Fractional Cauchy problems on bounded domains: survey of recent results

In a fractional Cauchy problem, the usual first order time derivative is replaced by a fractional derivative. This problem was first considered by \citet{nigmatullin}, and \citet{zaslavsky} in $\mathbb R^d$ for modeling some physical phenomena. The fractional derivative models time delays in a diffusion process. We will give a survey of the recent results on the fractional Cauchy problem and its generalizations on bounded domains D\subset \rd obtained in \citet{m-n-v-aop, mnv-2}. We also study the solutions of fractional Cauchy problem where the first time derivative is replaced with an infinite sum of fractional derivatives. We point out a connection to eigenvalue problems for the fractional time operators considered. The solutions to the eigenvalue problems are expressed by Mittag-Leffler functions and its generalized versions. The stochastic solution of the eigenvalue problems for the fractional derivatives are given by inverse subordinators

PKA Mediates Constitutive Activation of CFTR in Human Sweat Duct

The cystic fibrosis transmembrane conductance regulator (CFTR) Cl− channels are constitutively activated in sweat ducts. Since phosphorylation-dependent and -independent mechanisms can activate CFTR, we sought to determine the actual mechanism responsible for constitutive activation of these channels in vivo. We show that the constitutively activated CFTR Cl− conductance (gCFTR) in the apical membrane is completely deactivated following α-toxin permeabilization of the basolateral membrane. We investigated whether such inhibition of gCFTR following permeabilization is due to the loss of cytoplasmic glutamate or due to dephosphorylation of CFTR by an endogenous phosphatase in the absence of kinase activity (due to the loss of kinase agonist cAMP, cGMP or GTP through α-toxin pores). In order to distinguish between these two possibilities, we examined the effect of inhibiting the endogenous phosphatase activity with okadaic acid (10−8 M) on the permeabilization-induced deactivation of gCFTR. We show that okadaic acid (1) inhibits an endogenous phosphatase responsible for dephosphorylating cAMP but not cGMP or G protein-activated CFTR and (2) prevents deactivation of CFTR following permeabilization of the basolateral membrane. These results indicate that distinctly different phosphatases may be responsible for dephosphorylating different kinase-specific sites on CFTR. We conclude that the phosphorylation by PKA alone appears to be primarily responsible for constitutive activation of gCFTR in vivo

Inversions of Levy Measures and the Relation Between Long and Short Time Behavior of Levy Processes

The inversion of a Levy measure was first introduced (under a different name) in Sato 2007. We generalize the definition and give some properties. We then use inversions to derive a relationship between weak convergence of a Levy process to an infinite variance stable distribution when time approaches zero and weak convergence of a different Levy process as time approaches infinity. This allows us to get self contained conditions for a Levy process to converge to an infinite variance stable distribution as time approaches zero. We formulate our results both for general Levy processes and for the important class of tempered stable Levy processes. For this latter class, we give detailed results in terms of their Rosinski measures

Escherichia coli phylogenetic group determination and its application in the identification of the major animal source of fecal contamination

<p>Abstract</p> <p>Background</p> <p><it>Escherichia coli </it>strains are commonly found in the gut microflora of warm-blooded animals. These strains can be assigned to one of the four main phylogenetic groups, A, B1, B2 and D, which can be divided into seven subgroups (A₀, A₁, B1, B2₂, B2₃, D₁and D₂), according to the combination of the three genetic markers <it>chuA</it>, <it>yjaA </it>and DNA fragment TspE4.C2. Distinct studies have demonstrated that these phylo-groups differ in the presence of virulence factors, ecological niches and life-history. Therefore, the aim of this work was to analyze the distribution of these <it>E. coli </it>phylo-groups in 94 human strains, 13 chicken strains, 50 cow strains, 16 goat strains, 39 pig strains and 29 sheep strains and to verify the potential of this analysis to investigate the source of fecal contamination.</p> <p>Results</p> <p>The results indicated that the distribution of phylogenetic groups, subgroups and genetic markers is non-random in the hosts analyzed. Strains from group B1 were present in all hosts analyzed but were more prevalent in cow, goat and sheep samples. Subgroup B2₃was only found in human samples. The diversity and the similarity indexes have indicated a similarity between the <it>E. coli </it>population structure of human and pig samples and among cow, goat and sheep samples. Correspondence analysis using contingence tables of subgroups, groups and genetic markers frequencies allowed the visualization of the differences among animal samples and the identification of the animal source of an external validation set. The classifier tools Binary logistic regression and Partial least square -- discriminant analysis, using the genetic markers profile of the strains, differentiated the herbivorous from the omnivorous strains, with an average error rate of 17%.</p> <p>Conclusions</p> <p>This is the first work, as far as we are aware, that identifies the major source of fecal contamination of a pool of strains instead of a unique strain. We concluded that the analysis of the <it>E. coli </it>population structure can be useful as a supplementary bacterial source tracking tool.</p

Quantized Nambu-Poisson Manifolds in a 3-Lie Algebra Reduced Model

We consider dimensional reduction of the Bagger-Lambert-Gustavsson theory to a zero-dimensional 3-Lie algebra model and construct various stable solutions corresponding to quantized Nambu-Poisson manifolds. A recently proposed Higgs mechanism reduces this model to the IKKT matrix model. We find that in the strong coupling limit, our solutions correspond to ordinary noncommutative spaces arising as stable solutions in the IKKT model with D-brane backgrounds. In particular, this happens for S^3, R^3 and five-dimensional Neveu-Schwarz Hpp-waves. We expand our model around these backgrounds and find effective noncommutative field theories with complicated interactions involving higher-derivative terms. We also describe the relation of our reduced model to a cubic supermatrix model based on an osp(1|32) supersymmetry algebra.Comment: 22 page

Nel positively regulates the genesis of retinal ganglion cells by promoting their differentiation and survival during development

Peer reviewedPublisher PD

Feller Processes: The Next Generation in Modeling. Brownian Motion, L\'evy Processes and Beyond

We present a simple construction method for Feller processes and a framework for the generation of sample paths of Feller processes. The construction is based on state space dependent mixing of L\'evy processes. Brownian Motion is one of the most frequently used continuous time Markov processes in applications. In recent years also L\'evy processes, of which Brownian Motion is a special case, have become increasingly popular. L\'evy processes are spatially homogeneous, but empirical data often suggest the use of spatially inhomogeneous processes. Thus it seems necessary to go to the next level of generalization: Feller processes. These include L\'evy processes and in particular Brownian motion as special cases but allow spatial inhomogeneities. Many properties of Feller processes are known, but proving the very existence is, in general, very technical. Moreover, an applicable framework for the generation of sample paths of a Feller process was missing. We explain, with practitioners in mind, how to overcome both of these obstacles. In particular our simulation technique allows to apply Monte Carlo methods to Feller processes.Comment: 22 pages, including 4 figures and 8 pages of source code for the generation of sample paths of Feller processe

Tumours and tumour-like lesions of the lower face at Korle Bu Teaching Hospital, Ghana – an eight year study

<p>Abstract</p> <p>Background</p> <p>The oro-facial region including the jawbones, the maxilla and mandible and related tissues can be the site of a multitude of neoplastic conditions. These tumours have a predilection for the entire facial region; however, odontogenic tumours tend to affect the mandible more than the maxilla, especially, in West African children. We report results from a retrospective study spanning eight years on the frequency, clinical presentation, sites and character of lower face tumours seen in the main referral hospital in Ghana.</p> <p>Patients and methods</p> <p>Records of consecutive patients of all age and sex seen by the first author's team at the Department of Oral and Maxillofacial Surgery, Korle-Bu Teaching Hospital with tumours affecting the lower part of the face from January 1996 to December 2003 were retrieved, coded and entered into a database. The data were then analyzed by age, sex, presenting signs and symptoms, site of lesion, and their histology.</p> <p>Results</p> <p>A total of 394 patients with oro-facial swellings were retrieved from the registry out of which 210 had lower face tumour and tumour-like lesions. The complete data set was obtained for 171 patients, comprising 99 (58%) males and 72 (42%) females. The most common clinical presenting features were mandibular facial swelling (63%), intra-oral swelling (55%), pain (41%) and ulceration (29%). The tumours were predominantly found in the right (43%), anterior (19%) and left (18%) aspects of the lower face. The remainder making up 20% were found in the floor of the mouth, tongue and lips. Seventy eight (45.6%) of the patients presented with lesions that were classified as malignant of which 54 (62%) were diagnosed as squamous cell carcinoma (SCC). Sixty-two (36.3%) had benign odontogenic tumours and thirty-one (18.1%) had non-odontogenic tumour-like lesions. Fifty-four (62%) of malignant tumours were squamous cell carcinoma; 58 (93.6%) of the benign odontogenic tumours were classified as ameloblastoma. The mean age at presentation of all lesions was 40.4 years with over 50% of benign lesions in patients aged between 11 and 30 years. Malignant tumours were more commonly detected in patients between 41 and 70 years (63%).</p> <p>Conclusion</p> <p>Tumours and tumour-like lesions of the lower face comprising the mandible, tongue and adjacent structures are a diverse group of neoplasm and are seen commonly in practice of Maxillofacial surgery. Both malignant and benign tumours are seen in the Ghanaian population. In the present study, SCC and ameloblastoma were the commonest malignant and benign odontogenic tumours seen respectively; the two representing more than 65% of all tumours.</p

Gluino Decay as a Probe of High Scale Supersymmetry Breaking

A supersymmetric standard model with heavier scalar supersymmetric particles has many attractive features. If the scalar mass scale is O(10 - 10^4) TeV, the standard model like Higgs boson with mass around 125 GeV, which is strongly favored by the LHC experiment, can be realized. However, in this scenario the scalar particles are too heavy to be produced at the LHC. In addition, if the scalar mass is much less than O(10^4) TeV, the lifetime of the gluino is too short to be measured. Therefore, it is hard to probe the scalar particles at a collider. However, a detailed study of the gluino decay reveals that two body decay of the gluino carries important information on the scalar scale. In this paper, we propose a test of this scenario by measuring the decay pattern of the gluino at the LHC.Comment: 29 pages, 9 figures; version published in JHE

Superconductivity at the Border of Electron Localization and Itinerancy

The superconducting state of iron pnictides and chalcogenides exists at the border of antiferromagnetic order. Consequently, these materials could provide clues about the relationship between magnetism and unconventional superconductivity. One explanation, motivated by the so-called bad-metal behaviour of these materials, proposes that magnetism and superconductivity develop out of quasi-localized magnetic moments which are generated by strong electron-electron correlations. Another suggests that these phenomena are the result of weakly interacting electron states that lie on nested Fermi surfaces. Here we address the issue by comparing the newly discovered alkaline iron selenide superconductors, which exhibit no Fermi-surface nesting, to their iron pnictide counterparts. We show that the strong-coupling approach leads to similar pairing amplitudes in these materials, despite their different Fermi surfaces. We also find that the pairing amplitudes are largest at the boundary between electronic localization and itinerancy, suggesting that new superconductors might be found in materials with similar characteristics.Comment: Version of the published manuscript prior to final journal-editting. Main text (23 pages, 4 figures) + Supplementary Information (14 pages, 7 figures, 3 tables). Calculation on the single-layer FeSe is added. Enhancement of the pairing amplitude in the vicinity of the Mott transition is highlighted. Published version is at http://www.nature.com/ncomms/2013/131115/ncomms3783/full/ncomms3783.htm