Scale Estimation Research Articles

Towards accurate quantification of ice content in permafrost of the Central Andes – Part 2: An upscaling strategy of geophysical measurements to the catchment scale at two study sites

Abstract. With ongoing climate change, there is a pressing need to better understand how much water is stored as ground ice in areas with extensive permafrost occurrence, as well as how the regional water balance may alter in response to the potential generation of meltwater from permafrost degradation. However, field-based data on permafrost in remote and mountainous areas such as the South American Andes are scarce. Most current ground ice estimates are based on broadly generalized assumptions such as volume–area scaling and mean ground ice content estimates of rock glaciers. In addition, ground ice contents in permafrost areas outside of rock glaciers are usually not considered, resulting in a significant uncertainty regarding the volume of ground ice in the Andes and its hydrological role. In Part 1 of this contribution, Hilbich et al. (2022a) present an extensive geophysical data set based on electrical resistivity tomography and refraction seismic tomography surveys to detect and quantify ground ice of different landforms and surface types in several study regions in the semi-arid Andes of Chile and Argentina with the aim to contribute to the reduction of this data scarcity. In Part 2 we focus on the development of a strategy for the upscaling of geophysics-based ground ice quantification to an entire catchment to estimate the total ground ice volume (and its approximate water equivalent) in the study areas. In addition to the geophysical data, the upscaling approach is based on a permafrost distribution model and classifications of surface and landform types. In this paper, we introduce our upscaling strategy, and we demonstrate that the estimation of large-scale ground ice volumes can be improved by including (i) non-rock-glacier permafrost occurrences and (ii) field evidence through a large number of geophysical surveys and ground truthing information. The results of our study indicate that (i) conventional ground ice estimates for rock-glacier-dominated catchments without in situ data may significantly overestimate ground ice contents and (ii) substantial volumes of ground ice may also be present in catchments where rock glaciers are lacking.

Homography Decomposition Networks for Planar Object Tracking

Planar object tracking plays an important role in AI applications, such as robotics, visual servoing, and visual SLAM. Although the previous planar trackers work well in most scenarios, it is still a challenging task due to the rapid motion and large transformation between two consecutive frames. The essential reason behind this problem is that the condition number of such a non-linear system changes unstably when the searching range of the homography parameter space becomes larger. To this end, we propose a novel Homography Decomposition Networks~(HDN) approach that drastically reduces and stabilizes the condition number by decomposing the homography transformation into two groups. Specifically, a similarity transformation estimator is designed to predict the first group robustly by a deep convolution equivariant network. By taking advantage of the scale and rotation estimation with high confidence, a residual transformation is estimated by a simple regression model. Furthermore, the proposed end-to-end network is trained in a semi-supervised fashion. Extensive experiments show that our proposed approach outperforms the state-of-the-art planar tracking methods at a large margin on the challenging POT, UCSB and POIC datasets. Codes and models are available at https://github.com/zhanxinrui/HDN.

A simulation model of heterochromatin formation at submolecular detail

SummaryHeterochromatin is a physical state of the chromatin fiber that maintains gene repression during cell development. Although evidence exists on molecular mechanisms involved in heterochromatin formation, a detailed structural mechanism of heterochromatin formation needs a better understanding. We made use of a simple Monte Carlo simulation model with explicit representation of key molecular events to observe molecular self-organization leading to heterochromatin formation. Our simulations provide a structural interpretation of several important traits of the heterochromatinization process. In particular, this study provides a depiction of how small amounts of HP1 are able to induce a highly condensed chromatin state through HP1 dimerization and bridging of sequence-remote nucleosomes. It also elucidates structural roots of a yet poorly understood phenomenon of a nondeterministic nature of heterochromatin formation and subsequent gene repression. Experimental chromatin in vivo assay provides an unbiased estimate of time scale of repressive response to a heterochromatin-triggering event.

Spatial Scale Effect and Correction of Forest Aboveground Biomass Estimation Using Remote Sensing

Forest biomass is critically important for forest dynamics in the carbon cycle. However, large-scale AGB mapping applications from remote sensing data still carry large uncertainty. In this study, an AGB estimation model was first established with three different remote sensing datasets of GF-2, Sentinel-2 and Landsat-8. Next, the optimal scale estimation result was considered as a reference AGB to obtain the relative true AGB distribution at different scales based on the law of conservation of mass, and the error of the scale effect of AGB estimation at various spatial resolutions was analyzed. Then, the information entropy of land use type was calculated to identify the heterogeneity of pixels. Finally, a scale conversion method for the entropy-weighted index was developed to correct the scale error of the estimated AGB results from coarse-resolution remote sensing images. The results showed that the random forest model had better prediction accuracy for GF-2 (4 m), Sentinel-2 (10 m) and Landsat-8 (30 m) AGB mapping. The determination coefficient between predicted and measured AGB was 0.5711, 0.4819 and 0.4321, respectively. Compared to uncorrected AGB, R2 between scale-corrected results and relative true AGB increased from 0.6226 to 0.6725 for Sentinel-2, and increased from 0.5910 to 0.6704 for Landsat-8. The scale error was effectively corrected. This study can provide a reference for forest AGB estimation and scale error reduction for AGB production upscaling with consideration of the spatial heterogeneity of the forest surface.

Small Area Estimation in Diverse Timber Types Using Multiple Sources of Auxiliary Data

Abstract Informed forest management requires reliable information. As the demand for finer scale estimates has increased, so has the cost for obtaining them from design-based ground sampling. Small area estimation (SAE) is an estimation technique that leverages ancillary information to augment design-based samples with the goal of increasing estimate precision without increasing ground-based sample intensities. This work presents three case studies spanning an industrial timberland ownership in the United States making use of SAE techniques in operational forest inventories. Case studies include an inventory of pre-thin plantation loblolly pine (Pinus taeda L.) stands that had achieved crown closure in Alabama and Mississippi, a mixed pine–hardwood inventory in Alabama, and pre-thinning plantation Douglas-fir (Pseudotsuga menziesii [Mirb.] Franco) in Washington State. Using area-level SAE techniques, vegetation indices derived from 10 m Sentinel imagery were shown to reduce estimate uncertainty for common stand parameters. Additionally, when available, lidar and age were shown to offer additional improvements in estimate precision. The results of this study indicate the operational potential for using commonly available auxiliary data for producing forest parameter estimates with enhanced precision. The implications of these findings span multiple inventory objectives including, for example, commercial forest management, carbon accounting, and wildfire fuel assessments. Study Implications: Forest management requires reliable quantitative information for informed decisions. Data from ground-based forest inventories are commonly used to construct design-unbiased direct estimates. Due to logistical and cost constraints, samples often do not provide estimates with sufficient precision for making confident decisions. The statistical estimation procedure, small area estimation, is able to leverage linearly related ancillary data across areas of interest to form composite estimates that have less uncertainty than direct estimates alone. This study shows how combining ground-based data with auxiliary data from remote sensing and stand records produced more precise estimates of forest stand parameters in three distinct timber types spanning a large ownership in the United States. Results indicate that significant inventory efficiency and confidence can be realized by incorporating commonly available auxiliary data into the estimation of forest characteristics.

Evaluating the Accuracy of Self-Ratings of Language in Adults with Aphasia and Non-Brain Injured Adults: A Pilot Study.

Rating scales are frequently used in research and clinical practice with people with aphasia (PWA) to characterize communication in the home environment. However, it remains unclear whether responses provided on rating scales accurately reflect the communication that occurs. We aim to evaluate the accuracy of PWA's self-perceptions of verbal language use as measured by a rating scale and determine whether this accuracy is different from that of non-brain-injured (NBI) participants. Four PWA and four NBI participants completed a rating scale estimating their amount of verbal language production as compared with their communication partner. Audio recordings from participants' home environments were analyzed for proportion of words and conversational turns contributed by the participant, which were compared with rating scale estimates. Perceptions of verbal language output among both PWA and NBI participants showed variable accuracy, with discrepancies between estimates and objective data across both groups. The reliability of rating scales in quantifying language output appears questionable, suggesting they may not accurately represent naturalistic language environments of PWA. Additional research with larger sample sizes is warranted to investigate whether this trend is consistent across a larger population of individuals with aphasia.

Automatic flower detection and phenology monitoring using time‐lapse cameras and deep learning

AbstractThe advancement of spring is a widespread biological response to climate change observed across taxa and biomes. However, the species level responses to warming are complex and the underlying mechanisms are difficult to disentangle. This is partly due to a lack of data, which are typically collected by direct observations, and thus very time‐consuming to obtain. Data deficiency is especially pronounced in the Arctic where the warming is particularly severe. We present a method for automated monitoring of flowering phenology of specific plant species at very high temporal resolution through full growing seasons and across geographical regions. The method consists of image‐based monitoring of field plots using near‐surface time‐lapse cameras and subsequent automated detection and counting of flowers in the images using a convolutional neural network. We demonstrate the feasibility of collecting flower phenology data using automatic time‐lapse cameras and show that the temporal resolution of the results surpasses what can be collected by traditional observation methods. We focus on two Arctic species, the mountain avens Dryas octopetala and Dryas integrifolia in 20 image series from four sites. Our flower detection model proved capable of detecting flowers of the two species with a remarkable precision of 0.918 (adjusted to 0.966) and a recall of 0.907. Thus, the method can automatically quantify the seasonal dynamics of flower abundance at fine scale and return reliable estimates of traditional phenological variables such as the timing of onset, peak, and end of flowering. We describe the system and compare manual and automatic extraction of flowering phenology data from the images. Our method can be directly applied on sites containing mountain avens using our trained model, or the model could be fine‐tuned to other species. We discuss the potential of automatic image‐based monitoring of flower phenology and how the method can be improved and expanded for future studies.

Introduction to the Special Issue on “Energy Market Transition, Financialization and Integration”

Due to difficulties in accessing detailed energy modelling and usage data that are required to estimate energy needs that are responsive to local circumstances, we propose an equivalence scale approach to the determination of required energy consumption. Our method requires the estimation of energy equivalence scales that are used to rescale reference household energy consumption and, thus, yield household-specific energy requirements. We apply the method using readily available income and expenditure data, finding that estimated required energy is well above actual energy expenditure for low- and middle-income households, which is consistent with an expectation that basic energy needs for poor households may not be met. The proposed approach is general enough to incorporate other features that might be deemed relevant and available in other settings, and, therefore, can be used to examine the affordability component of SDG 7, undertake energy poverty analysis or design appropriate policies.

Parameter Estimation Processor for K-distribution Clutter Based on Deep Learning

This paper concerns the problem of parameter estimating of K-distribution. In previous work only the shape parameter of K-distribution is estimated from which the scale parameter is calculated. Therefore, the accuracy of the estimated scale parameter is largely determined by the accuracy of shape parameter estimation. In order to decouple the estimation of scale and shape parameters, in this work, deep learning is considered as the main tool to achieve K-distribution parameters estimation as a regression task. Specifically, a parameter estimation processor combining CNN with LSTM is constructed. The ground truth of the two parameters are taken as labels, and the weighted losses of the two parameters construct the total loss function of the network training. The effectiveness and superiority of the proposed estimation processor are verified on the simulated data and the real sea clutter data.

Direction of arrival and target scale estimation based on split beamforming algorithm

Based on the theory of split beamforming algorithm and the experimental data collected by circular array, this paper analyzes the characteristics of DOA and target size estimation. In this paper, the signal receiving model of planar circular array and the split beamforming algorithm are studied. Then, based on the data collected from the lake experiment, the DOA estimation results of conventional beamforming algorithm, multiple signal classification algorithm and split beamforming algorithm are analyzed, and the target scale estimation results of split beamforming algorithm is analyzed. The experimental data analysis shows that the split beamforming algorithm has good direction finding stability, and the target scale estimation error based on the split beamforming algorithm is small.

Clustering based detection of small target pedestrians for smart cities

Detecting small targets in large images is challenging, especially for pedestrian detection in the field of self-driving cars for smart cities, for at least two reasons: (1) the pixels of small targets are blurry and are affected by the background; (2) the distribution of small targets is generally sparse and uneven, leading to the reduction of the detection efficiency. In this manuscript, we propose a clustering based scheme for the detection of small target pedestrians to address above difficulties. Clustering detection yields object cluster regions and gives an estimation of the object scales for these regions, so the clustered region is consistent with the input size of the fine detection model. Then, the detection results of small target pedestrians in the clustered region are obtained and restored to the input image to achieve the final detection results. Our detection strategy has several advantages over previous solutions. It saves a lot of computational power and running time which is vital for self-driving cars. Furthermore, the detection model is replaceable, making our scheme an easy solution to more complex tasks. We demonstrate the effectiveness of our scheme on both YOLOv4 and Faster R-CNN as their detection performance can be greatly improved.

Carbon dioxide and particulate emissions from the 2013 Tasmanian firestorm: implications for Australian carbon accounting

BackgroundUncontrolled wildfires in Australian temperate Eucalyptus forests produce significant smoke emissions, particularly carbon dioxide (CO2) and particulates. Emissions from fires in these ecosystems, however, have received less research attention than the fires in North American conifer forests or frequently burned Australian tropical savannas. Here, we use the 2013 Forcett–Dunalley fire that caused the first recorded pyrocumulonimbus event in Tasmania, to understand CO2 and particulate matter (PM2.5) emissions from a severe Eucalyptus forest fire. We investigate the spatial patterns of the two emissions using a fine scale mapping of vegetation and fire severity (50 m resolution), and utilising available emission factors suitable for Australian vegetation types. We compare the results with coarse-scale (28 km resolution) emissions estimates from Global Fire Emissions Database (GFED) to determine the reliability of the global model in emissions estimation.ResultsThe fine scale inventory yielded total CO2 emission of 1.125 ± 0.232 Tg and PM2.5 emission of 0.022 ± 0.006 Tg, representing a loss of 56 t CO2 ha−1 and 1 t PM2.5 ha−1. The CO2 emissions were comparable to GFED estimates, but GFED PM2.5 estimates were lower by a factor of three. This study highlights the reliability of GFED for CO2 but not PM2.5 for estimating emissions from Eucalyptus forest fires. Our fine scale and GFED estimates showed that the Forcett–Dunalley fire produced 30% of 2013 fire carbon emissions in Tasmania, and 26–36% of mean annual fire emissions for the State, representing a significant single source of emissions.ConclusionsOur analyses highlight the need for improved PM2.5 emission factors specific to Australian vegetation, and better characterisation of fuel loads, particularly coarse fuel loads, to quantify wildfire particulate and greenhouse gas emissions more accurately. Current Australian carbon accountancy approach of excluding large wildfires from final GHG accounts likely exaggerates Tasmania’s claim to carbon neutrality; we therefore recommend that planned and unplanned emissions are included in the final national and state greenhouse gas accounting to international conventions. Advancing these issues is important given the trajectory of more frequent large fires driven by anthropogenic climate change.

A scale-up approach for industrial flotation cells based on particle size and liberation data

The current scaleup approaches usually consider the overall metallurgical results, without including the efficiency of flotation machines at different particle size and liberation classes. This approach can limit the prediction of the industrial metallurgical performance, mainly when the mineral feed characteristics change significantly over time. This paper presents a scale-up approach, which allows for estimating scale-up factors per size and liberation class. The plant survey was developed in a copper concentrator in Chile. Plant kinetic testing on three rougher circuits of 130 and 300 m3 cells, in parallel with batch flotation tests using the same rougher feed samples, allowed the estimation of average scale up factors in the range of 1.8–2.2, which are in good agreement with the typical values observed in flotation scale up. All the samples included sieving, and chemical and mineralogical analysis. Scale up factors, batch-plant, showed a correlation with particle size classes, where the scale up factor increases (1.5–2.5), when particle size increases (20–150 µm), according to the data. This effect becomes stronger for particle sizes larger than 100 µm, reaching scale up values around 3–4. This means that the scale up factors are sensitive to the particle size distribution in the plant feed and must be considered.An alternative estimation of scale up factors in terms of the mineral liberation showed a similar trend with those of particle size classes, where the less liberated (mainly coarser sizes) minerals have the largest scale up factors, while decreasing for the highly liberated (mainly finer sizes) minerals.

A new distance between multivariate clusters of varying locations, elliptical shapes, and directions

Clustering methods are based on the computations of both the distances between every pair of the n observations in a multivariate dataset as well as the distances between every pair of clusters in the dataset. The clusters can have different locations and varying elliptical shapes and directions. Numerous methods have been proposed in the literature for computing both of these two types of distances. The contributions of this paper are two folds. First, we propose a new elliptical distance between pairs of clusters in a dataset with different cluster centers and elliptical shapes and directions, Second, we proved analytically that the Ward distance and the Euclidean distance are equivalent. We propose a new classical method for computing the distance between a pair of clusters in the dataset. It is the only distance that does not assume spherical clusters. The proposed classical distances could also be made robust by replacing estimates of location and scale by their respective robust estimators. The proposed distance has a number of advantages including simplicity, interpretability, computational efficiency as well as the ability to accurately capture both the variability of the cluster centers as well as the variability of shapes and directions of their respective covariance matrices. The method is also illustrated by several motivating examples that demonstrate the need of the new proposed distance. The superiority of the proposed method is also demonstrated by application to real-life as well as challenging synthetic data.

Scale dependence of landscape-structure-based estimation of abundance of Eurasian skylark (Alauda arvensis)

The habitat and occurrence of farmland birds are strongly determined by the agricultural-landscape structure. Changes in land cover composition and configuration are one of the main causes of the significant decline in abundance of the Eurasian skylark (Alauda arvensis) in recent decades. This farmland-bird species is common in agricultural areas of Eurasia. In this study we investigate the land use factors involved in the decline in Central Europe, Hungary. We used two different land use/land cover (LULC) datasets, which were compiled at different scales: the Ecosystem Map of Hungary (EMH), a very precise LULC map based on a 0.04-ha minimum mapping unit, and the Corine Land cover (CLC) dataset, built using a 25-ha minimum mapping unit. We studied the impact of landscape composition and configuration on skylark abundance by using negative-binomial generalized linear models. After identifying skylark preferences among LULC categories at different scales, we calculated the EMH and CLC dataset-based landscape indices (such as mean patch size and mean fractal dimension index) of the skylark preferred (arable lands, pastures, grasslands and meadows) and the nonpreferred (artificial surfaces, forests, complex cultivation patterns and waters) LULC classes. Then we compared the results with field observations of skylark abundance in the database of Hungarian Common Bird Monitoring (MMM). On the basis of statistical analysis of connections between the landscape indices and the skylark-abundance data, we estimated skylark abundance for those areas where the skylark-abundance datasets from field observation were not available. We also tested the estimates by assessing model sensitivity when we input different-scale LULC data and used different observation windows (grain size). Our statistical model using EMH dataset explained 41.22% variance of the skylark abundance data, while the rest, 58.78% of variance is not accounted by the model presumably due to local environmental factors not considered in our model. The regional scale (CLC-based) estimation of skylark abundance yielded significantly lower accuracies (33.76% in 1200 m radius buffer zones and 34.11% in 600 m radius buffer zones). We conclude that the size of the landscape windows (grain size) land cover has a significant impact on the relationship between skylark and landscape structure. Our results can help to test the usefulness and limitations of the different-scale LULC databases and to find the optimal grain size for modelling and estimating farmland-bird abundance data and may support landscape scale conservation management plans.

Precipitation Scaling With Temperature in the Northeast US: Variations by Weather Regime, Season, and Precipitation Intensity

AbstractWe present a novel hierarchical Bayesian quantile regression model to estimate how precipitation scales with temperature depending on season, weather regime (WR; i.e., large‐scale patterns of atmospheric circulation), and precipitation percentile. The approach develops regional scaling estimates by partially pooling data across sites, accounting for uncertainty stemming from variable record lengths. Results using long‐term records of daily and hourly precipitation and both dry‐bulb and dew point temperature across the Northeast US suggest that regional precipitation scaling rates vary from 0% to 8% per °C. Scaling rate variability is driven most by season and the percentile of precipitation, with only modest variations across WRs. Daily scaling rates are highest in the winter and summer, while hourly rates at the highest percentiles are greatest in summer. Lower scaling rates for more extreme precipitation quantiles are driven by a handful of storms occurring at cooler temperatures but with strong vertical uplift and heavy precipitation.

Dynamic simulation of the energy consumption and carbon emissions for domestic hot water production in a touristic region

At a buildings’ level, domestic hot water consumption is amongst the most relevant examples of the water-energy nexus. As such, understanding its drivers and forecasting domestic hot water and associated energy consumption are of paramount importance for decision making from the individual household level to a national, or even international, sustainability policy level. However, detailed end-use measurements of either energy or water are seldom available and large scale (city, region or country) estimates are often done based on annual average values. The present research effort aims at large scale estimation of the energy use and carbon emissions due to domestic hot water consumption in two, predominantly residential, locations in a touristic region in Portugal. A novel dynamic modelling approach is proposed and used, which accounts for the variability of: i) the cold water temperature based on measured data; ii) the total amount of water consumed based on measured data; and iii) the fraction of the water consumed as domestic hot water corrected by the air temperature. The results are compared with alternative modelling approaches of the same degree of complexity, revealing differences ranging between −18% and +11% in both net energy required to produce the domestic hot water and the corresponding carbon emissions. Differences in the results are found to exist not only due to the modelling approach, but also between the locations, highlighting the importance of both the simulation approach and the particularities of the context being captured.

Natural mortality and body size in fish populations

Fisheries stock assessments increasingly account for size-dependence in natural mortality rates, usually by modeling mortality as a power function of body length. Various empirical studies have indicated a scaling of mortality with length in the range of − 0.84 to − 1.11, but substantially different scaling exponents ranging from − 0.75 to − 1.5 have been proposed on theoretical grounds or derived from some empirical models. To resolve these controversies and provide a well-supported default estimate of scaling for stock assessments, we re-analyzed two major data sets used in previous studies that supported different scaling exponents, and a combined data set. Both original data sets and the combined data yielded within-population exponents close to − 1 when analyzed using joint-slope mixed-effects models with population as a random effect. When population effects were disregarded, regression models yielded exponents that did not correctly reflect within-population scaling. The greatest deviations from the correct within-population scaling of approximately − 1 occurred in multiple regression models of mortality, size, and growth parameters. We conclude that within- and among-population scaling of natural mortality should be clearly distinguished, and that within-population scaling of natural mortality with length in fish populations is highly consistent at approximately − 1. We also explored empirical models for predicting the intercept of the mortality-length relationship for a given population from growth parameters.

DM-VIO: Delayed Marginalization Visual-Inertial Odometry

We present DM-VIO, a monocular visual-inertial odometry system based on two novel techniques called delayed marginalization and pose graph bundle adjustment. DM-VIO performs photometric bundle adjustment with a dynamic weight for visual residuals. We adopt marginalization, which is a popular strategy to keep the update time constrained, but it cannot easily be reversed, and linearization points of connected variables have to be fixed. To overcome this we propose delayed marginalization: The idea is to maintain a second factor graph, where marginalization is delayed. This allows us to later readvance this delayed graph, yielding an updated marginalization prior with new and consistent linearization points. In addition, delayed marginalization enables us to inject IMU information into already marginalized states. This is the foundation of the proposed pose graph bundle adjustment, which we use for IMU initialization. In contrast to prior works on IMU initialization, it is able to capture the full photometric uncertainty, improving the scale estimation. In order to cope with initially unobservable scale, we continue to optimize scale and gravity direction in the main system after IMU initialization is complete. We evaluate our system on the EuRoC, TUM-VI, and 4Seasons datasets, which comprise flying drone, large-scale handheld, and automotive scenarios. Thanks to the proposed IMU initialization, our system exceeds the state of the art in visual-inertial odometry, even outperforming stereo-inertial methods while using only a single camera and IMU. The code will be published at http://vision.in.tum.de/dm-vio

Determination of Relationships Between Stand Variables and Parameters of Weibull Function for Fagus orientalis Libsky Stands

Aim of study: Information about the diameter distribution of a stand is a key resource to determine planning strategies, silvicultural treatment options and product variety. In this study, the diameter distributions of Fagus orientalis Libsky stands located in Karabük region were researched, and relationship between parameters of Weibull function and stand variables was investigated. Area of study: Data used in this study were obtained from pure Oriental beech (Fagus orientalis Libsky) stands located in the Karabük region, north-central Turkey. Material and methods: For this study, sixty-two sample plots from pure Fagus orientalis Lipsky stands located in Karabük region were taken. Maximum likelihood method was used to estimate parameters of the two-parameter Weibull probability density function. The parameters estimated were then expressed as linear functions of stand variables such as mean diameter, basal area, minimum and maximum diameters etc. Main results: The regression model using arithmetic mean diameter as an independent variable and the model using maximum diameter of the stand as an independent variable were found superior for estimation of scale and shape parameters, respectively. Highlights: While the Weibull distributions determined by both methods give close results, the method of determining the distribution parameters with the developed regression models seems to be superior in terms of examining the diameter distribution changes according to different stand structure simulations.