Abstract:
Thom polynomials measure how global topology forces singularities. The power of Thom polynomials predestine them to be a useful tool not only in differential topology, but also in algebraic geometry (enumerative geometry, moduli spaces) and algebraic combinatorics. The main obstacle of their widespread application is that only a few, sporadic Thom polynomials have been known explicitly. In this paper we develop a general method for calculating Thom polynomials of contact singularities. Along the way, relations with the equivariant geometry of (punctual, local) Hilbert schemes, and with iterated residue identities are revealed.

Abstract:
R. Rim\'anyi defined the incidence class of two singularities X and Y as $[X]|_Y$, the restriction of the Thom polynomial of X to Y. He conjectured that (under mild conditions) the incidence is not zero if and only if Y is in the closure of X. Generalizing this notion we define the incidence class of two orbits X and Y of a representation. We give a sufficient condition (positivity) for Y to have the property that the incidence class $[X]|_Y$ is not zero if and only if Y is in the closure of X for any other orbit X. We show that for many interesting cases, e.g. the quiver representations of Dynkin type positivity holds for all orbits. In other words in these cases the incidence classes completely determine the hierarchy of the orbits. We also study the case of singularities where positivity doesn't hold for all orbits.

Abstract:
We study a 2-parameter family of enumerative problems over the reals. Over the complex field, these problems can be solved by Schubert calculus. In the real case the number of solutions can be different on the distinct connected components of the configuration space, resulting in a solution function. The cohomology calculation in the real case only gives the signed sum of the solutions, therefore in general it only gives a lower bound on the range of the solution function. We calculate the solution function for the 2-parameter family and we show that in the even cases the solution function is constant modulo 4. We show how to determine the sign of a solution and describe the connected components of the configuration space. We translate the problem to the language of quivers and also give a geometric interpretation of the sign. Finally, we discuss what aspects might be considered when solving other real enumerative problems.

Abstract:
The classification of the coadjoint orbits of the Virasoro algebra is reviewed and is then applied to analyze the so-called global Liouville equation. The review is self-contained, elementary and is tailor-made for the application. It is well-known that the Liouville equation for a smooth, real field $\phi$ under periodic boundary condition is a reduction of the SL(2,R) WZNW model on the cylinder, where the WZNW field g in SL(2,R) is restricted to be Gauss decomposable. If one drops this restriction, the Hamiltonian reduction yields, for the field $Q=\kappa g_{22}$ where $\kappa\neq 0$ is a constant, what we call the global Liouville equation. Corresponding to the winding number of the SL(2,R) WZNW model there is a topological invariant in the reduced theory, given by the number of zeros of Q over a period. By the substitution $Q=\pm\exp(- \phi/2)$, the Liouville theory for a smooth $\phi$ is recovered in the trivial topological sector. The nontrivial topological sectors can be viewed as singular sectors of the Liouville theory that contain blowing-up solutions in terms of $\phi$. Since the global Liouville equation is conformally invariant, its solutions can be described by explicitly listing those solutions for which the stress-energy tensor belongs to a set of representatives of the Virasoro coadjoint orbits chosen by convention. This direct method permits to study the `coadjoint orbit content' of the topological sectors as well as the behaviour of the energy in the sectors. The analysis confirms that the trivial topological sector contains special orbits with hyperbolic monodromy and shows that the energy is bounded from below in this sector only.

Abstract:
Discovering new fluorochromes is significantly advanced by high-throughput screening (HTS) methods. In the present study a combination of small molecule microarray (SMM) prescreening and confocal laser scanning microscopy (CLSM) was developed in order to discover novel cell staining fluorescent dyes. Compounds with high native fluorescence were selected from a 14,585-member library and further tested on living cells under the microscope. Eleven compartment-specific, cell-permeable (or plasma membrane-targeted) fluorochromes were identified. Their cytotoxicity was tested and found that between 1–10 micromolar range, they were non-toxic even during long-term incubations.

Abstract:
This paper investigates the effect of the ITER-like wall (ILW) on runaway electron (RE) generation through a comparative study of similar slow argon injection JET disruptions, performed with different wall materials. In the carbon wall case, a runaway electron plateau is observed, while in the ITER-like wall case, the current quench is slower and the runaway current is negligibly small. The aim of the paper is to shed light on the reason for these differences by detailed numerical modelling to study which factors affected the RE formation. The post-disruption current profile is calculated by a one-dimensional model of electric field, temperature and runaway current taking into account the impurity injection. Scans of various impurity contents are performed and agreement with the experimental scenarios is obtained for reasonable argon- and wall impurity contents. Our modelling shows that the reason for the changed RE dynamics is a complex, combined effect of the differences in plasma parameter profiles, the radiation characteristics of beryllium and carbon, and the difference of the injected argon amount. These together lead to a significantly higher Dreicer generation rate in the carbon wall case, which is less prone to be suppressed by RE loss mechanisms. The results indicate that the differences are greatly reduced above ~50% argon content, suggesting that significant RE current is expected in future massive gas injection experiments on both JET and ITER.

Abstract:
According to Etingof and Varchenko, the classical dynamical Yang-Baxter equation is a guarantee for the consistency of the Poisson bracket on certain Poisson-Lie groupoids. Here it is noticed that Dirac reductions of these Poisson manifolds give rise to a mapping from dynamical r-matrices on a pair $\L\subset \A$ to those on another pair $\K\subset \A$, where $\K\subset \L\subset \A$ is a chain of Lie algebras for which $\L$ admits a reductive decomposition as $\L=\K+\M$. Several known dynamical r-matrices appear naturally in this setting, and its application provides new r-matrices, too. In particular, we exhibit a family of r-matrices for which the dynamical variable lies in the grade zero subalgebra of an extended affine Lie algebra obtained from a twisted loop algebra based on an arbitrary finite dimensional self-dual Lie algebra.

Abstract:
A family of mappings from the solution spaces of certain generalized Drinfeld-Sokolov hierarchies to the self-dual Yang-Mills system on R^{2,2} is described. This provides an extension of the well-known relationship between self-dual connections and integrable hierarchies of AKNS and Drinfeld-Sokolov type.

Abstract:
Zearalenone (hereafter referred to as ZEA) is a nonsteroidal estrogenic mycotoxin produced by several Fusarium spp. on cereal grains. ZEA is one of the most hazardous natural endocrine disrupting chemicals (EDC) which induces hyper estrogenic responses in mammals. This can result in reproductive disorders in farm animals as well as in humans. Consequently, detoxification strategies for contaminated crops are crucial for food safety. In this study we have developed a bacterial based detoxification system using a non-pathogen Rhodococcus pyridinivorans K408 strain. Following 5 days treatment of ZEA with R. pyridinivorans K408 strain HPLC analyses showed an 87.21% ZEA-degradation efficiency of the bacterial enzyme systems. In another approach, the strain biotransformation ability has also been confirmed by a bioluminescent version of the yeast estrogen screening system (BLYES), which detected an 81.75% of biodegradability of ZEA, in a good agreement with the chemical analyses. Furthermore, the capacity of R. pyridinivorans to eliminate the estrogenic effects of ZEA was tested by using an immature uterotrophic assay. Prepubertal female rats were treated with vehicle (olive oil), 17β-estradiol, ZEA (0.1-1-5-10 mg/kg body weight) and LB broth containing 500 mg/l ZEA that has already been incubated with or without Rhodococcus pyridinivorans K408 strain. Uterine weights were measured and the mRNA level changes relating to apelin, aquaporin 5, complement component 2, and calbindin-3 genes were measured by qRT-PCR. These genes represent the major pathways that are affected by estromimetic compounds. Zearalenone feeding significantly increased the uterus weight in a dose dependent manner and at the same time upregulated complement component 2 and calbindin-3 expression as well as decreased apelin and aquaporin 5 mRNA levels comparable to that seen in 17β-estradiol exposed rats. In contrast, LB broth in which ZEA was incubated with Rhodococcus pyridinivorans K408 prior to the feeding did not display any estrogenic effect neither on uterine weight nor on the expression of estrogen-regulated genes. Consequently, the identification of Rhodococcus pyridinivorans K408 strain in ZEA biodegradation proved to be a very efficient biological tool that is able to eliminate the complete estrogenic effects of ZEA. It is also remarkable that this biotransformation pathway of ZEA did not result in any residual estrogenic effects.

Abstract:
Cytotoxicity was detected in different cell lines including melanoma, leukemia, hepatocellular carcinoma, glioblastoma at micromolar concentrations. The synthesized analogs are non-toxic to adult animals up to 1 g/kg but are teratogenic to zebrafish embryos at micromolar concentrations with defects in the developing muscle. Treatment of tumor cells resulted in calcium release from the endoplasmic reticulum (ER), induction of reactive oxygen species (ROS), ER stress and cell death. Antioxidants could partially, while an intracellular calcium chelator almost completely diminish ROS production. Exogenous docosahexaenoic acid or eicosapentaenoic acid induced calcium release and ROS generation, and synergized with the analogs in vitro, while oleic acid had no such an effect. Gene expression analysis confirmed the induction of ER stress-mediated apoptosis pathway components, such as GADD153, ATF3, Luman/CREB3 and the ER-associated degradation-related HERPUD1 genes. Tumor suppressors, P53, LATS2 and ING3 were also up-regulated in various cell lines after drug treatment. Amino-phthalimides down-regulated the expression of CCL2, which is implicated in tumor metastasis and angiogenesis.Because of the anticancer, anti-angiogenic action and the wide range of applicability of the immunomodulatory drugs, including thalidomide analogs, lipid droplet-binding members of this family could represent a new class of agents by affecting ER-membrane integrity and perturbations of ER homeostasis.Cytoplasmic lipid-droplets (LDs) are common inclusions of eukaryotic cells. Little is known about the composition or physiological role of LDs, however growing number of evidences imply that LDs are not solely static inclusions for storage of excess lipid, but they are dynamic and functionally active [1-4]. Although LD biogenesis is not well understood, it is assumed that the LDs form within the two leaflets of the ER membrane to function as lipid storage sites [5]. LDs are active inclusions with e