A Review of Operational Matrices and Spectral Techniques for Fractional Calculus

Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.

Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology

Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37

Maximum Principle and Its Application for the Time-Fractional Diffusion Equations

MSC 2010: 26A33, 33E12, 35B45, 35B50, 35K99, 45K05 Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th anniversary

Long-term survivor mixture model with random effects: application to a multi-centre clinical trial of carcinoma

A mixture model incorporating long-term survivors has been adopted in the field of biostatistics where some individuals may never experience the failure event under study. The surviving fractions may be considered as cured. In most applications, the survival times are assumed to be independent. However, when the survival data are obtained from a multi-centre clinical trial, it is conceived that the environ mental conditions and facilities shared within clinic affects the proportion cured as well as the failure risk for the uncured individuals. It necessitates a long-term survivor mixture model with random effects. In this paper, the long-term survivor mixture model is extended for the analysis of multivariate failure time data using the generalized linear mixed model (GLMM) approach. The proposed model is applied to analyse a numerical data set from a multi-centre clinical trial of carcinoma as an illustration. Some simulation experiments are performed to assess the applicability of the model based on the average biases of the estimates formed. Copyright (C) 2001 John Wiley & Sons, Ltd.

Multi-criteria short-term maintenance outage scheduling in smart distribution systems

Effective legislation and standards for the coordination procedures between consumers, producers and the system operator supports the advances in the technologies that lead to smart distribution systems. In short-term (ST) maintenance scheduling procedure, the energy producers in a distribution system access to the long-term (LT) outage plan that is released by the distribution system operator (DSO). The impact of this additional information on the decision-making procedure of producers in ST maintenance scheduling is studied in this paper. The final ST maintenance plan requires the approval of the DSO that has the responsibility to secure the network reliability and quality, and other players have to follow the finalized schedule. Maintenance scheduling in the producers’ layer and the coordination procedure between them and the DSO is modelled in this paper. The proposed method is applied to a 33-bus distribution system.

A multi-objective model for scheduling of short-term incentive-based demand response programs offered by electricity retailers

In this paper, we formulate the electricity retailers’ short-term decision-making problem in a liberalized retail market as a multi-objective optimization model. Retailers with light physical assets, such as generation and storage units in the distribution network, are considered. Following advances in smart grid technologies, electricity retailers are becoming able to employ incentive-based demand response (DR) programs in addition to their physical assets to effectively manage the risks of market price and load variations. In this model, the DR scheduling is performed simultaneously with the dispatch of generation and storage units. The ultimate goal is to find the optimal values of the hourly financial incentives offered to the end-users. The proposed model considers the capacity obligations imposed on retailers by the grid operator. The profit seeking retailer also has the objective to minimize the peak demand to avoid the high capacity charges in form of grid tariffs or penalties. The non-dominated sorting genetic algorithm II (NSGA-II) is used to solve the multi-objective problem. It is a fast and elitist multi-objective evolutionary algorithm. A case study is solved to illustrate the efficient performance of the proposed methodology. Simulation results show the effectiveness of the model for designing the incentive-based DR programs and indicate the efficiency of NSGA-II in solving the retailers’ multi-objective problem.

Multi-modal assessment of long-term erythropoietin treatment after neonatal hypoxic-ischemic injury in rat brain.

Erythropoietin (EPO) has been recognized as a neuroprotective agent. In animal models of neonatal brain injury, exogenous EPO has been shown to reduce lesion size, improve structure and function. Experimental studies have focused on short course treatment after injury. Timing, dose and length of treatment in preterm brain damage remain to be defined. We have evaluated the effects of high dose and long-term EPO treatment in hypoxic-ischemic (HI) injury in 3 days old (P3) rat pups using histopathology, magnetic resonance imaging (MRI) and spectroscopy (MRS) as well as functional assessment with somatosensory-evoked potentials (SEP). After HI, rat pups were assessed by MRI for initial damage and were randomized to receive EPO or vehicle. At the end of treatment period (P25) the size of resulting cortical damage and white matter (WM) microstructure integrity were assessed by MRI and cortical metabolism by MRS. Whisker elicited SEP were recorded to evaluate somatosensory function. Brains were collected for neuropathological assessment. The EPO treated animals did not show significant decrease of the HI induced cortical loss at P25. WM microstructure measured by diffusion tensor imaging was improved and SEP response in the injured cortex was recovered in the EPO treated animals compared to vehicle treated animals. In addition, the metabolic profile was less altered in the EPO group. Long-term treatment with high dose EPO after HI injury in the very immature rat brain induced recovery of WM microstructure and connectivity as well as somatosensory cortical function despite no effects on volume of cortical damage. This indicates that long-term high-dose EPO induces recovery of structural and functional connectivity despite persisting gross anatomical cortical alteration resulting from HI.

Face Short-Term Memory-Related Electroencephalographic Patterns can Differentiate Multi- versus Single-Domain Amnestic Mild Cognitive Impairment.

Amnestic mild cognitive impairment (aMCI) is characterized by memory deficits alone (single-domain, sd-aMCI) or associated with other cognitive disabilities (multi-domain, md-aMCI). The present study assessed the patterns of electroencephalographic (EEG) activity during the encoding and retrieval phases of short-term memory in these two aMCI subtypes, to identify potential functional differences according to the neuropsychological profile. Continuous EEG was recorded in 43 aMCI patients, whose 16 sd-aMCI and 27 md-aMCI, and 36 age-matched controls (EC) during delayed match-to-sample tasks for face and letter stimuli. At encoding, attended stimuli elicited parietal alpha (8-12 Hz) power decrease (desynchronization), whereas distracting stimuli were associated with alpha power increase (synchronization) over right central sites. No difference was observed in parietal alpha desynchronization among the three groups. For attended faces, the alpha synchronization underlying suppression of distracting letters was reduced in both aMCI subgroups, but more severely in md-aMCI cases that differed significantly from EC. At retrieval, the early N250r recognition effect was significantly reduced for faces in md-aMCI as compared to both sd-aMCI and EC. The results suggest a differential alteration of working memory cerebral processes for faces in the two aMCI subtypes, face covert recognition processes being specifically altered in md-aMCI.

Pilot study of the short-term physico-chemical stability of atenolol tablets stored in a multi-compartment compliance aid

Study objectives: There is a possibility that lower air, moisture and light protection could impact on physico-chemical stability of medicines inside multi-compartment compliance aids (MCCAs), although this has not yet been proved. The objectives of the study were to examine the physico-chemical stability of atenolol tablets stored in a compliance aid at room temperature, and at elevated temperature and humidity to simulate practice conditions. Methods: Atenolol 100 mg tablets in 28-chamber, plastic compliance aids with transparent lids were stored for four weeks at room temperature and at 40°C with 75% relative humidity. Tablets were also stored at room temperature in original packaging and Petri dishes. Physical tests were conducted to standards as laid down in the British Pharmacopoeia 2005, and dissolution to those of the United States Pharmacopoeia volume 24. Chemical stability was assessed by a validated high-performance liquid chromatography (HPLC) method. Results: Tablets at room temperature in original packaging, in compliance aids and Petri dishes remained the same in appearance and passed physico-chemical tests. Tablets exposed to 40°C with 75% relative humidity in compliance aids passed tests for uniformity of weight, friability and chemical stability but became pale and moist, softer (82 newtons ± 4; p< 0.0001) than tablets in the original packaging (118 newtons ± 6), more friable (0.14% loss of mass) compared with other tablets (0.005%), and failed the tests for disintegration (>15 minutes) and dissolution (only 15% atenolol released at 30 minutes). Conclusion: Although chemical stability was unaffected, storage in compliance aids at 40°C with 75% relative humidity softened atenolol tablets, prolonged disintegration time and hindered dissolution which could significantly reduce bioavailability. This formulation could be suitable for storage in compliance aids at 25°C, but not in hotter, humid weather.

Natural killer activity in a medium-term multi-organ bioassay for carcinogenesis

Natural killer (NK) cell activity was evaluated after the initiation and promotion steps in a medium-term multi-organ bioassay for carcinogenesis. NK cell activity was assessed in vitro by Cr-51 release assay at the 4th and 30th weeks of the experiment. Male Wistar rats were sequentially initiated with N-diethylnitrosamine (DEN i.p.), N-butyl-N-(4-hydroxybutyl)nitrosamine (BBN drinking water), N-methyl-N-nitrosourea (MNU i.p.), dihydroxy-di-N-propylnitrosamine (DHPN drinking water) and N,N'-dimethylhydrazine (DMH s.c.) at subcarcinogenic doses for 4 weeks (DMBDD initiation). One group was evaluated at the 4th week and the other was maintained without any further treatment until the 30th week. Two initiated groups were exposed through the diet to 2-acetylaminofluorene (2-AAF) or phenobarbital (PB), from the 6th until the 30th week, Five additional groups were studied to evaluate the effects of each initiator on NK activity. All groups submitted to initiation only, initiation plus promotion, or promotion only, developed significantly more preneoplastic lesions than the untreated control group. The main target organs for tumor development in the initiated animals n ere the liver and the colon, irrespective of treatment with 2-AAF or PB. NK cell activity was not affected bal exposure to genotoxic carcinogens after initiation, at the 4th week. Treatments only with PB or 2-AAF did not change NK cell activity, However, decreased NK cell activity was registered in the group only initiated with DMBDD and in the group given DMBDD+2-AAF. This late depression of NK cell activity at the 30th week could be related to the production of suppressing molecules by the tumor cells.

Lymphoproliferative response and T lymphocyte subsets in a medium-term multi-organ bioassay for carcinogenesis in Wistar rats

The lymphoproliferative response and T lymphocyte subsets were evaluated at different stages of carcinogenesis in male Wistar, rats sequentially initiated with N-diethylnitrosamine (DEN), N-butyl-N-4(hydroxybutyl)nitrosamine (BBN), N-methyl-N-nitrosourea (MNU), dihydroxy-di-N-propylnitrosamine (DHPN) and N,N'-dimethylhydrazine (DMH) (DMBDD initiation). One group was evaluated at the 4th week and other initiated group at the 30th week. Two initiated groups were also exposed through diet to 7-acetylaminofluorene (2-AAF) or phenobarbital (PB), from the 6th until the 30th week. Two groups received only 2-AAF or PB until the 30th week. Five groups were studied to evaluate the effects of each initiator. The lymphoproliferative response was induced in vitro by concanavalin A and the percentage of T lymphocyte subsets was determined by flow cytometry, All groups submitted to initiation only, initiation plus promotion, or promotion only, developed significantly more preneoplastic: lesions than the untreated control group. The main target organs for tumor development were the liver, colon, urinary bladder, kidneys and Zymbal glands, mainly in the group treated with DMBDD + 2-AAF, There were no alterations of the lymphoproliferative response and of the T lymphocyte subsets percentage in the DMBDD-treated group at the 4th and 30th weeks. At the 30th week, the T lymphocyte subsets percentage was also not affected in the initiated groups after treatments with 2-AAF or PB. The lymphoproliferative response, however, was decreased in the DMBDD + 2-AAF group and in the groups treated only with 2-AAF or PB, the present results indicate that the initiating chemicals used in the DMBDD initiation protocol do not exert any influence on the immune system. The alteration of lymphoproliferative response induced at the advanced stage of carcinogenesis without alteration of T lymphocyte subsets may indicate that the influence of 2-AAF and PB on the immune system is functional and not toxic. (C) 2000 Elsevier B.V. Ireland Ltd. All rights reserved.

Brazilian experience with the medium-term multi-organ bioassay: Scientific and regulatory developments

In 1996 the Brazilian Institute for the Environment (IBAMA) officially adopted a variation of the multiorgan initiation-promotion DMBDD bioassay as a valid source of evidence of the carcinogenic potential of pesticides. The protocol adopted by IBAMA was a modification of the one originally proposed by researchers led by Nobuyuki Ito, from the Nagoya City University Medical School. Among the modifications established in the Brazilian protocol were the use of both sexes of the outbreed Wistar strain of rats and two positive control test chemicals. The adoption of the modified DMBDD protocol was instrumental during the last decade for qualifying technical people and to spread knowledge on chemical carcinogenesis in Brazil.

Natural killer activity in a medium-term multi-organ bioassay for carcinogenesis

Natural killer (NK) cell activity was evaluated after the initiation and promotion steps in a medium-term multi-organ bioassay for carcinogenesis. NK cell activity was assessed in vitro by Cr51 release assay at the 4th and 30th weeks of the experiment. Male Wistar rats were sequentially initiated with N-diethylnitrosamine (DEN i.p.), N-butyl-N-(4-hydroxybutyl)nitrosamine (BBN drinking water), N-methyl-N-nitrosourea (MNU i.p.), dihydroxy-di-N-propylnitrosamine (DHPN drinking water) and N,N'-dimethylhydrazine (DMH s.c.) at subcarcinogenic doses for 4 weeks (DMBDD initiation). One group was evaluated at the 4th week and the other was maintained without any further treatment until the 30th week. Two initiated groups were exposed through the diet to 2-acetylaminofluorene (2-AAF) or phenobarbital (PB), from the 6th until the 30th week. Five additional groups were studied to evaluate the effects of each initiator on NK activity. All groups submitted to initiation only, initiation plus promotion, or promotion only, developed significantly more preneoplastic lesions than the untreated control group. The main target organs for tumor development in the initiated animals were the liver and the colon, irrespective of treatment with 2-AAF or PB. NK cell activity was not affected by exposure to genotoxic carcinogens after initiation, at the 4th week. Treatments only with PB or 2-AAF did not change NK cell activity. However, decreased NK cell activity was registered in the group only initiated with DMBDD and in the group given DMBDD+2-AAF. This late depression of NK cell activity at the 30th week could be related to the production of suppressing molecules by the tumor cells.