Optimal rates of convergence for covariance matrix estimation

Covariance matrix plays a central role in multivariate statistical analysis. Significant advances have been made recently on developing both theory and methodology for estimating large covariance matrices. However, a minimax theory has yet been developed. In this paper we establish the optimal rates of convergence for estimating the covariance matrix under both the operator norm and Frobenius norm. It is shown that optimal procedures under the two norms are different and consequently matrix estimation under the operator norm is fundamentally different from vector estimation. The minimax upper bound is obtained by constructing a special class of tapering estimators and by studying their risk properties. A key step in obtaining the optimal rate of convergence is the derivation of the minimax lower bound. The technical analysis requires new ideas that are quite different from those used in the more conventional function/sequence estimation problems.Comment: Published in at http://dx.doi.org/10.1214/09-AOS752 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Branching Ratios, Forward-backward Asymmetry and Angular Distributions of B→K1l+l−B\to K_1l^+l^- Decays

Using the $B\to K_1$ form factors evaluated in the perturbative QCD approach, we study semileptonic $B\to K_1(1270)l^+l^-$ and $B\to K_1(1400)l^+l^-$ decays, where $K_1(1270)$ and $K_1(1400)$ are mixtures of $K_{1A}$ and $K_{1B}$ which are $^3P_1$ and $^1P_1$ states, respectively. Using the technique of helicity amplitudes, we express the decay amplitudes in terms of several independent and Lorentz invariant pieces. We study the dilepton invariant mass distributions, branching ratios, polarizations and forward-backward asymmetries of $B\to K_1l^+l^-$ decays. The ambiguity in the sign of the mixing angle will induce much large differences to branching ratios of semileptonic B decays: branching ratios without resonant contributions either have the order of $10^{-6}$ or $10^{-8}$. But the polarizations and the forward-backward asymmetries are not sensitive to the mixing angles. We find that the resonant contributions will dramatically change the dilepton invariant mass distributions in the resonant region. We also provide the angular distributions of $B\to K_1l^+l^-\to (K\pi\pi)l^+l^-$ decays.Comment: 14 pages, 6 figures, version appears in PR

Observation of Landau level-like quantizations at 77 K along a strained-induced graphene ridge

Recent studies show that the electronic structures of graphene can be modified by strain and it was predicted that strain in graphene can induce peaks in the local density of states (LDOS) mimicking Landau levels (LLs) generated in the presence of a large magnetic field. Here we report scanning tunnelling spectroscopy (STS) observation of nine strain-induced peaks in LDOS at 77 K along a graphene ridge created when the graphene layer was cleaved from a sample of highly oriented pyrolytic graphite (HOPG). The energies of these peaks follow the progression of LLs of massless 'Dirac fermions' (DFs) in a magnetic field of 230 T. The results presented here suggest a possible route to realize zero-field quantum Hall-like effects at 77 K

What can we learn from B→a1(1260)(b1(1235))π(K)B\to a_1(1260)(b_1(1235))\pi(K) decays?

We investigate the $B\to a_1(1260)(b_1(1235))\pi(K)$ decays under the factorization scheme and find many discrepancies between theoretical predictions and the experimental data. In the tree dominated processes, large contributions from color-suppressed tree diagrams are required in order to accommodate with the large decay rates of $B^-\to a_1^0\pi^-$ and $B^-\to a_1^-\pi^0$. For $\bar B^0\to (a_1^+, b_1^+)K^-$ decays which are both induced by $b\to s$ transition, theoretical predictions on their decay rates are larger than the data by a factor of 2.8 and 5.5, respectively. Large electro-weak penguins or some new mechanism are expected to explain the branching ratios of $B^-\to b_1^0K^-$ and $B^-\to a_1^-\bar K^0$. The soft-collinear-effective-theory has the potential to explain large decay rates of $B^-\to a_1^0\pi^-$ and $B^-\to a_1^-\pi^0$ via a large hard-scattering form factor $\zeta_J^{B\to a_1}$. We will also show that, with proper charming penguins, predictions on the branching ratios of $\bar B^0\to (a_1^+, b_1^+)K^-$ can also be consistent with the data.Comment: 16 pages, no figur

Suppressing disease spreading by using information diffusion on multiplex networks

Although there is always an interplay between the dynamics of information diffusion and disease spreading, the empirical research on the systemic coevolution mechanisms connecting these two spreading dynamics is still lacking. Here we investigate the coevolution mechanisms and dynamics between information and disease spreading by utilizing real data and a proposed spreading model on multiplex network. Our empirical analysis finds asymmetrical interactions between the information and disease spreading dynamics. Our results obtained from both the theoretical framework and extensive stochastic numerical simulations suggest that an information outbreak can be triggered in a communication network by its own spreading dynamics or by a disease outbreak on a contact network, but that the disease threshold is not affected by information spreading. Our key finding is that there is an optimal information transmission rate that markedly suppresses the disease spreading. We find that the time evolution of the dynamics in the proposed model qualitatively agrees with the real-world spreading processes at the optimal information transmission rate.Comment: 11 pages, 8 figure

Identifying rodent olfactory bulb structures with micro-DTI

Conference Theme: Personalized Healthcare Through TechnologyOlfactory bulb (OB) is one of the most developed systems in rodent models with complex neuronal organization and anatomical structures. MR diffusion tensor imaging (DTI) is a non-invasive technique to probe tissue microstructures by examining the diffusion characteristics of water molecules. This paper presents how different OB layers can be identified and quantitatively characterized by micro-DTI using a specially constructed micro-imaging radio frequency (RF) coil. High spatial resolution and high signal to noise ratio (SNR) DTI images of ex vivo rat OBs were obtained. Distinct contrasts were observed between various olfactory bulb layers in trace map, fractional anisotropy (FA) map and FA color map, all in consistence with the known OB neuroanatomy. These experimental results demonstrate the utility of micro-DTI in investigation of complex OB organization. © 2008 IEEE.published_or_final_versio

The B(Bs)→D(s)PB(B_s)\to D_{(s)} P, D(s)VD_{(s)} V, D(s)∗PD_{(s)}^{*}P and D(s)∗VD_{(s)}^{*}V decays in the perturbative QCD approach

Two-body non-leptonic charmed decays $B_{(s)} \to D_{(s)}P$, $D_{(s)}^*P$, $D_{(s)}V$ and $D_{(s)}^*V$ are analyzed in perturbative QCD approach, where $P$ and $V$ denote the light pseudoscalar meson and vector meson, respectively. We test the $D$ meson wave function by a $\chi^2$ fit with experimental data of six $B\to DP$ channels. We give the branching ratios of all the charmed B decay channels, most of which agree with experiments amazingly well. The predicted $B_s$ decays can be confronted with the future experimental data. By straightforward calculations, our pQCD approach gives the right relative strong phase of $a_2/a_1$ with experiments. We also predict the percentage of transverse polarizations in $B_{(s)} \to D^* V$ decay channels.Comment: 25 pages, 4 figure

The effect of different baryons impurities

We demonstrate the different effect of different baryons impurities on the static properties of nuclei within the framework of the relativistic mean-field model. Systematic calculations show that $\Lambda_c^+$ and $\Lambda_b$ has the same attracting role as $\Lambda$ hyperon does in lighter hypernuclei. $\Xi^-$ and $\Xi_c^0$ hyperon has the attracting role only for the protons distribution, and has a repulsive role for the neutrons distribution. On the contrary, $\Xi^0$ and $\Xi^+_c$ hyperon attracts surrounding neutrons and reveals a repulsive force to the protons. We find that the different effect of different baryons impurities on the nuclear core is due to the different third component of their isospin.Comment: 9 page