Exact Optimized-cost Repair in Multi-hop Distributed Storage Networks

The problem of exact repair of a failed node in multi-hop networked distributed storage systems is considered. Contrary to the most of the current studies which model the repair process by the direct links from surviving nodes to the new node, the repair is modeled by considering the multi-hop network structure, and taking into account that there might not exist direct links from all the surviving nodes to the new node. In the repair problem of these systems, surviving nodes may cooperate to transmit the repair traffic to the new node. In this setting, we define the total number of packets transmitted between nodes as repair-cost. A lower bound of the repaircost can thus be found by cut-set bound analysis. In this paper, we show that the lower bound of the repair-cost is achievable for the exact repair of MDS codes in tandem and grid networks, thus resulting in the minimum-cost exact MDS codes. Further, two suboptimal (achievable) bounds for the large scale grid networks are proposed.Comment: (To appear in ICC 2014

Secure Partial Repair in Wireless Caching Networks with Broadcast Channels

We study security in partial repair in wireless caching networks where parts of the stored packets in the caching nodes are susceptible to be erased. Let us denote a caching node that has lost parts of its stored packets as a sick caching node and a caching node that has not lost any packet as a healthy caching node. In partial repair, a set of caching nodes (among sick and healthy caching nodes) broadcast information to other sick caching nodes to recover the erased packets. The broadcast information from a caching node is assumed to be received without any error by all other caching nodes. All the sick caching nodes then are able to recover their erased packets, while using the broadcast information and the nonerased packets in their storage as side information. In this setting, if an eavesdropper overhears the broadcast channels, it might obtain some information about the stored file. We thus study secure partial repair in the senses of information-theoretically strong and weak security. In both senses, we investigate the secrecy caching capacity, namely, the maximum amount of information which can be stored in the caching network such that there is no leakage of information during a partial repair process. We then deduce the strong and weak secrecy caching capacities, and also derive the sufficient finite field sizes for achieving the capacities. Finally, we propose optimal secure codes for exact partial repair, in which the recovered packets are exactly the same as erased packets.Comment: To Appear in IEEE Conference on Communication and Network Security (CNS

Minimum-Cost Coding for Distributed Storage Systems

In distributed storage systems reliability is achieved through redundant storage nodes distributed in the network. Then a data collector can recover source information even if some nodes fail. To maintain reliability, an autonomous and efficient protocol should be used to reconstruct the failed node. The repair process causes traffic in the network. Recent results in e.g., [1], [2] found the optimal traffic-storage tradeoff, and proposed regenerating codes to achieve the optimality. We investigate the link costs and the impact of network topologies during the repair process. We formulate the minimum cost repair problem in joint and decoupled methods. We investigate the required field size for the joint method. For the decoupled method, we show that the problem is linear for the linear cost. We further show that the cooperation of surviving nodes could efficiently exploit the network topology and reduce the repair cost. The numerical results in tandem, star and grid networks show the benefits of our methods in term of the repair cost

Coding, Computing, and Communication in Distributed Storage Systems

Conventional studies in communication networks mostly focus on securely and reliably transmitting  data from a source node (or multiple source nodes) to multiple destinations. A more general problem appears when the destination nodes are interested in obtaining  functions of the data available in distributed source nodes. For obtaining a function, transmitting all the data to a destination node and then computing the function might be inefficient. In order to exploit the network resources efficiently, the general problem offers distributed computing in combination with coding and communication. This problem has applications in distributed systems, e.g., in wireless sensor networks, in distributed storage systems, and in distributed computing systems. Following this general problem formulation, we study the optimal and secure recovery of the lost data in storage nodes and in reconstructing a version of a file in distributed storage systems.   The significance of this study is due to the fact that the new trends in communications including big data, Internet of things, low latency, and high reliability communications challenge the existing centralized data storage systems. Distributed storage systems can rectify those issues by  distributing  thousands of storage nodes (possibly around the globe), and then benefiting users by bringing data to their proximity.  Yet, distributing the storage nodes brings new challenges. In these distributed systems, where storage nodes  are connected through links and servers, communication plays a main role in their performance. In addition,  a part of network may fail or due to communication failure or delay there might exist multi versions of a file. Moreover, an intruder can overhear the communications between storage nodes and obtain some information about the stored data. Therefore, there are challenges on  reliability, security, availability, and consistency.   To increase reliability, systems need to store redundant data in storage nodes and employ error control codes. To maintain the  reliability  in a dynamic environment where storage nodes can fail, the system should have an autonomous repair process. Namely, it should regenerate the failed nodes by the help of other storage nodes. The repair process demands bandwidth, energy, or in general transmission costs.  We propose novel techniques to reduce the repair cost in distributed storage systems.   First, we propose {surviving nodes cooperation} in repair, meaning that surviving nodes can combine their received data with their own stored data and then transmit toward the new node. In addition, we study the repair problem in multi-hop networks and consider the cost of transmitting data between storage nodes.  While classical repair model assumes the availability of direct links between the new node and surviving nodes, we consider that such links may not be available either due to failure or their costs.  We formulate an optimization problem to minimize the repair cost and compare two systems, namely with and without surviving nodes cooperation.   Second, we study the repair problem where the links between storage nodes are lossy e.g., due to server congestion, load balancing, or unreliable physical layer (wireless links).  We model the lossy links by packet erasure channels and then derive the fundamental bandwidth-storage tradeoff in packet erasure networks. In addition, we propose dedicated-for-repair storage nodes to reduce the repair-bandwidth.   Third, we generalize the repair model by proposing the concept of partial repair. That is, storage nodes may lose parts of their stored data. Then in partial repair, the lost data is recovered by exchanging data between storage nodes and using the available data in storage nodes as side information. For efficient partial-repair,  we propose two-layer coding in distributed storage systems and then we derive the optimal bandwidth in partial repair.   Fourth, we study security in distributed storage systems.  We investigate security in partial repair. In particular, we propose codes that make the partial repair secure in the senses of strong and weak information-theoretic security definitions.   Finally, we study consistency in distributed storage systems. Consistency means that distinct users obtain the latest version of a file in a system that stores multi versions of a file. Given the probability of receiving a version by a storage node and the constraint on the node storage space, we aim to find the optimal encoding of multi versions of a file that maximizes the probability of obtaining the latest version of a file or a version close to the latest version by a read client that connects to a number of storage nodes.Pages 153-168 are removed due to copyright reasons.QC 20161012</p

Epidemiologic Study of Trauma Patients Admitted to Shahid Rajaee Hospital of Shiraz, Iran on National, Religious, and Cultural Occasions within 2009-2014

Introduction and purpose: Trauma is one of the major cause of mortality and&nbsp;disability in communities and annually leads to the death of millions of people&nbsp;worldwide. Based on the evidence, car accident injuries (especially on religious&nbsp;and cultural events) are at an impressive level in Iran. Regarding this, the aim of the&nbsp;present study was to investigate the prevalence of trauma patients admitted to Shahid&nbsp;Rajai Hospital, and its relationship with religious, cultural, and national occasions,&nbsp;such as Ramadan, Tasua and Ashura, and so forth.&nbsp;Methods: This descriptive, cross-sectional study was conducted on the trauma&nbsp;patients admitted to Shahid Rajai Hospital in Shiraz, Iran, on religious, cultural, and&nbsp;national occasions during 2009-2014. The data were collected through a checklist,&nbsp;including the demographic data, some questions about the mechanism of the&nbsp;accident (i.e., car and motorcycle accidents, pedestrian injuries, assault, as well as&nbsp;gun and knife attacks), and religious occasions of the admission day (e.g., holidays,&nbsp;Wednesday Feast, Yalda, Tasua and Ashura, and Ramadan). The data were analyzed&nbsp;in SPSS version 17 using the descriptive statistics and the frequency distribution table.Results: According to the results, on the celebrations and birthdays, the highest&nbsp;number of trauma patient admission was recorded. In addition, the mean number&nbsp;of hospitalized men was significantly higher than that of the women. There was no&nbsp;significant difference in the mean number of the admissions between the first and&nbsp;second half of Nowruz and between the Martyrs&rsquo; Days and birthdays regarding the&nbsp;accident mechanisms of the car accident, motorcycle accident, assaults, falls, and&nbsp;unexpected events.&nbsp;Conclusion: As the findings of the present study indicated, the highest number of&nbsp;the admissinos occurred on the birthdays and celebrations, especially among the&nbsp;males. Therefore, it is suggested that measures be taken to minimize the number&nbsp;of traumatic accidents, especially on holydays, and deliver more care for the&nbsp;pedestrians, motorcyclists, and car drivers in this regard

A generalization of the Balakrishnan skew-normal distribution

The skew-normal distribution belongs to a family of distributions which includes the normal distribution along with an extra parameter to regulate skewness. Azzalini [Azzalini A., 1985. A class of distributions which includes the normal ones. Scandinavian Journal of Statistics 12, 171-178] was the first to introduce the skew-normal distribution and studied some of its properties. Balakrishnan [Balakrishnan, N., 2002. Discussion of "skewed multivariate models related to hidden truncation and/or selective reporting". Test 11, 37-39], as a discussant of Arnold and Beaver [Arnold, B.C., Beaver, R.J., 2002. Skewed multivariate models related to hidden truncation and/or selective reporting (with discussion). Test II, 7-54], later proposed a generalization of this distribution. In this paper, we introduce a new generalization of the Balakrishnan skew-normal distribution by explaining some important properties of this distribution. Also, we have described three methods for constructing this distribution. Finally, its multivariate extension has been presented.