Evaluation of numerical integration schemes for a partial integro-differential equation

Numerical methods are important in computational neuroscience where complex nonlinear systems are studied. This report evaluates two methodologies, finite differences and Fourier series, for numerically integrating a nonlinear neural model based on a partial integro-differential equation. The stability and convergence criteria of four finite difference methods is investigated and their efficiency determined. Various ODE solvers in Matlab are used with the Fourier series method to solve the neural model, with an evaluation of the accuracy of the approximation versus the efficiency of the method. The two methodologies are then compared

Analysing the Transverse Structure of the Relativistic Jets of AGN

This paper describes a method of fitting total intensity and polarization profiles in VLBI images of astrophysical jets to profiles predicted by a theoretical model. As an example, the method is used to fit profiles of the jet in the Active Galactic Nucleus Mrk501 with profiles predicted by a model in which a cylindrical jet of synchrotron plasma is threaded by a magnetic field with helical and disordered components. This fitting yields model Stokes Q profiles that agree with the observed profiles to within the 1-2 \sigma uncertainties; the I model and observed profiles are overall not in such good agreement, with the model I profiles being generally more symmetrical than the observed profiles. Consistent fitting results are obtained for profiles derived from 6cm VLBI images at two distances from the core, and also for profiles obtained for different wavelengths at a single location in the VLBI jet. The most striking success of the model is its ability to reproduce the spine-sheath polarization structure observed across the jet. Using the derived viewing angle in the jet rest frame, \delta' approximately 83 degrees, together with a superluminal speed reported in the literature, \beta apparent = 3.3, yields a solution for the viewing angle and velocity of the jet in the observer's frame \delta degrees and \beta approximately 0.96. Although these results for Mrk501 must be considered tentative, the combined analysis of polarization profiles and apparent component speeds holds promise as a means of further elucidating the magnetic field structures and other parameters of parsec-scale AGN jets

An Attempt to Probe the Radio Jet Collimation Regions in NGC 4278, NGC 4374 (M84), and NGC 6166

NRAO Very Long Baseline Array (VLBA) observations of NGC 4278, NGC 4374 (M84), NGC 6166, and M87 (NGC 4486) have been made at 43 GHz in an effort to image the jet collimation region. This is the first attempt to image the first three sources at 43 GHz using Very Long Baseline Interferometry (VLBI) techniques. These three sources were chosen because their estimated black hole mass and distance implied a Schwarzschild radius with large angular size, giving hope that the jet collimation regions could be studied. Phase referencing was utilize for the three sources because of their expected low flux densities. M87 was chosen as the calibrator for NGC 4374 because it satisfied the phase referencing requirements: nearby to the source and sufficiently strong. Having observed M87 for a long integration time, we have detected its sub-parsec jet, allowing us to confirm previous high resolution observations made by Junor, Biretta & Livio, who have indicated that a wide opening angle was seen near the base of the jet. Phase referencing successfully improved our image sensitivity, yielding detections and providing accurate positions for NGC 4278, NGC 4374 and NGC 6166. These sources are point dominated, but show suggestions of extended structure in the direction of the large-scale jets. However, higher sensitivity will be required to study their sub-parsec jet structure

Chandra Observation of M84, Radio Lobe Elliptical in Virgo cluster

We analyzed a deep Chandra observation of M84, a bright elliptical galaxy in the core of the Virgo cluster. We find that the spatial distribution of the soft X-ray emission is defined by the radio structure of the galaxy. In particular we find two low density regions associated with the radio lobes and surrounded by higher density X-ray filaments. In addition to a central AGN and a population of galactic sources, we find a diffuse hard source filling the central 10 kpc region. Since the morphology of the hard source appears round and is different from that seen in the radio or in soft X-rays, we propose that it is hot gas heated by the central AGN. Finally, we find that the central elemental abundance in the X-ray gas is comparable to that measured optically.Comment: accepted to ApJ Letters, Oct 2000. 5 pages in emulateap

Love is . . . an abstract word: the influence of phonological and semantic factors on verbal short-term memory in Williams syndrome

It has been claimed that verbal short-term memory in Williams syndrome is characterised by an over-use of phonological coding alongside a reduced contribution of lexical semantics. We critically examine this hypothesis and present results from a memory span task comparing performance on concrete and abstract words, together with a replication of a span task using phonologically similar and phonologically dissimilar words. Fourteen participants with Williams syndrome were individually matched to two groups of typically developing children. The first control group was matched on digit span and the second on vocabulary level. Significant effects were found for both the semantic and the phonological variables in the WS group as well as in the control groups, with no interaction between experimental variable and group in either experiment. The results demonstrate that, despite claims to the contrary, children and adults with WS are able to access and make use of lexical semantics in a verbal short-term memory task in a manner comparable to typically developing individuals

Study protocol for a cluster-randomized controlled trial of an NCD access to medicines initative: Evaluation of Novartis Access in Kenya

INTRODUCTION: Novartis recently launched Novartis Access, an initiative to provide a basket of reduced price medicines for non-communicable diseases (NCDs) to be sold through the public and private nonprofit sectors in programme countries. This study will evaluate the impact of Novartis Access on the availability and price of NCD medicines at health facilities and households in Kenya, the first country to receive the programme. METHODS: This study will be a cluster randomised controlled trial. 8 counties in Kenya will be randomly assigned to the intervention or control group using a covariate constrained randomisation method to maximise balance on demographic and health characteristics. In intervention counties, public and private non-profit health facilities will be able to order Novartis Access NCD medicines from the Mission for Essential Drugs and Supplies (MEDS). Data will be collected from a random sample of 384 health facilities and 800 households at baseline, midline after 1-year of intervention, and end-line after 2 years. Quarterly surveillance data will also be collected from health facilities and a subsample of households through phone-based interviews. Households will be eligible if at least one resident has been previously diagnosed and prescribed a medicine for an NCD addressed by Novartis Access, including hypertension and diabetes. The primary outcomes will be availability and price of NCD medicines at health facilities, and availability, price, and expenditures on NCD medicines at households. Impacts will be estimated using intention-to-treat analysis. ETHICS AND DISSEMINATION: This protocol was approved by the Institutional Review Boards at Strathmore University and at Boston University. Informed consent will be obtained from all participants at the start of the trial. The findings of the trial will be disseminated through peer-reviewed journals, international conferences, and meetings and events organised with local stakeholders

Boson Sampling from Gaussian States

We pose a generalized Boson Sampling problem. Strong evidence exists that such a problem becomes intractable on a classical computer as a function of the number of Bosons. We describe a quantum optical processor that can solve this problem efficiently based on Gaussian input states, a linear optical network and non-adaptive photon counting measurements. All the elements required to build such a processor currently exist. The demonstration of such a device would provide the first empirical evidence that quantum computers can indeed outperform classical computers and could lead to applications

Dynamical Phase Transitions In Driven Integrate-And-Fire Neurons

We explore the dynamics of an integrate-and-fire neuron with an oscillatory stimulus. The frustration due to the competition between the neuron's natural firing period and that of the oscillatory rhythm, leads to a rich structure of asymptotic phase locking patterns and ordering dynamics. The phase transitions between these states can be classified as either tangent or discontinuous bifurcations, each with its own characteristic scaling laws. The discontinuous bifurcations exhibit a new kind of phase transition that may be viewed as intermediate between continuous and first order, while tangent bifurcations behave like continuous transitions with a diverging coherence scale.Comment: 4 pages, 5 figure