An Alternative Method for Solving a Certain Class of Fractional Kinetic Equations

An alternative method for solving the fractional kinetic equations solved earlier by Haubold and Mathai (2000) and Saxena et al. (2002, 2004a, 2004b) is recently given by Saxena and Kalla (2007). This method can also be applied in solving more general fractional kinetic equations than the ones solved by the aforesaid authors. In view of the usefulness and importance of the kinetic equation in certain physical problems governing reaction-diffusion in complex systems and anomalous diffusion, the authors present an alternative simple method for deriving the solution of the generalized forms of the fractional kinetic equations solved by the aforesaid authors and Nonnenmacher and Metzler (1995). The method depends on the use of the Riemann-Liouville fractional calculus operators. It has been shown by the application of Riemann-Liouville fractional integral operator and its interesting properties, that the solution of the given fractional kinetic equation can be obtained in a straight-forward manner. This method does not make use of the Laplace transform.Comment: 7 pages, LaTe

Neuroinflammation is a putative target for the prevention and treatment of perioperative neurocognitive disorders.

IntroductionThe demographics of aging of the surgical population has increased the risk for perioperative neurocognitive disorders in which trauma-induced neuroinflammation plays a pivotal role.Sources of dataAfter determining the scope of the review, the authors used PubMed with select phrases encompassing the words in the scope. Both preclinical and clinical reports were considered.Areas of agreementNeuroinflammation is a sine qua non for development of perioperative neurocognitive disorders.Areas of controversyWhat is the best method for ameliorating trauma-induced neuroinflammation while preserving inflammation-based wound healing.Growing pointsThis review considers how to prepare for and manage the vulnerable elderly surgical patient through the entire spectrum, from preoperative assessment to postoperative period.Areas timely for developing researchWhat are the most effective and safest interventions for preventing and/or reversing Perioperative Neurocognitive Disorders

Degree Ranking Using Local Information

Most real world dynamic networks are evolved very fast with time. It is not feasible to collect the entire network at any given time to study its characteristics. This creates the need to propose local algorithms to study various properties of the network. In the present work, we estimate degree rank of a node without having the entire network. The proposed methods are based on the power law degree distribution characteristic or sampling techniques. The proposed methods are simulated on synthetic networks, as well as on real world social networks. The efficiency of the proposed methods is evaluated using absolute and weighted error functions. Results show that the degree rank of a node can be estimated with high accuracy using only $1\%$ samples of the network size. The accuracy of the estimation decreases from high ranked to low ranked nodes. We further extend the proposed methods for random networks and validate their efficiency on synthetic random networks, that are generated using Erd\H{o}s-R\'{e}nyi model. Results show that the proposed methods can be efficiently used for random networks as well