Infinite order symmetries for two-dimensional separable Schrödinger equations

Consider a non-relativistic Hamiltonian operator H in 2 dimensions consisting of a kinetic energy term plus a potential. We show that if the associated Schrödinger eigenvalue equation admits an orthogonal separation of variables, there is a calculus to describe the (in general) infinite-order differential operator symmetries of the Schrödinger equation. The calculus is formal but can be made rigorous when all functions in the eigenvaue equation are analytic. The infinite-order calculus exhibits structure that is not apparent when one studies only finite-order symmetries. The search for finite-order symmetries can then be reposed as one of looking for solutions of a coupled system of PDEs that are polynomial in certain parameters. We go further and extend the calculus to the situation where the Schrödinger equation admits a second-order symmetry operator, not necessarily associated with orthogonal separable coordinates

Superintegrability in three-dimensional Euclidean space

Potentials for which the corresponding Schrödinger equation is maximally superintegrable in three-dimensional Euclidean space are studied. The quadratic algebra which is associated with each of these potentials is constructed and the bound state wave functions are computed in the separable coordinates

Summary of International Transport Energy Modeling Workshop

The NextSTEPS program at ITS-Davis convened a one-day workshop on international transportation energy modeling (iTEM), focused on comparing the frameworks and scenario projections from four major global transport models: -- Global Change Assessment Model (GCAM) by Pacific Northwest National Laboratory (PNNL) and ITS-Davis, -- MESSAGE-Transport (Model for Energy Supply Strategy Alternatives and their General Environmental Impact) by the International Institute for Applied Systems Analysis (IIASA), -- Mobility Model (MoMo) by the International Energy Agency, and -- Roadmap by the International Council on Clean Transportation (ICCT). Highlights: -- Projections of "baseline" global transportation energy use rise from 98 EJ in 2010 to 160-250 EJ by 2050. -- There are considerable differences in historical data for some modes, both globally and for individual countries (particularly non-OECD countries). Variability in estimates of transportation activity are in most cases much larger than energy differences. -- Global average vehicle ownership rates are projected to range from 270 to 450 per 1,000 people by 2050 with wide ranges across countries: 700-1,075 for the US by the middle of the century (US is around 700 today), 100-650 for China, and 80-380 for India across four models. -- All models rely mainly on GDP to estimate the future demand for freight and hold the base year modal shares (e.g. truck v. rail) roughly constant through 2050. In reality, future evolution will depend on characteristics of products (e.g. type of commodities) being shipped, technologies available for freight and their efficiencies, and policies and infrastructure. -- Current policy commitments toward EVs, PHEVs and H2FCVs (and thus baseline projections) maybe below the numbers suggested by iTEM models as required for meeting climate targets (e.g., 2 degrees C). -- Improvements in data quality and the representation of car ownership and use across the models were identified as priorities. Modeling transport energy use can either be done by estimating how far people travel and what mode of transportation they choose or by estimating how many vehicles there are and how far each one travels. These are complementary approaches, and in theory they should both lead to the same answer. The former approach, used in "service demand" models, seem more intuitive when one wants to model societal shifts in modes of transportation, either in emerging economies as they develop or in developed economies as they decarbonize; but collecting data on service demand is notoriously difficult. In contrast, vehicle stock models use readily-available vehicle sales data, but are harder to use in future-state, what-if scenarios (particularly in estimating modal shift behaviors) and thus require special attention by experts. The four iTEM models are different in terms of scope (GCAM and MESSAGE cover all sectors of the energy system vs. MoMo and Roadmap which cover transportation only) and model structure (GCAM and MESSAGE rely on internal drivers, particularly the costs of technology and travel, to project future changes whereas MoMo and Roadmap rely on experts' judgments and detailed analysis of technology and policies to drive long-term changes). Yet, owing to these differences, the models are highly complementary and in some cases can be used jointly to answer questions that no single model can tackle on its own. The following summary shares some of the comparisons and findings from the workshop

Excitation of High-Spin States by Inelastic Proton Scattering

This work was supported by National Science Foundation Grant PHY 76-84033 and Indiana Universit

Excitation of High-Spin States by Inelastic Proton Scattering

This work was supported by National Science Foundation Grant PHY 75-00289 and Indiana Universit

Cationic lipid-based nanoparticles mediate functional delivery of acetate to tumor cells in vivo leading to significant anticancer effects

Metabolic reengineering using nanoparticle delivery represents an innovative therapeutic approach to normalizing the deregulation of cellular metabolism underlying many diseases, including cancer. Here, we demonstrated a unique and novel application to the treatment of malignancy using a short-chain fatty acid (SCFA)-encapsulated lipid-based delivery system – liposome-encapsulated acetate nanoparticles for cancer applications (LITA-CAN). We assessed chronic in vivo administration of our nanoparticle in three separate murine models of colorectal cancer. We demonstrated a substantial reduction in tumor growth in the xenograft model of colorectal cancer cell lines HT-29, HCT-116 p53+/+ and HCT-116 p53-/-. Nanoparticle-induced reductions in histone deacetylase gene expression indicated a potential mechanism for these anti-proliferative effects. Together, these results indicated that LITA-CAN could be used as an effective direct or adjunct therapy to treat malignant transformation in vivo

Studies of Excited States in 208-Pb by Inelastic Proton Scattering at 135 and 100 MeV

Supported by the National Science Foundation and Indiana Universit

Simultaneous interval regression for K-nearest neighbor

International audienceIn some regression problems, it may be more reasonable to predict intervals rather than precise values. We are interested in finding intervals which simultaneously for all input instances x ∈X contain a β proportion of the response values. We name this problem simultaneous interval regression. This is similar to simultaneous tolerance intervals for regression with a high confidence level γ ≈ 1 and several authors have already treated this problem for linear regression. Such intervals could be seen as a form of confidence envelop for the prediction variable given any value of predictor variables in their domain. Tolerance intervals and simultaneous tolerance intervals have not yet been treated for the K-nearest neighbor (KNN) regression method. The goal of this paper is to consider the simultaneous interval regression problem for KNN and this is done without the homoscedasticity assumption. In this scope, we propose a new interval regression method based on KNN which takes advantage of tolerance intervals in order to choose, for each instance, the value of the hyper-parameter K which will be a good trade-off between the precision and the uncertainty due to the limited sample size of the neighborhood around each instance. In the experiment part, our proposed interval construction method is compared with a more conventional interval approximation method on six benchmark regression data sets

An entomocentric view of the Janzen-Connell hypothesis

In 1987, in the first issue of Conservation Biology, Edward O. Wilson wrote about the “little things that run the world” – the importance and conservation of insects (Wilson, 1987). Readers of Insect Conservation and Diversity will no doubt be very familiar with the concept. Sadly, however, this perception is not as widely shared among the rest of the scientific community as it should be, and insects are still comparatively neglected as a prime focus of scientific investigations

Dynamical aspects of quantum entanglement for weakly coupled kicked tops

We investigate how the dynamical production of quantum entanglement for weakly coupled, composite quantum systems is influenced by the chaotic dynamics of the corresponding classical system, using coupled kicked tops. The linear entropy for the subsystem (a kicked top) is employed as a measure of entanglement. A perturbative formula for the entanglement production rate is derived. The formula contains a correlation function that can be evaluated only from the information of uncoupled tops. Using this expression and the assumption that the correlation function decays exponentially which is plausible for chaotic tops, it is shown that {\it the increment of the strength of chaos does not enhance the production rate of entanglement} when the coupling is weak enough and the subsystems (kicked tops) are strongly chaotic. The result is confirmed by numerical experiments. The perturbative approach is also applied to a weakly chaotic region, where tori and chaotic sea coexist in the corresponding classical phase space, to reexamine a recent numerical study that suggests an intimate relationship between the linear stability of the corresponding classical trajectory and the entanglement production rate.Comment: 16 pages, 11 figures, submitted to Phys. Rev.