Small-world MCMC and convergence to multi-modal distributions: From slow mixing to fast mixing

We compare convergence rates of Metropolis--Hastings chains to multi-modal target distributions when the proposal distributions can be of ``local'' and ``small world'' type. In particular, we show that by adding occasional long-range jumps to a given local proposal distribution, one can turn a chain that is ``slowly mixing'' (in the complexity of the problem) into a chain that is ``rapidly mixing.'' To do this, we obtain spectral gap estimates via a new state decomposition theorem and apply an isoperimetric inequality for log-concave probability measures. We discuss potential applicability of our result to Metropolis-coupled Markov chain Monte Carlo schemes.Comment: Published at http://dx.doi.org/10.1214/105051606000000772 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Spatial opinion dynamics and the effects of two types of mixing

Spatially situated opinions that can be held with different degrees of conviction lead to spatiotemporal patterns such as clustering (homophily), polarization, and deadlock. Our goal is to understand how sensitive these patterns are to changes in the local nature of interactions. We introduce two different mixing mechanisms, spatial relocation and nonlocal interaction (“telephoning”), to an earlier fully spatial model (no mixing). Interestingly, the mechanisms that create deadlock in the fully spatial model have the opposite effect when there is a sufficient amount of mixing. With telephoning, not only is polarization and deadlock broken up, but consensus is hastened. The effects of mixing by relocation are even more pronounced. Further insight into these dynamics is obtained for selected parameter regimes via comparison to the mean-field differential equations

Multiple Sclerosis: Are Protective Immune Mechanisms Compromised by a Complex Infectious Background?

The immunological background of multiple sclerosis (MS) manifests as an altered reactivity against a diverse range of infections, particularly with the Epstein-Barr virus. Although this could be only an epiphenomenon of a more generalised dysfunction of the immune system in MS, it is also possible that a complex infectious background forms the basis of a specific immune dysregulation finally causing the disease. It is thus suggested that the complex infectious background bears the key for an understanding of the immune pathogenesis of the disease. It appears probable that improved standards of hygiene cause regulatory defects in the immune system, allowing the abnormal expression of human endogenous retroviral (HERV) genes. On the basis of epidemiological observations we describe how a failure of expansion or an eclipse of a subfraction of self-antigen-specific CD8+ T cells mediating immune repair, and a deleterious mode of action of HERV gene products, could underlie the pathogenesis of MS

Detecting stars, galaxies, and asteroids with Gaia

(Abridged) Gaia aims to make a 3-dimensional map of 1,000 million stars in our Milky Way to unravel its kinematical, dynamical, and chemical structure and evolution. Gaia's on-board detection software discriminates stars from spurious objects like cosmic rays and Solar protons. For this, parametrised point-spread-function-shape criteria are used. This study aims to provide an optimum set of parameters for these filters. We developed an emulation of the on-board detection software, which has 20 free, so-called rejection parameters which govern the boundaries between stars on the one hand and sharp or extended events on the other hand. We evaluate the detection and rejection performance of the algorithm using catalogues of simulated single stars, double stars, cosmic rays, Solar protons, unresolved galaxies, and asteroids. We optimised the rejection parameters, improving - with respect to the functional baseline - the detection performance of single and double stars, while, at the same time, improving the rejection performance of cosmic rays and of Solar protons. We find that the minimum separation to resolve a close, equal-brightness double star is 0.23 arcsec in the along-scan and 0.70 arcsec in the across-scan direction, independent of the brightness of the primary. We find that, whereas the optimised rejection parameters have no significant impact on the detectability of de Vaucouleurs profiles, they do significantly improve the detection of exponential-disk profiles. We also find that the optimised rejection parameters provide detection gains for asteroids fainter than 20 mag and for fast-moving near-Earth objects fainter than 18 mag, albeit this gain comes at the expense of a modest detection-probability loss for bright, fast-moving near-Earth objects. The major side effect of the optimised parameters is that spurious ghosts in the wings of bright stars essentially pass unfiltered.Comment: Accepted for publication in A&

A probabilistic approach to emission-line galaxy classification

We invoke a Gaussian mixture model (GMM) to jointly analyse two traditional emission-line classification schemes of galaxy ionization sources: the Baldwin-Phillips-Terlevich (BPT) and $\rm W_{H\alpha}$ vs. [NII]/H$\alpha$ (WHAN) diagrams, using spectroscopic data from the Sloan Digital Sky Survey Data Release 7 and SEAGal/STARLIGHT datasets. We apply a GMM to empirically define classes of galaxies in a three-dimensional space spanned by the $\log$ [OIII]/H$\beta$, $\log$ [NII]/H$\alpha$, and $\log$ EW(H${\alpha}$), optical parameters. The best-fit GMM based on several statistical criteria suggests a solution around four Gaussian components (GCs), which are capable to explain up to 97 per cent of the data variance. Using elements of information theory, we compare each GC to their respective astronomical counterpart. GC1 and GC4 are associated with star-forming galaxies, suggesting the need to define a new starburst subgroup. GC2 is associated with BPT's Active Galaxy Nuclei (AGN) class and WHAN's weak AGN class. GC3 is associated with BPT's composite class and WHAN's strong AGN class. Conversely, there is no statistical evidence -- based on four GCs -- for the existence of a Seyfert/LINER dichotomy in our sample. Notwithstanding, the inclusion of an additional GC5 unravels it. The GC5 appears associated to the LINER and Passive galaxies on the BPT and WHAN diagrams respectively. Subtleties aside, we demonstrate the potential of our methodology to recover/unravel different objects inside the wilderness of astronomical datasets, without lacking the ability to convey physically interpretable results. The probabilistic classifications from the GMM analysis are publicly available within the COINtoolbox (https://cointoolbox.github.io/GMM\_Catalogue/).Comment: Accepted for publication in MNRA

Application of Ecological Network Theory to the Human Microbiome

In healthy humans, many microbial consortia constitute rich ecosystems with dozens to hundreds of species, finely tuned to functions relevant to human health. Medical interventions, lifestyle changes, and the normal rhythms of life sometimes upset the balance in microbial ecosystems, facilitating pathogen invasions or causing other clinically relevant problems. Some diseases, such as bacterial vaginosis, have exactly this sort of community etiology. Mathematical network theory is ideal for studying the ecological networks of interacting species that comprise the human microbiome. Theoretical networks require little consortia specific data to provide insight into both normal and disturbed microbial community functions, but it is easy to incorporate additional empirical data as it becomes available. We argue that understanding some diseases, such as bacterial vaginosis, requires a shift of focus from individual bacteria to (mathematical) networks of interacting populations, and that known emergent properties of these networks will provide insights that would be otherwise elusive

Avian blood parasites in an endangered columbid: Leucocytozoon marchouxi in the Mauritian Pink Pigeon Columba mayeri

There is increasing evidence that pathogens can play a significant role in species decline. This study of a complete free-living species reveals a cost of blood parasitism to an endangered host, the Pink Pigeon Columba mayeri, endemic to Mauritius. We investigated the prevalence and effect of infection of the blood parasite, Leucocytozoon marchouxi, in the free-living Pink Pigeon population. Overall, L. marchouxi infection prevalence detected was 18·3%. Juveniles were more likely to be infected than older birds and there was geographical variation in infection prevalence. Survival of birds infected with L. marchouxi was lower than that of uninfected birds to 90 days post-sampling. This study suggests that while common haematozoa are well tolerated in healthy adults, these parasites may have greater pathogenic potential in susceptible juveniles. The study is unusual given its completeness of species sampling (96%) within a short time-period, the accurate host age data, and its focus on blood parasites in a threatened bird species. Species for which long-term life-history data are available for every individual serve as valuable models for dissecting the contribution of particular pathogens to species decline

A Robust and Ultra-Fast Short Circuit Detection in Half-Bridge Using Stray Voltage Capture:Applied in Electromagnetic Suspension

The paper proposes a robust and ultra-fast short circuit detection method based on the voltage dip in the half-bridge due to the presence of stray inductance. For the application of the inverter in electromagnetic suspension, the short circuit is detected in less than 100 ns, which is a promising solution against the Fault Under Load due to a Single-Event Burnout failure type