Lower Bounds for Sums of Powers of Low Degree Univariates

We consider the problem of representing a univariate polynomial f(x) as a sum of powers of low degree polynomials. We prove a lower bound of Omega(root d/t) for writing an explicit univariate degree-d polynomial f(x) as a sum of powers of degree-t polynomials.

Lack of Critical Slowing Down Suggests that Financial Meltdowns Are Not Critical Transitions, yet Rising Variability Could Signal Systemic Risk

Complex systems inspired analysis suggests a hypothesis that financial meltdowns are abrupt critical transitions that occur when the system reaches a tipping point. Theoretical and empirical studies on climatic and ecological dynamical systems have shown that approach to tipping points is preceded by a generic phenomenon called critical slowing down, i.e. an increasingly slow response of the system to perturbations. Therefore, it has been suggested that critical slowing down may be used as an early warning signal of imminent critical transitions. Whether financial markets exhibit critical slowing down prior to meltdowns remains unclear. Here, our analysis reveals that three major US (Dow Jones Index, S&P 500 and NASDAQ) and two European markets (DAX and FTSE) did not exhibit critical slowing down prior to major financial crashes over the last century. However, all markets showed strong trends of rising variability, quantified by time series variance and spectral function at low frequencies, prior to crashes. These results suggest that financial crashes are not critical transitions that occur in the vicinity of a tipping point. Using a simple model, we argue that financial crashes are likely to be stochastic transitions which can occur even when the system is far away from the tipping point. Specifically, we show that a gradually increasing strength of stochastic perturbations may have caused to abrupt transitions in the financial markets. Broadly, our results highlight the importance of stochastically driven abrupt transitions in real world scenarios. Our study offers rising variability as a precursor of financial meltdowns albeit with a limitation that they may signal false alarms.

Identidad y memoria como principio de legitimación : el caso de la construcción del poder imperial de Séptimo Severo

Abstract: I will focus on the Roman Empire during the final years of the 2nd century A.D., which are considered by Classical Historiography as critical. This epithet is based on the detection of estructural and circumstancial changes linked to state power’s concept. Emperor Pertinax’s murder in 193 can be understood as the trigger of the civil war extended up to the year 197. During those years the tutelary of state power was jeopardized, when four Emperors were crowned at the same time. By the time this struggle ended, Lucius Septimius Severus was recognized as the victorious general and the first of his name in the new dynastic line. Considering these facts, it is the purpose of my work to analize the rising figure of Septimius Severus, from civil war’s clashing context through which the Emperial legitimacy had to be set.

Some features of the turbulence produced by rising air bubbles in water

Presented in this paper is an experimental study on the characteristics of the turbulence produced by rising air bubbles in water. The measurements of turbulent velocities were made by using visualization technique of particle streak and computer image processing of the flow field. The turbulence features have been examined, showing that the rising bubble-produced turbulence can be approximately modeled by homogeneous turbulence as in the case of grid turbulence in air.

Numerical simulation of a single fluid particle rising in non-Newtonian fluids

In this work, a level set method is developed for simulating the motion of a fluid particle rising in non-Newtonian fluids described by generalized Newtonian as well as viscoelastic model fluids. As the shear-thinning model we use a Carreau-Yasuda model, and the viscoelastic effect can be modeled with Oldroyd-B constitutive equations. The control volume formulation with the SIMPLEC algorithm incorporated is used to solve the governing equations on a staggered Eulerian grid. The level set method is implemented to compute the motion of a bubble in a Newtonian fluid as one of typical examples for validation, and the computational results are in good agreement with the reported experimental data．The level set method is also applied for simulating a Newtonian drop rising in Carreau-Yasuda and Oldroyd-B fluids．Numerical results including noticeably negative wake behind the drop and viscosity field are obtained, and compare satisfactorily with the known literature data.

If the tide is rising, who pays for the ark?

Two common goals of this meeting are to arrest the effects of sea level rise and other phenomena caused by Greenhouse Gases from anthropogenic sources ("GHG",) and to mitigate the effects. The fundamental questions are: (1) how to get there and (2) who should shoulder the cost? Given Washington gridlock, states, NGO's and citizens such as the Inupiat of the Village of Kivalina have turned to the courts for solutions. Current actions for public nuisance seek (1) to reduce and eventually eliminate GHG emissions, (2) damages for health effects and property damage—plus hundreds of millions in dollars spent to prepare for the foregoing. The U.S. Court of Appeals just upheld the action against the generators of some 10% of the CO2 emissions from human activities in the U.S., clearing the way for a trial featuring the state of the art scientific linkage between GHG production and the effects of global warming. Climate change impacts on coastal regions manifest most prominently through sea level rise and its impacts: beach erosion, loss of private and public structures, relocation costs, loss of use and accompanying revenues (e.g. tourism), beach replenishment and armoring costs, impacts of flooding during high water events, and loss of tax base. Other effects may include enhanced storm frequency and intensity, increased insurance risks and costs, impacts to water supplies, fires and biological changes through invasions or local extinctions (IPCC AR4, 2007; Okmyung, et al., 2007). There is an increasing urgency for federal and state governments to focus on the local and regional levels and consistently provide the information, tools, and methods necessary for adaptation. Calls for action at all levels acknowledge that a viable response must engage federal, state and local expertise, perspectives, and resources in a coordinated and collaborative effort. A workshop held in December 2000 on coastal inundation and sea level rise proposes a shared framework that can help guide where investments should be made to enable states and local governments to assess impacts and initiate adaptation strategies over the next decade. (PDF contains 5 pages)

Nonlinear X-wave formation and conical emission at different powers of a femtosecond laser pulse in water

Nonlinear X-wave formation at different pulse powers in water is simulated using the standard model of nonlinear Schrodinger equation (NLSE). It is shown that in near field X-shape originally emerges from the interplay between radial diffraction and optical Kerr effect. At relatively low power group-velocity dispersion (GVD) arrests the collapse and leads to pulse splitting on axis. With high enough power, multi-photon ionization (NIPI) and multi-photon absorption (MPA) play great importance in arresting the collapse. The tailing part of pulse is first defocused by MPI and then refocuses. Pulse splitting on axis is a manifestation of this process. Double X-wave forms when the split sub-pulses are self-focusing. In the far field, the character of the central X structure of conical emission (CE) is directly related to the single or double X-shape in the near field. (c) 2007 Elsevier B.V. All rights reserved.

Fish for the poor under a rising global demand and changing fishery regime

In the past, agricultural researchers tended to ignore the fisheries factor in global food and nutritional security. However, the role of fish is becoming critical as a result of changes in fisheries regimes, income distribution, demand and increasing international trade. Fish has become the fastest growing food commodity in international trade and this is raising concern for the supply of fish for poorer people. As a result, the impact of international trade regimes on fish supply and demand, and the consequences on the availability of fish for developing countries need to be studied. Policies aimed at increasing export earnings are in conflict with those aimed at increasing food security in third world countries. Fisheries policy research will need to focus on three primary areas which have an impact on the marginal and poorer communities of developing countries: increased international demand for low-value fish on the supply of poorer countries; improved aquaculture technologies and productivity on poorer and marginal farmers; and land and water allocation policy on productivity, food security and sustainability across farm, fishery and related sectors. The key to local food security is in the integration of agriculture, aquaculture and natural resources but an important focus on fisheries policy research will be to look at the linkages between societal, economic and natural systems in order to develop adequate and flexible solutions to achieve sustainable use of aquatic resources systems.

Investigation of rising nitrate concentrations in groundwater in the Eden Valley, Cumbria: Phase 1 project scoping study

This is the Investigation of rising nitrate concentrations in groundwater in the Eden Valley, Cumbria report produced by the Environment Agency in 2003. This report focuses on groundwater nitrate concentrations in the Eden Valley. Most boreholes in the Eden Valley had nitrate concentrations less than 20 mg/l but a significant number had higher concentrations, some exceeding the EC maximum admissible concentration for drinking water of 50 mg/l. The main objectives of this report were to investigate the causes of rising nitrate concentrations in groundwater in the Permo-Triassic sandstone aquifers of the Eden Valley area and provide sufficient understanding of the groundwater and surface water flow system, including the sources of the nitrate contamination and the processes controlling nitrate movement, so that possible management options for reversing this trend can be considered.

Hybrid-electric propulsion for aircraft

Against a background of increasing energy demand and rising fuel prices, hybrid-electric propulsion systems (HEPS) have the potential to significantly reduce fuel consumption in the aviation industry, particularly in the lighter sectors. By taking advantage of both Electric Motor (EM) and Internal Combustion Engine (ICE), HEPS provide not only a benefit in fuel saving but also a reduction in take-off noise and the emission levels. This research considers the design and sizing process of a hybrid-electric propulsion system for a single-seat demonstrator aircraft, the experimental derivation of the ICE map and the EM parameters. In addition to the experimental data, a novel modeling approach including several linked desktop PC software packages is presented to analyze and optimize hybrid-electric technology for aircraft. Further to the analysis of a parallel hybrid-electric, mid-scale aircraft, this paper also presents a scaling approach for a 20 kg UAV and a 50 tonne inter-city airliner. At the smaller scale, two different mission profiles are analyzed: an ISR mission profile, where the simulation routine optimizes the component size of the hybrid-electric propulsion system with respect to fuel saving, and a maximum duration profile; where the flight endurance is determined as a function of payload weight. At the larger scale, the performance of a 50 tonne inter-city airliner is modeled, based on a hybrid-electric gas-turbine, assuming a range of electric boost powers and battery masses.