Regularization Paths for Cox's Proportional Hazards Model via Coordinate Descent

We introduce a pathwise algorithm for the Cox proportional hazards model, regularized by convex combinations of l_1 and l_2 penalties (elastic net). Our algorithm fits via cyclical coordinate descent, and employs warm starts to find a solution along a regularization path. We demonstrate the efficacy of our algorithm on real and simulated data sets, and find considerable speedup between our algorithm and competing methods.

Regularization Paths for Cox's Proportional Hazards Model via Coordinate Descent

We introduce a pathwise algorithm for the Cox proportional hazards model, regularized by convex combinations of l1 and l2 penalties (elastic net). Our algorithm fits via cyclical coordinate descent, and employs warm starts to find a solution along a regularization path. We demonstrate the efficacy of our algorithm on real and simulated data sets, and find considerable speedup between our algorithm and competing methods

A gauge invariant chiral unitary framework for kaon photo- and electroproduction on the proton

We present a gauge invariant approach to photoproduction of mesons on nucleons within a chiral unitary framework. The interaction kernel for meson-baryon scattering is derived from the chiral effective Lagrangian and iterated in a Bethe-Salpeter equation. Within the leading order approximation to the interaction kernel, data on kaon photoproduction from SAPHIR, CLAS and CBELSA/TAPS are analyzed in the threshold region. The importance of gauge invariance and the precision of various approximations in the interaction kernel utilized in earlier works are discussed.Comment: 23 pages, 13 figs, EPJ A styl

Group descent algorithms for nonconvex penalized linear and logistic regression models with grouped predictors

Penalized regression is an attractive framework for variable selection problems. Often, variables possess a grouping structure, and the relevant selection problem is that of selecting groups, not individual variables. The group lasso has been proposed as a way of extending the ideas of the lasso to the problem of group selection. Nonconvex penalties such as SCAD and MCP have been proposed and shown to have several advantages over the lasso; these penalties may also be extended to the group selection problem, giving rise to group SCAD and group MCP methods. Here, we describe algorithms for fitting these models stably and efficiently. In addition, we present simulation results and real data examples comparing and contrasting the statistical properties of these methods

Phase Segregation Dynamics in Particle Systems with Long Range Interactions I: Macroscopic Limits

We present and discuss the derivation of a nonlinear non-local integro-differential equation for the macroscopic time evolution of the conserved order parameter of a binary alloy undergoing phase segregation. Our model is a d-dimensional lattice gas evolving via Kawasaki exchange dynamics, i.e. a (Poisson) nearest-neighbor exchange process, reversible with respect to the Gibbs measure for a Hamiltonian which includes both short range (local) and long range (nonlocal) interactions. A rigorous derivation is presented in the case in which there is no local interaction. In a subsequent paper (part II), we discuss the phase segregation phenomena in the model. In particular we argue that the phase boundary evolutions, arising as sharp interface limits of the family of equations derived in this paper, are the same as the ones obtained from the corresponding limits for the Cahn-Hilliard equation.Comment: amstex with macros (included in the file), tex twice, 20 page

Study on Evolvement Complexity in an Artificial Stock Market

An artificial stock market is established based on multi-agent . Each agent has a limit memory of the history of stock price, and will choose an action according to his memory and trading strategy. The trading strategy of each agent evolves ceaselessly as a result of self-teaching mechanism. Simulation results exhibit that large events are frequent in the fluctuation of the stock price generated by the present model when compared with a normal process, and the price returns distribution is L\'{e}vy distribution in the central part followed by an approximately exponential truncation. In addition, by defining a variable to gauge the "evolvement complexity" of this system, we have found a phase cross-over from simple-phase to complex-phase along with the increase of the number of individuals, which may be a ubiquitous phenomenon in multifarious real-life systems.Comment: 4 pages and 4 figure

An optimal gap theorem

By solving the Cauchy problem for the Hodge-Laplace heat equation for $d$-closed, positive $(1, 1)$-forms, we prove an optimal gap theorem for K\"ahler manifolds with nonnegative bisectional curvature which asserts that the manifold is flat if the average of the scalar curvature over balls of radius $r$ centered at any fixed point $o$ is a function of $o(r^{-2})$. Furthermore via a relative monotonicity estimate we obtain a stronger statement, namely a `positive mass' type result, asserting that if $(M, g)$ is not flat, then $\liminf_{r\to \infty} \frac{r^2}{V_o(r)}\int_{B_o(r)}\mathcal{S}(y)\, d\mu(y)>0$ for any $o\in M$

Does backreaction enforce the averaged null energy condition in semiclassical gravity?

The expected stress-energy tensor of quantum fields generically violates the local positive energy conditions of general relativity. However, may satisfy some nonlocal conditions such as the averaged null energy condition (ANEC), which would rule out traversable wormholes. Although ANEC holds in Minkowski spacetime, it can be violated in curved spacetimes if one is allowed to choose the spacetime and quantum state arbitrarily, without imposition of the semiclassical Einstein equation G_{ab} = 8 \pi . In this paper we investigate whether ANEC holds for solutions to this equation, by studying a free, massless scalar field with arbitrary curvature coupling in perturbation theory to second order about the flat spacetime/vacuum solution. We "reduce the order" of the perturbation equations to eliminate spurious solutions, and consider the limit in which the lengthscales determined by the incoming state are much larger than the Planck length. We also need to assume that incoming classical gravitational radiation does not dominate the first order metric perturbation. We find that although the ANEC integral can be negative, if we average the ANEC integral transverse to the geodesic with a suitable Planck scale smearing function, then a strictly positive result is obtained in all cases except for the flat spacetime/vacuum solution. This result suggests --- in agreement with conclusions drawn by Ford and Roman from entirely independent arguments --- that if traversable wormholes do exist as solutions to the semiclassical equations, they cannot be macroscopic but must be ``Planck scale''. A large portion of our paper is devoted to the analysis of general issues concerning the nature of the semiclassical Einstein equation and of prescriptions for extracting physically relevant solutions.Comment: 54 pages, 3 figures, uses revtex macros and epsf.tex, to appear in Phys Rev D. A new appendix has been added showing consistency of our results with recent results of Visser [gr-qc/9604008]. Some corrections were made to Appendix A, and several other minor changes to the body of the paper also were mad

Zeros of the i.i.d. Gaussian power series: a conformally invariant determinantal process

Consider the zero set of the random power series f(z)=sum a_n z^n with i.i.d. complex Gaussian coefficients a_n. We show that these zeros form a determinantal process: more precisely, their joint intensity can be written as a minor of the Bergman kernel. We show that the number of zeros of f in a disk of radius r about the origin has the same distribution as the sum of independent {0,1}-valued random variables X_k, where P(X_k=1)=r^{2k}. Moreover, the set of absolute values of the zeros of f has the same distribution as the set {U_k^{1/2k}} where the U_k are i.i.d. random variables uniform in [0,1]. The repulsion between zeros can be studied via a dynamic version where the coefficients perform Brownian motion; we show that this dynamics is conformally invariant.Comment: 37 pages, 2 figures, updated proof

Dramatic age-related changes in nuclear and genome copy number in the nematode Caenorhabditis elegans

The nematode Caenorhabditis elegans has become one of the most widely used model systems for the study of aging, yet very little is known about how C. elegans age. The development of the worm, from egg to young adult has been completely mapped at the cellular level, but such detailed studies have not been extended throughout the adult lifespan. Numerous single gene mutations, drug treatments and environmental manipulations have been found to extend worm lifespan. To interpret the mechanism of action of such aging interventions, studies to characterize normal worm aging, similar to those used to study worm development are necessary. We have used 4′,6′-diamidino-2-phenylindole hydrochloride staining and quantitative polymerase chain reaction to investigate the integrity of nuclei and quantify the nuclear genome copy number of C. elegans with age. We report both systematic loss of nuclei or nuclear DNA, as well as dramatic age-related changes in nuclear genome copy number. These changes are delayed or attenuated in long-lived daf-2 mutants. We propose that these changes are important pathobiological characteristics of aging nematodes