Symmetric colorings of polypolyhedra

Polypolyhedra (after R. Lang) are compounds of edge-transitive 1-skeleta. There are 54 topologically different polypolyhedra, and each has icosidodecahedral, cuboctahedral, or tetrahedral symmetry, all are realizable as modular origami models with one module per skeleton edge. Consider a coloring in which each edge of a given component receives a different color, and where the coloring (up to global color permutation) is invariant under the polypolyhedron's symmetry group. On the Five Intersecting Tetrahedra, the edges of each color form visual bands on the model, and correspond to matchings on the dodecahedron graph. We count the number of such colorings and give three proofs. For each of the non-polygon-component polypolyhedra, there is a corresponding matching coloring, and we count the number of these matching colorings. For some of the non-polygon-component polypolyhedra, there is a corresponding visual-band coloring, and we count the number of these band colorings

Transact taxes in a price maker/taker market

We develop a price maker/taker model to study how a financial transaction tax affects markets. We find taxes widen quoted and effective spreads by more than twice the tax. Taxes increase volatility slightly (without intermediation) to significantly (with intermediation). High taxes may halve volumes and gains from trade while doubling search costs. Measures of market quality are more affected by taxes in markets with intermediaries. Investors and intermediaries competing for liquidity can triple search costs and increase quoted spreads while decreasing effective spreads. We also find revenue-optimal rates of 60-75 bp. Our results are particularly relevant to markets with high-frequency trading or thin depth

Binding conditions for atomic N-electron systems in non-relativistic QED

We examine the binding conditions for atoms in non-relativistic QED, and prove that removing one electron from an atom requires a positive energy. As an application, we establish the existence of a ground state for the Helium atom.Comment: LaTeX, uses AMS packag

Shared understandings of dementia? : An application of the Common Sense Self Regulation Model to a case study

Peer reviewedPostprin

High power modelocking using a nonlinear mirror

This thesis presents work on the high average power operation of pulsed diode-pumped solid-state lasers by using a laser configuration known as the bounce geometry. The bounce geometry has previously produced efficient, high power and high spatial quality laser outputs in continuous-wave, Q-switched and modelocked regimes. This thesis explores the capabilities of the bounce geometry for power scaling, shown using Nd:YVO4 and Nd:GdVO4 in both a passively Q-switched laser system and a variety of nonlinear mirror modelocked systems. The high gain experienced by Nd-doped gain media pumped at 808 nm has traditionally posed difficulties in producing stable passive Q-switching with Cr4+:YAG. By using a novel stigmatic design of the bounce geometry that experiences lower gain, but highly circular output, passive Q-switching with > 11 W of average power is produced, at a pulse repetition rate of 190 kHz. This is the highest output power ever achieved from a passively Q-switched Nd-doped vanadate laser to date. Nonlinear mirror modelocking is a passive modelocking technique that employs a χ(2) nonlinear medium in combination with a dichroic output coupler. The first nonlinear mirror modelocking of a bounce geometry laser is presented, obtaining 11.3 W of average power and 57 ps pulse duration using a type-II phase-matched KTP nonlinear crystal. Using type-I phase-matched BiBO, shorter pulses of 5.7 ps in duration are obtained at an average power of 6.1 W. The nonlinear mirror modelocking technique is then applied to the stigmatic bounce geometry laser, obtaining a highly stable train of modelocked pulses with pulse duration 14 ps and an average power of 12 W, with high spatial quality output. Mixed vanadate lasers offer customisation of the laser fluorescence spectrum, but tend to experience lower gain than single vanadates. Using the mixed vanadate combination Nd:Gd0.6Y0.4YVO4 in the bounce geometry, 27.5 W of average power in continuous-wave operation is shown. This is the highest power of any mixed vanadate laser ever reported. By then applying the nonlinear mirror modelocking technique to the mixed vanadate system, 16.8 W of average modelocked output power and a pulse duration of 12.7 ps is obtained. This is simultaneously the first time that the nonlinear mirror technique has been applied to mixed vanadate gain media and the highest power of any modelocked mixed vanadate laser to date. Finally, power scaling of a nonlinear mirror modelocked Nd:GdVO4 laser in the bounce geometry is achieved through use of the double bounce geometry design and through use of a high power pump diode. The system employing the high power pumping produced > 30 W of average power — world record power using the nonlinear mirror technique

On the ground state energy of the translation invariant Pauli-Fierz model

In this note, we determine the ground state energy of the translation invariant Pauli-Fierz model to subleading order $O(\alpha^3)$ with respect to powers of the finestructure constant $\alpha$, and prove rigorous error bounds of order $O(\alpha^{4})$. A main objective of our argument is its brevity.Comment: AMS Latex, 8 page

Usage of Videomosaic for Computer Aided Analysis of North Sea Hard Bottom Underwater Video for Baseline Study of Offshore Windmill Park

Windmill park on the open North Sea coast at Hävsul area in Norway is one of the first in the world to be build on such extreme high-energy coast. To determine possible environmental impact of this project, baseline study was performed in 2010-2011. Two areas, impacted (area where windmill park is planned to be build) and reference were chosen. For hard bottoms work class ROV was used to take underwater video, as no traditional sampling methods are suitable for such environment and depths. The system was equipped with powerful (400 Watt) xenon lights, USBL navigation and HDTV color camera. For video analysis videomosaicing approach was used. Combining overlapping frames into a single picture allows include in the analysis all visual information, and avoid over counting due to the possible presence of the same feature in the number of differnt frames. Bottom fauna and flora in the area include highly heterogenic small patches of various red algae, encrusting algae and encrusting animals. For lesser depths kelp “forests” are common, some megabenthos species are also present. Due to extreme patchiness of the bottom views, it is difficult to process them manually. To overcome this problem computer aided analysis method was developed. Computer aided videomosaics analysis method used for this study is based on color differences of different bottom features. After manually creating training color pallets for different features, it is possible to process large amount of visual data obtaining repeatable and reliable quantitative estimations on the coverage. Additional benefits of videomosaickning are extended abilities to manipulate visual data, what allows more accurate manual estimation of certain features, such as counts of mega benthos species individuals. Although initial study was successful and color based features extraction approach proved to be robust and accurate, it can’t reliably separate certain features (for example, different red algae species). Additional researches on implementing textures and shapes based analysis are needed

Physicians self selection of a payment mechanism: Capitation versus fee-for-service

The main question raised in this paper is whether GPs should self select their paymentmechanism or not. To answer it, we model GPs' behavior under the most commonpayment schemes (capitation and fee-for-service) and when GPs can select one amongthose. Our analysis considers GPs heterogeneity in terms of both ability and sense ofprofessional duty. We conclude that when savings on specialists costs are the mainconcern of a regulator, GPs should be paid on a fee-for-service basis. Instead, whenfailures to identify severe conditions are the main concern, then payment self selection byGPs can be optimal.GPs; gatekeeping; payment scheme; self selection; ability; professional duty

Provider Competition in a Dynamic Setting

In this paper, we examine provider and patient behaviour where effort is non-contractible and where competition between providers is modeled in an explicit way. More specifically, we construct a model where physicians repeatedly compete for patients and where patients’ outside options are solved for in equilibrium. In our model, physicians are characterized by an individual-specific ethical constraint which allows for unobserved heterogeneity in the physicians market. By doing so, we introduce uncertainty in the patient’s likely treatment if he were in fact to leave his current physician to seek care elsewhere. We find that competition between providers may serve as an important incentive for physicians in treating their patients with desired levels of care.Physician Payment Mechanisms, Physician heterogeneity, Competition, Information Asymmetry, Insurance.