Smooth Function Of Time Research Articles

The potential impact of climate change on annual and seasonal mortality for three cities in Québec, Canada

BackgroundThe impact of climate change and particularly increasing temperature on mortality has been examined for three cities in the province of Québec, Canada.MethodsGeneralized linear Poisson regression has been fitted to the total daily mortality for each city. Smooth parametric cubic splines of temperature and humidity have been used to do nonlinear modeling of these parameters. The model, to control for day of the week and for non-temperature seasonal factors, used a smooth function of time, including delayed effects. The model was then used to assess variation in mortality for simulated future temperatures obtained from an atmospheric General Circulation Model coupled with downscaling regression techniques. Two CO2 emission scenarios are considered (scenarios A2 and B2). Projections are made for future periods around year 2020 (2010–2039), 2050 (2040–2069) and 2080 (2070–2099).ResultsA significant association between mortality and current temperature has been found for the three cities. Under CO2 emission scenarios A2 and B2, the mortality model predicts a significant increase in mortality in the summertime, and a smaller, but significant decrease in the fall season. The slight variations in projected mortality for future winter and spring seasons were found to be not statistically significant. The variations in projected annual mortality are dominated by an increase in mortality in the summer, which is not balanced by the decrease in mortality in the fall and winter seasons. The summer increase and the annual mortality range respectively from about 2% and 0.5% for the 2020 period, to 10% and 3% for the years around 2080. The difference between the mortality variations projected with the A2 or B2 scenarios was not statistically significant.ConclusionFor the three cities, the two CO2 emission scenarios considered led to an increase in annual mortality, which contrasts with most European countries, where the projected increase in summer mortality with respect to climate change is overbalanced by the decrease in winter mortality. This highlights the importance of place in such analyses. The method proposed here to establish these estimates is general and can also be applied to small cities, where mortality rates are relatively low (ex. two deaths/day).

Nonparametric Detection of FM Signals Using Time-Frequency Ridge Energy

In many practical applications, signals to be detected are unknown nonlinear frequency modulated (FM) and are corrupted by strong noise. The phase histories of signals are assumed to be unknown smooth functions of time and these functions are poorly modeled or unmodeled by a small number of parameters. Thus, the conventional parametric-based detection methods are invalid in these cases. This paper proposes a nonparametric detection method using the ridge energy of observations. The detection process consists of three steps, TF ridge detection, ridge energy extraction, and decision. First, the directionally smoothed-pseudo-Wigner-Ville distribution (DSPWVD) is introduced to highlight the instantaneous frequency (IF) points along a special direction on the IF curve of a signal from noise. Further, an angular maximal distribution (AMAD) is constructed from a set of DSPWVDs to highlight the entire IF curve. As a result, the TF ridge of an observation can be estimated well from its AMAD by the maxima position detector. Second, the ridge energy, the total energy along the TF ridge on the pseudo-Wigner-Ville distribution (PWVD), is extracted. A noisy signal has larger ridge energy than a pure noise does, with a large probability, because pure noise energy is randomly distributed throughout the TF plane while the signal energy in a noisy signal is concentrated along the estimated TF ridge. Third, the ridge energy of an observation is used as the test statistic to decide whether or not a signal of interest is present in the observation, where the decision threshold is determined by a large number of Monte Carlo simulations using pure noise. Finally, the simulation experiments to two test signals are made to verify the effectiveness of the proposed method.

Trend, Growth Rate, and Change Point Analysis—A Data Driven Approach

A data-driven technique is proposed to estimate the trend and relative growth rate of time series data. The method is based on the local linear regression smoother and the only assumption about the form of the trend and growth rate function is that they are smooth functions of time. We also extended the method for handling sudden shifts or changes in the trend or growth rate functions by adding dummy variables for the jumps. Simulation studies are carried out to see the performance of the proposed procedure. The method is applied to study the trend and growth rate of wheat production in India from 1951–2005.

Stacked Laplace-EM algorithm for duration models with time-varying and random effects

An extension of the Cox proportional hazards model for clustered survival data is proposed. This allows both general random effects (frailties) and time-varying regression coefficients, the latter being smooth functions of time. The model is fitted using a mixed-model representation of penalized spline smoothing which offers a unified framework for estimation of the baseline hazard, the smooth effects and the random effects. The estimator is computed using a stacked laplace-EM (SLaEM) algorithm. More specifically, the smoothing parameters are integrated out in the log likelihood via a Laplace approximation. The approximation itself involves an integrated log-likelihood over the random cluster effects, for which the EM algorithm is used. A marginal Akaike information criterion is developed for selection among possible candidate models. The time-varying and mixed effects model is applied to unemployment data taken from the German Socio-Economic Panel. The duration of unemployment is modeled in a flexible way including smooth covariate effects and individual random effects.

Observation of q-profile dependence in noble gas injection radiative shutdown times in DIII-D

Massive injection of argon was used to terminate DIII-D discharges with different radial profiles of the safety factor q. An increasing delay before the onset of the central temperature collapse was observed as the overall (core and edge) q of the target plasma was increased. Additionally, an increase in the length of the current quench time was observed, consistent with reduced magnetohydrodynamic (MHD) mode amplitudes and reduced MHD mixing. These results are supported by measurements of heat and impurity mixing during the thermal collapse which observe that thermal transport and impurity mixing are not smooth functions of time but are accelerated when low-order (n=1) MHD modes are destabilized. These results demonstrate that low-order MHD modes play a central role in gas jet shutdowns and density-limit disruptions in tokamaks.

Are mortgage and capital markets integrated in the USA? A study of time-varying cointegration

Recent research has asserted that before 1980, mortgage and capital markets in the USA were not cointegrated as a result of credit rationing, but deregulation of financial institutions led to cointegrated mortgage and capital markets during the 1980s. In this paper, we investigate the causality and cointegration relationship between the mortgage and treasury yields. Our findings suggest that the mortgage and treasury yields are cointegrated before, but not cointegrated after, 1982. To circumvent the non-cointegration problem, this paper introduces a time-varying cointegration approach to the issue. It extends the cointegration theory in such a way that the cointegrating parameter is allowed to follow a smooth function of time. We apply this technique to study the cointegration relationship between the US mortgage and capital markets and find that they are cointegrated after 1982 with time-varying cointegrating parameter.

A Nonstationary Negative Binomial Time Series With Time-Dependent Covariates

Boston Harbor has a history of poor water quality, including contamination by enteric pathogens. We conduct a statistical analysis of data collected by the Massachusetts Water Resources Authority (MWRA) between 1996 and 2002 to evaluate the effects of court-mandated improvements in sewage treatment. Motivated by the ineffectiveness of standard Poisson mixture models and their zero-inflated counterparts, we propose a new negative binomial model for time series of Enterococcus counts in Boston Harbor, where nonstationarity and autocorrelation are modeled using a nonparametric smooth function of time in the predictor. Without further restrictions, this function is not identifiable in the presence of time-dependent covariates; consequently, we use a basis orthogonal to the space spanned by the covariates and use penalized quasi-likelihood (PQL) for estimation. We conclude that Enterococcus counts were greatly reduced near the Nut Island Treatment Plant (NITP) outfalls following the transfer of wastewaters from NITP to the Deer Island Treatment Plant (DITP) and that the transfer of wastewaters from Boston Harbor to the offshore diffusers in Massachusetts Bay reduced the Enterococcus counts near the DITP outfalls.

Pricing general insurance with constraints

Deterministic control theory is used to find the optimal premium strategy for an insurer in order to maximise a given objective. The optimal strategy can be loss-leading depending on the model parameters, which may result in negative premium values. In such circumstances, it is optimal to capture as much of the market as possible before making a profit towards the end of the time horizon. In reality, the amount by which an insurer can lower premiums is constrained by borrowing restrictions and the risk inherent in building up a large exposure. Consequently, the effect of constraining the pricing problem is analysed with two forms of constraint: a bounded premium and a solvency requirement. If a lower bound is placed on the premium then an analytical solution can be found, which is not necessarily a smooth function of time. The optimal premium strategy is described in qualitative terms, without recourse to specifying particular parameter values, by considering the value of the terminal optimal premium. Solvency constraints lead to an optimisation problem which is coupled to the state equations and so there is no analytical solution. Numerical results are presented for a subset of the parameter space using control parameterisation, which turns the optimisation problem into a nonlinear programming problem.

On the equivalence of case-crossover and time series methods in environmental epidemiology

The case-crossover design was introduced in epidemiology 15 years ago as a method for studying the effects of a risk factor on a health event using only cases. The idea is to compare a case's exposure immediately prior to or during the case-defining event with that same person's exposure at otherwise similar "reference" times. An alternative approach to the analysis of daily exposure and case-only data is time series analysis. Here, log-linear regression models express the expected total number of events on each day as a function of the exposure level and potential confounding variables. In time series analyses of air pollution, smooth functions of time and weather are the main confounders. Time series and case-crossover methods are often viewed as competing methods. In this paper, we show that case-crossover using conditional logistic regression is a special case of time series analysis when there is a common exposure such as in air pollution studies. This equivalence provides computational convenience for case-crossover analyses and a better understanding of time series models. Time series log-linear regression accounts for overdispersion of the Poisson variance, while case-crossover analyses typically do not. This equivalence also permits model checking for case-crossover data using standard log-linear model diagnostics.

An Optimization Principle for Determining Movement Duration

Movement duration is an integral component of motor control, but nearly all extant optimization models of motor planning prefix duration instead of explaining it. Here we propose a new optimization principle that predicts movement duration. The model assumes that the brain attempts to minimize movement duration under the constraint of meeting an accuracy criterion. The criterion is task and context dependent but is fixed for a given task and context. The model determines a unique duration as a trade-off between speed (time optimality) and accuracy (acceptable endpoint scatter). We analyzed the model for a linear motor plant, and obtained a closed-form equation for determining movement duration. By solving the equation numerically with specific plant parameters for the eye and arm, we found that the model can reproduce saccade duration as a function of amplitude (the main sequence), and arm-movement duration as a function of the ratio of target distance to size (Fitts's law). In addition, it explains the dependency of peak saccadic speed on amplitude and the dependency of saccadic duration on initial eye position. Furthermore, for arm movements, the model predicts a scaling relationship between peak velocity and distance and a reduction in movement duration with a moderate increase in viscosity. Finally, for a linear plant, our model predicts a neural control signal identical to that of the minimum-variance model set to the same movement duration. This control signal is a smooth function of time (except at the endpoint), in contrast to the discontinuous bang-bang control found in the time-optimal control literature. We suggest that one aspect of movement planning, as revealed by movement duration, may be to assign an endpoint accuracy criterion for a given task and context.

Numerical stability of mass transfer driven by Roche lobe overflow in close binaries

Numerical computation of the time evolution of the mass transfer rate in a close binary can be and, in particular, has been a computational challenge. Using a simple physical model to calculate the mass transfer rate, we show that for a simple explicit iteration scheme the mass transfer rate is numerically unstable unless the time steps are sufficiently small. In general, more sophisticated explicit algorithms do not provide any significant improvement since this instability is a direct result of time discretization. For a typical binary evolution, computation of the mass transfer rate as a smooth function of time limits the maximum tolerable time step and thereby sets the minimum total computational effort required for an evolutionary computation. By methods of ``Controlling Chaos'' it can be shown that a specific implicit iteration scheme, based on Newton's method, is the most promising solution for the problem.

Construction of the discrete geometric conservation law for high-order time-accurate simulations on dynamic meshes

The formulation and implementation of higher-order accurate temporal schemes for dynamic unstructured mesh problems which satisfy the discrete conservation law are presented. The general approach consists of writing the spatially-discretized equations for an arbitrary-Lagrange–Eulerian system (ALE) as a non-homogeneous coupled set of ODE’s where the dependent variables consist of the product of the flow variables with the control volume. Standard application of backwards difference (BDF) and implicit Runge–Kutta (IRK) schemes to these ODE’s, when grid coordinates and velocities are known smooth functions of time, results in the design temporal accuracy of these schemes. However, in general, these schemes do not satisfy the GCL and are therefore not conservative. Using a suitable approximation of the grid velocities evaluated at the locations in time prescribed by the specific ODE time integrator, a GCL compliant scheme can be constructed which retains the design temporal accuracy of the underlying ODE time integrator. This constitutes a practical approach, since the grid velocities are seldom known as continuous functions in time. Numerical examples demonstrating design accuracy and conservation are given for one, two, and three-dimensional inviscid flow problems.

Effect of air pollution on pediatric respiratory emergency room visits and hospital admissions

In order to assess the effect of air pollution on pediatric respiratory morbidity, we carried out a time series study using daily levels of PM10, SO2, NO2, ozone, and CO and daily numbers of pediatric respiratory emergency room visits and hospital admissions at the Children's Institute of the University of Sao Paulo Medical School, from August 1996 to August 1997. In this period there were 43,635 hospital emergency room visits, 4534 of which were due to lower respiratory tract disease. The total number of hospital admissions was 6785, 1021 of which were due to lower respiratory tract infectious and/or obstructive diseases. The three health end-points under investigation were the daily number of emergency room visits due to lower respiratory tract diseases, hospital admissions due to pneumonia, and hospital admissions due to asthma or bronchiolitis. Generalized additive Poisson regression models were fitted, controlling for smooth functions of time, temperature and humidity, and an indicator of weekdays. NO2 was positively associated with all outcomes. Interquartile range increases (65.04 microg/m3) in NO2 moving averages were associated with an 18.4% increase (95% confidence interval, 95% CI = 12.5-24.3) in emergency room visits due to lower respiratory tract diseases (4-day moving average), a 17.6% increase (95% CI = 3.3-32.7) in hospital admissions due to pneumonia or bronchopneumonia (3-day moving average), and a 31.4% increase (95% CI = 7.2-55.7) in hospital admissions due to asthma or bronchiolitis (2-day moving average). The study showed that air pollution considerably affects children's respiratory morbidity, deserving attention from the health authorities.

A method to determine atmospheric optical depth using observations of direct solar radiation

The proposed method of atmospheric total optical depth (TOD) determination is based on the assumption that TOD is an arbitrary smooth function of time. Any small section of this function can be approximated by a linear relationship. A redundant system of Bouguer equations corresponding to n solar observations (where n > 3) can be written for each linear section. This procedure is successively applied to each section of the TOD curve and yields (N − n + 1) systems of Bouguer equations, where N is the total number of solar observations during a day. Solving these systems of Bouguer equations gives an extra‐atmospheric value of the solar flux and TOD curve parameters. The accuracy of the method depends on the accuracy of TOD curve approximation, i.e., on the character of TOD variation with time and a total number of observations during a day. The new method (named approximation by linear sections (APLS)) has been used for TOD investigations in the Crimea (a peninsula in Ukraine) since 1996. In comparison with the classical Bouguer‐Langley method the new method allows us to achieve higher accuracy, when the conditions of astroclimate at the observational site are not very good and especially when the observations are carried out for a half day, i.e., only before noon or after.

A mathematically transparent low-pass filter for tidal estuaries

The tidally resolved mass conservation equation of solutes in a Eulerian reference frame is transformed to a new reference frame, which oscillates with the tide so as to maintain constant upstream volume. This transformation is mathematically transparent and removes almost all the tidal harmonics, which are present in the original solution. Tidal harmonics make the direct time integration in a Eulerian frame difficult. In contrast, after coordinate transformation, it is straightforward to derive an approximate time-average solute equation through the application of a time-smoothing operator. Using a simple model, it is demonstrated that the transient solute dynamics in the new, oscillating reference frame is a smooth function of time. As a result, the Reynolds rules for time averaging can readily be applied in the new frame and it is shown that the resulting solute equation, which describes the long-term solute dynamics, is indeed a very good approximation to the instantaneous, tidally resolved, mass conservation equation. The practical implementation of the time-smoothing operator is illustrated in the case of a real estuary, the Western Scheldt (Belgium–Netherlands).

Studying articulatory variability using functional data analysis

This paper examines articulatory variability across repetitions using functional data analysis. In this analysis, signals are time-normalized using a smooth function of time. The magnitude of the time-warping function provides an index of phasing (temporal) variability; a separate index of amplitude variability is calculated from the time-normalized signal. Here, lip, jaw, and tongue movements in vowel–consonant–vowel sequences recorded using a magnetometer were used for the analysis. Preliminary results suggest articulator specific patterns of variability. Thus vertical jaw movements showed small amplitude variability for alveolar consonants, like /s, t/. As expected, the amplitude variability of the tongue tip was small during alveolar consonants, where the tip is in contact with the alveolar ridge. However, the amplitude of the tongue tip movement varied considerably at the release of alveolar stops. The horizontal and vertical movements of the same articulator often showed a different amount of amplitude variability. For example, during the movement from the first to the second vowel in /api/, the tongue body showed small vertical and large horizontal variability. The results will be discussed in terms of articulatory, acoustic, and perceptual constraints on speech production. [Work supported by CNPq, Brazil, and NIH.]

The use of functional data analysis to study variability in childrens speech: Further data

Much previous research has reported increased token-to-token variability in children relative to adults, but the sources and implications of this variability remain matters of debate. Recently, functional data analysis has been used as a tool to gain greater insight into the nature of variability in children’s and adults’ speech data. In FDA, signals are time-normalized using a smooth function of time. The magnitude of the time-warping function provides an index of phasing (temporal) variability, and a separate index of amplitude variability is calculated from the time-normalized signal. Here, oral airflow data are analyzed from 5-year-olds, 10-year-olds, and adult women producing laryngeal and oral fricatives (/h, s, z/). The preliminary FDA results show that children generally have higher temporal and amplitude indices than adults, suggesting greater variability both in gestural timing and magnitude. However, individual patterns are evident in the relative magnitude of the two indices, and in which consonants show the highest values. The time-varying patterns of flow variability over time in /s/ are also explored as a method of inferring relative variability among laryngeal and oral gestures. [Work supported by NIH and CNPq, Brazil.]

Objective time-scale-dependent homogenization of early instrumental temperature series

An objective method for homogenization of early (pre ∼ 1850) instrumental near surface air temperature records is developed. The method is grounded on the same variational principle as used in the objective analysis of meteorological fields; i.e. the method consists of a statistically optimal spatial-coherence-based adjustment of nearby station temperature records. The adjustments are made for several different ranges of time scales, where the wavelet transform is used for the decomposition. The method takes into account that early instrumental temperature records are supposed to contain observational disturbances which are more or less smooth functions of time as a result of summations of numerous sources of biases. The method differs from traditional homogenization techniques in that corrections are not only made for a discrete number of abrupt or linear changes, but for continuously changing errors. The power of the method is illustrated with an example of homogenization of three very long temperature records from Sweden.

The joint estimation of term structures and credit spreads

We present a new framework for the joint estimation of the default-free government term structure and corporate credit spread curves. By using a data set of liquid, German mark denominated bonds, we show that this yields more realistic spreads than traditionally obtained spread curves that result from subtracting independently estimated government and corporate term structures. The obtained spread curves are smooth functions of time to maturity, as opposed to the twisting curves one gets from the traditional method, and are less sensitive to model specifications. To determine the ‘optimal’ model specification, we use a newly developed test statistic that compares spread curves from competing models.

Health effects of air pollution exposure on children and adolescents in São Paulo, Brazil

Children and adolescents have been considered more susceptible to the effects of air pollution than adults. In order to investigate the responses of children of different ages to air pollution exposure, daily records of hospital admissions for children in five age groups (equal or less than 2 years of age, 3-5, 6-13, 14-19, and all ages together, i.e., from 0-19 years of age) were obtained from January 1993 to November 1997 in São Paulo, Brazil, and were compared to daily records of PM10, O3, SO2, CO and NO2 concentrations in ambient air. For each age group a generalized additive Poisson regression was fitted controlling for smooth functions of time, temperature, humidity, and days of the week, with an additional indicator for holidays. Polynomial distributed lag models were used to estimate the 7-day cumulative effect of each pollutant. Children 2 years or less were the most susceptible to the effects of all five pollutants with an increase of 9.4% (95% CI: 7.9,10.9) in respiratory admissions associated with each interquartile range increase in PM10. The oldest group was the second most susceptible to air pollutants, with each interquartile range increase in PM10 associated with a 5.1% (95% CI: 0.3,9.8) increase in respiratory admissions. An interquartile range increase in CO was associated with an 11.3% (95% CI: 5.9,16.8) increase in respiratory hospitalizations. When a multipollutant model was used, the effect of PM10 on respiratory admissions for all ages together was unchanged, while the SO2 and the other pollutants effect was substantially reduced. This study showed that daily respiratory hospital admissions for children and adolescents in São Paulo increased with air pollution, and that the largest effects were found for the youngest (2 years or less) and oldest (14-19 years) age groups.