Numerical Computation of a Certain Dirichlet Series Attached to Siegel Modular Forms of Degree Two

The Rankin convolution type Dirichlet series D-F,D-G(s) of Siegel modular forms F and G of degree two, which was introduced by Kohnen and the second author, is computed numerically for various F and G. In particular, we prove that the series D-F,D-G(s), which shares the same functional equation and analytic behavior with the spinor L-functions of eigenforms of the same weight are not linear combinations of those. In order to conduct these experiments a numerical method to compute the Petersson scalar products of Jacobi Forms is developed and discussed in detail.

Efficient computation of discrete polynomial transforms

This letter presents a new recursive method for computing discrete polynomial transforms. The method is shown for forward and inverse transforms of the Hermite, binomial, and Laguerre transforms. The recursive flow diagrams require only 2 additions, 2( +1) memory units, and +1multipliers for the +1-point Hermite and binomial transforms. The recursive flow diagram for the +1-point Laguerre transform requires 2 additions, 2( +1) memory units, and 2( +1) multipliers. The transform computation time for all of these transforms is ( )

Computation of discrete cosine transform using Clenshaw's recurence formula

Clenshaw’s recurrenee formula is used to derive recursive algorithms for the discrete cosine transform @CT) and the inverse discrete cosine transform (IDCT). The recursive DCT algorithm presented here requires one fewer delay element per coefficient and one fewer multiply operation per coeflident compared with two recently proposed methods. Clenshaw’s recurrence formula provides a unified development for the recursive DCT and IDCT algorithms. The M v e al gorithms apply to arbitrary lengtb algorithms and are appropriate for VLSI implementation.

Structural and procedural properties important in promoting bio-enterprises as alternative livelihoods to pastoral and agro-pastoral livelihoods

Alternative livelihoods to pastoral and agro-pastoral livelihoods are increasingly gaining attention in rural development but few empirical evidence exist on how to go about supporting such initiatives. As pastoral and agro-pastoral production conditions change due to various factors including market conditions, climate variability and change, pastoralists and agro-pastoralists are increasingly faced with the challenge of finding alternative livelihoods. Bio-enterprises offer such alternatives or complementary activities for rural actors to adapt to changing socio-ecological conditions. This study examines the roles of bio-enterprise initiatives from a livelihood perspective and identifies the features important for such initiatives to reduce poverty and improve the adaptive capacities of pastoralists and agro-pastoralists. It draws on four different bio-enterprise initiatives on agro-pastoral and pastoral livelihoods and on improved natural resources management (NRM) in the drylands of Kenya. Data were collected through interviews, focus group discussions, informal discussions and the study of reports. Results shows among other factors that diversification into enterprises requires cooperation among the stakeholders with their varying experiences in development, NRM and business development. Other factors such as sustained financial support, capacity development to survive the market introduction phase, as well as quantity and quality of the product, are critical. Mentoring proved to be a driver of success in some initiatives.

THE RESONATE-AND-FIRE NEURON: TIME DEPENDENT AND FREQUENCY SELECTIVE NEURONS IN NEURAL NETWORKS

The means through which the nervous system perceives its environment is one of the most fascinating questions in contemporary science. Our endeavors to comprehend the principles of neural science provide an instance of how biological processes may inspire novel methods in mathematical modeling and engineering. The application ofmathematical models towards understanding neural signals and systems represents a vibrant field of research that has spanned over half a century. During this period, multiple approaches to neuronal modeling have been adopted, and each approach is adept at elucidating a specific aspect of nervous system function. Thus while bio-physical models have strived to comprehend the dynamics of actual physical processes occurring within a nerve cell, the phenomenological approach has conceived models that relate the ionic properties of nerve cells to transitions in neural activity. Further-more, the field of neural networks has endeavored to explore how distributed parallel processing systems may become capable of storing memory. Through this project, we strive to explore how some of the insights gained from biophysical neuronal modeling may be incorporated within the field of neural net-works. We specifically study the capabilities of a simple neural model, the Resonate-and-Fire (RAF) neuron, whose derivation is inspired by biophysical neural modeling. While reflecting further biological plausibility, the RAF neuron is also analytically tractable, and thus may be implemented within neural networks. In the following thesis, we provide a brief overview of the different approaches that have been adopted towards comprehending the properties of nerve cells, along with the framework under which our specific neuron model relates to the field of neuronal modeling. Subsequently, we explore some of the time-dependent neurocomputational capabilities of the RAF neuron, and we utilize the model to classify logic gates, and solve the classic XOR problem. Finally we explore how the resonate-and-fire neuron may be implemented within neural networks, and how such a network could be adapted through the temporal backpropagation algorithm.

Analysis of cytokines in the peritoneal fluid of endometriosis patients as a function of the menstrual cycle stage using the Bio-Plex® platform

Endometriosis is a painful disease affecting 10-15% of reproductive-age women. Concentrations of several cytokines and angiogenic factors in peritoneal fluid (PF) have been found to correlate with the severity of the disease. However, levels of some analytes vary across the menstrual cycle, and an ideal biomarker of endometriosis has not yet been identified. We have compared the PF concentrations of different cytokines in proliferative and secretory phases in women with and without the disease using the Bio-Plex platform.

Public, Private and University Collaboration: Applying a Retrospective Study of the Central Massachusetts Bio-Medical Cluster, Cluster Project Summary for Mosakowski Institute

Three Clark faculty members are studying the development of the Worcester Biotechnology Cluster for any lessons it might hold for current efforts to catalyze the growth of a sustainable energy/green jobs cluster in Worcester or elsewhere. Mary Ellen Boyle (GSOM), Jennie Stephens (IDCE/ESP), and Jing Zhang (GSOM) have conducted extensive in-depth interviews and combed the literature of cluster development to produce several articles and working papers.

Effect of Bio-Oss on osseointegration of dental implants surrounded by circumferential bone defects of different dimensions: an experimental study in the dog

OBJECTIVES: This study was designed to evaluate the effect of gap width and graft placement on bone healing around implants placed in simulated extraction sockets of various widths in four Labrador dogs. MATERIALS AND METHODS: Five Osseotite implants per dog were placed in the mandible of four dogs. Two implants were inserted into sites with a 2.37 mm and two with a 1 mm gap present between the implants and bone around the coronal 6 mm of the implants in each dog. For one of each gap sizes, the gap was filled with Bio-Oss, and the other two with blood alone. A fifth implant was inserted without a gap and used as a control. Ground sections were prepared from biopsies taken at 4 months and histometric measurements of osseointegration and bone between the threads made for the coronal 6 mm. RESULTS: The medians for osseointegration ranged from 5.2 mm for control to 1-2.6 mm for the test modalities. There were significant differences for linear measurements of osseointegration (chi(2) 18.27; df 4; P=0.0011) and bone area within threads (chi(2) 23.4; df 4; P=0.0001) between test modalities. CONCLUSIONS: The results suggest that the wider the gap around the implants, the less favourable the histological outcome at short time intervals following treatment. They also infer that bone grafting with an organic bovine bone xenograft seems to lead to a more favourable histological outcome for wider circumferential defects but not for narrower defects.

ON MARGINALIZED MULTILEVEL MODELS AND THEIR COMPUTATION

Clustered data analysis is characterized by the need to describe both systematic variation in a mean model and cluster-dependent random variation in an association model. Marginalized multilevel models embrace the robustness and interpretations of a marginal mean model, while retaining the likelihood inference capabilities and flexible dependence structures of a conditional association model. Although there has been increasing recognition of the attractiveness of marginalized multilevel models, there has been a gap in their practical application arising from a lack of readily available estimation procedures. We extend the marginalized multilevel model to allow for nonlinear functions in both the mean and association aspects. We then formulate marginal models through conditional specifications to facilitate estimation with mixed model computational solutions already in place. We illustrate this approach on a cerebrovascular deficiency crossover trial.

Learning real-world stimuli in a neural network with spike-driven synaptic dynamics

We present a model of spike-driven synaptic plasticity inspired by experimental observations and motivated by the desire to build an electronic hardware device that can learn to classify complex stimuli in a semisupervised fashion. During training, patterns of activity are sequentially imposed on the input neurons, and an additional instructor signal drives the output neurons toward the desired activity. The network is made of integrate-and-fire neurons with constant leak and a floor. The synapses are bistable, and they are modified by the arrival of presynaptic spikes. The sign of the change is determined by both the depolarization and the state of a variable that integrates the postsynaptic action potentials. Following the training phase, the instructor signal is removed, and the output neurons are driven purely by the activity of the input neurons weighted by the plastic synapses. In the absence of stimulation, the synapses preserve their internal state indefinitely. Memories are also very robust to the disruptive action of spontaneous activity. A network of 2000 input neurons is shown to be able to classify correctly a large number (thousands) of highly overlapping patterns (300 classes of preprocessed Latex characters, 30 patterns per class, and a subset of the NIST characters data set) and to generalize with performances that are better than or comparable to those of artificial neural networks. Finally we show that the synaptic dynamics is compatible with many of the experimental observations on the induction of long-term modifications (spike-timing-dependent plasticity and its dependence on both the postsynaptic depolarization and the frequency of pre- and postsynaptic neurons).