Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model

In the absence of external material deposition, crystal surfaces usually relax to become flat by decreasing their free energy. We study an asymmetry in the relaxation of macroscopic plateaus, facets, of a periodic surface corrugation in 1+1 dimensions via a continuum model below the roughening transition temperature. The model invokes a highly degenerate parabolic partial differential equation (PDE) for surface diffusion, which is related to the weighted-$H^{-1}$ (nonlinear) gradient flow of a convex, singular surface free energy in homoepitaxy. The PDE is motivated both by an atomistic broken-bond model and a mesoscale model for steps. By constructing an explicit solution to the PDE, we demonstrate the lack of symmetry in the evolution of top and bottom facets in periodic surface profiles. Our explicit, analytical solution is compared to numerical simulations of the PDE via a regularized surface free energy.Comment: 23 pages, 5 figures, comments welcome! Text slightly modified, references updated in Version 2. Referee comments addresse

Achieving precise mechanical control in intrinsically noisy systems

How can precise control be realized in intrinsically noisy systems? Here, we develop a general theoretical framework that provides a way of achieving precise control in signal-dependent noisy environments. When the control signal has Poisson or supra-Poisson noise, precise control is not possible. If, however, the control signal has sub-Poisson noise, then precise control is possible. For this case, the precise control solution is not a function, but a rapidly varying random process that must be averaged with respect to a governing probability density functional. Our theoretical approach is applied to the control of straight-trajectory arm movement. Sub-Poisson noise in the control signal is shown to be capable of leading to precise control. Intriguingly, the control signal for this system has a natural counterpart, namely the bursting pulses of neurons-trains of Dirac-delta functions-in biological systems to achieve precise control performance

Single-nucleotide polymorphism-based genetic risk score and patient age at prostate cancer diagnosis

Importance: Few studies have evaluated the association between a single-nucleotide polymorphism-based genetic risk score (GRS) and patient age at prostate cancer (PCa) diagnosis. Objectives: To test the association between a GRS and patient age at PCa diagnosis and to compare the performance of a GRS with that of family history (FH) in PCa risk stratification. Design, Setting, and Participants: A cohort study of 3225 white men was conducted as a secondary analysis of the Reduction by Dutasteride of Prostate Cancer Events (REDUCE) chemoprevention trial, a 4-year, randomized, double-blind, placebo-controlled multicenter study conducted from March 2003 to April 2009 to evaluate the safety and efficacy of dutasteride in reducing PCa events. Participants were confirmed to be cancer free by prostate biopsy (6-12 cores) within 6 months prior to the study and underwent 10 core biopsies every 2 years per protocol. The dates for performing data analysis were from July 2016 to October 2019. Interventions: A well-established, population-standardized GRS was calculated for each participant based on 110 known PCa risk-associated single-nucleotide polymorphisms, which is a relative risk compared with the general population. Men were classified into 3 GRS risk groups based on predetermined cutoff values: low (\u3c0.50), average (0.50-1.49), and high (≥1.50). Main Outcomes and Measures: Prostate cancer diagnosis-free survival among men of different risk groups. Results: Among 3225 men (median age, 63 years [interquartile range, 58-67 years]) in the study, 683 (21%) were classified as low risk, 1937 (60%) as average risk, and 605 (19%) as high risk based on GRS alone. In comparison, 2789 (86%) were classified as low or average risk and 436 (14%) as high risk based on FH alone. Men in higher GRS risk groups had a PCa diagnosis-free survival rate that was worse than that of those in the lower GRS risk group (χ2 = 53.3; P \u3c .001 for trend) and in participants with a negative FH of PCa (χ2 = 45.5; P \u3c .001 for trend). Combining GRS and FH further stratified overall genetic risk, indicating that 957 men (30%) were at high genetic risk (either high GRS or positive FH), 1667 men (52%) were at average genetic risk (average GRS and negative FH), and 601 men (19%) were at low genetic risk (low GRS and negative FH). The median PCa diagnosis-free survival was 74 years (95% CI, 73-75 years) for men at high genetic risk, 77 years (95% CI, 75 to \u3e80 years) for men at average genetic risk, and more than 80 years (95% CI, \u3e80 to \u3e80 years) for men at low genetic risk. In contrast, the median PCa diagnosis-free survival was 73 years (95% CI, 71-76 years) for men with a positive FH and 77 years (95% CI, 76-79 years) for men with a negative FH. Conclusions and Relevance: This study suggests that a GRS is significantly associated with patient age at PCa diagnosis. Combining FH and GRS may better stratify inherited risk than FH alone for developing personalized PCa screening strategies

Optical Limiting in SrBi₂Ta₂O₉ and PbZrxTi₁₋ₓO₃ Thin Films

Optical limiting effects in SrBi2Ta2O9 (SBT) and PbZrxTi1-xO3 (PZT) ferroelectric thin films have been observed with nanosecond laser pulses at 1.064 µm. Limiting thresholds were found to be 5.84 J/cm2 for SBT and between 4.53 and 5.93 J/cm2 for PZT, depending on composition, whereas saturation thresholds for the films were about 2.92 J/cm2 and between 2.27 J/cm2 to 2.97 J/cm2, respectively. Damage thresholds around 10.0 J/cm2 and between 10.37 J/cm2 to 10.54 J/cm2, respectively for SBT and PZT, were also determined. A possible mechanism for the observed limiting, nonlinear optical scattering from the ferroelectric domains, is discussed. These results elucidate the origin of the nonlinear optical properties in perovskite-type ferroelectric thin films and show the potential role such materials can play in photonic devices based on nonlinear optical effects

Analysis of a fourth order exponential PDE arising from a crystal surface jump process with Metropolis-type transition rates

We analytically and numerically study a fourth order PDE modeling rough crystal surface diffusion on the macroscopic level. We discuss existence of solutions globally in time and long time dynamics for the PDE model. The PDE, originally derived by the second author, is the continuum limit of a microscopic model of the surface dynamics, given by a Markov jump process with Metropolis type transition rates. We outline the convergence argument, which depends on a simplifying assumption on the local equilibrium measure that is valid in the high temperature regime. We provide numerical evidence for the convergence of the microscopic model to the PDE in this regime.Comment: 14 pages, 4 figures, comments welcome! Revised significantly thanks to very thorough referee reports. Some previous discussions have been removed and will be reported in a separate result by one of the author

Functional connectivity decreases in autism in emotion, self, and face circuits identified by knowledge-based enrichment analysis

A powerful new method is described called Knowledge based functional connectivity Enrichment Analysis (KEA) for interpreting resting state functional connectivity, using circuits that are functionally identified using search terms with the Neurosynth database. The method derives its power by focusing on neural circuits, sets of brain regions that share a common biological function, instead of trying to interpret single functional connectivity links. This provides a novel way of investigating how task- or function-related related networks have resting state functional connectivity differences in different psychiatric states, provides a new way to bridge the gap between task and resting-state functional networks, and potentially helps to identify brain networks that might be treated. The method was applied to interpreting functional connectivity differences in autism. Functional connectivity decreases at the network circuit level in 394 patients with autism compared with 473 controls were found in networks involving the orbitofrontal cortex, anterior cingulate cortex, middle temporal gyrus cortex, and the precuneus, in networks that are implicated in the sense of self, face processing, and theory of mind. The decreases were correlated with symptom severity