Placing regenerators in optical networks to satisfy multiple sets of requests.

The placement of regenerators in optical networks has become an active area of research during the last years. Given a set of lightpaths in a network G and a positive integer d, regenerators must be placed in such a way that in any lightpath there are no more than d hops without meeting a regenerator. While most of the research has focused on heuristics and simulations, the first theoretical study of the problem has been recently provided in [10], where the considered cost function is the number of locations in the network hosting regenerators. Nevertheless, in many situations a more accurate estimation of the real cost of the network is given by the total number of regenerators placed at the nodes, and this is the cost function we consider. Furthermore, in our model we assume that we are given a finite set of p possible traffic patterns (each given by a set of lightpaths), and our objective is to place the minimum number of regenerators at the nodes so that each of the traffic patterns is satisfied. While this problem can be easily solved when d = 1 or p = 1, we prove that for any fixed d,p ≥ 2 it does not admit a PTASUnknown control sequence '\textsc', even if G has maximum degree at most 3 and the lightpaths have length O(d)(d). We complement this hardness result with a constant-factor approximation algorithm with ratio ln (d ·p). We then study the case where G is a path, proving that the problem is NP-hard for any d,p ≥ 2, even if there are two edges of the path such that any lightpath uses at least one of them. Interestingly, we show that the problem is polynomial-time solvable in paths when all the lightpaths share the first edge of the path, as well as when the number of lightpaths sharing an edge is bounded. Finally, we generalize our model in two natural directions, which allows us to capture the model of [10] as a particular case, and we settle some questions that were left open in [10]

On Bootstrap Percolation in Living Neural Networks

Recent experimental studies of living neural networks reveal that their global activation induced by electrical stimulation can be explained using the concept of bootstrap percolation on a directed random network. The experiment consists in activating externally an initial random fraction of the neurons and observe the process of firing until its equilibrium. The final portion of neurons that are active depends in a non linear way on the initial fraction. The main result of this paper is a theorem which enables us to find the asymptotic of final proportion of the fired neurons in the case of random directed graphs with given node degrees as the model for interacting network. This gives a rigorous mathematical proof of a phenomena observed by physicists in neural networks

On the analysis of expected distance between sensor nodes and the base station in randomly deployed WSNs

In this study, we focus on the analytical derivation of the expected distance between all sensor nodes and the base station (i.e., E[dtoBS]) in a randomly deployed WSN. Although similar derivations appear in the related literature, to the best of our knowledge, our derivation, which assumes a particular scenario, has not been formulated before. In this specific scenario, the sensing field is a square-shaped region and the base station is located at some arbitrary distance to one of the edges of the square. Having the knowledge of E[dtoBS] value is important because E[dtoBS] provides a network designer with the opportunity to make a decision on whether it is energy-efficient to perform clustering for WSN applications that aim to pursue the clustered architectures. Similarly, a network designer might make use of this expected value during the process of deciding on the modes of communications (i.e., multi-hop or direct communication) after comparing it with the maximum transmission ranges of devices. Last but not least, the use of our derivation is not limited to WSN domain. It can be also exploited in any domain when there is a need for a probabilistic approach to find the average distance between any given number of points which are all assumed to be randomly and uniformly located in any square-shaped region and at a specific point outside this region. © Springer International Publishing Switzerland 2014

Atomic-scale visualization of multiferroicity in monolayer NiI2_2

Progress in layered van der Waals materials has resulted in the discovery of ferromagnetic and ferroelectric materials down to the monolayer limit. Recently, evidence of the first purely two-dimensional multiferroic material was reported in monolayer NiI$_2$. However, probing multiferroicity with scattering-based and optical bulk techniques is challenging on 2D materials, and experiments on the atomic scale are needed to fully characterize the multiferroic order at the monolayer limit. Here, we use scanning tunneling microscopy (STM) supported by theoretical calculations based on density functional theory (DFT) to probe and characterize the multiferroic order in monolayer NiI$_2$. We demonstrate that the type-II multiferroic order displayed by NiI$_2$, arising from the combination of a magnetic spin spiral order and a strong spin-orbit coupling, allows probing the multiferroic order in the STM experiments. Moreover, we directly probe the magnetoelectric coupling of NiI$_2$ by external electric field manipulation of the multiferroic domains. Our findings establish a novel point of view to analyse magnetoelectric effects at the microscopic level, paving the way towards engineering new multiferroic orders in van der Waals materials and their heterostructures

Joint Server Scheduling and Proxy Caching for Video Delivery

We consider the delivery of video assets over a best-effort network, possibly through a caching proxy located close to the clients generating the requests. We are interested in the joint server scheduling and prefix/partial caching strategy that minimizes the aggregate transmission rate over the backbone network (i.e., average output server rate) under a cache of given capacity. We present multiple schemes to address various service levels and client resources by enabling bandwidth and cache space tradeoffs. We also propose an optimization algorithm selecting the working set of asset prefixes. We detail algorithms for practical implementation of our schemes. Simulation results show our scheme dramatically outperforms the full caching technique

The cardiomyopathy of Friedreich's ataxia common in a family: A case report

Introduction and importance: Friedreich's Ataxia is an autosomal recessive disease and is usually associated with arterial dysfunction, muscle weakness, spasm in the lower extremities, scoliosis, bladder dysfunction, lack of reflexes in the lower extremities, and imbalance. Approximately 2.3 people have cardiomyopathy. In this article, we have reviewed a case of Friedreich's Ataxia with hypertrophic cardiomyopathy. Case presentation: A 19-year-old woman with Friedreich's Ataxia has been protesting since she was 11 years old and complained of chest pains, dyspnea, and heart palpitations without a medical history. In ECG, Asymmetrical invert T wave diffuse, diffuse ST-segment depression, and left ventricular hypertrophy were observed. In echocardiography, the left ventricle was reported as hyperimmobile with increased EF (70�75). Clinical discussion: In the present study, a patient with Friedrich Ataxia was diagnosed with chest pain, dyspnea, and palpitations without any medical history, and was discharged from the hospital after treatment. In the patients introduced and our patient, there was significant fibro-myocardial hypertrophy, in which the ventricular septal hypertrophy was marked by hypertrophic cardiomyopathy. Conclusion: Because early diagnosis of the disease is difficult, clinical signs and the patient's current profile at the time of referral will be very helpful. © 202

Constructing an information matrix for multivariate DCC-MGARCH (1, 1) method

The analytic form of Fisher Information Matrix (IM) for DCC-MGARCH (1, 1) was suggested. After that, it was applied for simplifying the general algorithm: the statistical hypothesis about constant correlation matrix usage was put forward and statistical verification was made. IM was employed for Russian share market: to do investigations the five equilibrium portfolios was compounded from four different shares in each case. Computations made showed that there are three types T1–T3 of trading days on the market and day type changing from T1 to T2 and vice versa is happening over the time moments T3. Moreover, the clustarisation effect of multivariate volatility that was investigated by scientists from all around the world in the univariate case was discovered and described