Using firm demographic microsimulation to evaluate land use and transport scenario evaluation - model calibration

Existing integrated land use transport interaction models simulate the level of employment in (aggregated) zones and lack the individual firm as a decision making unit. This research tries to improve the behavioural foundation of these models by applying a firm demographic modelling approach that first of all accounts for the individual firm as a decision making unit and secondly represents the urban system with high spatial detail. A firm demographic approach models transitions in the state of individual firms by simulating transitions and events such as the relocation decision, growth or shrinkage of firms or the death of a firm. Important advantage of such a decomposed approach is that it offers the opportunity to account for accessibility in each event in the desired way. The firm demographic model is linked to an urban transport model in order to obtain a dynamic simulation of mobility (and accessibility) developments. The paper describes the firm demographic model specifications as well as the interaction of the model with the urban transport model. The integrated simulation model can be used to analyse the effects of different spatial and transport planning scenarios on the location of economic activities and mobility.

Random sampling technique for ultra-fast computations of molecular opacities for exoplanet atmospheres

Opacities of molecules in exoplanet atmospheres rely on increasingly detailed line-lists for these molecules. The line lists available today contain for many species up to several billions of lines. Computation of the spectral line profile created by pressure and temperature broadening, the Voigt profile, of all of these lines is becoming a computational challenge. We aim to create a method to compute the Voigt profile in a way that automatically focusses the computation time into the strongest lines, while still maintaining the continuum contribution of the high number of weaker lines. Here, we outline a statistical line sampling technique that samples the Voigt profile quickly and with high accuracy. The number of samples is adjusted to the strength of the line and the local spectral line density. This automatically provides high accuracy line shapes for strong lines or lines that are spectrally isolated. The line sampling technique automatically preserves the integrated line opacity for all lines, thereby also providing the continuum opacity created by the large number of weak lines at very low computational cost. The line sampling technique is tested for accuracy when computing line spectra and correlated-k tables. Extremely fast computations (~3.5e5 lines per second per core on a standard current day desktop computer) with high accuracy (< 1 % almost everywhere) are obtained. A detailed recipe on how to perform the computations is given.Comment: Accepted for publication in A&

Niceness theorems

Many things in mathematics seem lamost unreasonably nice. This includes objects, counterexamples, proofs. In this preprint I discuss many examples of this phenomenon with emphasis on the ring of polynomials in a countably infinite number of variables in its many incarnations such as the representing object of the Witt vectors, the direct sum of the rings of representations of the symmetric groups, the free lambda ring on one generator, the homology and cohomology of the classifying space BU, ... . In addition attention is paid to the phenomenon that solutions to universal problems (adjoint functors) tend to pick up extra structure.Comment: 52 page

Hopf algebras of endomorphisms of Hopf algebras

In the last decennia two generalizations of the Hopf algebra of symmetric functions have appeared and shown themselves important, the Hopf algebra of noncommutative symmetric functions NSymm and the Hopf algebra of quasisymmetric functions QSymm. It has also become clear that it is important to understand the noncommutative versions of such important structures as Symm the Hopf algebra of symmetric functions. Not least because the right noncommmutative versions are often more beautiful than the commutaive ones (not all cluttered up with counting coefficients). NSymm and QSymm are not truly the full noncommutative generalizations. One is maximally noncommutative but cocommutative, the other is maximally non cocommutative but commutative. There is a common, selfdual generalization, the Hopf algebra of permutations of Malvenuto, Poirier, and Reutenauer (MPR). This one is, I feel, best understood as a Hopf algebra of endomorphisms. In any case, this point of view suggests vast generalizations leading to the Hopf algebras of endomorphisms and word Hopf algebras with which this paper is concerned. This point of view also sheds light on the somewhat mysterious formulas of MPR and on the question where all the extra structure (such as autoduality) comes from. The paper concludes with a few sections on the structure of MPR and the question of algebra retractions of the natural inclusion of Hopf algebras of NSymm into MPR and section of the naural projection of MPR onto QSymm.Comment: 40 pages. Revised and expanded version of a (nonarchived) preprint of 200

A short proof of a Chebotarev density theorem for function fields

In this article we discuss a version of the Chebotarev density for function fields over perfect fields with procyclic absolute Galois groups. Our version of this density theorem differs from other versions in two aspects: we include ramified primes and we do not have an error term.Comment: 6 pages, rewritten most of the pape