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

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sense of Riemann-Liouville while derivatives are of Caputo type.Comment: Submitted 26-Sept-2011; accepted 18-Oct-2011; withdrawn by the authors 21-Dec-2011; resubmitted 27-Dec-2011; revised 20-March-2012; accepted 13-April-2012; to 'Advances in Harmonic Analysis and Operator Theory', The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

Dynamics of cell growth: Exponential growth and division after a minimum cell size

In this paper, we consider a mathematical model for cell division using a Pantograph-type nonlocal partial differential equation, accompanied by relevant initial and boundary conditions. This formulation results in a nonlocal singular eigenvalue problem. We explore the possible eigenvalues that may lead to nontrivial solutions. We then consider cells that divide once they achieve a minimum size. Our model incorporates asymmetric cell division and exponential growth. We show that, unlike the constant growth rate case, a probability density function eigenvalue can be determined explicitly. Additionally, we demonstrate that a stochastic growth rate produces eigenfunctions expressed as an infinite series of modified Bessel functions. We extend our findings to encompass a wider range of dispersion and growth rates. The implications of this work are significant for understanding the dynamics of cell populations in biological systems. The work has potential applications in cancer research and developmental biology, where cell growth and division play critical roles.fals

Plant growth retardation and conserved miRNAs are correlated to hibiscus chlorotic ringspot virus infection

10.1371/journal.pone.0085476PLoS ONE812-POLN

Colour break in reverse bicolour daffodils is associated with the presence of Narcissus mosaic virus

<p>Abstract</p> <p>Background</p> <p>Daffodils (<it>Narcissus pseudonarcissus</it>) are one of the world's most popular ornamentals. They also provide a scientific model for studying the carotenoid pigments responsible for their yellow and orange flower colours. In reverse bicolour daffodils, the yellow flower trumpet fades to white with age. The flowers of this type of daffodil are particularly prone to colour break whereby, upon opening, the yellow colour of the perianth is observed to be 'broken' into patches of white. This colour break symptom is characteristic of potyviral infections in other ornamentals such as tulips whose colour break is due to alterations in the presence of anthocyanins. However, reverse bicolour flowers displaying colour break show no other virus-like symptoms such as leaf mottling or plant stunting, leading some to argue that the carotenoid-based colour breaking in reverse bicolour flowers may not be caused by virus infection.</p> <p>Results</p> <p>Although potyviruses have been reported to cause colour break in other flower species, enzyme-linked-immunoassays with an antibody specific to the potyviral family showed that potyviruses were not responsible for the occurrence of colour break in reverse bicolour daffodils. Colour break in this type of daffodil was clearly associated with the presence of large quantities of rod-shaped viral particles of lengths 502-580 nm in tepals. Sap from flowers displaying colour break caused red necrotic lesions on <it>Gomphrena globosa</it>, suggesting the presence of potexvirus. Red necrotic lesions were not observed in this indicator plant when sap from reverse bicolour flowers not showing colour break was used. The reverse transcriptase polymerase reactions using degenerate primers to carla-, potex- and poty-viruses linked viral RNA with colour break and sequencing of the amplified products indicated that the potexvirus <it>Narcissisus mosaic virus </it>was the predominant virus associated with the occurrence of the colour break.</p> <p>Conclusions</p> <p>High viral counts were associated with the reverse bicolour daffodil flowers that were displaying colour break but otherwise showed no other symptoms of infection. <it>Narcissus mosaic virus </it>was the virus that was clearly linked to the carotenoid-based colour break.</p

4 Gy versus 24 Gy radiotherapy for follicular and marginal zone lymphoma (FoRT): long-term follow-up of a multicentre, randomised, phase 3, non-inferiority trial

BACKGROUND: The optimal radiotherapy dose for indolent non-Hodgkin lymphoma is uncertain. We aimed to compare 24 Gy in 12 fractions (representing the standard of care) with 4 Gy in two fractions (low-dose radiation). METHODS: FoRT (Follicular Radiotherapy Trial) is a randomised, multicentre, phase 3, non-inferiority trial at 43 study centres in the UK. We enrolled patients (aged >18 years) with indolent non-Hodgkin lymphoma who had histological confirmation of follicular lymphoma or marginal zone lymphoma requiring radical or palliative radiotherapy. No limit on performance status was stipulated, and previous chemotherapy or radiotherapy to another site was permitted. Radiotherapy target sites were randomly allocated (1:1) either 24 Gy in 12 fractions or 4 Gy in two fractions using minimisation and stratified by histology, treatment intent, and study centre. Randomisation was centralised through the Cancer Research UK and University College London Cancer Trials Centre. Patients, treating clinicians, and investigators were not masked to random assignments. The primary endpoint was time to local progression in the irradiated volume based on clinical and radiological evaluation and analysed on an intention-to-treat basis. The non-inferiority threshold aimed to exclude the chance that 4 Gy was more than 10% inferior to 24 Gy in terms of local control at 2 years (HR 1·37). Safety (in terms of adverse events) was analysed in patients who received any radiotherapy and who returned an adverse event form. FoRT is registered with ClinicalTrials.gov, NCT00310167, and the ISRCTN Registry, ISRCTN65687530, and this report represents the long-term follow-up. FINDINGS: Between April 7, 2006, and June 8, 2011, 614 target sites in 548 patients were randomly assigned either 24 Gy in 12 fractions (n=299) or 4 Gy in two fractions (n=315). At a median follow-up of 73·8 months (IQR 61·9-88·0), 117 local progression events were recorded, 27 in the 24 Gy group and 90 in the 4 Gy group. The 2-year local progression-free rate was 94·1% (95% CI 90·6-96·4) after 24 Gy and 79·8% (74·8-83·9) after 4 Gy; corresponding rates at 5 years were 89·9% (85·5-93·1) after 24 Gy and 70·4% (64·7-75·4) after 4 Gy (hazard ratio 3·46, 95% CI 2·25-5·33; p<0·0001). The difference at 2 years remains outside the non-inferiority margin of 10% at -13·0% (95% CI -21·7 to -6·9). The most common events at week 12 were alopecia (19 [7%] of 287 sites with 24 Gy vs six [2%] of 301 sites with 4 Gy), dry mouth (11 [4%] vs five [2%]), fatigue (seven [2%] vs five [2%]), mucositis (seven [2%] vs three [1%]), and pain (seven [2%] vs two [1%]). No treatment-related deaths were reported. INTERPRETATION: Our findings at 5 years show that the optimal radiotherapy dose for indolent lymphoma is 24 Gy in 12 fractions when durable local control is the aim of treatment. FUNDING: Cancer Research UK

Metabolic model integration of the bibliome, genome, metabolome and reactome of Aspergillus niger

The release of the genome sequences of two strains of Aspergillus niger has allowed systems-level investigations of this important microbial cell factory. To this end, tools for doing data integration of multi-ome data are necessary, and especially interesting in the context of metabolism. On the basis of an A. niger bibliome survey, we present the largest model reconstruction of a metabolic network reported for a fungal species. The reconstructed gapless metabolic network is based on the reportings of 371 articles and comprises 1190 biochemically unique reactions and 871 ORFs. Inclusion of isoenzymes increases the total number of reactions to 2240. A graphical map of the metabolic network is presented. All levels of the reconstruction process were based on manual curation. From the reconstructed metabolic network, a mathematical model was constructed and validated with data on yields, fluxes and transcription. The presented metabolic network and map are useful tools for examining systemwide data in a metabolic context. Results from the validated model show a great potential for expanding the use of A. niger as a high-yield production platform

Measurements of integrated and differential cross sections for isolated photon pair production in pp collisions at √s=8 TeV with the ATLAS detector

A measurement of the production cross section for two isolated photons in proton-proton collisions at a center-of-mass energy of √s=8 TeV is presented. The results are based on an integrated luminosity of 20.2 fb−1 recorded by the ATLAS detector at the Large Hadron Collider. The measurement considers photons with pseudorapidities satisfying |ηγ|40GeV and EγT,2>30 GeV for the two leading photons ordered in transverse energy produced in the interaction. The background due to hadronic jets and electrons is subtracted using data-driven techniques. The fiducial cross sections are corrected for detector effects and measured differentially as a function of six kinematic observables. The measured cross section integrated within the fiducial volume is 16.8 ± 0.8  pb . The data are compared to fixed-order QCD calculations at next-to-leading-order and next-to-next-to-leading-order accuracy as well as next-to-leading-order computations including resummation of initial-state gluon radiation at next-to-next-to-leading logarithm or matched to a parton shower, with relative uncertainties varying from 5% to 20%

Search for supersymmetry in events with four or more leptons in √s =13 TeV pp collisions with ATLAS

Results from a search for supersymmetry in events with four or more charged leptons (electrons, muons and taus) are presented. The analysis uses a data sample corresponding to 36.1 fb −1 of proton-proton collisions delivered by the Large Hadron Collider at s √ =13 TeV and recorded by the ATLAS detector. Four-lepton signal regions with up to two hadronically decaying taus are designed to target a range of supersymmetric scenarios that can be either enriched in or depleted of events involving the production and decay of a Z boson. Data yields are consistent with Standard Model expectations and results are used to set upper limits on the event yields from processes beyond the Standard Model. Exclusion limits are set at the 95% confidence level in simplified models of General Gauge Mediated supersymmetry, where higgsino masses are excluded up to 295 GeV. In R -parity-violating simplified models with decays of the lightest supersymmetric particle to charged leptons, lower limits of 1.46 TeV, 1.06 TeV, and 2.25 TeV are placed on wino, slepton and gluino masses, respectively

Search for the direct production of charginos and neutralinos in final states with tau leptons in √s=13 TeV collisions with the ATLAS detector

A search for the direct production of charginos and neutralinos in final states with at least two hadronically decaying tau leptons is presented. The analysis uses a dataset of pp collisions corresponding to an integrated luminosity of 36.1 fb−1, recorded with the ATLAS detector at the Large Hadron Collider at a centre-of-mass energy of 13TeV.Nosignificant deviation from the expected Standard Model background is observed. Limits are derived in scenarios of ˜χ+1 ˜χ−1 pair production and of ˜χ±1 ˜χ02 and ˜χ+1 ˜χ−1 production in simplified models where the neutralinos and charginos decay solely via intermediate left-handed staus and tau sneutrinos, and the mass of the ˜ τL state is set to be halfway between the masses of the ˜χ±1 and the ˜χ01. Chargino masses up to 630 GeV are excluded at 95% confidence level in the scenario of direct production of ˜χ+1 ˜χ−1 for a massless ˜χ01. Common ˜χ±1 and ˜χ02 masses up to 760 GeV are excluded in the case of production of ˜χ±1 ˜χ02 and ˜χ+1 ˜χ−1 assuming a massless ˜χ01. Exclusion limits for additional benchmark scenarios with large and small mass-splitting between the ˜χ±1 and the ˜χ01 are also studied by varying the ˜ τL mass between the masses of the ˜χ±1 and the ˜χ01