Wall-Crossing in Coupled 2d-4d Systems

We introduce a new wall-crossing formula which combines and generalizes the Cecotti-Vafa and Kontsevich-Soibelman formulas for supersymmetric 2d and 4d systems respectively. This 2d-4d wall-crossing formula governs the wall-crossing of BPS states in an N=2 supersymmetric 4d gauge theory coupled to a supersymmetric surface defect. When the theory and defect are compactified on a circle, we get a 3d theory with a supersymmetric line operator, corresponding to a hyperholomorphic connection on a vector bundle over a hyperkahler space. The 2d-4d wall-crossing formula can be interpreted as a smoothness condition for this hyperholomorphic connection. We explain how the 2d-4d BPS spectrum can be determined for 4d theories of class S, that is, for those theories obtained by compactifying the six-dimensional (0,2) theory with a partial topological twist on a punctured Riemann surface C. For such theories there are canonical surface defects. We illustrate with several examples in the case of A_1 theories of class S. Finally, we indicate how our results can be used to produce solutions to the A_1 Hitchin equations on the Riemann surface C.Comment: 170 pages, 45 figure

The BPS Spectrum Generator In 2d-4d Systems

We apply the techniques provided by the recent works Gaiotto, Moore and Neitzke, to derive the most general spectrum generating functions for coupled 2d-4d $A_1$ theories of class ${\cal S}$, in presence of surface and line defects. As an application of the result, some well-known BPS spectra are reproduced. Our results apply to a large class of coupled 2d-4d systems, the corresponding spectrum generating functions can be easily derived from our general expressions.Comment: 38 pages; v2: references added; v3: references added, added introductory material in sections 1, 2.1, 2.2, 2.

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

The dynamics of measles in sub-Saharan Africa.

Although vaccination has almost eliminated measles in parts of the world, the disease remains a major killer in some high birth rate countries of the Sahel. On the basis of measles dynamics for industrialized countries, high birth rate regions should experience regular annual epidemics. Here, however, we show that measles epidemics in Niger are highly episodic, particularly in the capital Niamey. Models demonstrate that this variability arises from powerful seasonality in transmission-generating high amplitude epidemics-within the chaotic domain of deterministic dynamics. In practice, this leads to frequent stochastic fadeouts, interspersed with irregular, large epidemics. A metapopulation model illustrates how increased vaccine coverage, but still below the local elimination threshold, could lead to increasingly variable major outbreaks in highly seasonally forced contexts. Such erratic dynamics emphasize the importance both of control strategies that address build-up of susceptible individuals and efforts to mitigate the impact of large outbreaks when they occur

Why pharmacokinetic differences among oral triptans have little clinical importance: a comment

Triptans, selective 5-HT1B/1D receptor agonists, are specific drugs for the acute treatment of migraine that have the same mechanism of action. Here, it is discussed why the differences among kinetic parameters of oral triptans have proved not to be very important in clinical practice. There are three main reasons: (1) the differences among the kinetic parameters of oral triptans are smaller than what appears from their average values; (2) there is a large inter-subject, gender-dependent, and intra-subject (outside/during the attack) variability of kinetic parameters related to the rate and extent of absorption, i.e., those which are considered as critical for the response; (3) no dose-concentration–response curves have been defined and it is, therefore, impossible both to compare the kinetics of triptans, and to verify the objective importance of kinetic differences; (4) the importance of kinetic differences is outweighed by non-kinetic factors of variability of response to triptans. If no oral formulations are found that can allow more predictable pharmacokinetics, the same problems will probably also arise with new classes of drugs for the acute treatment of migraine

State–Space Forecasting of Schistosoma haematobium Time-Series in Niono, Mali

Adequate forecasting and early warning systems are based upon observations of human behavior, population, disease time-series, climate, environment, and/or a combination thereof, whichever option best compromises among realism, feasibility, robustness, and parsimony. Fully automatic and user-friendly state–space forecasting frameworks, incorporating myriad options (e.g., expert opinion, univariate, multivariate, and spatial-temporal), could considerably enhance disease control and hazard mitigation efforts in regions where vulnerability to neglected tropical diseases is pervasive and statistical expertise is scarce. The operational simplicity, generality, and flexibility of state–space frameworks, encapsulating multiple methods, could conveniently allow for 1) unsupervised model selection without disease-specific methodological tailoring, 2) on-line adaptation to disease time-series fluctuations, and 3) automatic switches between distinct forecasting methods as new time-series perturbations dictate. In this investigation, a univariate state–space framework with the aforementioned properties was successfully applied to the Schistosoma haematobium time-series for the district of Niono, Mali, to automatically generate contemporaneous on-line forecasts and hence, providing a basis for local re-organization and strengthening public health programs in this and potentially other Sahelian districts