Numerical computations of facetted pattern formation in snow crystal growth

Facetted growth of snow crystals leads to a rich diversity of forms, and exhibits a remarkable sixfold symmetry. Snow crystal structures result from diffusion limited crystal growth in the presence of anisotropic surface energy and anisotropic attachment kinetics. It is by now well understood that the morphological stability of ice crystals strongly depends on supersaturation, crystal size and temperature. Until very recently it was very difficult to perform numerical simulations of this highly anisotropic crystal growth. In particular, obtaining facet growth in combination with dendritic branching is a challenging task. We present numerical simulations of snow crystal growth in two and three space dimensions using a new computational method recently introduced by the authors. We present both qualitative and quantitative computations. In particular, a linear relationship between tip velocity and supersaturation is observed. The computations also suggest that surface energy effects, although small, have a larger effect on crystal growth than previously expected. We compute solid plates, solid prisms, hollow columns, needles, dendrites, capped columns and scrolls on plates. Although all these forms appear in nature, most of these forms are computed here for the first time in numerical simulations for a continuum model.Comment: 12 pages, 28 figure

Impurity Effects on Quantum Depinning of Commensurate Charge Density Waves

We investigate quantum depinning of the one-dimensional (1D) commensurate charge-density wave (CDW) in the presence of one impurity theoretically. Quantum tunneling rate below but close to the threshold field is calculated at absolute zero temperature by use of the phase Hamiltonian within the WKB approximation. We show that the impurity can induce localized fluctuation and enhance the quantum depinning. The electric field dependence of the tunneling rate in the presence of the impurity is different from that in its absence.Comment: 14 pages with 13 figures. Submitted to J. Phys. Soc. Jp

Deep generative modeling for single-cell transcriptomics.

Single-cell transcriptome measurements can reveal unexplored biological diversity, but they suffer from technical noise and bias that must be modeled to account for the resulting uncertainty in downstream analyses. Here we introduce single-cell variational inference (scVI), a ready-to-use scalable framework for the probabilistic representation and analysis of gene expression in single cells ( https://github.com/YosefLab/scVI ). scVI uses stochastic optimization and deep neural networks to aggregate information across similar cells and genes and to approximate the distributions that underlie observed expression values, while accounting for batch effects and limited sensitivity. We used scVI for a range of fundamental analysis tasks including batch correction, visualization, clustering, and differential expression, and achieved high accuracy for each task

Personality traits and cancer survival: a Danish cohort study

We conducted a population-based prospective cohort study in Denmark to investigate associations between the personality traits and cancer survival. Between 1976 and 1977, 1020 residents of the Copenhagen County completed a questionnaire eliciting information on personality traits and various health habits. The personality traits extraversion and neuroticism were measured using the short form of the Eysenck Personality Inventory. Follow-up in the Danish Cancer Registry for 1976–2002 revealed 189 incidents of primary cancer and follow-up for death from the date of the cancer diagnosis until 2005 revealed 82 deaths from all-cause in this group. A Cox proportional-hazards model was used to estimate the hazard ratios (HRs) of death from all-cause according to extraversion and neuroticism adjusting for potential confounding factors. A significant association was found between neuroticism and risk of death (HR, 2.3 (95% CI=1.1–4.7); Linear trend P=0.04) but not between extraversion and risk of death (HR, 0.9 (0.4–1.7); Linear trend P=0.34). Similar results were found when using cancer-related death. Stratification by gender revealed a strong positive association between neuroticism and the risk of death among women (Linear trend P=0.03). This study showed that neuroticism is positively associated with cancer survival. Further research on neuroticism and cancer survival is needed

Chiral patterns arising from electrostatic growth models

Recently, unusual and strikingly beautiful seahorse-like growth patterns have been observed under conditions of quasi-two-dimensional growth. These `S'-shaped patterns strongly break two-dimensional inversion symmetry; however such broken symmetry occurs only at the level of overall morphology, as the clusters are formed from achiral molecules with an achiral unit cell. Here we describe a mechanism which gives rise to chiral growth morphologies without invoking microscopic chirality. This mechanism involves trapped electrostatic charge on the growing cluster, and the enhancement of growth in regions of large electric field. We illustrate the mechanism with a tree growth model, with a continuum model for the motion of the one-dimensional boundary, and with microscopic Monte Carlo simulations. Our most dramatic results are found using the continuum model, which strongly exhibits spontaneous chiral symmetry breaking, and in particular finned `S' shapes like those seen in the experiments.Comment: RevTeX, 12 pages, 9 figure

Local Causal States and Discrete Coherent Structures

Coherent structures form spontaneously in nonlinear spatiotemporal systems and are found at all spatial scales in natural phenomena from laboratory hydrodynamic flows and chemical reactions to ocean, atmosphere, and planetary climate dynamics. Phenomenologically, they appear as key components that organize the macroscopic behaviors in such systems. Despite a century of effort, they have eluded rigorous analysis and empirical prediction, with progress being made only recently. As a step in this, we present a formal theory of coherent structures in fully-discrete dynamical field theories. It builds on the notion of structure introduced by computational mechanics, generalizing it to a local spatiotemporal setting. The analysis' main tool employs the \localstates, which are used to uncover a system's hidden spatiotemporal symmetries and which identify coherent structures as spatially-localized deviations from those symmetries. The approach is behavior-driven in the sense that it does not rely on directly analyzing spatiotemporal equations of motion, rather it considers only the spatiotemporal fields a system generates. As such, it offers an unsupervised approach to discover and describe coherent structures. We illustrate the approach by analyzing coherent structures generated by elementary cellular automata, comparing the results with an earlier, dynamic-invariant-set approach that decomposes fields into domains, particles, and particle interactions.Comment: 27 pages, 10 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/dcs.ht

Local Inhomogeneity Effects on Nucleation Process in a High External Bias

Quantum nucleation processes in the presence of local moderate inhomogeneities are studied theoretically at high biases. The quantum nucleation rate Gamma is calculated for one-dimensional systems in a form Gamma = A e^(-B/hbar) by using the `bounce' method. The bias-dependence of the exponent B is shown to be changed by inhomogeneities. This change is explained by the reduction of the effective spatial dimension of the system. By studying the system-size dependence of the prefactor A, the condition for the appearance of inhomogeneity effects is evaluated. Nucleation rates in thermal activation regimes are also calculated, and compared with quantum tunneling regimes. For higher-dimensional systems, it is shown that the local approximation of inhomogeneity does not hold, and that spatial profiles of inhomogeneity become important.Comment: 10 pages, 6 figure

Light scattering from an isotropic layer between uniaxial crystals

We develop a model for the reflection and transmission of plane waves by an isotropic layer sandwiched between two uniaxial crystals of arbitrary orientation. In the laboratory frame, reflection and transmission coefficients corresponding to the principal polarization directions in each crystal are given explicitly in terms of the c-axis and propagation directions. The solution is found by first deriving explicit expressions for reflection and transmission amplitude coefficients for waves propagating from an arbitrarily oriented uniaxial anisotropic material into an isotropic material. By combining these results with Lekner's (1991) earlier treatment of waves propagating from isotropic media to anisotropic media and employing a matrix method we determine a solution to the general form of the multiple reflection case. The example system of a wetted interface between two ice crystals is used to contextualize the results.Comment: 18 pages, 9 figures,updated with changes made to published versio

Search for Light Gluinos via the Spontaneous Appearance of pi+pi- Pairs with an 800 GeV/c Proton Beam at Fermilab

We searched for the appearance of pi+pi- pairs with invariant mass greater than 648 MeV in a neutral beam. Such an observation could signify the decay of a long-lived light neutral particle. We find no evidence for this decay. Our null result severely constrains the existence of an R0 hadron, which is the lightest bound state of a gluon and a light gluino, and thereby also the possibility of a light gluino. Depending on the photino mass, we exclude the R0 in the mass and lifetime ranges of 1.2 -- 4.6 GeV and 2E-10 -- 7E-4 seconds, respectively. (To Appear in Phys. Rev. Lett.)Comment: Documentstyle aps,epsfig,prl (revtex), 6 pages, 7 figure

Search for the Decay K_L -> pi^0 nu nubar using pi^0 -> e^+ e^- gamma

We report on a search for the decay K_L -> pi^0 nu nubar, carried out as a part of E799-II, a rare K_L decay experiment at Fermilab. Within the Standard Model, the K_L -> pi^0 nu nubar decay is dominated by direct CP violating processes, and thus an observation of the decay implies confirmation of direct CP violation. Due to theoretically clean calculations, a measurement of B(K_L -> pi^0 nu nubar) is one of the best ways to determine the CKM parameter eta. No events were observed, and we set an upper limit B(K_L -> pi^0 nu nubar) < 5.9 times 10^-7 at the 90% confidence level.Comment: 5 pages, 4 figure