Mean field approach for tracking similar objects

In this paper, we consider the problem of tracking similar objects. We show how a mean field approach can be used to deal with interacting targets and we compare it with Markov Chain Monte Carlo (MCMC). Two mean field implementations are presented. The first one is more general and uses particle filtering. We discuss some simplifications of the base algorithm that reduce the computation time. The second one is based on suitable Gaussian approximations of probability densities that lead to a set of self-consistent equations for the means and covariances. These equations give the Kalman solution if there is no interaction. Experiments have been performed on two kinds of sequences. The first kind is composed of a single long sequence of twenty roaming ants and was previously analysed using MCMC. In this case, our mean field algorithms obtain substantially better results. The second kind corresponds to selected sequences of a football match in which the interaction avoids tracker coalescence in situations where independent trackers fail.

Evaluation of genetic substructure in the Irish Study of High-Density Schizophrenia Families

The presence of genetic substructure has the potential to diminish the chances of detecting a linkage signal. Using a Markov chain Monte Carlo procedure developed by Pritchard and colleagues and implemented in the program STRUCTURE, we evaluated the evidence for genetic substructure using genotypes from 37 microsatellite markers in affected individuals selected at random from 263 multiplex families in the Irish Study of High-Density Schizophrenia Families. We found no evidence for the presence of genetic substructure in this sample.

Characterization of the Kepler-101 planetary system with HARPS-N. A hot super-Neptune with an Earth-sized low-mass companion

We characterize the planetary system Kepler-101 by performing a combined differential evolution Markov chain Monte Carlo analysisof Kepler data and forty radial velocities obtained with the HARPS-N spectrograph. This system was previously validated and iscomposed of a hot super-Neptune, Kepler-101b, and an Earth-sized planet, Kepler-101c. These two planets orbit the slightly evolvedand metal-rich G-type star in 3.49 and 6.03 days, respectively. With mass Mp = 51.1+5.1−4.7 M⊕, radius Rp = 5.77+0.85−0.79 R⊕, and density ρp = 1.45+0.83 −0.48 g cm−3, Kepler-101b is the first fully characterized super-Neptune, and its density suggests that heavy elements makeup a significant fraction of its interior; more than 60% of its total mass. Kepler-101c has a radius of 1.25+0.19−0.17 R⊕, which implies theabsence of any H/He envelope, but its mass could not be determined because of the relative faintness of the parent star for highly precise radial-velocity measurements (Kp = 13.8) and the limited number of radial velocities. The 1σ upper limit, Mp < 3.8 M⊕, excludes a pure iron composition with a probability of 68.3%. The architecture of the planetary system Kepler-101 − containing aclose-in giant planet and an outer Earth-sized planet with a period ratio slightly larger than the 3:2 resonance − is certainly of interest for scenarios of planet formation and evolution. This system does not follow the previously reported trend that the larger planet has the longer period in the majority of Kepler systems of planet pairs with at least one Neptune-sized or larger planet.

Solar Flare Impulsive Phase Emission Observed with SDO/EVE

Differential emission measures (DEMs) during the impulsive phase of solar flares were constructed using observations from the EUV Variability Experiment (EVE) and the Markov-Chain Monte Carlo method. Emission lines from ions formed over the temperature range log Te = 5.8-7.2 allow the evolution of the DEM to be studied over a wide temperature range at 10 s cadence. The technique was applied to several M- and X-class flares, where impulsive phase EUV emission is observable in the disk-integrated EVE spectra from emission lines formed up to 3-4 MK and we use spatially unresolved EVE observations to infer the thermal structure of the emitting region. For the nine events studied, the DEMs exhibited a two-component distribution during the impulsive phase, a low-temperature component with peak temperature of 1-2 MK, and a broad high-temperature component from 7 to 30 MK. A bimodal high-temperature component is also found for several events, with peaks at 8 and 25 MK during the impulsive phase. The origin of the emission was verified using Atmospheric Imaging Assembly images to be the flare ribbons and footpoints, indicating that the constructed DEMs represent the spatially average thermal structure of the chromospheric flare emission during the impulsive phase.

A new statistical framework for the quantification of covariate associations with species distributions

Identifying processes that shape species geographical ranges is a prerequisite for understanding environmental change. Currently, species distribution modelling methods do not offer credible statistical tests of the relative influence of climate factors and typically ignore other processes (e.g. biotic interactions and dispersal limitation). We use a hierarchical model fitted with Markov Chain Monte Carlo to combine ecologically plausible niche structures using regression splines to describe unimodal but potentially skewed response terms. We apply spatially explicit error terms that account for (and may help identify) missing variables. Using three example distributions of European bird species, we map model results to show sensitivity to change in each covariate. We show that the overall strength of climatic association differs between species and that each species has considerable spatial variation in both the strength of the climatic association and the sensitivity to climate change. Our methods are widely applicable to many species distribution modelling problems and enable accurate assessment of the statistical importance of biotic and abiotic influences on distributions.

Transit timing variations in WASP-10b induced by stellar activity

The hot-JupiterWASP-10bwas reported by Maciejewski et al. to showtransit timing variations (TTVs) with an amplitude of ~3.5 min. These authors proposed that the observed TTVs were caused by a 0.1M_Jup perturbing companion with an orbital period of ~5.23 d, and hence, close to the outer 5:3 mean-motion resonance with WASP-10b. To test this scenario, we present eight new transit light curves of WASP-10b obtained with the Faulkes Telescope North and the Liverpool Telescope. The new light curves, together with 22 previously published ones, were modelled with a Markov Chain Monte Carlo transit fitting code. Transit depth differences reported forWASP-10b are thought to be due to starspot-induced brightness modulation of the host star. Assuming the star is brighter at the activity minimum, we favour a small planetary radius. We find Rp = 1.039^+0.043 _-0.049R_Jup in agreement with Johnson et al. and Maciejewski et al. Recent studies find no evidence for a significant eccentricity in this system. We present consistent system parameters for a circular orbit and refine the orbital ephemeris ofWASP-10b. Our homogeneously derived transit times do not support the previous claimed TTV signal, which was strongly dependent on two previously published transits that have been incorrectly normalized. Nevertheless, a linear ephemeris is not a statistically good fit to the transit times of WASP-10b. We show that the observed transit time variations are due to spot occultation features or systematics. We discuss and exemplify the effects of occultation spot features in the measured transit times and show that despite spot occultation during egress and ingress being difficult to distinguish in the transit light curves, they have a significant effect in the measured transit times. We conclude that if we account for spot features, the transit times of WASP-10b are consistent with a linear ephemeris with the exception of one transit (epoch 143) which is a partial transit. Therefore, there is currently no evidence for the existence of a companion to WASP-10b. Our results support the lack of TTVs of hot-Jupiters reported for the Kepler sample. 

Reducing Parametric Uncertainty in Limit Cycle Oscillations

The assimilation of discrete higher fidelity data points with model predictions can be used to achieve a reduction in the uncertainty of the model input parameters which generate accurate predictions. The problem investigated here involves the prediction of limit-cycle oscillations using a High-Dimensional Harmonic Balance method (HDHB). The efficiency of the HDHB method is exploited to enable calibration of structural input parameters using a Bayesian inference technique. Markov-chain Monte Carlo is employed to sample the posterior distributions. Parameter estimation is carried out on both a pitch/plunge aerofoil and Goland wing configuration. In both cases significant refinement was achieved in the distribution of possible structural parameters allowing better predictions of their
true deterministic values.

Strong electronic correlation in the hydrogen chain: A variational Monte Carlo study

In this paper, we report a fully ab initio variational Monte Carlo study of the linear and periodic chain of hydrogen atoms, a prototype system providing the simplest example of strong electronic correlation in low dimensions. In particular, we prove that numerical accuracy comparable to that of benchmark density-matrix renormalization-group calculations can be achieved by using a highly correlated Jastrow-antisymmetrized geminal power variational wave function. Furthermore, by using the so-called "modern theory of polarization" and by studying the spin-spin and dimer-dimer correlations functions, we have characterized in detail the crossover between the weakly and strongly correlated regimes of this atomic chain. Our results show that variational Monte Carlo provides an accurate and flexible alternative to highly correlated methods of quantum chemistry which, at variance with these methods, can be also applied to a strongly correlated solid in low dimensions close to a crossover or a phase transition.

A Continuous Time Markov Chain Based Sequential Analytical Approach for Composite Power System Reliability Assessment

This paper proposes a continuous time Markov chain (CTMC) based sequential analytical approach for composite generation and transmission systems reliability assessment. The basic idea is to construct a CTMC model for the composite system. Based on this model, sequential analyses are performed. Various kinds of reliability indices can be obtained, including expectation, variance, frequency, duration and probability distribution. In order to reduce the dimension of the state space, traditional CTMC modeling approach is modified by merging all high order contingencies into a single state, which can be calculated by Monte Carlo simulation (MCS). Then a state mergence technique is developed to integrate all normal states to further reduce the dimension of the CTMC model. Moreover, a time discretization method is presented for the CTMC model calculation. Case studies are performed on the RBTS and a modified IEEE 300-bus test system. The results indicate that sequential reliability assessment can be performed by the proposed approach. Comparing with the traditional sequential Monte Carlo simulation method, the proposed method is more efficient, especially in small scale or very reliable power systems.

Density functional and Monte Carlo studies of sulfur. I. Structure and bonding in S-n rings and chains (n=2-18) (vol 118, pg 9257, 2003)

Density functional calculations have been performed for ring isomers of sulfur with up to 18 atoms, and for chains with up to ten atoms. There are many isomers of both types, and the calculations predict the existence of new forms. Larger rings and chains are very flexible, with numerous local energy minima. Apart from a small, but consistent overestimate in the bond lengths, the results reproduce experimental structures where known. Calculations are also performed on the energy surfaces of S8 rings, on the interaction between a pair of such rings, and the reaction between one S8 ring and the triplet diradical S8 chain. The results for potential energies, vibrational frequencies, and reaction mechanisms in sulfur rings and chains provide essential ingredients for Monte Carlo simulations of the liquid–liquid phase transition. The results of these simulations will be presented in Part II.

Density functional/Monte Carlo study of ring-opening polymerization

Density functional calculations of the structure, potential energy surface and reactivity for organic systems closely related to bisphenol-A-polycarbonate (BPA-PC) provide the basis for a model describing the ring-opening polymerization of its cyclic oligomers by nucleophilic molecules. Monte Carlo simulations using this model show a strong tendency to polymerize that is increased by increasing density and temperature, and is greater in 3D than in 2D. Entropy in the distribution of inter-particle bonds is the driving force for chain formation. (C) 2002 Elsevier Science B.V. All rights reserved.

Monte Carlo studies of quantum and classical annealing on a double well

We present results for a variety of Monte Carlo annealing approaches, both classical and quantum, benchmarked against one another for the textbook optimization exercise of a simple one-dimensional double well. In classical (thermal) annealing, the dependence upon the move chosen in a Metropolis scheme is studied and correlated with the spectrum of the associated Markov transition matrix. In quantum annealing, the path integral Monte Carlo approach is found to yield nontrivial sampling difficulties associated with the tunneling between the two wells. The choice of fictitious quantum kinetic energy is also addressed. We find that a "relativistic" kinetic energy form, leading to a higher probability of long real-space jumps, can be considerably more effective than the standard nonrelativistic one.

Density functional and Monte Carlo studies of sulfur. II. Equilibrium polymerization of the liquid phase

The equilibrium polymerization of sulfur is investigated by Monte Carlo simulations. The potential energy model is based on density functional results for the cohesive energy, structural, and vibrational properties as well as reactivity of sulfur rings and chains [Part I, J. Chem. Phys. 118, 9257 (2003)]. Liquid samples of 2048 atoms are simulated at temperatures 450less than or equal toTless than or equal to850 K and P=0 starting from monodisperse S-8 molecular compositions. Thermally activated bond breaking processes lead to an equilibrium population of unsaturated atoms that can change the local pattern of covalent bonds and allow the system to approach equilibrium. The concentration of unsaturated atoms and the kinetics of bond interchanges is determined by the energy DeltaE(b) required to break a covalent bond. Equilibrium with respect to the bond distribution is achieved for 15less than or equal toDeltaE(b)less than or equal to21 kcal/mol over a wide temperature range (Tgreater than or equal to450 K), within which polymerization occurs readily, with entropy from the bond distribution overcompensating the increase in enthalpy. There is a maximum in the polymerized fraction at temperature T-max that depends on DeltaE(b). This fraction decreases at higher temperature because broken bonds and short chains proliferate and, for Tless than or equal toT(max), because entropy is less important than enthalpy. The molecular size distribution is described well by a Zimm-Schulz function, plus an isolated peak for S-8. Large molecules are almost exclusively open chains. Rings tend to have fewer than 24 atoms, and only S-8 is present in significant concentrations at all T. The T dependence of the density and the dependence of polymerization fraction and degree on DeltaE(b) give estimates of the polymerization temperature T-f=450+/-20 K. (C) 2003 American Institute of Physics.