An empirical analysis of the distribution of overshoots in a stationary Gaussian stochastic process

The frequency distribution of overshoots in a stationary Gaussian stochastic process is analyzed. The primary processes involved in this analysis are computer simulation and statistical estimation. Computer simulation is used to simulate stationary Gaussian stochastic processes that have selected autocorrelation functions. An analysis of the simulation results reveals a frequency distribution for overshoots with a functional dependence on the mean and variance of the process. Statistical estimation is then used to estimate the mean and variance of a process. It is shown that for an autocorrelation function, the mean and the variance for the number of overshoots, a frequency distribution for overshoots can be estimated

Deconvolution of positron annihilation coincidence Doppler broadening spectra using an iterative projected Newton method with non-negativity constraints

A generalized least-square method with Tikonov-Miller regularization and non-negativity constarints was developed for deconvoluting two-dimensional coincidence Doppler broadening spectroscopy (CDBS) spectra. A projected Newton algorithm was developed to solve the generalized least-square problem. The algorithm was used to deconvolute experimental CDBS data from aluminum was tested on Monte Carlo generated spectra. The retrieval of the positron-electron momentum distributions in the low momentum region was also demonstrated.published_or_final_versio

A multi-resolution, non-parametric, Bayesian framework for identification of spatially-varying model parameters

This paper proposes a hierarchical, multi-resolution framework for the identification of model parameters and their spatially variability from noisy measurements of the response or output. Such parameters are frequently encountered in PDE-based models and correspond to quantities such as density or pressure fields, elasto-plastic moduli and internal variables in solid mechanics, conductivity fields in heat diffusion problems, permeability fields in fluid flow through porous media etc. The proposed model has all the advantages of traditional Bayesian formulations such as the ability to produce measures of confidence for the inferences made and providing not only predictive estimates but also quantitative measures of the predictive uncertainty. In contrast to existing approaches it utilizes a parsimonious, non-parametric formulation that favors sparse representations and whose complexity can be determined from the data. The proposed framework in non-intrusive and makes use of a sequence of forward solvers operating at various resolutions. As a result, inexpensive, coarse solvers are used to identify the most salient features of the unknown field(s) which are subsequently enriched by invoking solvers operating at finer resolutions. This leads to significant computational savings particularly in problems involving computationally demanding forward models but also improvements in accuracy. It is based on a novel, adaptive scheme based on Sequential Monte Carlo sampling which is embarrassingly parallelizable and circumvents issues with slow mixing encountered in Markov Chain Monte Carlo schemes

Bayesian reconstruction of the cosmological large-scale structure: methodology, inverse algorithms and numerical optimization

We address the inverse problem of cosmic large-scale structure reconstruction from a Bayesian perspective. For a linear data model, a number of known and novel reconstruction schemes, which differ in terms of the underlying signal prior, data likelihood, and numerical inverse extra-regularization schemes are derived and classified. The Bayesian methodology presented in this paper tries to unify and extend the following methods: Wiener-filtering, Tikhonov regularization, Ridge regression, Maximum Entropy, and inverse regularization techniques. The inverse techniques considered here are the asymptotic regularization, the Jacobi, Steepest Descent, Newton-Raphson, Landweber-Fridman, and both linear and non-linear Krylov methods based on Fletcher-Reeves, Polak-Ribiere, and Hestenes-Stiefel Conjugate Gradients. The structures of the up-to-date highest-performing algorithms are presented, based on an operator scheme, which permits one to exploit the power of fast Fourier transforms. Using such an implementation of the generalized Wiener-filter in the novel ARGO-software package, the different numerical schemes are benchmarked with 1-, 2-, and 3-dimensional problems including structured white and Poissonian noise, data windowing and blurring effects. A novel numerical Krylov scheme is shown to be superior in terms of performance and fidelity. These fast inverse methods ultimately will enable the application of sampling techniques to explore complex joint posterior distributions. We outline how the space of the dark-matter density field, the peculiar velocity field, and the power spectrum can jointly be investigated by a Gibbs-sampling process. Such a method can be applied for the redshift distortions correction of the observed galaxies and for time-reversal reconstructions of the initial density field.Comment: 40 pages, 11 figure

Ecological signals of arctic plant-microbe associations are consistent across eDNA and vegetation surveys

Understanding how different taxa respond to abiotic characteristics of the environment is of key interest for understanding the assembly of communities. Yet, whether eDNA data will suffice to accurately capture environmental imprints has been the topic of some debate. In this study, we characterised patterns of species occurrences and co-occurrences in Zackenberg in northeast Greenland using environmental DNA. To explore the potential for extracting ecological signals from eDNA data alone, we compared two approaches (visual vegetation surveys and soil eDNA metabarcoding) to describing plant communities and their responses to abiotic conditions. We then examined plant associations with microbes using a joint species distribution model. We found that most (68%) of plant genera were detectable by both vegetation surveys and eDNA signatures. Species-specific occurrence data revealed how plants, bacteria and fungi responded to their abiotic environment - with plants, bacteria and fungi all responding similarly to soil moisture. Nonetheless, a large proportion of fungi decreased in occurrences with increasing soil temperature. Regarding biotic associations, the nature and proportion of the plant-microbe associations detected were consistent between plant data identified via vegetation surveys and eDNA. Of pairs of plants and microbe genera showing statistically supported associations (while accounting for joint responses to the environment), plants and bacteria mainly showed negative associations, whereas plants and fungi mainly showed positive associations. Ample ecological signals detected by both vegetation surveys and by eDNA-based methods and a general correspondence in biotic associations inferred by both methods, suggested that purely eDNA-based approaches constitute a promising and easily applicable tool for studying plant-soil microbial associations in the Arctic and elsewhere

Filter-Based Fading Channel Modeling

A channel simulator is an essential component in the development and accurate performance evaluation of wireless systems. A key technique for producing statistically accurate fading variates is to shape the flat spectrum of Gaussian variates using digital filters. This paper addresses various challenges when designing real and complex spectrum shaping filters with quantized coefficients for efficient realization of both isotropic and nonisotropic fading channels. An iterative algorithm for designing stable complex infinite impulse response (IIR) filters with fixed-point coefficients is presented. The performance of the proposed filter design algorithm is verified with 16-bit fixed-point simulations of two example fading filters