Random Sampling with Interspike-Intervals of the Exponential Integrate and Fire Neuron: A Computational Interpretation of UP-States

Oscillations between high and low values of the membrane potential (UP and DOWN states respectively) are an ubiquitous feature of cortical neurons during slow wave sleep and anesthesia. Nevertheless, a surprisingly small number of quantitative studies have been conducted only that deal with this phenomenon’s implications for computation. Here we present a novel theory that explains on a detailed mathematical level the computational benefits of UP states. The theory is based on random sampling by means of interspike intervals (ISIs) of the exponential integrate and fire (EIF) model neuron, such that each spike is considered a sample, whose analog value corresponds to the spike’s preceding ISI. As we show, the EIF’s exponential sodium current, that kicks in when balancing a noisy membrane potential around values close to the firing threshold, leads to a particularly simple, approximative relationship between the neuron’s ISI distribution and input current. Approximation quality depends on the frequency spectrum of the current and is improved upon increasing the voltage baseline towards threshold. Thus, the conceptually simpler leaky integrate and fire neuron that is missing such an additional current boost performs consistently worse than the EIF and does not improve when voltage baseline is increased. For the EIF in contrast, the presented mechanism is particularly effective in the high-conductance regime, which is a hallmark feature of UP-states. Our theoretical results are confirmed by accompanying simulations, which were conducted for input currents of varying spectral composition. Moreover, we provide analytical estimations of the range of ISI distributions the EIF neuron can sample from at a given approximation level. Such samples may be considered by any algorithmic procedure that is based on random sampling, such as Markov Chain Monte Carlo or message-passing methods. Finally, we explain how spike-based random sampling relates to existing computational theories about UP states during slow wave sleep and present possible extensions of the model in the context of spike-frequency adaptation.

Computational Tools for Stereo and Light Field Photography

This thesis covers a broad part of the field of computational photography, including video stabilization and image warping techniques, introductions to light field photography and the conversion of monocular images and videos into stereoscopic 3D content. We present a user assisted technique for stereoscopic 3D conversion from 2D images. Our approach exploits the geometric structure of perspective images including vanishing points. We allow a user to indicate lines, planes, and vanishing points in the input image, and directly employ these as guides of an image warp that produces a stereo image pair. Our method is most suitable for scenes with large scale structures such as buildings and is able to skip the step of constructing a depth map. Further, we propose a method to acquire 3D light fields using a hand-held camera, and describe several computational photography applications facilitated by our approach. As the input we take an image sequence from a camera translating along an approximately linear path with limited camera rotations. Users can acquire such data easily in a few seconds by moving a hand-held camera. We convert the input into a regularly sampled 3D light field by resampling and aligning them in the spatio-temporal domain. We also present a novel technique for high-quality disparity estimation from light fields. Finally, we show applications including digital refocusing and synthetic aperture blur, foreground removal, selective colorization, and others.

Computational fluid dynamics modelling in cardiovascular medicine.

This paper reviews the methods, benefits and challenges associated with the adoption and translation of computational fluid dynamics (CFD) modelling within cardiovascular medicine. CFD, a specialist area of mathematics and a branch of fluid mechanics, is used routinely in a diverse range of safety-critical engineering systems, which increasingly is being applied to the cardiovascular system. By facilitating rapid, economical, low-risk prototyping, CFD modelling has already revolutionised research and development of devices such as stents, valve prostheses, and ventricular assist devices. Combined with cardiovascular imaging, CFD simulation enables detailed characterisation of complex physiological pressure and flow fields and the computation of metrics which cannot be directly measured, for example, wall shear stress. CFD models are now being translated into clinical tools for physicians to use across the spectrum of coronary, valvular, congenital, myocardial and peripheral vascular diseases. CFD modelling is apposite for minimally-invasive patient assessment. Patient-specific (incorporating data unique to the individual) and multi-scale (combining models of different length- and time-scales) modelling enables individualised risk prediction and virtual treatment planning. This represents a significant departure from traditional dependence upon registry-based, population-averaged data. Model integration is progressively moving towards 'digital patient' or 'virtual physiological human' representations. When combined with population-scale numerical models, these models have the potential to reduce the cost, time and risk associated with clinical trials. The adoption of CFD modelling signals a new era in cardiovascular medicine. While potentially highly beneficial, a number of academic and commercial groups are addressing the associated methodological, regulatory, education- and service-related challenges.

Computational Comparison of Continuous and Discontinuous Galerkin Time-Stepping Methods for Nonlinear Initial Value Problems

This article centers on the computational performance of the continuous and discontinuous Galerkin time stepping schemes for general first-order initial value problems in R n , with continuous nonlinearities. We briefly review a recent existence result for discrete solutions from [6], and provide a numerical comparison of the two time discretization methods.

Outcomes of Active Surveillance for Ductal Carcinoma in Situ: A Computational Risk Analysis.

BACKGROUND Ductal carcinoma in situ (DCIS) is a noninvasive breast lesion with uncertain risk for invasive progression. Usual care (UC) for DCIS consists of treatment upon diagnosis, thus potentially overtreating patients with low propensity for progression. One strategy to reduce overtreatment is active surveillance (AS), whereby DCIS is treated only upon detection of invasive disease. Our goal was to perform a quantitative evaluation of outcomes following an AS strategy for DCIS. METHODS Age-stratified, 10-year disease-specific cumulative mortality (DSCM) for AS was calculated using a computational risk projection model based upon published estimates for natural history parameters, and Surveillance, Epidemiology, and End Results data for outcomes. AS projections were compared with the DSCM for patients who received UC. To quantify the propagation of parameter uncertainty, a 95% projection range (PR) was computed, and sensitivity analyses were performed. RESULTS Under the assumption that AS cannot outperform UC, the projected median differences in 10-year DSCM between AS and UC when diagnosed at ages 40, 55, and 70 years were 2.6% (PR = 1.4%-5.1%), 1.5% (PR = 0.5%-3.5%), and 0.6% (PR = 0.0%-2.4), respectively. Corresponding median numbers of patients needed to treat to avert one breast cancer death were 38.3 (PR = 19.7-69.9), 67.3 (PR = 28.7-211.4), and 157.2 (PR = 41.1-3872.8), respectively. Sensitivity analyses showed that the parameter with greatest impact on DSCM was the probability of understaging invasive cancer at diagnosis. CONCLUSION AS could be a viable management strategy for carefully selected DCIS patients, particularly among older age groups and those with substantial competing mortality risks. The effectiveness of AS could be markedly improved by reducing the rate of understaging.