the long-term utility in the dynamic network environment. The optimal policy is proved to be a threshold strategy, and the thresholds have a monotonicity property. Numerical simulations verify our observations and the gain from transmission mode selection is observed.Comment: 7 pages, 6 figures. A shorter version is submitted to EUSIPC

A Novel Aptamer LL4A Specifically Targets Vemurafenib-Resistant Melanoma through Binding to the CD63 Protein.

Melanoma is a highly aggressive tumor with a poor prognosis, and half of all melanoma patients harbor BRAF mutations. A BRAF inhibitor, vemurafenib (PLX4032), has been approved by the US Food and Drug Administration (FDA) and European Medicines Agency (EMA) to treat advanced melanoma patients with BRAFV600E mutation. However, the efficacy of vemurafenib is impeded by adaptive resistance in almost all patients. In this study, using a cell-based SELEX (systematic evolution of ligands by exponential enrichment) strategy, we obtained a DNA aptamer (named LL4) with high affinity and specificity against vemurafenib-resistant melanoma cells. Optimized truncated form (LL4A) specifically binds to vemurafenib-resistant melanoma cells with dissociation constants in the nanomolar range and with excellent stability and low toxicity. Meanwhile, fluorescence imaging confirmed that LL4A significantly accumulated in tumors formed by vemurafenib-resistant melanoma cells, but not in control tumors formed by their corresponding parental cells in vivo. Further, a transmembrane protein CD63 was identified as the binding target of aptamer LL4A using a pull-down assay combined with the liquid chromatography-tandem mass spectrometry (LC-MS/MS) method. CD63 formed a supramolecular complex with TIMP1 and β1-integrin, activated the nuclear factor кB (NF-кB) and mitogen-activated protein kinase (MAPK) signaling pathways, and contributed to vemurafenib resistance. Potentially, the aptamer LL4A may be used diagnostically and therapeutically in humans to treat targeted vemurafenib-resistant melanoma