Certified Rapid Solution of Parametrized Linear Elliptic Equations: Application to Parameter Estimation

We present a technique for the rapid and reliable evaluation of linear-functional output of elliptic partial differential equations with affine parameter dependence. The essential components are (i) rapidly uniformly convergent reduced-basis approximations — Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N (optimally) selected points in parameter space; (ii) a posteriori error estimation — relaxations of the residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs; and (iii) offline/online computational procedures — stratagems that exploit affine parameter dependence to de-couple the generation and projection stages of the approximation process. The operation count for the online stage — in which, given a new parameter value, we calculate the output and associated error bound — depends only on N (typically small) and the parametric complexity of the problem. The method is thus ideally suited to the many-query and real-time contexts. In this paper, based on the technique we develop a robust inverse computational method for very fast solution of inverse problems characterized by parametrized partial differential equations. The essential ideas are in three-fold: first, we apply the technique to the forward problem for the rapid certified evaluation of PDE input-output relations and associated rigorous error bounds; second, we incorporate the reduced-basis approximation and error bounds into the inverse problem formulation; and third, rather than regularize the goodness-of-fit objective, we may instead identify all (or almost all, in the probabilistic sense) system configurations consistent with the available experimental data — well-posedness is reflected in a bounded "possibility region" that furthermore shrinks as the experimental error is decreased.

On the dominance of roots of characteristic equations for neutral functional differential equations

We present a sufficient condition for a zero of a function that arises typically as the characteristic equation of a linear functional differential equations of neutral type, to be simple and dominant. This knowledge is useful in order to derive the asymptotic behaviour of solutions of such equations. A simple characteristic equation, arisen from the study of delay equations with small delay, is analyzed in greater detail. (C) 2009 Elsevier Inc. All rights reserved.

Programação linear por partes: revisão teórica e aplicações

Procura-se resgatar a importância de uma subárea da Programação Matemática conhecida como Programação Linear Por Partes - PLP. de fato a PLP tem inúmeras aplicações tanto na área teórica como em situações reais. Este trabalho apresenta os resultados de uma pesquisa bibliográfica, efetuada nas principais revistas técnicas e livros disponíveis relacionados com Pesquisa Operacional, que visou situar o estado da'arte da Programação Linear por Partes, bem como a abrangência de sua aplicabilidade. Particularmente, no contexto da PLP, este texto deslaca a Programação em Redes Lineares por Partes devido a sua relevância em muitas situações práticas.

Frequency-domain source localization shows state-dependent diazepam effects in 47-channel EEG

The topic of this study was to evaluate state-dependent effects of diazepam on the frequency characteristics of 47-channel spontaneous EEG maps. A novel method, the FFT-Dipole-Approximation (Lehmann and Michel, 1990), was used to study effects on the strength and the topography of the maps in the different frequency bands. Map topography was characterized by the 3-dimensional location of the equivalent dipole source and map strength was defined as the spatial standard deviation (the Global Field Power) of the maps of each frequency point. The Global Field Power can be considered as a measure of the amount of energy produced by the system, while the source location gives an estimate of the center of gravity of all sources in the brain that were active at a certain frequency. State-dependency was studied by evaluating the drug effects before and after a continuous performance task of 25 min duration. Clear interactions between drug (diazepam vs. placebo) and time after drug intake (before and after the task) were found, especially in the inferior-superior location of the dipole sources. It supports the hypothesis that diazepam, like other drugs, has different effects on brain functions depending on the momentary functional state of the brain. In addition to the drug effects, clearly different source locations and Global Field Power were found for the different frequency bands, replicating earlier reports (Michel et al., 1992).

Low resolution brain electromagnetic tomography (LORETA) functional imaging in acute, neuroleptic-naive, first-episode, productive schizophrenia

Functional imaging of brain electrical activity was performed in nine acute, neuroleptic-naive, first-episode, productive patients with schizophrenia and 36 control subjects. Low-resolution electromagnetic tomography (LORETA, three-dimensional images of cortical current density) was computed from 19-channel of electroencephalographic (EEG) activity obtained under resting conditions, separately for the different EEG frequencies. Three patterns of activity were evident in the patients: (1) an anterior, near-bilateral excess of delta frequency activity; (2) an anterior-inferior deficit of theta frequency activity coupled with an anterior-inferior left-sided deficit of alpha-1 and alpha-2 frequency activity; and (3) a posterior-superior right-sided excess of beta-1, beta-2 and beta-3 frequency activity. Patients showed deviations from normal brain activity as evidenced by LORETA along an anterior-left-to-posterior-right spatial axis. The high temporal resolution of EEG makes it possible to specify the deviations not only as excess or deficit, but also as inhibitory, normal and excitatory. The patients showed a dis-coordinated brain functional state consisting of inhibited prefrontal/frontal areas and simultaneously overexcited right parietal areas, while left anterior, left temporal and left central areas lacked normal routine activity. Since all information processing is brain-state dependent, this dis-coordinated state must result in inadequate treatment of (externally or internally generated) information.

The functional significance of EEG microstates-Associations with modalities of thinking

The momentary, global functional state of the brain is reflected by its electric field configuration. Cluster analytical approaches consistently extracted four head-surface brain electric field configurations that optimally explain the variance of their changes across time in spontaneous EEG recordings. These four configurations are referred to as EEG microstate classes A, B, C, and D and have been associated with verbal/phonological, visual, attention reorientation, and subjective interoceptive-autonomic processing, respectively. The present study tested these associations via an intra-individual and inter-individual analysis approach. The intra-individual approach tested the effect of task-induced increased modality-specific processing on EEG microstate parameters. The inter-individual approach tested the effect of personal modality-specific parameters on EEG microstate parameters. We obtained multichannel EEG from 61 healthy, right-handed, male students during four eyes-closed conditions: object-visualization, spatial-visualization, verbalization (6 runs each), and resting (7 runs). After each run, we assessed participants' degrees of object-visual, spatial-visual, and verbal thinking using subjective reports. Before and after the recording, we assessed modality-specific cognitive abilities and styles using nine cognitive tests and two questionnaires. The EEG of all participants, conditions, and runs was clustered into four classes of EEG microstates (A, B, C, and D). RMANOVAs, ANOVAs and post-hoc paired t-tests compared microstate parameters between conditions. TANOVAs compared microstate class topographies between conditions. Differences were localized using eLORETA. Pearson correlations assessed interrelationships between personal modality-specific parameters and EEG microstate parameters during no-task resting. As hypothesized, verbal as opposed to visual conditions consistently affected the duration, occurrence, and coverage of microstate classes A and B. Contrary to associations suggested by previous reports, parameters were increased for class A during visualization, and class B during verbalization. In line with previous reports, microstate D parameters were increased during no-task resting compared to the three internal, goal-directed tasks. Topographic differences between conditions concerned particular sub-regions of components of the metabolic default mode network. Modality-specific personal parameters did not consistently correlate with microstate parameters except verbal cognitive style which correlated negatively with microstate class A duration and positively with class C occurrence. This is the first study that aimed to induce EEG microstate class parameter changes based on their hypothesized functional significance. Beyond, the associations of microstate classes A and B with visual and verbal processing, respectively and microstate class D with interoceptive-autonomic processing, our results suggest that a finely-tuned interplay between all four EEG microstate classes is necessary for the continuous formation of visual and verbal thoughts, as well as interoceptive-autonomic processing. Our results point to the possibility that the EEG microstate classes may represent the head-surface measured activity of intra-cortical sources primarily exhibiting inhibitory functions. However, additional studies are needed to verify and elaborate on this hypothesis.

Quantitative assessment based on kinematic measures of functional impairments during upper extremity movements: a review

Quantitative measures of human movement quality are important for discriminating healthy and pathological conditions and for expressing the outcomes and clinically important changes in subjects' functional state. However the most frequently used instruments for the upper extremity functional assessment are clinical scales, that previously have been standardized and validated, but have a high subjective component depending on the observer who scores the test. But they are not enough to assess motor strategies used during movements, and their use in combination with other more objective measures is necessary. The objective of the present review is to provide an overview on objective metrics found in literature with the aim of quantifying the upper extremity performance during functional tasks, regardless of the equipment or system used for registering kinematic data.

Functional polymers for biomedical application : synthesis and applications

Aromatic and aliphatic diacid chlorides were used to condense naturally occurring diamino acids and their esterified derivatives. It was anticipated the resulting functional polyamides would biodegrade to physiologically acceptable compounds and show pH dependant solubility could be used for biomedical applications ranging from enteric coatings to hydrosoluble drug delivery vehicles capable of targeting areas of low physiological pH. With these applications in mind the polymers were characterised by infra red spectroscopy, gel permeation chromatography and in the case of aqueous soluble polymers by potentiometric titration. Thin films of poly (lysine ethyl ester isophthalamide) plasticised with poly (caprolactone) were cast from DMSO/chloroform solutions and their mechanical properties measured on a Hounsfield Hti tensiometer. Interfacial synthesis was investigated as a synthetic route for the production of linear functional polyamides. High molecular weight polymer was obtained only when esterified diamino acids were condensed with aromatic diacid chlorides. The method was unsuitable for the production of copolymers of free and esterified amino acids with a diacid chloride. A novel miscible mixed solvent single phase reaction was investigated for production of copolymers of esterified and non-esterified amino acids with diacid chlorides. Aliphatic diacid chlorides were unsuitable for condensing diamino acids using this technique because of high rates of hydrolysis. The technique gave high molecular weight homopolymers from esterified diamino acids and aromatic diacid chlorides.

RELIBILITY ANALYSIS OF SIMPLE SLOPES AND SOIL-STRUCTURES WITH LINEAR LIMIT STATES

The first objective of this research was to develop closed-form and numerical probabilistic methods of analysis that can be applied to otherwise conventional methods of unreinforced and geosynthetic reinforced slopes and walls. These probabilistic methods explicitly include random variability of soil and reinforcement, spatial variability of the soil, and cross-correlation between soil input parameters on probability of failure. The quantitative impact of simultaneously considering the influence of random and/or spatial variability in soil properties in combination with cross-correlation in soil properties is investigated for the first time in the research literature. Depending on the magnitude of these statistical descriptors, margins of safety based on conventional notions of safety may be very different from margins of safety expressed in terms of probability of failure (or reliability index). The thesis work also shows that intuitive notions of margin of safety using conventional factor of safety and probability of failure can be brought into alignment when cross-correlation between soil properties is considered in a rigorous manner. The second objective of this thesis work was to develop a general closed-form solution to compute the true probability of failure (or reliability index) of a simple linear limit state function with one load term and one resistance term expressed first in general probabilistic terms and then migrated to a LRFD format for the purpose of LRFD calibration. The formulation considers contributions to probability of failure due to model type, uncertainty in bias values, bias dependencies, uncertainty in estimates of nominal values for correlated and uncorrelated load and resistance terms, and average margin of safety expressed as the operational factor of safety (OFS). Bias is defined as the ratio of measured to predicted value. Parametric analyses were carried out to show that ignoring possible correlations between random variables can lead to conservative (safe) values of resistance factor in some cases and in other cases to non-conservative (unsafe) values. Example LRFD calibrations were carried out using different load and resistance models for the pullout internal stability limit state of steel strip and geosynthetic reinforced soil walls together with matching bias data reported in the literature.

Neurochemical regulation of auditory information processing studied with EEG/MEG: application to schizophrenia

Cognitive impairments of attention, memory and executive functions are a fundamental feature of the pathophysiology of schizophrenia. The neurophysiological and neurochemical changes in the auditory cortex are shown to underlie cognitive impairmentsin schizophrenia patients. Functional state of the neural substrate of auditory information processing could be objectively and non-invasively probed with auditory event-related potentials (ERPs) and event- related fields (ERFs). In the current work, we explored the neurochemical effect on the neural origins of auditory information processing in relation to schizophrenia. By means of ERPs/ERFs we aimed to determine how neural substrates of auditory information processing are modulated by antipsychotic medication in schizophrenia spectrum patients (Studies I, II) and by neuropharmacological challenges in healthy human subjects (Studies III, IV). First, with auditory ERPs we investigated the effects of olanzapine (Study I) and risperidone (Study II) in a group of patients with schizophrenia spectrum disorders. After 2 and 4 weeks of treatment, olanzapine has no significant effects on mismatch negativity(MMN) and P300, which, as it has been suggested, respectively reflect preattentive and attention-dependent information processing. After 2 weeks of treatment, risperidone has no significant effect on P300, however risperidone reduces P200 amplitude. This latter effect of risperidone on neural resources responsible for P200 generation could be partly explained through the action of dopamine. Subsequently, we used simultaneous EEG/MEG to investigate the effects of memantine (Study III) and methylphenidate (Study IV) in healthy subjects. We found that memantine modulates MMN response without changing other ERP components. This could be interpreted as being due to the possible influence of memantine through the NMDA receptors on auditory change- detection mechanism, with processing of auditory stimuli remaining otherwise unchanged. Further, we found that methylphenidate does not modulate the MMN response. This finding could indicate no association between catecholaminergic activities and electrophysiological measures of preattentive auditory discrimination processes reflected in the MMN. However, methylphenidate decreases the P200 amplitudes. This could be interpreted as a modulation of auditory information processing reflected in P200 by dopaminergic and noradrenergic systems. Taken together, our set of studies indicates a complex pattern of neurochemical influences produced by the antipsychotic drugs in the neural substrate of auditory information processing in patients with schizophrenia spectrum disorders and by the pharmacological challenges in healthy subjects studied with ERPs and ERFs.

Single nucleotide polymorphisms in genes that are common targets of luteotropin and luteolysin in primate corpus luteum: Computational exploration

Luteal insufficiency affects fertility and hence study of mechanisms that regulate corpus luteum (CL) function is of prime importance to overcome infertility problems. Exploration of human genome sequence has helped to study the frequency of single nucleotide polymorphisms (SNPs). Clinical benefits of screening SNPs in infertility are being recognized well in recent times. Examining SNPs in genes associated with maintenance and regression of CL may help to understand unexplained luteal insufficiency and related infertility. Publicly available microarray gene expression databases reveal the global gene expression patterns in primate CL during the different functional state. We intend to explore computationally the deleterious SNPs of human genes reported to be common targets of luteolysin and luteotropin in primate CL Different computational algorithms were used to dissect out the functional significance of SNPs in the luteinizing hormone sensitive genes. The results raise the possibility that screening for SNPs might be integrated to evaluate luteal insufficiency associated with human female infertility for future studies. (C) 2012 Elsevier B.V. All rights reserved,

Time variant reliability model updating in instrumented dynamical systems based on Girsanov's transformation

The problem of updating the reliability of instrumented structures based on measured response under random dynamic loading is considered. A solution strategy within the framework of Monte Carlo simulation based dynamic state estimation method and Girsanov's transformation for variance reduction is developed. For linear Gaussian state space models, the solution is developed based on continuous version of the Kalman filter, while, for non-linear and (or) non-Gaussian state space models, bootstrap particle filters are adopted. The controls to implement the Girsanov transformation are developed by solving a constrained non-linear optimization problem. Numerical illustrations include studies on a multi degree of freedom linear system and non-linear systems with geometric and (or) hereditary non-linearities and non-stationary random excitations.

Dynamics and Regulation of RecA Polymerization and De-Polymerization on Double-Stranded DNA

The RecA filament formed on double-stranded (ds) DNA is proposed to be a functional state analogous to that generated during the process of DNA strand exchange. RecA polymerization and de-polymerization on dsDNA is governed by multiple physiological factors. However, a comprehensive understanding of how these factors regulate the processes of polymerization and de-polymerization of RecA filament on dsDNA is still evolving. Here, we investigate the effects of temperature, pH, tensile force, and DNA ends (in particular ssDNA overhang) on the polymerization and de-polymerization dynamics of the E. coli RecA filament at a single-molecule level. Our results identified the optimal conditions that permitted spontaneous RecA nucleation and polymerization, as well as conditions that could maintain the stability of a preformed RecA filament. Further examination at a nano-meter spatial resolution, by stretching short DNA constructs, revealed a striking dynamic RecA polymerization and de-polymerization induced saw-tooth pattern in DNA extension fluctuation. In addition, we show that RecA does not polymerize on S-DNA, a recently identified novel base-paired elongated DNA structure that was previously proposed to be a possible binding substrate for RecA. Overall, our studies have helped to resolve several previous single-molecule studies that reported contradictory and inconsistent results on RecA nucleation, polymerization and stability. Furthermore, our findings also provide insights into the regulatory mechanisms of RecA filament formation and stability in vivo.

Time variant reliability model updating in instrumented dynamical systems based on Girsanov’s transformation

The problem of updating the reliability of instrumented structures based on measured response under random dynamic loading is considered. A solution strategy within the framework of Monte Carlo simulation based dynamic state estimation method and Girsanov’s transformation for variance reduction is developed. For linear Gaussian state space models, the solution is developed based on continuous version of the Kalman filter, while, for non-linear and (or) non-Gaussian state space models, bootstrap particle filters are adopted. The controls to implement the Girsanov transformation are developed by solving a constrained non-linear optimization problem. Numerical illustrations include studies on a multi degree of freedom linear system and non-linear systems with geometric and (or) hereditary non-linearities and non-stationary random excitations.

A Gaussian network model study suggests that structural fluctuations are higher for inactive states than active states of protein kinases

We performed Gaussian network model based normal mode analysis of 3-dimensional structures of multiple active and inactive forms of protein kinases. In 14 different kinases, a more number of residues (1095) show higher structural fluctuations in inactive states than those in active states (525), suggesting that, in general, mobility of inactive states is higher than active states. This statistically significant difference is consistent with higher crystallographic B-factors and conformational energies for inactive than active states, suggesting lower stability of inactive forms. Only a small number of inactive conformations with the DFG motif in the ``in'' state were found to have fluctuation magnitudes comparable to the active conformation. Therefore our study reports for the first time, intrinsic higher structural fluctuation for almost all inactive conformations compared to the active forms. Regions with higher fluctuations in the inactive states are often localized to the aC-helix, aG-helix and activation loop which are involved in the regulation and/or in structural transitions between active and inactive states. Further analysis of 476 kinase structures involved in interactions with another domain/protein showed that many of the regions with higher inactive-state fluctuation correspond to contact interfaces. We also performed extensive GNM analysis of (i) insulin receptor kinase bound to another protein and (ii) holo and apo forms of active and inactive conformations followed by multi-factor analysis of variance. We conclude that binding of small molecules or other domains/proteins reduce the extent of fluctuation irrespective of active or inactive forms. Finally, we show that the perceived fluctuations serve as a useful input to predict the functional state of a kinase.