Improvement on Gauss circle Problem and Dirichlet divisor Problem

We establish an improvement for both Gauss circle problem and Dirichlet divisor problem, combining a new estimate of the first spacing problem and Huxley's results on the second spacing problem

A Dynamic Analysis of IRS-PKR Signaling in Liver Cells: A Discrete Modeling Approach

A major challenge in systems biology is to develop a detailed dynamic understanding of the functions and behaviors in a particular cellular system, which depends on the elements and their inter-relationships in a specific network. Computational modeling plays an integral part in the study of network dynamics and uncovering the underlying mechanisms. Here we proposed a systematic approach that incorporates discrete dynamic modeling and experimental data to reconstruct a phenotype-specific network of cell signaling. A dynamic analysis of the insulin signaling system in liver cells provides a proof-of-concept application of the proposed methodology. Our group recently identified that double-stranded RNA-dependent protein kinase (PKR) plays an important role in the insulin signaling network. The dynamic behavior of the insulin signaling network is tuned by a variety of feedback pathways, many of which have the potential to cross talk with PKR. Given the complexity of insulin signaling, it is inefficient to experimentally test all possible interactions in the network to determine which pathways are functioning in our cell system. Our discrete dynamic model provides an in silico model framework that integrates potential interactions and assesses the contributions of the various interactions on the dynamic behavior of the signaling network. Simulations with the model generated testable hypothesis on the response of the network upon perturbation, which were experimentally evaluated to identify the pathways that function in our particular liver cell system. The modeling in combination with the experimental results enhanced our understanding of the insulin signaling dynamics and aided in generating a context-specific signaling network

A Three Stage Integrative Pathway Search (TIPS©) framework to identify toxicity relevant genes and pathways

<p>Abstract</p> <p>Background</p> <p>The ability to obtain profiles of gene expressions, proteins and metabolites with the advent of high throughput technologies has advanced the study of pathway and network reconstruction. Genome-wide network reconstruction requires either interaction measurements or large amount of perturbation data, often not available for mammalian cell systems. To overcome these shortcomings, we developed a Three Stage Integrative Pathway Search (<it>TIPS</it>^©) approach to reconstruct context-specific active pathways involved in conferring a specific phenotype, from limited amount of perturbation data. The approach was tested on human liver cells to identify pathways that confer cytotoxicity.</p> <p>Results</p> <p>This paper presents a systems approach that integrates gene expression and cytotoxicity profiles to identify a network of pathways involved in free fatty acid (FFA) and tumor necrosis factor-α (TNF-α) induced cytotoxicity in human hepatoblastoma cells (HepG2/C3A). Cytotoxicity relevant genes were first identified and then used to reconstruct a network using Bayesian network (BN) analysis. BN inference was used subsequently to predict the effects of perturbing a gene on the other genes in the network and on the cytotoxicity. These predictions were subsequently confirmed through the published literature and further experiments.</p> <p>Conclusion</p> <p>The <it>TIPS</it>^©approach is able to reconstruct active pathways that confer a particular phenotype by integrating gene expression and phenotypic profiles. A web-based version of <it>TIPS</it>^©that performs the analysis described herein can be accessed at <url>http://www.egr.msu.edu/tips</url>.</p

Oral peripheral ameloblastoma : a retrospective series study of 25 cases

Peripheral ameloblastoma (PA) is a rare and unusual variant of odontogenic tumor, which was described only in isolated case reports in literature. The objective of this study was to investigate the clinical profile, treatment and outcome of PA in a consecutive case series. A total of 25 patients with histologically confirmed PA from 2001 to 2015 were retrospectively reviewed in our institution. Of the 25 patients, 22 males and 3 females were identified (male: female = 7.3:1). The average age was 48.3 years (range 11-81 years) with lingual or palate gingival region being the most common site (76%). The course of disease was less than 6 months in 92.0% (23/25) of all patients (mean, 3.3 months; range, 1-12 months). All patients underwent complete surgical removal of the lesions, and one lesion recurrence occurred during the follow-up period. The clinical profile and outcome of PA from Eastern China were elucidated in this retrospective analysis based on a case series. Our experience may provide some insights into the differential diagnosis and clinical management of PA. The first choice of treatment is surgical excision, which can result in a good prognosis

Event-Driven Learning for Spiking Neural Networks

Brain-inspired spiking neural networks (SNNs) have gained prominence in the field of neuromorphic computing owing to their low energy consumption during feedforward inference on neuromorphic hardware. However, it remains an open challenge how to effectively benefit from the sparse event-driven property of SNNs to minimize backpropagation learning costs. In this paper, we conduct a comprehensive examination of the existing event-driven learning algorithms, reveal their limitations, and propose novel solutions to overcome them. Specifically, we introduce two novel event-driven learning methods: the spike-timing-dependent event-driven (STD-ED) and membrane-potential-dependent event-driven (MPD-ED) algorithms. These proposed algorithms leverage precise neuronal spike timing and membrane potential, respectively, for effective learning. The two methods are extensively evaluated on static and neuromorphic datasets to confirm their superior performance. They outperform existing event-driven counterparts by up to 2.51% for STD-ED and 6.79% for MPD-ED on the CIFAR-100 dataset. In addition, we theoretically and experimentally validate the energy efficiency of our methods on neuromorphic hardware. On-chip learning experiments achieved a remarkable 30-fold reduction in energy consumption over time-step-based surrogate gradient methods. The demonstrated efficiency and efficacy of the proposed event-driven learning methods emphasize their potential to significantly advance the fields of neuromorphic computing, offering promising avenues for energy-efficiency applications