Constraints on the fundamental string coupling from B-mode experiments

We study signatures of cosmic superstring networks containing strings of multiple tensions and Y junctions, on the cosmic microwave background (CMB) temperature and polarization spectra. Focusing on the crucial role of the string coupling constant g(s), we show that the number density and energy density of the scaling network are dominated by different types of string in the g(s) ~ 1 and g(s) ? 1 limits. This can lead to an observable shift in the position of the B-mode peak--a distinct signal leading to a direct constraint on g(s). We forecast the joint bounds on g(s) and the fundamental string tension μ(F) from upcoming and future CMB polarization experiments, as well as the signal to noise in detecting the difference between B-mode signals in the limiting cases of large and small g(s). We show that such a detectable shift is within reach of planned experiments.     

A Cahn-Hilliard model in a domain with non-permeable walls

We consider in this article a Cahn-Hilliard model in a bounded domain with non-permeable walls, characterized by dynamic-type boundary conditions. Dynamic boundary conditions for the Cahn-Hilliard system have recently been proposed by physicists in order to account for the interactions with the walls in confined systems and are obtained by writing that the total bulk mass is conserved and that there is a relaxation dynamics on the boundary. However, in the case of non-permeable walls, one should also expect some mass on the boundary. It thus seems more realistic to assume that the total mass, in the bulk and on the boundary, is conserved, which leads to boundary conditions of a different type. For the resulting mathematical model, we prove the existence and uniqueness of weak solutions and study their asymptotic behavior as time goes to infinity.     

Kostant Partitions Functions and Flow Polytopes

This paper discusses volumes and Ehrhart polynomials in the context of flow polytopes. The general approach that studies these functions via rational functions with poles on arrangement of hyperplanes and the total residue of such functions allows us, via a unified approach, to reobtain many interesting calculations existing in the literature. In particular we generalize Lidskii formula relating the Ehrhart polynomial to the volume function.     

A zonally symmetric model for the monsoon-Hadley circulation with stochastic convective forcing

Idealized models of reduced complexity are important tools to understand key processes underlying a complex system. In climate science in particular, they are important for helping the community improve our ability to predict the effect of climate change on the earth system. Climate models are large computer codes based on the discretization of the fluid dynamics equations on grids of horizontal resolution in the order of 100 km, whereas unresolved processes are handled by subgrid models. For instance, simple models are routinely used to help understand the interactions between small-scale processes due to atmospheric moist convection and large-scale circulation patterns. Here, a zonally symmetric model for the monsoon circulation is presented and solved numerically. The model is based on the Galerkin projection of the primitive equations of atmospheric synoptic dynamics onto the first modes of vertical structure to represent free tropospheric circulation and is coupled to a bulk atmospheric boundary layer (ABL) model. The model carries bulk equations for water vapor in both the free troposphere and the ABL, while the processes of convection and precipitation are represented through a stochastic model for clouds. The model equations are coupled through advective nonlinearities, and the resulting system is not conservative and not necessarily hyperbolic. This makes the design of a numerical method for the solution of this system particularly difficult. Here, we develop a numerical scheme based on the operator time-splitting strategy, which decomposes the system into three pieces: a conservative part and two purely advective parts, each of which is solved iteratively using an appropriate method. The conservative system is solved via a central scheme, which does not require hyperbolicity since it avoids the Riemann problem by design. One of the advective parts is a hyperbolic diagonal matrix, which is easily handled by classical methods for hyperbolic equations, while the other advective part is a nilpotent matrix, which is solved via the method of lines. Validation tests using a synthetic exact solution are presented, and formal second-order convergence under grid refinement is demonstrated. Moreover, the model is tested under realistic monsoon conditions, and the ability of the model to simulate key features of the monsoon circulation is illustrated in two distinct parameter regimes.     

Exploratory studies toward the synthesis of the peroxylactone unit of plakortolides

Our efforts in construction the 1,2-dioxane ring of plakortolides through two approaches are described. The first one involved as a key step an acid catalyzed 6-endo ring closure of β-hydroperoxy trans-epoxides directed by a vinyl group adjacent to the epoxide function. By this route, an advanced intermediate of plakortolides was obtained in six steps and 35% overall yield. The second approach featured a 1,2-dioxane ring forming by a double opening of bis-epoxides by ethereal hydrogen peroxide. This reaction did not proceed in the expected sense and exclusive formation of hydroperoxy tetrahydropyran derivatives was observed via a tandem oxacyclization–hydroperoxidation sequence.     

Hierarchical and conditional combination of belief functions induced by visual tracking

In visual tracking, sources of information are often disrupted and deliver imprecise or unreliable data leading to major data fusion issues. In the Dempster-Shafer framework, such issues can be addressed by attempting to design robust combination rules. Instead of introducing another rule, we propose to use existing ones as part of a hierarchical and conditional combination scheme. The sources are represented by mass functions which are analysed and labelled regarding unreliability and imprecision. This conditional step divides the problem into specific sub-problems. In each of these sub-problems, the number of constraints is reduced and an appropriate rule is selected and applied. Two functions are thus obtained and analysed, allowing another rule to be chosen for a second (and final) fusion level. This approach provides a fast and robust way to combine disrupted sources using contextual information brought by a particle filter. Our experiments demonstrate its efficiency on several visual tracking situations.     

The Chern character of a transversally elliptic symbol and the equivariant index

Let G be a compact Lie group acting on a compact manifold M. In this article, we associate to a G-transversally elliptic symbol on M a G-invariant generalized function on G, constructed in terms of equivariant closed differential forms on the cotangent bundle T ^* M. Oblatum 24-VII-1995