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 k of n nodes. However regenerating codes possess in addition, the ability to repair a failed node by connecting to any arbitrary d 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 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 non-existence 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.Comment: 38 pages, 12 figures, submitted to the IEEE Transactions on Information Theory;v3 - The title has been modified to better reflect the contributions of the submission. The paper is extensively revised with several carefully constructed figures and example

Explicit Construction of Optimal Exact Regenerating Codes for Distributed Storage

Erasure coding techniques are used to increase the reliability of distributed storage systems while minimizing storage overhead. Also of interest is minimization of the bandwidth required to repair the system following a node failure. In a recent paper, Wu et al. characterize the tradeoff between the repair bandwidth and the amount of data stored per node. They also prove the existence of regenerating codes that achieve this tradeoff. In this paper, we introduce Exact Regenerating Codes, which are regenerating codes possessing the additional property of being able to duplicate the data stored at a failed node. Such codes require low processing and communication overheads, making the system practical and easy to maintain. Explicit construction of exact regenerating codes is provided for the minimum bandwidth point on the storage-repair bandwidth tradeoff, relevant to distributed-mail-server applications. A subspace based approach is provided and shown to yield necessary and sufficient conditions on a linear code to possess the exact regeneration property as well as prove the uniqueness of our construction. Also included in the paper, is an explicit construction of regenerating codes for the minimum storage point for parameters relevant to storage in peer-to-peer systems. This construction supports a variable number of nodes and can handle multiple, simultaneous node failures. All constructions given in the paper are of low complexity, requiring low field size in particular.Comment: 7 pages, 2 figures, in the Proceedings of Allerton Conference on Communication, Control and Computing, September 200

Comparison of Entrainment Rate in Acrylonitrile Reactors Using Plant Data and CFD Simulations

Accurate entrainment rates are important in fluidized bed reactors for several reasons, including determination of cyclone loadings and efficiencies, sizing of diplegs, and inputs to population balance models. Entrainment correlations exist in the literature and from other sources to predict entrainment rates from fluidized beds, but they can vary by orders of magnitude. In addition, many correlations do not take into account effects of internals which are present in many types of industrial reactors. A study was undertaken to better understand entrainment rates from Sohiotype acrylonitrile fluidized bed reactors containing catalyst classified as a Geldart type A powder. As part of this study, full scale CFD models were developed using the Barracuda® computational particle fluid dynamics (CPFD®) software and validated with the help of data collected from multiple plant reactors. These models compared two different sizes of industrial-scale reactors and included all major internals including cooling coils, cyclones, cyclone diplegs and gas spargers. Data on the pressure profile and actual entrainment rate to the cyclones generated by the Barracuda models were compared to the measured pressure data and derived entrainment rate in the plant reactors. The results showed good agreement. Additionally, evaluation of using the slip factor in the model to compare the particle volume fraction in the freeboard to the actual entrainment rate was done to determine if this technique could be used in the plant setting. The slip factor as calculated by Barracuda was between 1.55-1.95 which is similar to other values in the literature

Cervical length measurement by transvaginal sonography in predicting preterm labour in low risk women

Background: Preterm birth is the leading cause of perinatal morbidity and mortality. Transvaginal sonographic measurement of the cervix is a reliable alternative method for the assessment of cervical length as it allows better quality and more accurate visualization of the uterine cervix. Several studies have reported that cervical assessment on transvaginal sonography may be useful in the prediction of preterm delivery. The objective of this study was to assess cervical length at 20 to 24 weeks of gestation in low risk women and correlate with the gestational age at delivery.Methods: A prospective cohort study conducted in a tertiary care Military Hospital in Pune, India. 354 asymptomatic low risk antenatal women with gestational age of 20 to 24 weeks were studied. Cervical assessment with transvaginal sonography for the measurement of cervical length was performed using a 10 MHz transvaginal probe.Results: 7 percent women delivered preterm. The incidence of short cervix in low risk women was only 0.56%. 100% women with short cervix delivered preterm and, only 6.9% patients who had cervical length more than 25 mm delivered preterm. Cervical length 25 mm has got sensitivity and NPV of 100% and a specificity of 93.46%. However, the PPV was only 8%.Conclusions: The study reported significant inverse relation between short cervix and the occurrence of preterm delivery. Our findings suggest that cervical length can be used as a screening method for preterm labour in low risk women. However strong evidences from large randomized control trials would be required to assess its cost-effectiveness.

Radiological Spectrum of von Hippel-Lindau disease – A Case Report

Von Hippel-Lindau (VHL) disease is an autosomal dominant genetic disorder resulting from inactivation of tumor suppressiongenes located at the chromosome 3p 25.5. VHL comprises of many benign and malignant tumors along affecting varioussystems of the body with variable manifestations. A wide variation in radiological spectrum is seen as per the involvement ofparticular system or organ. The imaging modalities like Ultrasonogrphy (USG), Computerized Tomography (CT) andMagnetic Resonance Imaging (MRI) play an important role in diagnosing and treating the affected individuals. These also playequally important role in the screening and follow up of such cases. We present a case of an 18 year old female, who wasdiagnosed with VHL at the age of 10 years, where imaging modalities helped her management and follow up

Ciliogenesis Mechanisms Mediated by PAK2-ARL13B Signaling in Brain Endothelial Cells is Responsible for Vascular Stability

In the developing vasculature, cilia, microtubule-based organelles that project from the apical surface of endothelial cells (ECs), have been identified to function cell autonomously to promote vascular integrity and prevent hemorrhage. To date, the underlying mechanisms of endothelial cilia formation (ciliogenesis) are not fully understood. Understanding these mechanisms is likely to open new avenues for targeting EC-cilia to promote vascular stability. Here, we hypothesized that brain ECs ciliogenesis and the underlying mechanisms that control this process are critical for brain vascular stability. To investigate this hypothesis, we utilized multiple approaches including developmental zebrafish model system and primary cell culture systems. In the p21 activated kinase 2 (pak2a) zebrafish vascular stability mutant [redhead (rhd)] that shows cerebral hemorrhage, we observed significant decrease in cilia-inducing protein ADP Ribosylation Factor Like GTPase 13B (Arl13b), and a 4-fold decrease in cilia numbers. Overexpressing ARL13B-GFP fusion mRNA rescues the cilia numbers (1–2-fold) in brain vessels, and the cerebral hemorrhage phenotype. Further, this phenotypic rescue occurs at a critical time in development (24 h post fertilization), prior to initiation of blood flow to the brain vessels. Extensive biochemical mechanistic studies in primary human brain microvascular ECs implicate ligands platelet-derived growth factor-BB (PDGF-BB), and vascular endothelial growth factor-A (VEGF-A) trigger PAK2-ARL13B ciliogenesis and signal through cell surface VEGFR-2 receptor. Thus, collectively, we have implicated a critical brain ECs ciliogenesis signal that converges on PAK2-ARL13B proteins to promote vascular stability

Sucrose Nonfermenting-Related Kinase Enzyme-Mediated Rho-Associated Kinase Signaling is Responsible for Cardiac Function.

BACKGROUND: Cardiac metabolism is critical for the functioning of the heart, and disturbance in this homeostasis is likely to influence cardiac disorders or cardiomyopathy. Our laboratory has previously shown that SNRK (sucrose nonfermenting related kinase) enzyme, which belongs to the AMPK (adenosine monophosphate-activated kinase) family, was essential for cardiac metabolism in mammals. Snrk global homozygous knockout (KO) mice die at postnatal day 0, and conditional deletion of Snrk in cardiomyocytes (Snrk cmcKO) leads to cardiac failure and death by 8 to 10 months. METHODS AND RESULTS: We performed additional cardiac functional studies using echocardiography and identified further cardiac functional deficits in Snrk cmcKO mice. Nuclear magnetic resonance-based metabolomics analysis identified key metabolic pathway deficits in SNRK knockdown cardiomyocytes in vitro. Specifically, metabolites involved in lipid metabolism and oxidative phosphorylation are altered, and perturbations in these pathways can result in cardiac function deficits and heart failure. A phosphopeptide-based proteomic screen identified ROCK (Rho-associated kinase) as a putative substrate for SNRK, and mass spec-based fragment analysis confirmed key amino acid residues on ROCK that are phosphorylated by SNRK. Western blot analysis on heart lysates from Snrk cmcKO adult mice and SNRK knockdown cardiomyocytes showed increased ROCK activity. In addition, in vivo inhibition of ROCK partially rescued the in vivo Snrk cmcKO cardiac function deficits. CONCLUSIONS: Collectively, our data suggest that SNRK in cardiomyocytes is responsible for maintaining cardiac metabolic homeostasis, which is mediated in part by ROCK, and alteration of this homeostasis influences cardiac function in the adult heart