Single Data Point Research Articles

SPoFC: A framework for stream data aggregation with local differential privacy

AbstractCollecting and analysing customers' data plays an essential role in the more intense market competition. It is critical to perform data analysis effectively while ensuring the user's privacy, especially after various privacy regulations are enacted. In this paper, we consider the problem of aggregating the stream data generated from wearable devices in a specific time period in a privacy‐preserving manner. Specifically, we adopt the local differential privacy mechanism to provide a strong privacy guarantee for users. One major challenge is that all values of the stream need to be perturbed. The additive noise makes it hard to release an accurate data stream. One way to reduce the noise scale is to select some data points to perturb instead of all. The intuition is that more privacy budgets are applied to a single data point, which ensures the statistical accuracy. The perturbed data points are used to predict the un‐selected data points without consuming an extra privacy budget. Based on this idea, we propose a novel stream data statistical framework, which includes four components, data fitting, skeleton point selection, noisy stream generation, and data aggregation. Extensive experiment results show that our proposed method achieves a much smaller mean square error given a fixed privacy budget compared with the state‐of‐the‐art.

The Emptiness Inside: Finding Gaps, Valleys, and Lacunae with Geometric Data Analysis

Discoveries of gaps in data have been important in astrophysics. For example, there are kinematic gaps opened by resonances in dynamical systems, or exoplanets of a certain radius that are empirically rare. A gap in a data set is a kind of anomaly, but in an unusual sense: instead of being a single outlier data point, situated far from other data points, it is a region of the space, or a set of points, that is anomalous compared to its surroundings. Gaps are both interesting and hard to find and characterize, especially when they have nontrivial shapes. We present in this paper a statistic that can be used to estimate the (local) “gappiness” of a point in the data space. It uses the gradient and Hessian of the density estimate (and thus requires a twice-differentiable density estimator). This statistic can be computed at (almost) any point in the space and does not rely on optimization; it allows us to highlight underdense regions of any dimensionality and shape in a general and efficient way. We illustrate our method on the velocity distribution of nearby stars in the Milky Way disk plane, which exhibits gaps that could originate from different processes. Identifying and characterizing those gaps could help determine their origins. We provide in an appendix implementation notes and additional considerations for finding underdensities in data, using critical points and the properties of the Hessian of the density. 7 7 A Python implementation of t methods presented here is available at https://github.com/contardog/FindTheGap.

Human‐Driven Models: A Case Study of Geologists as They Engage with Data for Decision Making

AbstractThe value of geologic data is well established and demonstrated by efforts such as EarthChem and EarthCube. Although these communities are active in the documentation and preservation of geologic data, more work is needed to understand how geologists use this data to address specific problems. In this preliminary analysis, we focus on the information behaviors of professional geologists as they engage with multiple data streams to make decisions. Using semi‐structured interviews and grounded theory, our findings document how a single data point can drive changes to existing models. Responses also show that geologists view their experiences in data collection as critical and they use their knowledge and experience to iteratively re‐assess the context and fitness of their data as they search for coherent interpretations that resolve data‐model conflicts.

Interpretable stock price forecasting model using genetic algorithm-machine learning regressions and best feature subset selection

Recent stock market studies adopting machine learning and deep learning techniques have achieved remarkable performances with convenient accessibility. However, machine learning and deep learning models are notorious for their black-box structure. To build human-friendly interpretability in stock price prediction, many studies focus on the relationship between input features and the outcome by measuring the feature importance. However, the feature-importance-based interpretability methods have such drawbacks as relative feature importance, vague importance of correlated features, and impractical interpretability. Furthermore, they overlook two principal characteristics of time series stock price data: time-dependency and collective behavior of features. As a solution to catch the collective behavior of features over a whole data period, we propose the best feature subset selection. Additionally, for the solution to reflect the time-dependent characteristic of stock price data over a short data period, we propose piecewise best feature subset selection. The proposed algorithm uses two separate input feature sets: internal technical indicators and external market prices. This bilateral forecasting scheme goes through a two-stage feature selection process composed of feature set expansion, hybridized genetic algorithm-machine learning regressions to select important features, and importance score filtering to select optimal features. Finally, the best feature subset is selected for forecasting and interpretation. The proposed method achieves the best feature subset of parsimoniously fewer features for interpretability and improves average forecasting Root Mean Squared Error by 10.42% for the optimal feature set and 13.47% for the best feature subset of the internal technical indicators. For enhanced local interpretability in this study, we use Savitzky–Golay smoothing as part of piecewise optimal curve fitting to examine each potential grouping of external features. The proposed local interpretability technique using piecewise optimal curve fitting and piecewise best feature subset provides a more timely-flexible interpretation of stock price behavior using a few best features for piecewise data segments. Compared with other feature-importance interpretability techniques that only rely on either a single data point or a whole data period, the proposed interpretability technique overcomes their limitations, and reflects the main characteristics of time series data.

Systematic Comparison of Objects Classification Methods Based on ALS and Optical Remote Sensing Images in Urban Areas

Geographical object classification and information extraction is an important topic for the construction of 3D virtual reality and digital twin cities in urban areas. However, the majority of current multi-target classification of urban scenes uses only a single source data (optical remote sensing images or airborne laser scanning (ALS) point clouds), which is limited by the restricted information of the data source itself. In order to make full use of the information carried by multiple data sources, we often need to set more parameters as well as algorithmic steps. To address the above issues, we compared and analyzed the object classification methods based on data fusion of airborne LiDAR point clouds and optical remote sensing images, systematically. Firstly, the features were extracted and determined from airborne LiDAR point clouds and high-resolution optical images. Then, some key feature sets were selected and were composed of median absolute deviation of elevation, normalized elevation values, texture features, normal vectors, etc. The feature sets were fed into various classifiers, such as random forest (RF), decision tree (DT), and support vector machines (SVM). Thirdly, the suitable feature sets with appropriate dimensionality were composed, and the point clouds were classified into four categories, such as trees (Tr), houses and buildings (Ho), low-growing vegetation (Gr), and impervious surfaces (Is). Finally, the single data source and multiple data sources, the crucial feature sets and their roles, and the resultant accuracy of different classifier models were compared and analyzed. Under the conditions of different experimental regions, sampling proportion parameters and machine learning models, the results showed that: (1) the overall classification accuracy obtained by the feature-level data fusion method was 76.2% compared with the results of only a single data source, which could improve the overall classification accuracy by more than 2%; (2) the accuracy of the four classes in the urban scenes can reach 88.5% (Is), 76.7% (Gr), 87.2% (Tr), and 88.3% (Ho), respectively, while the overall classification accuracy can reach 87.6% with optimal sampling parameters and random forest classifiers; (3) the RF classifier outperforms DT and SVM for the same sample conditions. In this paper, the method based on ALS point clouds and image data fusion can accurately classify multiple targets in urban scenes, which can provide technical support for 3D scene reconstruction and digital twin cities in complex geospatial environments.

Fetal Dose from PET and CT in Pregnant Patients.

When pregnancy is discovered during or after a diagnostic examination, the physician or the patient may request an estimate of the radiation dose received by the fetus as per guidelines and standard operating procedures. This study provided the imaging community with dose estimates to the fetus from PET/CT with protocols that are adapted to University of Michigan low-dose protocols for patients known to be pregnant. Methods: There were 9 patients analyzed with data for the first, second, and third trimesters, the availability of which is quite rare. These images were used to calculate the size-specific dose estimate (SSDE) from the CT scan portion and the SUV and 18F-FDG uptake dose from the PET scan portion using the MIRD formulation. The fetal dose estimates were tested for correlation with each of the following independent measures: gestational age, fetal volume, average water-equivalent diameter of the patient along the length of the fetus, SSDE, SUV, and percentage of dose from 18F-FDG. Stepwise multiple linear regression analysis was performed to assess the partial correlation of each variable. To our knowledge, this was the first study to determine fetal doses from CT and PET images. Results: Fetal self-doses from 18F for the first, second, and third trimesters were 2.18 mGy (single data point), 0.74-1.82 mGy, and 0.017-0.0017 mGy, respectively. The combined SSDE and fetal self-dose ranged from 1.2 to 8.2 mGy. These types of images from pregnant patients are rare. Conclusion: Our data indicate that the fetal radiation exposure from 18F-FDG PET and CT performed, when medically necessary, on pregnant women with cancer is low. All efforts should be made to minimize fetal radiation exposure by modifying the protocol.

Embedded QRS complex detection based on ECG signal strength and trend

Cardiovascular diseases (CVD) are among the most fatal diseases and its mitigation is a huge challenge in healthcare. Electrocardiography (ECG) remains the most commonly used method and device for the visualization and analysis cardiac rhythm. QRS complex detection has been extensively used for this purpose. Recently, several PC based QRS detection algorithms were proposed wherein the QRS complex is detected from previously stored ECG signals. However, with the expansion of personalized medicine backed by advances in the field of wearable medical devices, it is imperative to have an algorithm that is robust, accurate, real-time, and computationally efficient for low resource microcontroller units (MCU). In this paper, a novel embedded QRS complex detection algorithm based on the ECG signal strength and its trend is presented. The algorithm is based on a simulated capacitor threshold that captures the signal strength two other thresholds based on the signal trend to find the position of the R-peak. Subsequently, the location of the end of the R-peak and the tangent to the ECG curve are used to find the onset of the QRS complex. The algorithm obtained average F1 scores of 99.75%, 99.84%, 97.39%, and 86.63% on the MIT-BIH Arrhythmia, MIT-BIH Normal Sinus, the MIT-BIH Noise Stress Test, and the 2014 PhysioNet/CinC Challenge databases respectively. Average run-times for the processing of a single data point were 3.38μs, and 383μs when the algorithm was running respectively on an ESP32-WROOM-32 MCU @240MHz and an Arduino Nano MCU @16MHz. This algorithm has a great potential in the field of wearable medical devices and remote monitoring systems.

Study of an improved and novel venturi scrubber configuration for removal of radioactive gases from NPP containment air during severe accident

Owing to the rising concerns about the safety of nuclear power plants (NPP), it is essential to study the venturi scrubber in detail, which is a key component of the filtered containment venting system (FCVS). FCVS alleviates the pressure in containment by filtering and venting out the contaminated air. The main objective of this research was to perform a CFD investigation of different configurations of a circular, non-submerged, self-priming venturi scrubber to estimate and improve the performance in the removal of elemental iodine from the air. For benchmarking, a mass transfer model which is based on two-film theory was selected and validated by experimental data where an alkaline solution was considered as the scrubbing solution. This mass transfer model was modified and implemented on a unique formation of two self-priming venturi scrubbers in series. Euler-Euler method was used for two-phase modeling and the realizable K−ε model was used for capturing the turbulence. The obtained results showed a remarkable improvement in the removal of radioactive iodine from the air using a series combination of venturi scrubbers. The removal efficiency was improved at every single data point.

A method for temperature error compensation in fiber-optic gyroscope based on machine learning

This work presents a machine-learning based method for temperature error compensation of fiber optic gyroscope (FOG). Alternative to existing methods for constructing samples by single data point, a novel method of constructing samples by sequence is proposed, which fully considers the hysteresis and delay of temperature error. Moreover, temperature experiments with three distinct temperature trends, i.e., heating, holding and cooling, are conducted. Following the construction of training and test sets, the relevant training and test processes are completed using SVR algorithm. According to the degree of approximation in predicted value relative to the real value and the degree of improvement in gyro stability, the effects of various sample construction methods on the corresponding error compensation are analyzed. Considering the root mean square error (RMSE), mean absolute value error (MAE) and improvement-factor of FOG zero-bias stability as measurement indicators, this work proposes to construct samples by sequence with temperature trend feature-extraction, which effectively improves the overall accuracy of gyroscope. Allan variance is also utilized to verify the effectiveness of our proposed method. Lastly, this study also provides a theoretical guidance and reference for temperature error compensation in other types of sensors.

Modelling mass transfer from a packed bed by fluid extraction

A mathematical model describing the erosion or leaching of a solid material by a flowing fluid in a column is developed. This involves an advection-diffusion equation coupled to a linear kinetic reaction describing the mass transfer between the solid and fluid. Two specific cases are analysed, the first where the extracted material has the same saturation solubility and rate of mass transfer throughout the process, the second where the solubility switches after a certain amount of erosion. In the first case there are only two model unknowns, the solubility and mass transfer coefficient, in the second there is a third unknown, the second solubility. Exploiting the fact that erosion is a slow process (relative to the flow rate) a perturbation solution based on the smallness of the amount removed is developed to describe the concentration and radius throughout the column. From this an analytical expression for the extracted fraction is obtained. The extracted fraction has a large linear section which results in a simple calculation to estimate the initial solubility from a very few or even a single data point. The remaining unknowns may also be easily calculated from the formula and later data points. A numerical solution, using finite differences, is developed to verify the perturbation solution. The analytical solution is also verified against experimental data for the removal of lanolin from wool fibres with a supercritical CO2/ethanol solvent. Values for the mass transfer rate and two solubilities are obtained for different pressures and shown to provide excellent agreement with a series of experimental results for the extracted fraction.

Generative Design Inspiration for Glyphs with Diatoms.

We introduce Diatoms, a technique that generates design inspiration for glyphs by sampling from palettes of mark shapes, encoding channels, and glyph scaffold shapes. Diatoms allows for a degree of randomness while respecting constraints imposed by columns in a data table: their data types and domains as well as semantic associations between columns as specified by the designer. We pair this generative design process with two forms of interactive design externalization that enable comparison and critique of the design alternatives. First, we incorporate a familiar small multiples configuration in which every data point is drawn according to a single glyph design, coupled with the ability to page between alternative glyph designs. Second, we propose a small permutables design gallery, in which a single data point is drawn according to each alternative glyph design, coupled with the ability to page between data points. We demonstrate an implementation of our technique as an extension to Tableau featuring three example palettes, and to better understand how Diatoms could fit into existing design workflows, we conducted interviews and chauffeured demos with 12 designers. Finally, we reflect on our process and the designers' reactions, discussing the potential of our technique in the context of visualization authoring systems. Ultimately, our approach to glyph design and comparison can kickstart and inspire visualization design, allowing for the serendipitous discovery of shape and channel combinations that would have otherwise been overlooked.

Detecting attention-related rhythms: When is behavior not enough? (Commentary on van der Werf et al. 2021).

Recent research suggests that environmental sampling is a fundamentally rhythmic process (Benedetto, Morrone, & Tomassini, 2019; Fiebelkorn & Kastner, 2019; Schroeder, Wilson, Radman, Scharfman, & Lakatos, 2010). In primates, both attention-related sampling and exploratory eye movements are seemingly shaped by theta-band activity (3-8 Hz) in the large-scale network that directs both spatial attention and goal-directed eye movements (i.e., the 'attention network').

Dose‐dependent mathematical modeling of interferon‐α‐treatment for personalized treatment of myeloproliferative neoplasms

AbstractLong‐term treatment with interferon‐alfa (IFN) can reduce the disease burden of patients diagnosed with myeloproliferative neoplasms (MPNs). Determining individual patient responses to IFN therapy may allow for efficient personalized treatment, reducing both drop‐out and disease burden. A mathematical model describing hematopoietic stem cells and the immune system is suggested. Considering the bone marrow and the blood allows for modeling disease dynamics both in the absence and presence of IFN treatment. Through comprehensive modeling of the effects of IFN, the model was related to individualized patient‐data consisting of longitudinal hematologic and molecular measurements. Treatment responses were modeled on a population level, allowing for personalized predictions from a single pretreatment data point. Personalized fits were found to agree well with data for individual patients. This allowed for a quantitative description of the treatment response, yielding a mechanistic interpretation of differences from patient to patient. The treatment responses of individual patients were combined and a formulation of treatment responses on the population level was described and simulated. Based on pretreatment data and the actual treatment scheduling, the population‐level response was found to predict the treatment response of particular patients accurately over a five‐year period. Mechanism‐based modeling of treatment effects demonstrates that hematologic and molecular observable quantities can be predicted on the level of individual patients. Personalized patient‐fits suggest that the effect of IFN treatment can be quantified and interpreted through mathematical modeling, despite variation in hematologic and molecular responses between patients. Mathematical modeling suggests that in general both hematologic and molecular markers must be considered to avoid early relapse. Furthermore, personalized model‐fits provide quantitative measures of the hematologic and molecular responses, determining when treatment‐cessation is appropriate. Proof‐of‐concept population‐level modeling of treatment responses from pretreatment data successfully predicted clinical measures for a 5‐year period. We believe that this approach could have direct clinical relevance, offering expert guidance for clinical decisions about IFN treatment of MPN patients.

Angular Modeling of the Components of Net Radiation in Agricultural Crops and Its Implications on Energy Balance Closure

Efficient water management in agricultural crops is necessary to increase productivity and adapt to climate change. Evapotranspiration (ET) data are key in determining the water requirements of crops and set efficient irrigation schedules. Estimating ET at the regional scale (for example, in irrigation districts) is a technically complex task that has been tackled by using data acquired by remote sensors on satellites that can be validated with scaled up field measurements when area sources are matched. Energy and matter flux measurements using the eddy covariance (EC) technique are challenging due to balance closure issues, claimed to be due to the different footprints of the energy-balance components. We describe net radiometer footprints in terms of the sun-sensor geometry to characterize the bidirectional distribution functions of albedo and thermal emissions. In this context, we describe a one-parameter model of the components of net radiation that can be calibrated with a single data point. The model was validated in an experiment with five agricultural crops (bean, sorghum, chickpea, safflower, and wheat) at Valle del Yaqui, in Sonora, Mexico, using different sun-sensor geometry configurations. The results from the experimental fits were satisfactory (R2 > 0.99) and support the use of the model for albedo and radiative (surface) temperature in order to estimate net radiation. The analysis of the implications regarding a mismatch among footprints of the components of the energy balance showed that net radiometer fluxes are overestimated most of the time, implying that the closure problem could be solved by using a similar footprint as the aerodynamic components of the energy balance.

Detecting Urban Anomalies Using Factor Analysis and One Class Support Vector Machine

AbstractThe detection of anomalies in spatiotemporal traffic data is not only critical for intelligent transportation systems and public safety but also very challenging. Anomalies in traffic data often exhibit complex forms in two aspects, (i) spatiotemporal complexity (i.e. we need to associate individual locations and time intervals formulating a panoramic view of an anomaly) and (ii) multi-source complexity (i.e. we need an algorithm that can model the anomaly degree of the multiple data sources of different densities, distributions and scales). To tackle these challenges, we proposed a three-step method that uses factor analysis to extract features, then uses the goodness-of-fit test to obtain the anomaly score of a single data point and then uses one class support vector machine to synthesize the anomaly score. Finally, we conduct extensive experiments on real-world trip data include taxi and bike data. And these extensive experiments demonstrate the effectiveness of our proposed approach.

Novel kernel density estimator based on ensemble unbiased cross-validation

Unbiased cross-validation (UCV) is a commonly-used method to calculate the optimal bandwidth for the kernel density estimator (KDE), which estimates the underlying probability density function (PDF) for a given data set. Since the UCV method was proposed, there have been few studies that have pointed out its instability when determining the KDE bandwidth. Following the principle of stability improvement, this paper presents a novel ensemble UCV based KDE (EUCV-KDE), which determines the expectation of an estimated PDF using an ensemble of data-block based UCVs rather than a single data-point based UCV. To derive the optimal bandwidth, a novel objective function is designed for EUCV-KDE by considering the empirical and structural risk of KDE together. We validate the rationality and effectiveness of EUCV-KDE on 10 probability distributions. The experimental results show that EUCV-KDE is convergent as the number of data-block based UCVs increases and can obtain a more stable and better prediction performance than the classical UCV-KDE and the revisited cross-validation (RCV) based KDE (RCV-KDE). In addition, a real-world application based on UK climate data is provided to further validate the effectiveness of EUCV-KDE by determining the optimal bandwidth for Nadaraya-Watson kernel regression estimator.

Technical note: On the reliability of laboratory beta-source calibration for luminescence dating

Abstract. The dose rate of the 90Sr / 90Y beta source used in most luminescence readers is a laboratory key parameter. There is a well-established body of knowledge about parameters controlling accuracy and precision of the calibration value but some hard-to-explain inconsistencies still exist. Here, we have investigated the impact of grain size, aliquot size and irradiation geometry on the resulting calibration value through experiments and simulations. The resulting data indicate that the dose rate of an individual beta source results from the interplay of a number of parameters, most of which are well established by previous studies. Our study provides evidence for the impact of aliquot size on the absorbed dose in particular for grain sizes of 50–200 µm. For this grain-size fraction, the absorbed dose is enhanced by ∼ 10 %–20 % as aliquot size decreases due to the radial increase of dose rate towards the centre of the aliquot. The enhancement is most variable for 50–100 µm grains mounted as aliquots of < 8 mm size. The enhancement is reversed when large grains are mounted as small aliquots due to the edge effect by which the dose induced by backscattered electrons is reduced. While the build-up of charge dictates the increase of absorbed dose with the increase of grain size, this principle becomes more variable with changing irradiation geometry. We conclude that future calibration samples should consist of subsamples composed of small, medium, large and very large quartz grains, each obtaining several gamma doses. The calibration value measured with small, medium and large aliquots is then obtained from the inverse slope of the fitted line, not from a single data point. In this way, all possible irradiation geometries of an individual beta source are covered, and the precision of the calibration is improved.

How Does Data Augmentation Affect Privacy in Machine Learning?

It is observed in the literature that data augmentation can significantly mitigate membership inference (MI) attack. However, in this work, we challenge this observation by proposing new MI attacks to utilize the information of augmented data. MI attack is widely used to measure the model's information leakage of the training set. We establish the optimal membership inference when the model is trained with augmented data, which inspires us to formulate the MI attack as a set classification problem, i.e., classifying a set of augmented instances instead of a single data point, and design input permutation invariant features. Empirically, we demonstrate that the proposed approach universally outperforms original methods when the model is trained with data augmentation. Even further, we show that the proposed approach can achieve higher MI attack success rates on models trained with some data augmentation than the existing methods on models trained without data augmentation. Notably, we achieve a 70.1\% MI attack success rate on CIFAR10 against a wide residual network while the previous best approach only attains 61.9\%. This suggests the privacy risk of models trained with data augmentation could be largely underestimated.

Long Term HbA1c Prediction Using Multi-Stage CGM Data Analysis

The glycated hemoglobin (HbA1c) is regarded as an essential biomarker for diabetes management. Having an elevated HbA1c level significantly increases the risk of developing diabetes-related health complications. Accurate prediction of HbA1c can greatly improve the way diabetic patients are treated and can potentially avoid related consequences. This study devises a framework to predict HbA1c levels 2-3 months in advance by using blood glucose data collected through continuous glucose monitoring (CGM) sensors and leveraging advanced feature extraction and machine learning techniques. The CGM data may often contain missing values due to sensor issues or not wearing the sensor for some period. Thus, in the paper, a novel missing data estimation method has been proposed for a single data point, multiple data points, and entire day CGM data imputation. The CGM data have been rigorously investigated, and pertinent features were created along with a multi-stage multi-class (MSMC) classification model to predict futuristic HbA1c levels. To evaluate the developed framework, a total of 150 patients' data were sourced from Sidra Medicine, Doha, Qatar, for analysis. The proposed three-staged and five-staged MSMC models predicted HbA1c levels 2-3 months in advance and obtained overall classification accuracies of 88.65% and 83.41%, respectively.

How much leaf area do insects eat? A data set of insect herbivory sampled globally with a standardized protocol.

Herbivory is ubiquitous. Despite being a potential driver of plant distribution and performance, herbivory remains largely undocumented. Some early attempts have been made to review, globally, how much leaf area is removed through insect feeding. Kozlov et al., in one of the most comprehensive reviews regarding global patterns of herbivory, have compiled published studies regarding foliar removal and sampled data on global herbivory levels using a standardized protocol. However, in the review by Kozlov et al., only 15 sampling sites, comprising 33 plant species, were evaluated in tropical areas around the globe. In Brazil, which ranks first in terms of plant biodiversity, with a total of 46,097 species, almost half (43%) being endemic, a single data point was sampled, covering only two plant species. In an attempt to increase knowledge regarding herbivory in tropical plant species and to provide the raw data needed to test general hypotheses related to plant-herbivore interactions across large spatial scales, we proposed a joint, collaborative network to evaluate tropical herbivory. This network allowed us to update and expand the data on insect herbivory in tropical and temperate plant species. Our data set, collected with a standardized protocol, covers 45 sampling sites from nine countries and includes leaf herbivory measurements of 57,239 leaves from 209 species of vascular plants belonging to 65 families from tropical and temperate regions. They expand previous data sets by including a total of 32 sampling sites from tropical areas around the globe, comprising 152 species, 146 of them being sampled in Brazil. For temperate areas, it includes 13 sampling sites, comprising 59 species. Thus, when compared to the most recent comprehensive review of insect herbivory (Kozlov et al.), our data set has increased the base of available data for the tropical plants more than 460% (from 33 to 152 species) and the Brazilian sampling was increased 7,300% (from 2 to 146 species). Data on precise levels of herbivory are presented for more than 57,000 leaves worldwide. There are no copyright restrictions. Please cite this paper when using the current data in publications; the authors request to be informed how the data is used in the publications.