Interference Alignment as a Tool in Network Coding as Applied to Distributed Storage

In this paper, we outline an approach to the task of designing network codes in a non-multicast setting. Our approach makes use of the concept of interference alignment. As an example, we consider the distributed storage problem where the data is stored across the network in n nodes and where a data collector can recover the data by connecting to any k of the n nodes and where furthermore, upon failure of a node, a new node can replicate the data stored in the failed node while minimizing the repair bandwidth.

Explicit Codes Uniformly Reducing Repair Bandwidth in Distributed Storage

A distributed storage setting is considered where a file of size B is to be stored across n storage nodes. A data collector should be able to reconstruct the entire data by downloading the symbols stored in any k nodes. When a node fails, it is replaced by a new node by downloading data from some of the existing nodes. The amount of download is termed as repair bandwidth. One way to implement such a system is to store one fragment of an (n, k) MDS code in each node, in which case the repair bandwidth is B. Since repair of a failed node consumes network bandwidth, codes reducing repair bandwidth are of great interest. Most of the recent work in this area focuses on reducing the repair bandwidth of a set of k nodes which store the data in uncoded form, while the reduction in the repair bandwidth of the remaining nodes is only marginal. In this paper, we present an explicit code which reduces the repair bandwidth for all the nodes to approximately B/2. To the best of our knowledge, this is the first explicit code which reduces the repair bandwidth of all the nodes for all feasible values of the system parameters.

Explicit and Optimal Codes for Distributed Storage

In the distributed storage coding problem we consider, data is stored across n nodes in a network, each capable of storing � symbols. It is required that the complete data can be reconstructed by downloading data from any k nodes. There is also the key additional requirement that a failed node be regenerated by connecting to any d nodes and downloading �symbols from each of them. Our goal is to minimize the repair bandwidth d�. In this paper we provide explicit constructions for several parameter sets of interest.

Synthesis, characterization, degradation of biodegradable castor oil based polyesters

A new family of castor oil based biodegradable polyesters was synthesized by catalyst free melt condensation reaction between two different diacids and castor oil with D-mannitol. The polymers synthesized were characterized by NMR spectroscopy, FF-IR and the thermal properties were analysed by DSC. The results of DSC show that the polymer is rubbery in physiological conditions. The contact angle measurement and hydration test results indicate that the surface of the polymer is hydrophilic. The mechanical properties, evaluated in the tensile mode, shows that the polymer has characteristics of a soft material. In vitro degradation of polymer in PBS solution carried out at physiological conditions indicates that the degradation goes to completion within 21 days and it was also found that the rate of degradation can be tuned by varying the curing conditions. (C) 2011 Elsevier Ltd. All rights reserved.

The selection of a sugar for transport and storage of carbon in plants

Sugars perform two vital functions in plants: as compatible solutes protecting the cell against osmotic stress and as mobile source of immediate and long-term energy requirement for growth and development. The two sugars that occur commonly in nature are sucrose and trehalose. Sucrose comprises one glucose and one fructose molecule; trehalose comprises two glucose molecules. Trehalose occurs in significant amounts in insects and fungi which greatly outnumber the plants. Surprisingly, in plants trehalose has been found in barely detectable amounts, if at all, raising the question `why did nature select sucrose instead of trehalose as the mobile energy source and as storage sugar for the plants'? Modelling revealed that when attached to the ribbon-shaped beta-1,4 glucan a trehalose molecule is shaped like a hook. This suggests that the beta-1,4 glucan chains with attached trehalose will fail to align to form inter-chain hydrogen bonds and coalesce into a cellulose microfibril, as a result of which in trehalose-accumulating plant cells, the cell wall will tend to become leaky. Thus in plants an evolutionary selection was made in favour of sucrose as the mobile energy source. Genetic engineering of plant cells for combating abiotic stresses through microbial trehalose-producing genes is fraught with risk of damage to plant cell walls.

Optimal Exact-Regenerating Codes for Distributed Storage at the MSR and MBR Points via a Product-Matrix Construction

Regenerating codes are a class of distributed storage codes that allow for efficient repair of failed nodes, as compared to traditional erasure codes. An [n, k, d] regenerating code permits the data to be recovered by connecting to any k of the n nodes in the network, while requiring that a failed node be repaired by connecting to any d nodes. The amount of data downloaded for repair is typically much smaller than the size of the source data. Previous constructions of exact-regenerating codes have been confined to the case n = d + 1. In this paper, we present optimal, explicit constructions of (a) Minimum Bandwidth Regenerating (MBR) codes for all values of [n, k, d] and (b) Minimum Storage Regenerating (MSR) codes for all [n, k, d >= 2k - 2], using a new product-matrix framework. The product-matrix framework is also shown to significantly simplify system operation. To the best of our knowledge, these are the first constructions of exact-regenerating codes that allow the number n of nodes in the network, to be chosen independent of the other parameters. The paper also contains a simpler description, in the product-matrix framework, of a previously constructed MSR code with [n = d + 1, k, d >= 2k - 1].

Long term stability studies of particle storage rings using polynomial Maps

Long-term stability studies of particle storage rings can not be carried out using conventional numerical integration algorithms. We require symplectic integration algorithms which are both fast and accurate. In this paper, we study a symplectic integration method wherein the sym-plectic map representing the Hamiltonian system is refactorized using polynomial symplectic maps. This method is used to perform long term integration on a particle storage ring.

V(2)O(5)-Anchored Carbon Nanotubes for Enhanced Electrochemical Energy Storage

Functionalized multiwalled carbon nanotubes (CNTs) are coated with a 4-5 nm thin layer of V(2)O(5) by controlled hydrolysis of vanadium alkoxide. The resulting V(2)O(5)/CNT composite has been investigated for electrochemical activity with lithium ion, and the capacity value shows both faradaic and capacitive (nonfaradaic) contributions. At high rate (1 C), the capacitive behavior dominates the intercalation as 2/3 of the overall capacity value out of 2700 C/g is capacitive, while the remaining is due to Li-ion intercalation. These numbers are in agreement with the Trasatti plots and are corroborated by X-ray photoelectron spectroscopy (XPS) studies on the V(2)O(5)/CNTs electrode, which show 85% of vanadium in the +4 oxidation state after the discharge at 1 C rate. The cumulative high-capacity value is attributed to the unique property of the nano V(2)O(5)/CNTs composite, which provides a short diffusion path for Lit-ions and an easy access to vanadium redox centers besides the high conductivity of CNTs. The composite architecture exhibits both high power density and high energy density, stressing the benefits of using carbon substrates to design high performance supercapacitor electrodes.