Fisher–Shannon Research Articles

3D Information-Theoretic Analysis of the Simplest Hydrogen Abstraction Reaction.

We investigate the course of an elementary chemical reaction from the perspective of information theory in 3D space through the hypersurface of several information-theoretic (IT) functionals such as disequilibrium (D), Shannon entropy (S), Fisher information (I), and the complexity measures of Fisher-Shannon (FS) and López-Mancini-Calbet (LMC). The probe for the study is the hydrogenic identity abstraction reaction. In order to perform the analysis, the reactivity pattern of the reaction is examined by use of the aforementioned functionals of the single-particle density, which is analyzed in position (r) and momentum (p) spaces. The 3D analyses revealed interesting reactivity patterns in the neighborhood of the intrinsic reaction coordinate (IRC) path, which allow to interpret the reaction mechanism for this reaction in a novel manner. In addition, the chemically interesting regions that have been characterized through the information functionals and their complexity measures are depicted and analyzed in the framework of the three-dimensional structure of the information-theoretical data of a chemical reaction, that is, the reactant/product (R/P) complexes, the transition state (TS), and the ones that are only revealed through IT measures such as the bond-cleavage energy region (BCER), the bond-breaking/forming (B-B/F) region, and the spin-coupling (SC) process. Furthermore, focus has been placed on the diagonal part of the hypersurface of the IT functionals, aside from the IRC path itself, with the purpose of analyzing the dissociation process of the triatomic transition-state complex that has revealed other interesting features of the bond-breaking (B-B) process. In other respects, it is shown throughout the combined analyses of the 3D structure of the IT functionals in conjugated spaces that the chemically significant regions occurring at the onset of the TS are completely characterized by information-theoretic aspects of localizability (S), uniformity (D), and disorder. Further, novel regions of low complexity seem to indicate new boundaries for chemically stable complex molecules. Finally, the study reveals that the chemical reaction occurs at low-complexity regions, where the concurrent phenomena take place: bond-breaking/forming (B-B/F), bond-cleavage energy reservoirs (BCER), spin-coupling (SC), and transition state (TS).

Informational analysis of MODIS NDVI and EVI time series of sites affected and unaffected by wildfires

Vegetation dynamic processes influenced by fires has represented a scientific topic of great importance because of the environmental impact of fires. The use of satellites to investigate vegetational trends has become quite common for the wide coverage and high spatial resolution of satellite images. In this paper, we study the temporal variability of MODIS Aqua and Terra Normalized Difference Vegetation Index (NDVI) and Enhanced Vegetation Index (EVI) data acquired from 2000 to 2020 and covering the area burned by Camp Fire (California) in 2018. In 2008 other two fires, the BTU Lightning Complex Fire and the Humboldt Fire burned a large part of the same area. The objective of our study, thus, is the characterization of the time dynamics of MODIS Aqua and Terra NDVI and EVI series of sites affected by one and two wildfires by using the Fisher–Shannon (FS) method that allows to have information about the organization/disorder of the time series in relationship with the vegetation post-fire recovery process. Our results suggest that multiple fires cause a decrease of organization and order of NDVI and EVI, indicating a loss a regularity of their time variation.

Analysis of Multifractal and Organization/Order Structure in Suomi-NPP VIIRS Normalized Difference Vegetation Index Series of Wildfire Affected and Unaffected Sites by Using the Multifractal Detrended Fluctuation Analysis and the Fisher-Shannon Analysis.

The analysis of vegetation dynamics affected by wildfires contributes to the understanding of ecological changes under disturbances. The use of the Normalized Difference Vegetation Index (NDVI) of satellite time series can effectively contribute to this investigation. In this paper, we employed the methods of multifractal detrended fluctuation analysis (MFDFA) and Fisher–Shannon (FS) analysis to investigate the NDVI series acquired from the Visible Infrared Imaging Radiometer Suite (VIIRS) of the Suomi National Polar-Orbiting Partnership (Suomi-NPP). Four study sites that were covered by two different types of vegetation were analyzed, among them two sites were affected by a wildfire (the Camp Fire, 2018). Our findings reveal that the wildfire increases the heterogeneity of the NDVI time series along with their organization structure. Furthermore, the fire-affected and fire-unaffected pixels are quite well separated through the range of the generalized Hurst exponents and the FS information plane. The analysis could provide deeper insights on the temporal dynamics of vegetation that are induced by wildfire.

Complexity analysis of two families of orthogonal functions

AbstractWe study the shape LMC (López‐Ruiz, Mancini and Calvet), Fisher‐Shannon (FS) and Cramér‐Rao (CR) complexities of two families of orthogonal functions associated with the solutions of isospectral deformations of the Pöschl‐Teller and Harmonic oscillator potentials. We have compared the behavior of these complexities for the orthogonal functions with the complexities associated with Pöschl‐Teller and Harmonic oscillator potentials whose solutions are given in terms of the classical orthogonal polynomials. All these complexities are discussed in terms of the quantum number n and isospectrality parameter λ.

Fisher-Shannon Complexity Analysis of High-Frequency Urban Wind Speed Time Series.

One-hertz wind time series recorded at different levels (from 1.5–25.5 m) in an urban area are investigated by using the Fisher–Shannon (FS) analysis. FS analysis is a well-known method to gain insight into the complex behavior of nonlinear systems, by quantifying the order/disorder properties of time series. Our findings reveal that the FS complexity, defined as the product between the Fisher information measure and the Shannon entropy power, decreases with the height of the anemometer from the ground, suggesting a height-dependent variability in the order/disorder features of the high-frequency wind speed measured in urban layouts. Furthermore, the correlation between the FS complexity of wind speed and the daily variance of the ambient temperature shows a similar decrease with the height of the wind sensor. Such correlation is larger for the lower anemometers, indicating that ambient temperature is an important forcing of the wind speed variability in the vicinity of the ground.

Fisher–Shannon and detrended fluctuation analysis of MODIS normalized difference vegetation index (NDVI) time series of fire-affected and fire-unaffected pixels

ABSTRACTMODIS-NDVI data from 2002 to 2014 were analysed to evaluate the effect of fire on vegetation in a test site located in Daxing'anling region (Inner Mongolia and Heilongjiang Province). Fire-affected and fire-unaffected areas were processed using two statistical approaches: detrended fluctuation analysis (DFA) and Fisher–Shannon (FS) method. The DFA allows the detection of scaling behaviour in nonstationary signals, whereas the FS method permits to identify the organization/order structure in complex signals. Our findings show that the results obtained by jointly using the two methods are consistent, enabling the characterization and discrimination between the fire-affected and fire-unaffected areas. In particular, among the investigated indices, the mean value of Fisher information measure (FIM) represents the most significant in discriminating between burned and unburned sites; its mean value for burned sites is about 2.5 that is significantly larger than that obtained for unburned sites (∼1.3). FIM is also characterized by the larger effectiveness in discriminating the two classes of sites on the base of its receiver operating characteristic based performance. The scaling exponents estimated by means of the DFA of the fire-affected pixels are averagely higher than those of the fire-unaffected ones, which, furthermore, are characterized by lower organization and higher disorder degree. Both of the two methods would contribute to identify the impact of fires on vegetation.

Fisher–Shannon analysis of the time variability of remotely sensed sea surface temperature at the Brazil–Malvinas Confluence

Summary The collision of the warm and salty southward flowing Brazil Current and the cold and relatively fresh northward flowing Malvinas Current produces a strong frontal zone known as the Brazil–Malvinas Confluence Zone (BMCZ). This is featured by intense presence of eddies and meanders and is one of the most energetic areas of the world oceans. We apply the statistical method of Fisher–Shannon (FS) to the time series of sea surface temperature, derived from the satellite Advanced Very High Resolution Radiometer (AVHRR) imagery, acquired from 1984 to 1999. The FS method consists of the joint application of Fisher information measure (FIM) and Shannon entropy (SE), measuring respectively the degree of organization and the disorder of a system. Our findings indicate that the FS method is able to locate very clearly the BMCZ, which corresponds to the less organized and more disordered area within the area of confluence between the Brazil and Malvinas Currents.

Discriminating Between Different Streamflow Regimes by Using the Fisher-Shan Method: An Application to the Colombia Rivers

The Fisher-Shannon (FS) information plane, defined by the Fisher information measure (FIM) and the Shannon entropy power (NX), was robustly used to investigate the complex dynamics of eight monthly streamflow time series in Colombia. In the FS plane the streamflow series seem to aggregate into two different clusters corresponding to two different climatological regimes in Colombia. Our findings suggest the use of the statistical quantity defined by the FS information plane as a tool to discriminate among different hydrological regimes.

Fisher–Shannon information plane analysis of SPOT/VEGETATION Normalized Difference Vegetation Index (NDVI) time series to characterize vegetation recovery after fire disturbance

The time dynamics of SPOT-VEGETATION Normalized Difference Vegetation Index (NDVI) time series are analyzed by using the statistical approach of the Fisher–Shannon (FS) information plane to assess and monitor vegetation recovery after fire disturbance. Fisher–Shannon information plane analysis allows us to gain insight into the complex structure of a time series to quantify its degree of organization and order. The analysis was carried out using 10-day Maximum Value Composites of NDVI (MVC-NDVI) with a 1km×1km spatial resolution. The investigation was performed on two test sites located in Galizia (North Spain) and Peloponnese (South Greece), selected for the vast fires which occurred during the summer of 2006 and 2007 and for their different vegetation covers made up mainly of low shrubland in Galizia test site and evergreen forest in Peloponnese. Time series of MVC-NDVI have been analyzed before and after the occurrence of the fire events. Results obtained for both the investigated areas clearly pointed out that the dynamics of the pixel time series before the occurrence of the fire is characterized by a larger degree of disorder and uncertainty; while the pixel time series after the occurrence of the fire are featured by a higher degree of organization and order. In particular, regarding the Peloponneso fire, such discrimination is more evident than in the Galizia fire. This suggests a clear possibility to discriminate the different post-fire behaviors and dynamics exhibited by the different vegetation covers.

Singular spectrum analysis and Fisher–Shannon analysis of spring flow time series: An application to Anjar Spring, Lebanon

In this study, the time dynamics of water flow from Anjar Spring was investigated, which is one of the major issuing springs in the central part of Lebanon. Likewise, many water sources in Lebanon, this spring has no continuous records for the discharge, and this would prevent the application of standard time series analysis tools. Furthermore, the highly nonstationary character of the series implies that suited methodologies can be employed to get insight into its dynamical features. Therefore, the Singular Spectrum Analysis (SSA) and Fisher–Shannon (FS) method, which are useful methods to disclose dynamical features in noisy nonstationary time series with gaps, are jointly applied to analyze the Anjar Spring water flow series. The SSA revealed that the series can be considered as the superposition of meteo-climatic periodic components, low-frequency trend and noise-like high-frequency fluctuations. The FS method allowed to extract and to identify among all the SSA reconstructed components the long-term trend of the series. The long-term trend is characterized by higher Fisher Information Measure (FIM) and lower Shannon entropy, and thus, represents the main informative component of the whole series. Generally water discharge time series presents very complex time structure, therefore the joint application of the SSA and the FS method would be very useful in disclosing the main informative part of such kind of data series in the view of existing climatic variability and/or anthropogenic challenges.

Investigating the time dynamics of monthly rainfall time series observed in northern Lebanon by means of the detrended fluctuation analysis and the Fisher-Shannon method

We investigate the time dynamics of monthly rainfall series intermittently recorded on seven climatic stations in northern Lebanon from 1939 to 2010 using the detrending fluctuation analysis (DFA) and the Fisher-Shannon (FS) method. The DFA is employed to study the scaling properties of the series, while the FS method to analyze their order/organization structure. The obtained results indicate that most all the stations show a significant persistent behavior, suggesting that the dynamics of the rainfall series is governed by positive feedback mechanisms. Furthermore, we found that the Fisher Information Measure (the Shannon entropy power) seems to decrease (increase) with the height of the rain gauge; this indicates that the rainfall series appear less organized and less regular for higher-located stations. Such findings could be useful for a better comprehension of the climatic regimes governing northern Lebanon.

Power spectrum and Fisher–Shannon information plane analysis of tidal records

The time dynamics of tidal fluctuations measured in three sites in Bahia Blanca Estuary (central Argentina), Ingeniero White, Puerto Belgrano and Torre Mareografica, are analyzed. To investigate the time series of the tidal waves we used two different approaches: the power spectral density (PSD) and the Fisher–Shannon (FS) information plane. The PSD permitted: (i) the identification of diurnal, semi-diurnal and higher frequency cycles in all the three tidal signals, and (ii) the detection of two different dynamical regimes (scaling and white-noise), involving respectively timescales lower and higher than about 2–2.5 days. The FS method, which allows to gain insight into the complex structure of a time series, quantifying its degree of organization and order, was applied to the residual tidal series (after removing the main cycles) and permitted to identify a period of low organization in the tidal signal measured at Puerto Belgrano.

Information-theoretical complexity for the hydrogenic identity S N 2 exchange reaction

We investigate the complexity of the hydrogenic identity S N 2 exchange reaction by means of information-theoretic functionals such as disequilibrium (D), exponential entropy (L), Fisher information (I), power entropy (J) and joint information-theoretic measures, i.e., the I–D, D–L and I–J planes and the Fisher–Shannon (FS) and Lopez-Mancini-Calbet (LMC) shape complexities. The several information-theoretic measures of the one-particle density were computed in position (r) and momentum (p) spaces. The analysis revealed that the chemically significant regions of this reaction can be identified through most of the information-theoretic functionals or planes, not only the ones which are commonly revealed by the energy, such as the reactant/product (R/P) and the transition state (TS), but also those that are not present in the energy profile such as the bond cleavage energy region (BCER), the bond breaking/forming regions (B–B/F) and the charge transfer process (CT). The analysis of the complexities shows that the energy profile of the identity S N 2 exchange reaction bears no simple behavior with respect to the LMC and FS measures. Most of the chemical features of interest (BCER, B–B/F and CT) are only revealed when particular information-theoretic aspects of localizability (L or J), uniformity (D) and disorder (I) are considered.

Discriminating climatological regimes in rainfall time series by using the Fisher-Shannon method

The Fisher-Shannon (FS) information plane, defined by the Fisher information measure (FIM) and the Shannon entropy power (Nx), was robustly used to investigate the complex dynamics of 8 long monthly rainfall time series in central Argentina, recorded from 1860 to 2006. In the FS plane, the rainfall series seem to aggregate into three different clusters corresponding to three different climatological regimes in central Argentina. Our findings suggest the use of the statistical quantity defined by the FS information plane as a tool to discriminate among different climatological regimes. Key words: Rain, Fisher information measure, Shannon entropy.

Analysis of the time dynamics in wind records by means of multifractal detrendedfluctuation analysis and the Fisher–Shannon information plane

The time structure of more than 10 years of hourly wind data measured at one site innorthern Italy from April 1996 to December 2007 is analysed. The data wererecorded by the Sodar Rass system, which measures the speed and the directionof the wind at several heights above the ground level. To investigate the windspeed time series at seven heights above the ground level we used two differentapproaches: (i) multifractal detrended fluctuation analysis (MF-DFA), which permits thedetection of multifractality in nonstationary series, and (ii) the Fisher–Shannon(FS) information plane, which allows the discrimination of dynamical featuresin complex time series. Our results point to the existence of multifractal timefluctuations in wind speed and to a dependence of the results on the height of thewind sensor. Even in the FS information plane a height-dependent pattern isrevealed, indicating a good agreement with the multifractality. The obtained resultscould contribute to a better understanding of the complex dynamics of windphenomena.

Atomic complexity measures in position and momentum spaces

Fisher-Shannon (FS) and Lopez-Ruiz, Mancini, and Calbet (LMC) complexity measures, detecting not only randomness but also structure, are computed by using near Hartree-Fock wave functions for neutral atoms with nuclear charge Z=1-103 in position, momentum, and product spaces. It is shown that FS and LMC complexities are qualitatively and numerically equivalent for these systems. New complexity candidates are defined, computed, and compared by using the following information-theoretic magnitudes: Shannon entropy, Fisher information, disequilibrium, and variance. Localization-delocalization planes are constructed for each complexity measure, where the subshell pattern of the periodic table is clearly shown. The complementary use of r and p spaces provides a compact and more complete understanding of the information content of these planes.