White matter fractional anisotrophy predicts balance performance in older adults

Aging is characterized by brain structural changes that may compromise motor functions. In the context of postural control, white matter integrity is crucial for the efficient transfer of visual, proprioceptive and vestibular feedback in the brain. To determine the role of age-related white matter decline as a function of the sensory feedback necessary to correct posture, we acquired diffusion weighted images in young and old subjects. A force platform was used to measure changes in body posture under conditions of compromised proprioceptive and/or visual feedback. In the young group, no significant brain structure-balance relations were found. In the elderly however, the integrity of a cluster in the frontal forceps explained 21% of the variance in postural control when proprioceptive information was compromised. Additionally, when only the vestibular system supplied reliable information, the occipital forceps was the best predictor of balance performance (42%). Age-related white matter decline may thus be predictive of balance performance in the elderly when sensory systems start to degrade.

The Utility of Fractional Exhaled Nitric Oxide Suppression in the Identification of Nonadherence in Difficult Asthma

Rationale: Nonadherence to inhaled corticosteroid therapy (ICS) is a major contributor to poor control in difficult asthma, yet it is challenging to ascertain. Objectives: Identify a test for nonadherence using fractional exhaled nitric oxide (FENO) suppression after directly observed inhaled corticosteroid (DOICS) treatment. Methods: Difficult asthma patients with an elevated FENO (>45 ppb) were recruited as adherent (ICS prescription filling >80%) or nonadherent (filling <50%). They received 7 days of DOICS (budesonide 1,600 µg) and a test for nonadherence based on changes in FENO was developed. Using this test, clinic patients were prospectively classified as adherent or nonadherent and this was then validated against prescription filling records, prednisolone assay, and concordance interview. Measurements and Main Results: After 7 days of DOICS nonadherent (n = 9) compared with adherent subjects (n = 13) had a greater reduction in FENO to 47 ± 21% versus 79 ± 26% of baseline measurement (P = 0.003), which was also evident after 5 days (P = 0.02) and a FENO test for nonadherence (area under the curve = 0.86; 95% confidence interval, 0.68-1.00) was defined. Prospective validation in 40 subjects found the test identified 13 as nonadherent; eight confirmed nonadherence during interview (three of whom had excellent prescription filling but did not take medication), five denied nonadherence, two had poor inhaler technique (unintentional nonadherence), and one also denied nonadherence to prednisolone despite nonadherent blood level. Twenty-seven participants were adherent on testing, which was confirmed in 21. Five admitted poor ICS adherence but of these, four were adherent with oral steroids and one with omalizumab. Conclusions: FENO suppression after DOICS provides an objective test to distinguish adherent from nonadherent patients with difficult asthma. Clinical trial registered with www.clinicaltrials.gov (NCT 01219036). Copyright © 2012 by the American Thoracic Society.

Calculus of variations on time scales and discrete fractional calculus

Estudamos problemas do cálculo das variações e controlo óptimo no contexto das escalas temporais. Especificamente, obtemos condições necessárias de optimalidade do tipo de Euler–Lagrange tanto para lagrangianos dependendo de derivadas delta de ordem superior como para problemas isoperimétricos. Desenvolvemos também alguns métodos directos que permitem resolver determinadas classes de problemas variacionais através de desigualdades em escalas temporais. No último capítulo apresentamos operadores de diferença fraccionários e propomos um novo cálculo das variações fraccionário em tempo discreto. Obtemos as correspondentes condições necessárias de Euler– Lagrange e Legendre, ilustrando depois a teoria com alguns exemplos.

Fractional calculus on time scales - Cálculo fraccional em escalas temporais

Introduzimos um cálculo das variações fraccional nas escalas temporais ℤ e (hℤ)!. Estabelecemos a primeira e a segunda condição necessária de optimalidade. São dados alguns exemplos numéricos que ilustram o uso quer da nova condição de Euler–Lagrange quer da nova condição do tipo de Legendre. Introduzimos também novas definições de derivada fraccional e de integral fraccional numa escala temporal com recurso à transformada inversa generalizada de Laplace.

Computational methods in the fractional calculus of variations and optimal control

The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the lack of analytic methods to solve such fractional problems, numerical techniques are developed. Here, we mainly investigate the approximation of fractional operators by means of series of integer-order derivatives and generalized finite differences. We give upper bounds for the error of proposed approximations and study their efficiency. Direct and indirect methods in solving fractional variational problems are studied in detail. Furthermore, optimality conditions are discussed for different types of unconstrained and constrained variational problems and for fractional optimal control problems. The introduced numerical methods are employed to solve some illustrative examples.

Forecasting overseas visitors into the United Kingdom using continuous time and autoregressive fractional integrated moving average models with discrete data

This paper applies Gaussian estimation methods to continuous time models for modelling overseas visitors into the UK. The use of continuous time modelling is widely used in economics and finance but not in tourism forecasting. Using monthly data for 1986–2010, various continuous time models are estimated and compared to autoregressive integrated moving average (ARIMA) and autoregressive fractionally integrated moving average (ARFIMA) models. Dynamic forecasts are obtained over different periods. The empirical results show that the ARIMA model performs very well, but that the constant elasticity of variance (CEV) continuous time model has the lowest root mean squared error (RMSE) over a short period.

Application of fractional delay filters to tune the centre frequency location of single-band sigma-delta modulators

This paper presents a novel technique for the design of narrow-band sigma-delta modulators with an embedded tunable centre frequency mechanism. This method demonstrates that the use of sum filters combined with a fractional delayer provide the flexibility of tuning the noise shaping band for any desired variable centre frequency input signal.

Increasing the variability of centre frequency locations in multiple-band sigma-delta modulators via the use of fractional delay filters

This paper presents the design analysis of novel tunable narrow-band bandpass sigma-delta modulators, that can achieve concurrent multiple noise-shaping for multi-tone input signals. This approach utilises conventional comb filters in conjunction with FIR, or allpass IIR fractional delay filters, to deliver the desired nulls for the quantisation noise transfer function. Detailed simulation results show that FIR fractional delay comb filter based sigma-delta modulators tune accurately to most centre frequencies, but suffer from degraded resolution at frequencies close to Nyquist. However, superior accuracies are obtained from their allpass IIR fractional delay counterpart at the expense of a slight shift in noise-shaping bands at very high frequencies.

Fractional dynamics in DNA

This paper addresses the DNA code analysis in the perspective of dynamics and fractional calculus. Several mathematical tools are selected to establish a quantitative method without distorting the alphabet represented by the sequence of DNA bases. The association of Gray code, Fourier transform and fractional calculus leads to a categorical representation of species and chromosomes.

Fractional dynamics and MDS visualization of earthquake phenomena

This paper analyses earthquake data in the perspective of dynamical systems and fractional calculus (FC). This new standpoint uses Multidimensional Scaling (MDS) as a powerful clustering and visualization tool. FC extends the concepts of integrals and derivatives to non-integer and complex orders. MDS is a technique that produces spatial or geometric representations of complex objects, such that those objects that are perceived to be similar in some sense are placed on the MDS maps forming clusters. In this study, over three million seismic occurrences, covering the period from January 1, 1904 up to March 14, 2012 are analysed. The events are characterized by their magnitude and spatiotemporal distributions and are divided into fifty groups, according to the Flinn–Engdahl (F–E) seismic regions of Earth. Several correlation indices are proposed to quantify the similarities among regions. MDS maps are proven as an intuitive and useful visual representation of the complex relationships that are present among seismic events, which may not be perceived on traditional geographic maps. Therefore, MDS constitutes a valid alternative to classic visualization tools for understanding the global behaviour of earthquakes.

Fractional model for malaria transmission under control strategies

We study a fractional model for malaria transmission under control strategies.Weconsider the integer order model proposed by Chiyaka et al. (2008) in [15] and modify it to become a fractional order model. We study numerically the model for variation of the values of the fractional derivative and of the parameter that models personal protection, b. From observation of the figures we conclude that as b is increased from 0 to 1 there is a corresponding decrease in the number of infectious humans and infectious mosquitoes, for all values of α. This means that this result is invariant for variation of fractional derivative, in the values tested. These results are in agreement with those obtained in Chiyaka et al.(2008) [15] for α = 1.0 and suggest that our fractional model is epidemiologically wellposed.

On a generalized Laguerre operational matrix of fractional integration

A new operationalmatrix of fractional integration of arbitrary order for generalized Laguerre polynomials is derived.The fractional integration is described in the Riemann-Liouville sense.This operational matrix is applied together with generalized Laguerre tau method for solving general linearmultitermfractional differential equations (FDEs).Themethod has the advantage of obtaining the solution in terms of the generalized Laguerre parameter. In addition, only a small dimension of generalized Laguerre operational matrix is needed to obtain a satisfactory result. Illustrative examples reveal that the proposedmethod is very effective and convenient for linear multiterm FDEs on a semi-infinite interval.

Symbolic fractional dynamics

Fractional dynamics reveals long range memory properties of systems described by means of signals represented by real numbers. Alternatively, dynamical systems and signals can adopt a representation where states are quantified using a set of symbols. Such signals occur both in nature and in man made processes and have the potential of a aftermath as relevant as the classical counterpart. This paper explores the association of Fractional calculus and symbolic dynamics. The results are visualized by means of the multidimensional technique and reveal the association between the fractal dimension and one definition of fractional derivative.

On development of fractional calculus during the last fifty years

Fractional calculus generalizes integer order derivatives and integrals. During the last half century a considerable progress took place in this scientific area. This paper addresses the evolution and establishes an assertive measure of the research development.