Persistence stability for geometric complexes

In this paper we study the properties of the homology of different geometric filtered complexes (such as Vietoris–Rips, ?ech and witness complexes) built on top of totally bounded metric spaces. Using recent developments in the theory of topological persistence, we provide simple and natural proofs of the stability of the persistent homology of such complexes with respect to the Gromov–Hausdorff distance. We also exhibit a few noteworthy properties of the homology of the Rips and ?ech complexes built on top of compact spaces.     

Analysis of magnetization instability patterns in spin-transfer nano-oscillators

The stability of large precessional magnetization motions induced by spin-polarized currents in spin-transfer nano-oscillators is discussed. Quantitative analytical predictions are obtained for the critical values of spin-polarized injected current and external magnetic field at which the oscillator magnetization precession becomes unstable. It is shown that the mechanism leading to instability is parametric resonance of well-defined pairs of magnetostatically coupled perturbation modes. The amplitude of these modes grows to large non-thermal values when the oscillator frequency matches the mean of the natural frequencies of the two coupled modes. Analytical predictions are obtained for the space-time structure and symmetry of the magnetization patterns that are formed at the instability. Analytical results are compared with numerical simulations of spin-transfer-driven magnetization dynamics.     

Gender effect on neurodegeneration and myelin markers in an animal model for multiple sclerosis

Background  

Multiple sclerosis (MS) varies considerably in its incidence and progression in females and males. In spite of clinical evidence, relatively few studies have explored molecular mechanisms possibly involved in gender-related differences. The present study describes possible cellular- and molecular-involved markers which are differentially regulated in male and female rats and result in gender-dependent EAE evolution and progression. Attention was focused on markers of myelination (MBP and PDGFαR) and neuronal distress and/or damage (GABA synthesis enzymes, GAD65 and GAD67, NGF, BDNF and related receptors), in two CNS areas, i.e. spinal cord and cerebellum, which are respectively severely and mildly affected by inflammation and demyelination. Tissues were sampled during acute, relapse/remission and chronic phases and results were analysed by two-way ANOVA.     

Comparison of alignment free string distances for complete genome phylogeny

In this paper, we compare the accuracy of four string distances on complete genomes to reconstruct phylogenies using simulated and real biological data. These distances are based on common words shared by raw genomic sequences and do not require preliminary processing steps such as gene identification or sequence alignment. Moreover, they are computable in linear time. The first distance is based on Maximum Significant Matches (MSM). The second is computed from the frequencies of all the words of length k (KW). The third distance is based on the Average length of maximum Common Substrings at any position (ACS). The last one is based on the Ziv–Lempel compression algorithm (ZL). We describe a simulation process of evolution to generate a set of sequences having evolved according to a random tree topology T. This process allows both base substitution and fragment insertion/deletion, including horizontal transfers. The distances between the generated sequences are computed using the four formulas and the corresponding trees T′ are reconstructed using Neighbor-Joining. T and T′ are compared according to topological criteria. These comparisons show that the MSM distance outperforms the others whatever the parameters used to generate sequences. Finally, we test the MSM and KW distances on real biological data (i.e. prokaryotic complete genomes) and we compare the NJ trees to a Maximum Likelihood 16S + 23S RNA tree. We show that the MSM distance provides accurate results to study intra-phylum relationships, much better than those given by KW.     

Heuristics and lower bounds for minimizing fuel consumption in hybrid-electrical vehicles

In hybrid electric vehicles, the electrical powertrain system has multiple energy sources that it can gather power from to satisfy the propulsion power requested by the vehicle at each instant. This paper focusses on the minimization of the fuel consumption of such a vehicle, taking advantage of the different energy sources. Based on global optimization approaches, the proposed heuristics find solutions that best split the power requested between the multi-electrical sources available. A lower bounding procedure is introduced to validate the quality of the solutions. Computational results show a significant improvement over previous results from the literature in both the computing time and the quality of the solutions.     

Disjoint Paths in Decomposable Digraphs

The k‐linkage problem is as follows: given a digraph and a collection of k terminal pairs such that all these vertices are distinct; decide whether D has a collection of vertex disjoint paths such that is from to for . A digraph is k‐linked if it has a k‐linkage for every choice of 2k distinct vertices and every choice of k pairs as above. The k‐linkage problem is NP‐complete already for [11] and there exists no function such that every ‐strong digraph has a k‐linkage for every choice of 2k distinct vertices of D [17]. Recently, Chudnovsky et al. [9] gave a polynomial algorithm for the k‐linkage problem for any fixed k in (a generalization of) semicomplete multipartite digraphs. In this article, we use their result as well as the classical polynomial algorithm for the case of acyclic digraphs by Fortune et al. [11] to develop polynomial algorithms for the k‐linkage problem in locally semicomplete digraphs and several classes of decomposable digraphs, including quasi‐transitive digraphs and directed cographs. We also prove that the necessary condition of being ‐strong is also sufficient for round‐decomposable digraphs to be k‐linked, obtaining thus a best possible bound that improves a previous one of . Finally we settle a conjecture from [3] by proving that every 5‐strong locally semicomplete digraph is 2‐linked. This bound is also best possible (already for tournaments) [1].     

A DC optimization-based clustering technique for edge detection

We introduce a method for edge detection which is based on clustering the pixels representing any given digital image into two sets (the edge pixels and the non-edge ones). The process is based on associating to each pixel an appropriate vector representing the differences in brightness w.r.t. the surrounding pixels. Clustering is driven by the norms of such vectors, thus it takes place in \(\mathbb {R}\), which allows us to use a (simple) DC (Difference of Convex) optimization algorithm to get the clusters. A novel thinning technique, based on calculation of the edge phase angles, refines the classification obtained by the clustering algorithm. The results of some numerical experiments are also provided.     

Coded transmissions for space links affected by solar scintillation: Baseband analysis

A thorough analysis of the behavior of error‐correcting codes over space links affected by solar scintillation is presented. The relevant channel parameters are fixed through the development of a model based on real missions' data. Both telecommand and telemetry links are considered in fast and slow fading conditions. Besides classical coherent modulation schemes, the possibility to use noncoherent modulation schemes is considered, to eliminate the problem of phase tracking. For the case of channels with very slow fading, the use of external interleavers or erasure coding is proposed to cope with error bursts.     

A Highly Warped Heptagon‐Containing sp2 Carbon Scaffold via Vinylnaphthyl π‐Extension

A new strategy is demonstrated for the synthesis of warped, negatively curved, all‐sp²‐carbon π‐scaffolds. Multifold C?C coupling reactions are used to transform a polyaromatic borinic acid into a saddle‐shaped polyaromatic hydrocarbon ( 2 ) bearing two heptagonal rings. Notably, this Schwarzite substructure is synthesized in only two steps from an unfunctionalized alkene. A highly warped structure of 2 was revealed by X‐ray crystallographic studies and pronounced flexibility of this π‐scaffold was ascertained by experimental and computational studies. Compound 2 exhibits excellent solubility, visible range absorption and fluorescence, and readily undergoes two reversible one‐electron oxidations at mild potentials.