Fractional Euler-Lagrange differential equations via Caputo derivatives

We review some recent results of the fractional variational calculus. Necessary optimality conditions of Euler-Lagrange type for functionals with a Lagrangian containing left and right Caputo derivatives are given. Several problems are considered: with fixed or free boundary conditions, and in presence of integral constraints that also depend on Caputo derivatives.Comment: This is a preprint of a paper whose final and definite form will appear as Chapter 9 of the book Fractional Dynamics and Control, D. Baleanu et al. (eds.), Springer New York, 2012, DOI:10.1007/978-1-4614-0457-6_9, in pres

An empirical evaluation of imputation accuracy for association statistics reveals increased type-I error rates in genome-wide associations

<p>Abstract</p> <p>Background</p> <p>Genome wide association studies (GWAS) are becoming the approach of choice to identify genetic determinants of complex phenotypes and common diseases. The astonishing amount of generated data and the use of distinct genotyping platforms with variable genomic coverage are still analytical challenges. Imputation algorithms combine directly genotyped markers information with haplotypic structure for the population of interest for the inference of a badly genotyped or missing marker and are considered a near zero cost approach to allow the comparison and combination of data generated in different studies. Several reports stated that imputed markers have an overall acceptable accuracy but no published report has performed a pair wise comparison of imputed and empiric association statistics of a complete set of GWAS markers.</p> <p>Results</p> <p>In this report we identified a total of 73 imputed markers that yielded a nominally statistically significant association at <it>P </it>< 10 ^-5for type 2 Diabetes Mellitus and compared them with results obtained based on empirical allelic frequencies. Interestingly, despite their overall high correlation, association statistics based on imputed frequencies were discordant in 35 of the 73 (47%) associated markers, considerably inflating the type I error rate of imputed markers. We comprehensively tested several quality thresholds, the haplotypic structure underlying imputed markers and the use of flanking markers as predictors of inaccurate association statistics derived from imputed markers.</p> <p>Conclusions</p> <p>Our results suggest that association statistics from imputed markers showing specific MAF (Minor Allele Frequencies) range, located in weak linkage disequilibrium blocks or strongly deviating from local patterns of association are prone to have inflated false positive association signals. The present study highlights the potential of imputation procedures and proposes simple procedures for selecting the best imputed markers for follow-up genotyping studies.</p

Fractional variational calculus of variable order

We study the fundamental problem of the calculus of variations with variable order fractional operators. Fractional integrals are considered in the sense of Riemann-Liouville while derivatives are of Caputo type.Comment: Submitted 26-Sept-2011; accepted 18-Oct-2011; withdrawn by the authors 21-Dec-2011; resubmitted 27-Dec-2011; revised 20-March-2012; accepted 13-April-2012; to 'Advances in Harmonic Analysis and Operator Theory', The Stefan Samko Anniversary Volume (Eds: A. Almeida, L. Castro, F.-O. Speck), Operator Theory: Advances and Applications, Birkh\"auser Verlag (http://www.springer.com/series/4850

Quantum networks reveal quantum nonlocality

The results of local measurements on some composite quantum systems cannot be reproduced classically. This impossibility, known as quantum nonlocality, represents a milestone in the foundations of quantum theory. Quantum nonlocality is also a valuable resource for information processing tasks, e.g. quantum communication, quantum key distribution, quantum state estimation, or randomness extraction. Still, deciding if a quantum state is nonlocal remains a challenging problem. Here we introduce a novel approach to this question: we study the nonlocal properties of quantum states when distributed and measured in networks. Using our framework, we show how any one-way entanglement distillable state leads to nonlocal correlations. Then, we prove that nonlocality is a non-additive resource, which can be activated. There exist states, local at the single-copy level, that become nonlocal when taking several copies of it. Our results imply that the nonlocality of quantum states strongly depends on the measurement context.Comment: 4 + 3 pages, 4 figure

H-Ferritin Is Essential for Macrophages' Capacity to Store or Detoxify Exogenously Added Iron

Macrophages are central cells both in the immune response and in iron homeostasis. Iron is both essential and potentially toxic. Therefore, iron acquisition, transport, storage, and release are tightly regulated, by several important proteins. Cytosolic ferritin is an iron storage protein composed of 24 subunits of either the L- or the H-type chains. H-ferritin differs from L-ferritin in the capacity to oxidize Fe2+ to Fe3+. In this work, we investigated the role played by H-ferritin in the macrophages' ability to respond to immune stimuli and to deal with exogenously added iron. We used mice with a conditional deletion of the H-ferritin gene in the myeloid lineage to obtain bone marrow-derived macrophages. These macrophages had normal viability and gene expression under basal culture conditions. However, when treated with interferon-gamma and lipopolysaccharide they had a lower activation of Nitric Oxide Synthase 2. Furthermore, H-ferritin-deficient macrophages had a higher sensitivity to iron-induced toxicity. This sensitivity was associated with a lower intracellular iron accumulation but a higher production of reactive oxygen species. These data indicate that H-ferritin modulates macrophage response to immune stimuli and that it plays an essential role in protection against iron-induced oxidative stress and cell death.Tis work was fnanced by FEDER - Fundo Europeu de Desenvolvimento Regional funds through the COMPETE2020 - Operacional Programme for Competitiveness and Internationalization (POCI), Portugal 2020, and by Portuguese funds through FCT - Fundação para a Ciência e a Tecnologia/Ministério da Ciência, Tecnologia e Ensino Superior in the framework of the project PTDC/IMI-MIC/1683/2014 (POCI-01-0145-FEDER-016590). PFO and MGA acknowledge FCT for the Investigador FCT 2015. We thank the valuable collaboration of the following i3S Scientifc Platforms: Cell Culture and Genotyping Core Facility (CCGen), [Histology and Electron Microscopy Service (HEMS), and BioSciences Screening], member of the PPBI (PPBI-POCI-01-0145-FEDER-022122)], Animal Facility, and Flow Cytometry Unit (TraCy). We acknowledge Lukas Kuhn (Swiss Institute for Experimental Cancer Research, Lausanne, Switzerland) for kindly providing the frst breeding pairs of Fth1−/− mice. Te authors also acknowledge Marisa Castro, from Departamento de Biologia Molecular from ICBAS, Clara Bento, from i3S, and Edgar Pinto from LAQV – REQUIMTE for technical assistance at diferent stages of the project

Evolutionary plasticity determination by orthologous groups distribution

<p>Abstract</p> <p>Background</p> <p>Genetic plasticity may be understood as the ability of a functional gene network to tolerate alterations in its components or structure. Usually, the studies involving gene modifications in the course of the evolution are concerned to nucleotide sequence alterations in closely related species. However, the analysis of large scale data about the distribution of gene families in non-exclusively closely related species can provide insights on how plastic or how conserved a given gene family is. Here, we analyze the abundance and diversity of all Eukaryotic Clusters of Orthologous Groups (KOG) present in STRING database, resulting in a total of 4,850 KOGs. This dataset comprises 481,421 proteins distributed among 55 eukaryotes.</p> <p>Results</p> <p>We propose an index to evaluate the evolutionary plasticity and conservation of an orthologous group based on its abundance and diversity across eukaryotes. To further KOG plasticity analysis, we estimate the evolutionary distance average among all proteins which take part in the same orthologous group. As a result, we found a strong correlation between the evolutionary distance average and the proposed evolutionary plasticity index. Additionally, we found low evolutionary plasticity in <it>Saccharomyces cerevisiae </it>genes associated with inviability and <it>Mus musculus </it>genes associated with early lethality. At last, we plot the evolutionary plasticity value in different gene networks from yeast and humans. As a result, it was possible to discriminate among higher and lower plastic areas of the gene networks analyzed.</p> <p>Conclusions</p> <p>The distribution of gene families brings valuable information on evolutionary plasticity which might be related with genetic plasticity. Accordingly, it is possible to discriminate among conserved and plastic orthologous groups by evaluating their abundance and diversity across eukaryotes.</p> <p>Reviewers</p> <p>This article was reviewed by Prof Manyuan Long, Hiroyuki Toh, and Sebastien Halary.</p

Poly(amidoamine)s synthesis, characterisation and interaction with BSA

Cationic poly(amidoamine)s (PAAs) were synthesised and characterised by NMR and gel permeation chromatography. Their thermal properties were investigated using thermogravimetric analysis and differential scanning calorimetry. Although poly(amidoamine)s have been used as endosomolytic polymers for protein intracellular delivery, the interaction of the polymers with the proteins still need to be investigated. BSA was used as a model protein and complexation with the different poly(amidoamine) s was investigated using gel retardation assays, fluorescence spectroscopy and high sensitivity differential scanning calorimetry. Our results indicate that the thermal stability of BSA was affected upon interaction and complexation with the poly(amidoamine)s, however these interactions did not seem to modify the structure of the protein. Polymer flexibility seemed to favour polymer/protein complexation and promoted thermal stability

Uniform semiclassical trace formula for U(3) --> SO(3) symmetry breaking

We develop a uniform semiclassical trace formula for the density of states of a three-dimensional isotropic harmonic oscillator (HO), perturbed by a term $\propto r^4$. This term breaks the U(3) symmetry of the HO, resulting in a spherical system with SO(3) symmetry. We first treat the anharmonic term in semiclassical perturbation theory by integration of the action of the perturbed periodic HO orbits over the manifold $\mathbb{C}$P$^2$ which characterizes their 4-fold degeneracy. Then we obtain an analytical uniform trace formula which in the limit of strong perturbations (or high energy) asymptotically goes over into the correct trace formula of the full anharmonic system with SO(3) symmetry, and in the limit $\epsilon$ (or energy) $\to 0$ restores the HO trace formula with U(3) symmetry. We demonstrate that the gross-shell structure of this anharmonically perturbed system is dominated by the two-fold degenerate diameter and circular orbits, and {\it not} by the orbits with the largest classical degeneracy, which are the three-fold degenerate tori with rational ratios $\omega_r:\omega_\phi=N:M$ of radial and angular frequencies. The same holds also for the limit of a purely quartic spherical potential $V(r)\propto r^4$.Comment: LaTeX (revtex4), 26pp., 5 figures, 1 table; final version to be published in J. Phys. A (without appendices C and D

The Growth Pattern of Brazilian Canela-Preta Chickens with Different Plumages Reared in Two Rearing Systems

ABSTRACT Growth pattern is essential for economically efficient poultry production. In this study, we aimed to describe the growth curve of chickens of the Canela-Preta breed reared in two different rearing systems, considering their different plumage colors. Initially, 204 one-day-old male and female chicks were randomly distributed in confinement and semi-confinement (102 animals in each system) without separation by gender. The animals were individually identified by wing and foot plastic brands and were weighted every seven days. The body weight and age records were used to estimate the growth curves of the following factors using the Richards model: plumage color, gender, and rearing system. The likelihood ratio test was used to verify the equality of parameters and identify nonlinear models to compare the growth patterns of the evaluated groups. The growth pattern of Canela-Preta chickens changed as a function of gender, plumage color, and rearing system. Females with black plumage, black and gold hens, and males with black and white plumage showed greater sensitivity to changes in rearing systems. Within-breed selection strategies for specific colors can improve the use of growth pattern differences, improving production efficiency. Semi-confinement is suitable for rearing Canela-Preta chickens with any plumage color, as these animals meet the free-range poultry niche market requirements