Mathematics Commons^™

Parametric Sensitivity Analysis For Biochemical Reaction Networks Based On Pathwise Information Theory, Yannis Pantazis, Markos Katsoulakis, Dionisios G. Vlachos

Markos Katsoulakis

Background: Stochastic modeling and simulation provide powerful predictive methods for the intrinsic understanding of fundamental mechanisms in complex biochemical networks. Typically, such mathematical models involve networks of coupled jump stochastic processes with a large number of parameters that need to be suitably calibrated against experimental data. In this direction, the parameter sensitivity analysis of reaction networks is an essential mathematical and computational tool, yielding information regarding the robustness and the identifiability of model parameters. However, existing sensitivity analysis approaches such as variants of the finite difference method can have an overwhelming computational cost in models with a high-dimensional parameter space. …

Data Combination From Multiple Sources Under Measurement Error, Hugo Gasca-Aragon

Open Access Dissertations

Regulatory Agencies are responsible for monitoring the performance of particular measurement communities. In order to achieve their objectives, they sponsor Intercomparison exercises between the members of these communities. The Intercomparison Exercise Program for Organic Contaminants in the Marine Environment is an ongoing NIST/NOAA program. It was started in 1986 and there have been 19 studies to date. Using this data as a motivation we review the theory and practices applied to its analysis.

It is a common practice to apply some kind of filter to the comparison study data. These filters go from outliers detection and exclusion to exclusion of …

Torus Orbits On Homogeneous Varieties And Kac Polynomials Of Quivers, Paul Gunnells, Emmanuel Letellier, Fernando Rodriguez Villegas

Paul Gunnells

In this paper we prove that the counting polynomials of certain torus orbits in products of partial flag varieties coincides with the Kac polynomials of supernova quivers, which arise in the study of the moduli spaces of certain irregular meromorphic connections on trivial bundles over the projective line. We also prove that these polynomials can be expressed as a specialization of Tutte polynomials of certain graphs providing a combinatorial proof of the non-negativity of their coefficients.

On The Cohomology Of Linear Groups Over Imaginary Quadratic Fields, Herbert Gangl, Paul Gunnells, Jonathan Hanke, Achill Schurmann, Mathieu Dutour Sikiric, Dan Yasaki

Paul Gunnells

Let 􀀀 be the group GLN(OD), where OD is the ring of integers in the imaginary quadratic field with discriminant D < 0. In this paper we investigate the cohomology of 􀀀 for N = 3, 4 and for a selection of discriminants: D −24 when N = 3, and D = −3,−4 when N = 4. In particular we compute the integral cohomology of 􀀀 up to p-power torsion for small primes p. Our main tool is the polyhedral reduction theory for 􀀀 developed by Ash [4, Ch. II] and Koecher [18]. Our results extend work of Staffeldt [29], who treated the case n = 3, D = −4. In a sequel [11] to this paper, we will apply some of these results to the computations with the K-groups K4(OD), when D = −3,−4.