First passage times in integrate-and-fire neurons with stochastic thresholds

We consider a leaky integrate--and--fire neuron with deterministic subthreshold dynamics and a firing threshold that evolves as an Ornstein-Uhlenbeck process. The formulation of this minimal model is motivated by the experimentally observed widespread variation of neural firing thresholds. We show numerically that the mean first passage time can depend non-monotonically on the noise amplitude. For sufficiently large values of the correlation time of the stochastic threshold the mean first passage time is maximal for non-vanishing noise. We provide an explanation for this effect by analytically transforming the original model into a first passage time problem for Brownian motion. This transformation also allows for a perturbative calculation of the first passage time histograms. In turn this provides quantitative insights into the mechanisms that lead to the non-monotonic behaviour of the mean first passage time. The perturbation expansion is in excellent agreement with direct numerical simulations. The approach developed here can be applied to any deterministic subthreshold dynamics and any Gauss-Markov processes for the firing threshold. This opens up the possibility to incorporate biophysically detailed components into the subthreshold dynamics, rendering our approach a powerful framework that sits between traditional integrate-and-fire models and complex mechanistic descriptions of neural dynamics

The Nikolaevskiy equation with dispersion

The Nikolaevskiy equation was originally proposed as a model for seismic waves and is also a model for a wide variety of systems incorporating a neutral, Goldstone mode, including electroconvection and reaction-diffusion systems. It is known to exhibit chaotic dynamics at the onset of pattern formation, at least when the dispersive terms in the equation are suppressed, as is commonly the practice in previous analyses. In this paper, the effects of reinstating the dispersive terms are examined. It is shown that such terms can stabilise some of the spatially periodic traveling waves; this allows us to study the loss of stability and transition to chaos of the waves. The secondary stability diagram (Busse balloon) for the traveling waves can be remarkably complicated.Comment: 24 pages; accepted for publication in Phys. Rev.

Orientation-dependent pinning and homoclinic snaking on a planar lattice

We study homoclinic snaking of one-dimensional, localized states on two-dimensional, bistable lattices via the method of exponential asymptotics. Within a narrow region of parameter space, fronts connecting the two stable states are pinned to the underlying lattice. Localized solutions are formed by matching two such stationary fronts back-to-back; depending on the orientation relative to the lattice, the solution branch may “snake” back and forth within the pinning region via successive saddle-node bifurcations. Standard continuum approximations in the weakly nonlinear limit (equivalently, the limit of small mesh size) do not exhibit this behavior, due to the resultant leading-order reaction-diffusion equation lacking a periodic spatial structure. By including exponentially small effects hidden beyond all algebraic orders in the asymptotic expansion, we find that exponentially small but exponentially growing terms are switched on via error function smoothing near Stokes lines. Eliminating these otherwise unbounded beyond-all-orders terms selects the origin (modulo the mesh size) of the front, and matching two fronts together yields a set of equations describing the snaking bifurcation diagram. This is possible only within an exponentially small region of parameter space—the pinning region. Moreover, by considering fronts orientated at an arbitrary angle ψ to the x-axis, we show that the width of the pinning region is nonzero only if tan ψ is rational or infinite. The asymptotic results are compared with numerical calculations, with good agreement

A First Look at the Auriga-California Giant Molecular Cloud With Herschel and the CSO: Census of the Young Stellar Objects and the Dense Gas

We have mapped the Auriga/California molecular cloud with the Herschel PACS and SPIRE cameras and the Bolocam 1.1 mm camera on the Caltech Submillimeter Observatory (CSO) with the eventual goal of quantifying the star formation and cloud structure in this Giant Molecular Cloud (GMC) that is comparable in size and mass to the Orion GMC, but which appears to be forming far fewer stars. We have tabulated 60 compact 70/160um sources that are likely pre-main-sequence objects and correlated those with Spitzer and WISE mid-IR sources. At 1.1 mm we find 18 cold, compact sources and discuss their properties. The most important result from this part of our study is that we find a modest number of additional compact young objects beyond those identified at shorter wavelengths with Spitzer. We also describe the dust column density and temperature structure derived from our photometric maps. The column density peaks at a few x 10^22 cm^-2 (N_H2) and is distributed in a clear filamentary structure along which nearly all the pre-main-sequence objects are found. We compare the YSO surface density to the gas column density and find a strong non-linear correlation between them. The dust temperature in the densest parts of the filaments drops to ~10K from values ~ 14--15K in the low density parts of the cloud. We also derive the cumulative mass fraction and probability density function of material in the cloud which we compare with similar data on other star-forming clouds.Comment: in press Astrophysical Journal, 201

A Study of Work Practices in Tasmanian Government Schools: Final report to the Australian Education Union – Tasmanian Branch

The Australian Council for Educational Research (ACER) conducted an online survey of members on behalf of the Tasmanian Branch of the Australian Education Union (AEU). The survey, which was open to teachers, school leaders (principals and assistant principals) and education support staff working in Tasmanian government schools and offices, was available to the majority of members of the Union in August 2017, and remained open for four weeks during Term 3. The survey was based on one conducted for the Victorian branch of the AEU in 2016. The survey of the work of union members in Tasmanian government schools focussed on the hours of work by school staff, staff perceptions of their work, and the relationship between work practices and the quality of teaching. More than 3000 teachers, school leaders and education support staff completed the survey, a response rate of 60%

Successful unrelated donor cord blood transplantation for Glanzmann’s thrombasthenia

GT, a rare disorder of platelet function, can lead to life-threatening bleeding, particularly following the development of antiplatelet antibodies. Curative therapy includes HCT but previous reports are limited predominantly to matched siblings and have excluded CBT. Delayed or non-engraftment of platelets because of antiplatelet antibodies might be particularly concerning after CBT for GT. Here, we report two successful unrelated cord blood transplants for GT. Recurrent life-threatening bleeding was the primary indication for HCT, with one patient developing antiplatelet antibodies pre-HCT. Bleeding risks associated with delivery of the conditioning regimen and the toxicity that follows should be carefully considered, including tunneled central venous line catheter placement, inclusion of B cell-specific therapy to potentially decrease antiplatelet antibody production, and targeted busulfan dosing. This is the first report of successful unrelated cord blood HCT for GT and indicates that modifications to supportive care can improve the safety of this potentially curative therapy for patients with severe, life-threatening disease manifestations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/78580/1/j.1399-3046.2009.01251.x.pd