Evaluation of decay times in coupled spaces: an efficient search algorithm within the Bayesian framework

This paper discusses an efficient method for evaluating multiple decay times within the Bayesian framework. Previous works [N. Xiang and P. M. Goggans, J. Acoust. Soc. Am. 110, 1415-1424 (2001); 113, 2685-2697 (2003); N. Xiang, P. M. Goggans, T. Jasa, and M. Kleiner, 117, 3707-3715 (2005)] have applied the Bayesian inference to cope with demanding tasks in estimating multiple decay times from Schroeder decay functions measured or calculated in acoustically coupled spaces. Since then a number of recent works call for efficient estimation methods within the Bayesian framework. An efficient analysis is of practical significance for better understanding and modeling the sound energy decay process in acoustically coupled spaces or even in single spaces for reverberation time estimation. This paper will first formulate the Bayesian posterior probability distribution function (PPDF) in a matrix form to reduce the dimensionality as applied to the decay time evaluation. Based on existence of only global extremes of PPDFs as observed from extensive experimental data, this paper describes a dedicated search algorithm for an efficient estimation of decay times.     

Evaluation of decay times in coupled spaces: reliability analysis of Bayeisan decay time estimation

This paper discusses quantitative tools to evaluate the reliability of "decay time estimates" and inter-relationships between multiple decay times for estimates made within a Bayesian framework. Previous works [Xiang and Goggans, J. Acoust. Soc. Am. 110, 1415-1424 (2001); 113, 2685-2697 (2003)] have applied Bayesian framework to cope with the demanding tasks in estimating multiple decay times from Schroeder decay functions measured in acoustically coupled spaces. A parametric model of Schroeder decay function [Xiang, J. Acoust. Soc. Am. 98, 2112-2121 (1995)] has been used for the Bayesian model-based analysis. The relevance of this work is that architectural acousticians need to know how well determined are the estimated decay times calculated within Bayesian framework using Schroeder decay function data. This paper will first address the estimation of global variance of the residual errors between the Schroeder function data and its model. Moreover, this paper discusses how the "landscape" shape of the posterior probability density function over the decay parameter space influences the individual decay time estimates, their associated variances, and their inter-relationships. This paper uses experimental results from measured room impulse responses in real halls to describe a model-based sampling method for an efficient estimation of decay times, and their individual variances. These parameters along with decay times are relevant decay parameters for evaluation and understanding of acoustically coupled spaces.     

Bayes in the sky: Bayesian inference and model selection in cosmology

The application of Bayesian methods in cosmology and astrophysics has flourished over the past decade, spurred by data sets of increasing size and complexity. In many respects, Bayesian methods have proven to be vastly superior to more traditional statistical tools, offering the advantage of higher efficiency and of a consistent conceptual basis for dealing with the problem of induction in the presence of uncertainty. This trend is likely to continue in the future, when the way we collect, manipulate and analyse observations and compare them with theoretical models will assume an even more central role in cosmology.

This review is an introduction to Bayesian methods in cosmology and astrophysics and recent results in the field. I first present Bayesian probability theory and its conceptual underpinnings, Bayes' Theorem and the role of priors. I discuss the problem of parameter inference and its general solution, along with numerical techniques such as Monte Carlo Markov Chain methods. I then review the theory and application of Bayesian model comparison, discussing the notions of Bayesian evidence and effective model complexity, and how to compute and interpret those quantities. Recent developments in cosmological parameter extraction and Bayesian cosmological model building are summarised, highlighting the challenges that lie ahead.     

Luminescence and decay times of CsI:In+

Luminescence spectra of single crystals of CsI:In⁺ excited in the A(304 nm), B(288 nm), C(268 nm) and D(257 nm) absorption bands have been studied in the temperature range 4.2–300 K. Excitation in the A band at 4.2 K gives rise to the principal emission at 2.22 eV accompanied by a partly-overlapping weak band at 2.49 eV. An additional emission band at about 2.96 eV is observed on excitation in the B, C or D bands. Yet another emission band located at 2.67 eV is excited only in the D band. The relative intensities of the bands are very sensitive to excitation wavelength as well as to temperature. The origin of all these bands is assigned in terms of a model for the relaxed excited states (RES). All the luminescence spectra were resolved into an appropriate number of skew-Gaussian components. Moments analysis leads to a value of (1.35 ± 0.02) × 10¹³ rad s^-1 for the effective frequency (ω_eff) of lattice vibrations coupled to the RES. At the lowest temperature, the radiative decay times of each of the intracenter emission bands (2.22, 2.49 and 2.96 eV) show a slow decay ( ～ 10–100 μs) and a fast decay ( ～ 10–100 ns). The 2.96 eV band, which is assigned to an emission process which is the inverse of the D-band absorption, exhibits a single decay mode ( ～ 10 μs). The intrinsic radiative decay rates (k₁, k₂), the one-phonon transition rate (K) and the second-order spin-orbit splitting (D) for the RES responsible for the principal emission are: k₁ = (6.0±-0.3)×10³ s^-1, k₂ = (1.33±-0.06)×10⁵ s^-1, K = (2.4±-0.4)×10⁷ s^-1 and D = (13.8±-0.5) cm^-1.     

Bayesian evidence computation for model selection in non-linear geoacoustic inference problems

This paper applies a general Bayesian inference approach, based on Bayesian evidence computation, to geoacoustic inversion of interface-wave dispersion data. Quantitative model selection is carried out by computing the evidence (normalizing constants) for several model parameterizations using annealed importance sampling. The resulting posterior probability density estimate is compared to estimates obtained from Metropolis-Hastings sampling to ensure consistent results. The approach is applied to invert interface-wave dispersion data collected on the Scotian Shelf, off the east coast of Canada for the sediment shear-wave velocity profile. Results are consistent with previous work on these data but extend the analysis to a rigorous approach including model selection and uncertainty analysis. The results are also consistent with core samples and seismic reflection measurements carried out in the area.     

Analysis of long corona charge decay times

Studies on materials with long charge decay times (notably pharmaceutical powders) have shown that the local charge decay time constant comes to increase linearly with time during the progress of charge decay. This is an empirical result. This linear increase provides the basis for calculating the time to 1/e and/or to 10% from much shorter periods of observation than the times to achieve these decays. The approach involves simple numerical processing of the rate of increase in the local charge decay time constant with time and the intercept of this at some selected time. This analysis is useful for assessing and comparing materials that have decay times over say 10⁴ s.     

A class of coupled spaces

The algebraic structure and analytic properties of a class of Einstein spaces whose metrics are coupled by a particular type of algebraic relation are analyzed. Several invariant relations among the geometric properties of these spaces are obtained; in particular, a detailed analysis is made of the transformation of time-like congruences. The particular case in which one of the spaces is planar is used to establish the consequences of the Herglotz-Noether theorem.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 52–57, September, 1970.     

Time decay of solutions of coupled Maxwell-Klein-Gordon equations

We obtain the optimal time decay of the solutions of the coupled Maxwell-Klein-Gordon equations in four dimensional spacetime, provided the initial data are what we define as Coulomb. In other words, the initial data are such that the Klein-Gordon field is smooth and compactly supported and the Maxwell field is electrostatic outside this support. The problem involves charge, therefore, the initial data do not satisfy either fast decay or any smallness condition. In spite of that, we are able to obtain our result using the inversion map of the lightcone of a carefully selected origin. We thus, avoided the blow-up that takes place when using the usual conformal transformation to the Einstein spacetime.Work partially supported by FAPESP and CNPq     

Radiative decay times for thermal pertubations in a nongray medium

The radiative decay time of harmonic thermal perturbations in a nongray medium of infinite extent is obtained in closed form for two specific band absorption models. These models are the frequently used gray band and the exponential band, the latter being considered more realistic for molecular gases. It is found that the decay time at the boundary of a semi-infinite medium can be obtained in terms of that in an infinite medium. The decay time for combined thermal radiation and conduction is also discussed. The difference in radiative decay rates for a medium with gray bands and one with exponential-tailed bands is marked; in an infinite medium at large Bouguer number, the former falls to zero while the latter rises to a maximum.     

Stimulated polarization echoes with long decay times in ferromagnetic powders

Stimulated polarization echoes with decay time, T₁, exceeding one minute at room temperature have been detected in powders of ferromagnetic materials.     

Absorbing surfaces in ray-tracing programs for coupled spaces

Nowadays architects commonly use the ‘coupled space concept’; examples are mezzanines, half-open office spaces and exhibition rooms. There is a need to predict acoustical quantities for this category of spaces, since half-open spaces may be a cause of noise annoyance. The transmission of sound between coupled spaces depends on design decisions like position, shape and dimensions of the surfaces and on the reflection characteristics. This paper deals with some problems related to the application of absorbing surfaces in coupled rooms, especially when they are modelled in a ray-tracing program. Absorption coefficients from meausurements in reverberation chambers may exceed 1.0 and they do not bear any information about angle dependent behavior, so an extra conversion must be made into input values for the ray-tracing model. Therefore ray-tracing calculations have been performed in a computer model of a reverberation chamber. From a comparison study between measurements and calculations in three coupled rooms it is found that the accuracy is good, provided that the sound reflections on the walls are introduced as angle dependent. Care should be taken in choosing a diffusion factor of flat surfaces.     

Different sound decay patterns and energy feedback in coupled volumes

Different non-exponential decays such as the concave and the convex double sloped decays in the coupled rooms provide distinct sound qualities. These are commonly considered to occur in the less reverberant sub-room and the more reverberant sub-room, respectively. However, numerical simulations and experiments in this paper show that the demarcation line is not located along the physical boundaries (e.g., the partition and the coupling aperture), but in the more reverberant sub-room. The sound field with the concave double sloped decay penetrates into the auxiliary sub-room to an extent which is influenced by the difference between the two natural reverberations of the sub-rooms. Furthermore the sound energy flows in different regions are investigated, demonstrating how energy feedback leads to the concave double sloped decay.     

Pre-equilibrium decay in the exciton model

A new closed-form formulation of the statistical exciton model which gives results very similar to the total pre-equilibrium spectrum obtained by solving a set of Boltzmann-like master equations that describe the nuclear equilibration process, is suggested. The effect of including the loss of strength from each exciton state of a composite nucleus due to the transitions of Δn = 0 (Δp = Δh = 0) in both the master equations and closed-form formalisms is discussed.     

Phosphorescence decay times of thiocyanate complexes of chromium (III) in DMSO

We report the phosphorescence spectra and decay times of chromium (III) solvo-complexes of the [Cr(NCS)_6?n(DMSO)_n]^n?3 type. It is shown that the decay times are linked with the number of solvated molecules. The rate of phosphorescence decay of mixed solvo-complexes depends mainly on the maximum vibrational frequency and number of coordinated molecules.     

Photoconductivity decay model in a-Si: H at low temperatures

Photoconductivity decay from steady-state level can be explained in terms of tunnel recombination through randomly distributed localized states in mobility gap. The calculations shows a good agreement between experiment and theory in the range of several orders of magnitude.     

Electronic states and tunneling times in coupled self-assembled quantum dots

Electron energy levels in single dots, and energy splitting and tunneling times in stacked quantum dots are calculated as functions of structure parameters. An effective mass approach is used to solve the Schrödinger equation for cylindrical dots with finite confinement potentials. Strong confinement due to small sizes produces quantized energy levels in single dots and strong interactions of the wavefunctions with adjacent dots. This electronic coupling induces significant energy splittings and short tunneling times for characteristic structures used in experiments. This coupling may even yield coherent artificial molecular states with different optical properties.     

Auditory discrimination of rise and decay times in tone and noise bursts.

There are indications in the literature on speech perception that differences in rise and decay times of the amplitude envelope are relevant physical correlates in phonemic contrasts. Yet, little is known about the perception of rise and decay times as such. In the present study we have attempted to establish JND's for both rise and decay times of 1000-Hz sine waves as well as white noise bursts by means of an adjustment method. The rise and decay of stimulus amplitude were synthesized to be linear functions of time. Results show that the JND for a change in rise/decay time is generally about 25% of the duration of the rise/decay time. This Weber fraction is a minimum at rise/decay times of about 80 ms and increases significantly for rise/decay times below 20 ms. Of the four signal condition noise bursts were performed with the greatest accuracy (at moderate rise/decay times), while changes in onset time of sine waves were discriminated best at very short rise times (where energy splatter may have contributed an additional cue).