Integrability, Recursion Operators and Soliton Interactions

This volume contains selected papers based on the talks,presented at the Conference "Integrability, Recursion Operators and Soliton Interactions", held in Sofia, Bulgaria (29 - 31 August 2012) at the Institute for Nuclear Research and Nuclear Energy of the Bulgarian Academy of Sciences. Included are also invited papers presenting new research developments in the thematic area. The Conference was dedicated to the 65-th birthday of our esteemed colleague and friend Vladimir Gerdjikov. The event brought together more than 30 scientists, from 6 European countries to celebrate Vladimir's scientific achievements. All participants enjoyed a variety of excellent talks in a friendly and stimulating atmosphere. The main topics of the conference were those where Vladimir has contributed enormously during his career: integrable nonlinear partial differential equations, underlying algebraic and geometric structures of the integrable systems, soliton solutions, soliton interactions, quantum integrable systems, discrete integrable systems and applications of the nonlinear models. The papers, included in this volume will be useful to researchers with interests in these areas

Numerical Calibration of Steiner trees

International audienceIn this paper we propose a variational approach to the Steiner tree problem, which is based on calibrations in a suitable algebraic environment for polyhedral chains which represent our candidates. This approach turns out to be very efficient from numerical point of view and allows to establish whether a given Steiner tree is optimal. Several examples are provided

The prognostic value of the hypoxia markers CA IX and GLUT 1 and the cytokines VEGF and IL 6 in head and neck squamous cell carcinoma treated by radiotherapy ± chemotherapy

BACKGROUND: Several parameters of the tumor microenvironment, such as hypoxia, inflammation and angiogenesis, play a critical role in tumor aggressiveness and treatment response. A major question remains if these markers can be used to stratify patients to certain treatment protocols. The purpose of this study was to investigate the inter-relationship and the prognostic significance of several biological and clinicopathological parameters in patients with head and neck squamous cell carcinoma (HNSCC) treated by radiotherapy ± chemotherapy. METHODS: We used two subgroups of a retrospective series for which CT-determined tumoral perfusion correlated with local control. In the first subgroup (n = 67), immunohistochemistry for carbonic anhydrase IX (CA IX) and glucose transporter-1 (GLUT-1) was performed on the pretreatment tumor biopsy. In the second subgroup (n = 34), enzyme linked immunosorbent assay (ELISA) was used to determine pretreatment levels of the cytokines vascular endothelial growth factor (VEGF) and interleukin-6 (IL-6) in serum. Correlation was investigated between tumoral perfusion and each of these biological markers, as well as between the markers mutually. The prognostic value of these microenvironmental parameters was also evaluated. RESULTS: For CA IX and GLUT-1, the combined assessment of patients with both markers expressed above the median showed an independent correlation with local control (p = 0.02) and disease-free survival (p = 0.04) with a trend for regional control (p = 0.06). In the second subgroup, IL-6 pretreatment serum level above the median was the only independent predictor of local control (p = 0.009), disease-free survival (p = 0.02) and overall survival (p = 0.005). CONCLUSION: To our knowledge, we are the first to report a link in HNSCC between IL-6 pretreatment serum levels and radioresistance in vivo. This link is supported by the strong prognostic association of pretreatment IL-6 with local control, known to be the most important parameter to judge radiotherapy responses. Furthermore, the combined assessment of CA IX and GLUT-1 correlated independently with prognosis. This is a valuable indication that a combined approach is important in the investigation of prognostic markers

Parent formulation at the Lagrangian level

The recently proposed first-order parent formalism at the level of equations of motion is specialized to the case of Lagrangian systems. It is shown that for diffeomorphism-invariant theories the parent formulation takes the form of an AKSZ-type sigma model. The proposed formulation can be also seen as a Lagrangian version of the BV-BRST extension of the Vasiliev unfolded approach. We also discuss its possible interpretation as a multidimensional generalization of the Hamiltonian BFV--BRST formalism. The general construction is illustrated by examples of (parametrized) mechanics, relativistic particle, Yang--Mills theory, and gravity.Comment: 26 pages, discussion of the truncation extended, typos corrected, references adde

Transfer RNA-derived small RNAs in the cancer transcriptome

The cellular lifetime includes stages such as differentiation, proliferation, division, senescence and apoptosis.These stages are driven by a strictly ordered process of transcription dynamics. Molecular disruption to RNA polymerase assembly, chromatin remodelling and transcription factor binding through to RNA editing, splicing, post-transcriptional regulation and ribosome scanning can result in significant costs arising from genome instability. Cancer development is one example of when such disruption takes place. RNA silencing is a term used to describe the effects of post-transcriptional gene silencing mediated by a diverse set of small RNA molecules. Small RNAs are crucial for regulating gene expression and microguarding genome integrity.RNA silencing studies predominantly focus on small RNAs such as microRNAs, short-interfering RNAs and piwi-interacting RNAs. We describe an emerging renewal of inter-est in a‘larger’small RNA, the transfer RNA (tRNA).Precisely generated tRNA-derived small RNAs, named tRNA halves (tiRNAs) and tRNA fragments (tRFs), have been reported to be abundant with dysregulation associated with cancer. Transfection of tiRNAs inhibits protein translation by displacing eukaryotic initiation factors from messenger RNA (mRNA) and inaugurating stress granule formation.Knockdown of an overexpressed tRF inhibits cancer cell proliferation. Recovery of lacking tRFs prevents cancer metastasis. The dual oncogenic and tumour-suppressive role is typical of functional small RNAs. We review recent reports on tiRNA and tRF discovery and biogenesis, identification and analysis from next-generation sequencing data and a mechanistic animal study to demonstrate their physiological role in cancer biology. We propose tRNA-derived small RNA-mediated RNA silencing is an innate defence mechanism to prevent oncogenic translation. We expect that cancer cells are percipient to their ablated control of transcription and attempt to prevent loss of genome control through RNA silencing

Smc5/6: a link between DNA repair and unidirectional replication?

Of the three structural maintenance of chromosome (SMC) complexes, two directly regulate chromosome dynamics. The third, Smc5/6, functions mainly in homologous recombination and in completing DNA replication. The literature suggests that Smc5/6 coordinates DNA repair, in part through post-translational modification of uncharacterized target proteins that can dictate their subcellular localization, and that Smc5/6 also functions to establish DNA-damage-dependent cohesion. A nucleolar-specific Smc5/6 function has been proposed because Smc5/6 yeast mutants display penetrant phenotypes of ribosomal DNA (rDNA) instability. rDNA repeats are replicated unidirectionally. Here, we propose that unidirectional replication, combined with global Smc5/6 functions, can explain the apparent rDNA specificity

Protein Pattern Formation

Protein pattern formation is essential for the spatial organization of many intracellular processes like cell division, flagellum positioning, and chemotaxis. A prominent example of intracellular patterns are the oscillatory pole-to-pole oscillations of Min proteins in \textit{E. coli} whose biological function is to ensure precise cell division. Cell polarization, a prerequisite for processes such as stem cell differentiation and cell polarity in yeast, is also mediated by a diffusion-reaction process. More generally, these functional modules of cells serve as model systems for self-organization, one of the core principles of life. Under which conditions spatio-temporal patterns emerge, and how these patterns are regulated by biochemical and geometrical factors are major aspects of current research. Here we review recent theoretical and experimental advances in the field of intracellular pattern formation, focusing on general design principles and fundamental physical mechanisms.Comment: 17 pages, 14 figures, review articl

On form factors in N=4 sym

In this paper we study the form factors for the half-BPS operators $\mathcal{O}^{(n)}_I$ and the $\mathcal{N}=4$ stress tensor supermultiplet current $W^{AB}$ up to the second order of perturbation theory and for the Konishi operator $\mathcal{K}$ at first order of perturbation theory in $\mathcal{N}=4$ SYM theory at weak coupling. For all the objects we observe the exponentiation of the IR divergences with two anomalous dimensions: the cusp anomalous dimension and the collinear anomalous dimension. For the IR finite parts we obtain a similar situation as for the gluon scattering amplitudes, namely, apart from the case of $W^{AB}$ and $\mathcal{K}$ the finite part has some remainder function which we calculate up to the second order. It involves the generalized Goncharov polylogarithms of several variables. All the answers are expressed through the integrals related to the dual conformal invariant ones which might be a signal of integrable structure standing behind the form factors.Comment: 35 pages, 7 figures, LATEX2

Carbonic anhydrase XII is a marker of good prognosis in invasive breast carcinoma

Hypoxia and pH influence gene expression in tumours, and it is becoming increasingly clear that the pattern of genes expressed by a tumour determines its growth and survival characteristics. Hypoxia-inducible factor-1 (HIF-1) is a key mediator of the cellular response to hypoxia and high HIF-1 expression has been identified as a poor prognostic factor in tumours. Recently, we identified the tumour-associated carbonic anhydrases (CA), CA9 and CA12 as hypoxia-inducible in tumour cell lines. Furthermore, we identified CA IX to be a poor prognostic factor in breast cancer. The aim of this study was to assess the prognostic significance of CA XII. CA XII expression was studied by immunohistochemistry in a series of 103 cases of invasive breast cancer and any association with recognised prognostic factors or relation with the outcome was examined. CA XII expression was present in 77 out of 103 (75%) cases and was associated with lower grade (P=0.001), positive estrogen receptor status (P<0.001), and negative epidermal growth factor receptor status (P<0.001). Furthermore, although CA XII expression was associated with an absence of necrosis (P<0.001), expression of CA XII in some high-grade tumours was induced in regions directly adjacent to morphological necrosis. Additionally, using univariate analysis, CA XII positive tumours were associated with a lower relapse rate (P=0.04) and a better overall survival (P=0.01). In conclusion, CA XII expression is influenced both by factors related to differentiation and hypoxia in breast cancer in vivo and CA XII expression is associated with a better prognosis in an unselected series of invasive breast carcinoma patients

A Membrane Fusion Protein αSNAP Is a Novel Regulator of Epithelial Apical Junctions

Tight junctions (TJs) and adherens junctions (AJs) are key determinants of the structure and permeability of epithelial barriers. Although exocytic delivery to the cell surface is crucial for junctional assembly, little is known about the mechanisms controlling TJ and AJ exocytosis. This study was aimed at investigating whether a key mediator of exocytosis, soluble N-ethylmaleimide sensitive factor (NSF) attachment protein alpha (αSNAP), regulates epithelial junctions. αSNAP was enriched at apical junctions in SK-CO15 and T84 colonic epithelial cells and in normal human intestinal mucosa. siRNA-mediated knockdown of αSNAP inhibited AJ/TJ assembly and establishment of the paracellular barrier in SK-CO15 cells, which was accompanied by a significant down-regulation of p120-catenin and E-cadherin expression. A selective depletion of p120 catenin effectively disrupted AJ and TJ structure and compromised the epithelial barrier. However, overexpression of p120 catenin did not rescue the defects of junctional structure and permeability caused by αSNAP knockdown thereby suggesting the involvement of additional mechanisms. Such mechanisms did not depend on NSF functions or induction of cell death, but were associated with disruption of the Golgi complex and down-regulation of a Golgi-associated guanidine nucleotide exchange factor, GBF1. These findings suggest novel roles for αSNAP in promoting the formation of epithelial AJs and TJs by controlling Golgi-dependent expression and trafficking of junctional proteins