On the Sensitivity Conjecture for Read-k Formulas

Various combinatorial/algebraic parameters are used to quantify the complexity of a Boolean function. Among them, sensitivity is one of the simplest and block sensitivity is one of the most useful. Nisan (1989) and Nisan and Szegedy (1991) showed that block sensitivity and several other parameters, such as certificate complexity, decision tree depth, and degree over R, are all polynomially related to one another. The sensitivity conjecture states that there is also a polynomial relationship between sensitivity and block sensitivity, thus supplying the "missing link". Since its introduction in 1991, the sensitivity conjecture has remained a challenging open question in the study of Boolean functions. One natural approach is to prove it for special classes of functions. For instance, the conjecture is known to be true for monotone functions, symmetric functions, and functions describing graph properties. In this paper, we consider the conjecture for Boolean functions computable by read-k formulas. A read-k formula is a tree in which each variable appears at most k times among the leaves and has Boolean gates at its internal nodes. We show that the sensitivity conjecture holds for read-once formulas with gates computing symmetric functions. We next consider regular formulas with OR and AND gates. A formula is regular if it is a leveled tree with all gates at a given level having the same fan-in and computing the same function. We prove the sensitivity conjecture for constant depth regular read-k formulas for constant k

Hitting Diamonds and Growing Cacti

We consider the following NP-hard problem: in a weighted graph, find a minimum cost set of vertices whose removal leaves a graph in which no two cycles share an edge. We obtain a constant-factor approximation algorithm, based on the primal-dual method. Moreover, we show that the integrality gap of the natural LP relaxation of the problem is \Theta(\log n), where n denotes the number of vertices in the graph.Comment: v2: several minor changes

Online Pattern Matching for String Edit Distance with Moves

Edit distance with moves (EDM) is a string-to-string distance measure that includes substring moves in addition to ordinal editing operations to turn one string to the other. Although optimizing EDM is intractable, it has many applications especially in error detections. Edit sensitive parsing (ESP) is an efficient parsing algorithm that guarantees an upper bound of parsing discrepancies between different appearances of the same substrings in a string. ESP can be used for computing an approximate EDM as the L1 distance between characteristic vectors built by node labels in parsing trees. However, ESP is not applicable to a streaming text data where a whole text is unknown in advance. We present an online ESP (OESP) that enables an online pattern matching for EDM. OESP builds a parse tree for a streaming text and computes the L1 distance between characteristic vectors in an online manner. For the space-efficient computation of EDM, OESP directly encodes the parse tree into a succinct representation by leveraging the idea behind recent results of a dynamic succinct tree. We experimentally test OESP on the ability to compute EDM in an online manner on benchmark datasets, and we show OESP's efficiency.Comment: This paper has been accepted to the 21st edition of the International Symposium on String Processing and Information Retrieval (SPIRE2014

Fast Arc-Annotated Subsequence Matching in Linear Space

An arc-annotated string is a string of characters, called bases, augmented with a set of pairs, called arcs, each connecting two bases. Given arc-annotated strings $P$ and $Q$ the arc-preserving subsequence problem is to determine if $P$ can be obtained from $Q$ by deleting bases from $Q$. Whenever a base is deleted any arc with an endpoint in that base is also deleted. Arc-annotated strings where the arcs are ``nested'' are a natural model of RNA molecules that captures both the primary and secondary structure of these. The arc-preserving subsequence problem for nested arc-annotated strings is basic primitive for investigating the function of RNA molecules. Gramm et al. [ACM Trans. Algorithms 2006] gave an algorithm for this problem using $O(nm)$ time and space, where $m$ and $n$ are the lengths of $P$ and $Q$, respectively. In this paper we present a new algorithm using $O(nm)$ time and $O(n + m)$ space, thereby matching the previous time bound while significantly reducing the space from a quadratic term to linear. This is essential to process large RNA molecules where the space is likely to be a bottleneck. To obtain our result we introduce several novel ideas which may be of independent interest for related problems on arc-annotated strings.Comment: To appear in Algoritmic

Emergence of hyperons in failed supernovae: trigger of the black hole formation

We investigate the emergence of strange baryons in the dynamical collapse of a non-rotating massive star to a black hole by the neutrino-radiation hydrodynamical simulations in general relativity. By following the dynamical formation and collapse of nascent proto-neutron star from the gravitational collapse of a 40Msun star adopting a new hyperonic EOS table, we show that the hyperons do not appear at the core bounce but populate quickly at ~0.5-0.7 s after the bounce to trigger the re-collapse to a black hole. They start to show up off center owing to high temperatures and later prevail at center when the central density becomes high enough. The neutrino emission from the accreting proto-neutron star with the hyperonic EOS stops much earlier than the corresponding case with a nucleonic EOS while the average energies and luminosities are quite similar between them. These features of neutrino signal are a potential probe of the emergence of new degrees of freedom inside the black hole forming collapse.Comment: 11 pages, 3 figures, accepted for publication in ApJ

Strobe sequence design for haplotype assembly

Abstract Background Humans are diploid, carrying two copies of each chromosome, one from each parent. Separating the paternal and maternal chromosomes is an important component of genetic analyses such as determining genetic association, inferring evolutionary scenarios, computing recombination rates, and detecting cis-regulatory events. As the pair of chromosomes are mostly identical to each other, linking together of alleles at heterozygous sites is sufficient to phase, or separate the two chromosomes. In Haplotype Assembly, the linking is done by sequenced fragments that overlap two heterozygous sites. While there has been a lot of research on correcting errors to achieve accurate haplotypes via assembly, relatively little work has been done on designing sequencing experiments to get long haplotypes. Here, we describe the different design parameters that can be adjusted with next generation and upcoming sequencing technologies, and study the impact of design choice on the length of the haplotype. Results We show that a number of parameters influence haplotype length, with the most significant one being the advance length (distance between two fragments of a clone). Given technologies like strobe sequencing that allow for large variations in advance lengths, we design and implement a simulated annealing algorithm to sample a large space of distributions over advance-lengths. Extensive simulations on individual genomic sequences suggest that a non-trivial distribution over advance lengths results a 1-2 order of magnitude improvement in median haplotype length. Conclusions Our results suggest that haplotyping of large, biologically important genomic regions is feasible with current technologies

On Feedback Vertex Set: New Measure and New Structures

We present a new parameterized algorithm for the {feedback vertex set} problem ({\sc fvs}) on undirected graphs. We approach the problem by considering a variation of it, the {disjoint feedback vertex set} problem ({\sc disjoint-fvs}), which finds a feedback vertex set of size $k$ that has no overlap with a given feedback vertex set $F$ of the graph $G$. We develop an improved kernelization algorithm for {\sc disjoint-fvs} and show that {\sc disjoint-fvs} can be solved in polynomial time when all vertices in $G \setminus F$ have degrees upper bounded by three. We then propose a new branch-and-search process on {\sc disjoint-fvs}, and introduce a new branch-and-search measure. The process effectively reduces a given graph to a graph on which {\sc disjoint-fvs} becomes polynomial-time solvable, and the new measure more accurately evaluates the efficiency of the process. These algorithmic and combinatorial studies enable us to develop an $O^*(3.83^k)$-time parameterized algorithm for the general {\sc fvs} problem, improving all previous algorithms for the problem.Comment: Final version, to appear in Algorithmic

Reversal Distances for Strings with Few Blocks or Small Alphabets

International audienceWe study the String Reversal Distance problem, an extension of the well-known Sorting by Reversals problem. String Reversal Distance takes two strings S and T as input, and asks for a minimum number of reversals to obtain T from S. We consider four variants: String Reversal Distance, String Prefix Reversal Distance (in which any reversal must include the first letter of the string), and the signed variants of these problems, namely Signed String Reversal Distance and Signed String Prefix Reversal Distance. We study algorithmic properties of these four problems, in connection with two parameters of the input strings: the number of blocks they contain (a block being maximal substring such that all letters in the substring are equal), and the alphabet size Σ. For instance, we show that Signed String Reversal Distance and Signed String Prefix Reversal Distance are NP-hard even if the input strings have only one letter

Time-frequency scaling transformation of the phonocardiogram based of the matching pursuit method.

International audienceA time-frequency scaling transformation based on the matching pursuit (MP) method is developed for the phonocardiogram (PCG). The MP method decomposes a signal into a series of time-frequency atoms by using an iterative process. The modification of the time scale of the PCG can be performed without perceptible change in its spectral characteristics. It is also possible to modify the frequency scale without changing the temporal properties. The technique has been tested on 11 PCG's containing heart sounds and different murmurs. A scaling/inverse-scaling procedure was used for quantitative evaluation of the scaling performance. Both the spectrogram and a MP-based Wigner distribution were used for visual comparison in the time-frequency domain. The results showed that the technique is suitable and effective for the time-frequency scale transformation of both the transient property of the heart sounds and the more complex random property of the murmurs. It is also shown that the effectiveness of the method is strongly related to the optimization of the parameters used for the decomposition of the signals

Primary Carcinoma of the Fallopian Tube: A Review of a Single Institution Experience of 8 Cases

Aims and Objectives. To evaluate the clinicopathologic features, response to cytoreductive surgery and adjuvant platinum-based chemotherapy with or without paclitaxel. Materials and Methods. A retrospective observational study of 8 women with a histopathologic diagnosis of primary fallopian tube carcinoma (PFTC) from January 2000 to February 2013. Results. 4/8 (50%) of the women were in the early stage and an intraoperative frozen section was 100% effective in identifying fallopian tube carcinoma and then a staging laparotomy was performed. All 4/8 cases in the early stage had received and responded to single agent carboplatin and all are alive without clinical, radiological, or biochemical evidence of recurrence at the end of 2 years and the longest survivor has completed 13 years. Primary optimal cytoreductive surgery was achievable in 3/4 (75%) in advanced disease. All showed response to adjuvant paclitaxel and carboplatin (T+C), but all had succumbed to the disease following recurrence with mean progression-free survival of 19 months (range 15–21 months) and mean overall survival of 27 months (range 22–36 months). Conclusion. The pivotal role played by a frozen section in diagnosing PFTC which is rare needs to be reemphasized, therefore justifying a primary staging laparotomy in an early stage. Prolonged survival observed in this group following an optimum tailored adjuvant single agent carboplatin is worth noting