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

Criteria of efficiency for conformal prediction

We study optimal conformity measures for various criteria of efficiency of classification in an idealised setting. This leads to an important class of criteria of efficiency that we call probabilistic; it turns out that the most standard criteria of efficiency used in literature on conformal prediction are not probabilistic unless the problem of classification is binary. We consider both unconditional and label-conditional conformal prediction.Comment: 31 page

Mdivi-1, a mitochondrial fission inhibitor, modulates T helper cells and suppresses the development of experimental autoimmune encephalomyelitis.

BACKGROUND: Unrestrained activation of Th1 and Th17 cells is associated with the pathogenesis of multiple sclerosis and its animal model, experimental autoimmune encephalomyelitis (EAE). While inactivation of dynamin-related protein 1 (Drp1), a GTPase that regulates mitochondrial fission, can reduce EAE severity by protecting myelin from demyelination, its effect on immune responses in EAE has not yet been studied. METHODS: We investigated the effect of Mdivi-1, a small molecule inhibitor of Drp1, on EAE. Clinical scores, inflammation, demyelination and Drp1 activation in the central nervous system (CNS), and T cell responses in both CNS and periphery were determined. RESULTS: Mdivi-1 effectively suppressed EAE severity by reducing demyelination and cellular infiltration in the CNS. Mdivi-1 treatment decreased the phosphorylation of Drp1 (ser616) on CD4+ T cells, reduced the numbers of Th1 and Th17 cells, and increased Foxp3+ regulatory T cells in the CNS. Moreover, Mdivi-1 treatment effectively inhibited IFN-γ+, IL-17+, and GM-CSF+ CD4+ T cells, while it induced CD4+ Foxp3+ regulatory T cells in splenocytes by flow cytometry. CONCLUSIONS: Together, our results demonstrate that Mdivi-1 has therapeutic potential in EAE by modulating the balance between Th1/Th17 and regulatory T cells

Leptogenesis and dark matter unified in a non-SUSY model for neutrino masses

We propose a unified explanation for the origin of dark matter and baryon number asymmetry on the basis of a non-supersymmetric model for neutrino masses. Neutrino masses are generated in two distinct ways, that is, a tree-level seesaw mechanism with a single right-handed neutrino, and one-loop radiative effects by a new additional doublet scalar. A spontaneously broken U(1)$^\prime$ brings a $Z_2$ symmetry which restricts couplings of this new scalar and controls the neutrino masses. It also guarantees the stability of a CDM candidate. We examine two possible candidate for the CDM. We also show that the decay of a heavy right-handed neutrino related to the seesaw mechanism can generate baryon number asymmetry through leptogenesis.Comment: 21 pages, 3 figures, extended version for publication, references adde

Observation of PeV Gamma Rays from the Monogem Ring with the Tibet Air Shower Array

We searched for steady PeV gamma-ray emission from the Monogem ring region with the Tibet air shower array from 1997 February to 2004 October. No evidence for statistically significant gamma-ray signals was found in a region 111\degr $\leq$ R.A. $<$ 114\degr, 12\fdg5 $\leq$ decl. $<$ 15\fdg5 in the Monogem ring where the MAKET-ANI experiment recently claimed a positive detection of PeV high-energy cosmic radiation, although our flux sensitivity is approximately 10 times better than MAKET-ANI's. We set the most stringent integral flux upper limit at a 99% confidence level of 4.0 $\times$ 10$^{-12}$ cm$^{-2}$ s$^{-1}$ sr$^{-1}$ above 1 PeV on diffuse gamma rays extended in the 3$^{\circ}$ $\times$ 3$^{\circ}$ region.Comment: 13 pages 3figures, 1 tabl

Criteria of efficiency for set-valued classification

We study optimal conformity measures for various criteria of efficiency of set-valued classification in an idealised setting. This leads to an important class of criteria of efficiency that we call probabilistic and argue for; it turns out that the most standard criteria of efficiency used in literature on conformal prediction are not probabilistic unless the problem of classification is binary. We consider both unconditional and label-conditional conformal prediction

What Does It Take to Synergistically Combine Sub-Potent Natural Products into Drug-Level Potent Combinations?

10.1371/journal.pone.0049969PLoS ONE711