This paper addresses the problem of constructing MDS codes that enable exact repair of each code block with small repair bandwidth, which refers to the total amount of information flow from the remaining code blocks during the repair process. This problem naturally arises in the context of distributed storage systems as the node repair problem [7]. The constructions of exact-repairable MDS codes with optimal repair-bandwidth require working with large sub-packetization levels, which restricts their employment in practice. This paper presents constructions for MDS codes that simultaneously provide both small repair bandwidth and small sub-packetization level. In particular, this paper presents two general approaches to construct exact-repairable MDS codes that aim at significantly reducing the required sub-packetization level at the cost of slightly sub-optimal repair bandwidth. The first approach gives MDS codes that have repair bandwidth at most twice the optimal repair-bandwidth. Additionally, these codes also have the smallest possible sub-packetization level @math , where @math denotes the number of parity blocks. This approach is then generalized to design codes that have their repair bandwidth approaching the optimal repair-bandwidth at the cost of graceful increment in the required sub-packetization level. The second approach transforms an MDS code with optimal repair-bandwidth and large sub-packetization level into a longer MDS code with small sub-packetization level and near-optimal repair bandwidth. For a given @math , the obtained codes have their sub-packetization level scaling logarithmically with the code length. In addition, the obtained codes require field size only linear in the code length and ensure load balancing among the intact code blocks in terms of the information downloaded from these blocks during the exact reconstruction of a code block.
The problem of constructing MSR codes, i.e., MDS codes that attain the cut-set bound (cf. ), has been explored by many researchers. In @cite_5 , present an explicit construction for MSR codes. This construction works with the sub-packetization level @math . However, this small sub-packetization is achieved at the expense of low rate which is bounded as @math . Towards constructing high-rate MSR codes, @cite_12 show the existence of such codes when sub-packetization level approaches infinity. Motivated by this result, the problem of designing high-rate MSR codes with finite sub-packetization level is explored in @cite_18 @cite_53 @cite_47 @cite_42 @cite_21 @cite_29 @cite_55 @cite_35 @cite_33 @cite_11 and references therein. The constructions presented in @cite_18 @cite_53 @cite_6 work with the sub-packetization level @math which is exponential in @math . For @math and all values of @math , @cite_23 construct MSR codes with the sub-packetization level @math . The constructions with @math and the similar sub-packetization levels that enable exact-repair of only @math systematic nodes are also presented in @cite_24 @cite_21 . The construction of @cite_23 is generalized for all possible values of @math with the sub-packetization level @math in @cite_37 .
@cite_35 @cite_18 @cite_37 @cite_33 @cite_53 @cite_42 @cite_21 @cite_29 @cite_55 @cite_6 @cite_24 @cite_23 @cite_5 @cite_47 @cite_12 @cite_11
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We present a high-rate @math -MSR code with a sub-packetization level that is polynomial in the dimension @math of the code. While polynomial sub-packetization level was achieved earlier for vector MDS codes that repair systematic nodes optimally, no such MSR code construction is known. In the low-rate regime (i. e., rates less than one-half), MSR code constructions with a linear sub-packetization level are available. But in the high-rate regime (i. e., rates greater than one-half), the known MSR code constructions required a sub-packetization level that is exponential in @math . In the present paper, we construct an MSR code for @math with a fixed rate @math achieveing a sub-packetization level @math . The code allows help-by-transfer repair, i. e., no computations are needed at the helper nodes during repair of a failed node. We present a high-rate (n, k, d = n  1)-MSR code with a sub-packetization level that is polynomial in the dimension k of the code. While polynomial sub-packetization level was achieved earlier for vector MDS codes that repair systematic nodes optimally, no such MSR code construction is known. In the low-rate regime (i. e., rates less than one-half), MSR code constructions with a linear sub-packetization level are available. But in the high-rate regime (i. e., rates greater than one-half), the known MSR code constructions required a sub-packetization level that is exponential in k. In the present paper, we construct an MSR code for d = n  1 with a fixed rate equation, achieveing a sub-packetization level  = O(kt). The code allows help-by-transfer repair, i. e., no computations are needed at the helper nodes during repair of a failed node. The first focus of the present paper, is on lower bounds on the sub-packetization level @math of an MSR code that is capable of carrying out repair in help-by-transfer fashion (also called optimal-access property). We prove here a lower bound on @math which is shown to be tight for the case @math by comparing with recent code constructions in the literature. We also extend our results to an @math MDS code over the vector alphabet. Our objective even here, is on lower bounds on the sub-packetization level @math of an MDS code that can carry out repair of any node in a subset of @math nodes, @math where each node is repaired (linear repair) by help-by-transfer with minimum repair bandwidth. We prove a lower bound on @math for the case of @math . This bound holds for any @math and is shown to be tight, again by comparing with recent code constructions in the literature. Also provided, are bounds for the case @math . We study the form of a vector MDS code having the property that we can repair failed nodes belonging to a fixed set of @math nodes with minimum repair bandwidth and in optimal-access fashion, and which achieve our lower bound on sub-packetization level @math . It turns out interestingly, that such a code must necessarily have a coupled-layer structure, similar to that of the Ye-Barg code. The first focus of the present paper, is on lower bounds on the sub-packetization level @math of an MSR code that is capable of carrying out repair in help-by-transfer fashion (also called optimal-access property). We prove here a lower bound on @math which is shown to be tight for the case @math by comparing with recent code constructions in the literature. We also extend our results to an @math MDS code over the vector alphabet. Our objective even here, is on lower bounds on the sub-packetization level @math of an MDS code that can carry out repair of any node in a subset of @math nodes, @math where each node is repaired (linear repair) by help-by-transfer with minimum repair bandwidth. We prove a lower bound on @math for the case of @math . This bound holds for any @math and is shown to be tight, again by comparing with recent code constructions in the literature. Also provided, are bounds for the case @math Q @math $ . It turns out interestingly, that such a code must necessarily have a coupled-layer structure, similar to that of the Ye-Barg code. An @math maximum distance separable (MDS) array code of length @math , dimension @math , and sub-packetization @math is formed of @math matrices over a finite field @math , with every column of the matrix stored on a separate node in the distributed storage system and viewed as a coordinate of the codeword. Repair of a failed node (recovery of one erased column) can be performed by accessing a set of @math surviving (helper) nodes. The code is said to have the optimal access property if the amount of data accessed at each of the helper nodes meets a lower bound on this quantity. For optimal-access MDS codes with @math , the sub-packetization @math satisfies the bound @math . In our previous work (IEEE Trans. Inf. Theory, vol. 63, no. 4, 2017), for any @math and @math , we presented an explicit construction of optimal-access MDS codes with sub-packetization @math . In this paper, we take up the question of reducing the sub-packetization value @math to make it to approach the lower bound. We construct an explicit family of optimal-access codes with @math , which differs from the optimal value by at most a factor of @math . These codes can be constructed over any finite field @math as long as @math , and afford low-complexity encoding and decoding procedures. We also define a version of the repair problem that bridges the context of regenerating codes and codes with locality constraints (LRC codes), which we call group repair with optimal access . In this variation, we assume that the set of @math nodes is partitioned into @math repair groups of size @math , and require that the amount of accessed data for repair is the smallest possible whenever the @math helper nodes include all the oth This paper presents an explicit construction for an @math regenerating code over a field @math operating at the Minimum Storage Regeneration (MSR) point. The MSR code can be constructed to have rate @math as close to @math as desired, sub-packetization given by @math , for @math , field size no larger than @math and where all code symbols can be repaired with the same minimum data download. The construction modifies a prior construction by Sasidharan et. al. which required far larger field-size. A building block appearing in the construction is a scalar MDS code of block length @math . The code has a simple layered structure with coupling across layers, that allows both node repair and data recovery to be carried out by making multiple calls to a decoder for the scalar MDS code. While this work was carried out independently, there is considerable overlap with a prior construction by Ye and Barg. It is shown here that essentially the same architecture can be employed to construct MSR codes using vector binary MDS codes as building blocks in place of scalar MDS codes. The advantage here is that computations can now be carried out over a field of smaller size potentially even over the binary field as we demonstrate in an example. Further, we show how the construction can be extended to handle the case of @math under a mild restriction on the choice of helper nodes. This paper presents a construction for high-rate MDS codes that enable bandwidth-efficient repair of a single node. Such MDS codes are also referred to as the minimum storage regenerating (MSR) codes in the distributed storage literature. The construction presented in this paper generates MSR codes for all possible number of helper nodes d as d is a design parameter in the construction. Furthermore, the obtained MSR codes have polynomial sub-packetization (a.k.a. node size) . The construction is built on the recent code proposed by [1], which works only for d = n  1, i.e., where all the remaining nodes serve as the helper nodes for the bandwidth-efficient repair of a single node. The results of this paper broaden the set of parameters where the constructions of MSR codes were known earlier. We investigate the minimization of Newton's functional for the problem of the body of minimal resistance with maximal height @math cite butt in the class of convex developable functions defined in a disc. This class is a natural candidate to find a (non-radial) minimizer in accordance with the results of cite lrp2. We prove that the minimizer in this class has a minimal set in the form of a regular polygon with @math sides centered in the disc, and numerical experiments indicate that the natural number @math is a non-decreasing function of @math . The corresponding functions all achieve a lower value of the functional than the optimal radially symmetric function with the same height @math . A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results. Regenerating codes for distributed storage have attracted much research interest in the past decade. Such codes trade the bandwidth needed to repair a failed node with the overall amount of data stored in the network. Minimum storage regenerating (MSR) codes are an important class of optimal regenerating codes that minimize (first) the amount of data stored per node and (then) the repair bandwidth. Specifically, an @math - @math MSR code @math over @math stores a file @math consisting of @math symbols over @math among @math nodes, each storing @math symbols, in such a way that: 1) the file @math can be recovered by downloading the content of any @math of the @math nodes and 2) the content of any failed node can be reconstructed by accessing any @math of the remaining @math nodes and downloading @math symbols from each of these nodes. In practice, the file @math is typically available in uncoded form on some @math of the @math nodes, known as systematic nodes , and the defining node-repair condition above can be relaxed to requiring the optimal repair bandwidth for systematic nodes only . Such codes are called systematicrepair MSR codes . Unfortunately, finite @math constructions of @math MSR codes are known only for certain special cases: either low rate, namely @math , or high repair connectivity, namely @math . Our main result in this paper is a finite @math construction of systematic-repair @math MSR codes for all possible values of parameters @math . We also introduce a generalized construction for @math MSR codes to achieve the optimal repair bandwidth for all values of @math simultaneously. We propose a generic transformation that can convert any nonbinary @math maximum distance separable (MDS) code into another @math MDS code over the same field such that: 1) some arbitrarily chosen @math nodes have the optimal repair bandwidth and the optimal rebuilding access; 2) for the remaining @math nodes, the normalized repair bandwidth and the normalized rebuilding access (over the file size) are preserved; and 3) the sub-packetization level is increased only by a factor of @math . Two immediate applications of this generic transformation are then presented. The first application is that we can transform any nonbinary MDS code with the optimal repair bandwidth or the optimal rebuilding access for the systematic nodes only, into a new MDS code which possesses the corresponding repair optimality for all nodes. The second application is that by applying the transformation multiple times, any nonbinary @math scalar MDS code can be converted into an @math MDS code with the optimal repair bandwidth and the optimal rebuilding access for all nodes, or only a subset of nodes, whose sub-packetization level is also optimal. In recent years scholars have built maps of science by connecting the academic fields that cite each other, are cited together, or that cite a similar literature. But since scholars cannot always publish in the fields they cite, or that cite them, these science maps are only rough proxies for the potential of a scholar, organization, or country, to enter a new academic field. Here we use a large dataset of scholarly publications disambiguated at the individual level to create a map of science-or research space-where links connect pairs of fields based on the probability that an individual has published in both of them. We find that the research space is a significantly more accurate predictor of the fields that individuals and organizations will enter in the future than citation based science maps. At the country level, however, the research space and citations based science maps are equally accurate. These findings show that data on career trajectories-the set of fields that individuals have previously published in-provide more accurate predictors of future research output for more focalized units-such as individuals or organizations-than citation based science maps. In a document network such as a citation network of scientific documents, web-logs, etc., the content produced by authors exhibits their interest in certain topics. In addition some authors influence other authors' interests. In this work, we propose to model the influence of cited authors along with the interests of citing authors. Moreover, we hypothesize that apart from the citations present in documents, the context surrounding the citation mention provides extra topical information about the cited authors. However, associating terms in the context to the cited authors remains an open problem. We propose novel document generation schemes that incorporate the context while simultaneously modeling the interests of citing authors and influence of the cited authors. Our experiments show significant improvements over baseline models for various evaluation criteria such as link prediction between document and cited author, and quantitatively explaining unseen text. Abstract Documents in computer-readable form can be used to provide information about other documents, i.e. those they cite. To do this efficiently requires procedures for computer recognition of citing statements. This is not easy, especially for multi-sentence citing statements. Computer recognition procedures have been developed which are accurate to the following extent: 73 of the words in statements selected by computer procedures as being citing statements are words which are correctly attributable to the corresponding documents. The retrieval effectiveness of computer-recognized citing statements was tested in the following way. First, for eight retrieval requests in inorganiic chemistry, average recall by search of Chemical Abstracts Service indexing and Chemical Abstracts abstract text words was found to be 50 . Words from citing statements referring to the papers to be retrieved were then added to the index terms and abstract words as additional access points, and searching was repeated. Average recall increased to 70 . Only words from citing statements published within a year of the cited papers were used. The retrieval effect of citing statement words alone (published within a year) without index or abstract terms was the following: average recall was 40 . When just the words of the titles of the cited papers were added to those citing statement words, average recall increased to 50 . Scholars are increasingly citing electronic web references which are not preserved in libraries or full text archives. WebCite is a new standard for citing web references. To webcite a document involves archiving the cited Web page through www.webcitation.org and citing the WebCite permalink instead of (or in addition to) the unstable live Web page. This journal has amended its instructions for authors accordingly, asking authors to archive cited Web pages before submitting a manuscript. Almost 200 other journals are already using the system. We discuss the rationale for WebCite, its technology, and how scholars, editors, and publishers can benefit from the service. Citing scholars initiate an archiving process of all cited Web references, ideally before they submit a manuscript. Authors of online documents and websites which are expected to be cited by others can ensure that their work is permanently available by creating an archived copy using WebCite and providing the citation information including the WebCite link on their Web document(s). Editors should ask their authors to cache all cited Web addresses (Uniform Resource Locators, or URLs) prospectively before submitting their manuscripts to their journal. Editors and publishers should also instruct their copyeditors to cache cited Web material if the author has not done so already. Finally, WebCite can process publisher submitted citing articles (submitted for example as eXtensible Markup Language [XML] documents) to automatically archive all cited Web pages shortly before or on publication. Finally, WebCite can act as a focussed crawler, caching retrospectively references of already published articles. Copyright issues Purpose  The purpose of this paper is to suggest an alternative to the widely used Times Cited criterion for analysing citation networks. The approach involves taking account of the natures of the papers that cite a given paper, so as to differentiate between papers that attract the same number of citations.Design methodology approach  ArticleRank is an algorithm that has been derived from Google's PageRank algorithm to measure the influence of journal articles. ArticleRank is applied to two datasets  a citation network based on an early paper on webometrics, and a selfcitation network based on the 19 most cited papers in the Journal of Documentation  using citation data taken from the Web of Knowledge database.Findings  ArticleRank values provide a different ranking of a set of papers from that provided by the corresponding Times Cited values, and overcomes the inability of the latter to differentiate between papers with the same numbers of citations. The difference in rankings between Times Cited ...