Maximum-likelihood estimation of lithospheric flexural rigidity, initial-loading fraction, and load correlation, under isotropy

Topography and gravity are geophysical fields whose joint statistical structure derives from interface-loading processes modulated by the underlying mechanics of isostatic and flexural compensation in the shallow lithosphere. Under this dual statistical-mechanistic viewpoint an estimation problem can be formulated where the knowns are topography and gravity and the principal unknown the elastic flexural rigidity of the lithosphere. In the guise of an equivalent "effective elastic thickness", this important, geographically varying, structural parameter has been the subject of many interpretative studies, but precisely how well it is known or how best it can be found from the data, abundant nonetheless, has remained contentious and unresolved throughout the last few decades of dedicated study. The popular methods whereby admittance or coherence, both spectral measures of the relation between gravity and topography, are inverted for the flexural rigidity, have revealed themselves to have insufficient power to independently constrain both it and the additional unknown initial-loading fraction and load-correlation fac- tors, respectively. Solving this extremely ill-posed inversion problem leads to non-uniqueness and is further complicated by practical considerations such as the choice of regularizing data tapers to render the analysis sufficiently selective both in the spatial and spectral domains. Here, we rewrite the problem in a form amenable to maximum-likelihood estimation theory, which we show yields unbiased, minimum-variance estimates of flexural rigidity, initial-loading frac- tion and load correlation, each of those separably resolved with little a posteriori correlation between their estimates. We are also able to separately characterize the isotropic spectral shape of the initial loading processes.Comment: 41 pages, 13 figures, accepted for publication by Geophysical Journal Internationa

Estimating orthant probabilities of high dimensional Gaussian vectors with an application to set estimation

The computation of Gaussian orthant probabilities has been extensively studied for low-dimensional vectors. Here, we focus on the high-dimensional case and we present a two-step procedure relying on both deterministic and stochastic techniques. The proposed estimator relies indeed on splitting the probability into a low-dimensional term and a remainder. While the low-dimensional probability can be estimated by fast and accurate quadrature, the remainder requires Monte Carlo sampling. We further refine the estimation by using a novel asymmetric nested Monte Carlo (anMC) algorithm for the remainder and we highlight cases where this approximation brings substantial efficiency gains. The proposed methods are compared against state-of-the-art techniques in a numerical study, which also calls attention to the advantages and drawbacks of the procedure. Finally, the proposed method is applied to derive conservative estimates of excursion sets of expensive to evaluate deterministic functions under a Gaussian random field prior, without requiring a Markov assumption. Supplementary material for this article is available online

Statistics for Fission-Track Thermochronology

This chapter introduces statistical tools to extract geologically meaningful information from fission-track (FT) data using both the external detector and LA-ICP-MS methods. The spontaneous fission of 238U is a Poisson process resulting in large single-grain age uncertainties. To overcome this imprecision, it is nearly always necessary to analyse multiple grains per sample. The degree to which the analytical uncertainties can explain the observed scatter of the single-grain data can be visually assessed on a radial plot and objectively quantified by a chi-square test. For sufficiently low values of the chi-square statistic (or sufficiently high p values), the pooled age of all the grains gives a suitable description of the underlying ‘true’ age population. Samples may fail the chi-square test for several reasons. A first possibility is that the true age population does not consist of a single discrete age component, but is characterised by a continuous range of ages. In this case, a ‘random effects’ model can constrain the true age distribution using two parameters: the ‘central age’ and the ‘(over)dispersion’. A second reason why FT data sets might fail the chi-square test is if they are underlain by multimodal age distributions. Such distributions may consist of discrete age components, continuous age distributions, or a combination of the two. Formalised statistical tests such as chi-square can be useful in preventing overfitting of relatively small data sets. However, they should be used with caution when applied to large data sets (including length measurements) which generate sufficient statistical ‘power’ to reject any simple yet geologically plausible hypothesis

Novel Methods for Analysing Bacterial Tracks Reveal Persistence in Rhodobacter sphaeroides

Tracking bacteria using video microscopy is a powerful experimental approach to probe their motile behaviour. The trajectories obtained contain much information relating to the complex patterns of bacterial motility. However, methods for the quantitative analysis of such data are limited. Most swimming bacteria move in approximately straight lines, interspersed with random reorientation phases. It is therefore necessary to segment observed tracks into swimming and reorientation phases to extract useful statistics. We present novel robust analysis tools to discern these two phases in tracks. Our methods comprise a simple and effective protocol for removing spurious tracks from tracking datasets, followed by analysis based on a two-state hidden Markov model, taking advantage of the availability of mutant strains that exhibit swimming-only or reorientating-only motion to generate an empirical prior distribution. Using simulated tracks with varying levels of added noise, we validate our methods and compare them with an existing heuristic method. To our knowledge this is the first example of a systematic assessment of analysis methods in this field. The new methods are substantially more robust to noise and introduce less systematic bias than the heuristic method. We apply our methods to tracks obtained from the bacterial species Rhodobacter sphaeroides and Escherichia coli. Our results demonstrate that R. sphaeroides exhibits persistence over the course of a tumbling event, which is a novel result with important implications in the study of this and similar species

Spectral-temporal EEG dynamics of speech discrimination processing in infants during sleep

BACKGROUND: Oddball paradigms are frequently used to study auditory discrimination by comparing event-related potential (ERP) responses from a standard, high probability sound and to a deviant, low probability sound. Previous research has established that such paradigms, such as the mismatch response or mismatch negativity, are useful for examining auditory processes in young children and infants across various sleep and attention states. The extent to which oddball ERP responses may reflect subtle discrimination effects, such as speech discrimination, is largely unknown, especially in infants that have not yet acquired speech and language. RESULTS: Mismatch responses for three contrasts (non-speech, vowel, and consonant) were computed as a spectral-temporal probability function in 24 infants, and analyzed at the group level by a modified multidimensional scaling. Immediately following an onset gamma response (30-50 Hz), the emergence of a beta oscillation (12-30 Hz) was temporally coupled with a lower frequency theta oscillation (2-8 Hz). The spectral-temporal probability of this coupling effect relative to a subsequent theta modulation corresponds with discrimination difficulty for non-speech, vowel, and consonant contrast features. DISCUSSION: The theta modulation effect suggests that unexpected sounds are encoded as a probabilistic measure of surprise. These results support the notion that auditory discrimination is driven by the development of brain networks for predictive processing, and can be measured in infants during sleep. The results presented here have implications for the interpretation of discrimination as a probabilistic process, and may provide a basis for the development of single-subject and single-trial classification in a clinically useful context. CONCLUSION: An infant's brain is processing information about the environment and performing computations, even during sleep. These computations reflect subtle differences in acoustic feature processing that are necessary for language-learning. Results from this study suggest that brain responses to deviant sounds in an oddball paradigm follow a cascade of oscillatory modulations. This cascade begins with a gamma response that later emerges as a beta synchronization, which is temporally coupled with a theta modulation, and followed by a second, subsequent theta modulation. The difference in frequency and timing of the theta modulations appears to reflect a measure of surprise. These insights into the neurophysiological mechanisms of auditory discrimination provide a basis for exploring the clinically utility of the MM

Cardiopoietic cell therapy for advanced ischemic heart failure: results at 39 weeks of the prospective, randomized, double blind, sham-controlled CHART-1 clinical trial

Cardiopoietic cells, produced through cardiogenic conditioning of patients' mesenchymal stem cells, have shown preliminary efficacy. The Congestive Heart Failure Cardiopoietic Regenerative Therapy (CHART-1) trial aimed to validate cardiopoiesis-based biotherapy in a larger heart failure cohort

The clinician and estimation of glomerular filtration rate by creatinine-based formulas: current limitations and quo vadis

Item does not contain fulltextThe GFR has a paramount diagnostic and staging role in the Kidney Disease Outcome Quality Initiative Clinical Practice Guidelines for Chronic Kidney Disease (K/DOQI-CKD). The most widely used serum creatinine-based formulas in adults for estimated GFR (eGFR) are the Cockcroft-Gault (CG) and Modification of Diet in Renal Disease Study (MDRD). Recently, a new Chronic Kidney Disease Epidemiology Collaboration equation has been developed. Review of the literature revealed that CG and MDRD formulas correctly assigned overall only 64% and 62%, respectively, of the subjects to their actual K/DOQI-CKD classification's GFR groups as determined by measured GFR (mGFR). This suggests that approximately 10 million (38%) subjects may have been misclassified on the basis of estimated CKD prevalence of 26.3 million adults in the United States. The purpose of this review is to help the clinician understand the limitations of using eGFR in daily practice. We also elaborate upon issues such as the differences among markers of mGFR, the validity of adjusting GFR for body surface area in certain populations, the limited data on boundaries for normal mGFR according to age, gender, and race, the need for calibration of a wide spectrum of serum creatinine measurements, the lack of actual eGFR value above 60 ml/min per 1.73 m(2) and reference for normal mGFR in the clinical laboratories' reports, and the performance evaluation of the eGFR formulas. Several pitfalls have to be overcome before we can reliably determine health and disease in daily nephrology practice to preserve the first rule of practicing medicine: primum non nocere