There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

We survey the current techniques to cope with the problem of string matching that allows errors. This is becoming a more and more relevant issue for many fast growing areas such as information retrieval and computational biology. We focus on online searching and mostly on edit distance, explaining the problem and its relevance, its statistical behavior, its history and current developments, and the central ideas of the algorithms and their complexities. We present a number of experiments to compare the performance of the different algorithms and show which are the best choices. We conclude with some directions for future work and open problems.

/pdf/a-guided-tour-to-approximate-string-matching-22fowlmq5b.pdf

A guided tour to approximate string matching

Clathrin-mediated endocytosis is the endocytic portal into cells through which cargo is packaged into vesicles with the aid of a clathrin coat. It is fundamental to neurotransmission, signal transduction and the regulation of many plasma membrane activities and is thus essential to higher eukaryotic life. Morphological stages of vesicle formation are mirrored by progression through various protein modules (complexes). The process involves the formation of a putative FCH domain only (FCHO) initiation complex, which matures through adaptor protein 2 (AP2)-dependent cargo selection, and subsequent coat building, dynamin-mediated scission and finally auxilin- and heat shock cognate 70 (HSC70)-dependent uncoating. Some modules can be used in other pathways, and additions or substitutions confer cell specificity and adaptability.

/pdf/molecular-mechanism-and-physiological-functions-of-clathrin-2hpvjtbosd.pdf

Molecular mechanism and physiological functions of clathrin-mediated endocytosis

Dynasore, a Cell-Permeable Inhibitor of Dynamin

Extracellular vesicles (EVs) are small vesicles released by donor cells that can be taken up by recipient cells. Despite their discovery decades ago, it has only recently become apparent that EVs play an important role in cell-to-cell communication. EVs can carry a range of nucleic acids and proteins which can have a significant impact on the phenotype of the recipient. For this phenotypic effect to occur, EVs need to fuse with target cell membranes, either directly with the plasma membrane or with the endosomal membrane after endocytic uptake. EVs are of therapeutic interest because they are deregulated in diseases such as cancer and they could be harnessed to deliver drugs to target cells. It is therefore important to understand the molecular mechanisms by which EVs are taken up into cells. This comprehensive review summarizes current knowledge of EV uptake mechanisms. Cells appear to take up EVs by a variety of endocytic pathways, including clathrin-dependent endocytosis, and clathrin-independent pathways such as caveolin-mediated uptake, macropinocytosis, phagocytosis, and lipid raft–mediated internalization. Indeed, it seems likely that a heterogeneous population of EVs may gain entry into a cell via more than one route. The uptake mechanism used by a given EV may depend on proteins and glycoproteins found on the surface of both the vesicle and the target cell. Further research is needed to understand the precise rules that underpin EV entry into cells. Keywords: extracellular vesicles; EV uptake; EV internalization; cell–EV interaction; endocytosis; cell communication; exosomes (Published: 4 August 2014) Citation: Journal of Extracellular Vesicles 2014, 3 : 24641 - http://dx.doi.org/10.3402/jev.v3.24641

/pdf/routes-and-mechanisms-of-extracellular-vesicle-uptake-g2q1wucbai.pdf

Routes and mechanisms of extracellular vesicle uptake.

http://web.mit.edu/7.61/restricted/readings/Kirchhausen_Cell_04.pdf

Endocytosis by Random Initiation and Stabilization of Clathrin-Coated Pits

(MATH) This paper obtains the following results on pattern matching problems in which the text has length n and the pattern has length mAn O(nlog m) time deterministic algorithm for the String Matching with Wildcards problems, even when the alphabet is large.An O(klog2 m) time Las Vegas algorithm for the Sparse String Matching with Wildcards problem, where k«n is the number of non-zeros in the text. We also give Las Vegas algorithms for the higher dimensional version of this problem.As an application of the above, an O(nlog2 m) time Las Vegas algorithm for the Subset Matching and Tree Pattern Matching problems, and a Las Vegas algorithm for the Geometric Pattern Matching problem.Finally, an O(nlog2 m) time deterministic algorithm for Subset Matching and Tree Pattern Matching..The crucial new idea underlying the first three results above is that of confirming matches by convolving vectors obtained by coding characters in the alphabet with non-boolean (i.e., rational or even complex) entries; in contrast, almost all previous pattern matching algorithms consider only boolean codes for the alphabet. The crucial new idea underlying the fourth result is a simpler method of shifting characters which ensures that each character occurs as a singleton in some shift.

/pdf/verifying-candidate-matches-in-sparse-and-wildcard-matching-2ewmb109g6.pdf

Verifying candidate matches in sparse and wildcard matching

We show how to maintain a data structure on trees which allows for the following operations, all in worst-case constant time: 1. insertion of leaves and internal nodes, 2. deletion of leaves, 3. deletion of internal nodes with only one child, 4. determining the least common ancestor of any two nodes. We also generalize the Dietz-Sleator "cup-filling" scheduling methodology, which may be of independent interest.

Dynamic LCA queries on trees

We give two algorithms for finding all approximate matches of a pattern in a text, where the edit distance between the pattern and the matching text substring is at most k. The first algorithm, which is quite simple, runs in time $O(\frac{nk^3}{m}+n+m)$ on all patterns except k-break periodic strings (defined later). The second algorithm runs in time $O(\frac{nk^4}{m}+n+m)$ on k-break periodic patterns. The two classes of patterns are easily distinguished in O(m)time.

/pdf/approximate-string-matching-a-simpler-faster-algorithm-hinmkd6hgk.pdf

Approximate String Matching: A Simpler Faster Algorithm

Given a weighted graph $G$ and an error parameter $\epsilon > 0$, the {\em graph sparsification} problem requires sampling edges in $G$ and giving the sampled edges appropriate weights to obtain a sparse graph $G_{\epsilon}$ (containing O(n\log n) edges in expectation) with the following property: the weight of every cut in $G_{\epsilon}$ is within a factor of $(1\pm \epsilon)$ of the weight of the corresponding cut in $G$. We provide a generic framework that sets out sufficient conditions for any particular sampling scheme to result in good sparsifiers, and obtain a set of results by simple instantiations of this framework. The results we obtain include the following: (1) We improve the time complexity of graph sparsification from O(m\log^3 n) to O(m + n\log^4 n) for graphs with polynomial edge weights. (2) We improve the time complexity of graph sparsification from O(m\log^3 n) to O(m\log^2 n) for graphs with arbitrary edge weights. (3) If the size of the sparsifier is allowed to be O(n\log^2 n/\epsilon^2) instead of O(n\log n/\epsilon^2), we improve the time complexity of sparsification to O(m) for graphs with polynomial edge weights. (4) We show that sampling using standard connectivities results in good sparsifiers, thus resolving an open question of Benczur and Karger. As a corollary, we give a simple proof of (a slightly weaker version of) a result due to Spielman and Srivastava showing that sampling using effective resistances produces good sparsifiers. (5) We give a simple proof showing that sampling using strong connectivities results in good sparsifiers, a result obtained previously using a more involved proof by Benczur and Karger. A key ingredient of our proofs is a generalization of bounds on the number of small cuts in an undirected graph due to Karger; this generalization might be of independent interest.

Ramesh Hariharan

Papers

Endocytosis by Random Initiation and Stabilization of Clathrin-Coated Pits

Verifying candidate matches in sparse and wildcard matching

Dynamic LCA queries on trees

Approximate String Matching: A Simpler Faster Algorithm

A General Framework for Graph Sparsification