Parameter estimation in pair hidden Markov models

This paper deals with parameter estimation in pair hidden Markov models (pair-HMMs). We first provide a rigorous formalism for these models and discuss possible definitions of likelihoods. The model being biologically motivated, some restrictions with respect to the full parameter space naturally occur. Existence of two different Information divergence rates is established and divergence property (namely positivity at values different from the true one) is shown under additional assumptions. This yields consistency for the parameter in parametrization schemes for which the divergence property holds. Simulations illustrate different cases which are not covered by our results.Comment: corrected typo

Mitochondrial Dna Replacement Versus Nuclear Dna Persistence

In this paper we consider two populations whose generations are not overlapping and whose size is large. The number of males and females in both populations is constant. Any generation is replaced by a new one and any individual has two parents for what concerns nuclear DNA and a single one (the mother) for what concerns mtDNA. Moreover, at any generation some individuals migrate from the first population to the second. In a finite random time $T$, the mtDNA of the second population is completely replaced by the mtDNA of the first. In the same time, the nuclear DNA is not completely replaced and a fraction $F$ of the ancient nuclear DNA persists. We compute both $T$ and $F$. Since this study shows that complete replacement of mtDNA in a population is compatible with the persistence of a large fraction of nuclear DNA, it may have some relevance for the Out of Africa/Multiregional debate in Paleoanthropology

A real-time hybrid aurora alert system:combining citizen science reports with an auroral oval model

Accurately predicting when, and from where, an aurora will be visible is particularly difficult, yet it is a service much desired by the general public. Several aurora alert services exist that attempt to provide such predictions but are, generally, based upon fairly coarse estimates of auroral activity (e.g. Kp or Dst). Additionally, these services are not able to account for a potential observer's local conditions (such as cloud cover or level of darkness). Aurorasaurus, however, combines data from the well-used, solar wind driven, OVATION Prime auroral oval model with real-time observational data provided by a global network of citizen scientists. This system is designed to provide more accurate and localized alerts for auroral visibility than currently available. Early results are promising and show that over 100,000 auroral visibility alerts have been issued, including nearly 200 highly localized alerts, to over 2,000 users located right across the globe

Mean-field methods in evolutionary duplication-innovation-loss models for the genome-level repertoire of protein domains

We present a combined mean-field and simulation approach to different models describing the dynamics of classes formed by elements that can appear, disappear or copy themselves. These models, related to a paradigm duplication-innovation model known as Chinese Restaurant Process, are devised to reproduce the scaling behavior observed in the genome-wide repertoire of protein domains of all known species. In view of these data, we discuss the qualitative and quantitative differences of the alternative model formulations, focusing in particular on the roles of element loss and of the specificity of empirical domain classes.Comment: 10 Figures, 2 Table

Harness processes and harmonic crystals

In the Hammersley harness processes the real-valued height at each site i in Z^d is updated at rate 1 to an average of the neighboring heights plus a centered random variable (the noise). We construct the process "a la Harris" simultaneously for all times and boxes contained in Z^d. With this representation we compute covariances and show L^2 and almost sure time and space convergence of the process. In particular, the process started from the flat configuration and viewed from the height at the origin converges to an invariant measure. In dimension three and higher, the process itself converges to an invariant measure in L^2 at speed t^{1-d/2} (this extends the convergence established by Hsiao). When the noise is Gaussian the limiting measures are Gaussian fields (harmonic crystals) and are also reversible for the process.Comment: 21 pages. Revised version with minor changes. Version almost identical to the one to be published in SP

High-resolution dielectric characterization of minerals: a step towards understanding the basic interactions between microwaves and rocks

Microwave energy was demonstrated to be potentially beneficial for reducing the cost of several steps of the mining process. Significant literature was developed about this topic but few studies are focused on understanding the interaction between microwaves and minerals at a fundamental level in order to elucidate the underlying physical processes that control the observed phenomena. This is ascribed to the complexity of such phenomena, related to chemical and physical transformations, where electrical, thermal and mechanical forces play concurrent roles. In this work a new characterization method for the dielectric properties of mineral samples at microwave frequencies is presented. The method is based upon the scanning microwave microscopy technique that enables measurement of the dielectric constant, loss factor and conductivity with extremely high spatial resolution and accuracy. As opposed to conventional dielectric techniques, the scanning microwave microscope can then access and measure the dielectric properties of micrometric-sized mineral inclusions within a complex structure of natural rock. In this work two micrometric hematite inclusions were characterized at a microwave frequency of 3 GHz. Scanning electron microscopy/energy-dispersive x-ray spectroscopy and confocal micro-Raman spectroscopy were used to determine the structural details and chemical and elemental composition of mineral sample on similar scale

Higgs Mediated EDMs in the Next-to-MSSM: An Application to Electroweak Baryogenesis

We perform a study on the predictions of electric-dipole moments (EDMs) of neutron, Mercury (Hg), Thallium (Tl), deuteron, and Radium (Ra) in the framework of next-to-minimal supersymmetric standard model (NMSSM) with CP-violating parameters in the superpotential and soft-supersymmetry-breaking sector. We confine to the case in which only the physical tree-level CP phase $(\phi'_\lambda - \phi'_\kappa)$, associated with the couplings of the singlet terms in the superpotential and with the vacuum-expectation-values (VEVs), takes on a nonzero value. We found that the one-loop contributions from neutralinos are mostly small while the two-loop Higgs-mediated contributions of the Barr-Zee (BZ) type diagrams dominate. We emphasize a scenario motivated by electroweak baryogenesis.Comment: 36 pages, 9 figures, to appear in PR

Effect of selection on ancestry: an exactly soluble case and its phenomenological generalization

We consider a family of models describing the evolution under selection of a population whose dynamics can be related to the propagation of noisy traveling waves. For one particular model, that we shall call the exponential model, the properties of the traveling wave front can be calculated exactly, as well as the statistics of the genealogy of the population. One striking result is that, for this particular model, the genealogical trees have the same statistics as the trees of replicas in the Parisi mean-field theory of spin glasses. We also find that in the exponential model, the coalescence times along these trees grow like the logarithm of the population size. A phenomenological picture of the propagation of wave fronts that we introduced in a previous work, as well as our numerical data, suggest that these statistics remain valid for a larger class of models, while the coalescence times grow like the cube of the logarithm of the population size.Comment: 26 page

Time-Changed Poisson Processes

We consider time-changed Poisson processes, and derive the governing difference-differential equations (DDE) these processes. In particular, we consider the time-changed Poisson processes where the the time-change is inverse Gaussian, or its hitting time process, and discuss the governing DDE's. The stable subordinator, inverse stable subordinator and their iterated versions are also considered as time-changes. DDE's corresponding to probability mass functions of these time-changed processes are obtained. Finally, we obtain a new governing partial differential equation for the tempered stable subordinator of index $0<\beta<1,$ when $\beta$ is a rational number. We then use this result to obtain the governing DDE for the mass function of Poisson process time-changed by tempered stable subordinator. Our results extend and complement the results in Baeumer et al. \cite{B-M-N} and Beghin et al. \cite{BO-1} in several directions.Comment: 18 page