Computing the Tutte Polynomial of a Matroid from its Lattice of Cyclic Flats

We show how the Tutte polynomial of a matroid $M$ can be computed from its condensed configuration, which is a statistic of its lattice of cyclic flats. The results imply that the Tutte polynomial of $M$ is already determined by the abstract lattice of its cyclic flats together with their cardinalities and ranks. They furthermore generalize a similiar statement for perfect matroid designs due to Mphako and help to understand families of matroids with identical Tutte polynomial as constructed by Ken Shoda.Comment: New version published in: Electronic Journal Of Combinatorics Volume 21, Issue 3 (2014) http://www.combinatorics.org/ojs/index.php/eljc/article/view/v21i3p4

The timing and magnitude of exchange rate overshooting

Empirical evidence suggests that a monetary shock induces the exchange rate to overshoot its long-run level. The estimated magnitude and timing of the overshooting, however, varies across studies. This paper generates delayed overshooting in a new Keynesian model of a small open economy by incorporating incomplete information about the true nature of the monetary shock. The framework allows for a sensitivity analysis of the overshooting result to underlying structural parameters. It is shown that policy objectives and measures of the economy's sensitivity to exchange rate dynamic affect the timing and magnitude of the overshooting in a predictable manner, suggesting a possible rationale for the cross-study variation of the delayed overshooting Phenomenon. --Exchange rate overshooting,Partial information,Learning

K-theory Soergel Bimodules

We initiate the study of K-theory Soergel bimodules-a K-theory analog of classical Soergel bimodules. Classical Soergel bimodules can be seen as a completed and infinitesimal version of their new K-theoretic analog. We show that morphisms of K-theory Soergel bimodules can be described geometrically in terms of equivariant K-theoretic correspondences between Bott-Samelson varieties. We thereby obtain a natural categorification of K-theory Soergel bimodules in terms of equivariant coherent sheaves. We introduce a formalism of stratified equivariant K-motives on varieties with an affine stratification, which is a K-theoretric analog of the equivariant derived category of Bernstein-Lunts. We show that Bruhat-stratified torus-equivariant K-motives on flag varieties can be described in terms of chain complexes of K-theory Soergel bimodules. Moreover, we propose conjectures regarding an equivariant/monodromic Koszul duality for flag varieties and the quantum K-theoretic Satake

K-Motives and Koszul Duality

We construct an \emph{ungraded version} of Beilinson--Ginzburg--Soergel's Koszul duality, inspired by Beilinson's construction of rational motivic cohomology in terms of $K$-theory. For this, we introduce and study the category $DK(X)$ of constructible $K$-motives on varieties $X$ with an affine stratification. There is a natural and geometric functor from the category of mixed sheaves $D_{mix}(X)$ to $DK(X).$ We show that when $X$ is the flag variety, this functor is Koszul dual to the realisation functor from $D_{mix}(X^\vee)$ to $D(X^\vee)$, the constructible derived category

A mechanistic framework for a priori pharmacokinetic predictions of orally inhaled drugs

The fate of orally inhaled drugs is determined by pulmonary pharmacokinetic (PK) processes such as particle deposition, pulmonary drug dissolution, and mucociliary clearance. Although each single process has been systematically investigated, a quantitative understanding on their interaction remains limited and hence identifying optimal drug and formulation characteristics for orally inhaled drugs is still challenging. To investigate this complex interplay, the pulmonary processes can be integrated into mathematical models. However, existing modeling attempts considerably simplify these processes or are not systematically evaluated against (clinical) data. In this work, we developed a mathematical framework based on physiologically-structured population equations to integrate all relevant pulmonary processes mechanistically. A tailored numerical resolution strategy was chosen and the mechanistic model was evaluated systematically against different clinical datasets. Without any parameter estimation based on individual study data, the developed model simultaneously predicted (1) lung retention profiles of inhaled insoluble particles, (2) particle size-dependent PK of inhaled monodisperse particles, (3) PK differences between inhaled fluticasone propionate and budesonide, and (4) PK differences between healthy volunteers and asthmatic patients. Finally, to identify the most impactful optimization criteria for orally inhaled drugs, we investigated the impact of input parameters on both pulmonary and systemic exposure. Solubility of the inhaled drug did not have any relevant impact on local and systemic PK. Instead, pulmonary dissolution rate, particle size, tissue affinity, and systemic clearance were impactful potential optimization parameters. In the future, the developed prediction framework should be considered a powerful tool to identify optimal drug and formulation characteristics