Andreev's Theorem on hyperbolic polyhedra

In 1970, E. M. Andreev published a classification of all three-dimensional compact hyperbolic polyhedra having non-obtuse dihedral angles. Given a combinatorial description of a polyhedron, $C$, Andreev's Theorem provides five classes of linear inequalities, depending on $C$, for the dihedral angles, which are necessary and sufficient conditions for the existence of a hyperbolic polyhedron realizing $C$ with the assigned dihedral angles. Andreev's Theorem also shows that the resulting polyhedron is unique, up to hyperbolic isometry. Andreev's Theorem is both an interesting statement about the geometry of hyperbolic 3-dimensional space, as well as a fundamental tool used in the proof for Thurston's Hyperbolization Theorem for 3-dimensional Haken manifolds. It is also remarkable to what level the proof of Andreev's Theorem resembles (in a simpler way) the proof of Thurston. We correct a fundamental error in Andreev's proof of existence and also provide a readable new proof of the other parts of the proof of Andreev's Theorem, because Andreev's paper has the reputation of being ``unreadable''.Comment: To appear les Annales de l'Institut Fourier. 47 pages and many figures. Revision includes significant modification to section 4, making it shorter and more rigorous. Many new references include

Hydrogeological Characterization of the South Oyster Bacterial Transport Site Using Geophysical Data

A multidisciplinary research team has conducted a field-scale bacterial transport study within an uncontaminated sandy Pleistocene aquifer near Oyster, Virginia. The overall goal of the project was to evaluate the importance of heterogeneities in controlling the field-scale transport of bacteria that are injected into the ground for remediation purposes. Geochemical, hydrological, geological, and geophysical data were collected to characterize the site prior to conducting chemical and bacterial injection experiments. In this paper we focus on results of a hydrogeological characterization effort using geophysical data collected across a range of spatial scales. The geophysical data employed include surface ground-penetrating radar, radar cross-hole tomography, seismic cross-hole tomography, cone penetrometer, and borehole electromagnetic flowmeter. These data were used to interpret the subregional and local stratigraphy, to provide high-resolution hydraulic conductivity estimates, and to provide information about the log conductivity spatial correlation function. The information from geophysical data was used to guide and assist the field operations and to constrain the numerical bacterial transport model. Although more field work of this nature is necessary to validate the usefulness and cost-effectiveness of including geophysical data in the characterization effort, qualitative and quantitative comparisons between tomographically obtained flow and transport parameter estimates with hydraulic well bore and bromide breakthrough measurements suggest that geophysical data can provide valuable, high-resolution information. This information, traditionally only partially obtainable by performing extensive and intrusive well bore sampling, may help to reduce the ambiguity associated with hydrogeological heterogeneity that is often encountered when interpreting field-scale bacterial transport data

Chronicles of Oklahoma

Notes and Documents section for Volume 48, Number 3, Autumn 1970. It includes a letter detailing life working at the Seneca Boarding School, a letter detailing the progress of a mission in Coyle, Oklahoma, and a note regarding how Oklahoma's lands have been shaped by a century of weather

Consumers' willingness to pay for an animal welfare food label

Consumers increasingly rate the ethical dimensions of food production, including animal welfare, as important to them but how these concerns influence their food choices remains unclear. To address this, a Discrete Choice Experiment assesses consumers' willingness to pay for chicken meat. The study aims to understand the effects of food labels (RSPCA Assured and Red Tractor), cause-related marketing campaigns, and price on consumers' willingness to pay. Drawing on a representative sample of 401 British consumers, we estimate a mixed logit model using the hierarchical Bayesian estimation method. The results for the full sample reveal a substantial price premium associated with the animal welfare label (RSPCA Assured); however, this is less pronounced than one of the cause-related marketing campaigns. A latent class analysis identifies two distinct market segments, price sensitive and concerned consumers, which differ on socio-economic and behavioural characteristics. Amongst price sensitive consumers, willingness to pay extra for an animal welfare label is negligible. Complementary, qualitative interviews reveal consumers' difficulties in comparing the varying standards that underpin quality assurance schemes

Neurocognitive Basis of Repetition Deficits in Primary Progressive Aphasia

Previous studies indicate that repetition is affected in primary progressive aphasia (PPA), particularly in the logopenic variant, due to limited auditory-verbal short-term memory (avSTM). We tested repetition of phrases varied by length (short, long) and meaning (meaningful, non-meaningful) in 58 participants (22 logopenic, 19 nonfluent, and 17 semantic variants) and 21 healthy controls using a modified Bayles repetition test. We evaluated the relation between cortical thickness and repetition performance and whether sub-scores could discriminate PPA variants. Logopenic participants showed impaired repetition across all phrases, specifically in repeating long phrases and any phrases that were non-meaningful. Nonfluent, semantic, and healthy control participants only had difficulty repeating long, non-meaningful phrases. Poor repetition of long phrases was associated with cortical thinning in left temporo-parietal areas across all variants, highlighting the importance of these areas in avSTM. Finally, Bayles repetition phrases can assist classification in PPA, discriminating logopenic from nonfluent/semantic participants with 89% accuracy

Effective charge-spin models for quantum dots

It is shown that at low densities, quantum dots with few electrons may be mapped onto effective charge-spin models for the low-energy eigenstates. This is justified by defining a lattice model based on a many-electron pocket-state basis in which electrons are localised near their classical ground-state positions. The equivalence to a single-band Hubbard model is then established leading to a charge-spin ($t-J-V$) model which for most geometries reduces to a spin (Heisenberg) model. The method is refined to include processes which involve cyclic rotations of a ``ring'' of neighboring electrons. This is achieved by introducing intermediate lattice points and the importance of ring processes relative to pair-exchange processes is investigated using high-order degenerate perturbation theory and the WKB approximation. The energy spectra are computed from the effective models for specific cases and compared with exact results and other approximation methods.Comment: RevTex, 24 pages, 7 figures submitted as compressed and PostScript file

Modeling the actinides with disordered local moments

A first-principles disordered local moment (DLM) picture within the local-spin-density and coherent potential approximations (LSDA+CPA) of the actinides is presented. The parameter free theory gives an accurate description of bond lengths and bulk modulus. The case of $\delta$-Pu is studied in particular and the calculated density of states is compared to data from photo-electron spectroscopy. The relation between the DLM description, the dynamical mean field approach and spin-polarized magnetically ordered modeling is discussed.Comment: 6 pages, 4 figure