The web of Calabi-Yau hypersurfaces in toric varieties

Recent results on duality between string theories and connectedness of their moduli spaces seem to go a long way toward establishing the uniqueness of an underlying theory. For the large class of Calabi-Yau 3-folds that can be embedded as hypersurfaces in toric varieties the proof of mathematical connectedness via singular limits is greatly simplified by using polytopes that are maximal with respect to certain single or multiple weight systems. We identify the multiple weight systems occurring in this approach. We show that all of the corresponding Calabi-Yau manifolds are connected among themselves and to the web of CICY's. This almost completes the proof of connectedness for toric Calabi-Yau hypersurfaces.Comment: TeX, epsf.tex; 24 page

Posttherapy I-131 Thymic Uptake Demonstrated with SPECT/CT in a Young Girl with Papillary Thyroid Carcinoma

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/63174/1/thy.2007.0394.pd

On Gerber-Shiu functions and optimal dividend distribution for a L\'{e}vy risk process in the presence of a penalty function

This paper concerns an optimal dividend distribution problem for an insurance company whose risk process evolves as a spectrally negative L\'{e}vy process (in the absence of dividend payments). The management of the company is assumed to control timing and size of dividend payments. The objective is to maximize the sum of the expected cumulative discounted dividend payments received until the moment of ruin and a penalty payment at the moment of ruin, which is an increasing function of the size of the shortfall at ruin; in addition, there may be a fixed cost for taking out dividends. A complete solution is presented to the corresponding stochastic control problem. It is established that the value-function is the unique stochastic solution and the pointwise smallest stochastic supersolution of the associated HJB equation. Furthermore, a necessary and sufficient condition is identified for optimality of a single dividend-band strategy, in terms of a particular Gerber-Shiu function. A number of concrete examples are analyzed.Comment: Published at http://dx.doi.org/10.1214/14-AAP1038 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Searching for K3 Fibrations

We present two methods for studying fibrations of Calabi-Yau manifolds embedded in toric varieties described by single weight systems. We analyse 184,026 such spaces and identify among them 124,701 which are K3 fibrations. As some of the weights give rise to two or three distinct types of fibrations, the total number we find is 167,406. With our methods one can also study elliptic fibrations of 3-folds and K3 surfaces. We also calculate the Hodge numbers of the 3-folds obtaining more than three times as many as were previously known.Comment: 21 pages, LaTeX2e, 4 eps figures, uses packages amssymb,latexsym,cite,epi

Three Endocrine Neoplasms: An Unusual Combination of Pheochromocytoma, Pituitary Adenoma, and Papillary Thyroid Carcinoma

Background: Three endocrine neoplasms?bilateral pheochromocytomas, somatotrophic pituitary adenoma inducing acromegaly, and papillary carcinoma of the thyroid?occurred concurrently in a patient. A genetic mutation was hypothesized. Possible previously described genetic mutations were explored. Methods: Clinical assessments, laboratory data, images of tumors, histopathology, and immunohistochemistry of excised tissues documented the three neoplasms. Clinical assessment of the patient, family history, and a review of the literature sought a familial basis for the disorders. Results: The methods confirmed the presence of three endocrine neoplasms. Each neoplasm was surgically excised and histologically verified. Surgical and 131I treatments reduced the papillary carcinoma, but eventually this tumor progressed to a lethal degree. History, including that of nine siblings, uncovered no familial neoplasms. No similar case was found in the literature, but possible associations with germline mutations were considered. Conclusions: The concurrent development of pheochromocytomas, pituitary somatotrophic adenoma, and papillary thyroid carcinoma appears to be unique. Nevertheless, such tumors, particularly bilateral pheochromocytomas, strongly suggest a de novo germline mutation in a gene not previously associated with multiple endocrine neoplasia syndromes.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98488/1/thy%2E2011%2E0345.pd

First-Principles Study of Optical Absorption Energies, Ligand Field and Spin-Hamiltonian Parameters of Cr³⁺ Ions in Emeralds

Herein, we study the electronic structure, energies, and vibronic structure of optical d-d transitions of Cr3+ ions doped in beryl (Be3Si6Al2O18:Cr3+, emerald). A computational protocol is developed that combines periodic density functional theory (for modeling of the bulk crystalline lattice of emerald) and the multireference configuration interaction complete active space self-consistent field method supplemented with n-electron valence second-order perturbation theory (for the calculation of the energy levels, wave functions, and spin-Hamiltonian and ligand-field parameters of the trigonal Cr3+ centers in the [CrO6]9– clusters embedded in an extended point charge field). Ligand-field parameters were extracted from mapping the effective ligand-field Hamiltonian onto the full many-particle Hamiltonian from one side and from a direct fit to energies of computed d-d transitions on the other side. These have been analyzed using ab initio ligand-field theory. The quality of the theoretical predictions is critically assessed through a detailed comparison with the available experimental data

On the Connectedness of the Moduli Space of Calabi--Yau Manifolds

We show that the moduli space of all Calabi-Yau manifolds that can be realized as hypersurfaces described by a transverse polynomial in a four dimensional weighted projective space, is connected. This is achieved by exploiting techniques of toric geometry and the construction of Batyrev that relate Calabi-Yau manifolds to reflexive polyhedra. Taken together with the previously known fact that the moduli space of all CICY's is connected, and is moreover connected to the moduli space of the present class of Calabi-Yau manifolds (since the quintic threefold P_4[5] is both CICY and a hypersurface in a weighted P_4, this strongly suggests that the moduli space of all simply connected Calabi-Yau manifolds is connected. It is of interest that singular Calabi-Yau manifolds corresponding to the points in which the moduli spaces meet are often, for the present class, more singular than the conifolds that connect the moduli spaces of CICY's.Comment: 22 pages plain TeX, Tables and references adde