Perturbative Couplings and Modular Forms in N=2 String Models with a Wilson Line

We consider a class of four parameter D=4, N=2 string models, namely heterotic strings compactified on K3 times T2 together with their dual type II partners on Calabi-Yau three-folds. With the help of generalized modular forms (such as Siegel and Jacobi forms), we compute the perturbative prepotential and the perturbative Wilsonian gravitational coupling F1 for each of the models in this class. We check heterotic/type II duality for one of the models by relating the modular forms in the heterotic description to the known instanton numbers in the type II description. We comment on the relation of our results to recent proposals for closely related models.Comment: 42 pages, LaTeX, revised version contains additional reference

New models for the action of Hecke operators in spaces of Maass wave forms

Utilizing the theory of the Poisson transform, we develop some new concrete models for the Hecke theory in a space $M_{\lambda}(N)$ of Maass forms with eigenvalue $1/4-\lambda^2$ on a congruence subgroup $\Gamma_1(N)$. We introduce the field $F_{\lambda} = {\mathbb Q} (\lambda ,\sqrt{n}, n^{\lambda /2} \mid \~n\in {\mathbb N})$ so that $F_{\lambda}$ consists entirely of algebraic numbers if $\lambda = 0$. The main result of the paper is the following. For a packet $\Phi = (\nu_p \mid p\nmid N)$ of Hecke eigenvalues occurring in $M_{\lambda}(N)$ we then have that either every $\nu_p$ is algebraic over $F_{\lambda}$, or else $\Phi$ will - for some $m\in {\mathbb N}$ - occur in the first cohomology of a certain space $W_{\lambda,m}$ which is a space of continuous functions on the unit circle with an action of $\mathrm{SL}_2({\mathbb R})$ well-known from the theory of (non-unitary) principal representations of $\mathrm{SL}_2({\mathbb R})$.Comment: To appear in Ann. Inst. Fourier (Grenoble

Sampling and Inference for Beta Neutral-to-the-Left Models of Sparse Networks

Empirical evidence suggests that heavy-tailed degree distributions occurring in many real networks are well-approximated by power laws with exponents $\eta$ that may take values either less than and greater than two. Models based on various forms of exchangeability are able to capture power laws with $\eta < 2$, and admit tractable inference algorithms; we draw on previous results to show that $\eta > 2$ cannot be generated by the forms of exchangeability used in existing random graph models. Preferential attachment models generate power law exponents greater than two, but have been of limited use as statistical models due to the inherent difficulty of performing inference in non-exchangeable models. Motivated by this gap, we design and implement inference algorithms for a recently proposed class of models that generates $\eta$ of all possible values. We show that although they are not exchangeable, these models have probabilistic structure amenable to inference. Our methods make a large class of previously intractable models useful for statistical inference.Comment: Accepted for publication in the proceedings of Conference on Uncertainty in Artificial Intelligence (UAI) 201

Functional Forms and Parametrization of CGE Models

This study focused on the choice of functional forms and their parametrization (estimation of free parameters and calibration of other parameters) in the context of CGE models. Various types of elasticities are defined, followed by a presentation of the functional forms most commonly used in these models and various econometric methods for estimating their free parameters. Following this presentation of the theoretical framework, we review parameter estimates used in the literature. This brief literature review was carried out to be used as a guideline for the choice of parameters for CGE models of developing countries.Trade liberalization, Poverty, Elasticities, Functional forms, Calibration, Computable General Equilibrium (CGE)Model

Topological Theory in Bioconstructivism

In the essay “Landscapes of Change: Boccioni’s Stati d’animo as a General Theory of Models,” in Assemblage 19, 1992, Sanford Kwinter proposed a number of theoretical models which could be applied to computer-generated forms in Bioconstructivism. These included topological theory, epigenesis, the epigenetic landscape, morphogenesis, catastrophe and catastrophe theory. Topological theory entails transformational events or deformations in nature which introduce discontinuities into the evolution of a system. Epigenesis entails the generation of smooth landscapes, in waves or the surface of the earth, for example, formed by complex underlying topological interactions. The epigenetic landscape is the smooth forms of relief which are the products of the underlying complex networks of interactions. Morphogenesis describes the structural changes occurring during the development of an organism, wherein forms are seen as discontinuities in a system, as moments of structural instability rather than stability. A catastrophe is a morphogenesis, a jump in a system resulting in a discontinuity. Catastrophe theory is a topological theory describing the discontinuities in the evolution of a system in nature. A project which applies these models, and which helps to establish a theoretical basis for Bioconstructivism by applying topological models, is a design for a theater by Amy Lewis in a Graduate Architecture Design Studio directed by Associate Professor Andrew Thurlow at Roger Williams University, in Spring 2011. In the project, moments of structural stability are juxtaposed with moments of structural instability, to represent the contradiction inherent in self-generation or immanence. The singularity of the surfaces of the forms in the epigenetic landscape contradicts the complex network of interactions of topological forces from which they result. Actions in the environment on unstable, unstructured forms, and undifferentiated structures, result in stable, structured forms, and differentiated structures