Penalized Least Squares Fitting

* Supported by the Army Research Office under grant DAAD-19-02-10059.

Time stability of soil water storage measured by neutron probe and the effects of calibration procedures in a small watershed

The knowledge of soil water storage (SWS) of soil profiles is crucial for the adoption of vegetation restoration practices. With the aim of identifying representative sites to obtain the mean SWS of a watershed, a time stability analysis of neutron probe evaluations of SWS was performed by the means of relative differences and Spearman rank correlation coefficients. At the same time, the effects of different neutron probe calibration procedures were explored on time stability analysis. mean SWS estimation. and preservation of the spatial variability of SWS. The selected watershed, with deep gullies and undulating slopes which cover an area of 20 ha, is characterized by an Ust-Sandiic Entisol and an Aeolian sandy soil. The dominant vegetation species are bunge needlegrass (Stipa bungeana Trim) and korshinsk peashrub (Carugano Korshinskii kom.). From June 11, 2007 to July 23,2008, SWS of the top1 m soil layer was evaluated for 20 dates, based on neutron probe data of 12 sampling sites. Three calibration procedures were employed: type 1, most complete, with each site having its own linear calibration equation (TrE); type II. with TrE equations extended over the whole field: and type III, with one single linear calibration curve for the whole field (UnE) and also correcting its intercept based on site specific relative difference analysis (RdE) and on linear fitting of data (RcE), both maintaining the same slope. A strong time stability of SWS estimated by TrE equations was identified. Soil particle size and soil organic matter content were recognized as the influencing factors for spatial variability of SWS. Land use influenced neither the spatial variability nor the time stability of SWS. Time stability analysis identified one site to represent the mean SWS of the whole watershed with mean absolute percentage errors of less than 10%, therefore. this site can be used as a predictor for the mean SWS of the watershed. Some equations of type II were found to be unsatisfactory to yield reliable mean SWS values or in preserving the associated soil spatial variability. Hence, it is recommended to be cautious in extending calibration equations to other sites since they might not consider the field variability. For the equations with corrected intercept (type III), which consider the spatial variability of calibration in a different way in relation to TrE, it was found that they can yield satisfactory means and standard deviation of SWS, except for the RdE equations, which largely leveled off the SWS values in the watershed. Correlation analysis showed that the neutron probe calibration was linked to soil bulk density and to organic matter content. Therefore, spatial variability of soil properties should be taken into account during the process of neutron probe calibration. This study provides useful information on the mean SWS observation with a time stable site and on distinct neutron probe calibration procedures, and it should be extended to soil water management studies with neutron probes, e.g., the process of vegetation restoration in wider area and soil types of the Loess Plateau in China. (C) 2009 Elsevier B.V. All rights reserved.

Determination of pore size distributions by regularization and finite element collocation

The problem of extracting pore size distributions from characterization data is solved here with particular reference to adsorption. The technique developed is based on a finite element collocation discretization of the adsorption integral, with fitting of the isotherm data by least squares using regularization. A rapid and simple technique for ensuring non-negativity of the solutions is also developed which modifies the original solution having some negativity. The technique yields stable and converged solutions, and is implemented in a package RIDFEC. The package is demonstrated to be robust, yielding results which are less sensitive to experimental error than conventional methods, with fitting errors matching the known data error. It is shown that the choice of relative or absolute error norm in the least-squares analysis is best based on the kind of error in the data. (C) 1998 Elsevier Science Ltd. All rights reserved.

Miocene marine-continental correlations in the Lisbon area and some discussion related to personnal experience

Sandpit exploitation near Lisbon allowed collecting of many Miocene, non marine fossils. These sands are part of the mostly marine Miocene series in the Lower Tagus basin. The particularly favourable situation led several researchers to deal with marine-continental correlations. Difficulties often concern methodologic aspects. Some poorly based interpretations exerced a lasting influence. A critical approach is presented. Analysis requires data. Methods based upon models often lead to the temptation of fitting data in order to confirm a priori conclusions, or of mixing up data as if of equal statistic value while they have not at all the same weight. Erroneous interpretations' uncritical repetition for many years "upgraded" them into absolute truth. Another point is endemism vs. europeism. Miocene mammals from Lisbon compared well with corresponding French, contemporaneous taxa, while this was apparently not true for Spanish ones. Too much accent had been put on the endemic character of Spanish, or even regional, mammalian faunas. Nationalist bias and sensationalism also weigh, albeit negatively. Meanwhile nearly all the more evident examples as the rhinoceros Hispanotherium are discredited as Iberian endemisms. Taxa may appear as endemic just because they have not yet been found elsewhere. At least for the medium to large-sized mammals, with their huge geographic distribution, faunal differences depend much more on ecology, climate and environmental conditions. Emphasis on differences may also result from researchers that are often in a precarious situation and need very much to achieve short-term, preferably sensational results. Overvalued differences may mask real similarities. Unethic and not scientific behaviour are further enhanced by "nomina nuda" tricks that may simply be a way to circunvent or cheat the Priority Rule. On the other hand, access to communication networks may present as sensational novelties items that are not new at all, misleading the audience. A new class of "science people" arose, created by the media and not by the value of their real achievements. Discussion is presented on sedimentation processes and discontinuities that are often regarded as absolute precision dating tools, as well as on some geochemical and paleomagnetic interpretations. A very good chronologie frame has been obtained for the basin under study on the basis of an impressive set of data, providing a rather detailed and accurate frame for Miocene marine-continental correlations.

Stochastic dominance and absolute risk aversion

In this paper we propose the infimum of the Arrow-Pratt index of absolute risk aversion as a measure of global risk aversion of a utility function. We then show that, for any given arbitrary pair of distributions, there exists a threshold level of global risk aversion such that all increasing concave utility functions with at least as much global risk aversion would rank the two distributions in the same way. Furthermore, this threshold level is sharp in the sense that, for any lower level of global risk aversion, we can find two utility functions in this class yielding opposite preference relations for the two distributions.

A critical analysis of dimensions and curve fitting practice in economics

When dealing with sustainability we are concerned with the biophysical as well as the monetary aspects of economic and ecological interactions. This multidimensional approach requires that special attention is given to dimensional issues in relation to curve fitting practice in economics. Unfortunately, many empirical and theoretical studies in economics, as well as in ecological economics, apply dimensional numbers in exponential or logarithmic functions. We show that it is an analytical error to put a dimensional unit x into exponential functions ( a x ) and logarithmic functions ( x a log ). Secondly, we investigate the conditions of data sets under which a particular logarithmic specification is superior to the usual regression specification. This analysis shows that logarithmic specification superiority in terms of least square norm is heavily dependent on the available data set. The last section deals with economists’ “curve fitting fetishism”. We propose that a distinction be made between curve fitting over past observations and the development of a theoretical or empirical law capable of maintaining its fitting power for any future observations. Finally we conclude this paper with several epistemological issues in relation to dimensions and curve fitting practice in economics

Advantages of digital holographic microscopy for real-time full field absolute phase imaging

Different interferometric techniques were developed last decade to obtain full field, quantitative, and absolute phase imaging, such as phase-shifting, Fourier phase microscopy, Hilbert phase microscopy or digital holographic microscopy (DHM). Although, these techniques are very similar, DHM combines several advantages. In contrast, to phase shifting, DHM is indeed capable of single-shot hologram recording allowing a real-time absolute phase imaging. On the other hand, unlike to Fourier phase or Hilbert phase microscopy, DHM does not require to record in focus images of the specimen on the digital detector (CCD or CMOS camera), because a numerical focalization adjustment can be performed by a numerical wavefront propagation. Consequently, the depth of view of high NA microscope objectives is numerically extended. For example, two different biological cells, floating at different depths in a liquid, can be focalized numerically from the same digital hologram. Moreover, the numerical propagation associated to digital optics and automatic fitting procedures, permits vibrations insensitive full- field phase imaging and the complete compensation for a priori any image distortion or/and phase aberrations introduced for example by imperfections of holders or perfusion chamber. Examples of real-time full-field phase images of biological cells have been demonstrated. ©2008 COPYRIGHT SPIE

Stochastic dominance and absolute risk aversion

In this paper we proose the infimum of the Arrow-Pratt index of absoluterisk aversion as a measure of global risk aversion of a utility function.We then show that, for any given arbitrary pair of distributions, thereexists a threshold level of global risk aversion such that all increasingconcave utility functions with at least as much global risk aversion wouldrank the two distributions in the same way. Furthermore, this thresholdlevel is sharp in the sense that, for any lower level of global riskaversion, we can find two utility functions in this class yielding oppositepreference relations for the two distributions.

Speed of convergence of recursive least squares learning with ARMA perceptions

This paper fills a gap in the existing literature on least squareslearning in linear rational expectations models by studying a setup inwhich agents learn by fitting ARMA models to a subset of the statevariables. This is a natural specification in models with privateinformation because in the presence of hidden state variables, agentshave an incentive to condition forecasts on the infinite past recordsof observables. We study a particular setting in which it sufficesfor agents to fit a first order ARMA process, which preserves thetractability of a finite dimensional parameterization, while permittingconditioning on the infinite past record. We describe how previousresults (Marcet and Sargent [1989a, 1989b] can be adapted to handlethe convergence of estimators of an ARMA process in our self--referentialenvironment. We also study ``rates'' of convergence analytically and viacomputer simulation.

Skew deviation [Skew deviation]

BACKGROUND: Skew deviation is a vertical ocular misalignment of prenuclear origin. Although well described in the literature, it is still probably underdiagnosed. Natural history of skew deviation is not well described in the literature. PURPOSE: To describe the clinical presentations, etiologies and follow-up of skew deviation. METHODS: Retrospective study of 29 patients diagnosed with skew deviation between 1993 and 1996. RESULTS: The commonest cause was cerebrovascular accident (12/29) and the commonest localisation was mesencephalic (9/29). Other causes included surgery (7/29), tumor (4/29), trauma (3/29), degeneration (3/29), inflammatory (2/29), increased intracranial pressure (1/29). Other localisations included cerebellum (5/29), ponto-mesencephalic (3/29), and medulla (2/29). Vertical diplopia was always accompanied by other neuro-ophthalmologic abnormalities. 69.2% (18/26) patients were totally asymptomatic after 7.5 months. 30.8% (8/26) were still symptomatic (diplopia). One patient required surgery, three patients were relieved with prisms, one patient needed monocular occlusion. One patient died during follow-up and precise data were lacking in two symptomatic patients. CONCLUSION: Skew deviation is not so rare, 10% of the cases referred to us for diplopia in 3 years. The diagnosis of skew deviation should be entertained when vertical diplopia cannot be explained by pathology of extraocular muscles, peripheral or central cranial nerve III or IV palsies, myasthenia, or orbital pathology. Prognosis for recovery in patients with skew deviation is good. 70% will recover, after a median time of 7.5 months. Surgery should be postponed at least for 12 months.

The data treatment dependent variability of U-Pb zircon ages obtained using mono-collector, sector field, laser ablation ICP-MS

U-Pb dating of zircons by laser ablation inductively coupled plasma mass spectrometry (LA-ICPMS) is a widely used analytical technique in Earth Sciences. For U-Pb ages below 1 billion years (1 Ga), Pb-206/U-238 dates are usually used, showing the least bias by external parameters such as the presence of initial lead and its isotopic composition in the analysed mineral. Precision and accuracy of the Pb/U ratio are thus of highest importance in LA-ICPMS geochronology. We consider the evaluation of the statistical distribution of the sweep intensities based on goodness-of-fit tests in order to find a model probability distribution fitting the data to apply an appropriate formulation for the standard deviation. We then discuss three main methods to calculate the Pb/U intensity ratio and its uncertainty in the LA-ICPMS: (1) ratio-of-the-mean intensities method, (2) mean-of-the-intensity-ratios method and (3) intercept method. These methods apply different functions to the same raw intensity vs. time data to calculate the mean Pb/U intensity ratio. Thus, the calculated intensity ratio and its uncertainty depend on the method applied. We demonstrate that the accuracy and, conditionally, the precision of the ratio-of-the-mean intensities method are invariant to the intensity fluctuations and averaging related to the dwell time selection and off-line data transformation (averaging of several sweeps); we present a statistical approach how to calculate the uncertainty of this method for transient signals. We also show that the accuracy of methods (2) and (3) is influenced by the intensity fluctuations and averaging, and the extent of this influence can amount to tens of percentage points; we show that the uncertainty of these methods also depends on how the signal is averaged. Each of the above methods imposes requirements to the instrumentation. The ratio-of-the-mean intensities method is sufficiently accurate provided the laser induced fractionation between the beginning and the end of the signal is kept low and linear. We show, based on a comprehensive series of analyses with different ablation pit sizes, energy densities and repetition rates for a 193 nm ns-ablation system that such a fractionation behaviour requires using a low ablation speed (low energy density and low repetition rate). Overall, we conclude that the ratio-of-the-mean intensities method combined with low sampling rates is the most mathematically accurate among the existing data treatment methods for U-Pb zircon dating by sensitive sector field ICPMS.

Least squares regression with errors in both variables: case studies

Analytical curves are normally obtained from discrete data by least squares regression. The least squares regression of data involving significant error in both x and y values should not be implemented by ordinary least squares (OLS). In this work, the use of orthogonal distance regression (ODR) is discussed as an alternative approach in order to take into account the error in the x variable. Four examples are presented to illustrate deviation between the results from both regression methods. The examples studied show that, in some situations, ODR coefficients must substitute for those of OLS, and, in other situations, the difference is not significant.

Development and characterization of concentric capillary nebulizer used in inductively coupled plasma analysis /

A simple, low-cost concentric capillary nebulizer (CCN) was developed and evaluated for ICP spectrometry. The CCN could be operated at sample uptake rates of 0.050-1.00 ml min'^ and under oscillating and non-oscillating conditions. Aerosol characteristics for the CCN were studied using a laser Fraunhofter diffraction analyzer. Solvent transport efficiencies and transport rates, detection limits, and short- and long-term stabilities were evaluated for the CCN with a modified cyclonic spray chamber at different sample uptake rates. The Mg II (280.2nm)/l\/lg 1(285.2nm) ratio was used for matrix effect studies. Results were compared to those with conventional nebulizers, a cross-flow nebulizer with a Scott-type spray chamber, a GemCone nebulizer with a cyclonic spray chamber, and a Meinhard TR-30-K3 concentric nebulizer with a cyclonic spray chamber. Transport efficiencies of up to 57% were obtained for the CCN. For the elements tested, short- and long-term precisions and detection limits obtained with the CCN at 0.050-0.500 ml min'^ are similar to, or better than, those obtained on the same instrument using the conventional nebulizers (at 1.0 ml min'^). The depressive and enhancement effects of easily ionizable element Na, sulfuric acid, and dodecylamine surfactant on analyte signals with the CCN are similar to, or better than, those obtained with the conventional nebulizers. However, capillary clog was observed when the sample solution with high dissolved solids was nebulized for more than 40 min. The effects of data acquisition and data processing on detection limits were studied using inductively coupled plasma-atomic emission spectrometry. The study examined the effects of different detection limit approaches, the effects of data integration modes, the effects of regression modes, the effects of the standard concentration range and the number of standards, the effects of sample uptake rate, and the effect of Integration time. All the experiments followed the same protocols. Three detection limit approaches were examined, lUPAC method, the residual standard deviation (RSD), and the signal-to-background ratio and relative standard deviation of the background (SBR-RSDB). The study demonstrated that the different approaches, the integration modes, the regression methods, and the sample uptake rates can have an effect on detection limits. The study also showed that the different approaches give different detection limits and some methods (for example, RSD) are susceptible to the quality of calibration curves. Multicomponents spectral fitting (MSF) gave the best results among these three integration modes, peak height, peak area, and MSF. Weighted least squares method showed the ability to obtain better quality calibration curves. Although an effect of the number of standards on detection limits was not observed, multiple standards are recommended because they provide more reliable calibration curves. An increase of sample uptake rate and integration time could improve detection limits. However, an improvement with increased integration time on detection limits was not observed because the auto integration mode was used.

An investigation into observational characteristics of rainfall and temperature in Central Northeast India—a historical perspective 1889–2008

Mann–Kendall non-parametric test was employed for observational trend detection of monthly, seasonal and annual precipitation of five meteorological subdivisions of Central Northeast India (CNE India) for different 30-year normal periods (NP) viz. 1889–1918 (NP1), 1919–1948 (NP2), 1949–1978 (NP3) and 1979–2008 (NP4). The trends of maximum and minimum temperatures were also investigated. The slopes of the trend lines were determined using the method of least square linear fitting. An application of Morelet wavelet analysis was done with monthly rainfall during June– September, total rainfall during monsoon season and annual rainfall to know the periodicity and to test the significance of periodicity using the power spectrum method. The inferences figure out from the analyses will be helpful to the policy managers, planners and agricultural scientists to work out irrigation and water management options under various possible climatic eventualities for the region. The long-term (1889–2008) mean annual rainfall of CNE India is 1,195.1 mm with a standard deviation of 134.1 mm and coefficient of variation of 11%. There is a significant decreasing trend of 4.6 mm/year for Jharkhand and 3.2 mm/day for CNE India. Since rice crop is the important kharif crop (May– October) in this region, the decreasing trend of rainfall during themonth of July may delay/affect the transplanting/vegetative phase of the crop, and assured irrigation is very much needed to tackle the drought situation. During themonth of December, all the meteorological subdivisions except Jharkhand show a significant decreasing trend of rainfall during recent normal period NP4. The decrease of rainfall during December may hamper sowing of wheat, which is the important rabi crop (November–March) in most parts of this region. Maximum temperature shows significant rising trend of 0.008°C/year (at 0.01 level) during monsoon season and 0.014°C/year (at 0.01 level) during post-monsoon season during the period 1914– 2003. The annual maximum temperature also shows significant increasing trend of 0.008°C/year (at 0.01 level) during the same period. Minimum temperature shows significant rising trend of 0.012°C/year (at 0.01 level) during postmonsoon season and significant falling trend of 0.002°C/year (at 0.05 level) during monsoon season. A significant 4– 8 years peak periodicity band has been noticed during September over Western UP, and 30–34 years periodicity has been observed during July over Bihar subdivision. However, as far as CNE India is concerned, no significant periodicity has been noticed in any of the time series.

A Lateglacial archaeological site in the far north-west of Europe at Rubha Port an t-Seilich, Isle of Islay, western Scotland: Ahrensburgian-style artefacts, absolute dating and geoarchaeology

The exact pattern, process and timing of the human re-colonization of northern Europe after the end of the last Ice Age remain controversial. Recent research has provided increasingly early dates for at least pioneer explorations of latitudes above 54°N in many regions, yet the far north-west of the European landmass, Scotland, has remained an unexplained exception to this pattern. Although the recently described Hamburgian artefacts from Howburn and an assemblage belonging to the arch-backed point complex from Kilmelfort Cave have established at least a sporadic human presence during earlier stages of the Lateglacial Interstadial, we currently lack evidence for Younger Dryas/Greenland Stadial 1 (GS-1) activity other than rare stray finds that have been claimed to be of Ahrensburgian affiliation but are difficult to interpret in isolation. We here report the discovery of chipped stone artefacts with technological and typological characteristics similar to those of the continental Ahrensburgian at a locality in western Scotland. A preliminary analysis of associated tephra, pollen and phytoliths, along with microstratigraphic analysis, suggest the artefacts represent one or more episodes of human activity that fall within the second half of GS-1 and the Preboreal period