Continuous Spatial Representation Research Articles

A Deep Learning Framework for Satellite-Derived Surface PM2.5 Estimation: Enhancing Spatial Analysis in the United States

Abstract Monitoring fine particulate matter (PM2.5) is crucial for evaluating air quality and its effects on public health. However, the limited distribution of monitoring stations presents a challenge in accurately assessing air pollution, especially in areas distant from these stations. To address this challenge, our study introduces a two-step deep learning approach for estimating daily gap-free surface PM2.5 concentrations across the contiguous United States (CONUS) from 2018 to 2022, with a spatial resolution of 4 km. In the first phase, we employ a Depthwise-Partial Convolutional Neural Network (DW-PCNN) to fill gaps between surface PM2.5 stations, utilizing Aerosol Optical Depth (AOD) data from the Moderate Resolution Imaging Spectroradiometer (MODIS). In the second phase, we integrate the PM2.5 grids imputed by the DW-PCNN with meteorological and anthropogenic variables into a Deep Convolutional Neural Network (Deep-CNN) to further enhance the accuracy of our estimation. This enables us to estimate gap-free surface PM2.5 concentrations accurately, evidenced by a Pearson’s correlation coefficient (R) of 0.92 and an Index of Agreement (IOA) of 0.96 in ten-fold cross-validation. We also introduce a grid-based method for calculating PM2.5 Design Values (DV), providing a continuous spatial representation of PM2.5 DV that enhances the traditional station-based approach. Our grid-based DV representations offer a comprehensive perspective on air quality, facilitating more detailed analysis. Furthermore, our model's ability to provide spatiotemporally consistent, gap-free PM2.5 data addresses the issue of missing values, supporting health impact research, policy formulation, and the accuracy of environmental assessments.

The spatial representation of loudness in a timbre discrimination task.

When participants decide whether a presented tone is loud or soft they react faster to loud tones with a top-sided response key in comparison to a bottom-sided response key and vice versa for soft tones. This effect is comparable to the well-established horizontal Spatial-Numerical Association of Response Codes (SNARC) effect and is often referred to as Spatial-Musical Association of Response Codes (SMARC) effect for loudness. The SMARC effect for loudness is typically explained by the assumption of a spatial representation or by the polarity correspondence principle. Crucially, both theories differ in the prediction of the SMARC effect when loudness is task-irrelevant. Therefore, we investigated whether the SMARC effect still occurs in a timbre discrimination task: Participants (N = 36) heard a single tone and classified its timbre with vertically arranged response keys. Additionally, the tone's loudness level varied in six levels. In case of a spatial representation, the SMARC effect should still occur while in case of polarity corresponding principle, the effect should be absent. Results showed that the SMARC effect was still present and that the differences between top-sided and bottom-sided responses were a linear function of loudness level indicating a continuous spatial representation of loudness.

An Automatic Generalization Method for a Dense Road Network Area Considering Spatial Structural Features as Constraints

Road networks are the skeletal elements of topographic maps at different scales, and road selection is a prerequisite for implementing continuous multiscale spatial representations of road networks. The mesh-based approach is a common, advanced and powerful method for road selection in dense road areas in which small meshes are removed and road segments with the least importance in each mesh are eliminated. However, small meshes in a map can be classified into two types: aggregated small meshes and isolated small meshes. The number of the former is small, and that of the latter is large. Existing methods are generally applicable for the latter, and some or even most spatial characteristics will be lost when they are applied to the former; as a result, the road selection quality will be affected. Therefore, as a supplement to the mesh-based selection method, this paper proposed an automatic generalization method of dense road network areas (areas formed by aggregated small meshes) considering spatial structural features as constraints. First, the aggregated areas of small meshes were identified based on the number of adjoining small meshes, and the boundaries of aggregated areas are extracted and used as hard constraints during mesh elimination. Second, the starting meshes were redefined by simultaneously considering the edge features and mesh density of small meshes, and an ordinal elimination algorithm was proposed to eliminate the meshes in the stroke connection direction. Third, road selection was implemented by identifying the starting meshes and sequentially processing the related mesh pairs. This iterative process continued until all mesh densities of the newly formed meshes are beyond the threshold or the problem becomes a simple elimination problem involving two adjoining small meshes or one isolated small mesh. Finally, a 1:10,000 standard topographic road map for Jiangsu Province, China, was used for validation. The experimental results showed that in the aggregated areas with two small meshes, 31% of the areas obtained the same selection results by using the mesh-based method and the proposed method, and the remaining 69% obtained a more compact result with the proposed method. Moreover, for all aggregated areas with more than two small meshes, the spatial distribution structure of small meshes was preserved better by the proposed method.

Examination of hydrogen cross-feeders using a colonic microbiota model

BackgroundHydrogen cross-feeding microbes form a functionally important subset of the human colonic microbiota. The three major hydrogenotrophic functional groups of the colon: sulphate-reducing bacteria (SRB), methanogens and reductive acetogens, have been linked to wide ranging impacts on host physiology, health and wellbeing.ResultsAn existing mathematical model for microbial community growth and metabolism was combined with models for each of the three hydrogenotrophic functional groups. The model was further developed for application to the colonic environment via inclusion of responsive pH, host metabolite absorption and the inclusion of host mucins. Predictions of the model, using two existing metabolic parameter sets, were compared to experimental faecal culture datasets. Model accuracy varied between experiments and measured variables and was most successful in predicting the growth of high relative abundance functional groups, such as the Bacteroides, and short chain fatty acid (SCFA) production. Two versions of the colonic model were developed: one representing the colon with sequential compartments and one utilising a continuous spatial representation. When applied to the colonic environment, the model predicted pH dynamics within the ranges measured in vivo and SCFA ratios comparable to those in the literature. The continuous version of the model simulated relative abundances of microbial functional groups comparable to measured values, but predictions were sensitive to the metabolic parameter values used for each functional group. Sulphate availability was found to strongly influence hydrogenotroph activity in the continuous version of the model, correlating positively with SRB and sulphide concentration and negatively with methanogen concentration, but had no effect in the compartmentalised model version.ConclusionsAlthough the model predictions compared well to only some experimental measurements, the important features of the colon environment included make it a novel and useful contribution to modelling the colonic microbiota.

An elimination method for isolated meshes in a road network considering stroke edge feature

The road network is the skeletal element of topographic maps at different scales. In general, urban roads are connected by road segments, thus forming a series of road meshes. Mesh elimination is a key step in evaluating the importance of roads during the road network data management and a prerequisite to the implementation of continuous multiscale spatial representation of road networks. The existing mesh-based method is an advanced road elimination method whereby meshes with the largest density are sequentially selected and road segments with the least importance in each mesh are eliminated. However, the road connectivity and integrity may be destroyed in specific areas by this method because some eliminated road segments could be located in the middle of road strokes. Therefore, this paper proposed an elimination method for isolated meshes in a road network considering stroke edge feature. First, small meshes were identified by using mesh density thresholds, which can be obtained by the sample data statistical algorithm. Thereafter, the small meshes related to the edge segments of road strokes were taken out and defined as stroke edge meshes, and the remaining small meshes were defined as stroke non-edge meshes. Second, by computing the mesh density of all stroke edge meshes, the mesh with the largest density was selected as the starting mesh, and the least important edge segment in the mesh was eliminated. The difference between the existing mesh-based method and the proposed method is that the starting mesh is a stroke edge mesh, not any given small mesh, and the eliminated segment is just only one of edge segments of strokes not chosen from among all segments. Third, mesh elimination was implemented by iteratively processing the stroke edge meshes with the largest mesh density until all of them were eliminated and their mesh density exceeded the threshold. The stroke non-edge meshes were directly preserved. Finally, a 1:10,000 topographic road map of an area in Jiangsu Province of China was used for validation. The experimental results show that for all stroke non-edge meshes and 23% of the stroke edge meshes, compared to the mesh-based method, the road stroke connectivity and integrity of road strokes were better preserved by the proposed method, and the remaining 77% of the elimination results for the stroke edge meshes were the same under the two methods.

Warped Hypertime Representations for Long-Term Autonomy of Mobile Robots

This letter presents a novel method for introducing time into discrete and continuous spatial representations used in mobile robotics, by modeling long-term, pseudo-periodic variations caused by human activities or natural processes. Unlike previous approaches, the proposed method does not treat time and space separately, and its continuous nature respects both the temporal and spatial continuity of the modeled phenomena. The key idea is to extend the spatial model with a set of wrapped time dimensions that represent the periodicities of the observed events. By performing clustering over this extended representation, we obtain a model that allows the prediction of probabilistic distributions of future states and events in both discrete and continuous spatial representations. We apply the proposed algorithm to several long-term datasets acquired by mobile robots and show that the method enables a robot to predict future states of representations with different dimensions. The experiments further show that the method achieves more accurate predictions than the previous state of the art.

Distinct hippocampal-cortical memory representations for experiences associated with movement versus immobility.

While ongoing experience proceeds continuously, memories of past experience are often recalled as episodes with defined beginnings and ends. The neural mechanisms that lead to the formation of discrete episodes from the stream of neural activity patterns representing ongoing experience are unknown. To investigate these mechanisms, we recorded neural activity in the rat hippocampus and prefrontal cortex, structures critical for memory processes. We show that during spatial navigation, hippocampal CA1 place cells maintain a continuous spatial representation across different states of motion (movement and immobility). In contrast, during sharp-wave ripples (SWRs), when representations of experience are transiently reactivated from memory, movement- and immobility-associated activity patterns are most often reactivated separately. Concurrently, distinct hippocampal reactivations of movement- or immobility-associated representations are accompanied by distinct modulation patterns in prefrontal cortex. These findings demonstrate a continuous representation of ongoing experience can be separated into independently reactivated memory representations.

Assessing the performance of the independence method in modeling spatial extreme rainfall

Spatial statistical methods are often employed to improve precision when estimating marginal distributions of extreme rainfall. Methods such as max-stable and copula models parameterize the spatial dependence and provide a continuous spatial representation. Alternatively, the independence method can be used to estimate marginal parameters without the need for parameterizing the spatial dependence, and this method has been under-utilized in hydrologic applications. This paper investigates the effectiveness of the independence method for marginal parameter estimation of spatially dependent extremes. Its performance is compared with three spatial dependence models (max-stable Brown-Resnick, max-stable Schlather, and Gaussian copula) by means of a simulation study. The independence method is statistically robust in estimating parameters and their associated confidence intervals for spatial extremes with various underlying dependence structures. The spatial dependence models perform comparably with the independence method when the spatial dependence structure is correctly specified; otherwise they exhibit considerably worse performance. We conclude that the independence method is more appealing for modeling the marginal distributions of spatial extremes (e.g., regional estimation of trends in rainfall extremes) due to its greater robustness and simplicity. The four statistical methods are illustrated using a spatial data set comprising 69 subdaily rainfall series from the Greater Sydney region, Australia.

Modelling total evacuation strategies for high-rise buildings

This paper focuses on the use of egress models to assess the optimal strategy in the case of total evacuation in high-rise buildings. The model case study consists of two identical twin towers linked with two sky-bridges at different heights. Each tower is a 50-floor office building. The use of either horizontal or vertical egress components or a combination of them is simulated. The egress components under consideration are stairs (either 2 or 3 stairs), occupant evacuation elevators, service elevators (available or not for the evacuation of the occupants), transfer floors and sky-bridges. Seven different evacuation strategies have been tested which consider the total evacuation of a single tower. The evacuation scenarios have been simulated with a continuous spatial representation evacuation model (Pathfinder). In order to perform a cross validation of the model results, two strategies involving the evacuation using stairs or occupant evacuation elevators have also been simulated using a fine network model (STEPS). Results refer to the analysis of total evacuation times. The simulation work highlights the assumptions required to represent the possible behaviours of the occupants in order to qualitatively rank the strategies. The lowest evacuation times are obtained simulating strategies involving the sole use of occupant evacuation elevators and the combined use of transfer floors and sky-bridges. This study suggests that the effectiveness of evacuation strategies involving the combination of stairs and elevators significantly decreases in high-rise buildings if they are not combined with appropriate messaging/signage to guide occupants in their behaviours.

Modelización espacialmente distribuida de la erosión y el transporte de sedimento en cuencas de montaña del Pirineo aragonés: retos para la calibración y validación

Most erosion models applied at basin scale are based on spatially aggregated representation, for example, in a space subdivision of the surfaces to which behavior is assumed homogeneous (sub-basins, hydrological units, etc.). This approach leads to a desirable simplification of the calculations, but presents difficulties in addressing problems related to sediment transport and identification of sediment source areas, which should be treated by a continuous spatial representation. Spatially distributed models, however, allow a more accurate approach to this problem, at the cost of an increased computational complexity. The objective of this work is the calibration and validation of the model WATEM/SEDEM, an empirical-conceptual spatially distributed model, to predict erosion and sediment yield in two watersheds in the Central Spanish Pyrenees: i) the watershed of the Barasona Reservoir (1504 km2), which is drained by the Ésera and Isábena Rivers, the model calibration and validation was based on the depositional history of the Barasona Reservoir and suspended sediment records over 3 years (May 2005–May 2008) at the outlet of the Isábena River; ii) the experimental Arnás catchment (2.84 km2), the model calibration was performed based on a dataset of soil redistribution rates derived from point 137Cs inventories, allowing capture differences per land use in the main model parameters. The validation process was carried with the registration of six years of suspended sediment at the outlet of the Arnás catchment. The calibration process for watershed of the Barasona Reservoir showed the problem you have when trying to calibrate the parameters of transport capacity with a single variable (the export of sediment to the basin outlet), making impossible to find a single set of parameters that optimize the error function, making it necessary to adopt a compromise solution. For the experimental Arnás catchment the model calibration processes using spatially distributed sediment yield derived from 137Cs inventories allowed calibrating the empirical parameters of transport capacity in a satisfactory way, finding a single combination of values that optimizes the error function. These results show that the calibration parameters of transport capacity are a fundamental aspect of the model WATEM/SEDEM and other similar models. To obtain a reliable estimate of the spatial distribution of erosion and sediment transport requires a calibration and validation by means of spatially distributed data of soil loss, which in turn allows a calibration of spatially distributed parameters concerning transport capacity

Mixed convolved action

A stationary principle is developed for dynamical systems by formulating the concept of mixed convolved action, which is written in terms of displacement and force variables, using temporal convolutions and fractional derivatives. The classical canonical single-degree-of-freedom dynamical system is considered as an initial application. With this new formulation, a single real scalar functional provides the governing differential equations, along with all the pertinent initial conditions, as the Euler-Lagrange equations emanating from the stationarity of the mixed convolved action. Both conservative and non-conservative processes can be considered within a common framework, thus resolving a long-standing limitation of variational approaches for dynamical systems. Several results in fractional calculus also are developed.

Integration of linear and areal hierarchies for continuous multi-scale representation of road networks

Spatial data can be represented at different scales, and this leads to the issue of multi-scale spatial representation. Multi-scale spatial representation has been widely applied to online mapping products (e.g., Google Maps and Yahoo Maps). However, in most current products, multi-scale representation can only be achieved through a series of maps at fixed scales, resulting in a discontinuity (i.e., with jumps) in the transformation between scales and a mismatch between the available scales and users' desired scales. Therefore, it is very desirable to achieve smoothly continuous multi-scale spatial representations. This article describes an integrated approach to build a hierarchical structure of a road network for continuous multi-scale representation purposes, especially continuous selective omission of roads in a network. In this hierarchical structure, the linear and areal hierarchies are constructed, respectively, using two existing approaches for the linear and areal patterns in a road network. Continuous multi-scale representation of a road network can be achieved by searching in these hierarchies. This approach is validated by applying it to two study areas, and the results are evaluated by both quantitative analysis with two measures (i.e., similarity and average connectivity) and visual inspection. Experimental results show that this integrated approach performs better than existing approaches, especially in terms of preservation of connectivity and patterns of a road network. With this approach, efficient and continuous multi-scale selective omission of road networks becomes feasible.

Spatial analysis of binary health indicators with local smoothing techniques: The Viadana study

IntroductionWhen pollution data from a monitoring network is not available, mapping the spatial distribution of disease can be useful to identify populations at risk and to suggest a potential role for suspected emission sources. We aimed at obtaining a continuous spatial representation of the prevalence of symptoms that are potentially associated with the exposure to the pollutants emitted from the wood factories in the children who live in the district of Viadana (Northern Italy). MethodsIn 2006, all the parents of the children aged 3–14years residing in the Viadana district (n=3854), filled in a questionnaire on respiratory symptoms, irritation symptoms of the eyes and skin, use of health services. The children's residential addresses were also collected and geocoded. Generalized additive models and local weighted regression (LOWESS) were used to estimate the distribution of the symptoms, to test for spatial trends of the symptoms' prevalence and to control for potential confounders. Permutation tests were used to identify the areas of significantly increased risk (“hot spots”). ResultsThe prevalence of respiratory symptoms, eye symptoms and the use of health services showed a statistically significant spatial variation (p<0.05), but skin symptoms did not. Symptoms' prevalence was lower in the northern part of the district, where no wood factories were present, and it was higher in the southern part, where the two big chipboard industries were located. Hot spots were identified fairly near to one of the two chipboard industries in the district. ConclusionsThe north-to-south trend in the prevalence of respiratory and eye symptoms, but not of skin symptoms, as well as the location of hot spots, are consistent with the potential exposure to air pollutants both emitted by the wood factories and related to traffic. In these “high risk areas” monitoring of pollution and preventive actions are clearly needed.

Continuous spatial representations in the olfactory bulb may reflect perceptual categories

In sensory processing of odors, the olfactory bulb is an important relay station, where odor representations are noise-filtered, sharpened, and possibly re-organized. An organization by perceptual qualities has been found previously in the piriform cortex, however several recent studies indicate that the olfactory bulb code reflects behaviorally relevant dimensions spatially as well as at the population level. We apply a statistical analysis on 2-deoxyglucose images, taken over the entire bulb of glomerular layer of the rat, in order to see how the recognition of odors in the nose is translated into a map of odor quality in the brain. We first confirm previous studies that the first principal component could be related to pleasantness, however the next higher principal components are not directly clear. We then find mostly continuous spatial representations for perceptual categories. We compare the space spanned by spatial and population codes to human reports of perceptual similarity between odors and our results suggest that perceptual categories could be already embedded in glomerular activations and that spatial representations give a better match than population codes. This suggests that human and rat perceptual dimensions of odorant coding are related and indicates that perceptual qualities could be represented as continuous spatial codes of the olfactory bulb glomerulus population.

High-order Finite Volume Methods and Multiresolution Reproducing Kernels

This paper presents a review of some of the most successful higher-order numerical schemes for the compressible Navier-Stokes equations on unstructured grids. A suitable candidate scheme would need to be able to handle potentially discontinuous flows, arising from the predominantly hyperbolic character of the equations, and at the same time be well suited for elliptic problems, in order to deal with the viscous terms. Within this context, we explore the performance of Moving Least-Squares (MLS) approximations in the construction of higher order finite volume schemes on unstructured grids. The scope of the application of MLS is threefold: 1) computation of high order derivatives of the field variables for a Godunov-type approach to hyperbolic problems or terms of hyperbolic character, 2) direct reconstruction of the fluxes at cell edges, for elliptic problems or terms of elliptic character, and 3) multiresolution shock detection and selective limiting. The proposed finite volume method is formulated within a continuous spatial representation framework, provided by the MLS approximants, which is “broken” locally (inside each cell) into piecewise polynomial expansions, in order to make use of the specialized finite volume technology for hyperbolic problems. This approach is in contrast with the usual practice in the finite volume literature, which proceeds bottom-up, starting from a piecewise constant spatial representation. Accuracy tests show that the proposed method achieves the expected convergence rates. Representative simulations show that the methodology is applicable to problems of engineering interest, and very competitive when compared to other existing procedures.

Microclimatic variation of thermal comfort in a district of Lisbon (Telheiras) at night

The microclimatic spatial variation of air temperature, wind speed, radiative fluxes and Physiological Equivalent Temperature (PET) was studied in Telheiras, a northern district of the city of Lisbon. The main goal was to assess how to improve outdoor thermal conditions based on research results. An empirical model was developed to estimate PET in Telheiras under different weather types; the model allows the continuous spatial representation of PET, using a Geographical Information System (GIS) and can be used in other areas of Lisbon. Although there is a small microclimatic variation in air temperature, the PET presents a much stronger variation, due to the influence of wind and radiative fluxes. Urban geometry, expressed by the Sky View Factor (SVF), is the main factor controlling the microclimatic diversity of the neighbourhood. The coolest conditions occur in open areas (centre of large courtyards and marginal areas) and the warmest in streets with low SVF that are sheltered from the wind.

Modeling Rail Fatigue Behavior with Multiple Hazards

Derailments can be caused by rail fatigue failures, which are of great concern to railroad companies. These companies, therefore, have as an objective to predict the locations and times of potential failures and to perform preventive maintenance. Understanding the relationship between fatigue failures and factors affecting fatigue is essential to estimate when and where rail fatigue failures will occur. This paper presents a statistical rail fatigue model in four stages: 1) the model describes the relationship between probability of failure and usage; 2) the model extends to cases of multiple types of failures; 3) the model is derived for discrete usage categories or time intervals with a continuous spatial representation of rail units; and 4) explanatory variables capturing geometry, maintenance, and material properties are included to explain differences in fatigue behavior among heterogeneous rail units. Using available rail fatigue data, the model is estimated. The modeling framework is useful for other multitype failure behavior and for reliability problems, such as vehicle breakdown.

Scaling Sociomatrices by Optimizing an Explicit Function: Correspondence Analysis of Binary Single Response Sociomatrices.

Most methods for detecting structure in sociometric data involve either continuous spatial representations (e.g. MDS) or discrete hierarchical clustering analysis (e.g. CONCOR). By producing either spatial or clustering representations, these methods can highlight only some of the theoretically interesting group structures. Correspondence analysis, in contrast, can provide either spatial or clustering representations by assigning spatial coordinates to minimize the distance between individuals linked by a sociometric relationship. These scales may then be used to identify individuals' locations in a multidimensional representation of a group's structure or to reorder the rows and columns of a sociomatrix. Unlike many other methods of sociometric analysis, the numerical methods of correspondence analysis also are well understood and the optimization of the goodness-of-fit measure allows an evaluation of a particular model of group structure.

Indclus: An individual differences generalization of the adclus model and the mapclus algorithm

We present a new model and associated algorithm, INDCLUS, that generalizes the Shepard-Arabie ADCLUS (ADditive CLUStering) model and the MAPCLUS algorithm, so as to represent in a clustering solution individual differences among subjects or other sources of data. Like MAPCLUS, the INDCLUS generalization utilizes an alternating least squares method combined with a mathematical programming optimization procedure based on a penalty function approach to impose discrete (0,1) constraints on parameters defining cluster membership. All subjects in an INDCLUS analysis are assumed to have a common set of clusters, which are differentially weighted by subjects in order to portray individual differences. As such, INDCLUS provides a (discrete) clustering counterpart to the Carroll-Chang INDSCAL model for (continuous) spatial representations. Finally, we consider possible generalizations of the INDCLUS model and algorithm.

GEOGRAPHIC POTENTIALS∗

ABSTRACT The total differential is a measure of the influence of one place on another in a discrete spatial representation of a dynamic system. This is equal to the total direct and indirect interaction between two places. For a continuous spatial representation, potential theory is a measure of influence, and has an identical interpretation. Potential thus represents a consistent and unifying definition of influence, requiring no analogy from social physics. Some of the many possibilities for application include: providing an interpretation of accessibility, constructing spatial multipliers, developing a model of commodity flows, and formulating the spatial dimension of temporal processes.