Penalized Likelihood Methods for Estimation of Sparse High Dimensional Directed Acyclic Graphs

Directed acyclic graphs (DAGs) are commonly used to represent causal relationships among random variables in graphical models. Applications of these models arise in the study of physical, as well as biological systems, where directed edges between nodes represent the influence of components of the system on each other. The general problem of estimating DAGs from observed data is computationally NP-hard, Moreover two directed graphs may be observationally equivalent. When the nodes exhibit a natural ordering, the problem of estimating directed graphs reduces to the problem of estimating the structure of the network. In this paper, we propose a penalized likelihood approach that directly estimates the adjacency matrix of DAGs. Both lasso and adaptive lasso penalties are considered and an efficient algorithm is proposed for estimation of high dimensional DAGs. We study variable selection consistency of the two penalties when the number of variables grows to infinity with the sample size. We show that although lasso can only consistently estimate the true network under stringent assumptions, adaptive lasso achieves this task under mild regularity conditions. The performance of the proposed methods is compared to alternative methods in simulated, as well as real, data examples.Comment: 19 pages, 8 figure

Free-standing all-polymer microring resonator optical filter

Free-standing all-polymer microring resonator optical filters as prototypical elements in flexible integrated lightwave circuits are demonstrated. The fabrication and measurement methods are discussed. The measured spectrum shows good agreement with theoretical expectations. The crucial 'critical' coupling condition is achieved, resulting in a measurement limited -27 dB extinction of the filter output on resonances

Weak gravity conjecture constraints on inflation

We consider the gravitational correction to the coupling of the scalar fields. Weak gravity conjecture says that the gravitational correction to the running of scalar coupling should be less than the contribution from scalar fields. For instance, a new scale $\Lambda=\lambda_4^{1/2}M_p$ sets a UV cutoff on the validity of the effective $\lambda_4 \phi^4$ theory. Furthermore, this conjecture implies a possible constraint on the inflation model, e.g. the chaotic inflation model might be in the swampland.Comment: 11 pages, 3 figs; monor corrections; some clarifying remarks added and the final version for publication in JHE

Enhancement of superconductivity near the ferromagnetic quantum critical point in UCoGe

We report a high-pressure single crystal study of the superconducting ferromagnet UCoGe. Ac-susceptibility and resistivity measurements under pressures up to 2.2 GPa show ferromagnetism is smoothly depressed and vanishes at a critical pressure $p_c = 1.4$ GPa. Near the ferromagnetic critical point superconductivity is enhanced. Upper-critical field measurements under pressure show $B_{c2}(0)$ attains remarkably large values, which provides solid evidence for spin-triplet superconductivity over the whole pressure range. The obtained $p-T$ phase diagram reveals superconductivity is closely connected to a ferromagnetic quantum critical point hidden under the superconducting `dome'.Comment: 4 pages, 3 figures; accepted for publication in PR

Agegraphic Chaplygin gas model of dark energy

We establish a connection between the agegraphic models of dark energy and Chaplygin gas energy density in non-flat universe. We reconstruct the potential of the agegraphic scalar field as well as the dynamics of the scalar field according to the evolution of the agegraphic dark energy. We also extend our study to the interacting agegraphic generalized Chaplygin gas dark energy model.Comment: 8 page

Nonlinear effects for island coarsening and stabilization during strained film heteroepitaxy

Nonlinear evolution of three-dimensional strained islands or quantum dots in heteroepitaxial thin films is studied via a continuum elasticity model and the development of a nonlinear dynamic equation governing the film morphological profile. All three regimes of island array evolution are identified and examined, including a film instability regime at early stage, a nonlinear coarsening regime at intermediate times, and the crossover to a saturated asymptotic state, with detailed behavior depending on film-substrate misfit strains but not qualitatively on finite system sizes. The phenomenon of island stabilization and saturation, which corresponds to the formation of steady but non-ordered arrays of strained quantum dots, occurs at later time for smaller misfit strain. It is found to be controlled by the strength of film-substrate wetting interaction which would constrain the valley-to-peak mass transport and hence the growth of island height, and also determined by the effect of elastic interaction between surface islands and the high-order strain energy of individual islands at late evolution stage. The results are compared to previous experimental and theoretical studies on quantum dots coarsening and saturation.Comment: 19 pages, 12 figures; submitted to Phys. Rev.

Tumbling of polymers in semidilute solution under shear flow

The tumbling dynamics of individual polymers in semidilute solution is studied by large-scale non-equilibrium mesoscale hydrodynamic simulations. We find that the tumbling time is equal to the non-equilibrium relaxation time of the polymer end-to-end distance along the flow direction and strongly depends on concentration. In addition, the normalized tumbling frequency as well as the widths of the alignment distribution functions for a given concentration-dependent Weissenberg number exhibit a weak concentration dependence in the cross-over regime from a dilute to a semidilute solution. For semidilute solutions a universal behavior is obtained. This is a consequence of screening of hydrodynamic interactions at polymer concentrations exceeding the overlap concentration

Cosmological perturbations and noncommutative tachyon inflation

The motivation for studying the rolling tachyon and non-commutative inflation comes from string theory. In the tachyon inflation scenario, metric perturbations are created by tachyon field fluctuations during inflation. We drive the exact mode equation for scalar perturbation of the metric and investigate the cosmological perturbations in the commutative and non-commutative inflationary spacetime driven by the tachyon field which have a Born-Infeld Lagrangian.Comment: 6 two-column pages, no figur

Eternal Chaotic Inflation is Prohibited by Weak Gravity Conjecture

We investigate whether the eternal chaotic inflation can be achieved when the weak gravity conjecture is taken into account. We show that even the assisted chaotic inflation with potential $\lambda\phi^4$ or $m^2\phi^2$ can not be eternal. The effective field theory description for the inflaton field breaks down before inflation reaches the eternal regime. We also find that the total number of e-folds is still bounded by the inflationary entropy for the assisted inflation.Comment: 10 page

Numerical Study of a Particle Method for Gradient Flows

We study the numerical behaviour of a particle method for gradient flows involving linear and nonlinear diffusion. This method relies on the discretisation of the energy via non-overlapping balls centred at the particles. The resulting scheme preserves the gradient flow structure at the particle level, and enables us to obtain a gradient descent formulation after time discretisation. We give several simulations to illustrate the validity of this method, as well as a detailed study of one-dimensional aggregation-diffusion equations.Comment: 27 pages, 21 figure