Evaluations of infinite series involving reciprocal hyperbolic functions

This paper presents a approach of summation of infinite series of hyperbolic functions. The approach is based on simple contour integral representions and residue computations with the help of some well known results of Eisenstein series given by Ramanujan and Berndt et al. Several series involving quadratic hyperbolic functions are evaluated, which can be expressed in terms of $z={}_2F_1(1/2,1/2;1;x)$ and $z'=dz/dx$. When a certain parameter in these series equal to $\pi$ the series are summable in terms of $\Gamma$ functions. Moreover, some interesting new consequences and illustrative examples are considered

Unsupervised Learning of Frustrated Classical Spin Models I: Principle Component Analysis

This work aims at the goal whether the artificial intelligence can recognize phase transition without the prior human knowledge. If this becomes successful, it can be applied to, for instance, analyze data from quantum simulation of unsolved physical models. Toward this goal, we first need to apply the machine learning algorithm to well-understood models and see whether the outputs are consistent with our prior knowledge, which serves as the benchmark of this approach. In this work, we feed the compute with data generated by the classical Monte Carlo simulation for the XY model in frustrated triangular and union jack lattices, which has two order parameters and exhibits two phase transitions. We show that the outputs of the principle component analysis agree very well with our understanding of different orders in different phases, and the temperature dependences of the major components detect the nature and the locations of the phase transitions. Our work offers promise for using machine learning techniques to study sophisticated statistical models, and our results can be further improved by using principle component analysis with kernel tricks and the neural network method.Comment: 8 pages, 11 figure

Liberate your avatar; the revolution will be social networked

This paper brings together the practice-based creative research of artists Charlotte Gould and Paul Sermon, culminating in a collaborative interactive installation that investigates new forms of social and political narrative in multi-user virtual environments. The authors' artistic projects deal with the ironies and stereotypes that are found within Second Life in particular. Paul Sermon’s current creative practice looks specifically at the concepts of presence and performance within Second Life and 'first life', and attempts to bridge these two spaces through mixed reality techniques and interfaces. Charlotte Gould’s Ludic Second Life Narrative radically questions the way that users embody themselves in on-line virtual environments and identifies a counter-aesthetic that challenges the conventions of digital realism and consumerism. These research activities and outcomes come together within a collaborative site-specific public installation entitled Urban Intersections for ISEA09, focusing on contested virtual spaces that mirror the social and political history of Belfast. The authors' current collaborative practice critically investigates social, cultural and creative interactions in Second Life. Through these practice-based experiments the authors' argue that an enhanced social and cultural discourse within multi-user virtual environments will inevitably lead to growth, cohesion and public empowerment, and like all social networking platforms, contribute to greater social and political change in first life

A Hybrid Multi-Distance Phase and Broadband Spatially Resolved Spectrometer and Algorithm for Resolving Absolute Concentrations of Chromophores in the Near-Infrared Light Spectrum

For resolving absolute concentration of tissue chromophores in the human adult brain with near-infrared spectroscopy it is necessary to calculate the light scattering and absorption, at multiple wavelengths with some depth resolution. To achieve this we propose an instrumentation configuration that combines multi-distance frequency and broadband spectrometers to quantify chromophores in turbid media by using a hybrid spatially resolved algorithm. Preliminary results in solid phantoms as well as liquid dynamic homogeneous and inhomogeneous phantoms and in-vivo muscle measurements showed encouraging results

GM-Net: Learning Features with More Efficiency

Deep Convolutional Neural Networks (CNNs) are capable of learning unprecedentedly effective features from images. Some researchers have struggled to enhance the parameters' efficiency using grouped convolution. However, the relation between the optimal number of convolutional groups and the recognition performance remains an open problem. In this paper, we propose a series of Basic Units (BUs) and a two-level merging strategy to construct deep CNNs, referred to as a joint Grouped Merging Net (GM-Net), which can produce joint grouped and reused deep features while maintaining the feature discriminability for classification tasks. Our GM-Net architectures with the proposed BU_A (dense connection) and BU_B (straight mapping) lead to significant reduction in the number of network parameters and obtain performance improvement in image classification tasks. Extensive experiments are conducted to validate the superior performance of the GM-Net than the state-of-the-arts on the benchmark datasets, e.g., MNIST, CIFAR-10, CIFAR-100 and SVHN.Comment: 6 Pages, 5 figure