Searching for degeneracies of real Hamiltonians using homotopy classification of loops in SO(nn)

Topological tests to detect degeneracies of Hamiltonians have been put forward in the past. Here, we address the applicability of a recently proposed test [Phys. Rev. Lett. {\bf 92}, 060406 (2004)] for degeneracies of real Hamiltonian matrices. This test relies on the existence of nontrivial loops in the space of eigenbases SO$(n)$. We develop necessary means to determine the homotopy class of a given loop in this space. Furthermore, in cases where the dimension of the relevant Hilbert space is large the application of the original test may not be immediate. To remedy this deficiency, we put forward a condition for when the test is applicable to a subspace of Hilbert space. Finally, we demonstrate that applying the methodology of [Phys. Rev. Lett. {\bf 92}, 060406 (2004)] to the complex Hamiltonian case does not provide any new information.Comment: Minor changes, journal reference adde

Sodium Density Associates with Nighttime Systolic Blood Pressure in Young Healthy Adults

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Nontangential limits and Fatou-type theorems on post-critically finite self-similar sets

In this paper we study the boundary limit properties of harmonic functions on $\mathbb R_+\times K$, the solutions $u(t,x)$ to the Poisson equation $$\frac{\partial^2 u}{\partial t^2} + \Delta u = 0,$$ where $K$ is a p.c.f. set and $\Delta$ its Laplacian given by a regular harmonic structure. In particular, we prove the existence of nontangential limits of the corresponding Poisson integrals, and the analogous results of the classical Fatou theorems for bounded and nontangentially bounded harmonic functions.Comment: 22 page

Which Depressive Symptoms and Medication Side Effects Are Perceived by Patients as Interfering Most with Occupational Functioning?

Background. Major depressive disorder (MDD) is associated with significant impairment in occupational functioning. This study sought to determine which depressive symptoms and medication side effects were perceived by patients with MDD to have the greatest interference on work functioning. Methods. 164 consecutive patients with MDD by DSM-IV criteria completed a standard assessment that included a self-rated questionnaire about the degree to which symptoms and side effects interfered with work functioning. Results. The symptoms perceived by patients as interfering most with work functioning were fatigue and low energy, insomnia, concentration and memory problems, anxiety, and irritability. The medication side effects rated as interfering most with work functioning were daytime sedation, insomnia, headache, and agitation/anxiety. There were no differences between men and women in symptoms or side effects that were perceived as interfering with work functioning. Limitations. This was a cross-sectional study; only subjective assessments of work functioning were obtained; the fact that patients were using varied medications acts as a potential confound. Conclusions. Specific depressive symptoms and medication side effects were perceived by patients as interfering more with occupational functioning than others. These factors should be considered in treatment selection (e.g., in the choice of antidepressant) in working patients with MDD

From chemical Langevin equations to Fokker-Planck equation: application of Hodge decomposition and Klein-Kramers equation

The stochastic systems without detailed balance are common in various chemical reaction systems, such as metabolic network systems. In studies of these systems, the concept of potential landscape is useful. However, what are the sufficient and necessary conditions of the existence of the potential function is still an open problem. Use Hodge decomposition theorem in differential form theory, we focus on the general chemical Langevin equations, which reflect complex chemical reaction systems. We analysis the conditions for the existence of potential landscape of the systems. By mapping the stochastic differential equations to a Hamiltonian mechanical system, we obtain the Fokker-Planck equation of the chemical reaction systems. The obtained Fokker-Planck equation can be used in further studies of other steady properties of complex chemical reaction systems, such as their steady state entropies.Comment: 6 pages, 0 figure, submitted to J. Phys. A: Math. Theo

Lake Mead prefertilization study: Preliminary nutrient enhancement studies in Lake Mead

Studies conducted by the University of Nevada-Las Vegas (UNLV), the Nevada Department of Wildlife (NDOW), the Arizona Game and Fish Department (AGFD), The Nevada Division of Environmental Protection (NDEP), and the United States Bureau of Reclamation (USBR) have identified decreased algal production as a major factor involved in the decline of the Lake Mead sport fishery. Phosphorus-laden silt particles in the Colorado River have been sedimenting out in Lake Powell since the completion of Glen Canyon Dam 286 miles upstream in 1963. This sharp decrease in phosphorus loading to Lake Mead (\u3e5000 tons per year) has resulted in decreased biomass and growth at all levels of the food chain. Phosphorus loading to the lower basin (Boulder Basin) has decreased even further since 1981 when Clark County and the City of Las Vegas began removing phosphorus from wastewaters discharged into Las Vegas Bay. Most of Lake Mead is now oligotrophic according to almost all of the trophic status indices which have been developed. Only the inner and middle regions of Las Vegas Bay (treated wastewater influent), the Overton Arm upstream of Fish Island (Muddy and Virgin River discharges), and the Iceberg Canyon/Grand Wash area (Colorado River influence) have been found to have phosphorus levels sufficient to sustain relatively higher productivity. Phytoplankton production becomes tightly regulated by the supply of phosphorus during most of the growing season. Zooplankton graze on planktonic algae, and threadfin shad feed primarily on these zooplankton and phytoplankton. Since game fish feed primarily on either zooplankton or shad at different stages of their life cycle, it is clear how a nutrient limitation of phytoplankton growth can cascade up the food chain. The declines in the sport fisheries, particularly largemouth bass, striped bass and trout, began in the early 1960\u27s and have become much more dramatic since the mid to late 1970\u27s as evidenced by declines in total yields of largemouth bass and trout, and striped bass condition factors, and increased angler effort. It is likely that as fish were increasingly stressed by food shortages, conditions were worsened by indirect factors such as lack of suitable cover for littoral populations and by fish predation. The only way to restore the previous fertility of the lake water is to add nutrients. Large-scale fertilization programs in British Columbia and Alaska have been very successful at stimulating the productivity of all levels of the food chain, ultimately producing more salmon. Nevada and Arizona completed an intensive study of the black bass (largemouth bass) fishery in Lake Mead in 1982 which was funded by the U.S. Bureau of Reclamation (USBR). A major recommendation was that pilot fertilizations be conducted as a demonstration project for future large-scale nutrient enrichment. UNLV subsequently submitted a proposal to the Bureau of Reclamation in November 1984 to artificially fertilize about 30,000 acres in the Overton Arm and about 11,000 acres in Gregg Basin. Since that time a technical advisory panel (the Lake Mead Nutrient Enhancement Technical Committee) comprised of representatives from UNLV, NDOW, AGFD, USBR, NDEP, the National Park Service (NPS), and the U.S. Fish and Wildlife Service (USFWS), was formed to review the original proposal and develop a feasible plan for implementing an experimental program of large-scale fertilization. Subsequently, the USBR funded the present study for 16 months (May 1986-August 1987) to conduct laboratory and pilot-scale field experiments designed to evaluate the potential for successfully stimulating algal growth on a large scale in Lake Mead using artificial fertilization

Scaling Limits for Internal Aggregation Models with Multiple Sources

We study the scaling limits of three different aggregation models on Z^d: internal DLA, in which particles perform random walks until reaching an unoccupied site; the rotor-router model, in which particles perform deterministic analogues of random walks; and the divisible sandpile, in which each site distributes its excess mass equally among its neighbors. As the lattice spacing tends to zero, all three models are found to have the same scaling limit, which we describe as the solution to a certain PDE free boundary problem in R^d. In particular, internal DLA has a deterministic scaling limit. We find that the scaling limits are quadrature domains, which have arisen independently in many fields such as potential theory and fluid dynamics. Our results apply both to the case of multiple point sources and to the Diaconis-Fulton smash sum of domains.Comment: 74 pages, 4 figures, to appear in J. d'Analyse Math. Main changes in v2: added "least action principle" (Lemma 3.2); small corrections in section 4, and corrected the proof of Lemma 5.3 (Lemma 5.4 in the new version); expanded section 6.

Environmental Indicators for the Coastal Region of the U.S. Great Lakes

The goal of this research collaboration was to develop indicators that both estimate environmental condition and suggest plausible causes of ecosystem degradation in the coastal region of the U.S. Great Lakes. The collaboration consisted of 8 broad components, each of which generated different types of environmental responses and characteristics of the coastal region. These indicators included biotic communities of amphibians, birds, diatoms, fish, macroinvertebrates, and wetland plants as well as indicators of polycyclic aromatic hydrocarbon (PAH) photo-induced toxicity and landscape characterization. These components are summarized below and discussed in more detailed in 5 separate reports (Section II). Stress gradients within the U.S. Great Lakes coastal region were defined from 207 variables (e.g., agriculture, atmospheric deposition, land use/land cover, human populations, point source pollution, and shoreline modification) from 19 different data sources that were publicly available for the coastal region. Biotic communities along these gradients were sampled with a stratified, random design among representative ecosystems within the coastal zone. To achieve the sampling across this massive area, the coastal region was subdivided into 2 major ecological provinces and further subdivided into 762 segment sheds. Stress gradients were defined for the major categories of human-induced disturbance in the coastal region and an overall stress index was calculated which represented a combination of all the stress gradients. Investigators of this collaboration have had extensive interactions with the Great Lakes community. For instance, the Lake Erie Lakewide Area Management Plan (LAMP) has adopted many of the stressor measures as integral indicators of the condition of watersheds tributary to Lake Erie. Furthermore, the conceptual approach and applications for development of a generalized stressor gradient have been incorporated into a document defining the tiered aquatic life criteria for defining biological integrity of the nation’s waters. A total of 14 indicators of the U.S. Great Lakes coastal region are presented for potential application. Each indicator is summarized with respect to its use, methodology, spatial context, and diagnosis capability. In general, the results indicate that stress related to agricultural activity and human population density/development had the largest impacts on the biotic community indicators. In contrast, the photoinduced PAH indicator was primarily related to industrial activity in the U.S. Great Lakes, and over half of the sites sampled were potentially at risk of PAH toxicity to larval fish. One of the indicators developed for land use/land change was developed from Landsat imagery for the entire U.S. Great Lakes basin and for the period from 1992 to 2001. This indicator quantified the extensive conversions of both agricultural and forest land to residential area that has occurred during a short 9 year period. Considerable variation in the responses were manifest at different spatial scales and many at surprisingly large scales. Significant advances were made with respect to development of methods for identifying and testing environmental indicators. In addition, many indicators and concepts developed from this project are being incorporated into management plans and U.S. 8 EPA methods documents. Further details, downloadable documents, and updates on these indicators can be found at the GLEI website - http://glei.nrri.umn.edu

Standardized Measures of Coastal Wetland Condition: Implementation at a Laurentian Great Lakes Basin-Wide Scale

Since European settlement, over 50 % of coastal wetlands have been lost in the Laurentian Great Lakes basin, causing growing concern and increased monitoring by government agencies. For over a decade, monitoring efforts have focused on the development of regional and organism-specific measures. To facilitate collaboration and information sharing between public, private, and government agencies throughout the Great Lakes basin, we developed standardized methods and indicators used for assessing wetland condition. Using an ecosystem approach and a stratified random site selection process, birds, anurans, fish, macroinvertebrates, vegetation, and physico-chemical conditions were sampled in coastal wetlands of all five Great Lakes including sites from the United States and Canada. Our primary objective was to implement a standardized basin-wide coastal wetland monitoring program that would be a powerful tool to inform decision-makers on coastal wetland conservation and restoration priorities throughout the Great Lakes basin

Uniform algebras and approximation on manifolds

Let $\Omega \subset \mathbb{C}^n$ be a bounded domain and let $\mathcal{A} \subset \mathcal{C}(\bar{\Omega})$ be a uniform algebra generated by a set $F$ of holomorphic and pluriharmonic functions. Under natural assumptions on $\Omega$ and $F$ we show that the only obstruction to $\mathcal{A} = \mathcal{C}(\bar{\Omega})$ is that there is a holomorphic disk $D \subset \bar{\Omega}$ such that all functions in $F$ are holomorphic on $D$, i.e., the only obstruction is the obvious one. This generalizes work by A. Izzo. We also have a generalization of Wermer's maximality theorem to the (distinguished boundary of the) bidisk