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.

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.

Direct detection of Salmonella without pre-enrichment in milk, ice-cream and fruit juice by PCR against hilA gene

A novel PCR based assay was devised to specifically detect contamination of any Salmonella serovar in milk, fruit juice and ice-cream without pre-enrichment. This method utilizes primers against hilA gene which is conserved in all Salmonella serovars and absent from the close relatives of Salmonella. An optimized protocol, in terms time and money, is provided for the reduction of PCR contaminants from milk, ice-cream and juice through the use of routine laboratory chemicals. The simplicity, efficiency (time taken 3-4 h) and sensitivity (to about 5-10 CFU/ml) of this technique confers a unique advantage over other previously used time consuming detection techniques. This technique does not involve pre-enrichment of the samples or extensive sample processing, which was a pre-requisite in most of the other reported studies. Hence, this assay can be ideal for adoption, after further fine tuning, by food quality control for timely detection of Salmonella contamination as well as other food-borne pathogens (with species specific primers) in food especially milk, ice-cream and fruit juice. (C) 2011 Elsevier Ltd. All rights reserved.

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.

Scalable processes for fabricating non-volatile memory devices using self-assembled 2D arrays of gold nanoparticles as charge storage nodes

We propose robust and scalable processes for the fabrication of floating gate devices using ordered arrays of 7 nm size gold nanoparticles as charge storage nodes. The proposed strategy can be readily adapted for fabricating next generation (sub-20 nm node) non-volatile memory devices.

Filling Characteristics for an Activated Carbon Based Adsorbed Natural Gas Storage System

The storage capacity of an activated carbon bed is studied using a 2D transport model with constant inlet flow conditions. The predicted filling times and variation in bed pressure and temperature are in good agreement with experimental observations obtained using a 1.82 L prototype ANG storage cylinder. Storage efficiencies based on the maximum achievable V/V (volume of gas/volume of container) and filling times are used to quantify the performance of the charging process. For the high permeability beds used in the experiments, storage efficiencies are controlled by the rate of heat removal. Filling times, defined as the time at which the bed pressure reaches 3.5 MPa, range from 120 to 3.4 min for inlet flow rates of 1.0 L min(-1) and 30.0 L min(-1), respectively. The corresponding storage efficiencies, eta(s), vary from 90% to 76%, respectively. Simulations with L/D ratios ranging from 0.35 to 7.8 indicate that the storage efficiencies can be improved with an increase in the LID ratios and/or with water cooled convection. Thus for an inlet flow rate of 30.0 L min(-1), an eta(s) value of 90% can be obtained with water cooling for an L/D ratio of 7.8 and a filling time of a few minutes. In the absence of water cooling the eta(s) value reduces to 83% at the same L/D ratio. Our study suggests that with an appropriate choice of cylinder dimensions, solutions based on convective cooling during adsorptive storage are possible with some compromise in the storage capacity.

Enhancement of charge and energy storage in sol-gel derived pure and La-modified PbZrO3 thin films

Antiferroelectric lanthanum-modified PbZrO3 thin films with La contents between 0 and 6 at. % have been deposited on Pt(111)/Ti/SiO2/Si substrate by sol-gel route. On the extent of La-modification, maximum polarization (Pmax) and recoverable energy density (W) have been enhanced followed by their subsequent reduction. A maximum Pmax ( ∼ 0.54 C/m2 at ∼ 60 MV/m) as well as a maximum W ( ∼ 14.9 J/cc at ∼ 60 MV/m) have been achieved on 5% La modification. Both Pmax and W have been found to be strongly dependent on La-induced crystallographic orientations.

Electrical-energy storage in hybrid ultracapacitors

There are several ways of storing electrical energy in chemical and physical forms and retrieving it on demand, and ultracapacitors are one among them. This article presents the taxonomy of ultracapacitor and describes various types of rechargeable-battery electrodes that can be used to realize the hybrid ultracapacitors in conjunction with a high-surface-area-graphitic-carbon electrode. While the electrical energy is stored in a battery electrode in chemical form, it is stored in physical form as charge in the electrical double-layer formed between the electrolyte and the high-surface-area-carbon electrodes. This article discusses various types of hybrid ultracapacitors along with the possible applications.

Distributed Storage Codes With Repair-by-Transfer and Nonachievability of Interior Points on the Storage-Bandwidth Tradeoff

Regenerating codes are a class of recently developed codes for distributed storage that, like Reed-Solomon codes, permit data recovery from any subset of k nodes within the n-node network. However, regenerating codes possess in addition, the ability to repair a failed node by connecting to an arbitrary subset of d nodes. It has been shown that for the case of functional repair, there is a tradeoff between the amount of data stored per node and the bandwidth required to repair a failed node. A special case of functional repair is exact repair where the replacement node is required to store data identical to that in the failed node. Exact repair is of interest as it greatly simplifies system implementation. The first result of this paper is an explicit, exact-repair code for the point on the storage-bandwidth tradeoff corresponding to the minimum possible repair bandwidth, for the case when d = n-1. This code has a particularly simple graphical description, and most interestingly has the ability to carry out exact repair without any need to perform arithmetic operations. We term this ability of the code to perform repair through mere transfer of data as repair by transfer. The second result of this paper shows that the interior points on the storage-bandwidth tradeoff cannot be achieved under exact repair, thus pointing to the existence of a separate tradeoff under exact repair. Specifically, we identify a set of scenarios which we term as ``helper node pooling,'' and show that it is the necessity to satisfy such scenarios that overconstrains the system.

Interference Alignment in Regenerating Codes for Distributed Storage: Necessity and Code Constructions

Regenerating codes are a class of recently developed codes for distributed storage that, like Reed-Solomon codes, permit data recovery from any arbitrary of nodes. However regenerating codes possess in addition, the ability to repair a failed node by connecting to any arbitrary nodes and downloading an amount of data that is typically far less than the size of the data file. This amount of download is termed the repair bandwidth. Minimum storage regenerating (MSR) codes are a subclass of regenerating codes that require the least amount of network storage; every such code is a maximum distance separable (MDS) code. Further, when a replacement node stores data identical to that in the failed node, the repair is termed as exact. The four principal results of the paper are (a) the explicit construction of a class of MDS codes for d = n - 1 >= 2k - 1 termed the MISER code, that achieves the cut-set bound on the repair bandwidth for the exact repair of systematic nodes, (b) proof of the necessity of interference alignment in exact-repair MSR codes, (c) a proof showing the impossibility of constructing linear, exact-repair MSR codes for d < 2k - 3 in the absence of symbol extension, and (d) the construction, also explicit, of high-rate MSR codes for d = k+1. Interference alignment (IA) is a theme that runs throughout the paper: the MISER code is built on the principles of IA and IA is also a crucial component to the nonexistence proof for d < 2k - 3. To the best of our knowledge, the constructions presented in this paper are the first explicit constructions of regenerating codes that achieve the cut-set bound.