A maximum entropy approach to disturbed ecosystems

The current climate crisis requires a comprehensive understanding of biodiversity to acknowledge how ecosystems’ responses to anthropogenic disturbances may result in feedback that can either mitigate or exacerbate global warming. Although ecosystems are dynamic and macroecological patterns change drastically in response to disturbance, dynamic macroecology has received insufficient attention and theoretical formalisation. In this context, the maximum entropy principle (MaxEnt) could provide an effective inference procedure to study ecosystems. Since the improper usage of entropy outside its scope often leads to misconceptions, the opening chapter will clarify its meaning by following its evolution from classical thermodynamics to information theory. The second chapter introduces the study of ecosystems from a physicist’s viewpoint. In particular, the MaxEnt Theory of Ecology (METE) will be the cornerstone of the discussion. METE predicts the shapes of macroecological metrics in relatively static ecosystems using constraints imposed by static state variables. However, in disturbed ecosystems with macroscale state variables that change rapidly over time, its predictions tend to fail. In the final chapter, DynaMETE is therefore presented as an extension of METE from static to dynamic. By predicting how macroecological patterns are likely to change in response to perturbations, DynaMETE can contribute to a better understanding of disturbed ecosystems’ fate and the improvement of conservation and management of carbon sinks, like forests. Targeted strategies in ecosystem management are now indispensable to enhance the interdependence of human well-being and the health of ecosystems, thus avoiding climate change tipping points.

Predicting the distribution of forest tree species using topographic variables and vegetation index in eastern Acre, Brazil

Species distribution modeling has relevant implications for the studies of biodiversity, decision making about conservation and knowledge about ecological requirements of the species. The aim of this study was to evaluate if the use of forest inventories can improve the estimation of occurrence probability, identify the limits of the potential distribution and habitat preference of a group of timber tree species. The environmental predictor variables were: elevation, slope, aspect, normalized difference vegetation index (NDVI) and height above the nearest drainage (HAND). To estimate the distribution of species we used the maximum entropy method (Maxent). In comparison with a random distribution, using topographic variables and vegetation index as features, the Maxent method predicted with an average accuracy of 86% the geographical distribution of studied species. The altitude and NDVI were the most important variables. There were limitations to the interpolation of the models for non-sampled locations and that are outside of the elevation gradient associated with the occurrence data in approximately 7% of the basin area. Ceiba pentandra (samaúma), Castilla ulei (caucho) and Hura crepitans (assacu) is more likely to occur in nearby water course areas. Clarisia racemosa (guariúba), Amburana acreana (cerejeira), Aspidosperma macrocarpon (pereiro), Apuleia leiocarpa (cumaru cetim), Aspidosperma parvifolium (amarelão) and Astronium lecointei (aroeira) can also occur in upland forest and well drained soils. This modeling approach has potential for application on other tropical species still less studied, especially those that are under pressure from logging.

Climatic factors influencing triatomine occurrence in Central-West Brazil

We estimated the geographic distributions of triatomine species in Central-West Region of Brazil (CW) and analysed the climatic factors influencing their occurrence. A total of 3,396 records of 27 triatomine species were analysed. Using the maximum entropy method, ecological niche models were produced for eight species occurring in at least 20 municipalities based on 13 climatic variables and elevation. Triatoma sordida and Rhodnius neglectus were the species with the broadest geographic distributions in CW Brazil. The Cerrado areas in the state of Goiás were found to be more suitable for the occurrence of synanthropic triatomines than the Amazon forest areas in the northern part of the state of Mato Grosso. The variable that best explains the evaluated models is temperature seasonality. The results indicate that almost the entire region presents climatic conditions that are appropriate for at least one triatomine species. Therefore, it is recommended that entomological surveillance be reinforced in CW Brazil.

Development of phase retrieval algorithm and techniques for optical spectrum analysis

Coherent anti-Stokes Raman scattering is the powerful method of laser spectroscopy in which significant successes are achieved. However, the non-linear nature of CARS complicates the analysis of the received spectra. The objective of this Thesis is to develop a new phase retrieval algorithm for CARS. It utilizes the maximum entropy method and the new wavelet approach for spectroscopic background correction of a phase function. The method was developed to be easily automated and used on a large number of spectra of different substances.. The algorithm was successfully tested on experimental data.

Multifrequency VLBI Observations of Selected Active Galactic Nuclei

In this dissertation, active galactic nuclei (AGN) are discussed, as they are seen with the high-resolution radio-astronomical technique called Very Long Baseline Interferometry (VLBI). This observational technique provides very high angular resolution (_ 10−300 = 1 milliarcsecond). VLBI observations, performed at different radio frequencies (multi-frequency VLBI), allow to penetrate deep into the core of an AGN to reveal an otherwise obscured inner part of the jet and the vicinity of the AGN’s central engine. Multi-frequency VLBI data are used to scrutinize the structure and evolution of the jet, as well as the distribution of the polarized emission. These data can help to derive the properties of the plasma and the magnetic field, and to provide constraints to the jet composition and the parameters of emission mechanisms. Also VLBI data can be used for testing the possible physical processes in the jet by comparing observational results with results of numerical simulations. The work presented in this thesis contributes to different aspects of AGN physics studies, as well as to the methodology of VLBI data reduction. In particular, Paper I reports evidence of optical and radio emission of AGN coming from the same region in the inner jet. This result was obtained via simultaneous observations of linear polarization in the optical and in radio using VLBI technique of a sample of AGN. Papers II and III describe, in detail, the jet kinematics of the blazar 0716+714, based on multi-frequency data, and reveal a peculiar kinematic pattern: plasma in the inner jet appears to move substantially faster that that in the large-scale jet. This peculiarity is explained by the jet bending, in Paper III. Also, Paper III presents a test of the new imaging technique for VLBI data, the Generalized Maximum Entropy Method (GMEM), with the observed (not simulated) data and compares its results with the conventional imaging. Papers IV and V report the results of observations of the circularly polarized (CP) emission in AGN at small spatial scales. In particular, Paper IV presents values of the core CP for 41 AGN at 15, 22 and 43 GHz, obtained with the help of the standard Gain transfer (GT) method, which was previously developed by D. Homan and J.Wardle for the calibration of multi-source VLBI observations. This method was developed for long multi-source observations, when many AGN are observed in a single VLBI run. In contrast, in Paper V, an attempt is made to apply the GT method to single-source VLBI observations. In such observations, the object list would include only a few sources: a target source and two or three calibrators, and it lasts much shorter than the multi-source experiment. For the CP calibration of a single-source observation, it is necessary to have a source with zero or known CP as one of the calibrators. If the archival observations included such a source to the list of calibrators, the GT could also be used for the archival data, increasing a list of known AGN with the CP at small spatial scale. Paper V contains also calculation of contributions of different sourced of errors to the uncertainty of the final result, and presents the first results for the blazar 0716+714.

Linear prediction in optical spectroscopy

A linear prediction procedure is one of the approved numerical methods of signal processing. In the field of optical spectroscopy it is used mainly for extrapolation known parts of an optical signal in order to obtain a longer one or deduce missing signal samples. The first is needed particularly when narrowing spectral lines for the purpose of spectral information extraction. In the present paper the coherent anti-Stokes Raman scattering (CARS) spectra were under investigation. The spectra were significantly distorted by the presence of nonlinear nonresonant background. In addition, line shapes were far from Gaussian/Lorentz profiles. To overcome these disadvantages the maximum entropy method (MEM) for phase spectrum retrieval was used. The obtained broad MEM spectra were further underwent the linear prediction analysis in order to be narrowed.

Análises estrutural, nanoestrutural, e quantitativa de fases em materiais cerâmicos de interesse tecnológico, utilizando difração de raios X pelo método do pó

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Environmental suitability of a highly fragmented and heterogeneous landscape for forest bird species in south-eastern Brazil

Assessment of the suitability of anthropogenic landscapes for wildlife species is crucial for setting priorities for biodiversity conservation. This study aimed to analyse the environmental suitability of a highly fragmented region of the Brazilian Atlantic Forest, one of the world's 25 recognized biodiversity hotspots, for forest bird species. Eight forest bird species were selected for the analyses, based on point counts (n = 122) conducted in April-September 2006 and January-March 2009. Six additional variables (landscape diversity, distance from forest and streams, aspect, elevation and slope) were modelled in Maxent for (1) actual and (2) simulated land cover, based on the forest expansion required by existing Brazilian forest legislation. Models were evaluated by bootstrap or jackknife methods and their performance was assessed by AUC, omission error, binomial probability or p value. All predictive models were statistically significant, with high AUC values and low omission errors. A small proportion of the actual landscape (24.41 +/- 6.31%) was suitable for forest bird species. The simulated landscapes lead to an increase of c. 30% in total suitable areas. In average, models predicted a small increase (23.69 +/- 6.95%) in the area of suitable native forest for bird species. Being close to forest increased the environmental suitability of landscapes for all bird species; landscape diversity was also a significant factor for some species. In conclusion, this study demonstrates that species distribution modelling (SDM) successfully predicted bird distribution across a heterogeneous landscape at fine spatial resolution, as all models were biologically relevant and statistically significant. The use of landscape variables as predictors contributed significantly to the results, particularly for species distributions over small extents and at fine scales. This is the first study to evaluate the environmental suitability of the remaining Brazilian Atlantic Forest for bird species in an agricultural landscape, and provides important additional data for regional environmental planning.

Bayesian Approach to Spectral Function Reconstruction for Euclidean Quantum Field Theories

We present a novel approach to the inference of spectral functions from Euclidean time correlator data that makes close contact with modern Bayesian concepts. Our method differs significantly from the maximum entropy method (MEM). A new set of axioms is postulated for the prior probability, leading to an improved expression, which is devoid of the asymptotically flat directions present in the Shanon-Jaynes entropy. Hyperparameters are integrated out explicitly, liberating us from the Gaussian approximations underlying the evidence approach of the maximum entropy method. We present a realistic test of our method in the context of the nonperturbative extraction of the heavy quark potential. Based on hard-thermal-loop correlator mock data, we establish firm requirements in the number of data points and their accuracy for a successful extraction of the potential from lattice QCD. Finally we reinvestigate quenched lattice QCD correlators from a previous study and provide an improved potential estimation at T2.33TC.

Hard thermal loop benchmark for the extraction of the nonperturbative QQ[over ¯] potential

The extraction of the finite temperature heavy quark potential from lattice QCD relies on a spectral analysis of the Wilson loop. General arguments tell us that the lowest lying spectral peak encodes, through its position and shape, the real and imaginary parts of this complex potential. Here we benchmark this extraction strategy using leading order hard-thermal loop (HTL) calculations. In other words, we analytically calculate the Wilson loop and determine the corresponding spectrum. By fitting its lowest lying peak we obtain the real and imaginary parts and confirm that the knowledge of the lowest peak alone is sufficient for obtaining the potential. Access to the full spectrum allows an investigation of spectral features that do not contribute to the potential but can pose a challenge to numerical attempts of an analytic continuation from imaginary time data. Differences in these contributions between the Wilson loop and gauge fixed Wilson line correlators are discussed. To better understand the difficulties in a numerical extraction we deploy the maximum entropy method with extended search space to HTL correlators in Euclidean time and observe how well the known spectral function and values for the real and imaginary parts are reproduced. Possible venues for improvement of the extraction strategy are discussed.

A new Bayesian approach to the reconstruction of spectral functions

We present a novel approach for the reconstruction of spectra from Euclidean correlator data that makes close contact to modern Bayesian concepts. It is based upon an axiomatically justified dimensionless prior distribution, which in the case of constant prior function m(ω) only imprints smoothness on the reconstructed spectrum. In addition we are able to analytically integrate out the only relevant overall hyper-parameter α in the prior, removing the necessity for Gaussian approximations found e.g. in the Maximum Entropy Method. Using a quasi-Newton minimizer and high-precision arithmetic, we are then able to find the unique global extremum of P[ρ|D] in the full Nω » Nτ dimensional search space. The method actually yields gradually improving reconstruction results if the quality of the supplied input data increases, without introducing artificial peak structures, often encountered in the MEM. To support these statements we present mock data analyses for the case of zero width delta peaks and more realistic scenarios, based on the perturbative Euclidean Wilson Loop as well as the Wilson Line correlator in Coulomb gauge.

Three species distribution models for the marine diatom Fragilariopsis kerguelensis of the Southern Ocean, links to NetCDF files

Fragilariopsis kerguelensis, a dominant diatom species throughout the Antarctic Circumpolar Current, is coined to be one of the main drivers of the biological silicate pump. Here, we study the distribution of this important species and expected consequences of climate change upon it, using correlative species distribution modeling and publicly available presence-only data. As experience with SDM is scarce for marine phytoplankton, this also serves as a pilot study for this organism group. We used the maximum entropy method to calculate distribution models for the diatom F. kerguelensis based on yearly and monthly environmental data (sea surface temperature, salinity, nitrate and silicate concentrations). Observation data were harvested from GBIF and the Global Diatom Database, and for further analyses also from the Hustedt Diatom Collection (BRM). The models were projected on current yearly and seasonal environmental data to study current distribution and its seasonality. Furthermore, we projected the seasonal model on future environmental data obtained from climate models for the year 2100. Projected on current yearly averaged environmental data, all models showed similar distribution patterns for F. kerguelensis. The monthly model showed seasonality, for example, a shift of the southern distribution boundary toward the north in the winter. Projections on future scenarios resulted in a moderately to negligibly shrinking distribution area and a change in seasonality. We found a substantial bias in the publicly available observation datasets, which could be reduced by additional observation records we obtained from the Hustedt Diatom Collection. Present-day distribution patterns inferred from the models coincided well with background knowledge and previous reports about F. kerguelensis distribution, showing that maximum entropy-based distribution models are suitable to map distribution patterns for oceanic planktonic organisms. Our scenario projections indicate moderate effects of climate change upon the biogeography of F. kerguelensis.

Caracterización de señales sísmicas del Volcán Cotopaxi utilizando estimadores espectrales clásicos y de máxima entropía

Se presenta un estudio de detección y caracterización de eventos sísmicos del tipo volcano tectónicos y largo periodo de registros sísmicos generados por el volcán Cotopaxi. La estructura secuencial de detección propuesta permite en un registro sísmico maximizar la probabilidad de presencia de un evento y minimizar la ausencia de este. La detección se la realiza en el dominio del tiempo en cuasi tiempo real manteniendo una tasa constante de falsa alarma para posteriormente realizar un estudio del contenido espectral de los eventos mediante el uso de estimadores espectrales clásicos como el periodograma y paramétricos como el método de máxima entropía de Burg, logrando así, categorizar a los eventos detectados como volcano tectónicos, largo periodo y otros cuando no poseen características pertenecientes a los otros dos tipos como son los rayos.

Active Learning of Very-High Resolution Optical Imagery with SVM: Entropy vs Margin Sampling

An active learning method is proposed for the semi-automatic selection of training sets in remote sensing image classification. The method adds iteratively to the current training set the unlabeled pixels for which the prediction of an ensemble of classifiers based on bagged training sets show maximum entropy. This way, the algorithm selects the pixels that are the most uncertain and that will improve the model if added in the training set. The user is asked to label such pixels at each iteration. Experiments using support vector machines (SVM) on an 8 classes QuickBird image show the excellent performances of the methods, that equals accuracies of both a model trained with ten times more pixels and a model whose training set has been built using a state-of-the-art SVM specific active learning method

Analysis of System Signals Based on Cross Recurrence Method for System Dynamics Characterization

Natural systems are inherently non linear. Recurrent behaviours are typical of natural systems. Recurrence is a fundamental property of non linear dynamical systems which can be exploited to characterize the system behaviour effectively. Cross recurrence based analysis of sensor signals from non linear dynamical system is presented in this thesis. The mutual dependency among relatively independent components of a system is referred as coupling. The analysis is done for a mechanically coupled system specifically designed for conducting experiment. Further, cross recurrence method is extended to the actual machining process in a lathe to characterize the chatter during turning. The result is verified by permutation entropy method. Conventional linear methods or models are incapable of capturing the critical and strange behaviours associated with the dynamical process. Hence any effective feature extraction methodologies should invariably gather information thorough nonlinear time series analysis. The sensor signals from the dynamical system normally contain noise and non stationarity. In an effort to get over these two issues to the maximum possible extent, this work adopts the cross recurrence quantification analysis (CRQA) methodology since it is found to be robust against noise and stationarity in the signals. The study reveals that the CRQA is capable of characterizing even weak coupling among system signals. It also divulges the dependence of certain CRQA variables like percent determinism, percent recurrence and entropy to chatter unambiguously. The surrogate data test shows that the results obtained by CRQA are the true properties of the temporal evolution of the dynamics and contain a degree of deterministic structure. The results are verified using permutation entropy (PE) to detect the onset of chatter from the time series. The present study ascertains that this CRP based methodology is capable of recognizing the transition from regular cutting to the chatter cutting irrespective of the machining parameters or work piece material. The results establish this methodology to be feasible for detection of chatter in metal cutting operation in a lathe.