RG Flow Irreversibility, C-Theorem and Topological Nature of 4D N=2 SYM

We determine the exact beta function and a RG flow Lyapunov function for N=2 SYM with gauge group SU(n). It turns out that the classical discriminants of the Seiberg-Witten curves determine the RG potential. The radial irreversibility of the RG flow in the SU(2) case and the non-perturbative identity relating the $u$-modulus and the superconformal anomaly, indicate the existence of a four dimensional analogue of the c-theorem for N=2 SYM which we formulate for the full SU(n) theory. Our investigation provides further evidence of the essentially topological nature of the theory.Comment: 9 pages, LaTeX file. Discussion on WDVV and integrability. References added. Version published in PR

Abelian gerbes as a gauge theory of quantum mechanics on phase space

We construct a U(1) gerbe with a connection over a finite-dimensional, classical phase space P. The connection is given by a triple of forms A,B,H: a potential 1-form A, a Neveu-Schwarz potential 2-form B, and a field-strength 3-form H=dB. All three of them are defined exclusively in terms of elements already present in P, the only external input being Planck's constant h. U(1) gauge transformations acting on the triple A,B,H are also defined, parametrised either by a 0-form or by a 1-form. While H remains gauge invariant in all cases, quantumness vs. classicality appears as a choice of 0-form gauge for the 1-form A. The fact that [H]/2i\pi is an integral class in de Rham cohomology is related with the discretisation of symplectic area on P. This is an equivalent, coordinate-free reexpression of Heisenberg's uncertainty principle. A choice of 1-form gauge for the 2-form B relates our construction with generalised complex structures on classical phase space. Altogether this allows one to interpret the quantum mechanics corresponding to P as an Abelian gauge theory.Comment: 18 pages, 1 figure available from the authors upon reques

One-pot homologation of boronic acids : a platform for diversity-oriented synthesis

Formal homologation of sp2-hybridized boronic acids is achieved via cross-coupling of boronic acids with conjunctive haloaryl BMIDA components in the presence of a suitably balanced basic phase. The utility of this approach to provide a platform for diversity-oriented synthesis in discovery medicinal chemistry is demonstrated in the context of the synthesis of a series of analogues of a BET bromodomain inhibitor

Observation of Small Cluster Formation in Concentrated Monoclonal Antibody Solutions and Its Implications to Solution Viscosity

AbstractMonoclonal antibodies (mAbs) are a major class of biopharmaceuticals. It is hypothesized that some concentrated mAb solutions exhibit formation of a solution phase consisting of reversibly self-associated aggregates (or reversible clusters), which is speculated to be responsible for their distinct solution properties. Here, we report direct observation of reversible clusters in concentrated solutions of mAbs using neutron spin echo. Specifically, a stable mAb solution is studied across a transition from dispersed monomers in dilute solution to clustered states at more concentrated conditions, where clusters of a preferred size are observed. Once mAb clusters have formed, their size, in contrast to that observed in typical globular protein solutions, is observed to remain nearly constant over a wide range of concentrations. Our results not only conclusively establish a clear relationship between the undesirable high viscosity of some mAb solutions and the formation of reversible clusters with extended open structures, but also directly observe self-assembled mAb protein clusters of preferred small finite size similar to that in micelle formation that dominate the properties of concentrated mAb solutions

Torus knots and mirror symmetry

We propose a spectral curve describing torus knots and links in the B-model. In particular, the application of the topological recursion to this curve generates all their colored HOMFLY invariants. The curve is obtained by exploiting the full Sl(2, Z) symmetry of the spectral curve of the resolved conifold, and should be regarded as the mirror of the topological D-brane associated to torus knots in the large N Gopakumar-Vafa duality. Moreover, we derive the curve as the large N limit of the matrix model computing torus knot invariants.Comment: 30 pages + appendix, 3 figure

A population density grid for Spain

This is an author's accepted manuscript of an article published in "International Journal of Geographical Information Science"; Volume 27, Issue 12, 2013; copyright Taylor & Francis; available online at: http://www.tandfonline.com/doi/abs/10.1080/13658816.2013.799283This article describes a high-resolution land cover data set for Spain and its application to dasymetric population mapping (at census tract level). Eventually, this vector layer is transformed into a grid format. The work parallels the effort of the Joint Research Centre (JRC) of the European Commission, in collaboration with Eurostat and the European Environment Agency (EEA), in building a population density grid for the whole of Europe, combining CORINE Land Cover with population data per commune. We solve many of the problems due to the low resolution of CORINE Land Cover, which are especially visible with Spanish data. An accuracy assessment is carried out from a simple aggregation of georeferenced point population data for the region of Madrid. The bottom-up grid constructed in this way is compared to our top-down grid. We show a great improvement over what has been reported from commune data and CORINE Land Cover, but the improvements seem to come entirely from the higher resolution data sets and not from the statistical modeling in the downscaling exercise. This highlights the importance of providing the research community with more detailed land cover data sets, as well as more detailed population data. The dasymetric grid is available free of charge from the authors upon request.The authors acknowledge financial support from the BBVA Foundation-Ivie research programme and the first author also acknowledges support from the Spanish Ministry of Science and Technology, ECO2011-23248 project. Results mentioned, but not shown, are available from the authors upon request. The grid numbers are also available from the authors.Goerlich Sanchis, FJ.; Cantarino Martí, I. (2013). A population density grid for Spain. International Journal of Geographical Information Science. 27(12):1-17. https://doi.org/10.1080/13658816.2013.799283S117271

Argyres-Douglas Loci, Singularity Structures and Wall-Crossings in Pure N=2 Gauge Theories with Classical Gauge Groups

N=2 Seiberg-Witten theories allow an interesting interplay between the Argyres-Douglas loci, singularity structures and wall-crossing formulae. In this paper we investigate this connection by first studying the singularity structures of hyper-elliptic Seiberg-Witten curves for pure N=2 gauge theories with SU(r+1) and Sp(2r) gauge groups, and propose new methods to locate the Argyres-Douglas loci in the moduli space, where multiple mutually non-local BPS states become massless. In a region of the moduli space, we compute dyon charges for all 2r+2 and 2r+1 massless dyons for SU(r+1) and Sp(2r) gauge groups respectively for rank r>1. From here we elucidate the connection to the wall-crossing phenomena for pure Sp(4) Seiberg-Witten theory near the Argyres-Douglas loci, despite our emphasis being only at the massless sector of the BPS spectra. We also present 2r-1 candidates for the maximal Argyres-Douglas points for pure SO(2r+1) Seiberg-Witten theory.Comment: 81 pages, 41 figures, LaTeX; v2: Minor cosmetic changes and correction of a typographical error in acknowledgement. Final version to appear in JHE

Deformation Quantization of Geometric Quantum Mechanics

Second quantization of a classical nonrelativistic one-particle system as a deformation quantization of the Schrodinger spinless field is considered. Under the assumption that the phase space of the Schrodinger field is $C^{\infty}$, both, the Weyl-Wigner-Moyal and Berezin deformation quantizations are discussed and compared. Then the geometric quantum mechanics is also quantized using the Berezin method under the assumption that the phase space is $CP^{\infty}$ endowed with the Fubini-Study Kahlerian metric. Finally, the Wigner function for an arbitrary particle state and its evolution equation are obtained. As is shown this new "second quantization" leads to essentially different results than the former one. For instance, each state is an eigenstate of the total number particle operator and the corresponding eigenvalue is always ${1 \over \hbar}$.Comment: 27+1 pages, harvmac file, no figure

Characterisation of IL-23 receptor antagonists and disease relevant mutants using fluorescent probes

Association of single nucleotide polymorphisms in the IL-23 receptor with several auto-inflammatory diseases, led to the heterodimeric receptor and its cytokine-ligand IL-23, becoming important drug targets. Successful antibody-based therapies directed against the cytokine have been licenced and a class of small peptide antagonists of the receptor have entered clinical trials. These peptide antagonists may offer therapeutic advantages over existing anti-IL-23 therapies, but little is known about their molecular pharmacology. In this study, we use a fluorescent version of IL-23 to characterise antagonists of the full-length receptor expressed by living cells using a NanoBRET competition assay. We then develop a cyclic peptide fluorescent probe, specific to the IL23p19:IL23R interface and use this molecule to characterise further receptor antagonists. Finally, we use the assays to study the immunocompromising C115Y IL23R mutation, demonstrating that the mechanism of action is a disruption of the binding epitope for IL23p19

Non-holomorphic terms in N=2 SUSY Wilsonian actions and RG equation

In this paper we first investigate the Ansatz of one of the present authors for K(\Psi,\bar\Psi), the adimensional modular invariant non-holomorphic correction to the Wilsonian effective Lagrangian of an N=2 globally supersymmetric gauge theory. The renormalisation group beta-function of the theory crucially allows us to express K(\Psi,\bar\Psi) in a form that easily generalises to the case in which the theory is coupled to N_F hypermultiplets in the fundamental representation of the gauge group. This function satisfies an equation which should be viewed as a fully non-perturbative ``non-chiral superconformal Ward identity". We also determine its renormalisation group equation. Furthermore, as a first step towards checking the validity of this Ansatz, we compute the contribution to K(\Psi,\bar\Psi) from instantons of winding number k=1 and k=2. As a by-product of our analysis we check a non-renormalisation theorem for N_F=4.Comment: 39 pages, LaTex file, no figure