The Bell states in noncommutative algebraic geometry

We introduce new mathematical aspects of the Bell states using matrix factorizations, nonnoetherian singularities, and noncommutative blowups. A matrix factorization of a polynomial $p$ consists of two matrices $\phi_1,\phi_2$ such that $\phi_1\phi_2 = \phi_2\phi_1 = p \operatorname{id}$. Using this notion, we show how the Bell states emerge from the separable product of two mixtures, by defining pure states over complex matrices rather than just the complex numbers. We then show in an idealized algebraic setting that pure states are supported on nonnoetherian singularities. Moreover, we find that the collapse of a Bell state is intimately related to the representation theory of the noncommutative blowup along its singular support. This presents an exchange in geometry: the nonlocal commutative spacetime of the entangled state emerges from an underlying local noncommutative spacetime.Comment: 18 pages. Previously titled "Quantum entanglement, emergence, and noncommutative blowups

PRICING STRATEGY UNDER MONOPOLY CONDITIONS: AN EXPERIMENT FOR THE CLASSROOM

This classroom experiment allows students to explore pricing strategies available to the monopolist. Students are given full information about their costs but know nothing about demand except that it is simulated by the instructor. They submit their price-asked and quantity-offered records on one day and receive the quantity-sold response from the instructor on the next day, continuing this routine until they discover the profit-maximizing price and quantity. One of the objectives is to demonstrate that search strategies based on economic principles (MC=MR) can be more efficient than trial-and-error.Experimental economics, Games, Monopolistic, Teaching, Demand and Price Analysis, Teaching/Communication/Extension/Profession,

Cerebrovascular atherosclerosis in type III hyperlipidemia is modulated by variation in the Apolipoprotein A5 gene

<p>Abstract</p> <p>Objective</p> <p>Type III Hyperlipoproteinemia is a rare lipid disorder with a frequency of 1-5 in 5000. It is characterized by the accumulation of triglyceride rich lipoproteins and patients are at increased risk of developping atherosclerosis. Type III HLP is strongly associated with the homozygous presence of the ε2 allele of the <it>APOE </it>gene.</p> <p>However only about 10% of subjects with APOE2/2 genotype develop hyperlipidemia and it is therefore assumed that further genetic and environmental factors are necessary for the expression of disease. It has recently been shown that variation in the <it>APOA5 </it>gene is one of these co-factors. The aim of this study is to investigate the development of cerebrovascular atherosclerosis in patients with Type III hyperlipoproteinemia (Type III HLP) and the role of variation in the APOA5 gene as a risk factor.</p> <p>Methods</p> <p>60 patients with type III hyperlipidemia and ApoE2/2 genotype were included in the study after informed consent. The presence of cerebrovascular atherosclerosis was investigated using B-mode ultra-sonography of the carotid artery. Serum lipid levels were measured by standard procedures. The APOE genotype and the 1131T > C and S19W SNPs in the APOA5 gene and the APOC3 sstI SNP were determined by restriction isotyping Allele frequencies were determined by gene counting and compared using Fisher's exact test. Continuous variables were compared using the Mann Whitney test. A p value of 0.05 or below was considered statistically significant. Analysis was performed using Statistica 7 software.</p> <p>Results</p> <p>The incidence of the APOA5 SNPs, -1131T > C and S19W and the APOC3 sstI SNP were determined as a potential risk modifier. After correction for conventional risk factors, the C allele of the 1131T > C SNP in the APOA5 gene was associated with an increased risk for the development of carotid plaque in patients with Type III HLP with an odds ratio of 3.69. Evaluation of the genotype distribution was compatible with an independent effect of APOA5.</p> <p>Conclusions</p> <p>The development of atherosclerosis in patients with Type III HLP is modulated by variation in the <it>APOA5 </it>gene.</p

Tidal tensors in the description of gravity and electromagnetism

In 2008-2009, F. Costa and C. Herdeiro proposed a new gravito-electromagnetic analogy, based on tidal tensors. We show that connections on the tangent bundle of the space-time manifold can help not only in finding a covnenient geometrization of their ideas, but also a common mathematical description of the main equations of gravity and electromagnetism.Comment: submitted to: Journal of Nonlinear Mathematical Physic

Pygmy dipole strength close to particle-separation energies - the case of the Mo isotopes

The distribution of electromagnetic dipole strength in 92, 98, 100 Mo has been investigated by photon scattering using bremsstrahlung from the new ELBE facility. The experimental data for well separated nuclear resonances indicate a transition from a regular to a chaotic behaviour above 4 MeV of excitation energy. As the strength distributions follow a Porter-Thomas distribution much of the dipole strength is found in weak and in unresolved resonances appearing as fluctuating cross section. An analysis of this quasi-continuum - here applied to nuclear resonance fluorescence in a novel way - delivers dipole strength functions, which are combining smoothly to those obtained from (g,n)-data. Enhancements at 6.5 MeV and at ~9 MeV are linked to the pygmy dipole resonances postulated to occur in heavy nuclei.Comment: 6 pages, 5 figures, proceedings Nuclear Physics in Astrophysics II, May 16-20, Debrecen, Hungary. The original publication is available at www.eurphysj.or

Sub-100 femtosecond pulses from a SESAM modelocked thin disk laser

We present the first passively modelocked thin disk laser (TDL) with sub-100-fs pulse duration using the broadband sesquioxide gain material Yb:LuScO3 and an optimized SEmiconductor Saturable Absorber Mirror (SESAM). In this proof-of-principle experiment, we obtained 5.1W of average power at a repetition rate of 77.5MHz and a pulse duration of 96fs. We carefully explored and optimized the different parameters on the soliton pulse formation process for the generation of short pulses. In particular, SESAMs combining fast recovery time, high modulation depth and low nonsaturable losses proved crucial to achieve this result even though they are expected to only play a minor role in soliton modelocking. To our knowledge, these are the shortest pulses ever obtained with a modelocked TDL, reaching for the first time the sub-100-fs milestone. This result opens the door to sub-100-fs oscillators with substantially higher power levels in the near futur

The Middle to Late Miocene “Carbonate Crash” in the Equatorial Indian Ocean

We integrate benthic foraminiferal stable isotopes, X‐ray fluorescence elemental ratios, and carbonate accumulation estimates in a continuous sedimentary archive recovered at International Ocean Discovery Program Site U1443 (Ninetyeast Ridge, Indian Ocean) to reconstruct changes in carbonate deposition and climate evolution over the interval 13.5 to 8.2 million years ago. Declining carbonate percentages together with a marked decrease in carbonate accumulation rates after ~13.2 Ma signal the onset of a prolonged episode of reduced carbonate deposition. This extended phase, which lasted until ~8.7 Ma, coincides with the middle to late Miocene carbonate crash, originally identified in the eastern equatorial Pacific Ocean and the Caribbean Sea. Interocean comparison reveals that intense carbonate impoverishment at Site U1443 (~11.5 to ~10 Ma) coincides with prolonged episodes of reduced carbonate deposition in all major tropical ocean basins. This implies that global changes in the intensity of chemical weathering and riverine input of calcium and carbonate ions into the ocean reservoir were instrumental in driving the carbonate crash. An increase in U1443 Log (Ba/Ti) together with a change in sediment color from red to green indicate a rise in organic export flux to the sea floor after ~11.2 Ma, which predates the global onset of the biogenic bloom. This early rise in export flux from biological production may have been linked to increased advection of nutrients and intensification of upper ocean mixing, associated with changes in the seasonality and intensity of the Indian Monsoon