Augmenting graphs to minimize the diameter

We study the problem of augmenting a weighted graph by inserting edges of bounded total cost while minimizing the diameter of the augmented graph. Our main result is an FPT 4-approximation algorithm for the problem.Comment: 15 pages, 3 figure

Speeding up shortest path algorithms

Given an arbitrary, non-negatively weighted, directed graph $G=(V,E)$ we present an algorithm that computes all pairs shortest paths in time $\mathcal{O}(m^* n + m \lg n + nT_\psi(m^*, n))$, where $m^*$ is the number of different edges contained in shortest paths and $T_\psi(m^*, n)$ is a running time of an algorithm to solve a single-source shortest path problem (SSSP). This is a substantial improvement over a trivial $n$ times application of $\psi$ that runs in $\mathcal{O}(nT_\psi(m,n))$. In our algorithm we use $\psi$ as a black box and hence any improvement on $\psi$ results also in improvement of our algorithm. Furthermore, a combination of our method, Johnson's reweighting technique and topological sorting results in an $\mathcal{O}(m^*n + m \lg n)$ all-pairs shortest path algorithm for arbitrarily-weighted directed acyclic graphs. In addition, we also point out a connection between the complexity of a certain sorting problem defined on shortest paths and SSSP.Comment: 10 page

Is there a social gradient of sarcopenia? A meta-analysis and systematic review protocol

Introduction: Sarcopenia (or loss of muscle mass and function) is a relatively new area within the field of musculoskeletal research and medicine. Investigating whether there is a social gradient, including occupation type and income level, of sarcopenia, as observed for other diseases, will contribute significantly to the limited evidence base for this disease. This new information may inform the prevention and management of sarcopenia and widen the evidence base to support existing and future health campaigns. Methods and analysis: We will conduct a systematic search of the databases PubMed, Ovid, CINAHL, Scopus and EMBASE to identify articles that investigate associations between social determinants of health and sarcopenia in adults aged 50 years and older. Eligibility of the selected studies will be determined by two independent reviewers. The methodological quality of eligible studies will be assessed according to predetermined criteria. Established statistical methods to identify and control for heterogeneity will be used, and where appropriate, we will conduct a meta-analysis. In the event that heterogeneity prevents numerical synthesis, a best evidence analysis will be employed. This systematic review protocol adheres to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses Protocols reporting guidelines and will be registered with the International Prospective Register of Systematic Reviews (PROSPERO). Ethics and dissemination: This systematic review will use published data, thus ethical permissions will not be required. In addition to peer-reviewed publication, our results will be presented at (inter)national conferences relevant to the field of sarcopenia, ageing and/or musculoskeletal health and disseminated both electronically and in print. PROSPERO registration number: CRD4201707225

Stable Noncrossing Matchings

Given a set of $n$ men represented by $n$ points lying on a line, and $n$ women represented by $n$ points lying on another parallel line, with each person having a list that ranks some people of opposite gender as his/her acceptable partners in strict order of preference. In this problem, we want to match people of opposite genders to satisfy people's preferences as well as making the edges not crossing one another geometrically. A noncrossing blocking pair w.r.t. a matching $M$ is a pair $(m,w)$ of a man and a woman such that they are not matched with each other but prefer each other to their own partners in $M$, and the segment $(m,w)$ does not cross any edge in $M$. A weakly stable noncrossing matching (WSNM) is a noncrossing matching that does not admit any noncrossing blocking pair. In this paper, we prove the existence of a WSNM in any instance by developing an $O(n^2)$ algorithm to find one in a given instance.Comment: This paper has appeared at IWOCA 201

Bringing Order to Special Cases of Klee's Measure Problem

Klee's Measure Problem (KMP) asks for the volume of the union of n axis-aligned boxes in d-space. Omitting logarithmic factors, the best algorithm has runtime O*(n^{d/2}) [Overmars,Yap'91]. There are faster algorithms known for several special cases: Cube-KMP (where all boxes are cubes), Unitcube-KMP (where all boxes are cubes of equal side length), Hypervolume (where all boxes share a vertex), and k-Grounded (where the projection onto the first k dimensions is a Hypervolume instance). In this paper we bring some order to these special cases by providing reductions among them. In addition to the trivial inclusions, we establish Hypervolume as the easiest of these special cases, and show that the runtimes of Unitcube-KMP and Cube-KMP are polynomially related. More importantly, we show that any algorithm for one of the special cases with runtime T(n,d) implies an algorithm for the general case with runtime T(n,2d), yielding the first non-trivial relation between KMP and its special cases. This allows to transfer W[1]-hardness of KMP to all special cases, proving that no n^{o(d)} algorithm exists for any of the special cases under reasonable complexity theoretic assumptions. Furthermore, assuming that there is no improved algorithm for the general case of KMP (no algorithm with runtime O(n^{d/2 - eps})) this reduction shows that there is no algorithm with runtime O(n^{floor(d/2)/2 - eps}) for any of the special cases. Under the same assumption we show a tight lower bound for a recent algorithm for 2-Grounded [Yildiz,Suri'12].Comment: 17 page

String Indexing for Patterns with Wildcards

We consider the problem of indexing a string $t$ of length $n$ to report the occurrences of a query pattern $p$ containing $m$ characters and $j$ wildcards. Let $occ$ be the number of occurrences of $p$ in $t$, and $\sigma$ the size of the alphabet. We obtain the following results. - A linear space index with query time $O(m+\sigma^j \log \log n + occ)$. This significantly improves the previously best known linear space index by Lam et al. [ISAAC 2007], which requires query time $\Theta(jn)$ in the worst case. - An index with query time $O(m+j+occ)$ using space $O(\sigma^{k^2} n \log^k \log n)$, where $k$ is the maximum number of wildcards allowed in the pattern. This is the first non-trivial bound with this query time. - A time-space trade-off, generalizing the index by Cole et al. [STOC 2004]. We also show that these indexes can be generalized to allow variable length gaps in the pattern. Our results are obtained using a novel combination of well-known and new techniques, which could be of independent interest

Separating Hierarchical and General Hub Labelings

In the context of distance oracles, a labeling algorithm computes vertex labels during preprocessing. An $s,t$ query computes the corresponding distance from the labels of $s$ and $t$ only, without looking at the input graph. Hub labels is a class of labels that has been extensively studied. Performance of the hub label query depends on the label size. Hierarchical labels are a natural special kind of hub labels. These labels are related to other problems and can be computed more efficiently. This brings up a natural question of the quality of hierarchical labels. We show that there is a gap: optimal hierarchical labels can be polynomially bigger than the general hub labels. To prove this result, we give tight upper and lower bounds on the size of hierarchical and general labels for hypercubes.Comment: 11 pages, minor corrections, MFCS 201

Cnidarian microRNAs frequently regulate targets by cleavage

In bilaterians, which comprise most of extant animals, microRNAs (miRNAs) regulate the majority of messenger RNAs (mRNAs) via base-pairing of a short sequence (the miRNA seed ) to the target, subsequently promoting translational inhibition and transcript instability. In plants, many miRNAs guide endonucleolytic cleavage of highly complementary targets. Because little is known about miRNA function in nonbilaterian animals, we investigated the repertoire and biological activity of miRNAs in the sea anemone Nematostella vectensis, a representative of Cnidaria, the sister phylum of Bilateria. Our work uncovers scores of novel miRNAs in Nematostella, increasing the total miRNA gene count to 87. Yet only a handful are conserved in corals and hydras, suggesting that microRNA gene turnover in Cnidaria greatly exceeds that of other metazoan groups. We further show that Nematostella miRNAs frequently direct the cleavage of their mRNA targets via nearly perfect complementarity. This mode of action resembles that of small interfering RNAs (siRNAs) and plant miRNAs. It appears to be common in Cnidaria, as several of the miRNA target sites are conserved among distantly related anemone species, and we also detected miRNA-directed cleavage in Hydra. Unlike in bilaterians, Nematostella miRNAs are commonly coexpressed with their target transcripts. In light of these findings, we propose that post-transcriptional regulation by miRNAs functions differently in Cnidaria and Bilateria. The similar, siRNA-like mode of action of miRNAs in Cnidaria and plants suggests that this may be an ancestral state

Multiple phenotypic changes in mice after knockout of the B3gnt5 gene, encoding Lc3 synthase--a key enzyme in lacto-neolacto ganglioside synthesis

<p>Abstract</p> <p>Background</p> <p>Ganglioside biosynthesis occurs through a multi-enzymatic pathway which at the lactosylceramide step is branched into several biosynthetic series. Lc3 synthase utilizes a variety of galactose-terminated glycolipids as acceptors by establishing a glycosidic bond in the beta-1,3-linkage to GlcNaAc to extend the lacto- and neolacto-series gangliosides. In order to examine the lacto-series ganglioside functions in mice, we used gene knockout technology to generate Lc3 synthase gene <it>B3gnt5-</it>deficient mice by two different strategies and compared the phenotypes of the two null mouse groups with each other and with their wild-type counterparts.</p> <p>Results</p> <p><it>B3gnt5 </it>gene knockout mutant mice appeared normal in the embryonic stage and, if they survived delivery, remained normal during early life. However, about 9% developed early-stage growth retardation, 11% died postnatally in less than 2 months, and adults tended to die in 5-15 months, demonstrating splenomegaly and notably enlarged lymph nodes. Without lacto-neolacto series gangliosides, both homozygous and heterozygous mice gradually displayed fur loss or obesity, and breeding mice demonstrated reproductive defects. Furthermore, <it>B3gnt5 </it>gene knockout disrupted the functional integrity of B cells, as manifested by a decrease in B-cell numbers in the spleen, germinal center disappearance, and less efficiency to proliferate in hybridoma fusion.</p> <p>Conclusions</p> <p>These novel results demonstrate unequivocally that lacto-neolacto series gangliosides are essential to multiple physiological functions, especially the control of reproductive output, and spleen B-cell abnormality. We also report the generation of anti-IgG response against the lacto-series gangliosides 3'-isoLM1 and 3',6'-isoLD1.</p

Beyond Hypergraph Dualization

International audienceThis problem concerns hypergraph dualization and generalization to poset dualization. A hypergraph H = (V, E) consists of a finite collection E of sets over a finite set V , i.e. E ⊆ P(V) (the powerset of V). The elements of E are called hyperedges, or simply edges. A hypergraph is said simple if none of its edges is contained within another. A transversal (or hitting set) of H is a set T ⊆ V that intersects every edge of E. A transversal is minimal if it does not contain any other transversal as a subset. The set of all minimal transversal of H is denoted by T r(H). The hypergraph (V, T r(H)) is called the transversal hypergraph of H. Given a simple hypergraph H, the hypergraph dualization problem (Trans-Enum for short) concerns the enumeration without repetitions of T r(H). The Trans-Enum problem can also be formulated as a dualization problem in posets. Let (P, ≤) be a poset (i.e. ≤ is a reflexive, antisymmetric, and transitive relation on the set P). For A ⊆ P , ↓ A (resp. ↑ A) is the downward (resp. upward) closure of A under the relation ≤ (i.e. ↓ A is an ideal and ↑ A a filter of (P, ≤)). Two antichains (B + , B −) of P are said to be dual if ↓ B + ∪ ↑ B − = P and ↓ B + ∩ ↑ B − = ∅. Given an implicit description of a poset P and an antichain B + (resp. B −) of P , the poset dualization problem (Dual-Enum for short) enumerates the set B − (resp. B +), denoted by Dual(B +) = B − (resp. Dual(B −) = B +). Notice that the function dual is self-dual or idempotent, i.e. Dual(Dual(B)) = B