Piecewise polynomial approximation of probability density functions with application to uncertainty quantification for stochastic PDEs

The probability density function (PDF) associated with a given set of samples is approximated by a piecewise-linear polynomial constructed with respect to a binning of the sample space. The kernel functions are a compactly supported basis for the space of such polynomials, i.e. finite element hat functions, that are centered at the bin nodes rather than at the samples, as is the case for the standard kernel density estimation approach. This feature naturally provides an approximation that is scalable with respect to the sample size. On the other hand, unlike other strategies that use a finite element approach, the proposed approximation does not require the solution of a linear system. In addition, a simple rule that relates the bin size to the sample size eliminates the need for bandwidth selection procedures. The proposed density estimator has unitary integral, does not require a constraint to enforce positivity, and is consistent. The proposed approach is validated through numerical examples in which samples are drawn from known PDFs. The approach is also used to determine approximations of (unknown) PDFs associated with outputs of interest that depend on the solution of a stochastic partial differential equation

Исправление к статье «Бифункциональные хелаторы к катиону галлия»

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Бифункциональные хелаторы к катиону галлия

Objectives. The chemistry of 67Ga and 68Ga radionuclides plays a key role in nuclear medicine for applications in radiopharmaceuticals, in particular, in noninvasive in vivo molecular imaging techniques. The use of radiometals for labeling biomolecules typically requires the use of bifunctional chelators, which contain a functional group for covalent bonding with the targeting vector in addition to the polydentate fragment coordinating the metal. The aim of the present review article is to analyze the currently accumulated experimental material on the development and application of bifunctional chelators of gallium cations in medical research, as well as to identify the main requirements for the structure of the chelator and its complexes with 68Ga, which are used to create effective Gabased pharmaceutical preparations.Results. The review analyzed macrocyclic bifunctional chelators forming stable in vivo complexes with 68Ga and acyclic chelators, whose main advantage is faster complexation kinetics due to the short half-life of 68Ga. The advantages and disadvantages of both types of ligands were evaluated. In addition, a critical analysis of the binding constants and the conditions for the formation of complexes was presented. Examples of the influence of the geometry, lipophilicity, and total charge of the metal complex on the biodistribution of target radiopharmaceuticals were also given.Conclusions. Despite the progress made in the considered areas of bifunctional chelators, the problem of correlating the chemical structure of a metal-based radiopharmaceutical with its behavior in vivo remains important. Comparative studies of drugs having an identical targeting vector but containing different bifunctional chelating agents could help further elucidate the effectof metal chelate moiety on pharmacokinetics. In order to create effective bifunctional chelating agents, it is necessary to take into account such factors as the stability and inertness of the chelator and its complexes under physiological conditions, lipophilicity, complexation kinetics, chelation selectivity, combinatoriality of the basic structure, along with economic aspects, e.g., the availability of raw materials and the complexity of the synthesis scheme.Цели. Химия радионуклидов 67Ga и 68Ga играет одну из ключевых ролей в ядерной медици­не для применения в радиофармпрепаратах, в частности, в неинвазивных методах мо­лекулярной визуализации in vivo. Использование радиометаллов для мечения биомолекул обычно требует использования бифункциональных хелаторов, которые, кроме полиден­татного фрагмента, координирующего металл, содержат функциональную группу для ковалентного связывания с вектором-мишенью. Цели данного обзора – проанализировать накопленный к настоящему времени экспериментальный материал, касающийся разра­ботки и применения в медицинских исследованиях бифункциональных хелаторов к кати­ону галлия, а также выявить и проанализировать основные требования, предъявляемые к структуре хелатора и его комплексов с 68Ga, необходимые для создания эффективных фармакологических препаратов на его основе.Результаты. Рассмотрены макроциклические бифункциональные хелаторы, образую­щие стабильные in vivo комплексы с 68Ga, а также ациклические хелаторы, преимуще­ство которых заключается в более быстрой кинетике комплексообразования, что явля­ется ключевым фактором, учитывающим короткий период полураспада 68Ga. Проведена оценка достоинств и недостатков обоих типов лигандов. Кроме того, осуществлен кри­тический анализ констант связывания и условий образования комплексов. Рассмотрены примеры влияния природы металлического комплекса (геометрия, липофильность, об­щий заряд) на биораспределение целевых радиофармацевтических препаратов.Выводы. Несмотря на достигнутые успехи в рассмотренных направлениях создания би­фунциональных хелаторов, по-прежнему важной остается проблема корреляции хими­ческой структуры радиофармпрепаратов на основе металлов с их поведением in vivo. В этом отношении сравнительные исследования препаратов, имеющих идентичный вектор нацеливания, но включающих разные бифункциональные хелатируюшие агенты, могут помочь в дальнейшем выявлении влияния металл-хелатного фрагмента на фар­макокинетику. В целом можно отметить, что для создания эффективного бифункци­онального хелатирующего агента нужно принимать во внимание целую совокупность факторов, включающую стабильность и инертность хелатора и его комплексов в физиологических условиях, липофильность, кинетику комплексообразования, селективность хеланирования, комбинаторность базовой структуры, а также экономические аспекты: доступность сырья, сложность схемы синтеза

Recognizing Interactions Between People from Video Sequences

his research study proposes a new approach to group activ- ity recognition which is fully automatic. The approach adopted is hierar- chical, starting with tracking and modelling local movement leading to the segmentation of moving regions. Interactions between moving regions are modelled using Kullback-Leibler (KL) divergence. Then the statistics of such movement interactions or as relative positions of moving regions is represented using kernel density estimation (KDE). The dynamics of such movement interactions and relative locations is modelled as well in a development of the approach. Eventually, the KDE representations are subsampled and considered as inputs of a support vector machines (SVM) classifier. The proposed approach does not require any interven- tion by an operato

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

Factors affecting glomerular filtration rate, as measured by iohexol disappearance, in men with or at risk for HIV infection

Objective: Formulae used to estimate glomerular filtration rate (GFR) underestimate higher GFRs and have not been well-studied in HIV-infected (HIV(+)) people; we evaluated the relationships of HIV infection and known or potential risk factors for kidney disease with directly measured GFR and the presence of chronic kidney disease (CKD). Design: Cross-sectional measurement of iohexol-based GFR (iGFR) in HIV(+) men (n = 455) receiving antiretroviral therapy, and HIV-uninfected (HIV(-)) men (n = 258) in the Multicenter AIDS Cohort Study. Methods: iGFR was calculated from disappearance of infused iohexol from plasma. Determinants of GFR and the presence of CKD were compared using iGFR and GFR estimated by the CKD-Epi equation (eGFR). Results: Median iGFR was higher among HIV(+) than HIV(-) men (109 vs. 106 ml/min/1.73 m2, respectively, p = .046), and was 7 ml/min higher than median eGFR. Mean iGFR was lower in men who were older, had chronic hepatitis C virus (HCV) infection, or had a history of AIDS. Low iGFR (≤90 ml/min/1.73 m2) was associated with these factors and with black race. Other than age, factors associated with low iGFR were not observed with low eGFR. CKD was more common in HIV(+) than HIV(-) men; predictors of CKD were similar using iGFR and eGFR. Conclusions: iGFR was higher than eGFR in this population of HIV-infected and -uninfected men who have sex with men. Presence of CKD was predicted equally well by iGFR and eGFR, but associations of chronic HCV infection and history of clinically-defined AIDS with mildly decreased GFR were seen only with iGFR. © 2014 Margolick et al

Automatic Mapping of Discontinuity Persistence on Rock Masses Using 3D Point Clouds

Finding new ways to quantify discontinuity persistence values in rock masses in an automatic or semi-automatic manner is a considerable challenge, as an alternative to the use of traditional methods based on measuring patches or traces with tapes. Remote sensing techniques potentially provide new ways of analysing visible data from the rock mass. This work presents a methodology for the automatic mapping of discontinuity persistence on rock masses, using 3D point clouds. The method proposed herein starts by clustering points that belong to patches of a given discontinuity. Coplanar clusters are then merged into a single group of points. Persistence is measured in the directions of the dip and strike for each coplanar set of points, resulting in the extraction of the length of the maximum chord and the area of the convex hull. The proposed approach is implemented in a graphic interface with open source software. Three case studies are utilized to illustrate the methodology: (1) small-scale laboratory setup consisting of a regular distribution of cubes with similar dimensions, (2) more complex geometry consisting of a real rock mass surface in an excavated cavern and (3) slope with persistent sub-vertical discontinuities. Results presented good agreement with field measurements, validating the methodology. Complexities and difficulties related to the method (e.g. natural discontinuity waviness) are reported and discussed. An assessment on the applicability of the method to the 3D point cloud is also presented. Utilization of remote sensing data for a more objective characterization of the persistence of planar discontinuities affecting rock masses is highlighted herein

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