Solving Nonlinear Parabolic Equations by a Strongly Implicit Finite-Difference Scheme

We discuss the numerical solution of nonlinear parabolic partial differential equations, exhibiting finite speed of propagation, via a strongly implicit finite-difference scheme with formal truncation error $\mathcal{O}\left[(\Delta x)^2 + (\Delta t)^2 \right]$. Our application of interest is the spreading of viscous gravity currents in the study of which these type of differential equations arise. Viscous gravity currents are low Reynolds number (viscous forces dominate inertial forces) flow phenomena in which a dense, viscous fluid displaces a lighter (usually immiscible) fluid. The fluids may be confined by the sidewalls of a channel or propagate in an unconfined two-dimensional (or axisymmetric three-dimensional) geometry. Under the lubrication approximation, the mathematical description of the spreading of these fluids reduces to solving the so-called thin-film equation for the current's shape $h(x,t)$. To solve such nonlinear parabolic equations we propose a finite-difference scheme based on the Crank--Nicolson idea. We implement the scheme for problems involving a single spatial coordinate (i.e., two-dimensional, axisymmetric or spherically-symmetric three-dimensional currents) on an equispaced but staggered grid. We benchmark the scheme against analytical solutions and highlight its strong numerical stability by specifically considering the spreading of non-Newtonian power-law fluids in a variable-width confined channel-like geometry (a "Hele-Shaw cell") subject to a given mass conservation/balance constraint. We show that this constraint can be implemented by re-expressing it as nonlinear flux boundary conditions on the domain's endpoints. Then, we show numerically that the scheme achieves its full second-order accuracy in space and time. We also highlight through numerical simulations how the proposed scheme accurately respects the mass conservation/balance constraint.Comment: 36 pages, 9 figures, Springer book class; v2 includes improvements and corrections; to appear as a contribution in "Applied Wave Mathematics II

Loss of Arc renders the visual cortex impervious to the effects of sensory experience or deprivation

A myriad of mechanisms have been suggested to account for the full richness of visual cortical plasticity. We found that visual cortex lacking Arc is impervious to the effects of deprivation or experience. Using intrinsic signal imaging and chronic visually evoked potential recordings, we found that Arc−/− mice did not exhibit depression of deprived-eye responses or a shift in ocular dominance after brief monocular deprivation. Extended deprivation also failed to elicit a shift in ocular dominance or open-eye potentiation. Moreover, Arc−/− mice lacked stimulus-selective response potentiation. Although Arc−/− mice exhibited normal visual acuity, baseline ocular dominance was abnormal and resembled that observed after dark-rearing. These data suggest that Arc is required for the experience-dependent processes that normally establish and modify synaptic connections in visual cortex.Howard Hughes Medical InstituteNational Science Foundation (U.S.

The Evolution of Compact Binary Star Systems

We review the formation and evolution of compact binary stars consisting of white dwarfs (WDs), neutron stars (NSs), and black holes (BHs). Binary NSs and BHs are thought to be the primary astrophysical sources of gravitational waves (GWs) within the frequency band of ground-based detectors, while compact binaries of WDs are important sources of GWs at lower frequencies to be covered by space interferometers (LISA). Major uncertainties in the current understanding of properties of NSs and BHs most relevant to the GW studies are discussed, including the treatment of the natal kicks which compact stellar remnants acquire during the core collapse of massive stars and the common envelope phase of binary evolution. We discuss the coalescence rates of binary NSs and BHs and prospects for their detections, the formation and evolution of binary WDs and their observational manifestations. Special attention is given to AM CVn-stars -- compact binaries in which the Roche lobe is filled by another WD or a low-mass partially degenerate helium-star, as these stars are thought to be the best LISA verification binary GW sources.Comment: 105 pages, 18 figure

Accelerating Policy Decisions to Adopt Haemophilus influenzae Type b Vaccine: A Global, Multivariable Analysis

Jessica Shearer and colleagues analyze data from 147 countries to identify factors that influence the time taken to introduce routine vaccination against Haemophilus influenzae type b (Hib)

Serine phosphorylation regulates paxillin turnover during cell migration

BACKGROUND: Paxillin acts as an adaptor protein that localizes to focal adhesion. This protein is regulated during cell migration by phosphorylation on tyrosine, serine and threonine residues. Most of these phosphorylations have been implicated in the regulation of different steps of cell migration. The two major phosphorylation sites of paxillin in response to adhesion to an extracellular matrix are serines 188 and 190. However, the function of this phosphorylation event remains unknown. The purpose of this work was to determine the role of paxillin phosphorylation on residues S188 and S190 in the regulation of cell migration. RESULTS: We used NBT-II epithelial cells that can be induced to migrate when plated on collagen. To examine the role of paxillin serines 188/190 in cell migration, we constructed an EGFP-tagged paxillin mutant in which S188/S190 were mutated into unphosphorylatable alanine residues. We provide evidence that paxillin is regulated by proteasomal degradation following polyubiquitylation of the protein. During active cell migration on collagen, paxillin is protected from proteasome-dependent degradation. We demonstrate that phosphorylation of serines 188/190 is necessary for the protective effect of collagen. In an effort to understand the physiological relevance of paxillin protection from degradation, we show that cells expressing the paxillin S188/190A interfering mutant spread less, have reduced protrusive activity but migrate more actively. CONCLUSION: Our data demonstrate for the first time that serine-regulated degradation of paxillin plays a key role in the modulation of membrane dynamics and consequently, in the control of cell motility

The regulatory role of long-term depression in juvenile and adult mouse ocular dominance plasticity

The study of experience-dependent ocular dominance (OD) plasticity has greatly contributed to the understanding of visual development. During the critical period, preventing input from one eye results in a significant impairment of vision, and loss of cortical responsivity via the deprived eye. Residual ocular dominance plasticity has recently been observed in adulthood. Accumulating evidence suggests that OD plasticity involves N-methyl-D-aspartate receptor (NMDAR)-dependent long-term depression (LTD). Here we report that the administration of a selective LTD antagonist prevented the ocular dominance shift during the critical period. The NMDAR co-agonist D-serine facilitated adult visual cortical LTD and the OD shift in short-term monocularly deprived (MD) adult mice. When combined with reverse suture, D-serine proved effective in restoring a contralaterally-dominated visual input pattern in long-term MD mice. This work suggests LTD as a key mechanism in both juvenile and adult ocular dominance plasticity, and D-serine as a potential therapeutic in human amblyopic subjects

Modelling stereotyping in cooperation systems

Cooperation is a sophisticated example of collective intelligence. This is particularly the case for indirect reciprocity, where benefit is provided to others without a guarantee of a future return. This is becoming increasingly relevant to future technology, where autonomous machines face cooperative dilemmas. This paper addresses the problem of stereotyping, where traits belonging to an individual are used as proxy when assessing their reputation. This is a cognitive heuristic that humans frequently use to avoid deliberation, but can lead to negative societal implications such as discrimination. It is feasible that machines could be equally susceptible. Our contribution concerns a new and general framework to examine how stereotyping affects the reputation of agents engaging in indirect reciprocity. The framework is flexible and focuses on how reputations are shared. This offers the opportunity to assess the interplay between the sharing of traits and the cost, in terms of reduced cooperation, through opportunities for shirkers to benefit. This is demonstrated using a number of key scenarios. In particular, the results show that cooperation is sensitive to the structure of reputation sharing between individuals