On Codes for Optimal Rebuilding Access

MDS (maximum distance separable) array codes are widely used in storage systems due to their computationally efficient encoding and decoding procedures. An MDS code with r redundancy nodes can correct any r erasures by accessing (reading) all the remaining information in both the systematic nodes and the parity (redundancy) nodes. However, in practice, a single erasure is the most likely failure event; hence, a natural question is how much information do we need to access in order to rebuild a single storage node? We define the rebuilding ratio as the fraction of remaining information accessed during the rebuilding of a single erasure. In our previous work we showed that the optimal rebuilding ratio of 1/r is achievable (using our newly constructed array codes) for the rebuilding of any systematic node, however, all the information needs to be accessed for the rebuilding of the parity nodes. Namely, constructing array codes with a rebuilding ratio of 1/r was left as an open problem. In this paper, we solve this open problem and present array codes that achieve the lower bound of 1/r for rebuilding any single systematic or parity node

The Internet and the Informational Bulimia

AbstractUmberto Eco formulated the phrase that there is “no greater silence than the absolute noise”. The immensity of the online-information in any field is overwhelming today. In this paper I will formulate and look for answers for two key-questions: How much information do we need? How much information can we deal with?The paper deals with the informational bulimia, pointing to the way we are fed with information every day, being often driven to a consumption we aren’t able to control. My attention will be focused on online information: online news, online information for researchers and professionals and the online publishing of books

Optimal Rebuilding of Multiple Erasures in MDS Codes

MDS array codes are widely used in storage systems due to their computationally efficient encoding and decoding procedures. An MDS code with $r$ redundancy nodes can correct any $r$ node erasures by accessing all the remaining information in the surviving nodes. However, in practice, $e$ erasures is a more likely failure event, for $1\le e<r$. Hence, a natural question is how much information do we need to access in order to rebuild $e$ storage nodes? We define the rebuilding ratio as the fraction of remaining information accessed during the rebuilding of $e$ erasures. In our previous work we constructed MDS codes, called zigzag codes, that achieve the optimal rebuilding ratio of $1/r$ for the rebuilding of any systematic node when $e=1$, however, all the information needs to be accessed for the rebuilding of the parity node erasure. The (normalized) repair bandwidth is defined as the fraction of information transmitted from the remaining nodes during the rebuilding process. For codes that are not necessarily MDS, Dimakis et al. proposed the regenerating codes framework where any $r$ erasures can be corrected by accessing some of the remaining information, and any $e=1$ erasure can be rebuilt from some subsets of surviving nodes with optimal repair bandwidth. In this work, we study 3 questions on rebuilding of codes: (i) We show a fundamental trade-off between the storage size of the node and the repair bandwidth similar to the regenerating codes framework, and show that zigzag codes achieve the optimal rebuilding ratio of $e/r$ for MDS codes, for any $1\le e\le r$. (ii) We construct systematic codes that achieve optimal rebuilding ratio of $1/r$, for any systematic or parity node erasure. (iii) We present error correction algorithms for zigzag codes, and in particular demonstrate how these codes can be corrected beyond their minimum Hamming distances.Comment: There is an overlap of this work with our two previous submissions: Zigzag Codes: MDS Array Codes with Optimal Rebuilding; On Codes for Optimal Rebuilding Access. arXiv admin note: text overlap with arXiv:1112.037

Synthetic Biology: A Bridge between Artificial and Natural Cells.

Artificial cells are simple cell-like entities that possess certain properties of natural cells. In general, artificial cells are constructed using three parts: (1) biological membranes that serve as protective barriers, while allowing communication between the cells and the environment; (2) transcription and translation machinery that synthesize proteins based on genetic sequences; and (3) genetic modules that control the dynamics of the whole cell. Artificial cells are minimal and well-defined systems that can be more easily engineered and controlled when compared to natural cells. Artificial cells can be used as biomimetic systems to study and understand natural dynamics of cells with minimal interference from cellular complexity. However, there remain significant gaps between artificial and natural cells. How much information can we encode into artificial cells? What is the minimal number of factors that are necessary to achieve robust functioning of artificial cells? Can artificial cells communicate with their environments efficiently? Can artificial cells replicate, divide or even evolve? Here, we review synthetic biological methods that could shrink the gaps between artificial and natural cells. The closure of these gaps will lead to advancement in synthetic biology, cellular biology and biomedical applications

Optimal Rebuilding of Multiple Erasures in MDS Codes

Maximum distance separable (MDS) array codes are widely used in storage systems due to their computationally efficient encoding and decoding procedures. An MDS code with r redundancy nodes can correct any r node erasures by accessing (reading) all the remaining information in the surviving nodes. However, in practice, e erasures are a more likely failure event, for some 1≤e<r . Hence, a natural question is how much information do we need to access in order to rebuild e storage nodes. We define the rebuilding ratio as the fraction of remaining information accessed during the rebuilding of e erasures. In our previous work, we constructed MDS codes, called zigzag codes, that achieve the optimal rebuilding ratio of 1/r for the rebuilding of any systematic node when e=1 ; however, all the information needs to be accessed for the rebuilding of the parity node erasure. The (normalized) repair bandwidth is defined as the fraction of information transmitted from the remaining nodes during the rebuilding process. For codes that are not necessarily MDS, Dimakis et al. proposed the regenerating codes framework where any r erasures can be corrected by accessing some of the remaining information, and any e=1 erasure can be rebuilt from some subsets of surviving nodes with optimal repair bandwidth. In this paper, we present three results on rebuilding of codes: 1) we show a fundamental outer bound on the storage size of the node and the repair bandwidth similar to the regenerating codes framework, and show that zigzag codes achieve the optimal rebuilding ratio of e/r for systematic nodes of MDS codes, for any 1≤e≤r ; 2) we construct systematic codes that achieve optimal rebuilding ratio of 1/r , for any systematic or parity node erasure; and 3) we present error correction algorithms for zigzag codes, and in particular demonstrate how these codes can be corrected beyond their minimum Hamming distances

Genus two partition functions of chiral conformal field theories

A systematic analysis of the genus two vacuum amplitudes of chiral self-dual conformal field theories is performed. It is explained that the existence of a modular invariant genus two partition function implies infinitely many relations among the structure constants of the theory. All of these relations are shown to be a consequence of the associativity of the operator product expansion, as well as the modular covariance properties of the torus one-point functions. U sing these techniques we prove that for the proposed extremal conformal field theories at c = 24k a consistent genus two vacuum amplitude exists for all k, but that this does not actually check the consistency of these theories beyond what is already testable at genus one

On the capacity of information processing systems

We propose and analyze a family of information processing systems, where a finite set of experts or servers are employed to extract information about a stream of incoming jobs. Each job is associated with a hidden label drawn from some prior distribution. An inspection by an expert produces a noisy outcome that depends both on the job's hidden label and the type of the expert, and occupies the expert for a finite time duration. A decision maker's task is to dynamically assign inspections so that the resulting outcomes can be used to accurately recover the labels of all jobs, while keeping the system stable. Among our chief motivations are applications in crowd-sourcing, diagnostics, and experiment designs, where one wishes to efficiently learn the nature of a large number of items, using a finite pool of computational resources or human agents. We focus on the capacity of such an information processing system. Given a level of accuracy guarantee, we ask how many experts are needed in order to stabilize the system, and through what inspection architecture. Our main result provides an adaptive inspection policy that is asymptotically optimal in the following sense: the ratio between the required number of experts under our policy and the theoretical optimal converges to one, as the probability of error in label recovery tends to zero

Adaptive Endpointing with Deep Contextual Multi-armed Bandits

Current endpointing (EP) solutions learn in a supervised framework, which does not allow the model to incorporate feedback and improve in an online setting. Also, it is a common practice to utilize costly grid-search to find the best configuration for an endpointing model. In this paper, we aim to provide a solution for adaptive endpointing by proposing an efficient method for choosing an optimal endpointing configuration given utterance-level audio features in an online setting, while avoiding hyperparameter grid-search. Our method does not require ground truth labels, and only uses online learning from reward signals without requiring annotated labels. Specifically, we propose a deep contextual multi-armed bandit-based approach, which combines the representational power of neural networks with the action exploration behavior of Thompson modeling algorithms. We compare our approach to several baselines, and show that our deep bandit models also succeed in reducing early cutoff errors while maintaining low latency

Explaining Customers’ Utilitarian and Hedonic Perceptions in the Context of Product Search within Social Network-Enabled Shopping Websites

Online social networks and e-Commerce have recently begun to converge into hybrid configurations via which online users search for products in the context of their social relationships. The present study explains how shoppers’ differences in two aspects of their social capital (centrality: their number of online friends, and quality: the relevance of these friends) influence the extent to which their product search experiences are perceived to be useful and enjoyable. For that matter, three value-creation paths (social network activation, effort reduction, and curiosity arousal) are proposed as the main explanatory mechanisms. Providing insights into this process is important as it will help develop a clearer understanding of the mechanisms via which digital networks influence customers’ product search experiences