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.     

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     

Identification of a β1/β2‐Specific Sulfonamide Proteasome Ligand by Crystallographic Screening

The proteasome represents a validated drug target for the treatment of cancer, however, new types of inhibitors are required to tackle the development of resistant tumors. Current fluorescence‐based screening methods suffer from low sensitivity and are limited to the detection of ligands with conventional binding profiles. In response to these drawbacks, a crystallographic screening procedure for the discovery of agents with a novel mode of action was utilized. The optimized workflow was applied to the screening of a focused set of compounds, resulting in the discovery of a β1/β2‐specific sulfonamide derivative that noncovalently binds between subunits β1 and β2. The binding pocket displays significant differences in size and polarity between the immuno‐ and constitutive proteasome. The identified ligand thus provides valuable insights for the future structure‐based design of subtype‐specific proteasome inhibitors.     

Predicting the cell-wall compositions of <Emphasis Type="Italic">Pinus radiata</Emphasis> (radiata pine) wood using ATR and transmission FTIR spectroscopies

Because plant cell walls vary in their polysaccharide compositions and lignin contents, their monosaccharide compositions and lignin contents are often determined, but these analyses are time consuming and laborious. We therefore investigated Fourier transform infrared (FTIR) spectroscopy coupled with partial least squares (PLS) regression analysis as a way of rapidly predicting the monosaccharide compositions and lignin contents of the cell walls of compression wood (CW) and opposite wood (OW) of the gymnosperm Pinus radiata. The effects were investigated of sample moisture content (ambient or dry) and sample particle size (large particles, < 0.422 mm or small particles, < 0.178 mm) of milled wood on attenuated total reflectance (ATR) and transmission FTIR spectra, as well as the PLS-1 models and subsequent predictions. PLS-1 models were built using mixtures of CW and OW as the training set, to provide a linear range of monosaccharide compositions and lignin contents. Models were externally validated by predicting another set of wood mixtures before predicting CW and OW of a separate test set. Most of the monosaccharide amounts in the separate test set were best predicted by ATR spectroscopy of ambient large particles, achieving the lowest standard error values for the monosaccharides arabinose (0.36%), xylose (1.05%), galactose (1.79%), glucose (6.32%), and 4-O-methylglucuronic acid (0.20%). The results show the feasibility of using ATR spectroscopy of ambient large particles for the rapid prediction of monosaccharide compositions and lignin contents of plant cell walls.     

Iterated Stochastic Processes: Simulation and Relationship with High Order Partial Differential Equations

In this paper, we consider the composition of two independent processes: one process corresponds to position and the other one to time. Such processes will be called iterated processes. We first propose an algorithm based on the Euler scheme to simulate the trajectories of the corresponding iterated processes on a fixed time interval. This algorithm is natural and can be implemented easily. We show that it converges almost surely, uniformly in time, with a rate of convergence of order 1/4 and propose an estimation of the error. We then extend the well known Feynman-Kac formula which gives a probabilistic representation of partial differential equations (PDEs), to its higher order version using iterated processes. In particular we consider general position processes which are not necessarily Markovian or are indexed by the real line but real valued. We also weaken some assumptions from previous works. We show that intertwining diffusions are related to transformations of high order PDEs. Combining our numerical scheme with the Feynman-Kac formula, we simulate functionals of the trajectories and solutions to fourth order PDEs that are naturally associated to a general class of iterated processes.     

Solubility of methane in pure non-ionic surfactants and pure and mixtures of linear alcohols at 298 K and 101.3 kPa

The emissions of methane (CH₄), a powerful greenhouse gas (GES), contribute to the increase in GES concentration level in the atmosphere. For this reason, the importance of controlling CH₄ emissions of anthropogenic origin has increased over the last decades. Physicochemical and biological processes are available for treating CH₄. For this reason, such properties as the solubility of CH₄ in aqueous solutions and organic solvents are of great relevance in different applications in environmental engineering and biotechnology. In this study, the solubility of CH₄ was determined at 298 K and 101.3 kPa in organic solvents, such as polyoxyethylenesorbates (Tween 20, Tween 40, and Tween 60), and linear alcohols (methanol, ethanol, and butan-1-ol) alone and in their admixtures. Admixtures of methanol with butan-1-ol exhibited the highest solubility of CH₄, of around 0.49 g m⁻³ of solvent, whereas the solubility of CH₄ in linear alcohols varied from 0.167 g m⁻³ to 0.41 g m⁻³ of solvent. In the case of Tweens, CH₄ solubility decreased with the hydrophilic-lipophilic balance (HLB) number.