On Local Bifurcations in Neural Field Models with Transmission Delays

Neural field models with transmission delay may be cast as abstract delay differential equations (DDE). The theory of dual semigroups (also called sun-star calculus) provides a natural framework for the analysis of a broad class of delay equations, among which DDE. In particular, it may be used advantageously for the investigation of stability and bifurcation of steady states. After introducing the neural field model in its basic functional analytic setting and discussing its spectral properties, we elaborate extensively an example and derive a characteristic equation. Under certain conditions the associated equilibrium may destabilise in a Hopf bifurcation. Furthermore, two Hopf curves may intersect in a double Hopf point in a two-dimensional parameter space. We provide general formulas for the corresponding critical normal form coefficients, evaluate these numerically and interpret the results

Towards a computational model for stimulation of the Pedunculopontine nucleus

The pedunculopontine nucleus (PPN) has recently been suggested as a new therapeutic target for deep brain stimulation (DBS) in patients suffering from Parkinson's disease, particularly those with severe gait and postural impairment [1]. Stimulation at this site is typically delivered at low frequencies in contrast to the high frequency stimulation required for therapeutic benefit in the subthalamic nucleus (STN) [1]. Despite real therapeutic successes, the fundamental physiological mechanisms underlying the effect of DBS are still not understood. A hypothesis is that DBS masks the pathological synchronized firing patterns of the basal ganglia that characterize the Parkinsonian state with a regularized firing pattern. It remains unclear why stimulation of PPN should be applied with low frequency in contrast to the high frequency stimulation of STN. To get a better understanding of PPN stimulation we construct a computational model for the PPN Type I neurons in a network

On the reduction of the degree of linear differential operators

Let L be a linear differential operator with coefficients in some differential field k of characteristic zero with algebraically closed field of constants. Let k^a be the algebraic closure of k. For a solution y, Ly=0, we determine the linear differential operator of minimal degree M and coefficients in k^a, such that My=0. This result is then applied to some Picard-Fuchs equations which appear in the study of perturbations of plane polynomial vector fields of Lotka-Volterra type

A Framework for Directional and Higher-Order Reconstruction in Photoacoustic Tomography

Photoacoustic tomography is a hybrid imaging technique that combines high optical tissue contrast with high ultrasound resolution. Direct reconstruction methods such as filtered backprojection, time reversal and least squares suffer from curved line artefacts and blurring, especially in case of limited angles or strong noise. In recent years, there has been great interest in regularised iterative methods. These methods employ prior knowledge on the image to provide higher quality reconstructions. However, easy comparisons between regularisers and their properties are limited, since many tomography implementations heavily rely on the specific regulariser chosen. To overcome this bottleneck, we present a modular reconstruction framework for photoacoustic tomography. It enables easy comparisons between regularisers with different properties, e.g. nonlinear, higher-order or directional. We solve the underlying minimisation problem with an efficient first-order primal-dual algorithm. Convergence rates are optimised by choosing an operator dependent preconditioning strategy. Our reconstruction methods are tested on challenging 2D synthetic and experimental data sets. They outperform direct reconstruction approaches for strong noise levels and limited angle measurements, offering immediate benefits in terms of acquisition time and quality. This work provides a basic platform for the investigation of future advanced regularisation methods in photoacoustic tomography.Comment: submitted to "Physics in Medicine and Biology". Changes from v1 to v2: regularisation with directional wavelet has been added; new experimental tests have been include

When Organizational Identification Elicits Moral Decision-Making:A Matter of the Right Climate

To advance current knowledge on ethical decision-making in organizations, we integrate two perspectives that have thus far developed independently: the organizational identification perspective and the ethical climate perspective. We illustrate the interaction between these perspectives in two studies (Study 1, N = 144, US sample; and Study 2, N = 356, UK sample), in which we presented participants with moral business dilemmas. Specifically, we found that organizational identification increased moral decision-making only when the organization’s climate was perceived to be ethical. In addition, we disentangle this effect in Study 2 from participants’ moral identity. We argue that the interactive influence of organizational identification and ethical climate, rather than the independent influence of either of these perspectives, is crucial for understanding moral decision-making in organizations

On Kink-Dynamics of Stacked-Josephson Junctions

Dynamics of a fluxon in a stack of coupled long Josephson junctions is studied numericallv. Based on the numerical simulations, we show that the dependence of the propagation velocity c on the external bias current γ is determined by the ratio of the critical currents of thc two junctions J

Static and dynamic properties of fluxons in a zig-zag 0-π Josephson junction

We consider a long Josephson junction with alternating 0- and $\pi$-facets with different facet lengths between the 0- and the $\pi$-parts. Depending on the combinations between the 0- and the $\pi$-facet lengths, an antiferromagnetically ordered semifluxons array can be the ground state of the system. Due to the fact that in that case there are two independent ground states, an externally introduced 2$\pi$ fluxon will be splintered or fractionalized. The magnitude of the flux in the fractional fluxons is a function of the difference between the 0 and the $\pi$-facet lengths. Here, we present an analytical calculation of the flux of splintered Josephson fluxons for any combination of 0- and $\pi$-facet lengths. In the presence of an applied bias current, we show numerically that only one of the two fractional fluxons can be moved. We also consider the I–V characteristics of the ground state and the one of a 2$\pi$-fluxon in a zig-zag junction

Synchronization of the parkinsonian globus pallidus by gap junctions

We introduce pallidal gap junctional coupling as a possible mechanism for synchronization of the GPe after dopamine depletion. In a confocal imaging study, we show the presence of the neural gap junction protein Cx36 in the human GPe, including a possible remodeling process in PD patients. Dopamine has been shown to down-regulate the conductance of gap junctions in different regions of the brain [2,3], making dopamine depletion a possible candidate for increased influence of gap junctional coupling in PD