A rigorous but gentle introduction for economists

This open access textbook is the first to provide Business and Economics Ph.D. students with a precise and intuitive introduction to the formal backgrounds of modern financial theory. It explains Brownian motion, random processes, measures, and Lebesgue integrals intuitively, but without sacrificing the necessary mathematical formalism, making them accessible for readers with little or no previous knowledge of the field. It also includes mathematical definitions and the hidden stories behind the terms discussing why the theories are presented in specific ways.

Rotational equilibrium of C2 in interstellar clouds

In this work the understanding of the rotational equilibrium of C2 in interstellar clouds is updated. It is critical for this equilibrium to be well understood if C2 is to be used as a probe of the physical conditions in these clouds. Although new data continues to be published, the model was last updated in 1987. In this work, new data is collected and incorporated into the model using the program Radex, which will provide a standard format for sharing data, facilitate future updates, and enable the model to quickly run for a grid of temperature and density conditions

Lanthanide Ionization Energies and the Sub-Shell Break. Part 2. The Third and Fourth Ionization Energies

By interpolating a 4fq6s → 4fq7s transition within the sequence f1 → f14 rather than between f0 and f14, revised third and fourth ionization energies of the lanthanides have been obtained. The revised values, together with the second ionization energies calculated in a previous paper, are used to calculate values of the standard enthalpies of formation of the gaseous tripositive ions, ΔfHƟ(M3+,g), and of the lattice and hydration enthalpies of some lanthanide compounds and ions in the trivalent and tetravalent states. The displacements of f0 values from nearly smooth f1 → f14 variations exceed 30 kJ mol-1 and indicate substantial subshell breaks

Systems Biology Markup Language (SBML) Level 2: Structures and Facilities for Model Definitions

Not applicabl

Systems Biology Markup Language (SBML) Level 2: Structures and Facilities for Model Definitions

With the rise of Systems Biology as a new paradigm for understanding biological processes, the development of quantitative models is no longer restricted to a small circle of theoreticians. The dramatic increase in the number of these models precipitates the need to exchange and reuse both existing and newly created models. The Systems Biology Markup Language (SBML) is a free, open, XML-based format for representing quantitative models of biological interest that advocates the consistent specification of such models and thus facilitates both software development and model exchange.

Principally oriented towards describing systems of biochemical reactions, such as cell signalling pathways, metabolic networks and gene regulation etc., SBML can also be used to encode any kinetic model. SBML offers mechanisms to describe biological components by means of compartments and reacting species, as well as their dynamic behaviour, using reactions, events and arbitrary mathematical rules. SBML also offers all the housekeeping structures needed to ensure an unambiguous understanding of quantitative descriptions.

This is Release 1 of the specification for SBML Level 2 Version 4, describing the structures of the language and the rules used to build a valid model. SBML XML Schema and other related documents and software are also available from the SBML project web site, "http://sbml.org/":http://sbml.org/

Determination of the top quark mass from leptonic observables

We present a procedure for the determination of the mass of the top quark at the LHC based on leptonic observables in dilepton $t\bar{t}$ events. Our approach utilises the shapes of kinematic distributions through their few lowest Mellin moments; it is notable for its minimal sensitivity to the modelling of long-distance effects, for not requiring the reconstruction of top quarks, and for having a competitive precision, with theory errors on the extracted top mass of the order of 0.8 GeV. A novel aspect of our work is the study of theoretical biases that might influence in a dramatic way the determination of the top mass, and which are potentially relevant to all template-based methods. We propose a comprehensive strategy that helps minimise the impact of such biases, and leads to a reliable top mass extraction at hadron colliders.Comment: 29 pages, 3 figure

Dynamic Display of Changing Posterior in Bayesian Survival Analysis: The Software

We consider the problem of estimating an unknown distribution function in the presence of censoring under the conditions that a parametric model is believed to hold approximately. We use a Bayesian approach, in which the prior on is a mixture of Dirichlet distributions. A hyperparameter of the prior determines the extent to which this prior concentrates its mass around the parametric family. A Gibbs sampling algorithm to estimate the posterior distributions of the parameters of interest is reviewed. An importance sampling scheme enables us to use the output of the Gibbs sampler to very quickly recalculate the posterior when we change the hyperparameters of the prior. The calculations can be done sufficiently fast to enable the dynamic display of the changing posterior as the prior hyperparameters are varied. This paper provides a literate program completely documenting the code for performing the dynamic graphics.