An Optimal Linear Time Algorithm for Quasi-Monotonic Segmentation

Monotonicity is a simple yet significant qualitative characteristic. We consider the problem of segmenting a sequence in up to K segments. We want segments to be as monotonic as possible and to alternate signs. We propose a quality metric for this problem using the l_inf norm, and we present an optimal linear time algorithm based on novel formalism. Moreover, given a precomputation in time O(n log n) consisting of a labeling of all extrema, we compute any optimal segmentation in constant time. We compare experimentally its performance to two piecewise linear segmentation heuristics (top-down and bottom-up). We show that our algorithm is faster and more accurate. Applications include pattern recognition and qualitative modeling.Comment: This is the extended version of our ICDM'05 paper (arXiv:cs/0702142

Tame group actions on central simple algebras

We study actions of linear algebraic groups on finite-dimensional central simple algebras. We describe the fixed algebra for a broad class of such actions.Comment: 19 pages, LaTeX; slightly revised; final version will appear in Journal of Algebr

On the Classification of Diagonal Coset Modular Invariants

We relate in a novel way the modular matrices of GKO diagonal cosets without fixed points to those of WZNW tensor products. Using this we classify all modular invariant partition functions of $su(3)_k\oplus su(3)_1/su(3)_{k+1}$ for all positive integer level $k$, and $su(2)_k\oplus su(2)_\ell/su(2)_{k+\ell}$ for all $k$ and infinitely many $\ell$ (in fact, for each $k$ a positive density of $\ell$). Of all these classifications, only that for $su(2)_k\oplus su(2)_1/su(2)_{k+1}$ had been known. Our lists include many new invariants.Comment: 24 pp (plain tex

SUP: an extension to SLINK to allow a larger number of marker loci to be simulated in pedigrees conditional on trait values

BACKGROUND: With the recent advances in high-throughput genotyping technologies that allow for large-scale association mapping of human complex traits, promising statistical designs and methods have been emerging. Efficient simulation software are key elements for the evaluation of the properties of new statistical tests. SLINK is a flexible simulation tool that has been widely used to generate the segregation and recombination processes of markers linked to, and possibly associated with, a trait locus, conditional on trait values in arbitrary pedigrees. In practice, its most serious limitation is the small number of loci that can be simulated, since the complexity of the algorithm scales exponentially with this number. RESULTS: I describe the implementation of a two-step algorithm to be used in conjunction with SLINK to enable the simulation of a large number of marker loci linked to a trait locus and conditional on trait values in families, with the possibility for the loci to be in linkage disequilibrium. SLINK is used in the first step to simulate genotypes at the trait locus conditional on the observed trait values, and also to generate an indicator of the descent path of the simulated alleles. In the second step, marker alleles or haplotypes are generated in the founders, conditional on the trait locus genotypes simulated in the first step. Then the recombination process between the marker loci takes place conditionally on the descent path and on the trait locus genotypes. This two-step implementation is often computationally faster than other software that are designed to generate marker data linked to, and possibly associated with, a trait locus. CONCLUSION: Because the proposed method uses SLINK to simulate the segregation process, it benefits from its flexibility: the trait may be qualitative with the possibility of defining different liability classes (which allows for the simulation of gene-environment interactions or even the simulation of multi-locus effects between unlinked susceptibility regions) or it may be quantitative and normally distributed. In particular, this implementation is the only one available that can generate a large number of marker loci conditional on the set of observed quantitative trait values in pedigrees

Fourier analysis of 2-point Hermite interpolatory subdivision schemes

Two subdivision schemes with Hermite data on Z are studied. These schemes use 2 or 7 parameters respectively depending on whether Hermite data involve only first derivatives or include second derivatives. For a large region in the parameters space, the schemes are C1 or C2 convergent or at least are convergent on the space of Schwartz distributions. The Fourier transform of any interpolating function can be computed through products of matrices of order 2 or 3. The Fourier transform is related to a specific system of functional equations whose analytic solution is unique except for a multiplicative constant. The main arguments for these results come from Paley-Wiener-Schwartz theorem on the characterization of the Fourier transforms of distributions with compact support and a theorem of Artzrouni about convergent products of matrices

A Heuristic Based on the Intrinsic Dimensionality for Reducing the Number of Cyclic DTW Comparisons in Shape Classification and Retrieval Using AESA

Cyclic Dynamic Time Warping (CDTW) is a good dissimilarity of shape descriptors of high dimensionality based on contours, but it is computationally expensive. For this reason, to perform recognition tasks, a method to reduce the number of comparisons and avoid an exhaustive search is convenient. The Approximate and Eliminate Search Algorithm (AESA) is a relevant indexing method because of its drastic reduction of comparisons, however, this algorithm requires a metric distance and that is not the case of CDTW. In this paper, we introduce a heuristic based on the intrinsic dimensionality that allows to use CDTW and AESA together in classification and retrieval tasks over these shape descriptors. Experimental results show that, for descriptors of high dimensionality, our proposal is optimal in practice and significantly outperforms an exhaustive search, which is the only alternative for them and CDTW in these tasks

A Novel Strategy Involved Anti-Oxidative Defense: The Conversion of NADH into NADPH by a Metabolic Network

The reduced nicotinamide adenine dinucleotide phosphate (NADPH) is pivotal to the cellular anti-oxidative defence strategies in most organisms. Although its production mediated by different enzyme systems has been relatively well-studied, metabolic networks dedicated to the biogenesis of NADPH have not been fully characterized. In this report, a metabolic pathway that promotes the conversion of reduced nicotinamide adenine dinucleotide (NADH), a pro-oxidant into NADPH has been uncovered in Pseudomonas fluorescens exposed to oxidative stress. Enzymes such as pyruvate carboxylase (PC), malic enzyme (ME), malate dehydrogenase (MDH), malate synthase (MS), and isocitrate lyase (ICL) that are involved in disparate metabolic modules, converged to create a metabolic network aimed at the transformation of NADH into NADPH. The downregulation of phosphoenol carboxykinase (PEPCK) and the upregulation of pyruvate kinase (PK) ensured that this metabolic cycle fixed NADH into NADPH to combat the oxidative stress triggered by the menadione insult. This is the first demonstration of a metabolic network invoked to generate NADPH from NADH, a process that may be very effective in combating oxidative stress as the increase of an anti-oxidant is coupled to the decrease of a pro-oxidant

Bacteriophage Crosstalk: Coordination of Prophage Induction by Trans-Acting Antirepressors

Many species of bacteria harbor multiple prophages in their genomes. Prophages often carry genes that confer a selective advantage to the bacterium, typically during host colonization. Prophages can convert to infectious viruses through a process known as induction, which is relevant to the spread of bacterial virulence genes. The paradigm of prophage induction, as set by the phage Lambda model, sees the process initiated by the RecA-stimulated self-proteolysis of the phage repressor. Here we show that a large family of lambdoid prophages found in Salmonella genomes employs an alternative induction strategy. The repressors of these phages are not cleaved upon induction; rather, they are inactivated by the binding of small antirepressor proteins. Formation of the complex causes the repressor to dissociate from DNA. The antirepressor genes lie outside the immunity region and are under direct control of the LexA repressor, thus plugging prophage induction directly into the SOS response. GfoA and GfhA, the antirepressors of Salmonella prophages Gifsy-1 and Gifsy-3, each target both of these phages' repressors, GfoR and GfhR, even though the latter proteins recognize different operator sites and the two phages are heteroimmune. In contrast, the Gifsy-2 phage repressor, GtgR, is insensitive to GfoA and GfhA, but is inactivated by an antirepressor from the unrelated Fels-1 prophage (FsoA). This response is all the more surprising as FsoA is under the control of the Fels-1 repressor, not LexA, and plays no apparent role in Fels-1 induction, which occurs via a Lambda CI-like repressor cleavage mechanism. The ability of antirepressors to recognize non-cognate repressors allows coordination of induction of multiple prophages in polylysogenic strains. Identification of non-cleavable gfoR/gtgR homologues in a large variety of bacterial genomes (including most Escherichia coli genomes in the DNA database) suggests that antirepression-mediated induction is far more common than previously recognized

Interacting Preformed Cooper Pairs in Resonant Fermi Gases

We consider the normal phase of a strongly interacting Fermi gas, which can have either an equal or an unequal number of atoms in its two accessible spin states. Due to the unitarity-limited attractive interaction between particles with different spin, noncondensed Cooper pairs are formed. The starting point in treating preformed pairs is the Nozi\`{e}res-Schmitt-Rink (NSR) theory, which approximates the pairs as being noninteracting. Here, we consider the effects of the interactions between the Cooper pairs in a Wilsonian renormalization-group scheme. Starting from the exact bosonic action for the pairs, we calculate the Cooper-pair self-energy by combining the NSR formalism with the Wilsonian approach. We compare our findings with the recent experiments by Harikoshi {\it et al.} [Science {\bf 327}, 442 (2010)] and Nascimb\`{e}ne {\it et al.} [Nature {\bf 463}, 1057 (2010)], and find very good agreement. We also make predictions for the population-imbalanced case, that can be tested in experiments.Comment: 10 pages, 6 figures, accepted version for PRA, discussion of the imbalanced Fermi gas added, new figure and references adde