Non-classical error bounds in the central limit theorem

The classical central limit theorem states the uniform convergence of the distribution functions of the standardized sums of independent and identically distributed square integrable real-valued random variables to the standard normal distribution function. While first versions of the central limit theorem are already due to Moivre (1730) and Laplace (1812), a systematic study of this topic started at the beginning of the last century with the fundamental work of Lyapunov (1900, 1901). Meanwhile, extensions of the central limit theorem are available for a multitude of settings. This includes, e.g., Banach space valued random variables as well as substantial relaxations of the assumptions of independence and identical distributions. Furthermore, explicit error bounds are established and asymptotic expansions are employed to obtain better approximations. Classical error estimates like the famous bound of Berry and Esseen are stated in terms of absolute moments of the random summands and therefore do not reflect a potential closeness of the distributions of the single random summands to a normal distribution. Non-classical approaches take this issue into account by providing error estimates based on, e.g., pseudomoments. The latter field of investigation was initiated by work of Zolotarev in the 1960's and is still in its infancy compared to the development of the classical theory. For example, non-classical error bounds for asymptotic expansions seem not to be available up to now ...

Mitochondrial localization ot two brain proteins, p42IP4/centaurin-[alpha]1/ADAP1 and CNP, and their involvement in regulation of mitochondrial Ca 2+

Magdeburg, Univ., Fak. für Naturwiss., Diss., 2010

A comparative analysis of Cobb-Douglas model with additive and multiplicative error

This paper dis cusses the fitting of a Cobb-Doug las response curve Yi = αXβi, with additive error, Yi = αXβi + e i, instead of the usual multiplicative error Yi = αXβi (1 + e i). The estimation of the parameters A and B is discussed. An example is given with use of both types of error.

Stability and error analysis for a numerical scheme to approximate elastic flow

Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, Univ., Dissertation, 2015

Restriction site-associated DNA sequencing, genotyping error estimation and de novo assembly optimization for population genetic inference.

Restriction site-associated DNA sequencing (RADseq) provides researchers with the ability to record genetic polymorphism across thousands of loci for nonmodel organisms, potentially revolutionizing the field of molecular ecology. However, as with other genotyping methods, RADseq is prone to a number of sources of error that may have consequential effects for population genetic inferences, and these have received only limited attention in terms of the estimation and reporting of genotyping error rates. Here we use individual sample replicates, under the expectation of identical genotypes, to quantify genotyping error in the absence of a reference genome. We then use sample replicates to (i) optimize de novo assembly parameters within the program Stacks, by minimizing error and maximizing the retrieval of informative loci; and (ii) quantify error rates for loci, alleles and single-nucleotide polymorphisms. As an empirical example, we use a double-digest RAD data set of a nonmodel plant species, Berberis alpina, collected from high-altitude mountains in Mexico.

The role of the right parietal cortex in sound localization: a chronometric single pulse transcranial magnetic stimulation study.

Auditory spatial functions, including the ability to discriminate between the positions of nearby sound sources, are subserved by a large temporo-parieto-frontal network. With the aim of determining whether and when the parietal contribution is critical for auditory spatial discrimination, we applied single pulse transcranial magnetic stimulation on the right parietal cortex 20, 80, 90 and 150 ms post-stimulus onset while participants completed a two-alternative forced choice auditory spatial discrimination task in the left or right hemispace. Our results reveal that transient TMS disruption of right parietal activity impairs spatial discrimination when applied at 20 ms post-stimulus onset for sounds presented in the left (controlateral) hemispace and at 80 ms for sounds presented in the right hemispace. We interpret our finding in terms of a critical role for controlateral temporo-parietal cortices over initial stages of the building-up of auditory spatial representation and for a right hemispheric specialization in integrating the whole auditory space over subsequent, higher-order processing stages.

Localization of algebras over coloured operads

We give sufficient conditions for homotopical localization functors to preserve algebras over coloured operads in monoidal model categories. Our approach encompasses a number of previous results about preservation of structures under localizations, such as loop spaces or infinite loop spaces, and provides new results of the same kind. For instance, under suitable assumptions, homotopical localizations preserve ring spectra (in the strict sense, not only up to homotopy), modules over ring spectra, and algebras over commutative ring spectra, as well as ring maps, module maps, and algebra maps. It is principally the treatment of module spectra and their maps that led us to the use of coloured operads (also called enriched multicategories) in this context.

Ventricular arrhythmia in coronary artery disease: limits of a risk stratification strategy based on the ejection fraction alone and impact of infarct localization.

AIMS: Estimates of the left ventricular ejection fraction (LVEF) in patients with life-threatening ventricular arrhythmias related to coronary artery disease (CAD) have rarely been reported despite it has become the basis for determining patient's eligibility for prophylactic defibrillator. We aimed to determine the extent and distribution of reduced LVEF in patients with sustained ventricular tachycardia or ventricular fibrillation. METHODS AND RESULTS: 252 patients admitted for ventricular arrhythmia related to CAD were included: 149 had acute myocardial infarction (MI) (Group I, 59%), 54 had significant chronic obstructive CAD suggestive of an ischaemic arrhythmic trigger (Group II, 21%) and 49 patients had an old MI without residual ischaemia (Group III, 19%). 34% of the patients with scar-related arrhythmias had an LVEF > or =40%. Based on pre-event LVEF evaluation, it can be estimated that less than one quarter of the whole study population had a known chronic MI with severely reduced LVEF. In Group III, the proportion of inferior MI was significantly higher than anterior MI (81 vs. 19%; absolute difference, -62; 95% confidence interval, -45 to -79; P < or = 0.0001), though median LVEF was higher in inferior MI (0.37 +/- 10 vs. 0.29 +/- 10; P = 0.0499). CONCLUSION: Patients included in defibrillator trials represent only a minority of the patients at risk of sudden cardiac death. By applying the current risk stratification strategy based on LVEF, more than one third of the patients with old MI would not have qualified for a prophylactic defibrillator. Our study also suggests that inferior scars may be more prone to ventricular arrhythmia compared to anterior scars.

Stochastic Search Variable Selection in Vector Error Correction Models with an Application to a Model of the UK Macroeconomy

This paper develops methods for Stochastic Search Variable Selection (currently popular with regression and Vector Autoregressive models) for Vector Error Correction models where there are many possible restrictions on the cointegration space. We show how this allows the researcher to begin with a single unrestricted model and either do model selection or model averaging in an automatic and computationally efficient manner. We apply our methods to a large UK macroeconomic model.

Hemispheric competence for auditory spatial representation.

Sound localization relies on the analysis of interaural time and intensity differences, as well as attenuation patterns by the outer ear. We investigated the relative contributions of interaural time and intensity difference cues to sound localization by testing 60 healthy subjects: 25 with focal left and 25 with focal right hemispheric brain damage. Group and single-case behavioural analyses, as well as anatomo-clinical correlations, confirmed that deficits were more frequent and much more severe after right than left hemispheric lesions and for the processing of interaural time than intensity difference cues. For spatial processing based on interaural time difference cues, different error types were evident in the individual data. Deficits in discriminating between neighbouring positions occurred in both hemispaces after focal right hemispheric brain damage, but were restricted to the contralesional hemispace after focal left hemispheric brain damage. Alloacusis (perceptual shifts across the midline) occurred only after focal right hemispheric brain damage and was associated with minor or severe deficits in position discrimination. During spatial processing based on interaural intensity cues, deficits were less severe in the right hemispheric brain damage than left hemispheric brain damage group and no alloacusis occurred. These results, matched to anatomical data, suggest the existence of a binaural sound localization system predominantly based on interaural time difference cues and primarily supported by the right hemisphere. More generally, our data suggest that two distinct mechanisms contribute to: (i) the precise computation of spatial coordinates allowing spatial comparison within the contralateral hemispace for the left hemisphere and the whole space for the right hemisphere; and (ii) the building up of global auditory spatial representations in right temporo-parietal cortices.

Differential subcellular localization of phosphorylated neurofilament and tau proteins in degenerating neurons of the human entorhinal cortex.

A panel of novel monoclonal antibodies was tested on the human entorhinal cortex for the recognition of age- and disease-related changes of neurofilament proteins (NF). Several antibodies identified phosphorylated NF-H subunit, which occurred preferentially in those aged between 60 and 80 years and were localized in degenerating neurons. Such neurons also contained neurofibrillary tangles, but neurofilament aggregates did not co-localize with tangles, nor did the quantity nor the number of NF-positive neurons correlate with the severity of Alzheimer's disease. This points to a susceptibility of NF in a subset of neurons for phosphorylation- and metabolically related morphological changes during neurodegeneration.

Cell-specific localization of monocarboxylate transporters, MCT1 and MCT2, in the adult mouse brain revealed by double immunohistochemical labeling and confocal microscopy.

Recent evidence suggests that lactate could be a preferential energy substrate transferred from astrocytes to neurons. This would imply the presence of specific transporters for lactate on both cell types. We have investigated the immunohistochemical localization of two monocarboxylate transporters, MCT1 and MCT2, in the adult mouse brain. Using specific antibodies raised against MCT1 and MCT2, we found strong immunoreactivity for each transporter in glia limitans, ependymocytes and several microvessel-like elements. In addition, small processes distributed throughout the cerebral parenchyma were immunolabeled for monocarboxylate transporters. Double immunofluorescent labeling and confocal microscopy examination of these small processes revealed no co-localization between glial fibrillary acidic protein and monocarboxylate transporters, although many glial fibrillary acidic protein-positive processes were often in close apposition to elements labeled for monocarboxylate transporters. In contrast, several elements expressing the S100beta protein, another astrocytic marker found to be located in distinct parts of the same cell when compared with glial fibrillary acidic protein, were also strongly immunoreactive for MCT1, suggesting expression of this transporter by astrocytes. In contrast, MCT2 was expressed in a small subset of microtubule-associated protein-2-positive elements, indicating a neuronal localization. In conclusion, these observations are consistent with the possibility that lactate, produced and released by astrocytes (via MCT1), could be taken up (via MCT2) and used by neurons as an energy substrate.