The Geometry of Warped Product Singularities

In this article the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Riemannian manifolds with the warping function satisfying a certain condition is a semi-regular semi-Riemannian manifold. The connection and the Riemann curvature of the warped product are expressed in terms of those of the factor manifolds. Examples of singular semi-Riemannian manifolds which are semi-regular are constructed as warped products. Applications include cosmological models and black holes solutions with semi-regular singularities. Such singularities are compatible with a certain reformulation of the Einstein equation, which in addition holds at semi-regular singularities too.Comment: 14 page

Reducing Congestion Effects by Multipath Routing in Wireless Networks

We propose a solution to improve fairness and increasethroughput in wireless networks with location information.Our approach consists of a multipath routing protocol, BiasedGeographical Routing (BGR), and two congestion controlalgorithms, In-Network Packet Scatter (IPS) and End-to-EndPacket Scatter (EPS), which leverage BGR to avoid the congestedareas of the network. BGR achieves good performancewhile incurring a communication overhead of just 1 byte perdata packet, and has a computational complexity similar togreedy geographic routing. IPS alleviates transient congestion bysplitting traffic immediately before the congested areas. In contrast,EPS alleviates long term congestion by splitting the flow atthe source, and performing rate control. EPS selects the pathsdynamically, and uses a less aggressive congestion controlmechanism on non-greedy paths to improve energy efficiency.Simulation and experimental results show that our solutionachieves its objectives. Extensive ns-2 simulations show that oursolution improves both fairness and throughput as compared tosingle path greedy routing. Our solution reduces the variance ofthroughput across all flows by 35%, reduction which is mainlyachieved by increasing throughput of long-range flows witharound 70%. Furthermore, overall network throughput increasesby approximately 10%. Experimental results on a 50-node testbed are consistent with our simulation results, suggestingthat BGR is effective in practice

Avatar: A Time- and Space-Efficient Self-Stabilizing Overlay Network

Overlay networks present an interesting challenge for fault-tolerant computing. Many overlay networks operate in dynamic environments (e.g. the Internet), where faults are frequent and widespread, and the number of processes in a system may be quite large. Recently, self-stabilizing overlay networks have been presented as a method for managing this complexity. \emph{Self-stabilizing overlay networks} promise that, starting from any weakly-connected configuration, a correct overlay network will eventually be built. To date, this guarantee has come at a cost: nodes may either have high degree during the algorithm's execution, or the algorithm may take a long time to reach a legal configuration. In this paper, we present the first self-stabilizing overlay network algorithm that does not incur this penalty. Specifically, we (i) present a new locally-checkable overlay network based upon a binary search tree, and (ii) provide a randomized algorithm for self-stabilization that terminates in an expected polylogarithmic number of rounds \emph{and} increases a node's degree by only a polylogarithmic factor in expectation

Gene Therapy for Amyotrophic Lateral Sclerosis: An AAV Delivered Artifical MicroRNA Against Human SOD1 Increases Survival and Delays Disease Progression of the SOD1\u3csup\u3eG93A\u3c/sup\u3e Mouse Model: A Dissertation

Amyotrophic lateral sclerosis (ALS) is a fatal neurodegenerative disease characterized by loss of motor neurons, resulting in progressive muscle weakness, atrophy, paralysis and death within five years of diagnosis. About ten percent of cases are inherited, of which twenty percent are due to mutations in the superoxide dismutase 1 (SOD1) gene. Since the only FDA approved ALS drug prolongs survival by just a few months, new therapies for this disease are needed. Experiments in transgenic ALS mouse models have shown that decreasing levels of mutant SOD1 protein alters and in some cases entirely prevents disease progression. We explored this potential therapeutic approach by using a single stranded AAV9 vector encoding an artificial microRNA against human SOD1 injected bilaterally into the cerebral lateral ventricles of neonatal SOD1G93A mice. This therapy extended median survival from 135 to 206 days (a 50% increase) and delayed hind limb paralysis. Animals remained ambulatory until endpoint, as defined by a sharp drop in body weight. Treated animals had a reduction of mutant human SOD1 mRNA levels in upper and lower motor neurons. As compared to untreated SOD1G93A mice, the AAV9 treated mice also had significant improvements in multiple parameters including the number of motor neurons, diameter of ventral root axons, and degree of neuroinflammation in the spinal cord. These studies clearly show that an AAV9-delivered artificial microRNA is a translatable therapeutic approach for ALS

Survival trends and complications in surgical interventions for colorectal cancer: an overview of patients hospitalized in Clinical Emergency Hospital Bucharect

The preoperative imaging diagnosis of rectal cancer lies at the heart of oncological staging and has a crucial influence on patient management and therapy planning. Rectal cancer is common, and accurate preoperative staging of tumors using high-resolution magnetic resonance imaging (MRI) is a crucial part of modern multidisciplinary team management (MDT). Indeed, rectal MRI has the ability to accurately evaluate a number of important findings that maBay impact patient management, including distance of the tumor to the mesorectal fascia, presence of lymph nodes, presence of extramural vascular invasion (EMVI), and involvement of the anterior peritoneal reflection/peritoneum and the sphincter complex. Many of these findings are difficult to assess in nonexpert hands. In this lecture, we present currently used staging modalities with focus on MRI, including optimization of imaging techniques, tumor staging, interpretation help as well as essentials for reporting