A comparison of computational methods and algorithms for the complex gamma function

A survey and comparison of some computational methods and algorithms for gamma and log-gamma functions of complex arguments are presented. Methods and algorithms reported include Chebyshev approximations, Pade expansion and Stirling's asymptotic series. The comparison leads to the conclusion that Algorithm 421 published in the Communications of ACM by H. Kuki is the best program either for individual application or for the inclusion in subroutine libraries

In vivo characterization of hippocampal electrophysiological processes in the heterozygous Pten knockout model of autism

While cognitive deficits have been described in the heterozygous Pten (+/-) KO mouse model of autism, little work has been done to demonstrate how corresponding in vitro physiological alterations in this model may underpin these cognitive deficits in vivo. As Pten KO (+/-) is known to alter electrophysiological characteristics of neurons in vitro, this study measures the in vivo electrophysiological characteristics of CA1 interneurons, pyramidal cells, and place cells which may underlie the spatial cognitive deficits seen in the model. Four transgenic conditional heterozygous Pten+/loxPloxP;Gfap-cre mice (HetPten) and four homozygous Pten littermate control mice were used in this study. This transgene drives cre expression and excision of the Pten gene in hippocampal granule cells of the dentate gyrus, and neurons in CA2 and CA1, but not astrocytes. In vivo local field potentials and single cell recordings were made in CA1 of each mouse during an open field foraging task in two distinct arenas. HetPten mice were found to have increased interneuron and pyramidal cell firing rates. In addition, place cells demonstrated abnormal properties including increased out-of-field firing rates, an increased number of fields, and trends towards larger field sizes that were less stable in comparison to controls. HetPten mice had slower CA1 fast gamma oscillations and more variable speed/theta oscillation correlations. Behaviorally, there were weak trends towards decreased motor output compared to controls. These data suggest that the electrophysiological alterations due to Pten KO (+/-) in mouse hippocampal neurons lead to hyperactivation of CA1 interneurons, pyramidal cells, and place cells

Modeling Heterogeneous Network Interference Using Poisson Point Processes

Cellular systems are becoming more heterogeneous with the introduction of low power nodes including femtocells, relays, and distributed antennas. Unfortunately, the resulting interference environment is also becoming more complicated, making evaluation of different communication strategies challenging in both analysis and simulation. Leveraging recent applications of stochastic geometry to analyze cellular systems, this paper proposes to analyze downlink performance in a fixed-size cell, which is inscribed within a weighted Voronoi cell in a Poisson field of interferers. A nearest out-of-cell interferer, out-of-cell interferers outside a guard region, and cross-tier interference are included in the interference calculations. Bounding the interference power as a function of distance from the cell center, the total interference is characterized through its Laplace transform. An equivalent marked process is proposed for the out-of-cell interference under additional assumptions. To facilitate simplified calculations, the interference distribution is approximated using the Gamma distribution with second order moment matching. The Gamma approximation simplifies calculation of the success probability and average rate, incorporates small-scale and large-scale fading, and works with co-tier and cross-tier interference. Simulations show that the proposed model provides a flexible way to characterize outage probability and rate as a function of the distance to the cell edge.Comment: Submitted to the IEEE Transactions on Signal Processing, July 2012, Revised December 201

Maturation trajectories of cortical resting-state networks depend on the mediating frequency band

The functional significance of resting state networks and their abnormal manifestations in psychiatric disorders are firmly established, as is the importance of the cortical rhythms in mediating these networks. Resting state networks are known to undergo substantial reorganization from childhood to adulthood, but whether distinct cortical rhythms, which are generated by separable neural mechanisms and are often manifested abnormally in psychiatric conditions, mediate maturation differentially, remains unknown. Using magnetoencephalography (MEG) to map frequency band specific maturation of resting state networks from age 7 to 29 in 162 participants (31 independent), we found significant changes with age in networks mediated by the beta (13–30 Hz) and gamma (31–80 Hz) bands. More specifically, gamma band mediated networks followed an expected asymptotic trajectory, but beta band mediated networks followed a linear trajectory. Network integration increased with age in gamma band mediated networks, while local segregation increased with age in beta band mediated networks. Spatially, the hubs that changed in importance with age in the beta band mediated networks had relatively little overlap with those that showed the greatest changes in the gamma band mediated networks. These findings are relevant for our understanding of the neural mechanisms of cortical maturation, in both typical and atypical development.This work was supported by grants from the Nancy Lurie Marks Family Foundation (TK, SK, MGK), Autism Speaks (TK), The Simons Foundation (SFARI 239395, TK), The National Institute of Child Health and Development (R01HD073254, TK), National Institute for Biomedical Imaging and Bioengineering (P41EB015896, 5R01EB009048, MSH), and the Cognitive Rhythms Collaborative: A Discovery Network (NFS 1042134, MSH). (Nancy Lurie Marks Family Foundation; Autism Speaks; SFARI 239395 - Simons Foundation; R01HD073254 - National Institute of Child Health and Development; P41EB015896 - National Institute for Biomedical Imaging and Bioengineering; 5R01EB009048 - National Institute for Biomedical Imaging and Bioengineering; NFS 1042134 - Cognitive Rhythms Collaborative: A Discovery Network

Improving Classification When a Class Hierarchy is Available Using a Hierarchy-Based Prior

We introduce a new method for building classification models when we have prior knowledge of how the classes can be arranged in a hierarchy, based on how easily they can be distinguished. The new method uses a Bayesian form of the multinomial logit (MNL, a.k.a. ``softmax'') model, with a prior that introduces correlations between the parameters for classes that are nearby in the tree. We compare the performance on simulated data of the new method, the ordinary MNL model, and a model that uses the hierarchy in different way. We also test the new method on a document labelling problem, and find that it performs better than the other methods, particularly when the amount of training data is small