Solving Linear Coupled Fractional Differential Equations by Direct Operational Method and Some Applications

A new direct operational inversion method is introduced for solving coupled linear systems of ordinary fractional differential equations. The solutions so-obtained can be expressed explicitly in terms of multivariate Mittag-Leffler functions. In the case where the multiorders are multiples of a common real positive number, the solutions can be reduced to linear combinations of Mittag-Leffler functions of a single variable. The solutions can be shown to be asymptotically oscillatory under certain conditions. This technique is illustrated in detail by two concrete examples, namely, the coupled harmonic oscillator and the fractional Wien bridge circuit. Stability conditions and simulations of the corresponding solutions are given

Accelerating and Retarding Anomalous Diffusion

In this paper Gaussian models of retarded and accelerated anomalous diffusion are considered. Stochastic differential equations of fractional order driven by single or multiple fractional Gaussian noise terms are introduced to describe retarding and accelerating subdiffusion and superdiffusion. Short and long time asymptotic limits of the mean squared displacement of the stochastic processes associated with the solutions of these equations are studied. Specific cases of these equations are shown to provide possible descriptions of retarding or accelerating anomalous diffusion.Comment: 18 page, 1 figur

Finite Temperature Casimir Effect for a Massless Fractional Klein-Gordon field with Fractional Neumann Conditions

This paper studies the Casimir effect due to fractional massless Klein-Gordon field confined to parallel plates. A new kind of boundary condition called fractional Neumann condition which involves vanishing fractional derivatives of the field is introduced. The fractional Neumann condition allows the interpolation of Dirichlet and Neumann conditions imposed on the two plates. There exists a transition value in the difference between the orders of the fractional Neumann conditions for which the Casimir force changes from attractive to repulsive. Low and high temperature limits of Casimir energy and pressure are obtained. For sufficiently high temperature, these quantities are dominated by terms independent of the boundary conditions. Finally, validity of the temperature inversion symmetry for various boundary conditions is discussed.Comment: 31 page

Revisiting special relativity: A natural algebraic alternative to Minkowski spacetime

Minkowski famously introduced the concept of a space-time continuum in 1908, merging the three dimensions of space with an imaginary time dimension $i c t$, with the unit imaginary producing the correct spacetime distance $x^2 - c^2 t^2$, and the results of Einstein's then recently developed theory of special relativity, thus providing an explanation for Einstein's theory in terms of the structure of space and time. As an alternative to a planar Minkowski space-time of two space dimensions and one time dimension, we replace the unit imaginary $i = \sqrt{-1}$, with the Clifford bivector $\iota = e_1 e_2$ for the plane that also squares to minus one, but which can be included without the addition of an extra dimension, as it is an integral part of the real Cartesian plane with the orthonormal basis $e_1$ and $e_2$. We find that with this model of planar spacetime, using a two-dimensional Clifford multivector, the spacetime metric and the Lorentz transformations follow immediately as properties of the algebra. This also leads to momentum and energy being represented as components of a multivector and we give a new efficient derivation of Compton's scattering formula, and a simple formulation of Dirac's and Maxwell's equations. Based on the mathematical structure of the multivector, we produce a semi-classical model of massive particles, which can then be viewed as the origin of the Minkowski spacetime structure and thus a deeper explanation for relativistic effects. We also find a new perspective on the nature of time, which is now given a precise mathematical definition as the bivector of the plane.Comment: 29 pages, 2 figure

Somatic mutations of CADM1 in aldosterone-producing adenomas and gap junction-dependent regulation of aldosterone production

Aldosterone-producing adenomas (APAs) are the commonest curable cause of hypertension. Most have gain-of-function somatic mutations of ion channels or transporters. Herein we report the discovery, replication and phenotype of mutations in the neuronal cell adhesion gene CADM1. Independent whole exome sequencing of 40 and 81 APAs found intramembranous p.Val380Asp or p.Gly379Asp variants in two patients whose hypertension and periodic primary aldosteronism were cured by adrenalectomy. Replication identified two more APAs with each variant (total, n = 6). The most upregulated gene (10- to 25-fold) in human adrenocortical H295R cells transduced with the mutations (compared to wildtype) was CYP11B2 (aldosterone synthase), and biological rhythms were the most differentially expressed process. CADM1 knockdown or mutation inhibited gap junction (GJ)-permeable dye transfer. GJ blockade by Gap27 increased CYP11B2 similarly to CADM1 mutation. Human adrenal zona glomerulosa (ZG) expression of GJA1 (the main GJ protein) was patchy, and annular GJs (sequelae of GJ communication) were less prominent in CYP11B2-positive micronodules than adjacent ZG. Somatic mutations of CADM1 cause reversible hypertension and reveal a role for GJ communication in suppressing physiological aldosterone production

Prevalence and determinants of HPV infection among Colombian women with normal cytology

Human papillomavirus is the principal risk factor associated with cervical cancer, the most common malignancy among women in Colombia. We conducted a survey, aiming to report type specific prevalence and determinants of human papillomavirus infection in women with normal cytology. A total of 1859 women from Bogota, Colombia were interviewed and tested for human papillomavirus using a general primer GP5+/GP6+ mediated PCR–EIA. The overall HPV DNA prevalence was 14.8%; 9% of the women were infected by high risk types, 3.1% by low risk types, 2.3% by both high risk/low risk types and 0.4% by uncharacterized types (human papillomavirus X). Thirty-two different human papillomavirus types were detected, being human papillomavirus 16, 58, 56, 81(CP8304) and 18 the most common types. The human papillomavirus prevalence was 26.1% among women younger than 20 years, 2.3% in women aged 45–54 years, and 13.2% in women aged 55 years or more. For low risk types the highest peak of prevalence was observed in women aged 55 years or more. Compared to women aged 35–44 years, women aged less than 20 years had a 10-fold increased risk of having multiple infections. Besides age, there was a positive association between the risk of human papillomavirus infection and number of regular sexual partners and oral contraceptive use. In women aged below 25 years, high educational level and having had casual sexual partners predicted infection risk. In conclusion, there was a broad diversity of human papillomavirus infections with high risk types being the most common types detected. In this population multiplicity of sexual partners and, among young women, high educational level and casual sexual partners seem to determine risk

A historical overview of the classification, evolution, and dispersion of Leishmania parasites and sandflies

Background The aim of this study is to describe the major evolutionary historical events among Leishmania, sandflies, and the associated animal reservoirs in detail, in accordance with the geographical evolution of the Earth, which has not been previously discussed on a large scale. Methodology and Principal Findings Leishmania and sandfly classification has always been a controversial matter, and the increasing number of species currently described further complicates this issue. Despite several hypotheses on the origin, evolution, and distribution of Leishmania and sandflies in the Old and New World, no consistent agreement exists regarding dissemination of the actors that play roles in leishmaniasis. For this purpose, we present here three centuries of research on sandflies and Leishmania descriptions, as well as a complete description of Leishmania and sandfly fossils and the emergence date of each Leishmania and sandfly group during different geographical periods, from 550 million years ago until now. We discuss critically the different approaches that were used for Leishmana and sandfly classification and their synonymies, proposing an updated classification for each species of Leishmania and sandfly. We update information on the current distribution and dispersion of different species of Leishmania (53), sandflies (more than 800 at genus or subgenus level), and animal reservoirs in each of the following geographical ecozones: Palearctic, Nearctic, Neotropic, Afrotropical, Oriental, Malagasy, and Australian. We propose an updated list of the potential and proven sandfly vectors for each Leishmania species in the Old and New World. Finally, we address a classical question about digenetic Leishmania evolution: which was the first host, a vertebrate or an invertebrate? Conclusions and Significance We propose an updated view of events that have played important roles in the geographical dispersion of sandflies, in relation to both the Leishmania species they transmit and the animal reservoirs of the parasites