Determining the degree of chaos from analysis of ISI time series in the nervous system: a comparison between correlation dimension and nonlinear forecasting methods

Two different chaotic time series analysis methods – the correlation dimension and nonlinear forecasting – are introduced and then used to process the interspike intervals (ISI) of the action potential trains propagated along a single nerve fiber of the anesthetized rat. From the results, the conclusion is drawn that compared with the correlation dimension, nonlinear forecasting is more efficient and robust for chaotic ISI time series analysis in a noisy environment. Moreover, the evolution of the correlation coefficient curves calculated from nonlinear forecasting can qualitatively give a better reflection of the unpredictability of the system's future behavior and is in good agreement with the values of the largest Lyapunov exponent that quantitatively measures the degree of chaos. Received: 19 November 1996 / Accepted in revised form: 15 September 1997     

Aeropalynological and phenological study in two different Mediterranean olive areas: Cordoba (Spain) and Perugia (Italy)

ABSTRACT

An aerobiological and phenological investigation on the olive tree was carried out during three years in two areas: Cordoba (Spain) and Perugia (Italy). In these countries, this species is economically important and those areas were chosen because of the long series of aeropalynological data (1982–1998) available, obtained by means of identical volumetric pollen traps. The aim of this study was to use phenological observations to prove the real contribution to the pollen curves in different cultivated areas. Results show that in Cordoba province (302.152 ha) the pollen curve is characterised by different peaks because of the pollination of different cultivated crops. In some cases, these crops are located far from the pollen trap (50 km) but pollen is transported thanks to favourable winds during the flowering period. In Perugia (750 ha) the pollen curve is characterised by only one peak; it is very concentrated because of the proximity of the investigated crops. The objective of this research was to obtain information on this species in order to elaborate statistical models aimed at forecasting the potential fruit production based on the amount of pollen released into the atmosphere.     

The reliability of geostatistic interpolation in olive field floral phenology

Floral phenology, as most of natural phenomena, shows, as an inherent feature, a high degree of spatial continuity. Geostatistics are a family of statistics that describe correlations through space/time and they can be used for both quantifying spatial correlation and interpolating no monitored sampling points. The combined use of Geographical Information Systems (GIS) and geostatistics can be an essential tool for spatial analysis in phenological and aerobiological studies. In the present work, Kriging interpolation by using linear geostatistic analysis has allow us to estimate phenological data of a wide olive crop area of the province of Cordoba (Andalusia, Southern Spain), on the basis of a limited number of␣phenology sampling points. The main a priori hypothesis was that 7 traditionally observed sampling points (with 10 olive trees in each site) uniformly distributed through the main olive crop areas could be enough for interpolating phenological information of the whole Cordoba olive area. Geostatistical results reject this hypothesis. The optimum/minimum number and location of sampling points was determined in 13 sites (including the original 7 sites and 6 new sites). The obtained phenological maps will improve␣olive pollen aerobiological information and forecasting in the area. The application of such new combined space analysis tools on floral phenology allows optimising human and economic resources on field phenology campaigns. Moreover, an appropriate use of GIS and geostatistic software to create phenological maps will be an essential complement in pollen aerobiological studies, given the increased interest in obtaining automatic aerobiological forecasting maps.     

A statistical approach to bioclimatic trend detection in the airborne pollen records of Catalonia (NE Spain)

Airborne pollen records are a suitable indicator for the study of climate change. The present work focuses on the role of annual pollen indices for the detection of bioclimatic trends through the analysis of the aerobiological spectra of 11 taxa of great biogeographical relevance in Catalonia over an 18-year period (1994–2011), by means of different parametric and non-parametric statistical methods. Among others, two non-parametric rank-based statistical tests were performed for detecting monotonic trends in time series data of the selected airborne pollen types and we have observed that they have similar power in detecting trends. Except for those cases in which the pollen data can be well-modeled by a normal distribution, it is better to apply non-parametric statistical methods to aerobiological studies. Our results provide a reliable representation of the pollen trends in the region and suggest that greater pollen quantities are being liberated to the atmosphere in the last years, specially by Mediterranean taxa such as Pinus, Total Quercus and Evergreen Quercus, although the trends may differ geographically. Longer aerobiological monitoring periods are required to corroborate these results and survey the increasing levels of certain pollen types that could exert an impact in terms of public health.     

Time series predictions with neural nets: Application to airborne pollen forecasting

Pollen allergy is a common disease causing rhinoconjunctivitis (hay fever) in 5–10% of the population. Medical studies have indicated that pollen related diseases could be highly reduced if future pollen contents in the air could be predicted. In this work we have developed a new forecasting method that applies the ability of neural nets to predict the future behaviour of chaotic systems in order to make accurate predictions of the airborne pollen concentration. The method requires that the neural net be fed with non-zero values, which restricts the method predictions to the period following the start of pollen flight. The operational method outlined here constitutes a different point of view with respect to the more generally used forecasts of time series analysis, which require input of many meteorological parameters. Excellent forecasts were obtained training a neural net by using only the time series pollen concentration values.     

Analysis of cedar pollen time series: no evidence of low-dimensional chaotic behavior

Much of the current interest in pollen time series analysis is motivated by the possibility that pollen series arise from low-dimensional chaotic systems. If this is the case, short-range prediction using nonlinear modeling is justified and would produce high-quality forecasts that could be useful in providing pollen alerts to allergy sufferers. To date, contradictory reports about the characterization of the dynamics of pollen series can be found in the literature. Pollen series have been alternatively described as featuring and not featuring deterministic chaotic behavior. We showed that the choice of test for detection of deterministic chaos in pollen series is difficult because pollen series exhibit power spectra. This is a characteristic that is also produced by colored noise series, which mimic deterministic chaos in most tests. We proposed to apply the Ikeguchi–Aihara test to properly detect the presence of deterministic chaos in pollen series. We examined the dynamics of cedar (Cryptomeria japonica) hourly pollen series by means of the Ikeguchi–Aihara test and concluded that these pollen series cannot be described as low-dimensional deterministic chaos. Therefore, the application of low-dimensional chaotic deterministic models to the prediction of short-range pollen concentration will not result in high-accuracy pollen forecasts even though these models may provide useful forecasts for certain applications. We believe that our conclusion can be generalized to pollen series from other wind-pollinated plant species, as wind speed, the forcing parameter of the pollen emission and transport, is best described as a nondeterministic series that originates in the high dimensionality of the atmosphere.     

Short-term prediction of Betula airborne pollen concentration in Vigo (NW Spain) using logistic additive models and partially linear models

Betula pollen is a common cause of pollinosis in localities in NW Spain and between 13% and 60% of individuals who are immunosensitive to pollen grains respond positively to its allergens. It is important in the case of all such people to be able to predict pollen concentrations in advance. We therefore undertook an aerobiological study in the city of Vigo (Pontevedra, Spain) from 1995 to 2001, using a Hirst active-impact pollen trap (VPPS 2000) situated in the city centre. Vigo presents a temperate maritime climate with a mean annual temperature of 14.9 °C and 1,412 mm annual total precipitation. This paper analyses two ways of quantifying the prediction of pollen concentration: first by means of a generalized additive regression model with the object of predicting whether the series of interest exceeds a certain threshold; second using a partially linear model to obtain specific prediction values for pollen grains. Both models use a self-explicative part and another formed by exogenous meteorological factors. The models were tested with data from 2001 (year in which the total precipitation registered was almost twice the climatological average overall during the flowering period), which were not used in formulating the models. A highly satisfactory classification and good forecasting results were achieved with the first and second approaches respectively. The estimated line taking into account temperature and a calm S–SW wind, corresponds to the real line recorded during 2001, which gives us an idea of the proposed models validity.     

Examining high magnitude grass pollen episodes at Worcester,United Kingdom,using back-trajectory analysis

Trajectory analysis is a valuable tool that has been used before in aerobiological studies, to investigate the movement of airborne pollen. This study has employed back-trajectories to examine the four highest grass pollen episodes at Worcester, during the 2001 grass pollen season. The results have shown that the highest grass pollen counts of the 2001 season were reached when air masses arrived from a westerly direction. Back-trajectory analysis has a limited value to forecasters because the method is retrospective and cannot be employed directly for forecasting. However, when used in conjunction with meteorological data this technique can be used to examine high magnitude events in order to identify conditions that lead to high pollen counts.     

Ambrosia elatior (L.) in Hungary (1989–1990)

Summary Weeds and among themAmbrosia are probably the most important vascular plants related to pollinosis in Hungary. Sampling was carried out in central (Budapest) and in southern (Paks, Szeged) Hungary. The results of two years (1989–1990) of aerobiological study onAmbrosia airborne pollen are reported. The highest percentage of airborne pollen was found in the mid-August to mid-September period, having a good correlation with clinical data on pollinosis. The implications of these results are considered in the context of forecasting and prevention of seasonal ragweed pollinosis.     

Airborne pollen patterns in Mar del Plata atmosphere (Argentina) and its relationship with meteorological conditions

This work is part of a series of aerobiological researches conducted in the city of Mar del Plata, Argentina. The annual, seasonal and daily features of the pollen cloud were analyzed over 2 years, together with the effects of the meteorological variables. Cupressaceae amounted to 75 and 54% of the annual total in each year, and it was analyzed separately due to its proven overrepresentation. Eighty-five pollen types were registered during the 2 years, bearing a similar annual pattern (more than 50% from August to November, December also being an important month). Arboreal pollen predominated between late winter and spring (61 and 49% of the annual total), while non-arboreal pollen did so from late spring to summer. The observed seasonality was significantly correlated with the monthly mean temperatures and associated with its effect on phenology. No significant differences along the day were detected between years and 50% of the daily total was recorded between 1000 and 1600 hours. The maximum concentration was registered at 1000 hours in spring and summer, but later in autumn and winter. Regarding the hourly scale, the significant correlation of total pollen with temperature and wind speed was positive, albeit negative with relative humidity. These effects are linked to airborne pollen release and transport. The role rainfall plays on airborne pollen is discussed. To interpret the results, it is important to consider the time scale at which the aerobiological phenomenon is analyzed.     

Airborne pollen concentration in Seville (Spain), 1993–1996. First results obtained with Hirst’s method

The data presented constitute the longest historical series of results obtained in Seville with a Hirst-type sampler, and are a further contribution to earlier aerobiological studies carried out in the city with a Cour trap. This work supplies an updated pollen calendar of the city, together with pollen counts and other aerobiological parameters for the 14 most important types in the 4-year period of sampling. These werePlatanus hispanica, Olea europaea, Quercus, Cupressaceae, Poaceae, Urticaceae, Moraceae, Chenopodiaceae/ Amaranthaceae,Plantago, Pinaceae,Rumex, Myrtaceae, Compositae, andCasuarina.     

Predictive models in aerobiology: data transformation

This paper attempts to evaluate the effect of mathematical transformations of pollen and meteorogical data used in aerobiological forecasting models. Stepwise multiple regression equations were developed in order to facilitate short term forecasts during the pre-peak period. The daily mean pollen data (x _i) expressed as number of pollen grains per cubic metre of air were used directly and transformed into different scales: log(x _i + 1), ln((x ₁1000/Σp) + 1) and √x _i, where Σp is the sum of the daily mean values throughout the season. Thirteen meteorological parameters and the variable time were used as forecasting variables. The most reliable forecasts were obtained with data transformed by ‘square root’ and with untransformed data. Based on the results obtained, we recommend that the data be transformed by means of the square root if they do not show a normal distribution and that non-linear statistics be used in this kind of study.     

Forecasting model of <Emphasis Type="Italic">Corylus</Emphasis>, <Emphasis Type="Italic">Alnus</Emphasis>, and <Emphasis Type="Italic">Betula</Emphasis> pollen concentration levels using spatiotemporal correlation properties of pollen count

The aim of the study was to create and evaluate models for predicting high levels of daily pollen concentration of Corylus, Alnus, and Betula using a spatiotemporal correlation of pollen count. For each taxon, a high pollen count level was established according to the first allergy symptoms during exposure. The dataset was divided into a training set and a test set, using a stratified random split. For each taxon and city, the model was built using a random forest method. Corylus models performed poorly. However, the study revealed the possibility of predicting with substantial accuracy the occurrence of days with high pollen concentrations of Alnus and Betula using past pollen count data from monitoring sites. These results can be used for building (1) simpler models, which require data only from aerobiological monitoring sites, and (2) combined meteorological and aerobiological models for predicting high levels of pollen concentration.     

Airborne-pollen map for Olea europaea L. in eastern Andalusia (Spain) using GIS: Estimation models

Estimations based upon geostatistics and mapping have enabled the construction of a spatial model to predict the presence of biological particles in a particular region. This methodological proposal has been tested in a case study, at a regional scale, of airborne Olea pollen, using the data acquired from␣various sampling stations that are designed for the aerobiological monitoring of pollen levels. These sampling stations have been set up in cities throughout the region of Andalusia (southern Spain) at sites with very different characteristics in terms of biogeography, bioclimate, topography and vegetation. Pollen counts were made daily at all sites during 2003 using a volumetric spore-trap. Data were comparatively analysed in classical diagrams and by means of spatial-temporal maps. Space-time models were constructed using three coordinates, x, y (the UTM coordinates of each sampling station) and z, (the aerobiological data compiled for a specific period). The aerobiological data were interpolated by applying the traditional geostatistical method of Kriging. The introduction of the variable “space” into the model allowed us to predict pollen levels in different areas throughout the region. The interpolation method was used to make weekly estimations of Olea pollen values in areas where there was no aerobiological sampling station. In addition, the maps generated present a two-dimensional vision of the study area, showing that bioclimatic diversity of this region promotes a step-wise flowering of Olea.     

Free orbicules of Cupressaceae detected in daily aerobiological samples by optical and confocal microscopy

Members of Cupressaceae and Taxaceae are known to release large amounts of highly allergenic pollen grains into the atmosphere, which are responsible for the onset of pollinosis in many countries throughout the world. In addition to pollen grains, their pollen sacs produce orbicules, which are submicron particles reported to carry allergens and which are potentially able to reach much further down the respiratory tract than pollen grains. Previous research has postulated the presence of orbicules in the atmosphere; however, direct observations have not yet been reported. The aim of this research was to provide the first direct evidence that Cupressaceae orbicules are released into the atmosphere by detecting them in daily aerobiological samples. We observed pollen sacs, pollen grains, and orbicules of nine species of Cupressaceae using scanning electron microscope (SEM). We then used a light and confocal microscope, to examine daily aerobiological samples. Under SEM, we measured the orbicule size (0.494–0.777 µm) and detected unknown nanometric particles (130–200 nm). Under the light microscope, aerobiological samples showed clusters of stained dots surrounding the pollen grains of Cupressaceae. Under the confocal microscope, the same clusters were resolved into submicron particles with the same autofluorescence as the pollen grains. These features enabled us to identify them as orbicules. We believe that our findings help to explain the onset of pollinosis and allergic asthma related to Cupressaceae pollen grains in many countries, even before pollen grains are actually detected or after they are no longer observed in aerobiological monitoring samples.     

New biomolecular tools for aerobiological monitoring: Identification of major allergenic Poaceae species through fast real‐time PCR

Grasses (Poaceae) are very common plants, which are widespread in all environments and urban areas. Despite their economical importance, they can represent a problem to humans due to their abundant production of allergenic pollen. Detailed information about the pollen season for these species is needed in order to plan adequate therapies and to warn allergic people about the risks they take in certain areas at certain moments. Moreover, precise identification of the causative species and their allergens is necessary when the patient is treated with allergen‐specific immunotherapy. The intrafamily morphological similarity of grass pollen grains makes it impossible to distinguish which particular species is present in the atmosphere at a given moment. This study aimed at developing new biomolecular tools to analyze aerobiological samples and identifying major allergenic Poaceae taxa at subfamily or species level, exploiting fast real‐time PCR. Protocols were tested for DNA extraction from pollen sampled with volumetric and gravimetric methods. A fragment of the matK plastidial gene was amplified and sequenced in Poaceae species known to have high allergological impact. Species‐ and subfamily‐specific primer–probe systems were designed and tested in fast real‐time PCRs to evaluate the presence of these taxa in aerobiological pollen samples. Species‐specific systems were obtained for four of five studied species. A primer–probe set was also proposed for the detection of Pooideae (a grass subfamily that includes also major cereal grains) in aerobiological samples, as this subfamily includes species carrying both grass allergens from groups 1 and 5. These, among the 11 groups in which grass pollen allergens are classified, are considered responsible for the most frequent and severe symptoms.     

Benford’s law applied to aerobiological data and its potential as a quality control tool

Benford’s phenomenological law gives the expected frequencies of the first significant digits of any given series of numbers. According to this law, the frequency of 1 is higher than that of 2; this in turn appears more often 3, and so on. Similarly, Benford’s law can also be applied to the first two significant digits (i.e., from 10 to 99), and so on. Here, we show that gross data sets of daily pollen counts from three aerobiological stations (located in European cities with different features regarding vegetation and climatology) fit Benford’s law for the first significant digits, but this is not always true for the data transformed by a correction factor used in aerobiological studies. That is to say, the biases introduced by rounding and lower and upper built-in limits in pollen counts are detected by Benford’s law analysis. The analysis of the first two significant digits from transformed data is better explained by a Power law than Benford’s law. We propose that Benford’s law could be used as a quality control tool for numerical aerobiological data sets.     

Contribution of upwind pollen sources to the characterization of Juniperus ashei phenology

Local and long-range components of Juniperus ashei pollen deposition were isolated to provide a more accurate record of local pollination activity in the Arbuckle Mountains of south central Oklahoma. An aerobiological sampler recorded airborne pollen concentrations and deposition at the sample site from mid-December 1998 to the end of January 1999. Grid-based weather data was used to model the movement, position, and elevation (air mass trajectories) across the region. While a normal concentration distribution is expected for a pollination event at a single site, "very high" concentrations (>1500 pollen grains per cubic meter) creating "peaks" in the deposition record were identified using bi-hourly sample analysis of the pollen registrations in the sampler. These occurrences happened over a 2 1/2 week period beginning January 11 and are coincident with the occurrence of southerly winds throughout the region. Modeled trajectories indicate that the air masses associated with those occurrences traveled at ground level through the J. ashei population on the Edwards Plateau, some 200 kilometers to the south in Texas, then gained altitude prior to crossing the sample site, thus introducing a long-range pollen component at the sample site. Peaks with "high" concentrations (90 to 1500 pollen grains per cubic meter) were evaluated using the same methodology. Those peaks associated with trajectories having the potential of introducing a long-range component to the pollen deposition record were removed from the aerobiological record. The resulting adjusted aerobiological record shows a more normal pollen concentration distribution, reduced hourly variability, and a marked shift in the pollination initiation date. Based on the comparison of non-adjusted and adjusted aerobiological records, contributions from upwind pollen sources account for 55% of the total pollen record.     

A numerical model of birch pollen emission and dispersion in the atmosphere. Description of the emission module

A birch pollen emission model is described and its main features are discussed. The development of the model is based on a double-threshold temperature sum model that describes the propagation of the flowering season and naturally links to the thermal time models to predict the onset and duration of flowering. For the flowering season, the emission model considers ambient humidity and precipitation rate, both of which suppress the pollen release, as well as wind speed and turbulence intensity, which promote it. These dependencies are qualitatively evaluated using the aerobiological observations. Reflecting the probabilistic character of the flowering of an individual tree in a population, the model introduces relaxation functions at the start and end of the season. The physical basis of the suggested birch pollen emission model is compared with another comprehensive emission module reported in literature. The emission model has been implemented in the SILAM dispersion modelling system, the results of which are evaluated in a companion paper.