Counting algebraic points in expansions of o-minimal structures by a dense set

The Pila-Wilkie theorem states that if a set $X\subseteq \mathbb R^n$ is definable in an o-minimal structure $\mathcal R$ and contains `many' rational points, then it contains an infinite semialgebraic set. In this paper, we extend this theorem to an expansion $\widetilde{\mathcal R}=\langle \mathcal R, P\rangle$ of $\mathcal R$ by a dense set $P$, which is either an elementary substructure of $\mathcal R$, or it is independent, as follows. If $X$ is definable in $\widetilde{\mathcal R}$ and contains many rational points, then it is dense in an infinite semialgebraic set. Moreover, it contains an infinite set which is $\emptyset$-definable in $\langle \overline{\mathbb R}, P\rangle$, where $\overline {\mathbb R}$ is the real field

Why Max-min Fairness Is Not Suitable For Multi-Hop Wireless Networks

We consider the issue of which criteria to use when evaluating the design of a wireless multihop network. It is known, and we illustrate in this paper, that maximizing the total capacity, or transport capacity, leads to gross imbalance and is not suitable. An alternative, which is often used in networking, is to consider the max-min fair allocation of rates, or of transport rates per node. We apply max-min fairness to the class of wireless, multi-hop networks for which the rate of a wireless link is an increasing functions of signal-to-noise ratio. This class includes CDMA and UWB. We show that, for a network in this class, the max-min fair allocation of bit or transport rates always gives the same rate to all flows. We show on one example that such an allocation is highly undesirable when the network is asymmetric. Another form of fairness, utility fairness, does not appear to have the same problem

Bmi1 Is Expressed in Postnatal Myogenic Satellite Cells, Controls Their Maintenance and Plays an Essential Role in Repeated Muscle Regeneration

PMCID: PMC3212532This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Complications of Laparoscopic Cholecystectomy: Our Experience from a Retrospective Analysis

AIM: The aim of this study was to evaluate the intraoperative and postoperative complications of laparoscopic cholecystectomy, as well as the frequency of conversions. MATERIAL AND METHODS: Medical records of 740 patients who had laparoscopic cholecystectomy were analysed retrospectively. We evaluated patients for the presence of potential risk factors that could predict the development of complications such as age, gender, body mass index, white blood cell count and C-reactive protein (CRP), gallbladder ultrasonographic findings, and pathohistological analysis of removed gallbladders. The correlation between these risk factors was also analysed. RESULTS: There were 97 (13.1%) intraoperative complications (IOC). Iatrogenic perforations of a gallbladder were the most common complication - 39 patients (5.27%). Among the postoperative complications (POC), the most common ones were bleeding from abdominal cavity 27 (3.64%), biliary duct leaks 14 (1.89%), and infection of the surgical wound 7 patients (0.94%). There were 29 conversions (3.91%). The presence of more than one complication was more common in males (OR = 2.95, CI 95%, 1.42-4.23, p < 0.001). An especially high incidence of complications was noted in patients with elevated white blood cell count (OR = 3.98, CI 95% 1.68-16.92, p < 0.01), and CRP (OR = 2.42, CI 95% 1.23-12.54, p < 0.01). The increased incidence of complications was noted in patients with ultrasonographic finding of gallbladder empyema and increased thickness of the gallbladder wall > 3 mm (OR = 4.63, CI 95% 1.56-17.33, p < 0.001), as well as in patients with acute cholecystitis that was confirmed by pathohistological analysis (OR = 1.75, CI 95% 2.39-16.46, p < 0.001).CONCLUSION: Adopting laparoscopic cholecystectomy as a new technique for treatment of cholelithiasis, introduced a new spectrum of complications. Major biliary and vascular complications are life threatening, while minor complications cause patient discomfort and prolongation of the hospital stay. It is important recognising IOC complications during the surgery so they are taken care of in a timely manner during the surgical intervention. Conversion should not be considered a complication.Â

Communication complexity of approximate maximum matching in the message-passing model

We consider the communication complexity of finding an approximate maximum matching in a graph in a multi-party message-passing communication model. The maximum matching problem is one of the most fundamental graph combinatorial problems, with a variety of applications. The input to the problem is a graph G that has n vertices and the set of edges partitioned over k sites, and an approximation ratio parameter α. The output is required to be a matching in G that has to be reported by one of the sites, whose size is at least factor α of the size of a maximum matching in G. We show that the communication complexity of this problem is Ω(α2kn)information bits. This bound is shown to be tight up to a log n factor, by constructing an algorithm, establishing its correctness, and an upper bound on the communication cost. The lower bound also applies to other graph combinatorial problems in the message-passing communication model, including max-flow and graph sparsification

A Joint PHY/MAC Architecture for Low-Radiated Power TH-UWB Wireless Ad-Hoc Networks

Due to environmental concerns and strict constraints on interference imposed on other networks, the radiated power of emerging pervasive wireless networks needs to be strictly limited, yet without sacrificing acceptable data rates. Pulsed Time-Hopping Ultra-Wide Band (TH-UWB) is a radio technology that has the potential to satisfy this requirement. Although TH-UWB is a multi-user radio technology, non-zero cross-correlation between time-hopping sequences, time-asynchronicity between sources and a multipath channel environment make it sensitive to strong interferers and near-far scenarios. While most protocols manage interference and multiple-access through power control or mutual exclusion (CSMA/CA or TDMA), we base our design on rate control, a relatively unexplored dimension for multiple-access and interference management. We further take advantage of the nature of pulsed TH-UWB to propose an interference mitigation scheme that reduces the impact of strong interferers. A source is always allowed to send and continuously adapts its channel code (hence its rate) to the interference experienced at the destination. In contrast to power control or exclusion, our MAC layer is local to sender and receiver and does not need coordination among neighbors not involved in the transmission. We show by simulation that we achieve a significant increase in network throughput

A new anatomical variation of the musculocutaneous and the median nerve anastomosis

Variations of the brachial plexus and its terminal branches are not uncommon.Therein, the anatomical variations of the musculocutaneous and the median nerve are classified into 5 types, while the communicating branches between the musculocutaneous and the median nerve are classified into 3 types, depending on their position related to the coracobrachial muscle. The case reviewed in this paper presents a variation similar to that of the second variety, but is significantly different due to the appearance of the proximal musculocutaneous nerve and its communicating branching, the site rising from the communicating branch (through the coracobrachial), and important clinical implications of this new variation. Despite the communicating branch being located in the upper third of the upper arm, it should not be considered as being a double lateral root of the median nerve