Superintegrability of the Fock-Darwin system

The Fock-Darwin system is analysed from the point of view of its symmetry properties in the quantum and classical frameworks. The quantum Fock-Darwin system is known to have two sets of ladder operators, a fact which guarantees its solvability. We show that for rational values of the quotient of two relevant frequencies, this system is superintegrable, the quantum symmetries being responsible for the degeneracy of the energy levels. These symmetries are of higher order and close a polynomial algebra. In the classical case, the ladder operators are replaced by ladder functions and the symmetries by constants of motion. We also prove that the rational classical system is superintegrable and its trajectories are closed. The constants of motion are also generators of symmetry transformations in the phase space that have been integrated for some special cases. These transformations connect different trajectories with the same energy. The coherent states of the quantum superintegrable system are found and they reproduce the closed trajectories of the classical one.Comment: 21 pages,16 figure

Built Seawalls: A Protected Investment Or Subordinate To The Public Interest

Over half of the population in the United States lives within fifty miles of the coast, and the number of people living along the coast continues to increase. Sea levels are rising at accelerating rates due to global warming threatening coastal communities. A 2009 report on the impact of global climate change in the United States by an advisory committee to the federal government predicted that, in the future, “more Americans will be living in the areas that are most vulnerable to the effects of climate change.” High levels of greenhouse gases in the atmosphere, such as carbon dioxide, are raising temperatures worldwide. Higher temperatures cause sea levels to rise by expanding ocean water, melting glaciers and ice caps, and causing parts of ice caps to break off and melt into the ocean. Global sea levels rose about 1.7 millimeters per year in the twentieth century, but changed very little over the previous two thousand years. The Intergovernmental Panel on Climate Change (IPCC) has concluded that the average rate of global sea level rise will very likely increase in the twenty-first century. The IPCC predicted that sea levels will rise between nineteen and fifty-nine centimeters (or between seven and twenty-three inches) over the next one hundred years. Although posing potentially staggering consequences, the IPCC prediction is relatively benign compared to a March 2012 study by Climate Central that reported that scientists anticipate sea levels along the U.S. coasts to likely rise twenty to eighty inches this century. Specifically, the Climate Central report projects a rise of one to eight inches by 2030 and four to nineteen inches by 2050, depending on location. Most of the U.S. coast has faced rising seas over the past several decades, and these levels are expected to continue to rise throughout the coming centuries. Sea levels are rising more rapidly along some areas of the U.S. coast, such as the mid-Atlantic, than others due to subsidence and particularly low elevations. Some areas of the Atlantic coast have experienced sea level increases of eight inches or more in the past fifty years. Studies indicate that sea levels along this vulnerable region, from New York to North Carolina, are rising more quickly than the global average, and rose between 2.4 and 4.4 millimeters per year (or a total of one foot) throughout the twentieth century. Rising sea levels threaten coastal development and ecosystems, including wetlands, barrier islands, and beaches. Higher sea levels erode beaches and permanently flood wetlands. Erosion is a significant problem along the coasts. Thirty-one percent of Maryland’s ocean coast is eroding, and estimates of how much shore Maryland loses per year as a result of erosion vary from 260 acres to 580 acres. Many beach towns and resorts pay thousands of dollars per year to replace sand that has washed away. North Beach, Maryland, for example, spends $25,000 each year to rebuild its beach, and the state, local, and federal governments spent seven million dollars to bring in sand to Ocean City in 2006 alone. Rising sea levels are expected to contribute to the severity of storms, one of the most serious impacts of climate change. Higher sea levels result in larger waves, which crash against the shore with greater force than smaller waves and increase the rate of erosion. Scientists have hypothesized that higher seas increased the intensity of Hurricane Isabel, which struck the Atlantic coast of the U.S. in 2003. An infamous 1933 hurricane that hit the same region was more powerful than Hurricane Isabel, but both hurricanes had about the same storm tide, or maximum water level, because the mean sea level in 2003 was about 1.4 feet higher than it was seventy years before. Both hurricanes were Category Two storms, but Isabel caused much more damage. An increase in the water level by one foot caused a forty percent increase in wave power, and sea levels in the Chesapeake Bay are expected to increase by at least two feet. In addition, wetlands and barrier islands protect coasts from storm surges by soaking up excess water and mitigating the impacts of larger waves and flooding. The loss of wetlands and barrier islands results in further increased erosion. Wetlands significantly assist in flood control, pollution control, erosion prevention, and aquifer recharge. Gradual increases in sea levels, as well as abrupt flooding due to storm surges, threaten wetlands. Rising sea levels have already submerged tidal wetlands in Louisiana and Maryland, and the U.S. Climate Change Science Program has concluded that, “it is likely that most wetlands [in the mid-Atlantic region] will not survive acceleration in sea-level rise by [seven] millimeters per year.” Over 200 square miles of coastal lands and wetlands were flooded and lost as a result of hurricanes Rita and Katrina in 2005. Without adequate planning and management, coastal states will continue to lose the aesthetic, recreational, and economic values of coastal ecosystems. Wetlands also provide wildlife habitats, including nurseries for commercial fish and shellfish. Many plants and animals depend on coastal ecosystems, and as their habitats are lost, they will likely be threatened or forced to move. Seawalls and similar erosion protection measures also prevent wildlife from coming ashore. For example, horseshoe crabs in Maryland have difficulty coming ashore to spawn as they get stuck in the small openings of revetments along Maryland’s “armored coast.” Coastal ecosystems can survive rising sea levels by migrating inland, or growing vertically or laterally, but development prevents this migration. On the Atlantic coast, about sixty percent of land below one meter is already developed or is expected to be developed. State and local governments plan to conserve less than ten percent of land below one meter. In addition, many remaining wetlands are unable to generate new soil quickly enough to keep up with rising sea levels. These wetlands will become submerged. While recent studies suggest a three or four-foot increase in sea levels this century, a two-foot increase alone would destroy much of the remaining coastal wetlands in the U.S. Thus, there is a critical need to protect the remaining wetlands in order to mitigate, rather than exacerbate, rising sea levels. Seawalls, bulkheads, and other forms of coastal defense armor a significant portion of the coast. Almost half of New Jersey’s developed coast is armored with these barriers, as is over twenty percent of Maryland’s shoreline (and 16.5% of the state’s coast along the bays). These structural stabilization measures are important for protecting development and populations from rising seas and storms. However, they prevent the inland migration of wetlands and beaches, and they have significant cumulative impacts. Seawalls actually increase coastal erosion. Without a seawall, beaches naturally migrate inland. Seawalls and similar structures prevent this natural migration as waves rebound off of the seawalls, taking sand away with greater force. Seawalls also cumulatively increase the intensity of storms because as the beaches disappear, they no longer absorb the impacts of the waves. In addition, seawalls increase erosion of neighboring lands that are not protected by seawalls, stimulating more seawall construction. Instead of moving inland as the rising sea erodes the shoreline, these barriers cause ecosystems to become trapped between the seawalls and the rising water until eventually the ecosystems are destroyed. Throughout this century, coastal ecosystems will disappear; where there used to be beaches, the water will meet a wall. Examples of such former Maryland beaches include Dares Beach, Columbia Beach, Mason’s Beach, North Beach Park (or Holland Point), and Scotland Beach. Many states have permitting systems for seawalls and other shoreline protection measures. Permitting systems often seem like mere formalities, however; in the last 10 years, the New Jersey State Department of Environmental Protection approved 95% of the applications for development in the state’s coastal review zone, and the Army Corps of Engineers approved all but six of the thousands of applications to construct or modify docks. Between 1996 and 2005, the Maryland Department of the Environment permitted armoring of over 200 miles of coastal land. Despite the coast’s vulnerabilities to rising sea levels, people continue to move to the coasts and develop delicate areas. James Titus of the Environmental Protection Agency (EPA) has suggested for over a decade that states can mitigate impacts of rising sea levels through rolling easements. There are a variety of rolling easements that preserve natural shorelines by ensuring that the rights of landowners are subordinate to the public’s rights. Depending on the common law or statutory law of a state, a rolling easement may transfer title of coastal property to the state as sea levels rise; this may be a form of codifying the state’s property law. The state’s easement “rolls” inland as the sea rises. Alternatively, the state may hold rolling easements on coastal property that give the state title to the coastal land if a private landowner builds a seawall. Or the state’s easement may allow the state to purchase a property right to private land if the sea rises by a certain amount. Rolling easements allow property owners to use and develop their land, but they cannot hold back the sea. This effect can be accomplished through easements, covenants, defeasible estates, or statutes clarifying the state’s property law. Unlike setbacks, rolling easements do not prevent property owners from developing their land.59 Perhaps rolling easements could successfully prevent further shoreline armoring, but, ultimately, much of the U.S. coast is already armored. Although seawalls can serve the public interest when in appropriate places, they are also located in many places that are harmful to the public interest. Rather than always serving a calculated public interest, as opposed to private interests, seawalls are ubiquitous and pose significant threats to public resources. What can states that allowed landowners to build seawalls as they please do? Given the precarious position of the state of Maryland in particular, in light of its high rate of sea level rise and subsidence, as well as its high rate of shoreline armoring, this paper focuses on the seawall problem in that state. Part II discusses how coastal landowners in Maryland have been able to construct hundreds of miles of shoreline armor and analyzes whether landowners have a vested right in those structures. This section also examines whether those property owners have title to the land beneath and behind the seawall, which might otherwise be submerged had the seawall not been built. Part III examines states’ options for addressing the armored shoreline problem, and whether these options pose any takings problems or are protected by the public trust doctrine. Part IV discusses recommendations for moving forward including recommendations for the permitting process regarding seawalls, the importance of educating the public about armored shorelines, and recommendations for addressing existing seawalls. Part V concludes that there is no easy solution to the problem of armored shorelines, but there are options, and states are obliged to protect public trust property, including tidelands

Partial coherent states in graphene

Producción CientíficaWe employ a symmetric gauge to describe the interaction of electrons in graphene with a magnetic field which is orthogonal to the layer surface and to build the so-called partial and bidimensional coherent states for this system in the Barut-Girardello sense. We also evaluate the corresponding probability and current densities as well as the mean energy value.Junta de Castilla y León (projects VA137G18 and BU229P18)Ministerio de Economía, Industria y Competitividad (project MTM2014-57129-C2-1-P

Ethical and legal issues related to health access for migrant populations in the Euro-Mediterranean area

The Institut National d’Hygiène (Morocco) and the Instituto de Salud Carlos III (Spain) are involved as a consortium in a project called "Impact of migration on HIV and TB Epidemiology in the Mediterranean Area", funded by the Sixth Framework Programme for research of the European Commission. The project started in May 2007 and is intended as a specific support action to promote international research cooperation in the Euro-Mediterranean area. In particular, its objective is to improve the capacity of the countries around the Mediterranean Basin for obtaining quality epidemiological information on human immunodeficiency virus (HIV) and tuberculosis (TB) among migrants, while taking into consideration ethical and legal issues related to health in migrant populations. To this end, the project proposed to hold two workshops to bring together all the relevant stakeholders: delegates of international and national non-governmental organisations (NGOs) concerned with the process, experts and health professionals, researchers, representatives of the United Nations Agencies and other decision makers.The authors gratefully acknowledge the contribution of all participants of the second workshop of the project "Impact of migration on HIV and TB Epidemiology in the Mediterranean Area" and the financial support of the European Commission through the VI Framework Programme for Research (FP6) of DG RESEARCH.S

Discrete derivatives and symmetries of difference equations

We show on the example of the discrete heat equation that for any given discrete derivative we can construct a nontrivial Leibniz rule suitable to find the symmetries of discrete equations. In this way we obtain a symmetry Lie algebra, defined in terms of shift operators, isomorphic to that of the continuous heat equation.Comment: submitted to J.Phys. A 10 Latex page

Hydrogen peroxide is a neuronal alarmin that triggers specific RNAs, local translation of Annexin A2, and cytoskeletal remodeling in Schwann cells

Schwann cells are key players in neuro-regeneration: They sense "alarm" signals released by degenerating nerve terminals and differentiate toward a proregenerative phenotype, with phagocytosis of nerve debris and nerve guidance. At the murine neuromuscular junction, hydrogen peroxide (H2O2) is a key signal of Schwann cells' activation in response to a variety of nerve injuries. Here we report that Schwann cells exposed to low doses of H2O2 rewire the expression of several RNAs at both transcriptional and translational levels. Among the genes positively regulated at both levels, we identified an enriched cluster involved in cytoskeleton remodeling and cell migration, with the Annexin (Anxa) proteins being the most represented family. We show that both Annexin A2 (Anxa2) transcript and protein accumulate at the tips of long pseudopods that Schwann cells extend upon H2O2 exposure. Interestingly, Schwann cells reply to this signal and to nerve injury by locally translating Anxa2 in pseudopods, and undergo an extensive cytoskeleton remodeling. Our results show that, similarly to neurons, Schwann cells take advantage of local protein synthesis to change shape and move toward damaged axonal terminals to facilitate axonal regeneration