Extreme statistics for time series: Distribution of the maximum relative to the initial value

The extreme statistics of time signals is studied when the maximum is measured from the initial value. In the case of independent, identically distributed (iid) variables, we classify the limiting distribution of the maximum according to the properties of the parent distribution from which the variables are drawn. Then we turn to correlated periodic Gaussian signals with a 1/f^alpha power spectrum and study the distribution of the maximum relative height with respect to the initial height (MRH_I). The exact MRH_I distribution is derived for alpha=0 (iid variables), alpha=2 (random walk), alpha=4 (random acceleration), and alpha=infinity (single sinusoidal mode). For other, intermediate values of alpha, the distribution is determined from simulations. We find that the MRH_I distribution is markedly different from the previously studied distribution of the maximum height relative to the average height for all alpha. The two main distinguishing features of the MRH_I distribution are the much larger weight for small relative heights and the divergence at zero height for alpha>3. We also demonstrate that the boundary conditions affect the shape of the distribution by presenting exact results for some non-periodic boundary conditions. Finally, we show that, for signals arising from time-translationally invariant distributions, the density of near extreme states is the same as the MRH_I distribution. This is used in developing a scaling theory for the threshold singularities of the two distributions.Comment: 29 pages, 4 figure

On alpha stable distribution of wind driven water surface wave slope

We propose a new formulation of the probability distribution function of wind driven water surface slope with an $\alpha$-stable distribution probability. The mathematical formulation of the probability distribution function is given under an integral formulation. Application to represent the probability of time slope data from laboratory experiments is carried out with satisfactory results. We compare also the $\alpha$-stable model of the water surface slopes with the Gram-Charlier development and the non-Gaussian model of Liu et al\cite{Liu}. Discussions and conclusions are conducted on the basis of the data fit results and the model analysis comparison.Comment: final version of the manuscript: 25 page

Improving the accuracy and utility of harmful algal bloom forecasting systems

Author Posting. © The Author(s), 2006. This is the author's version of the work. It is posted here by permission of Geological Society for the Micropalaeontological Society for personal use, not for redistribution. The definitive version was published in Biological and Geological Perspectives of Dinoflagellates, edited by Jane Lewis, F. Marret, L.Bradley, :141-147. London: Geological Society for the Micropalaeontological Society, 2013. ISBN: 9781862393684.One of the goals of harmful algal bloom (HAB) research has been to develop predictive capabilities for blooms. Major steps have been made towards this goal, including the development of physical-biological models of HAB species that simulate bloom dynamics in specific regions. In the Gulf of Maine region of the northeastern U.S., models have been developed that have considerable skill in simulating blooms of Alexandrium fundyense, the causative organism for paralytic shellfish poisoning (PSP) outbreaks in the region. This model is now being used for both short-term and long-term forecasts. This paper describes several ongoing activities that will improve the accuracy and usefulness of the model and forecasts. These include efforts to streamline or minimize the sampling and analysis requirements of annual A. fundyense cyst surveys, efforts to quantitatively describe or characterize the severity of predicted outbreaks, and plans to obtain real-time data on Alexandrium cell abundance and toxicity that can be assimilated into the models. Together, these and other activities are moving us towards an operational forecasting system for Alexandrium blooms in the region.Woods Hole Center for Oceans and Human Health, National Science Foundation (NSF) Grants OCE-0430724, and OCE-0911031; and National Institute of Environmental Health Sciences (NIEHS) Grant 1-P50-ES012742-01, the ECOHAB Grant program through NOAA Grants NA06NOS4780245 and NA09NOS4780193, and the MERHAB Grant program through NOAA Grant NA11NOS4780025

Sustainability, innovation, and efficiency:A key relationship

Sustainability has become the emerging goal for countries, companies, and people. Sustainability usually refers to the need to develop models necessary for both human beings and our planet to survive. However, sustainability is not a short-term problem; it is above all a long-term issue, posing intergenerational equity problems. Moreover, sustainability needs efficiency. The efficient use of energy, natural, material, and informational resources is vital for sustainability and sustainable development, which should be the major goal of every country, as established in Rio in 1992, and reaffirmed at Rio+ 20 in 2012. But any strategy aiming at sustainability and efficient use of resources must focus on innovation and technological progress. Consequently, innovation is fundamental to making sustainability possible and improving efficiency. Yet, innovation for sustainability must be environmentally friendly (e.g., green technologies). The principle behind such a strategy is better instead of more. This paper aims at highlighting the key relationship among sustainability, innovation, and efficiency. First, it examines the concept of sustainability, looking at the neoclassical literature on sustainability and its relationship with innovation. Then, it analyzes different theoretical approaches and discusses the policy issues for sustainability where innovation, natural capital, human capital, population, and institutions are fundamental factors

Sagittal jaw position in relation to body posture in adult humans – a rasterstereographic study

BACKGROUND: The correlations between the sagittal jaw position and the cranio – cervical inclination are described in literature. Only few studies focus on the sagittal jaw position and the body posture using valid and objective orthopaedic examination methods. The aim of this study was to test the hypothesis that patients with malocclusions reveal significant differences in body posture compared to those without (upper thoracic inclination, kyphotic angle, lordotic angle and lower lumbar inclination). METHODS: Eighty-four healthy adult patients (with a mean age = 25.6 years and ranging from 16.1 to 55.8 years) were examined with informed consent. The orthodontic examination horizontal overjet (distance between upper and lower incisors) was determined by using an orthodontic digital sliding calliper. The subjects were subdivided in respect of the overjet with the following results: 18 revealed a normal overjet (Class I), 38 had an increased overjet (Class II) and 28 had an reversed overjet (Class III). Rasterstereography was used to carry out a three – dimensional back shape analysis. This method is based on photogrammetry. A three-dimensional shape was produced by analysing the distortion of parallel horizontal white light lines projected on the patient's back, followed by mathematical modelling. On the basis of the sagittal profile the upper thoracic inclination, the thoracic angle, the lordotic angle and the pelvic inclination were determined with a reported accuracy of 2.8° and the correlations to the sagittal jaw position were calculated by means of ANOVA, Scheffé and Kruskal-Wallis procedures. RESULTS: Between the different overjet groups, no statistically significant differences or correlations regarding the analysed back shape parameters could be obtained. However, comparing males and females there were statistically significant differences in view of the parameters 'lordotic angle' and 'pelvic inclination'. CONCLUSION: No correlations between overjet and variables of the thoracic, lordotic or the pelvic inclination could be observed

Understanding interannual, decadal level variability in paralytic shellfish poisoning toxicity in the Gulf of Maine : the HAB Index

Author Posting. © The Author(s), 2013. This is the author's version of the work. It is posted here by permission of Elsevier for personal use, not for redistribution. The definitive version was published in Deep Sea Research Part II: Topical Studies in Oceanography 103 (2014): 264-276, doi:10.1016/j.dsr2.2013.09.018.A major goal in harmful algal bloom (HAB) research has been to identify mechanisms underlying interannual variability in bloom magnitude and impact. Here the focus is on variability in Alexandrium fundyense blooms and paralytic shellfish poisoning (PSP) toxicity in Maine, USA, over 34 years (1978 – 2011). The Maine coastline was divided into two regions - eastern and western Maine, and within those two regions, three measures of PSP toxicity (the percent of stations showing detectable toxicity over the year, the cumulative amount of toxicity per station measured in all shellfish (mussel) samples during that year, and the duration of measurable toxicity) were examined for each year in the time series. These metrics were combined into a simple HAB Index that provides a single measure of annual toxin severity across each region. The three toxin metrics, as well as the HAB Index that integrates them, reveal significant variability in overall toxicity between individual years as well as long-term, decadal patterns or regimes. Based on different conceptual models of the system, we considered three trend formulations to characterize the long-term patterns in the Index – a three-phase (mean-shift) model, a linear two-phase model, and a pulse-decline model. The first represents a “regime shift” or multiple equilibria formulation as might occur with alternating periods of sustained high and low cyst abundance or favorable and unfavorable growth conditions, the second depicts a scenario of more gradual transitions in cyst abundance or growth conditions of vegetative cells, and the third characterizes a ”sawtooth” pattern in which upward shifts in toxicity are associated with major cyst recruitment events, followed by a gradual but continuous decline until the next pulse. The fitted models were compared using both residual sum of squares and Akaike’s Information Criterion. There were some differences between model fits, but none consistently gave a better fit than the others. This statistical underpinning can guide efforts to identify physical and/or biological mechanisms underlying the patterns revealed by the HAB Index. Although A. fundyense cyst survey data (limited to 9 years) do not span the entire interval of the shellfish toxicity records, this analysis leads us to hypothesize that major changes in the abundance of A. fundyense cysts may be a primary factor contributing to the decadal trends in shellfish toxicity in this region. The HAB Index approach taken here is simple but represents a novel and potentially useful tool for resource managers in many areas of the world subject to toxic HABs.Research support provided through the Woods Hole Center for Oceans and Human Health, National Science Foundation (NSF) Grants OCE- 1128041 and OCE-1314642; and National Institute of Environmental Health Sciences (NIEHS) Grant 1-P50-ES021923-01, the ECOHAB Grant program through NOAA Grants NA06NOS4780245 and NA09NOS4780193, the MERHAB Grant program through NOAA Grant NA11NOS4780025, the PCMHAB Grant program through NOAA Grant NA11NOS4780023, and funding through the states of ME, NH, and MA. Funding for J.L. Martin was provided by Fisheries and Oceans Canada

WARNING: Physics Envy May Be Hazardous To Your Wealth!

The quantitative aspirations of economists and financial analysts have for many years been based on the belief that it should be possible to build models of economic systems - and financial markets in particular - that are as predictive as those in physics. While this perspective has led to a number of important breakthroughs in economics, "physics envy" has also created a false sense of mathematical precision in some cases. We speculate on the origins of physics envy, and then describe an alternate perspective of economic behavior based on a new taxonomy of uncertainty. We illustrate the relevance of this taxonomy with two concrete examples: the classical harmonic oscillator with some new twists that make physics look more like economics, and a quantitative equity market-neutral strategy. We conclude by offering a new interpretation of tail events, proposing an "uncertainty checklist" with which our taxonomy can be implemented, and considering the role that quants played in the current financial crisis.Comment: v3 adds 2 reference

Technological Progress, Employment and the Lifetime of Capital

We study the impact of technological progress on the level of employment in a vintage capital model where: i) capital and labor are gross complementary; ii) labor supply is endogenous and indivisible; iii) there is full employment, and iv) the rate of labor-saving technological progress is endogenous. We characterize the stationary distributions of vintage capital goods and the corresponding equilibrium values for employment and capital lifetime. It is shown that both variables are non-monotonic functions of technological progress indicators. Technological accelerations are found to increase employment provided innovations are not too radical

Inequality, Mobility and the Financial Accumulation Process: A Computational Economic Analysis

Our computational economic analysis investigates the relationship between inequality, mobility and the financial accumulation process. Extending the baseline model by Levy et al., we characterise the economic process through stylised return structures generating alternative evolutions of income and wealth through time. First, we explore the limited heuristic contribution of one and two-factors models comprising one single stock (capital wealth) and one single flow factor (labour) as pure drivers of income and wealth generation and allocation over time. Second, we introduce heuristic modes of taxation in line with the baseline approach. Our computational economic analysis corroborates that the financial accumulation process featuring compound returns plays a significant role as source of inequality, while institutional arrangements including taxation play a significant role in framing and shaping the aggregate economic process that evolves over socioeconomic space and time