Search results for "Names"
showing 10 items of 6843 documents
Breathers and solitons of generalized nonlinear Schrödinger equations as degenerations of algebro-geometric solutions
2011
We present new solutions in terms of elementary functions of the multi-component nonlinear Schr\"odinger equations and known solutions of the Davey-Stewartson equations such as multi-soliton, breather, dromion and lump solutions. These solutions are given in a simple determinantal form and are obtained as limiting cases in suitable degenerations of previously derived algebro-geometric solutions. In particular we present for the first time breather and rational breather solutions of the multi-component nonlinear Schr\"odinger equations.
A Stochastic Approach to Quantum Statistics Distributions: Theoretical Derivation and Monte Carlo Modelling
2009
Abstract. We present a method aimed at a stochastic derivation of the equilibrium distribution of a classical/quantum ideal gas in the framework of the canonical ensemble. The time evolution of these ideal systems is modelled as a series of transitions from one system microstate to another one and thermal equilibrium is reached via a random walk in the single-particle state space. We look at this dynamic process as a Markov chain satisfying the condition of detailed balance and propose a variant of the Monte Carlo Metropolis algorithm able to take into account indistinguishability of identical quantum particles. Simulations performed on different two-dimensional (2D) systems are revealed to…
Modeling the coupled return-spread high frequency dynamics of large tick assets
2015
Large tick assets, i.e. assets where one tick movement is a significant fraction of the price and bid-ask spread is almost always equal to one tick, display a dynamics in which price changes and spread are strongly coupled. We introduce a Markov-switching modeling approach for price change, where the latent Markov process is the transition between spreads. We then use a finite Markov mixture of logit regressions on past squared returns to describe the dependence of the probability of price changes. The model can thus be seen as a Double Chain Markov Model. We show that the model describes the shape of return distribution at different time aggregations, volatility clustering, and the anomalo…
Bayesian regularization for flexible baseline hazard functions in Cox survival models.
2019
Fully Bayesian methods for Cox models specify a model for the baseline hazard function. Parametric approaches generally provide monotone estimations. Semi-parametric choices allow for more flexible patterns but they can suffer from overfitting and instability. Regularization methods through prior distributions with correlated structures usually give reasonable answers to these types of situations. We discuss Bayesian regularization for Cox survival models defined via flexible baseline hazards specified by a mixture of piecewise constant functions and by a cubic B-spline function. For those "semi-parametric" proposals, different prior scenarios ranging from prior independence to particular c…
Binary distributions of concentric rings
2014
We introduce families of jointly symmetric, binary distributions that are generated over directed star graphs whose nodes represent variables and whose edges indicate positive dependences. The families are parametrized in terms of a single parameter. It is an outstanding feature of these distributions that joint probabilities relate to evenly spaced concentric rings. Kronecker product characterizations make them computationally attractive for a large number of variables. We study the behavior of different measures of dependence and derive maximum likelihood estimates when all nodes are observed and when the inner node is hidden.
Testing Goodness-of-Fit with the Kernel Density Estimator: GoFKernel
2015
To assess the goodness-of-fit of a sample to a continuous random distribution, the most popular approach has been based on measuring, using either L∞ - or L2 -norms, the distance between the null hypothesis cumulative distribution function and the empirical cumulative distribution function. Indeed, as far as I know, almost all the tests currently available in R related to this issue (ks.test in package stats, ad.test in package ADGofTest, and ad.test, ad2.test, ks.test, v.test and w2.test in package truncgof) use one of these two distances on cumulative distribution functions. This paper (i) proposes dgeometric.test, a new implementation of the test that measures the discrepancy between a s…
MLML2R: an R package for maximum likelihood estimation of DNA methylation and hydroxymethylation proportions.
2019
Abstract Accurately measuring epigenetic marks such as 5-methylcytosine (5-mC) and 5-hydroxymethylcytosine (5-hmC) at the single-nucleotide level, requires combining data from DNA processing methods including traditional (BS), oxidative (oxBS) or Tet-Assisted (TAB) bisulfite conversion. We introduce the R package MLML2R, which provides maximum likelihood estimates (MLE) of 5-mC and 5-hmC proportions. While all other available R packages provide 5-mC and 5-hmC MLEs only for the oxBS+BS combination, MLML2R also provides MLE for TAB combinations. For combinations of any two of the methods, we derived the pool-adjacent-violators algorithm (PAVA) exact constrained MLE in analytical form. For the…
Statistical inference and Monte Carlo algorithms
1996
This review article looks at a small part of the picture of the interrelationship between statistical theory and computational algorithms, especially the Gibbs sampler and the Accept-Reject algorithm. We pay particular attention to how the methodologies affect and complement each other.
Intensity estimation for inhomogeneous Gibbs point process with covariates-dependent chemical activity
2014
Recent development of intensity estimation for inhomogeneous spatial point processes with covariates suggests that kerneling in the covariate space is a competitive intensity estimation method for inhomogeneous Poisson processes. It is not known whether this advantageous performance is still valid when the points interact. In the simplest common case, this happens, for example, when the objects presented as points have a spatial dimension. In this paper, kerneling in the covariate space is extended to Gibbs processes with covariates-dependent chemical activity and inhibitive interactions, and the performance of the approach is studied through extensive simulation experiments. It is demonstr…
Noise decomposition in random telegraph signals using the wavelet transform
2007
Abstract By using the continuous wavelet transform with Haar basis the second-order properties of the wavelet coefficients are derived for the random telegraph signal (RTS) and for the 1 / f noise which is obtained by summation of many RTSs. The correlation structure of the Haar wavelet coefficients for these processes is found. For the wavelet spectrum of the 1 / f noise some characteristics related to the distribution of the relaxation times of the RTS are derived. A statistical test based on the characterization of the time evolution of the scalogram is developed, which allows to detect non-stationarity in the times τ 's which compose the 1 / f process and to identify the time scales of …