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

Model of the Belousov-Zhabotinsky reaction

The article describes results of the modified model of the Belousov-Zhabotinsky reaction, which resembles rather well the limit set observed upon experimental performance of the reaction in the Petri dish. We discuss the concept of the ignition of circular waves and show that only the asymmetrical ignition leads to the formation of spiral structures. From the qualitative assumptions on the behavior of dynamic systems, we conclude that the Belousov-Zhabotinsky reaction likely forms a regular grid.Comment: 17 pages, 12 figure

Bub1 as a recruitment platform for Spindle Assembly Checkpoint components

Motivation: The Spindle Assembly Checkpoint (SAC) is a safeguard mechanism conserved in all the eukaryotes that ensures the correct chromosome segregation in mitosis by preventing the premature mitotic exit in condition of unattached kinetochores. SAC defects lead to chromosome mis-segregation provoking aneuploidies that has been widely associated with cancer. Kinase Bub1 is a key player in SAC function because it maintains a proper centromeric cohesion and serves as a platform for other SAC components such as Mad1, Mad2 and Mad3. In this study, we are characterizing a bub1 mutant allele which exhibits an impaired SAC function. The phenotype shown by this mutant has not been previously described. This mutant can provide new insights about the Bub1-dependent recruitment of SAC components to the kinetochores and the mechanism of mitosis arrest.Methods: We made use of live imaging techniques to study SAC function by using GFP-tagged alleles of the main SAC components (like Mad1, Mad2 and Mad3), comparing the wild type background versus the bub1 mutant allele. Furthermore, we have used a cold sensitive tubulin mutant that allows us to test SAC activity; in response to microtubules damage induced by this mutant, cells activate the SAC and arrest in metaphase. We have also tested Bub1 protein levels in a wild-type and in the Bub1-mutant by Western Blot. Finally, we are performing a two-hybrid screening using a S. pombe library-strain to detect differences in the interactome of the Bub1-mutant compared with the wild-type. Results: We have demonstrated that in the Bub1-mutant background, Mad1 correctly localizes at the kinetochores meanwhile Mad2 does not. Bub1 protein levels turned out to be quite similar in both strain. Additionally, we have observed that the SAC defects notice in the Bub1-mutant in the cold sensitive background partially phenocopies the one seen in the Bub1-deleted cells.Conclusions: Our Bub1-mutant is unable to maintain a proper metaphase block in the cold-sensitive tubulin background and exhibit a SAC failure. We are working in a model where Bub1 could be regulating SAC activity by promoting Mad2 recruitment to kinetochores

Ab initio prediction of Boron compounds arising from Borozene: Structural and electronic properties

Structure and electronic properties of two unusual boron clusters obtained by fusion of borozene rings has been studied by means of first principles calculations, based on the generalized-gradient approximation of the density functional theory, and the semiempirical tight-binding method was used for the transport calculations. The role of disorder has also been considered with single vacancies and substitutional atoms. Results show that the pure boron clusters are topologically planar and characterized by (3c-2e) bonds, which can explain, together with the aromaticity (estimated by means of NICS), the remarkable cohesive energy values obtained. Such feature makes these systems competitive with the most stable boron clusters to date. On the contrary, the introduction of impurities compromises stability and planarity in both cases. The energy gap values indicate that these clusters possess a semiconducting character, while when the larger system is considered, zero-values of the density of states are found exclusively within the HOMO-LUMO gap. Electron transport calculations within the Landauer formalism confirm these indications, showing semiconductor-like low bias differential conductance for these stuctures. Differences and similarities with Carbon clusters are highlighted in the discussion.Comment: 10 pages, 2 tables, 5 figure

The relationship between quality of life (EORTC QLQ-C30) and survival in patients with gastro-oesopohageal cancer

It remains unclear whether any aspect of quality of life has a role in predicting survival in an unselected cohort of patients with gastro-oesophageal cancer. Therefore the aim of the present study was to examine the relationship between quality of life (EORTC QLQ-C30), clinico-pathological characteristics and survival in patients with gastro-oesophageal cancer. Patients presenting with gastric or oesophageal cancer, staged using the UICC tumour node metastasis (TNM) classification and who received either potentially curative surgery or palliative treatment between November 1997 and December 2002 (n=152) participated in a quality of life study, using the EORTC QLQ-C30 core questionnaire. On univariate analysis, age (P < 0.01), tumour length (P < 0.0001), TNM stage (P<0.0001), weight loss (P<0.0001), dysphagia score (P<0.001), performance status (P<0.1) and treatment (P<0.0001) were significantly associated with cancer-specific survival. EORTC QLQ-C30, physical functioning (P<0.0001), role functioning (P<0.001), cognitive functioning (P<0.01), social functioning (P<0.0001), global quality of life (P<0.0001), fatigue (P<0.0001), nausea/vomiting (P<0.01), pain (P<0.001), dyspnoea (P<0.0001), appetite loss (P<0.0001) and constipation (P<0.05) were also significantly associated with cancer-specific survival. On multivariate survival analysis, tumour stage (P<0.0001), treatment (P<0.001) and appetite loss (P<0.0001) were significant independent predictors of cancer-specific survival. The present study highlights the importance of quality of life (EORTC QLQ-C30) measures, in particular appetite loss, as a prognostic factor in these patients

Facteurs Predictifs De Malignite D\'un Nodule Thyroidien

Buts : étudier les facteurs prédictifs de malignité des nodules thyroïdiens et comparer nos résultats à ceux de la littérature. Patients et méthodes : Il s\'agit d\'une étude rétrospective a propos de 282 cas de nodules thyroïdiens opérés à l\' hôpital de Mahdia entre 1988 et 2003. Résultats : L\'âge moyen était de 44 ans. Le risque de malignité des nodules thyroïdiens était de 15,6% . Ce risque était plus important chez les hommes (50%) que chez les femmes (13,3%). Certains facteurs étaient hautement prédictifs de malignité comme l\'âge supérieur à 60 ans, les signes de compression, les adénopathies cervicales et le caractère fixe et dure du nodule thyroidien Conclusion : Certains signes cliniques et para cliniques ont une grande valeur en matière de bénignité ou de malignité des nodules thyroïdiens.Aim : Study the predictive factors of malignancy of thyroid gland nodules and compare our results to those of the literature. Patients and methods : A retrospective study about 282 cases of thyroid gland nodules treated in Madhya hospital between 1988 and 2003. Results : The middle age was 44 years. The risk of malignancy was 15,6 %. This risk was higher in men (50 %) then in women (13,3 %). Some factors were highly predictive of malignancy like age superior then 60 years, neck lymph nodes … Conclusion: Some clinic and para clinic signs have an important value in benignancy or malignancy of thyroid gland nodules. Journal Tunisien d\'ORL et de chirurgie cervico-faciale Vol. 18 2007: pp. 20-2

Scattering and duality in the 2 dimensional OSP(2|2) Gross Neveu and sigma models

We write the thermodynamic Bethe ansatz for the massive OSp(2|2) Gross Neveu and sigma models. We find evidence that the GN S matrix proposed by Bassi and Leclair [12] is the correct one. We determine features of the sigma model S matrix, which seem highly unconventional; we conjecture in particular a relation between this sigma model and the complex sine-Gordon model at a particular value of the coupling. We uncover an intriguing duality between the OSp(2|2) GN (resp. sigma) model on the one hand, and the SO(4) sigma (resp. GN model) on the other, somewhat generalizing to the massive case recent results on OSp(4|2). Finally, we write the TBA for the (SUSY version of the) flow into the random bond Ising model proposed by Cabra et al. [39], and conclude that their S matrix cannot be correct.Comment: 41 pages, 27 figures. v2: minor revisio

The low-energy limit of AdS(3)/CFT2 and its TBA

We investigate low-energy string excitations in AdS3 × S3 × T4. When the worldsheet is decompactified, the theory has gapless modes whose spectrum at low energies is determined by massless relativistic integrable S matrices of the type introduced by Al. B. Zamolodchikov. The S matrices are non-trivial only for excitations with identical worldsheet chirality, indicating that the low-energy theory is a CFT2. We construct a Thermodynamic Bethe Ansatz (TBA) for these excitations and show how the massless modes’ wrapping effects may be incorporated into the AdS3 spectral problem. Using the TBA and its associated Y-system, we determine the central charge of the low-energy CFT2 to be c = 6 from calculating the vacuum energy for antiperiodic fermions — with the vacuum energy being zero for periodic fermions in agreement with a supersymmetric theory — and find the energies of some excited states

One-point functions in massive integrable QFT with boundaries

We consider the expectation value of a local operator on a strip with non-trivial boundaries in 1+1 dimensional massive integrable QFT. Using finite volume regularisation in the crossed channel and extending the boundary state formalism to the finite volume case we give a series expansion for the one-point function in terms of the exact form factors of the theory. The truncated series is compared with the numerical results of the truncated conformal space approach in the scaling Lee-Yang model. We discuss the relevance of our results to quantum quench problems.Comment: 43 pages, 20 figures, v2: typos correcte