Fractional derivatives of random walks: Time series with long-time memory

We review statistical properties of models generated by the application of a (positive and negative order) fractional derivative operator to a standard random walk and show that the resulting stochastic walks display slowly-decaying autocorrelation functions. The relation between these correlated walks and the well-known fractionally integrated autoregressive (FIGARCH) models, commonly used in econometric studies, is discussed. The application of correlated random walks to simulate empirical financial times series is considered and compared with the predictions from FIGARCH and the simpler FIARCH processes. A comparison with empirical data is performed.Comment: 10 pages, 14 figure

Anomalous Rotational Relaxation: A Fractional Fokker-Planck Equation Approach

In this study we obtained analytically relaxation function in terms of rotational correlation functions based on Brownian motion for complex disordered systems in a stochastic framework. We found out that rotational relaxation function has a fractional form for complex disordered systems, which indicates relaxation has non-exponential character obeys to Kohlrausch-William-Watts law, following the Mittag-Leffler decay.Comment: Revtex4, 9 pages. Paper was revised. References adde

Using the fractional interaction law to model the impact dynamics in arbitrary form of multiparticle collisions

Using the molecular dynamics method, we examine a discrete deterministic model for the motion of spherical particles in three-dimensional space. The model takes into account multiparticle collisions in arbitrary forms. Using fractional calculus we proposed an expression for the repulsive force, which is the so called fractional interaction law. We then illustrate and discuss how to control (correlate) the energy dissipation and the collisional time for an individual article within multiparticle collisions. In the multiparticle collisions we included the friction mechanism needed for the transition from coupled torsion-sliding friction through rolling friction to static friction. Analysing simple simulations we found that in the strong repulsive state binary collisions dominate. However, within multiparticle collisions weak repulsion is observed to be much stronger. The presented numerical results can be used to realistically model the impact dynamics of an individual particle in a group of colliding particles.Comment: 17 pages, 8 figures, 1 table; In review process of Physical Review

Non-Markovian Levy diffusion in nonhomogeneous media

We study the diffusion equation with a position-dependent, power-law diffusion coefficient. The equation possesses the Riesz-Weyl fractional operator and includes a memory kernel. It is solved in the diffusion limit of small wave numbers. Two kernels are considered in detail: the exponential kernel, for which the problem resolves itself to the telegrapher's equation, and the power-law one. The resulting distributions have the form of the L\'evy process for any kernel. The renormalized fractional moment is introduced to compare different cases with respect to the diffusion properties of the system.Comment: 7 pages, 2 figure

Homeless drug users' awareness and risk perception of peer "Take Home Naloxone" use – a qualitative study

BACKGROUND Peer use of take home naloxone has the potential to reduce drug related deaths. There appears to be a paucity of research amongst homeless drug users on the topic. This study explores the acceptability and potential risk of peer use of naloxone amongst homeless drug users. From the findings the most feasible model for future treatment provision is suggested. METHODS In depth face-to-face interviews conducted in one primary care centre and two voluntary organisation centres providing services to homeless drug users in a large UK cosmopolitan city. Interviews recorded, transcribed and analysed thematically by framework techniques. RESULTS Homeless people recognise signs of a heroin overdose and many are prepared to take responsibility to give naloxone, providing prior training and support is provided. Previous reports of the theoretical potential for abuse and malicious use may have been overplayed. CONCLUSION There is insufficient evidence to recommend providing "over the counter" take home naloxone" to UK homeless injecting drug users. However a programme of peer use of take home naloxone amongst homeless drug users could be feasible providing prior training is provided. Peer education within a health promotion framework will optimise success as current professionally led health promotion initiatives are failing to have a positive impact amongst homeless drug users

Active Semantic Electronic Medical Record

The healthcare industry is rapidly advancing towards the widespread use of electronic medical records systems to manage the increasingly large amount of patient data and reduce medical errors. In addition to patient data there is a large amount of data describing procedures, treatments, diagnoses, drugs, insurance plans, coverage, formularies and the relationships between these data sets. While practices have benefited from the use of EMRs, infusing these essential programs with rich domain knowledge and rules can greatly enhance their performance and ability to support clinical decisions. Active Semantic Electronic Medical Record (ASEMR) application discussed here uses Semantic Web technologies to reduce medical errors, improve physician efficiency with accurate completion of patient charts, improve patient safety and satisfaction in medical practice, and improve billing due to more accurate coding. This results in practice efficiency and growth by enabling physicians to see more patients with improved care. ASEMR has been deployed and in daily use for managing all patient records at the Athens Heart Center since December 2005. This showcases an application of Semantic Web in health care, especially small clinics

Measuring subdiffusion parameters

We propose a method to extract from experimental data the subdiffusion parameter $\alpha$ and subdiffusion coefficient $D_\alpha$ which are defined by means of the relation $=2D_\alpha/\Gamma(1+\alpha) t^\alpha$ where $$ denotes a mean square displacement of a random walker starting from $x=0$ at the initial time $t=0$. The method exploits a membrane system where a substance of interest is transported in a solvent from one vessel to another across a thin membrane which plays here only an auxiliary role. Using such a system, we experimentally study a diffusion of glucose and sucrose in a gel solvent. We find a fully analytic solution of the fractional subdiffusion equation with the initial and boundary conditions representing the system under study. Confronting the experimental data with the derived formulas, we show a subdiffusive character of the sugar transport in gel solvent. We precisely determine the parameter $\alpha$, which is smaller than 1, and the subdiffusion coefficient $D_\alpha$.Comment: 17 pages, 9 figures, revised, to appear in Phys. Rev.

Stationarity-conservation laws for certain linear fractional differential equations

The Leibniz rule for fractional Riemann-Liouville derivative is studied in algebra of functions defined by Laplace convolution. This algebra and the derived Leibniz rule are used in construction of explicit form of stationary-conserved currents for linear fractional differential equations. The examples of the fractional diffusion in 1+1 and the fractional diffusion in d+1 dimensions are discussed in detail. The results are generalized to the mixed fractional-differential and mixed sequential fractional-differential systems for which the stationarity-conservation laws are obtained. The derived currents are used in construction of stationary nonlocal charges.Comment: 28 page

Some blood indices in finisher broiler chickens fed cocoa pod husk (Theobroma cacao L.) fermented with Pleurotus ostreatus or treated with enzymes as ingredients in their diets

The dietary effects of pre-treated cocoa pod husk (CPH) on some blood indices of 21-day old COBB-500 finisher broiler chicks were evaluated in a 35-day experiment with a completely randomized design. The birds were allotted to seven treatments (diets) having 0-g kg-1, 100- g kg-1, 200-g kg-1 and 300-g kg-1 of either Pleurotus ostreatus fermented CPH (PF-CPH) or enzyme (Viscoyme®L+Pectinex®5XL) supplemented CPH (E-CPH). Each treatment was replicated three times with 12 chicks per replicate. The haemoglobin concentration (Hb), packed cell volume (PCV), activities of the enzymes aspartate aminotransferase (AST) and alanine aminotransferase (ALT), serum levels of cholesterol (CH), uric acid, total protein, albumin and globulin were determined. Across dietary treatments Hb, PCV, CH, uric acid and AST activity level in blood of birds varied significantly (P < 0.05). However, there was insignificant influence (P > 0.05) of pre-treated CPH on all the other evaluated parameters among treatment groups. All blood indices measured were within acceptable or reference ranges. The study has revealed that incorporating either E-CPH or PF-CPH up to 30 per cent of broiler finisher diet had no adverse effect on the blood values of the broiler chickens. However, up to 20 per cent PF-CPH and 10 per cent E-CPH incorporation rates for broiler finisher diets, based on best results observed for growth and feed conversion, is recommende

The decline in youth drinking in England – is everyone drinking less? A quantile regression analysis

Background and Aims: Youth alcohol consumption has declined significantly over the past 15 years in many high income countries, which may have significant public health benefits. However, if the reductions in drinking occur mostly among lighter drinkers who are at lower risk, then rates of alcohol-related harm among young people today and adults in future may not fall in line with consumption. There is conflicting evidence from Swedish school studies with some suggesting all young people are drinking less while others suggest alcohol consumption among heavier drinkers may be stable or rising while average consumption declines. This paper extends the geographic focus of previous research and examines whether the decline in youth drinking is consistent across the consumption distribution in England. Design: Quantile regression of 15 waves of repeat cross-sectional survey data. Setting: England, 2001-2016. Participants: 31, 882 schoolchildren (50.7% male) aged 11-15 who responded to the Smoking Drinking and Drug Use amongst Young People surveys. Measurements: Past-week alcohol consumption in UK units at each fifth percentile of the consumption distribution. Findings: Reductions in alcohol consumption occurred at all percentiles of the consumption distribution analysed between 2001 and 2016 but the magnitude of the decline differed across percentiles. The decline in consumption at the 90th percentile (β = -.21, CI = -.24, - .18) was significantly larger than among either lighter drinkers at the 50th percentile (β = - .02, CI = -.02, -.01) or heavier drinkers at the 95th percentile (β = -.16, CI = -.18, -.13). Conclusions: Alcohol consumption among young people in England appears to be declining across the consumption distribution, and peaks among heavy drinkers. The magnitude of this decline differs significantly between percentiles of the consumption distribution, with consumption falling proportionally less among the lightest, moderate and very heaviest youth drinkers