A one-dimensional prescribed curvature equation modeling the corneal shape.

We prove existence, uniqueness, and stability of solutions of the prescribed curvature problem (u'/root 1 + u'(2))' = au - b/root 1 + u'(2) in [0, 1], u'(0) = u(1) = 0, for any given a > 0 and b > 0. We also develop a linear monotone iterative scheme for approximating the solution. This equation has been proposed as a model of the corneal shape in the recent paper (Okrasinski and Plociniczak in Nonlinear Anal., Real World Appl. 13:1498-1505, 2012), where a simplified version obtained by partial linearization has been investigated.

Optimal approximation of fractional derivatives through discrete-time fractions using genetic algorithms

This study addresses the optimization of rational fraction approximations for the discrete-time calculation of fractional derivatives. The article starts by analyzing the standard techniques based on Taylor series and Padé expansions. In a second phase the paper re-evaluates the problem in an optimization perspective by tacking advantage of the flexibility of the genetic algorithms.

On lattices from combinatorial game theory modularity and a representation theorem: finite case

We show that a self-generated set of combinatorial games, S. may not be hereditarily closed but, strong self-generation and hereditary closure are equivalent in the universe of short games. In [13], the question "Is there a set which will give a non-distributive but modular lattice?" appears. A useful necessary condition for the existence of a finite non-distributive modular L(S) is proved. We show the existence of S such that L(S) is modular and not distributive, exhibiting the first known example. More, we prove a Representation Theorem with Games that allows the generation of all finite lattices in game context. Finally, a computational tool for drawing lattices of games is presented. (C) 2014 Elsevier B.V. All rights reserved.

Mode III interlaminar fracture of carbon/epoxy laminates using the edge crack torsion (ECT) test

The mode III interlaminar fracture of carbon/epoxy laminates was evaluated with the edge crack torsion (ECT) test. Three-dimensional finite element analyses were performed in order to select two specimen geometries and an experimental data reduction scheme. Test results showed considerable non-linearity before the maximum load point and a significant R-curve effect. These features prevented an accurate definition of the initiation point. Nevertheless, analyses of non-linearity zones showed two likely initiation points corresponding to GIIIc values between 850 and 1100 J/m2 for both specimen geometries. Although any of these values is realistic, the range is too broad, thus showing the limitations of the ECT test and the need for further research.

Finite Element Analysis (FEA) applied to heat transfer optimization process of pultrusion die systems

The aim of this study is to optimize the heat flow through the pultrusion die assembly system on the manufacturing process of a specific glass-fiber reinforced polymer (GFRP) pultrusion profile. The control of heat flow and its distribution through whole die assembly system is of vital importance in optimizing the actual GFRP pultrusion process. Through mathematical modeling of heating-die process, by means of Finite Element Analysis (FEA) program, an optimum heater selection, die position and temperature control was achieved. The thermal environment within the die was critically modeled relative not only to the applied heat sources, but also to the conductive and convective losses, as well as the thermal contribution arising from the exothermic reaction of resin matrix as it cures or polymerizes from the liquid to solid condition. Numerical simulation was validated with basis on thermographic measurements carried out on key points along the die during pultrusion process.

Optimizing the embedded heaters position in the pultrusion process using finite element analysis

This study is based on a previous experimental work in which embedded cylindrical heaters were applied to a pultrusion machine die, and resultant energetic performance compared with that achieved with the former heating system based on planar resistances. The previous work allowed to conclude that the use of embedded resistances enhances significantly the energetic performance of pultrusion process, leading to 57% decrease of energy consumption. However, the aforementioned study was developed with basis on an existing pultrusion die, which only allowed a single relative position for the heaters. In the present work, new relative positions for the heaters were investigated in order to optimize heat distribution process and energy consumption. Finite Elements Analysis was applied as an efficient tool to identify the best relative position of the heaters into the die, taking into account the usual parameters involved in the process and the control system already tested in the previous study. The analysis was firstly developed with basis on eight cylindrical heaters located in four different location plans. In a second phase, in order to refine the results, a new approach was adopted using sixteen heaters with the same total power. Final results allow to conclude that the correct positioning of the heaters can contribute to about 10% of energy consumption reduction, decreasing the production costs and leading to a better eco-efficiency of pultrusion process.

Congruences on monoids of transformations preserving the orientation on a finite chain

Journal of Algebra, 321 (2009), p. 743–757

Analysis of sandwich beam structures using kriging based higher order models

Functionally graded composite materials can provide continuously varying properties, which distribution can vary according to a specific location within the composite. More frequently, functionally graded materials consider a through thickness variation law, which can be more or less smoother, possessing however an important characteristic which is the continuous properties variation profiles, which eliminate the abrupt stresses discontinuities found on laminated composites. This study aims to analyze the transient dynamic behavior of sandwich structures, having a metallic core and functionally graded outer layers. To this purpose, the properties of the particulate composite metal-ceramic outer layers, are estimated using Mod-Tanaka scheme and the dynamic analyses considers first order and higher order shear deformation theories implemented though kriging finite element method. The transient dynamic response of these structures is carried out through Bossak-Newmark method. The illustrative cases presented in this work, consider the influence of the shape functions interpolation domain, the properties through-thickness distribution, the influence of considering different materials, aspect ratios and boundary conditions. (C) 2014 Elsevier Ltd. All rights reserved.

Toroid inductor development for a SIC DC-DC converter up to 150kW, based on finite element method

Dissertação para a obtenção do grau de Mestre em Engenharia Electrotécnica Ramo de Energia

Delay approximation of fractional integrals

This paper explores the calculation of fractional integrals by means of the time delay operator. The study starts by reviewing the memory properties of fractional operators and their relationship with time delay. Based on the time response of the Mittag-Leffler function an approximation of fractional integrals consisting of time delayed samples is proposed. The tuning of the approximation is optimized by means of a genetic algorithm. The results demonstrate the feasibility of the new perspective and the limits of their application.

Alterações da substância branca cerebral relacionadas com o envelhecimento

INTRODUÇÃO: Estudos prévios, com técnicas de imagem, documentam de forma consistente a existência de alterações da substância branca cerebral relacionadas com o envelhecimento (ASBRE). Tais alterações poderão ter um papel importante no declínio funcional do idoso, reflectindo‐se sobretudo no desempenho motor e cognitivo, com repercussão evidente na prática clínica. Apesar disso, a caracterização em definitivo dos fenótipos clínicos e da evolução das ASBRE continua por esclarecer, possivelmente pelas dificuldades metodológicas de que se reveste o seu estudo, incluindo: a adequação das baterias neuropsicológicas, a utilização de amostras de doentes com diferentes graus de severidade e de envolvimento regional, as limitações das diferentes escalas e a sensibilidade dos diferentes métodos de imagem. A Ressonância Magnética (RM) de difusão tem revelado grande sensibilidade para as alterações isquémicas, admitindo‐se que poderá permitir uma melhor caracterização das ASBRE e deste modo possibilitar uma correlação mais precisa com as variáveis cognitivas e motoras, permitindo avaliar ainda a substância branca aparentemente normal (SBAN). OBJECTIVOS: Descrever a evolução imagiológica das ASBRE no intervalo de um ano e analisar a sua expressão clínica e impacto funcional; identificar factores preditivos de progressão das ASBRE e de declínio funcional associado. Descrever a expressão clínica e perfil evolutivo dos doentes com ASBRE com envolvimento preferencial da região parieto‐occipital; comparar este grupo de doentes com os doentes com ASBRE, sem envolvimento preferencial desta região. Medir os coeficientes de difusão aparente (CDA), utilizando regiões de interesse (RDI), em diferentes localizações da substância branca, incluindo substância branca lesada e SBAN, descrever sua evolução temporal no intervalo de um ano e determinar suas correlações clínicas e imagiológicas. MÉTODOS: Utilizando uma amostra de conveniência, foram estudados 30 doentes, com mais de 65 anos, sem incapacidade funcional ou com incapacidade mínima, avaliada pela escala de actividades instrumentais da vida diária (IADL), apresentando ASBRE em TC. Foi utilizado um protocolo exaustivo de avaliação clínica (com particular destaque para as funções motoras e cognitivas) e imagiológica, em dois momentos de avaliação separados por um ano de intervalo (t0 e t1). As ASBRE foram avaliadas com escalas visuais, escala ARWMC e escala de Fazekas, e os doentes foram estudados em função do grau de severidade (ligeiro versus moderado a grave na escala de Fazekas) e de um envolvimento preferencial posterior (definido como 2 ou mais pontos na escala ARWMC na região parieto‐occipital por comparação com a região frontal). Os CDA foram avaliados mediante estudo de RDI, na substância branca frontal lesada (SBFL) e SBAN frontal, parieto‐occipital e dos pedúnculos cerebelosos. Para verificar diferenças na ordem de distribuição das variáveis foi usado o teste de Mann‐Whitney e para comparação de proporções, o teste exacto de Fisher. Na comparação entre a avaliação em t0 e t1 foi usado o teste Wilcoxon Signed Ranks na comparação da distribuição da ordem das variáveis e o teste McNemar na análise de frequências. Na análise correlacional foram utilizados os testes de T para variáveis emparelhadas e as correlações entre estas foram efectuadas com o coeficiente de correlação de Spearman ou de Pearson. O trabalho foi aprovado pela Comissão de Ética do hospital onde foi realizado e todos os doentes incluídos assinaram um consentimento informado. RESULTADOS: A idade média da população estudada foi 72,5 anos (17 doentes eram do sexo masculino). No final de um ano, 1 doente tinha falecido e 3 doentes não completaram a avaliação imagiológica. Registou‐se uma progressão significativa das ASBRE segundo a escala ARWMC (t0: 8,37 / t1: 9,65 ; p<0,001). Na análise funcional, motora e cognitiva, não houve um agravamento significativo. Avaliando os doentes em t0 e t1 segundo o grau de severidade das ASBRE, o grupo com atingimento moderado a grave (ASBRE2) comparado com o grupo com atingimento ligeiro (ASBRE1) apresentava: maior extensão de lesão da substância branca (ARWMC t0: 11,9 / 4,8 ; p<0.001 ; t1: 14,0 / 5,9 ; p<0,001); tendência a pior desempenho funcional (IADL t0: 90,7 / 99,2 ; p=0,023; t1: 86,4 / 96,7 ; p=n.s.) e motor (SPPB t0: 9,8 / 10,3 ; p=n.s. ; t1: 9,5 / 10,5 ; p=0,058); tendência a maior compromisso do humor (Escala Cornell t0: 6,7 / 3,5 ; p=0,037; t1: 6,2 / 4,5 ; p=n.s.). Analisando a evolução, de t0 para t1, de cada um dos grupos (ASBRE2 e ASBRE1) registou‐se: aumento da extensão da lesão da substância branca em ambos (ASBRE2: 12,0 / 14,0;z=‐2,687 ; p=0,007; ASBR1: 4,8 / 5,9 ; z=‐2,724 ; p=0,006); variação não significativa funcional e motora; tendência ao agravamento em ambos na prova de Cancelamento de dígitos (ASBRE2: 17,5 / 17,4 ; p=n.s. ; ASBRE1: 19,9 / 16,9 ; z=‐2,096 ; p=0,036);tendência à melhoria em ambos no MMS (ASBRE2: 25,7 / 27,5 ; z=‐2,155 ; p=0,031; ASBRE1: 27,5 / 28,2 ; p=n.s). Avaliando os doentes em t0 e t1 em função do padrão de distribuição das ASBRE, os doentes com um envolvimento preferencial posterior (ASBREP) comparados com os restantes (ASBREnP), apresentavam: maior extensão da lesão (ARWMC t0: 10,8 / 6,9 ; p=0,025; t1: 12,9 / 7,6 ; p=0,011); diferenças não significativas no desempenho motor; tendência a melhor desempenho na prova dos Labirintos (t0: 8,1 / 11,8 ; p=0,06; t1: 8,7 / 9,5 ; p=n.s.) e Cancelamento de dígitos (t0: 20,9 / 17,4 ; p=0,045; t1: 18,5 / 16,3 ; p=n.s.); tendência a maior compromisso depressivo na GDS (t0: 5,0 / 3,68 ; p=n.s. ; t1: 5,7 / 3,3 p=0,033). Analisando o perfil evolutivo de t0 para t1, registou‐se: aumento da extensão da lesão nos dois grupos (ASBREP: 10,8 / 12,9 ; z=‐2,555 ; P=0,011; ASBREnP: 6,4 / 7,6 ; z=‐2,877 ; p=0,04); variação em sentidos diferentes com melhoria funcional no grupo ASBREP (91,0 / 95,5 ; z=‐0,926 ; p=0,036) e agravamento no grupo ASBREnP (96,7 / 89,8 ; z=‐2,032 ; p=0,042); variação sem sentidos diferentes, com agravamento significativo no grupo ASBREnP no item estação de pé do SPPB (ASBREP 3,8/3,9 p=n.s.; ASBREnP 3,9/3,6; z=‐2,236 ; p=0,025); tendência à melhoria nos dois grupos no MMS (ASBREP: 27,2 / 28,2 ; p=n.s.; ASBREnP: 26,3 / 27,7 ; z=‐2,413 ; p=0,016) e tendência em sentidos diferentes no Trail Making, com eventual melhoria no grupo ASBREP (113,9 / 91,6 ; p=n.s.) e agravamento no grupo ASBREnP (113,7 / 152,0 ; z=‐2,155 ; p=0,031). Na análise da imagem, utilizando a escala ARWMC e o estudo dos CDA, na avaliação transversal na inclusão, a comparação entre as pontuações médias da escala ARWML nas diferentes regiões mostrava diferenças significativas (F=39,54 , p<0,0001). A análise comparativa post‐hoc de Bonferroni mostrou valores significativamente mais altos para as regiões frontais e parieto‐occipitais (p<0,0001). Os valores médios dos CDA eram significativamente diferentes entre regiões (F=44,56; p<0,0001), sendo mais altos na SBFL (p<0,0001). Não existia diferença significativa entre os valores registados na SBAN nas regiões frontais e parieto‐occipitais. As pontuações regionais da escala ARWMC e os valores médios dos CDA correlacionavam‐se todos de forma positiva. A pontuação da escala ARWMC na região frontal correlacionava‐se significativamente com os valores do CDA da SBFL (r=0,467 ; p=0,012). Existia tendência para uma correlação positiva entre as pontuações da escala ARWMC na região frontal e os valores médios dos CDA na SBAN frontal (r=0,276 ; p=0,155). As pontuações da escala ARWMC e os CDA correlacionavam‐se de forma positiva com a idade e com a tensão arterial (TA). Foram encontradas correlações significativas entre: idade e SBAN frontal (r=0,440 ; p=0,019); TA diastólica e SBFL (r=0,386 ; p=0,034); TA sistólica e SBAN Parieto‐occipital (r=0,407 ; P=0,032). Na avaliação motora e cognitiva, dado elevado número de variáveis, foi efectuada uma análise de factor principal. Registou‐se uma tendência global negativa na correlação entre as pontuações da escala visual na região frontal, os valores dos CDA, e o desempenho motor e cognitivo. Na análise evolutiva, (n=19), registou‐se variação significativa dos CDA, com aumento na SBFL (Direita: z=‐2,875 ; p=0,004 ; Esquerda: z=‐2,113 ; p=0,035) e diminuição na SBAN dos pedúnculos cerebelosos (Direita: z=‐2,094 ; p=0,036 ; Esquerda: z=‐1,989 ; p=0,047). Foi observada uma correlação negativa entre a variação do CDA na SBAN dos pedúnculos cerebelosos e na SBFL contralateral (SBAN pedúnculo cerebeloso Esquerdo / SBFL Direita: r=‐0,133 ; p=n.s.; SBAN pedúnculo cerebeloso Direito / SBFL Esquerda: r=‐0,561 ; p=0,012). Os valores dos CDA à direita correlacionavam‐se de forma positiva com a velocidade da marcha (r=0,562 ; p=0,012). CONCLUSÕES: A progressão das ASBRE pode ser observada com uma escala visual detalhada no intervalo de um ano. Contudo, o eventual agravamento da incapacidade funcional, motora e cognitiva, não parece ser apreciável em igual intervalo de tempo. A maior severidade das ASBRE associa‐se a uma tendência para um maior compromisso funcional, motor e possivelmente do humor. A questão da progressão em escalas simplificadas, de um estádio ligeiro para um estádio moderado a grave, não é elucidada pelos resultados do presente trabalho. Os doentes com um envolvimento preferencial da região parieto‐occipital poderão constituir um subgrupo distinto que, apesar de ter maior extensão de lesão, parece ter um melhor desempenho motor e cognitivo. O perfil evolutivo destes doentes parece igualmente ser distinto, não se observando a tendência ao agravamento funcional, motor e cognitivo (sobretudo em provas de função executiva) que se encontra nos restantes doentes. A análise transversal na inclusão, utilizando uma escala visual e o estudo dos CDA, sugere que a severidade das ASBRE se correlaciona com o compromisso motor e cognitivo, bem como com a idade e com a TA. Uma maior vulnerabilidade da substância branca frontal à lesão vascular parece ter um papel importante no compromisso motor e na disfunção executiva, (essencialmente à custa do compromisso da atenção), possivelmente associada à desconexão dos circuitos fronto‐subcorticais. A análise dos CDA sugere que isso é válido igualmente para a SBAN e sublinha que, as imagens de RM convencional poderão não traduzir a verdadeira extensão da lesão e consequentemente do compromisso motor e cognitivo. A relação entre a progressão da doença vascular em lesões frontais constituídas e a redução do CDA no pedúnculo cerebeloso contralateral poderá estar associada a um pior desempenho motor. A disrupção dos circuitos fronto‐cerebelosos, determinando hipometabolismo e diminuição da perfusão no cerebelo, poderá ser responsável pela diminuição do CDA no cerebelo. ABSTRACT INTRODUCTION: Previous studies, with new imaging techniques, have consistently documented the presence of age‐related white matter lesions (ARWML), emphasizing their role in agerelated functional decline, mainly related to motor and cognitive impairment, and inherent consequences in clinical practice. However clinical significance of ARWML remains to be elucidated, probably on account of methodological difficulties such as: specific neuropsychological batteries, utilization of samples with different degrees of severity and regional involvement, utilization of different imaging scales and different sensitivity of imaging techniques. Recently, Diffusion Weighted Magnetic Ressonance imaging (DWI) has shown a higher sensitivity to ischemic lesions, suggesting it might be superior for characterization of ARWML, allowing more precise correlation with motor and cognitive variables, and evaluating also normal appearing white matter (NAWM). OBJECTIVES: To describe imagiologic evolution of ARWML within one year interval and to analyse its clinical and functional significance. To identify predictors of ARWML progression and associated functional impairment. To describe clinical characteristics and evolution profile of patients with predominantly posterior lesions; to compare this group of patients with patients without predominantly posterior lesions. To study average Apparent Diffusion Coeficcients (ADC) in different white matter regions using regions of interest (ROI); to analyse their evolution profile and to determine their clinical and imagiologic correlations. METHODS: A sample of 30 patients older than 65 years, without functional impairment or with minimal impairment, according to the Instrumental Activities of Daily Lliving scale, with ARWML on CT scan, were studied in a cross‐sectional design. An extensive clinical(with detailed motor and cognitive evaluation) and imagiologic protocol was applied in two one‐year interval separate moments (t0 and t1). ARWML were studied using visual scales, ARWMC and Fazekas’s scale, and patients were studied according to degree of severity (Fazekas scale mild versus moderate / severe) and preferential involvement of the posterior region (defined as 2 or more points in the ARWMC scale in the parietooccipital region compared with frontal region). Evaluation of ADC was performed using ROI in frontal lesioned white matter (FLWM) and NAWM (frontal, parieto‐occipital and cerebellar regions). To study differences in the distribution of variables the Mann‐Whitney test was used and to compare proportions the exact Fisher Test was used. To compare temporal evolution profile between t0 and t1, the Wilcoxon Signed ranks Test was used to analyse the distribution of variables and the Mc Nemar Test to analyse frequencies. Correlation analysis was performed using Spearman or Pearson tests. The study was approved by the local Ethics Committee and all patients signed an informed consent. RESULTS: Mean age was 72.5 years (17 patients were male). By the end of the study, one patient was dead and 3 patients did not undergo brain imaging. There was a higher extent of ARWML evaluated with the ARWMC scale (t0: 8.37 / t1: 9.65 ; p<0.001). Functional, motor and cognitive performance did not progress significantly. Evaluating patients in t0 and t1 according to the degree of severity (Fazekas scale), the moderate / severe group of patients (WML2), compared with the mild group (WML1), showed: higher extent of lesion (ARWMC scale t0: 11.9 / 4.8 ; p<0.001 ; t1: 14.0 / 5.9 ; p<0.001); tendency to worse functional (IADL t0: 90.7 / 99.2 ; p=0.023; t1: 86.4 / 96.7 ; p=n.s.) and motor (SPPB t0: 9.8 / 10.3 ; p=n.s. ; t1: 9.5 / 10.5 ; p=0.058) performance; tendency to higher depressive scores (Cornell Scale t0: 6.7 / 3.5 ; p=0.037; t1: 6.2 / 4.5; p=n.s.). Analysing the evolution profile from t0 to t1 of each group (WML2 and WML1), there was a higher extent of lesion (ARWMC scale) in both (WML2: 12.0 / 14.0; z=‐2.687 ; p=0.007; WML1: 4.8 / 5.9 ; z=‐2.724 ; p=0.006); non‐significant variation in functional and motor performances; tendency to worse performance on the Digit Cancelling (WML2: 17.5 / 17.4 ; p=n.s. ; WML1: 19.9 / 16.9 ; z=‐2.096 ; p=0,036) and to better performance on the MMS (WML2: 25.7 / 27.5 ; z=‐2.155 ; p=0.031; WML1: 27.5/ 28.2 ; p=n.s). Evaluating patients in t0 and t1 according to the regional distribution of ARWML, patients with predominantly posterior lesions (WMLP) compared with the rest of the group (WMLnP), showed: higher extent of lesion (ARWMC scale t0: 10.8 / 6.9 ; p=0.025; t1:12.9 / 7.6 ; p=0.011); non significant differences on motor evaluation; tendency to a better performance on Maze (t0: 8.1 / 11.8 ; p=0.06; t1: 8.7 / 9.5 ; p=n.s.) and Digit cancelling (t0: 20.9 / 17.4 ; p=0.045; t1: 18.5 / 16.3 ; p=n.s.) tests;tendency to higher scores on GDS (t0: 5.0 / 3.68 ; p=n.s. ; t1: 5.7 / 3.3 p=0.033). Analysing the evolution profile from t0 to t1 of each group (WMLP and WMLnP), there was: higher extent of lesion (ARWMC scale) in both groups (WMLP: 10.8 / 12.9 ;z=‐2,555 ; P=0,011; WMLnP: 6.4 / 7.6 ; z=‐2.877; p=0.04); variation in different directions with better functional performance in the group WMLP (91.0 / 95.5 ;z=‐0.926 ; p=0.036) and worse in WMLnP (96.7 / 89.8 ; z=‐2.032 ; p=0.042); variation in different directions with worse motor performance in one SPPB item (total stands) in the group WMLnP (WMLP 3.8/3.9 p=n.s.; ASBREnP 3.9/3.6; z=‐2.236 ; p=0.025);tendency to improvement in both groups in MMS (WMLP: 27.2 / 28.2 ; p=n.s.; WMLnP:26.3 / 27.7 ; z=‐2.413 ; p=0.016); tendency to a variation in different directions in the Trail Making Test, with possible improvement in the group WMLP (113.9 / 91.6 ;p=n.s.) and worsening in the group WMLnP (113.7 / 152.0 ; z=‐2.155 ; p=0.031). Imaging analysis in the inclusion, using the ARWMC scale and ADC evaluation, showed significant differences in different regions (F=39.54, p<0.0001). Comparative post‐hoc Bonferroni analysis showed significantly higher scores in the frontal and parieto‐occipital regions (p<0.0001. ADC values were significantly different between regions (F=44.56; p<0.0001), being higher in FLWM (p<0‐0001). There was no significant difference between ADC in NAWM in frontal and parieto‐occipital regions. ARWMC scores and ADC values correlated positively. Significant correlations were found between frontal ARWMC score and FLWM ADC values (r=0.467 ; p=0.012). ARWMC scores and ADC values correlated positively with age and blood pressure. Significant correlations were: age and frontal NAWM (r=0.440 ; p=0.019); Diastolic blood pressure and FLWM (r=0.386 ; p=0.034); sistolic blood pressure and parietooccipital NAWM (r=0.407 ; P=0.032). Due to the higher number of motor and cognitive variables a preliminary study was done, using principal component analysis. A global tendency to a negative correlation was found between ARWMC scores, ADC values and motor and cognitive performances. Evolutive analysis of ADC (n=19), showed a significant variation, with higher values in t1 in FLWM (Right: z=‐2.875 ; p=0.004 ; Left: z=‐2.113 ; p=0.035) and lower values in t1 in cerebellar NAWM (Right: z=‐2.094 ; p=0.036 ; Left: z=‐1.989 ; p=0.047). A negative correlation was found between ADC variation in cerebellar NAWM and contralateral FLWM (Left cerebellar NAWM / Right FLWM: r=‐0.133 ; p=n.s.; Right cerebellar NAWM/ Left FLWM: r=‐0.561 ; p=0.012). ADC values on the right correlated positively with walking speed (r=0,562 ; p=0,012). CONCLUSIONS: Progression of ARWML can be documented with a detailed visual scale in a one year interval. However, functional, motor and cognitive impairment, do not seem to progress significantly within the same period. A higher severity of ARWML is associated with a tendency to a worse functional and motor performance (and possibly to higher scores in depression scales). The issue of progression in a simplified visual scale from a mild to a moderate / severe degree of ARWML is not further elucidated. Patients with predominantly posterior lesions may be a subset of ARWML patients, with a different profile, that despite higher extent of lesion, seem to fair better than the rest of the group, namely with better performance on motor and cognitive tests. Evolution profile of this subset of patients also seems to be different, without a clearcut tendency to worsening functional, motor and cognitive (particularly for executive function tests) performance that is observed in the rest of the group. Imaging analysis, with a visual scale and ADC evaluation, suggests that severity of ARWML correlates negatively with cognitive and motor performance and positively with age and blood pressure. A higher vulnerability of frontal white matter to vascular disease seems to play an important role in motor and cognitive dysfunction, mainly determined by impairment of attention skills associated with frontal‐subcortical disconnection. DWI results, suggest that this may also be true for NAWM, underlining that conventional MR images may not represent the true extent of cognitive decline. The relation between vascular disease progression inside frontal lesions and ADC reduction in contralateral cerebellar peduncles, may be associated with a worse motor performance. Disruption of fronto‐cerebellar cicuits, with associated regional hypometabolism, may be responsible for the reduction of cerebellar ADC.

Vertex component analysis: a geometric-based approach to unmix hyperspectral data

Hyperspectral remote sensing exploits the electromagnetic scattering patterns of the different materials at specific wavelengths [2, 3]. Hyperspectral sensors have been developed to sample the scattered portion of the electromagnetic spectrum extending from the visible region through the near-infrared and mid-infrared, in hundreds of narrow contiguous bands [4, 5]. The number and variety of potential civilian and military applications of hyperspectral remote sensing is enormous [6, 7]. Very often, the resolution cell corresponding to a single pixel in an image contains several substances (endmembers) [4]. In this situation, the scattered energy is a mixing of the endmember spectra. A challenging task underlying many hyperspectral imagery applications is then decomposing a mixed pixel into a collection of reflectance spectra, called endmember signatures, and the corresponding abundance fractions [8–10]. Depending on the mixing scales at each pixel, the observed mixture is either linear or nonlinear [11, 12]. Linear mixing model holds approximately when the mixing scale is macroscopic [13] and there is negligible interaction among distinct endmembers [3, 14]. If, however, the mixing scale is microscopic (or intimate mixtures) [15, 16] and the incident solar radiation is scattered by the scene through multiple bounces involving several endmembers [17], the linear model is no longer accurate. Linear spectral unmixing has been intensively researched in the last years [9, 10, 12, 18–21]. It considers that a mixed pixel is a linear combination of endmember signatures weighted by the correspondent abundance fractions. Under this model, and assuming that the number of substances and their reflectance spectra are known, hyperspectral unmixing is a linear problem for which many solutions have been proposed (e.g., maximum likelihood estimation [8], spectral signature matching [22], spectral angle mapper [23], subspace projection methods [24,25], and constrained least squares [26]). In most cases, the number of substances and their reflectances are not known and, then, hyperspectral unmixing falls into the class of blind source separation problems [27]. Independent component analysis (ICA) has recently been proposed as a tool to blindly unmix hyperspectral data [28–31]. ICA is based on the assumption of mutually independent sources (abundance fractions), which is not the case of hyperspectral data, since the sum of abundance fractions is constant, implying statistical dependence among them. This dependence compromises ICA applicability to hyperspectral images as shown in Refs. [21, 32]. In fact, ICA finds the endmember signatures by multiplying the spectral vectors with an unmixing matrix, which minimizes the mutual information among sources. If sources are independent, ICA provides the correct unmixing, since the minimum of the mutual information is obtained only when sources are independent. This is no longer true for dependent abundance fractions. Nevertheless, some endmembers may be approximately unmixed. These aspects are addressed in Ref. [33]. Under the linear mixing model, the observations from a scene are in a simplex whose vertices correspond to the endmembers. Several approaches [34–36] have exploited this geometric feature of hyperspectral mixtures [35]. Minimum volume transform (MVT) algorithm [36] determines the simplex of minimum volume containing the data. The method presented in Ref. [37] is also of MVT type but, by introducing the notion of bundles, it takes into account the endmember variability usually present in hyperspectral mixtures. The MVT type approaches are complex from the computational point of view. Usually, these algorithms find in the first place the convex hull defined by the observed data and then fit a minimum volume simplex to it. For example, the gift wrapping algorithm [38] computes the convex hull of n data points in a d-dimensional space with a computational complexity of O(nbd=2cþ1), where bxc is the highest integer lower or equal than x and n is the number of samples. The complexity of the method presented in Ref. [37] is even higher, since the temperature of the simulated annealing algorithm used shall follow a log( ) law [39] to assure convergence (in probability) to the desired solution. Aiming at a lower computational complexity, some algorithms such as the pixel purity index (PPI) [35] and the N-FINDR [40] still find the minimum volume simplex containing the data cloud, but they assume the presence of at least one pure pixel of each endmember in the data. This is a strong requisite that may not hold in some data sets. In any case, these algorithms find the set of most pure pixels in the data. PPI algorithm uses the minimum noise fraction (MNF) [41] as a preprocessing step to reduce dimensionality and to improve the signal-to-noise ratio (SNR). The algorithm then projects every spectral vector onto skewers (large number of random vectors) [35, 42,43]. The points corresponding to extremes, for each skewer direction, are stored. A cumulative account records the number of times each pixel (i.e., a given spectral vector) is found to be an extreme. The pixels with the highest scores are the purest ones. N-FINDR algorithm [40] is based on the fact that in p spectral dimensions, the p-volume defined by a simplex formed by the purest pixels is larger than any other volume defined by any other combination of pixels. This algorithm finds the set of pixels defining the largest volume by inflating a simplex inside the data. ORA SIS [44, 45] is a hyperspectral framework developed by the U.S. Naval Research Laboratory consisting of several algorithms organized in six modules: exemplar selector, adaptative learner, demixer, knowledge base or spectral library, and spatial postrocessor. The first step consists in flat-fielding the spectra. Next, the exemplar selection module is used to select spectral vectors that best represent the smaller convex cone containing the data. The other pixels are rejected when the spectral angle distance (SAD) is less than a given thresh old. The procedure finds the basis for a subspace of a lower dimension using a modified Gram–Schmidt orthogonalizati on. The selected vectors are then projected onto this subspace and a simplex is found by an MV T pro cess. ORA SIS is oriented to real-time target detection from uncrewed air vehicles using hyperspectral data [46]. In this chapter we develop a new algorithm to unmix linear mixtures of endmember spectra. First, the algorithm determines the number of endmembers and the signal subspace using a newly developed concept [47, 48]. Second, the algorithm extracts the most pure pixels present in the data. Unlike other methods, this algorithm is completely automatic and unsupervised. To estimate the number of endmembers and the signal subspace in hyperspectral linear mixtures, the proposed scheme begins by estimating sign al and noise correlation matrices. The latter is based on multiple regression theory. The signal subspace is then identified by selectin g the set of signal eigenvalue s that best represents the data, in the least-square sense [48,49 ], we note, however, that VCA works with projected and with unprojected data. The extraction of the end members exploits two facts: (1) the endmembers are the vertices of a simplex and (2) the affine transformation of a simplex is also a simplex. As PPI and N-FIND R algorithms, VCA also assumes the presence of pure pixels in the data. The algorithm iteratively projects data on to a direction orthogonal to the subspace spanned by the endmembers already determined. The new end member signature corresponds to the extreme of the projection. The algorithm iterates until all end members are exhausted. VCA performs much better than PPI and better than or comparable to N-FI NDR; yet it has a computational complexity between on e and two orders of magnitude lower than N-FINDR. The chapter is structure d as follows. Section 19.2 describes the fundamentals of the proposed method. Section 19.3 and Section 19.4 evaluate the proposed algorithm using simulated and real data, respectively. Section 19.5 presents some concluding remarks.

Viscosity and self-diffusion coefficients of dialkyl adipates: a correlation scheme with predictive capabilities

A correlation and predictive scheme for the viscosity and self-diffusivity of liquid dialkyl adipates is presented. The scheme is based on the kinetic theory for dense hard-sphere fluids, applied to the van der Waals model of a liquid to predict the transport properties. A "universal" curve for a dimensionless viscosity of dialkyl adipates was obtained using recently published experimental viscosity and density data of compressed liquid dimethyl (DMA), dipropyl (DPA), and dibutyl (DBA) adipates. The experimental data are described by the correlation scheme with a root-mean-square deviation of +/- 0.34 %. The parameters describing the temperature dependence of the characteristic volume, V-0, and the roughness parameter, R-eta, for each adipate are well correlated with one single molecular parameter. Recently published experimental self-diffusion coefficients of the same set of liquid dialkyl adipates at atmospheric pressure were correlated using the characteristic volumes obtained from the viscosity data. The roughness factors, R-D, are well correlated with the same single molecular parameter found for viscosity. The root-mean-square deviation of the data from the correlation is less than 1.07 %. Tests are presented in order to assess the capability of the correlation scheme to estimate the viscosity of compressed liquid diethyl adipate (DEA) in a range of temperatures and pressures by comparison with literature data and of its self-diffusivity at atmospheric pressure in a range of temperatures. It is noteworthy that no data for DEA were used to build the correlation scheme. The deviations encountered between predicted and experimental data for the viscosity and self-diffusivity do not exceed 2.0 % and 2.2 %, respectively, which are commensurate with the estimated experimental measurement uncertainty, in both cases.

Presentations for monoids of finite partial isometries

In this paper we give presentations for the monoid DPn of all partial isometries on {1,..., n} and for its submonoid ODPn of all order-preserving partial isometries.

Congruences on monoids of order-preserving or order-reversing transformations on a finite chain

Glasgow Mathematical Journal, nº 47 (2005), pg. 413-424