Reliability of Erasure Coded Storage Systems: A Geometric Approach

We consider the probability of data loss, or equivalently, the reliability function for an erasure coded distributed data storage system under worst case conditions. Data loss in an erasure coded system depends on probability distributions for the disk repair duration and the disk failure duration. In previous works, the data loss probability of such systems has been studied under the assumption of exponentially distributed disk failure and disk repair durations, using well-known analytic methods from the theory of Markov processes. These methods lead to an estimate of the integral of the reliability function. Here, we address the problem of directly calculating the data loss probability for general repair and failure duration distributions. A closed limiting form is developed for the probability of data loss and it is shown that the probability of the event that a repair duration exceeds a failure duration is sufficient for characterizing the data loss probability. For the case of constant repair duration, we develop an expression for the conditional data loss probability given the number of failures experienced by a each node in a given time window. We do so by developing a geometric approach that relies on the computation of volumes of a family of polytopes that are related to the code. An exact calculation is provided and an upper bound on the data loss probability is obtained by posing the problem as a set avoidance problem. Theoretical calculations are compared to simulation results.Comment: 28 pages. 8 figures. Presented in part at IEEE International Conference on BigData 2013, Santa Clara, CA, Oct. 2013 and to be presented in part at 2014 IEEE Information Theory Workshop, Tasmania, Australia, Nov. 2014. New analysis added May 2015. Further Update Aug. 201

Cancer-Associated Thrombosis in Cirrhotic Patients with Hepatocellular Carcinoma.

It is common knowledge that cancer patients are more prone to develop venous thromboembolic complications (VTE). It is therefore not surprising that patients with hepatocellular carcinoma (HCC) present with a significant risk of VTE, with the portal vein being the most frequent site (PVT). However, patients with HCC are peculiar as both cancer and liver cirrhosis are conditions that can perturb the hemostatic balance towards a prothrombotic state. Because HCC-related hypercoagulability is not clarified at all, the aim of the present review is to summarize the currently available knowledge on epidemiology and pathogenesis of non-malignant thrombotic complications in patients with liver cirrhosis and HCC. They are at increased risk to develop both PVT and non-splanchnic VTE, indicating that both local and systemic factors can foster the development of site-specific thrombosis. Recent studies have suggested multiple and often interrelated mechanisms through which HCC can tip the hemostatic balance of liver cirrhosis towards hypercoagulability. Described mechanisms include increased fibrinogen concentration/polymerization, thrombocytosis, and release of tissue factor-expressing extracellular vesicles. Currently, there are no specific guidelines on the use of thromboprophylaxis in this unique population. There is the urgent need of prospective studies assessing which patients have the highest prothrombotic profile and would therefore benefit from early thromboprophylaxis

Efficient Computation of Multiple Density-Based Clustering Hierarchies

HDBSCAN*, a state-of-the-art density-based hierarchical clustering method, produces a hierarchical organization of clusters in a dataset w.r.t. a parameter mpts. While the performance of HDBSCAN* is robust w.r.t. mpts in the sense that a small change in mpts typically leads to only a small or no change in the clustering structure, choosing a "good" mpts value can be challenging: depending on the data distribution, a high or low value for mpts may be more appropriate, and certain data clusters may reveal themselves at different values of mpts. To explore results for a range of mpts values, however, one has to run HDBSCAN* for each value in the range independently, which is computationally inefficient. In this paper, we propose an efficient approach to compute all HDBSCAN* hierarchies for a range of mpts values by replacing the graph used by HDBSCAN* with a much smaller graph that is guaranteed to contain the required information. An extensive experimental evaluation shows that with our approach one can obtain over one hundred hierarchies for the computational cost equivalent to running HDBSCAN* about 2 times.Comment: A short version of this paper appears at IEEE ICDM 2017. Corrected typos. Revised abstrac

Algebraic lattice Codes achieve the capacity of the compound block-fading channel

We propose a lattice coding scheme that achieves the capacity of the compound block-fading channel. Our lattice construction exploits the multiplicative structure of number fields and their group of units to absorb ill-conditioned channel realizations. To shape the constellation, a discrete Gaussian distribution over the lattice points is applied. A by-product of our results is a refined analysis of the probability of error of the lattice Gaussian distribution in the AWGN channel