MCMC methods for functions modifying old algorithms to make\ud them faster

Many problems arising in applications result in the need\ud to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become arbitrarily slow under the mesh refinement dictated by nonparametric description of the unknown function. We describe an approach to modifying a whole range of MCMC methods which ensures that their speed of convergence is robust under mesh refinement. In the applications of interest the data is often sparse and the prior specification is an essential part of the overall modeling strategy. The algorithmic approach that we describe is applicable whenever the desired probability measure has density with respect to a Gaussian process or Gaussian random field prior, and to some useful non-Gaussian priors constructed through random truncation. Applications are shown in density estimation, data assimilation in fluid mechanics, subsurface geophysics and image registration. The key design principle is to formulate the MCMC method for functions. This leads to algorithms which can be implemented via minor modification of existing algorithms, yet which show enormous speed-up on a wide range of applied problems

MEXIT: Maximal un-coupling times for stochastic processes

Classical coupling constructions arrange for copies of the \emph{same} Markov process started at two \emph{different} initial states to become equal as soon as possible. In this paper, we consider an alternative coupling framework in which one seeks to arrange for two \emph{different} Markov (or other stochastic) processes to remain equal for as long as possible, when started in the \emph{same} state. We refer to this "un-coupling" or "maximal agreement" construction as \emph{MEXIT}, standing for "maximal exit". After highlighting the importance of un-coupling arguments in a few key statistical and probabilistic settings, we develop an explicit \MEXIT construction for stochastic processes in discrete time with countable state-space. This construction is generalized to random processes on general state-space running in continuous time, and then exemplified by discussion of \MEXIT for Brownian motions with two different constant drifts.Comment: 28 page

Violation of the equivalence principle from light scalar fields: from Dark Matter candidates to scalarized black holes

Tensor-scalar theory is a wide class of alternative theory of gravitation that can be motivated by higher dimensional theories, by models of dark matter or dark ernergy. In the general case, the scalar field will couple non-universally to matter producing a violation of the equivalence principle. In this communication, we review a microscopic model of scalar/matter coupling and its observable consequences in terms of universality of free fall, of frequencies comparison and of redshifts tests. We then focus on two models: (i) a model of ultralight scalar dark matter and (ii) a model of scalarized black hole in our Galactic Center. For both these models, we present constraints using recent measurements: atomic clocks comparisons, universality of free fall measurements, measurement of the relativistic redshift with the short period star S0-2 orbiting the supermassive black hole in our Galactic Center.Comment: 8 pages, 1 figure, contribution to the 2019 Gravitation session of the 54th Rencontres de Morion

Genetic mapping, synteny, and physical location of two loci for Fusarium oxysporum f. sp. tracheiphilum race 4 resistance in cowpea [Vignaunguiculata (L.) Walp].

Fusarium wilt is a vascular disease caused by the fungus Fusariumoxysporum f.sp. tracheiphilum (Fot) in cowpea [Vignaunguiculata (L.) Walp]. In this study, we mapped loci conferring resistance to Fot race 4 in three cowpea RIL populations: IT93K-503-1 × CB46, CB27 × 24-125B-1, and CB27 × IT82E-18/Big Buff. Two independent loci which confer resistance to Fot race 4 were identified, Fot4-1 and Fot4-2. Fot4-1 was identified in the IT93K-503-1 (resistant) × CB46 (susceptible) population and was positioned on the cowpea consensus genetic map, spanning 21.57-29.40 cM on linkage group 5. The Fot4-2 locus was validated by identifying it in both the CB27 (resistant) × 24-125B-1 (susceptible) and CB27 (resistant) × IT82E-18/Big Buff (susceptible) populations. Fot4-2 was positioned on the cowpea consensus genetic map on linkage group 3; the minimum distance spanned 71.52-71.75 cM whereas the maximum distance spanned 64.44-80.23 cM. These genomic locations of Fot4-1 and Fot4-2 on the cowpea consensus genetic map, relative to Fot3-1 which was previously identified as the locus conferring resistance to Fot race 3, established that all three loci were independent. The Fot4-1 and Fot4-2 syntenic loci were examined in Glycine max, where several disease-resistance candidate genes were identified for both loci. In addition, Fot4-1 and Fot4-2 were coarsely positioned on the cowpea physical map. Fot4-1 and Fot4-2 will contribute to molecular marker development for future use in marker-assisted selection, thereby expediting introgression of Fot race 4 resistance into future cowpea cultivars

CLTs and asymptotic variance of time-sampled Markov chains

For a Markov transition kernel P and a probability distribution μ on nonnegative integers, a time-sampled Markov chain evolves according to the transition kernel Pμ = Σkμ(k)Pk. In this note we obtain CLT conditions for time-sampled Markov chains and derive a spectral formula for the asymptotic variance. Using these results we compare efficiency of Barker's and Metropolis algorithms in terms of asymptotic variance

Kinematic dynamo action in a sphere. I. Effects of differential rotation and meridional circulation on solutions with axial dipole symmetry

A sphere containing electrically conducting fluid can generate a magnetic field by dynamo action, provided the flow is sufficiently complicated and vigorous. The dynamo mechanism is thought to sustain magnetic fields in planets and stars. The kinematic dynamo problem tests steady flows for magnetic instability, but rather few dynamos have been found so far because of severe numerical difficulties. Dynamo action might, therefore, be quite unusual, at least for large-scale steady flows. We address this question by testing a two-parameter class of flows for dynamo generation of magnetic fields containing an axial dipole. The class of flows includes two completely different types of known dynamos, one dominated by differential rotation (D) and one with none. We find that 36% of the flows in seven distinct zones in parameter space act as dynamos, while the remaining 64% either fail to generate this type of magnetic field or generate fields that are too small in scale to be resolved by our numerical method. The two previously known dynamo types lie in the same zone, and it is therefore possible to change the flow continuously from one to the other without losing dynamo action. Differential rotation is found to promote large-scale axisymmetric toroidal magnetic fields, while meridional circulation (M) promotes large-scale axisymmetric poloidal fields concentrated at high latitudes near the axis. Magnetic fields resembling that of the Earth are generated by D > 0, corresponding to westward flow at the surface, and M of either sign but not zero. Very few oscillatory solutions are found