Linear-Space Approximate Distance Oracles for Planar, Bounded-Genus, and Minor-Free Graphs

A (1 + eps)-approximate distance oracle for a graph is a data structure that supports approximate point-to-point shortest-path-distance queries. The most relevant measures for a distance-oracle construction are: space, query time, and preprocessing time. There are strong distance-oracle constructions known for planar graphs (Thorup, JACM'04) and, subsequently, minor-excluded graphs (Abraham and Gavoille, PODC'06). However, these require Omega(eps^{-1} n lg n) space for n-node graphs. We argue that a very low space requirement is essential. Since modern computer architectures involve hierarchical memory (caches, primary memory, secondary memory), a high memory requirement in effect may greatly increase the actual running time. Moreover, we would like data structures that can be deployed on small mobile devices, such as handhelds, which have relatively small primary memory. In this paper, for planar graphs, bounded-genus graphs, and minor-excluded graphs we give distance-oracle constructions that require only O(n) space. The big O hides only a fixed constant, independent of \epsilon and independent of genus or size of an excluded minor. The preprocessing times for our distance oracle are also faster than those for the previously known constructions. For planar graphs, the preprocessing time is O(n lg^2 n). However, our constructions have slower query times. For planar graphs, the query time is O(eps^{-2} lg^2 n). For our linear-space results, we can in fact ensure, for any delta > 0, that the space required is only 1 + delta times the space required just to represent the graph itself

The word and Riemannian metrics on lattices of semisimple groups

Let G be a semisimple Lie group of rank ≥ 2 and Γ an irreducible lattice. Γ has two natural metrics: a metric inherited from a Riemannian metric on the ambient Lie group and a word metric defined with respect to some finite set of generators. Confirming a conjecture of D. Kazhdan (cf. Gromov [Gr2]) we show that these metrics are Lipschitz equivalent. It is shown that a cyclic subgroup of Γ is virtually unipotent if and only if it has exponential growth with respect to the generators of Γ

Equidistribution of expanding translates of curves and Dirichlet's theorem on Diophantine approximation

We show that for almost all points on any analytic curve on R^{k} which is not contained in a proper affine subspace, the Dirichlet's theorem on simultaneous approximation, as well as its dual result for simultaneous approximation of linear forms, cannot be improved. The result is obtained by proving asymptotic equidistribution of evolution of a curve on a strongly unstable leaf under certain partially hyperbolic flow on the space of unimodular lattices in R^{k+1}. The proof involves ergodic properties of unipotent flows on homogeneous spaces.Comment: 26 page

Ultrametric Logarithm Laws, II

We prove positive characteristic versions of the logarithm laws of Sullivan and Kleinbock-Margulis and obtain related results in Metric Diophantine Approximation.Comment: submitted to Montasefte Fur Mathemati

Applications of yeast flocculation in biotechnological processes

A review on the main aspects associated with yeast flocculation and its application in biotechnological processes is presented. This subject is addressed following three main aspects – the basics of yeast flocculation, the development of “new” flocculating yeast strains and bioreactor development. In what concerns the basics of yeast flocculation, the state of the art on the most relevant aspects of mechanism, physiology and genetics of yeast flocculation is reported. The construction of flocculating yeast strains includes not only the recombinant constitutive flocculent brewer’s yeast, but also recombinant flocculent yeast for lactose metabolisation and ethanol production. Furthermore, recent work on the heterologous β-galactosidase production using a recombinant flocculent Saccharomyces cerevisiae is considered. As bioreactors using flocculating yeast cells have particular properties, mainly associated with a high solid phase hold-up, a section dedicated to its operation is presented. Aspects such as bioreactor productivity and culture stability as well as bioreactor hydrodynamics and mass transfer properties of flocculating cell cultures are considered. Finally, the paper concludes describing some of the applications of high cell density flocculation bioreactors and discussing potential new uses of these systems.Fundação para a Ciência e a Tecnologia (FCT) – PRAXIS XXI - BD11306/97

Diagnostic accuracy of non-invasive tests to screen for at-risk MASH—An individual participant data meta-analysis

\ua9 2024 The Authors. Liver International published by John Wiley & Sons Ltd.Background & Aims: There is a need to reduce the screen failure rate (SFR) in metabolic dysfunction-associated steatohepatitis (MASH) clinical trials (MASH+F2-3; MASH+F4) and identify people with high-risk MASH (MASH+F2-4) in clinical practice. We aimed to evaluate non-invasive tests (NITs) screening approaches for these target conditions. Methods: This was an individual participant data meta-analysis for the performance of NITs against liver biopsy for MASH+F2-4, MASH+F2-3 and MASH+F4. Index tests were the FibroScan-AST (FAST) score, liver stiffness measured using vibration-controlled transient elastography (LSM-VCTE), the fibrosis-4 score (FIB-4) and the NAFLD fibrosis score (NFS). Area under the receiver operating characteristics curve (AUROC) and thresholds including those that achieved 34% SFR were reported. Results: We included 2281 unique cases. The prevalence of MASH+F2-4, MASH+F2-3 and MASH+F4 was 31%, 24% and 7%, respectively. Area under the receiver operating characteristics curves for MASH+F2-4 were.78,.75,.68 and.57 for FAST, LSM-VCTE, FIB-4 and NFS. Area under the receiver operating characteristics curves for MASH+F2-3 were.73,.67,.60,.58 for FAST, LSM-VCTE, FIB-4 and NFS. Area under the receiver operating characteristics curves for MASH+F4 were.79,.84,.81,.76 for FAST, LSM-VCTE, FIB-4 and NFS. The sequential combination of FIB-4 and LSM-VCTE for the detection of MASH+F2-3 with threshold of.7 and 3.48, and 5.9 and 20 kPa achieved SFR of 67% and sensitivity of 60%, detecting 15 true positive cases from a theoretical group of 100 participants at the prevalence of 24%. Conclusions: Sequential combinations of NITs do not compromise diagnostic performance and may reduce resource utilisation through the need of fewer LSM-VCTE examinations

The Effect of Insecticide Synergists on the Response of Scabies Mites to Pyrethroid Acaricides

Synergists are commonly used in combination with pesticides to suppress metabolism-based resistance and increase the efficacy of the agents. They are also useful as tools for laboratory investigation of specific resistance mechanisms based on their ability to inhibit specific metabolic pathways. To determine the role of metabolic degradation as a mechanism for acaricide resistance in human scabies, PBO (piperonyl butoxide), DEF (S,S,S-tributyl phosphorotrithioate) and DEM (diethyl maleate) were used with permethrin as synergists in a bioassay of mite killing. A statistically significant difference in survival time of permethrin-resistant Sarcoptes scabiei variety canis was noted when any of the three synergists were used in combination with permethrin compared to survival time of mites exposed to permethrin alone (p<0.0001). These results indicate the potential utility of synergists in reversing tolerance to pyrethroid-based acaricides (i.e. the addition of synergists to permethrin-containing topical acaricide cream commonly used to treat scabies). To further verify specific metabolic pathways being inhibited by these synergists, enzyme assays were developed to measure esterase, glutathione S-transferase (GST) and cytochrome P450 monooxygenase activity in scabies mites. Results of in vitro enzyme inhibition experiments showed lower levels of esterase activity with DEF; lower levels of GST activity with DEM and lower levels of cytochrome monooxygenase activity with PBO. These findings indicate a metabolic mechanism as mediating pyrethroid resistance in scabies mites

Fast MCMC sampling for hidden markov models to determine copy number variations

<p>Abstract</p> <p>Background</p> <p>Hidden Markov Models (HMM) are often used for analyzing Comparative Genomic Hybridization (CGH) data to identify chromosomal aberrations or copy number variations by segmenting observation sequences. For efficiency reasons the parameters of a HMM are often estimated with maximum likelihood and a segmentation is obtained with the Viterbi algorithm. This introduces considerable uncertainty in the segmentation, which can be avoided with Bayesian approaches integrating out parameters using Markov Chain Monte Carlo (MCMC) sampling. While the advantages of Bayesian approaches have been clearly demonstrated, the likelihood based approaches are still preferred in practice for their lower running times; datasets coming from high-density arrays and next generation sequencing amplify these problems.</p> <p>Results</p> <p>We propose an approximate sampling technique, inspired by compression of discrete sequences in HMM computations and by <it>kd</it>-trees to leverage spatial relations between data points in typical data sets, to speed up the MCMC sampling.</p> <p>Conclusions</p> <p>We test our approximate sampling method on simulated and biological ArrayCGH datasets and high-density SNP arrays, and demonstrate a speed-up of 10 to 60 respectively 90 while achieving competitive results with the state-of-the art Bayesian approaches.</p> <p><it>Availability: </it>An implementation of our method will be made available as part of the open source GHMM library from <url>http://ghmm.org</url>.</p