Fractional Variations for Dynamical Systems: Hamilton and Lagrange Approaches

Fractional generalization of an exterior derivative for calculus of variations is defined. The Hamilton and Lagrange approaches are considered. Fractional Hamilton and Euler-Lagrange equations are derived. Fractional equations of motion are obtained by fractional variation of Lagrangian and Hamiltonian that have only integer derivatives.Comment: 21 pages, LaTe

Psi-Series Solution of Fractional Ginzburg-Landau Equation

One-dimensional Ginzburg-Landau equations with derivatives of noninteger order are considered. Using psi-series with fractional powers, the solution of the fractional Ginzburg-Landau (FGL) equation is derived. The leading-order behaviours of solutions about an arbitrary singularity, as well as their resonance structures, have been obtained. It was proved that fractional equations of order $alpha$ with polynomial nonlinearity of order $s$ have the noninteger power-like behavior of order $\alpha/(1-s)$ near the singularity.Comment: LaTeX, 19 pages, 2 figure

Algebraic damping in the one-dimensional Vlasov equation

We investigate the asymptotic behavior of a perturbation around a spatially non homogeneous stable stationary state of a one-dimensional Vlasov equation. Under general hypotheses, after transient exponential Landau damping, a perturbation evolving according to the linearized Vlasov equation decays algebraically with the exponent -2 and a well defined frequency. The theoretical results are successfully tested against numerical $N$-body simulations, corresponding to the full Vlasov dynamics in the large $N$ limit, in the case of the Hamiltonian mean-field model. For this purpose, we use a weighted particles code, which allows us to reduce finite size fluctuations and to observe the asymptotic decay in the $N$-body simulations.Comment: 26 pages, 8 figures; text slightly modified, references added, typos correcte

Life Satisfaction and Sense of Coherence of Breast Cancer Survivors Compared to Women with Mental Depression, Arterial Hypertension and Healthy Controls

The purpose of the study was to compare the life satisfaction (LS) and sense of coherence (SOC) of women recovering from breast cancer (BC) to LS and SOC of women with depression or hypertension and of healthy controls. Finnish Health and Social Support (HeSSup) follow-up survey data in 2003 was linked with national health registries. BC patients were followed up for mortality until the end of 2012. The statistical computations were carried out with SAS (R). There were no significant differences in LS and SOC between the groups with BC, arterial hypertension or healthy controls. Women recovering from BC are as satisfied with their life as healthy controls, and their perceived LS is better and SOC is stronger compared to women with depression. SOC correlated positively (r(2) = 0.36, p <0.001) with LS. However, more studies on determinants of the LS are needed for designing and organizing health care services for BC survivors.Peer reviewe

Continuous Limit of Discrete Systems with Long-Range Interaction

Discrete systems with long-range interactions are considered. Continuous medium models as continuous limit of discrete chain system are defined. Long-range interactions of chain elements that give the fractional equations for the medium model are discussed. The chain equations of motion with long-range interaction are mapped into the continuum equation with the Riesz fractional derivative. We formulate the consistent definition of continuous limit for the systems with long-range interactions. In this paper, we consider a wide class of long-range interactions that give fractional medium equations in the continuous limit. The power-law interaction is a special case of this class.Comment: 23 pages, LaTe

A randomised, phase II, unblinded trial of an Exercise and Nutrition-based Rehabilitation programme (ENeRgy) versus standard care in patients with cancer:feasibility trial protocol

Acknowledgements - The authors would like to thank Marie Curie and the Chief Scientist Office (UK) for funding this work (MCRGS-07-16-73), as well as acknowledge the support offered from the trial sponsors (ACCORD & NHS Lothian Edinburgh, UK). Also the valued contributions from the Southampton Clinical Trials Unit (UK), the Cicely Saunders Institute of Palliative Care, Policy and Rehabilitation, Kings College London (UK) as well as colleagues from different institutes within Edinburgh University (UK). Thanks to all the St Columba’s staff who helped get the trial set up, or assisted with the administration and the smooth running of the trial. Particular thanks to St Columba’s day therapies team especially Yvonne Whitehouse. Thanks to our dedicated ENeRgy clinic volunteers, Gillian Reid and Tommy Dalgleish for their commitment and helping make our participants feel welcomed and at ease, and for keeping the clinics running smoothly. Thanks to the clinical administration team and both community nurse specialist teams who showed great enthusiasm in identifying potential participants. Thanks to Marie Curie Hospice Edinburgh and the support from Dr. Emma Carduff (Marie Curie Glasgow) for their engagement and assistance with the trial. Thanks also to Abbott Nutrition, for supplying the oral nutritional supplements for the trial (ProSure), also for support from the Abbott team, in particular Dr Anne Voss.Erna Haraldsdottir - ORCID: 0000-0002-6451-1374 https://orcid.org/0000-0002-6451-1374Patients are living longer with incurable cancer [1] such that in many cases, cancer is likened to a chronic disease [2, 3, 4]. This development has wide-ranging implications for both patients and wider society, with increased longevity comes increased morbidity and associated socio-economic burden [5, 6]. Primary cost drivers for patients with advanced cancer are hospitalisation, GP and domiciliary visits [7]. Rehabilitation has been advocated as one such way of optimising the function and quality of life in this group of patients [8]; however, the optimal components of a rehabilitation model for patients with incurable cancer remain to be elucidated...The trial was funded by Marie Curie and the Chief Scientist Office (funding reference MCRGS-07-16-73). The funding bodies specified where changes were required to the design of the trial (including incorporating the impact upon carers and any health-economic impact as outcomes of the trial).4pubpub19

Plexiform neurofibroma of the submandibular gland in patient with von Recklinghausen's disease

Plexiform neurofibroma of the submandibular gland is an extremely rare tumor. Herein, we report a case of plexiform neurofibroma in a patient with a von Recklinghausen's disease (NF-1) who presented with a submandibular mass mimicking a submandibular gland tumor. Complete surgical excision provides the best treatment and final diagnosis. A neurofibroma should be considered in the differential diagnosis for submandibular mass

Validation of a brief telephone battery for neurocognitive assessment of patients with pulmonary arterial hypertension

BACKGROUND: The effects of pulmonary arterial hypertension on brain function are not understood, despite patients' frequent complaints of cognitive difficulties. Using clinical instruments normally administered during standard in-person assessment of neurocognitive function in adults, we assembled a battery of tests designed for administration over the telephone. The purpose was to improve patient participation, facilitate repeated test administration, and reduce the cost of research on the neuropsychological consequences of acute and chronic cardiorespiratory diseases. We undertook this study to validate telephone administration of the tests. METHODS: 23 adults with pulmonary arterial hypertension underwent neurocognitive assessment using both standard in-person and telephone test administration, and the results of the two methods compared using interclass correlations. RESULTS: For most of the tests in the battery, scores from the telephone assessment correlated strongly with those obtained by in-person administration of the same tests. Interclass correlations between 0.5 and 0.8 were observed for tests that assessed attention, memory, concentration/working memory, reasoning, and language/crystallized intelligence (p ≤ 0.05 for each). Interclass correlations for the Hayling Sentence Completion test of executive function approached significance (p = 0.09). All telephone tests were completed within one hour. CONCLUSION: Administration of this neurocognitive test battery by telephone should facilitate assessment of neuropsychological deficits among patients with pulmonary arterial hypertension living across broad geographical areas, and may be useful for monitoring changes in neurocognitive function in response to PAH-specific therapy or disease progression

Jets, Stickiness and Anomalous Transport

Dynamical and statistical properties of the vortex and passive particle advection in chaotic flows generated by four and sixteen point vortices are investigated. General transport properties of these flows are found anomalous and exhibit a superdiffusive behavior with typical second moment exponent (\mu \sim 1.75). The origin of this anomaly is traced back to the presence of coherent structures within the flow, the vortex cores and the region far from where vortices are located. In the vicinity of these regions stickiness is observed and the motion of tracers is quasi-ballistic. The chaotic nature of the underlying flow dictates the choice for thorough analysis of transport properties. Passive tracer motion is analyzed by measuring the mutual relative evolution of two nearby tracers. Some tracers travel in each other vicinity for relatively large times. This is related to an hidden order for the tracers which we call jets. Jets are localized and found in sticky regions. Their structure is analyzed and found to be formed of a nested sets of jets within jets. The analysis of the jet trapping time statistics shows a quantitative agreement with the observed transport exponent.Comment: 17 pages, 17 figure

True heterotopic bone in the paralyzed patient

In past years the clinical and radiologic presentation of true heterotopic bone in the paralyzed patient has been confused with osteomyelitis, neoplasm, trauma, and thrombophlebitis. We reviewed 376 paralyzed patients' roentgenographic files and found 78 patients with soft tissue ossification unassociated with infection, neoplasm, or underlying fractures, which we called true heterotopic bone. From this population the usual spectrum of radiologic findings is described, so that the radiologist may separate roentgenographically a group of patients from other types of ectopic ossification.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46816/1/256_2004_Article_BF00347167.pd