A binary string transmitted via a memoryless i.i.d. deletion channel is received as a subsequence of the original input. From this, one obtains a posterior distribution on the channel input, corresponding to a set of candidate supersequences weighted by the number of times the received subsequence can be embedded in them. In a previous work it is conjectured on the basis of experimental data that the entropy of the posterior is minimized and maximized by the constant and the alternating strings, respectively. In this work, we present an algorithm for counting the number of subsequence embeddings using a run-length encoding of strings. We then describe two different ways of clustering the space of supersequences and prove that their cardinality depends only on the length of the received subsequence and its Hamming weight, but not its exact form. Then, we consider supersequences that contain a single embedding of a fixed subsequence, referred to as singletons, and provide a closed form expression for enumerating them using the same run-length encoding. We prove an analogous result for the minimization and maximization of the number of singletons, by the alternating and the uniform strings, respectively. Next, we prove the original minimal entropy conjecture for the special cases of single and double deletions using similar clustering techniques and the same run-length encoding, which allow us to characterize the distribution of the number of subsequence embeddings in the space of compatible supersequences to demonstrate the effect of an entropy decreasing operation.
Studies involving subsequences and supersequences encompass a wide variety of problems that arise in various contexts such as formal languages, coding theory, computer intrusion detection and DNA sequencing to name a few. Despite their prevalence in such a wide range of disciplines, they remain largely unexplored and still present a considerable wealth of unanswered questions. In the realm of stringology and formal languages, the problem of determining the number of distinct subsequences obtainable from a fixed number of deletions, and closely related problems, have been studied extensively in @cite_26 @cite_24 @cite_5 @cite_15 . Perhaps it is worth noting that the same entropy minimizing and maximizing strings conjectured in @cite_22 and characterized in the present work, have been shown to lead to the minimum and maximum number of distinct subsequences, respectively. The problems of finding shortest common supersequences (SCS) and longest common subsequences (LCS) represent two well-known NP-hard problems @cite_6 @cite_9 @cite_0 that involve subproblems similar to our work. Finally, devising efficient algorithms for subsequence combinatorics based on dynamic programming for counting the number of occurrences of a subsequence in DNA sequencing is yet another important and closely related line of research @cite_3 @cite_19 .
@cite_26 @cite_22 @cite_9 @cite_6 @cite_3 @cite_24 @cite_0 @cite_19 @cite_5 @cite_15
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Abstract In this paper we investigate the complexity of finding various kinds of common super- and subsequences with respect to one or two given sets of strings. We show that Longest Minimal Common Supersequence, Shortest Maximal Common Subsequence, and Shortest Maximal Common Non-Supersequence are MAX SNP-hard over a binary alphabet. Moreover, we show that Shortest Common Supersequence, Longest Common Subsequence, Longest Common Non-Supersequence, Shortest Common Non-Subsequence, and Longest Minimal Common Non-Supersequence are MAX SNP-hard over a binary alphabet if the number of zeros is fixed (by the instance). We show how these problems can be related to finding sequences consistent with respect to two given sets of strings. This leads to a unified approach for characterizing the complexity of such problems. 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. 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 self‐citation 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 ... A subsequence is obtained from a string by deleting any number of characters; thus in contrast to a substring, a subsequence is not necessarily a contiguous part of the string. Counting subsequences under various constraints has become relevant to biological sequence analysis, to machine learning, to coding theory, to the analysis of categorical time series in the social sciences, and to the theory of word complexity. We present theorems that lead to efficient dynamic programming algorithms to count (1) distinct subsequences in a string, (2) distinct common subsequences of two strings, (3) matching joint embeddings in two strings, (4) distinct subsequences with a given minimum span, and (5) sequences generated by a string allowing characters to come in runs of a length that is bounded from above. 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. The longest common subsequence problem is examined from the point of view of parameterized computational complexity. There are several different ways in which parameters enter the problem, such as the number of sequences to be analyzed, the length of the common subsequence, and the size of the alphabet. Lower bounds on the complexity of this basic problem imply lower bounds on a number of other sequence alignment and consensus problems. An issue in the theory of parameterized complexity is whether a problem which takes input (x, k) can be solved in time ƒ(k) · nα where α is independent of k (termed fixed-parameter tractability). It can be argued that this is the appropriate asymptotic model of feasible computability for problems for which a small range of parameter values covers important applications — a situation which certainly holds for many problems in biological sequence analysis. Our main results show that: 1. (1) The longest common subsequence (LCS) parameterized by the number of sequences to be analyzed is hard for W[t] for all t. 2. (2) The LCS problem, parameterized by the length of the common subsequence, belongs to W[P] and is hard for W[2]. 3. (3) The LCS problem parameterized both by the number of sequences and the length of the common subsequence, is complete for W[1]. All of the above results are obtained for unrestricted alphabet sizes. For alphabets of a fixed size, problems (2) and (3) are fixed-parameter tractable. We conjecture that (1) remains hard. 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 are addressed by honouring respective Internet standards (robot exclusion files, no-cache and no-archive tags). Long-term preservation is ensured by agreements with libraries and digital preservation organizations. The resulting WebCite Index may also have applications for research assessment exercises, being able to measure the impact of Web services and published Web documents through access and Web citation metrics. @PARASPLIT [J Med Internet Res 2005;7(5):e60] Super- substring problems and super- subsequence problems are well-known problems in stringology that have applications in a variety of areas, such as manufacturing systems design and molecular biology. Here we investigate the complexity of a new type of such problem that forms a combination of a super- substring and a super- subsequence problem. Moreover we introduce different types of minimal superstring and maximal substring problems. In particular, we consider the following problems: given a set L of strings and a string S, (i) find a minimal superstring (or maximal substring) of L that is also a supersequence (or a subsequence) of S, (ii) find a minimal supersequence (or maximal subsequence) of L that is also a superstring (or a substring) of S. In addition some non-super- non-substring and non-super- nonsubsequence variants are studied. We obtain several NP-hardness or even MAX SNP-hardness results and also identify types of "weak minimal" superstrings and "weak maximal" substrings for which (i) is polynomial-time solvable. Citation relationship between scientific publications has been successfully used for scholarly bibliometrics, information retrieval and data mining tasks, and citation-based recommendation algorithms are well documented. While previous studies investigated citation relations from various viewpoints, most of them share the same assumption that, if paper1 cites paper2 (or author1 cites author2), they are connected, regardless of citation importance, sentiment, reason, topic, or motivation. However, this assumption is oversimplified. In this study, we employ an innovative "context-rich heterogeneous network" approach, which paves a new way for citation recommendation task. In the network, we characterize 1) the importance of citation relationships between citing and cited papers, and 2) the topical citation motivation. Unlike earlier studies, the citation information, in this paper, is characterized by citation textual contexts extracted from the full-text citing paper. We also propose algorithm to cope with the situation when large portion of full-text missing information exists in the bibliographic repository. Evaluation results show that, context-rich heterogeneous network can significantly enhance the citation recommendation performance. The problems of finding shortest common supersequences (SCS) and longest common subsequences (LCS) are two well-known NP -hard problems that have applications in many areas including computational molecular biology, data compression, robot motion planning and scheduling, text editing, etc. A lot of fruitless effort has been spent in searching for good approximation algorithms for these problems. In this paper, we show that these problems are inherently hard to approximate in the worst case. In particular, we prove that (i) SCS does not have a polynomial time linear approximation algorithm, unless P = NP ; (ii) There exists a constant @math such that, if SCS has a polynomial time approximation algorithm with ratio @math , where @math is the number of input sequences, then NP is contained in DTIME @math ; (iii) There exists a constant @math such that, if LCS has a polynomial time approximation algorithm with performance ratio @math , then P = NP . The proofs utilize the recent results of [Proc. 23rd IEEE Symposium on Foundations of Computer Science, 1992, pp. 14-23] on the complexity of approximation problems. In the second part of the paper, we introduce a new method for analyzing the average-case performance of algorithms for sequences, based on Kolmogorov complexity. Despite the above nonapproximability results, we show that near optimal solutions for both SCS and LCS can be found on the average. More precisely, consider a fixed alphabet @math and suppose that the input sequences are generated randomly according to the uniform probability distribution and are of the same length @math . Moreover, assume that the number of input sequences is polynomial in @math . Then, there are simple greedy algorithms which approximate SCS and LCS with expected additive errors @math and @math for any @math , respectively. Incidentally, our analyses also provide tight upper and lower bounds on the expected LCS and SCS lengths for a set of random sequences, solving a generalization of another well-known open question on the expected LCS length for two random sequences [K. Alexander, The rate of convergence of the mean length of the longest common subsequence, 1992, manuscript],[V. Chvatal and D. Sankoff, J. Appl. Probab., 12 (1975), pp. 306-315], [D. Sankoff and J. Kruskall, eds., Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison, Addison-Wesley, Reading, MA, 1983]. We investigate combinatorial enumeration problems related to subsequences of strings; in contrast to substrings, subsequences need not be contiguous. For a finite alphabet E, the following three problems are solved. (1) Number of distinct subsequences: Given a sequence s ∈ Σ n and a nonnegative integer k ≤ n, how many distinct subsequences of length k does s contain? A previous result by Chase states that this number is maximized by choosing s as a repeated permutation of the alphabet. This has applications in DNA microarray production. (2) Number of ρ-restricted p-generated sequences: Given s ∈ Σ n and integers k ≥ 1 and p > 1, how many distinct sequences in Σ k contain no single nucleotide repeat longer than p and can be written as s[ r1 1 ... s rn n with 0 1, determine the number of sequences in E whose longest strictly increasing subsequence has length k, where 0 < k < K. This has applications to significance computations for chaining algorithms. In the paper two combinatorial problems for the set Fnq of sequences of length n over the alphabet Fq= 0, 1, ?, q?1 are considered. The maximum size N?q(n, t) of the set of common subsequences of length n?t and the maximum size N+q(n, t) of the set of common supersequences of length n+t of two different sequences of Fnq are found for any nonnegative integers n and t. The number N?q(n, t)+1 (respectively, N+q(n, t)+1) is equal to the minimum number N of different subsequences of length n?t (supersequences of length n+t) of an unknown sequence X?Fnq which are sufficient for its reconstruction. Simple algorithms to recover X?Fnq from N?q(n, t)+1 of its subsequences of length n?t and from N+q(n, t)+1 of its supersequences of length n+t are given. 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 . A new form of document coupling called co-citation is defined as the frequency with which two documents are cited together. The co-citation frequency of two scientific papers can be determined by comparing lists of citing documents in the Science Citation Index and counting identical entries. Networks of co-cited papers can be generated for specific scientific specialties, and an example is drawn from the literature of particle physics. Co-citation patterns are found to differ significantly from bibliographic coupling patterns, but to agree generally with patterns of direct citation. Clusters of co-cited papers provide a new way to study the specialty structure of science. They may provide a new approach to indexing and to the creation of SDI profiles. One way to detect intruders on the Internet is to compare the similarity of two thumbprints. A thumbprint is a summary of a connection that characterizes the connection. The packet gap thumbprint consists of sequences of non-negative real number representing the time gaps between "send" packets. This paper formalized definitions of similarity between two non-negative real number sequences, by introducing spl epsiv -similarity, partial sum and longest spl epsiv -similar subsequence (LSS). Length of LSS is a measurement of similarity between two sequences. The longest spl epsiv -similar subsequence (LSS) problem is a generalization of the well known longest common subsequence (LCS) problem. The goal of this paper is to find an optimal solution to the LSS problem. We analyzed the property of partial sums and proposed to focus on the minimum matched partial sum which leads to an optimal solution to LSS while reduce the problem space. As the LSS problem has optimal structure, we proposed an algorithm based on dynamic programming technique. Time complexity of this algorithm is O(m sup 2 n sup 2 ). By using a property of the partial sums, we reduced the time complexity to O(mn(m+n)). The old Asian legend about the blind men and the elephant comes to mind when looking at how different authors of scientific papers describe a piece of related prior work. It turns out that different citations to the same paper often focus on different aspects of that paper and that neither provides a full description of its full set of contributions. In this article, we will describe our investigation of this phenomenon. We studied citation summaries in the context of research papers in the biomedical domain. A citation summary is the set of citing sentences for a given article and can be used as a surrogate for the actual article in a variety of scenarios. It contains information that was deemed by peers to be important. Our study shows that citation summaries overlap to some extent with the abstracts of the papers and that they also differ from them in that they focus on different aspects of these papers than do the abstracts. In addition to this, co-cited articles (which are pairs of articles cited by another article) tend to be similar. We show results based on a lexical similarity metric called cohesion to justify our claims. © 2008 Wiley Periodicals, Inc. 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. An overwhelming number of news articles are available every day via the internet. Unfortunately, it is impossible for us to peruse more than a handful; furthermore it is difficult to ascertain an article’s social context, i.e., is it popular, what sorts of people are reading it, etc. In this paper, we develop a system to address this problem in the restricted domain of political news by harnessing implicit and explicit contextual information from the blogosphere. Specifically, we track thousands of blogs and the news articles they cite, collapsing news articles that have highly overlapping content. We then tag each article with the number of blogs citing it, the political orientation of those blogs, and the level of emotional charge expressed in the blog posts that link to the news article. We summarize and present the results to the user via a novel visualization which displays this contextual information; the user can then find the most popular articles, the articles most cited by liberals, the articles most emotionally discussed in the political blogosphere, etc. 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 natural problem in extremal combinatorics is to maximize the number of distinct subsequences for any length- @math string over a finite alphabet @math ; this value grows exponentially, but slower than @math . We use the probabilistic method to determine the maximizing string, which is a cyclically repeating string. The number of distinct subsequences is exactly enumerated by a generating function, from which we also derive asymptotic estimates. For the alphabet @math , @math has the maximum number of distinct subsequences, namely @math . We also consider the same problem with sub strings in lieu of sub sequences . Here, we show that an appropriately truncated de Bruijn word attains the maximum. For both problems, we compare the performance of random strings with that of the optimal ones.