A probabilistic treatment of uncertainty in nonlinear dynamical systems

In this work, computationally efficient approximate methods are developed for analyzing uncertain dynamical systems. Uncertainties in both the excitation and the modeling are considered and examples are presented illustrating the accuracy of the proposed approximations.

For nonlinear systems under uncertain excitation, methods are developed to approximate the stationary probability density function and statistical quantities of interest. The methods are based on approximating solutions to the Fokker-Planck equation for the system and differ from traditional methods in which approximate solutions to stochastic differential equations are found. The new methods require little computational effort and examples are presented for which the accuracy of the proposed approximations compare favorably to results obtained by existing methods. The most significant improvements are made in approximating quantities related to the extreme values of the response, such as expected outcrossing rates, which are crucial for evaluating the reliability of the system.

Laplace's method of asymptotic approximation is applied to approximate the probability integrals which arise when analyzing systems with modeling uncertainty. The asymptotic approximation reduces the problem of evaluating a multidimensional integral to solving a minimization problem and the results become asymptotically exact as the uncertainty in the modeling goes to zero. The method is found to provide good approximations for the moments and outcrossing rates for systems with uncertain parameters under stochastic excitation, even when there is a large amount of uncertainty in the parameters. The method is also applied to classical reliability integrals, providing approximations in both the transformed (independently, normally distributed) variables and the original variables. In the transformed variables, the asymptotic approximation yields a very simple formula for approximating the value of SORM integrals. In many cases, it may be computationally expensive to transform the variables, and an approximation is also developed in the original variables. Examples are presented illustrating the accuracy of the approximations and results are compared with existing approximations.

Statistical and econometric analysis of the treatment of HIV/AIDS

The epidemic of HIV/AIDS in the United States is constantly changing and evolving, starting from patient zero to now an estimated 650,000 to 900,000 Americans infected. The nature and course of HIV changed dramatically with the introduction of antiretrovirals. This discourse examines many different facets of HIV from the beginning where there wasn't any treatment for HIV until the present era of highly active antiretroviral therapy (HAART). By utilizing statistical analysis of clinical data, this paper examines where we were, where we are and projections as to where treatment of HIV/AIDS is headed.

Chapter Two describes the datasets that were used for the analyses. The primary database utilized was collected by myself from an outpatient HIV clinic. The data included dates from 1984 until the present. The second database was from the Multicenter AIDS Cohort Study (MACS) public dataset. The data from the MACS cover the time between 1984 and October 1992. Comparisons are made between both datasets.

Chapter Three discusses where we were. Before the first anti-HIV drugs (called antiretrovirals) were approved, there was no treatment to slow the progression of HIV. The first generation of antiretrovirals, reverse transcriptase inhibitors such as AZT (zidovudine), DDI (didanosine), DDC (zalcitabine), and D4T (stavudine) provided the first treatment for HIV. The first clinical trials showed that these antiretrovirals had a significant impact on increasing patient survival. The trials also showed that patients on these drugs had increased CD4+ T cell counts. Chapter Three examines the distributions of CD4 T cell counts. The results show that the estimated distributions of CD4 T cell counts are distinctly non-Gaussian. Thus distributional assumptions regarding CD4 T cell counts must be taken, into account when performing analyses with this marker. The results also show the estimated CD4 T cell distributions for each disease stage: asymptomatic, symptomatic and AIDS are non-Gaussian. Interestingly, the distribution of CD4 T cell counts for the asymptomatic period is significantly below that of the CD4 T cell distribution for the uninfected population suggesting that even in patients with no outward symptoms of HIV infection, there exists high levels of immunosuppression.

Chapter Four discusses where we are at present. HIV quickly grew resistant to reverse transcriptase inhibitors which were given sequentially as mono or dual therapy. As resistance grew, the positive effects of the reverse transcriptase inhibitors on CD4 T cell counts and survival dissipated. As the old era faded a new era characterized by a new class of drugs and new technology changed the way that we treat HIV-infected patients. Viral load assays were able to quantify the levels of HIV RNA in the blood. By quantifying the viral load, one now had a faster, more direct way to test antiretroviral regimen efficacy. Protease inhibitors, which attacked a different region of HIV than reverse transcriptase inhibitors, when used in combination with other antiretroviral agents were found to dramatically and significantly reduce the HIV RNA levels in the blood. Patients also experienced significant increases in CD4 T cell counts. For the first time in the epidemic, there was hope. It was hypothesized that with HAART, viral levels could be kept so low that the immune system as measured by CD4 T cell counts would be able to recover. If these viral levels could be kept low enough, it would be possible for the immune system to eradicate the virus. The hypothesis of immune reconstitution, that is bringing CD4 T cell counts up to levels seen in uninfected patients, is tested in Chapter Four. It was found that for these patients, there was not enough of a CD4 T cell increase to be consistent with the hypothesis of immune reconstitution.

In Chapter Five, the effectiveness of long-term HAART is analyzed. Survival analysis was conducted on 213 patients on long-term HAART. The primary endpoint was presence of an AIDS defining illness. A high level of clinical failure, or progression to an endpoint, was found.

Chapter Six yields insights into where we are going. New technology such as viral genotypic testing, that looks at the genetic structure of HIV and determines where mutations have occurred, has shown that HIV is capable of producing resistance mutations that confer multiple drug resistance. This section looks at resistance issues and speculates, ceterus parabis, where the state of HIV is going. This section first addresses viral genotype and the correlates of viral load and disease progression. A second analysis looks at patients who have failed their primary attempts at HAART and subsequent salvage therapy. It was found that salvage regimens, efforts to control viral replication through the administration of different combinations of antiretrovirals, were not effective in 90 percent of the population in controlling viral replication. Thus, primary attempts at therapy offer the best change of viral suppression and delay of disease progression. Documentation of transmission of drug-resistant virus suggests that the public health crisis of HIV is far from over. Drug resistant HIV can sustain the epidemic and hamper our efforts to treat HIV infection. The data presented suggest that the decrease in the morbidity and mortality due to HIV/AIDS is transient. Deaths due to HIV will increase and public health officials must prepare for this eventuality unless new treatments become available. These results also underscore the importance of the vaccine effort.

The final chapter looks at the economic issues related to HIV. The direct and indirect costs of treating HIV/AIDS are very high. For the first time in the epidemic, there exists treatment that can actually slow disease progression. The direct costs for HAART are estimated. It is estimated that the direct lifetime costs for treating each HIV infected patient with HAART is between $353,000 to $598,000 depending on how long HAART prolongs life. If one looks at the incremental cost per year of life saved it is only $101,000. This is comparable with the incremental costs per year of life saved from coronary artery bypass surgery.

Policy makers need to be aware that although HAART can delay disease progression, it is not a cure and HIV is not over. The results presented here suggest that the decreases in the morbidity and mortality due to HIV are transient. Policymakers need to be prepared for the eventual increase in AIDS incidence and mortality. Costs associated with HIV/AIDS are also projected to increase. The cost savings seen recently have been from the dramatic decreases in the incidence of AIDS defining opportunistic infections. As patients who have been on HAART the longest start to progress to AIDS, policymakers and insurance companies will find that the cost of treating HIV/AIDS will increase.

Acceleration of ultra-thin electron layer.Analytical treatment compared with 1D-PIC simulation

In this paper, we apply an analytical model [V.V. Kulagin et al., Phys. Plasmas 14, 113101 (2007)] to describe the acceleration of an ultra-thin electron layer by a schematic single-cycle laser pulse and compare with one-dimensional particle-in-cell (1D-PIC) simulations. This is in the context of creating a relativistic mirror for coherent backscattering and supplements two related papers in this EPJD volume. The model is shown to reproduce the 1D-PIC results almost quantitatively for the short time of a few laser periods sufficient for the backscattering of ultra-short probe pulses.

Excreção urinária de glicosaminoglicanos em crianças com bexiga neurogênica secundária a mielomeningocele

A excreção urinária de glicosaminoglicanos (GAG) está alterada em várias patologias do trato urinário; o padrão de excreção pode estar associado com o estado da doença. A excreção urinária de GAG em crianças com bexiga neurogênica (BN) secundária a mielomeningocele (MMC) pode também estar alterada, mas até a presente data não há detalhamento epidemiológico dos pacientes e não se correlacionou o padrão de excreção com grau de disfunção vesical. Analisamos a excreção urinária de um grupo bem definido de crianças com MMC e correlacionamos os resultados com escore cistométrico. As amostras de urina de 17 pacientes com MMC, 10 meninos e 7 meninas (média de idade DP de 4,6 2,9 anos) foram obtidas durante o exame cistométrico. As amostras do grupo controle foram obtidas de 18 crianças normais, 13 meninos e 5 meninas (6,9 2,2 anos). Todas as crianças não estavam com infecção urinária, tinham função renal normal e não estavam sob tratamento farmacológico. A quantificação do GAG urinário total foi expressa em μg de ácido hexurônico / mg de creatinina e a proporção dos diferentes tipos de GAGs sulfatados foi obtida por eletroforese em gel de agarose. A avaliação cistométrica foi realizada utilizando aparelho de urodinâmica Dynapack modelo MPX816 (Dynamed, São Paulo, Brasil), a partir da qual o escore cistométrico foi calculado de acordo com procedimento recente publicado. [14]. Não observamos diferença significativa na excreção urinária de GAG total entre meninos e meninas tanto no grupo com MMC ( 0,913 0,528 vs 0,867 0,434, p>0,05) como no grupo controle (0,546 0,240 vs 0,699 0,296, p>0,05). Os resultados mostraram também que a excreção de GAG urinário não se correlacionou com a idade tanto no grupo com MMC ( r = -0,28, p> 0,05) como no grupo controle (r = -0,40, p> 0,05). Entretanto, a comparação dos dois grupos mostrou que o grupo com MMC excretava 52% a mais de GAG total que o grupo controle (0,894 0,477 vs 0,588 0,257, p <0,04). Nesses pacientes a excreção de GAG total não se correlacionou com a complacência vesical isoladamente (r = -0,18, p> 0,05) mas foi significativa e negativamente correlacionada ao escore cistométrico (r= -0,56, p<0,05). Em média, os pacientes com piores escores (<9) excretaram 81% a mais de GAG que os pacientes com melhor escore (>9) (1,157 0,467 vs 0,639 0,133, p<0,04). O sulfato de condroitin foi o GAG sulfatado predominante nos grupos neurogênico e controles (92,5 7,6% vs 96,4 4,8%, respectivamente, p> 0,05), enquanto o sulfato do heparan estava presente em quantidades marcadamente menores; o dermatam sulfato não foi detectado. A excreção urinária de GAG em pacientes com MMC é significativamente maior que a excreção das crianças normais e os altos valores encontrados estão correlacionados a um maior compromentimento da função vesical. Evidências em modelos animais com MMC induzida sugerem que alterações no detrusor estão associadas a um elevado turnover da matriz extra celular (MEC) vesical, o que pode explicar a elevada excreção de GAG nos pacientes com MMC. Além disso, esses resultados indicam que a excreção urinária de GAG pode ser usada como fator adjuvante para a caracterização da disfunção vesical em pacientes com MMC.

A generalized treatment of the order-disorder transformation in alloys and its effects on their magnetic properties

A theory of the order-disorder transformation is developed in complete generality. The general theory is used to calculate long range order parameters, short range order parameters, energy, and phase diagrams for a face centered cubic binary alloy. The theoretical results are compared to the experimental determination of the copper-gold system, Values for the two adjustable parameters are obtained.

An explanation for the behavior of magnetic alloys is developed, Curie temperatures and magnetic moments of the first transition series elements and their alloys in both the ordered and disordered states are predicted. Experimental agreement is excellent in most cases. It is predicted that the state of order can effect the magnetic properties of an alloy to a considerable extent in alloys such as Ni₃Mn. The values of the adjustable parameter used to fix the level of the Curie temperature, and the adjustable parameter that expresses the effect of ordering on the Curie temperature are obtained.

I. Quantum mechanics of one-dimensional two-particle models. II. A quantum mechanical treatment of inelastic collisions

Part I

Solutions of Schrödinger’s equation for system of two particles bound in various stationary one-dimensional potential wells and repelling each other with a Coulomb force are obtained by the method of finite differences. The general properties of such systems are worked out in detail for the case of two electrons in an infinite square well. For small well widths (1-10 a.u.) the energy levels lie above those of the noninteresting particle model by as much as a factor of 4, although excitation energies are only half again as great. The analytical form of the solutions is obtained and it is shown that every eigenstate is doubly degenerate due to the “pathological” nature of the one-dimensional Coulomb potential. This degeneracy is verified numerically by the finite-difference method. The properties of the square-well system are compared with those of the free-electron and hard-sphere models; perturbation and variational treatments are also carried out using the hard-sphere Hamiltonian as a zeroth-order approximation. The lowest several finite-difference eigenvalues converge from below with decreasing mesh size to energies below those of the “best” linear variational function consisting of hard-sphere eigenfunctions. The finite-difference solutions in general yield expectation values and matrix elements as accurate as those obtained using the “best” variational function.

The system of two electrons in a parabolic well is also treated by finite differences. In this system it is possible to separate the center-of-mass motion and hence to effect a considerable numerical simplification. It is shown that the pathological one-dimensional Coulomb potential gives rise to doubly degenerate eigenstates for the parabolic well in exactly the same manner as for the infinite square well.

Part II

A general method of treating inelastic collisions quantum mechanically is developed and applied to several one-dimensional models. The formalism is first developed for nonreactive “vibrational” excitations of a bound system by an incident free particle. It is then extended to treat simple exchange reactions of the form A + BC →AB + C. The method consists essentially of finding a set of linearly independent solutions of the Schrödinger equation such that each solution of the set satisfies a distinct, yet arbitrary boundary condition specified in the asymptotic region. These linearly independent solutions are then combined to form a total scattering wavefunction having the correct asymptotic form. The method of finite differences is used to determine the linearly independent functions.

The theory is applied to the impulsive collision of a free particle with a particle bound in (1) an infinite square well and (2) a parabolic well. Calculated transition probabilities agree well with previously obtained values.

Several models for the exchange reaction involving three identical particles are also treated: (1) infinite-square-well potential surface, in which all three particles interact as hard spheres and each two-particle subsystem (i.e. BC and AB) is bound by an attractive infinite-square-well potential; (2) truncated parabolic potential surface, in which the two-particle subsystems are bound by a harmonic oscillator potential which becomes infinite for interparticle separations greater than a certain value; (3) parabolic (untruncated) surface. Although there are no published values with which to compare our reaction probabilities, several independent checks on internal consistency indicate that the results are reliable.

On statistical treatment of the results of parallel trails with special reference to fishery research

Parallel trials form a most important part of the technique of scientific experimentation. Such trials may be divided into two; categories. In the first the results are comparable measurements of one kind or another. In the second the data consist of records of the number of times a certain 'event' has occurred in the two sets of trials compared. Only trials of the second category are dealt with here. In this paper all the reliable methods of testing for significance the results of parallel trials of a certain type with special reference to fishery research are described fully. Some sections relate to exact, others to approximate tests. The only advantage in the use of the latter lies in the fact that they are often the more expeditious. Apart from this it is always preferable to use exact methods.

Analyses of treated sewage effluent from Grasmere Treatment Unit (1974-1976), England [Dataset]

This dataset provides raw data of chemical analyses made during studies on seasonal variations of treated sewage effluent from Grasmere Treatment Unit in Cumbria. Measurements of sodium, calcium, potassium, magnesium and chloride ions were taken between 1974 and 1976.

Compliance verification methodology for renewable generation integration. Application to island power grids

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As relações interpessoais no cuidar do cliente em espaço onco-hematológico: uma contribuição do enfermeiro

Durante minha trajetória profissional experenciando o cuidar de clientes portadores de doença onco-hematológica percebi a luta destes seres humanos pela vida e como a relação enfermeiro-cliente era vital para a realização do cuidado. O enfermeiro interage grande parte do tempo com esta clientela a qual percorre uma trajetória de re-internações e longos períodos de tratamento. Nesse sentido, entendendo que a relação interpessoal como uma condição importante para que o enfermeiro compreenda o outro em sua totalidade e preste um cuidado singular, delimitei como objeto de estudo as relações interpessoais do enfermeiro na ação de cuidar do cliente internado para tratamento onco-hematológico. Para tanto, o objetivo foi compreender o significado das relações interpessoais na ação de cuidar do enfermeiro junto ao cliente internado para tratamento onco-hematlógico. Trata-se de estudo de natureza qualitativa, cujo referencial teórico pautou-se nas concepções da fenomenologia sociológica de Alfred Schutz. O cenário de realização do estudo foi a enfermaria de Hematologia de um Hospital Universitário Federal do estado do Rio de Janeiro e os sujeitos foram todos os seis enfermeiros lotados nessa unidade. Antes da etapa de campo e em cumprimento aos princípios éticos da Resolução 196/96 do CNS que trata da pesquisa com seres humanos, o projeto foi submetido ao Comitê de Ética dessa instituição cenário do estudo, sendo aprovado com o Parecer n 092/11. A captação das falas deu-se por meio de entrevista com a utilização das seguintes questões orientadoras: fale para mim sobre as ações que você desenvolve junto ao cliente internado para tratamento onco-hematológico; o que significam as relações interpessoais na ação de cuidar do cliente internado para tratamento onco-hematológico?; e o que você faz para que esta relação aconteça? A análise compreensiva das falas possibilitou a apreensão das categorias: cuidar através de procedimentos técnicos e científicos, orientando para o enfrentamento da doença e atender o paciente na perspectiva de suas necessidades estabelecendo a relação interpessoal entre enfermeiro e o cliente. O enfermeiro descreve as ações desenvolvidas junto ao cliente em tratamento onco-hematológico como um fazer técnico, rico em procedimentos, que tem em vista apoiar o cliente para enfrentar o tratamento difícil de uma doença grave, a partir de suas necessidades, estabelecendo uma relação íntima, transparente e forte, ocorrendo de forma espontânea e natural. Para estabelecer esta relação os enfermeiros utilizam estratégias como: a empatia, a brincadeira, o carinho, a confiança e a disponibilidade para promover o cuidado de enfermagem. As relações interpessoais se mostraram inerentes à ação de cuidar desse enfermeiro, ator social da equipe de saúde, o qual possui a disponibilidade para interagir com o cliente, transcendendo o aspecto tecnicista, fazendo parte de sua identidade profissional o constituinte relacional.

Efficacy and safety of autologous platelet rich plasma for the treatment of vascular ulcers in primary care: Phase III study

Background: Vascular ulcers are commonly seen in daily practice at all levels of care and have great impact at personal, professional and social levels with a high cost in terms of human and material resources. Given that the application of autologous platelet rich plasma has been shown to decrease healing times in various different studies in the hospital setting, we considered that it would be interesting to assess the efficacy and feasibility of this treatment in primary care. The objectives of this study are to assess the potential efficacy and safety of autologous platelet rich plasma for the treatment of venous ulcers compared to the conventional treatment (moist wound care) in primary care patients with chronic venous insufficiency (C, clinical class, E, aetiology, A, anatomy and P, pathophysiology classification C6). Design: We will conduct a phase III, open-label, parallel-group, multicentre, randomized study. The subjects will be 150 patients aged between 40 and 100 years of age with an at least 2-month history of a vascular venous ulcer assigned to ten primary care centres. For the treatment with autologous platelet rich plasma, all the following tasks will be performed in the primary care setting: blood collection, centrifugation, separation of platelet rich plasma, activation of coagulation adding calcium chloride and application of the PRP topically after gelification. The control group will receive standard moist wound care. The outcome variables to be measured at baseline, and at weeks 5 and 9 later include: reduction in the ulcer area, Chronic Venous Insufficiency Quality of Life Questionnaire score, and percentage of patients who require wound care only once a week. Discussion: The results of this study will be useful to improve the protocol for using platelet rich plasma in chronic vascular ulcers and to favour wider use of this treatment in primary care.