Monte Carlo Algorithm for Solving Integral Equations with Polynomial Non-Linearity. Parallel Implementation

An iterative Monte Carlo algorithm for evaluating linear functionals of the solution of integral equations with polynomial non-linearity is proposed and studied. The method uses a simulation of branching stochastic processes. It is proved that the mathematical expectation of the introduced random variable is equal to a linear functional of the solution. The algorithm uses the so-called almost optimal density function. Numerical examples are considered. Parallel implementation of the algorithm is also realized using the package ATHAPASCAN as an environment for parallel realization.The computational results demonstrate high parallel efficiency of the presented algorithm and give a good solution when almost optimal density function is used as a transition density.

Essays on international macroeconomics and conflict analysis

This dissertation addressed two broad problems in international macroeconomics and conflict analysis. The first problem in the first chapter looked at the behavior of exchange rate and its interaction with industry-level tradable goods prices for three countries, USA, UK and Japan. This question has important monetary policy implications. Here, I computed to what extent changes in exchange rate affected prices of consumer, producer, and export goods. I also studied the timing of these changes in these prices. My results, based on thirty-four industrial prices for USA, UK and Japan, supported the view that changes in exchange rates significantly affect prices of industrial and consumer goods. It also provided an insight to the underlying economic process that led to changes in relative prices. ^ In the second chapter, I explored the predictability of future inflation by incorporating shocks to exchange rates and clearly specified the transmission mechanisms that link exchange rates to industry-level consumer and producer prices. Employing a variety of linear and state-of-the-art nonlinear models, I also predicted growth rates of future prices. Comparing levels of inflation obtained from the above approaches showed superiority of the structural model incorporating the exchange rate pass-through effect. ^ The second broad issue addressed in the third chapter of the dissertation investigated the economic motives for conflict, manifested by rebellion and civil war for seventeen Latin American countries. Based on the analytical framework of Garfinkel, Skaperdas and Syropoulos (2004), I employed ordinal regressions and Markov switching for a panel of seventeen countries to identify trade and openness factors responsible for conflict occurrence and intensity. The results suggested that increased trade openness reduced high intensity domestic conflicts but overdependence on agricultural exports, along with a lack of income earning opportunities lead to more conflicts. Thereafter, using the Cox Proportional Hazard model I studied “conflict duration” and found that over-reliance on agricultural exports explained a major part of the length of conflicts in addition to various socio-political factors. ^

Regenerative Cues of Myeloid Cells on Pancreatic Epithelium

Thesis (Ph.D.)--University of Washington, 2016-07

Role of membrane lipids in the regulation of erythrocytic oxygen-transport function in cardiovascular diseases

The composition and condition of membrane lipids, the morphology of erythrocytes, and hemoglobin distribution were explored with the help of laser interference microscopy (LIM) and Raman spectroscopy. It is shown that patients with cardiovascular diseases (CVD) have significant changes in the composition of their phospholipids and the fatty acids of membrane lipids. Furthermore, the microviscosity of the membranes and morphology of the erythrocytes are altered causing disordered oxygen transport by hemoglobin. Basic therapy carried out with the use of antiaggregants, statins, antianginals, beta-blockers, and calcium antagonists does not help to recover themorphofunctional properties of erythrocytes. Based on the results the authors assume that, for the relief of the ischemic crisis and further therapeutic treatment, it is necessary to include, in addition to cardiovascular disease medicines, medication that increases the ability of erythrocytes’ hemoglobin to transport oxygen to the tissues. We assume that the use of LIM and Raman spectroscopy is advisable for early diagnosis of changes in the structure and functional state of erythrocytes when cardiovascular diseases develop.

Lateralization of temporal lobe epilepsy based on resting-state functional magnetic resonance imaging and machine learning

Lateralization of temporal lobe epilepsy (TLE) is critical for successful outcome of surgery to relieve seizures. TLE affects brain regions beyond the temporal lobes and has been associated with aberrant brain networks, based on evidence from functional magnetic resonance imaging. We present here a machine learning-based method for determining the laterality of TLE, using features extracted from resting-state functional connectivity of the brain. A comprehensive feature space was constructed to include network properties within local brain regions, between brain regions, and across the whole network. Feature selection was performed based on random forest and a support vector machine was employed to train a linear model to predict the laterality of TLE on unseen patients. A leave-one-patient-out cross validation was carried out on 12 patients and a prediction accuracy of 83% was achieved. The importance of selected features was analyzed to demonstrate the contribution of resting-state connectivity attributes at voxel, region, and network levels to TLE lateralization.

Response of linear, viscous damped systems to excitations having time-varying frequency

The response of linear, viscous damped systems to excitations having time-varying frequency is the subject of exact and approximate analyses, which are supplemented by an analog computer study of single degree of freedom system response to excitations having frequencies depending linearly and exponentially on time.

The technique of small perturbations and the methods of stationary phase and saddle-point integration, as well as a novel bounding procedure, are utilized to derive approximate expressions characterizing the system response envelope—particularly near resonances—for the general time-varying excitation frequency.

Descriptive measurements of system resonant behavior recorded during the course of the analog study—maximum response, excitation frequency at which maximum response occurs, and the width of the response peak at the half-power level—are investigated to determine dependence upon natural frequency, damping, and the functional form of the excitation frequency.

The laboratory problem of determining the properties of a physical system from records of its response to excitations of this class is considered, and the transient phenomenon known as “ringing” is treated briefly.

It is shown that system resonant behavior, as portrayed by the above measurements and expressions, is relatively insensitive to the specifics of the excitation frequency-time relation and may be described to good order in terms of parameters combining system properties with the time derivative of excitation frequency evaluated at resonance.

One of these parameters is shown useful for predicting whether or not a given excitation having a time-varying frequency will produce strong or subtle changes in the response envelope of a given system relative to the steady-state response envelope. The parameter is shown, additionally, to be useful for predicting whether or not a particular response record will exhibit the “ringing” phenomenon.

A linear O(N) model: a functional renormalization group approach for flat and curved space

In questa tesi sono state applicate le tecniche del gruppo di rinormalizzazione funzionale allo studio della teoria quantistica di campo scalare con simmetria O(N) sia in uno spaziotempo piatto (Euclideo) che nel caso di accoppiamento ad un campo gravitazionale nel paradigma dell'asymptotic safety. Nel primo capitolo vengono esposti in breve alcuni concetti basilari della teoria dei campi in uno spazio euclideo a dimensione arbitraria. Nel secondo capitolo si discute estensivamente il metodo di rinormalizzazione funzionale ideato da Wetterich e si fornisce un primo semplice esempio di applicazione, il modello scalare. Nel terzo capitolo è stato studiato in dettaglio il modello O(N) in uno spaziotempo piatto, ricavando analiticamente le equazioni di evoluzione delle quantità rilevanti del modello. Quindi ci si è specializzati sul caso N infinito. Nel quarto capitolo viene iniziata l'analisi delle equazioni di punto fisso nel limite N infinito, a partire dal caso di dimensione anomala nulla e rinormalizzazione della funzione d'onda costante (approssimazione LPA), già studiato in letteratura. Viene poi considerato il caso NLO nella derivative expansion. Nel quinto capitolo si è introdotto l'accoppiamento non minimale con un campo gravitazionale, la cui natura quantistica è considerata a livello di QFT secondo il paradigma di rinormalizzabilità dell'asymptotic safety. Per questo modello si sono ricavate le equazioni di punto fisso per le principali osservabili e se ne è studiato il comportamento per diversi valori di N.

Abnormal left and right amygdala-orbitofrontal cortical functional connectivity to emotional faces:state versus trait vulnerability markers of depression in bipolar disorder

Background - Amygdala-orbitofrontal cortical (OFC) functional connectivity (FC) to emotional stimuli and relationships with white matter remain little examined in bipolar disorder individuals (BD). Methods - Thirty-one BD (type I; n = 17 remitted; n = 14 depressed) and 24 age- and gender-ratio-matched healthy individuals (HC) viewed neutral, mild, and intense happy or sad emotional faces in two experiments. The FC was computed as linear and nonlinear dependence measures between amygdala and OFC time series. Effects of group, laterality, and emotion intensity upon amygdala-OFC FC and amygdala-OFC FC white matter fractional anisotropy (FA) relationships were examined. Results - The BD versus HC showed significantly greater right amygdala-OFC FC (p = .001) in the sad experiment and significantly reduced bilateral amygdala-OFC FC (p = .007) in the happy experiment. Depressed but not remitted female BD versus female HC showed significantly greater left amygdala-OFC FC (p = .001) to all faces in the sad experiment and reduced bilateral amygdala-OFC FC to intense happy faces (p = .01). There was a significant nonlinear relationship (p = .001) between left amygdala-OFC FC to sad faces and FA in HC. In BD, antidepressants were associated with significantly reduced left amygdala-OFC FC to mild sad faces (p = .001). Conclusions - In BD, abnormally elevated right amygdala-OFC FC to sad stimuli might represent a trait vulnerability for depression, whereas abnormally elevated left amygdala-OFC FC to sad stimuli and abnormally reduced amygdala-OFC FC to intense happy stimuli might represent a depression state marker. Abnormal FC measures might normalize with antidepressant medications in BD. Nonlinear amygdala-OFC FC–FA relationships in BD and HC require further study.

Time-Dependent Density Functional Molecular Orbital and Excited State Calculations on Bis(porphyrinyl)butadiynes in the Monocationic, Neutral, Monoanionic, and Dianionic Oxidation States

We report a theoretical study of the multiple oxidation states (1+, 0, 1−, and 2−) of a meso,meso-linked diporphyrin, namely bis[10,15,20-triphenylporphyrinatozinc(II)-5-yl]butadiyne (4), using Time-Dependent Density Functional Theory (TDDFT). The origin of electronic transitions of singlet excited states is discussed in comparison to experimental spectra for the corresponding oxidation states of the close analogue bis{10,15,20-tris[3‘,5‘-di-tert-butylphenyl]porphyrinatozinc(II)-5-yl}butadiyne (3). The latter were measured in previous work under in situ spectroelectrochemical conditions. Excitation energies and orbital compositions of the excited states were obtained for these large delocalized aromatic radicals, which are unique examples of organic mixed-valence systems. The radical cations and anions of butadiyne-bridged diporphyrins such as 3 display characteristic electronic absorption bands in the near-IR region, which have been successfully predicted with use of these computational methods. The radicals are clearly of the “fully delocalized” or Class III type. The key spectral features of the neutral and dianionic states were also reproduced, although due to the large size of these molecules, quantitative agreement of energies with observations is not as good in the blue end of the visible region. The TDDFT calculations are largely in accord with a previous empirical model for the spectra, which was based simplistically on one-electron transitions among the eight key frontier orbitals of the C4 (1,4-butadiyne) linked diporphyrins.

Asset life prediction and maintenance decision-making using a non-linear non-Gaussian state space model

Estimating and predicting degradation processes of engineering assets is crucial for reducing the cost and insuring the productivity of enterprises. Assisted by modern condition monitoring (CM) technologies, most asset degradation processes can be revealed by various degradation indicators extracted from CM data. Maintenance strategies developed using these degradation indicators (i.e. condition-based maintenance) are more cost-effective, because unnecessary maintenance activities are avoided when an asset is still in a decent health state. A practical difficulty in condition-based maintenance (CBM) is that degradation indicators extracted from CM data can only partially reveal asset health states in most situations. Underestimating this uncertainty in relationships between degradation indicators and health states can cause excessive false alarms or failures without pre-alarms. The state space model provides an efficient approach to describe a degradation process using these indicators that can only partially reveal health states. However, existing state space models that describe asset degradation processes largely depend on assumptions such as, discrete time, discrete state, linearity, and Gaussianity. The discrete time assumption requires that failures and inspections only happen at fixed intervals. The discrete state assumption entails discretising continuous degradation indicators, which requires expert knowledge and often introduces additional errors. The linear and Gaussian assumptions are not consistent with nonlinear and irreversible degradation processes in most engineering assets. This research proposes a Gamma-based state space model that does not have discrete time, discrete state, linear and Gaussian assumptions to model partially observable degradation processes. Monte Carlo-based algorithms are developed to estimate model parameters and asset remaining useful lives. In addition, this research also develops a continuous state partially observable semi-Markov decision process (POSMDP) to model a degradation process that follows the Gamma-based state space model and is under various maintenance strategies. Optimal maintenance strategies are obtained by solving the POSMDP. Simulation studies through the MATLAB are performed; case studies using the data from an accelerated life test of a gearbox and a liquefied natural gas industry are also conducted. The results show that the proposed Monte Carlo-based EM algorithm can estimate model parameters accurately. The results also show that the proposed Gamma-based state space model have better fitness result than linear and Gaussian state space models when used to process monotonically increasing degradation data in the accelerated life test of a gear box. Furthermore, both simulation studies and case studies show that the prediction algorithm based on the Gamma-based state space model can identify the mean value and confidence interval of asset remaining useful lives accurately. In addition, the simulation study shows that the proposed maintenance strategy optimisation method based on the POSMDP is more flexible than that assumes a predetermined strategy structure and uses the renewal theory. Moreover, the simulation study also shows that the proposed maintenance optimisation method can obtain more cost-effective strategies than a recently published maintenance strategy optimisation method by optimising the next maintenance activity and the waiting time till the next maintenance activity simultaneously.

On optimal control of constrained linear systems with imperfect state information and stochastic disturbances

We address the problem of finite horizon optimal control of discrete-time linear systems with input constraints and uncertainty. The uncertainty for the problem analysed is related to incomplete state information (output feedback) and stochastic disturbances. We analyse the complexities associated with finding optimal solutions. We also consider two suboptimal strategies that could be employed for larger optimization horizons.

Heritability of head motion during resting state functional MRI in 462 healthy twins

Head motion (HM) is a critical confounding factor in functional MRI. Here we investigate whether HM during resting state functional MRI (RS-fMRI) is influenced by genetic factors in a sample of 462 twins (65% fema≤ 101 MZ (monozygotic) and 130 DZ (dizygotic) twin pairs; mean age: 21 (SD=3.16), range 16-29). Heritability estimates for three HM components-mean translation (MT), maximum translation (MAXT) and mean rotation (MR)-ranged from 37 to 51%. We detected a significant common genetic influence on HM variability, with about two-thirds (genetic correlations range 0.76-1.00) of the variance shared between MR, MT and MAXT. A composite metric (HM-PC1), which aggregated these three, was also moderately heritable (h2=42%). Using a sub-sample (N=35) of the twins we confirmed that mean and maximum translational and rotational motions were consistent "traits" over repeated scans (r=0.53-0.59); reliability was even higher for the composite metric (r=0.66). In addition, phenotypic and cross-trait cross-twin correlations between HM and resting state functional connectivities (RS-FCs) with Brodmann areas (BA) 44 and 45, in which RS-FCs were found to be moderately heritable (BA44: h2-=0.23 (sd=0.041), BA45: h2-=0.26 (sd=0.061)), indicated that HM might not represent a major bias in genetic studies using FCs. Even so, the HM effect on FC was not completely eliminated after regression. HM may be a valuable endophenotype whose relationship with brain disorders remains to be elucidated.

A functional MRI study of the relationship between naming treatment outcomes and resting state functional connectivity in post-stroke aphasia

Background: The majority of studies investigating the neural mechanisms underlying treatment in people with aphasia have examined task-based brain activity. However, the use of resting-state fMRI may provide another method of examining the brain mechanisms responsible for treatment-induced recovery, and allows for investigation into connectivity within complex functional networks Methods: Eight people with aphasia underwent 12 treatment sessions that aimed to improve object naming. Half the sessions employed a phonologically-based task, and half the sessions employed a semantic-based task, with resting-state fMRI conducted pre- and post-treatment. Brain regions in which the amplitude of low frequency fluctuations (ALFF) correlated with treatment outcomes were used as seeds for functional connectivity (FC) analysis. FC maps were compared from pre- to post-treatment, as well as with a group of 12 healthy older controls Results: Pre-treatment ALFF in the right middle temporal gyrus (MTG) correlated with greater outcomes for the phonological treatment, with a shift to the left MTG and supramarginal gyrus, as well as the right inferior frontal gyrus, post-treatment. When compared to controls, participants with aphasia showed both normalization and up-regulation of connectivity within language networks post-treatment, predominantly in the left hemisphere Conclusions: The results provide preliminary evidence that treatments for naming impairments affect the FC of language networks, and may aid in understanding the neural mechanisms underlying the rehabilitation of language post-stroke.