On Spatial Consensus Formation: Is the Sznajd Model Different from a Voter Model?

In this paper, we investigate the so-called ``Sznajd Model'' (SM) in one dimension, which is a simple cellular automata approach to consensus formation among two opposite opinions (described by spin up or down). To elucidate the SM dynamics, we first provide results of computer simulations for the spatio-temporal evolution of the opinion distribution $L(t)$, the evolution of magnetization $m(t)$, the distribution of decision times $P(\tau)$ and relaxation times $P(\mu)$. In the main part of the paper, it is shown that the SM can be completely reformulated in terms of a linear VM, where the transition rates towards a given opinion are directly proportional to frequency of the respective opinion of the second-nearest neighbors (no matter what the nearest neighbors are). So, the SM dynamics can be reduced to one rule, ``Just follow your second-nearest neighbor''. The equivalence is demonstrated by extensive computer simulations that show the same behavior between SM and VM in terms of $L(t)$, $m(t)$, $P(\tau)$, $P(\mu)$, and the final attractor statistics. The reformulation of the SM in terms of a VM involves a new parameter $\sigma$, to bias between anti- and ferromagnetic decisions in the case of frustration. We show that $\sigma$ plays a crucial role in explaining the phase transition observed in SM. We further explore the role of synchronous versus asynchronous update rules on the intermediate dynamics and the final attractors. Compared to the original SM, we find three additional attractors, two of them related to an asymmetric coexistence between the opposite opinions.Comment: 22 pages, 20 figures. For related publications see http://www.ais.fraunhofer.de/~fran

Implied volatility of basket options at extreme strikes

In the paper, we characterize the asymptotic behavior of the implied volatility of a basket call option at large and small strikes in a variety of settings with increasing generality. First, we obtain an asymptotic formula with an error bound for the left wing of the implied volatility, under the assumption that the dynamics of asset prices are described by the multidimensional Black-Scholes model. Next, we find the leading term of asymptotics of the implied volatility in the case where the asset prices follow the multidimensional Black-Scholes model with time change by an independent increasing stochastic process. Finally, we deal with a general situation in which the dependence between the assets is described by a given copula function. In this setting, we obtain a model-free tail-wing formula that links the implied volatility to a special characteristic of the copula called the weak lower tail dependence function

Chronic intrastriatal quinolinic acid produces reversible changes in perikaryal calbindin and parvalbumin immunoreactivity

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31558/1/0000485.pd

Parkinson's disease biomarkers: perspective from the NINDS Parkinson's Disease Biomarkers Program

Biomarkers for Parkinson's disease (PD) diagnosis, prognostication and clinical trial cohort selection are an urgent need. While many promising markers have been discovered through the National Institute of Neurological Disorders and Stroke Parkinson's Disease Biomarker Program (PDBP) and other mechanisms, no single PD marker or set of markers are ready for clinical use. Here we discuss the current state of biomarker discovery for platforms relevant to PDBP. We discuss the role of the PDBP in PD biomarker identification and present guidelines to facilitate their development. These guidelines include: harmonizing procedures for biofluid acquisition and clinical assessments, replication of the most promising biomarkers, support and encouragement of publications that report negative findings, longitudinal follow-up of current cohorts including the PDBP, testing of wearable technologies to capture readouts between study visits and development of recently diagnosed (de novo) cohorts to foster identification of the earliest markers of disease onset

Determinant and Weyl anomaly of Dirac operator: a holographic derivation

We present a holographic formula relating functional determinants: the fermion determinant in the one-loop effective action of bulk spinors in an asymptotically locally AdS background, and the determinant of the two-point function of the dual operator at the conformal boundary. The formula originates from AdS/CFT heuristics that map a quantum contribution in the bulk partition function to a subleading large-N contribution in the boundary partition function. We use this holographic picture to address questions in spectral theory and conformal geometry. As an instance, we compute the type-A Weyl anomaly and the determinant of the iterated Dirac operator on round spheres, express the latter in terms of Barnes' multiple gamma function and gain insight into a conjecture by B\"ar and Schopka.Comment: 11 pages; new comments and references added, typos correcte

Excitatory amino acid binding sites in the basal ganglia of the rat: A quantitative autoradiographic study

Quantitative receptor autoradiography was used to determine the distribution of excitatory amino acid binding sites in the basal ganglia of rat brain. [alpha]-Amino-3-hydroxy-5-methylisoxazole-4-propionic acid, , kainate, quisqualate-sensitive metabotropic and , non-kainate, non-quisqualate glutamate binding sites had their highest density in striatum, nucleus accumbens, and olfactory tubercle. Kainate binding was higher in the lateral striatum but there was no medial-lateral striatal gradient for other binding sites. and [alpha]-amino-3-hydroxy-5-methylisoxazole-4-propionic acid binding sites were most dense in the nucleus accumbens and olfactory tubercle. There was no dorsal-ventral gradient within the striatal complex for the other binding sites. Other regions of the basal ganglia had lower densities of ligand binding. To compare binding site density within non-striatal regions, binding for each ligand was normalized to the striatal binding density. When compared to the striatal complex, [alpha]-amino-3-hydroxy-5-methylisoxazole-4-propionic acid and metabotropic binding sites had higher relative density in the globus pallidus, ventral pallidum, and subthalamic nucleus than other binding sites. Metabotropic binding also had a high relative density in the substantia nigra. , non-kainate, non-quisqualate glutamate binding sites had a high relative density in globus pallidus, ventral pallidum, and substantia nigra. binding sites had a low relative density in pallidum, subthalamic nucleus, substantia nigra and ventral tegmental area.Our data indicate heterogeneous distribution of excitatory amino acid binding sites within rat basal ganglia and suggest that the character of excitatory amino acid-mediated neurotransmission within the basal ganglia is also heterogeneous.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30265/1/0000666.pd