Stability of Negative Image Equilibria in Spike-Timing Dependent Plasticity

We investigate the stability of negative image equilibria in mean synaptic weight dynamics governed by spike-timing dependent plasticity (STDP). The neural architecture of the model is based on the electrosensory lateral line lobe (ELL) of mormyrid electric fish, which forms a negative image of the reafferent signal from the fish's own electric discharge to optimize detection of external electric fields. We derive a necessary and sufficient condition for stability, for arbitrary postsynaptic potential functions and arbitrary learning rules. We then apply the general result to several examples of biological interest.Comment: 13 pages, revtex4; uses packages: graphicx, subfigure; 9 figures, 16 subfigure

Analytical Approximations of Critical Clearing Time for Parametric Analysis of Power System Transient Stability

An analytic approximation for the critical clearing time (CCT) metric is derived from direct methods for power system stability. The formula has been designed to incorporate as many features of transient stability analysis as possible such as different fault locations and different post-fault network states. The purpose of this metric is to analyse trends in stability (in terms of CCT) of power systems under the variation of a system parameter. The performance of this metric to measure stability trends is demonstrated on an aggregated power network, the so-called two machine infinite bus network, by varying load parameters in the full bus admittance matrix using numerical continuation. The metric is compared to two other expressions for the CCT which incorporate additional non-linearities present in the model

Mathematical modelling of a magnetic immunoassay

© The authors 2017. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. A mathematical model is developed to describe the action of a novel form of fluidic biosensor that uses paramagnetic particles (PMPs) that have been pre-coated with target-specific antibodies. In an initial phase the particles are introduced to a sample solution containing the target which then binds to the particles via antigen-antibody reactions. During the test phase a magnet is used to draw the PMPs to the sensor surface which is similarly coated with specific antibodies. During this process, cross-links are formed by the antigens thereby binding the PMPs to the sensor surface. After the magnetic field is removed, a voltage change across an inductor below the sensor surface is recorded, which is deemed to depend on the number of magnetic particles that have been bound to the sensor surface. The fundamental question addressed is to explain the range of experimentally observed dose-response curves, and how this depends on the various parameters of the problem. In particular, observations have shown both rising and falling dose-response curves, as well as 'hooked' dose-response curves possessing local maxima. Initially a particle-dynamics computational model is produced to determine the time scales of the key processes involved, but is shown to be unable to produce differently shaped dose-response curves. The computational model suggests spatio-temporal effects are unimportant, therefore a homogenized rateequation model is developed for each of the key phases of the immunoassay process. Binding rates are shown to depend on various geometric factors related to the diameter of the PMPs and the size of the sensor surface. The dose-response is shown to depend crucially on various saturation effects during each phase, and conditions can be derived, in some cases analytically, for each of the three qualitatively different curve types. Furthermore, non-dimensionalization reveals 5 key dimensionless parameters and the dependence of these curve shapes on each is revealed. The results point to future quantitative approaches to sensor design and calibration

Random Walks for Spike-Timing Dependent Plasticity

Random walk methods are used to calculate the moments of negative image equilibrium distributions in synaptic weight dynamics governed by spike-timing dependent plasticity (STDP). The neural architecture of the model is based on the electrosensory lateral line lobe (ELL) of mormyrid electric fish, which forms a negative image of the reafferent signal from the fish's own electric discharge to optimize detection of sensory electric fields. Of particular behavioral importance to the fish is the variance of the equilibrium postsynaptic potential in the presence of noise, which is determined by the variance of the equilibrium weight distribution. Recurrence relations are derived for the moments of the equilibrium weight distribution, for arbitrary postsynaptic potential functions and arbitrary learning rules. For the case of homogeneous network parameters, explicit closed form solutions are developed for the covariances of the synaptic weight and postsynaptic potential distributions.Comment: 18 pages, 8 figures, 15 subfigures; uses revtex4, subfigure, amsmat

Association Between Early Hyperoxia Exposure After Resuscitation From Cardiac Arrest and Neurological Disability: Prospective Multicenter Protocol-Directed Cohort Study

BACKGROUND: Studies examining the association between hyperoxia exposure after resuscitation from cardiac arrest and clinical outcomes have reported conflicting results. Our objective was to test the hypothesis that early postresuscitation hyperoxia is associated with poor neurological outcome. METHODS: This was a multicenter prospective cohort study. We included adult patients with cardiac arrest who were mechanically ventilated and received targeted temperature management after return of spontaneous circulation. We excluded patients with cardiac arrest caused by trauma or sepsis. Per protocol, partial pressure of arterial oxygen (Pao2) was measured at 1 and 6 hours after return of spontaneous circulation. Hyperoxia was defined as a Pao2 >300 mm Hg during the initial 6 hours after return of spontaneous circulation. The primary outcome was poor neurological function at hospital discharge, defined as a modified Rankin Scale score >3. Multivariable generalized linear regression with a log link was used to test the association between Pao2 and poor neurological outcome. To assess whether there was an association between other supranormal Pao2 levels and poor neurological outcome, we used other Pao2 cut points to define hyperoxia (ie, 100, 150, 200, 250, 350, 400 mm Hg). RESULTS: Of the 280 patients included, 105 (38%) had exposure to hyperoxia. Poor neurological function at hospital discharge occurred in 70% of patients in the entire cohort and in 77% versus 65% among patients with versus without exposure to hyperoxia respectively (absolute risk difference, 12%; 95% confidence interval, 1-23). Hyperoxia was independently associated with poor neurological function (relative risk, 1.23; 95% confidence interval, 1.11-1.35). On multivariable analysis, a 1-hour-longer duration of hyperoxia exposure was associated with a 3% increase in risk of poor neurological outcome (relative risk, 1.03; 95% confidence interval, 1.02-1.05). We found that the association with poor neurological outcome began at ≥300 mm Hg. CONCLUSIONS: Early hyperoxia exposure after resuscitation from cardiac arrest was independently associated with poor neurological function at hospital discharge

Transplanting Kidneys Without Points for HLA‐B Matching: Consequences of the Policy Change

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87103/1/j.1600-6143.2011.03606.x.pd

Autologous chondrocyte implantation for cartilage repair: monitoring its success by magnetic resonance imaging and histology

Autologous chondrocyte implantation is being used increasingly for the treatment of cartilage defects. In spite of this, there has been a paucity of objective, standardised assessment of the outcome and quality of repair tissue formed. We have investigated patients treated with autologous chondrocyte implantation (ACI), some in conjunction with mosaicplasty, and developed objective, semiquantitative scoring schemes to monitor the repair tissue using MRI and histology. Results indicate repair tissue to be on average 2.5 mm thick. It was of varying morphology ranging from predominantly hyaline in 22% of biopsy specimens, mixed in 48%, through to predominantly fibrocartilage, in 30%, apparently improving with increasing time postgraft. Repair tissue was well integrated with the host tissue in all aspects viewed. MRI scans provide a useful assessment of properties of the whole graft area and adjacent tissue and is a noninvasive technique for long-term follow-up. It correlated with histology (P = 0.02) in patients treated with ACI alone

Sensitivity of marine protected area network connectivity to atmospheric variability

International efforts are underway to establish well-connected systems of marine protected areas (MPAs) covering at least 10% of the ocean by 2020. But the nature and dynamics of ocean ecosystem connectivity are poorly understood, with unresolved effects of climate variability. We used 40-year runs of a particle tracking model to examine the sensitivity of an MPA network for habitat-forming cold-water corals in the northeast Atlantic to changes in larval dispersal driven by atmospheric cycles and larval behaviour. Trajectories of Lophelia pertusa larvae were strongly correlated to the North Atlantic Oscillation (NAO), the dominant pattern of interannual atmospheric circulation variability over the northeast Atlantic. Variability in trajectories significantly altered network connectivity and source–sink dynamics, with positive phase NAO conditions producing a well-connected but asymmetrical network connected from west to east. Negative phase NAO produced reduced connectivity, but notably some larvae tracked westward-flowing currents towards coral populations on the mid-Atlantic ridge. Graph theoretical metrics demonstrate critical roles played by seamounts and offshore banks in larval supply and maintaining connectivity across the network. Larval longevity and behaviour mediated dispersal and connectivity, with shorter lived and passive larvae associated with reduced connectivity. We conclude that the existing MPA network is vulnerable to atmospheric-driven changes in ocean circulation

3D Seismic reflection evidence for lower crustal intrusions beneath the Faroe–Shetland Basin, NE Atlantic Margin

Lower crustal intrusion is considered to be a common process along volcanic or magma-rich passive margins, including the NE Atlantic Margin, where it is thought to have occurred during phases of Paleogene magmatism, both prior to and during continental break-up between NW Europe and Greenland. Evidence of Paleogene magmatism is prevalent throughout the sub-basins of the Faroe–Shetland Basin as extensive lava flows and pervasive suites of igneous intrusions. However, in contrast with other areas located along the NE Atlantic Margin, no lower crustal reflectivity indicative of lower crustal intrusion has been documented beneath the Faroe–Shetland Basin. The nearest documentation of lower crustal reflectivity and interpretation of lower crustal intrusion to the Faroe–Shetland Basin is NW of the Fugloy Ridge, beneath the Norwegian Basin of the Faroese sector. Despite this, the addition of magma within the lower crust and/or at the Mohorovičić discontinuity is thought to have played a part in Paleogene uplift and the subsequent deposition of Paleocene–Eocene sequences. Advances in sub-basalt seismic acquisition and processing have made significant improvements in facilitating the imaging of deep crustal structures along the NE Atlantic Margin. This study used broadband 3D seismic reflection data to map a series of deep (c. 14–20 km depth) high-amplitude reflections that may represent igneous intrusions within the lower crust beneath the central-northern Corona Ridge. We estimate that the cumulative thicknesses of the reflections may be >5 km in places, which is consistent with published values of magmatic underplating within the region based on geochemical and petrological data. We also estimate that the total volume of lower crustal high-amplitude reflections within the 3D dataset may be >2000 km3. 2D gravity modelling of a seismic line located along the central-northern Corona Ridge supports the interpretation of lower crustal intrusions beneath this area. This study provides evidence of a potential mechanism for Paleogene uplift within the region. If uplift occurred as a result of lower crustal intrusions emplaced within the crust during the Paleogene, then we estimate that c. 300 m of uplift may have been generated within the Corona Ridge area