Continuous Spatial Domain Research Articles

Bayesian spatio-temporal statistical modeling of violent-related fatality in western and central Africa

Fatality arising from violent events is a critical public health problem in Africa. Although numerous studies on crime and violent events have been conducted, adequate attention has not been given to the distribution of fatalities arising from these events. This study unraveled the spatio-temporal pattern of fatality from violent events in Western and Central Africa. A two-component spatio-temporal zero-inflated model on a continuous spatial domain within a Bayesian framework was adopted. The stochastic partial differential equation was used to quantify the continuous pattern and make projections in unsampled regions. Fatality data from 1997 to 2021 was obtained from the Armed Conflict Location and Event Data Project (ACLED). Findings from the result revealed a spatial and temporal divide in the prevalence of fatality in the study region. Between the years 1997 and 2010, fatality from violence was most prevalent in Central Africa, whereas in more recent years, it was most prevalent in Western Africa. The posterior predictive probabilities of fatality occurrence due to violent events in Nigeria and Cameroon were highest and above 0.6, and the probability of more than one death per violent event is highest in Angola and Chad with probability 0.2. On violent event type, findings showed that suicide bombs had the highest likelihood of fatality occurrence whereas the event of violent non-state actors overtaking territory had the highest impact on the likelihood of multiple fatality counts. Among the armed actors who participated in violent events, armed religious groups were linked to the highest likelihood of fatality occurrence whereas Military forces were linked to the highest likelihood of multiple fatality counts per event. The finding also revealed that there is a higher likelihood of multiple fatalities in the Winter temperate season. These findings could be used for planning and policy design geared towards mitigating fatality and providing a guide towards resource distribution to support the affected communities.

Neural representations of cryo-EM maps and a graph-based interpretation

BackgroundAdvances in imagery at atomic and near-atomic resolution, such as cryogenic electron microscopy (cryo-EM), have led to an influx of high resolution images of proteins and other macromolecular structures to data banks worldwide. Producing a protein structure from the discrete voxel grid data of cryo-EM maps involves interpolation into the continuous spatial domain. We present a novel data format called the neural cryo-EM map, which is formed from a set of neural networks that accurately parameterize cryo-EM maps and provide native, spatially continuous data for density and gradient. As a case study of this data format, we create graph-based interpretations of high resolution experimental cryo-EM maps.ResultsNormalized cryo-EM map values interpolated using the non-linear neural cryo-EM format are more accurate, consistently scoring less than 0.01 mean absolute error, than a conventional tri-linear interpolation, which scores up to 0.12 mean absolute error. Our graph-based interpretations of 115 experimental cryo-EM maps from 1.15 to 4.0 Å resolution provide high coverage of the underlying amino acid residue locations, while accuracy of nodes is correlated with resolution. The nodes of graphs created from atomic resolution maps (higher than 1.6 Å) provide greater than 99% residue coverage as well as 85% full atomic coverage with a mean of 0.19 Å root mean squared deviation. Other graphs have a mean 84% residue coverage with less specificity of the nodes due to experimental noise and differences of density context at lower resolutions.ConclusionsThe fully continuous and differentiable nature of the neural cryo-EM map enables the adaptation of the voxel data to alternative data formats, such as a graph that characterizes the atomic locations of the underlying protein or macromolecular structure. Graphs created from atomic resolution maps are superior in finding atom locations and may serve as input to predictive residue classification and structure segmentation methods. This work may be generalized to transform any 3D grid-based data format into non-linear, continuous, and differentiable format for downstream geometric deep learning applications.

Super-resolution method for coherent DOA estimation of multiple wideband sources

We focus on coherent Direction Of Arrival (DOA) estimation of wideband sources based on spatial sparsity. By development of super-resolution algorithms, DOA estimation of narrowband sources has already been addressed based on gridless sparse algorithms and atomic norm minimization. In this paper, a super-resolution based method is proposed for coherent DOA estimation of multiple wideband sources. To do so, we first develop a new focusing method to map the subband with the largest center frequency to the other ones with no requirement for any initial estimates. Then, using the latter focusing method, we introduce an atomic norm problem by defining a new set of atoms and exploiting the signal joint sparsity of different frequency subbands in a continuous spatial domain. This problem is then cast as a semidefinite program, which leads to implementing a new coherent DOA estimation method with higher resolution and more robustness to noise. Our method only needs one single snapshot for each frequency subband, although it can also be used for multiple snapshots. Numerical simulations show the outperformance of the proposed method compared to the conventional ones.

A multi-resolution deep feature framework for dynamic displacement measurement of bridges using vision-based tracking system

Structural displacement is an imperative indicator for safety evaluation and maintenance. To address the limitations of conventional displacement sensors, advanced non-contact vision-based trackers offer a promising alternative. Based on the reconstructed Efficient Convolution Operator (ECO), a more powerful multi-resolution deep feature framework is proposed to efficiently encode the informative representation. The fusion of the shallow convolutional and the deep convolutional features is discriminative while preserving spatial and structural information. Furthermore, the discrete feature map is transferred to the continuous spatial domain by introducing an interpolation operator to achieve accurate sub-pixel registration. A careful comparison of the results on the steel suspension bridge demonstrates the high accuracy of the multi-resolution deep feature tracker (MDFT) for displacement measurement. The performances in the time and frequency domain show decent agreement with the results acquired by the laser displacement sensor (LDS), which confirm the low-cost, target-free, high resolution, and non-contact measurement capacities.

Optimal stock–enhancement of a spatially distributed renewable resource

We study the economic management of a renewable resource, the stock of which is spatially distributed and moves over a discrete or continuous spatial domain. In contrast to standard harvesting models where the agent can control the take-out from the stock, we consider the case of optimal stock enhancement. In other words, we model an agent who is, either because of ecological concerns or because of economic incentives, interested in the conservation and enhancement of the abundance of the resource, and who may foster its growth by some costly stock–enhancement activity (e.g., cultivation, breeding, fertilizing, or nourishment). By investigating the optimal control problem with infinite time horizon in both spatially discrete and spatially continuous (1D and 2D) domains, we show that the optimal stock–enhancement policy may feature spatially heterogeneous (or patterned) steady states. We numerically compute the global bifurcation structure and optimal time-dependent paths to govern the system from some initial state to a patterned optimal steady state. Our findings extend the previous results on patterned optimal control to a class of ecological systems with important ecological applications, such as the optimal design of restoration areas.

Method of information entropy for convergence assessment of molecular dynamics simulations

The lack of a reliable method to evaluate the convergence of molecular dynamics simulations has contributed to discrepancies in different areas of molecular dynamics. In the present work, the method of information entropy is introduced to molecular dynamics for stationarity assessment. The Shannon information entropy formalism is used to monitor the convergence of the atom motion to a steady state in a continuous spatial domain and is also used to assess the stationarity of calculated multidimensional fields such as the temperature field in a discrete spatial domain. It is demonstrated in this work that monitoring the information entropy of the atom position matrix provides a clear indicator of reaching steady state in radiation damage simulations, non-equilibrium molecular dynamics thermal conductivity computations, and simulations of Poiseuille and Couette flow in nanochannels. A main advantage of the present technique is that it is non-local and relies on fundamental quantities available in all molecular dynamics simulations. Unlike monitoring average temperature, the technique is applicable to simulations that conserve total energy such as reverse non-equilibrium molecular dynamics thermal conductivity computations and to simulations where energy dissipates through a boundary as in radiation damage simulations. The method is applied to simulations of iron using the Tersoff/ZBL splined potential, silicon using the Stillinger–Weber potential, and to Lennard–Jones fluid. Its applicability to both solids and fluids shows that the technique has potential for generalization to other areas in molecular dynamics.

Applications of the worldline Monte Carlo formalism in quantum mechanics

In recent years efficient algorithms have been developed for the numerical computation of relativistic single-particle path integrals in quantum field theory. Here, we adapt this “worldline Monte Carlo” approach to the standard problem of the numerical approximation of the non-relativistic path integral, resulting in a formalism whose characteristic feature is the fast, non-recursive generation of an ensemble of trajectories that is independent of the potential, and is thus universally applicable. The numerical implementation discretises the trajectories with respect to their time parametrisation but maintains a continuous spatial domain. In the case of singular potentials, the discretised action gets adapted to the singularity through a “smoothing” procedure. We show for a variety of examples (the harmonic oscillator in various dimensions, the modified Pöschl–Teller potential, delta-function potentials, the Coulomb and Yukawa potentials) that the method allows one to obtain fast and reliable estimates for the Euclidean propagator and use them in a certain time window suitable for extracting the ground state energy. Usually Monte Carlo calculations in quantum mechanics are performed using algorithms that involve a more specific adaptation to the potential, and we briefly compare our method with the most widely used such algorithms, which are of Metropolis type. As an aside, we apply it for studying the classical limit where nearly classical trajectories are expected to dominate in the path integral. We expect the advances made here to be useful also in the relativistic case.

Process modeling for slope and aspect with application to elevation data maps

Learning about the behavior of land surface gradients and, in particular, slope and aspect over a region from a dataset of levels obtained at a set of (possibly) irregularly spaced locations assumes importance in a variety of applications. A primary example considers digital terrain models for exploring roughness of land surfaces. In a geographic information system software package, gradient information is typically extracted from a digital elevation/terrain model (DEM/DTM), which usually presents the topography of the surface in terms of a set of pre-specified regular grid points, each with an assigned elevation value. That is, the DEM arises from preprocessing of an originally irregularly spaced set of elevation observations. Slope in one dimension is defined as “rise over run”. However, in two dimensions, at a given location, there is a rise over run in every direction. Then, the slope at the location is customarily taken as the maximum slope over all directions. It can be expressed as an angle whose tangent is the ratio of the rise to the run at the maximum. In practice, at each point of the grid, rise/run is obtained through comparison of the elevation at the point to that of a set of neighboring grid points, usually the eight compass neighbors, to find the maximum. Aspect is defined as the angular direction of maximum slope over the compass neighbors. We present a fully model-based approach for inference regarding slope and aspect. In particular, we define process versions of the slope and aspect over a continuous spatial domain. Modeling slopes takes us to directional derivative processes; modeling angles takes us to spatial processes for angular data. Using a stationary Gaussian process model for the elevation data, we obtain distribution theory for slope and associated aspect as well as covariance structure. Hierarchical models emerge; fitting in a Bayesian framework enables attachment of uncertainty. We illustrate with both a simulation example and a real data example using elevations from a collection of monitoring station locations in South Africa.

Linking otolith microchemistry and dendritic isoscapes to map heterogeneous production of fish across river basins.

Production patterns of highly mobile species, such as anadromous fish, often exhibit high spatial and temporal heterogeneity across landscapes. Such variability is often asynchronous in time among habitats, which stabilizes production at aggregate scales of complexity. Reconstructing production patterns explicitly in space and time across multiple scales, however, remains difficult but is important for prioritizing habitat conservation. This is especially true for fishes inhabiting river basins due to long-range dispersal, high mortality at early life stages, complex population structure and elusive life history variation. We develop a new approach for mapping production patterns of Pacific salmon across a large river basin by integrating otolith microchemistry and dendritic isoscape models. The geographically continuous Bayesian assignment framework presented here yielded high accuracies (>90%) and relatively high precisions (precisions <4%; i.e., assignment areas of <530 river km of the 13 100km total river length) when used to determine the natal source of known-origin juvenile Chinook salmon captured throughout the study region. Integrating these methods enabled us to base estimates of provenance and habitat use of individuals on a per location basis using strontium isotopic data throughout the continuous spatial domain of a river network. Such a framework provides substantial advantages over the more common nominal approach to employing otolith microchemistry to reconstruct movement patterns of fish. In doing so, we reconstructed the spatial production patterns of adult Chinook salmon returning to a large watershed in Bristol Bay, Alaska and illustrate the power of such an approach to conservation efforts.

Models for the spread of white pine blister rust

White pine blister rust (WPBR, Cronartium ribicola) is a fungal pathogen and a threat to whitebark pines (Pinus albicaulis). It has a complex life cycle that requires two hosts, a white pine and an alternate host, typically a currant or gooseberry (Ribes spp.). WPBR is transmitted between hosts by means of two types of airborne spores whose average dispersal distances differ by several orders of magnitude. In this paper, we introduce a discrete-time model based on the life cycle of WPBR. We then extend this model to include a continuous spatial domain, disease-induced mortality in the pines, and a latency period. After each extension, we find the pathogen׳s asymptotic speed of invasion analytically using exponential transforms and the method of steepest descent. Our results show that invasion speeds are strongly reduced by the latency period in the pine host. In addition, these speeds are highly dependent on the carrying capacity and infectiousness of each host type. If these parameters are sufficiently small, high mortality in pines may stop the spread of WPBR completely.

False Discovery Control in Large-Scale Spatial Multiple Testing.

This article develops a unified theoretical and computational framework for false discovery control in multiple testing of spatial signals. We consider both point-wise and cluster-wise spatial analyses, and derive oracle procedures which optimally control the false discovery rate, false discovery exceedance and false cluster rate, respectively. A data-driven finite approximation strategy is developed to mimic the oracle procedures on a continuous spatial domain. Our multiple testing procedures are asymptotically valid and can be effectively implemented using Bayesian computational algorithms for analysis of large spatial data sets. Numerical results show that the proposed procedures lead to more accurate error control and better power performance than conventional methods. We demonstrate our methods for analyzing the time trends in tropospheric ozone in eastern US.

The Nonlinear Heat Equation on Dense Graphs and Graph Limits

The continuum limit of coupled dynamical systems is an approximate procedure, by which the dynamical problem on a sequence of large graphs is replaced by an evolution integral equation on a continuous spatial domain. While this method has been widely used in the analysis of pattern formation in nonlocally coupled networks, its mathematical basis remained little understood. In this paper, we use the combination of ideas and results from the theory of graph limits and nonlinear evolution equations to provide a rigorous mathematical justification for taking the continuum limit and to extend this method to cover many complex networks, for which it has not been applied before. Specifically, for dynamical networks on convergent sequences of simple and weighted graphs, we prove convergence of solutions of the initial-value problems for discrete models to those of the limiting continuous equations. In addition, for sequences of simple graphs converging to \0, 1\-valued graphons, it is shown that the convergence r...

Range limits in spatially explicit models of quantitative traits

In an influential paper, Kirkpatrick and Barton (Am Nat 150:1-23 1997) presented a system of diffusive partial differential equations modeling the joint evolution of population density and the mean of a quantitative trait when the trait optimum varies over a continuous spatial domain. We present a stability theorem for steady states of a simplified version of the system, originally studied in Kirkpatrick and Barton (Am Nat 150:1-23 1997). We also present a derivation of the system.

Spatial methods for plot-based sampling of wildlife populations

Classical sampling methods can be used to estimate the mean of a finite or infinite population. Block kriging also estimates the mean, but of an infinite population in a continuous spatial domain. In this paper, I consider a finite population version of block kri- ging (FPBK) for plot-based sampling. The data are assumed to come from a spatial stochastic process. Minimizing mean-squared-prediction errors yields best linear unbiased predictions that are a finite population version of block kriging. FPBK has versions comparable to simple random sampling and stratified sampling, and includes the general linear model. This method has been tested for several years for moose surveys in Alaska, and an example is given where results are compared to stratified random sampling. In general, assuming a spatial model gives three main advantages over classical sampling: (1) FPBK is usually more precise than simple or stratified random sampling, (2) FPBK allows small area estimation, and (3) FPBK allows nonrandom sampling designs.

Residual-based specification of a hidden random field included in a hierarchical spatial model

A method for specifying a hidden random field (HRF) included in a hierarchical spatial model is proposed. In hierarchical models of interest the first stage describes, conditional on a realization of the HRF, a response variable which is observable on a continuous spatial domain; the second stage models the HRF which reflects unobserved spatial heterogeneity. The question which is investigated is how can the HRF be modeled, i.e. specified. The method developed to address this question is based on residuals obtained when the base model, i.e. the hierarchical model in which the HRF is assumed constant, is fitted to data. It is shown that the residuals are linked with the HRF, and the link is used to specify the HRF. The method is applied to simulated data in order to assess its performance, and then to real data on radionuclide concentrations on Rongelap Island.

Maximum likelihood parametric blur identification based on a continuous spatial domain model

A formulation for maximum-likelihood (ML) blur identification based on parametric modeling of the blur in the continuous spatial coordinates is proposed. Unlike previous ML blur identification methods based on discrete spatial domain blur models, this formulation makes it possible to find the ML estimate of the extent, as well as other parameters, of arbitrary point spread functions that admit a closed-form parametric description in the continuous coordinates. Experimental results are presented for the cases of 1-D uniform motion blur, 2-D out-of-focus blur, and 2-D truncated Gaussian blur at different signal-to-noise ratios.

An adaptive finite element technique for structural dynamic analysis

An adaptive finite element discretization technique, which utilizes specially derived Ritz vectors, is presented for solving structural dynamics problems. The special Ritz vectors are applied as the bases of transformation in geometric coordinates for mode superposition dynamic analysis. To capture the low frequency response and the high frequency response using multigrid principles, a hierarchical formulation for the formation of the coefficient matrices is proposed and it is utilized in the framework of the adaptive h-refinement. Assuming that the solution can be resolved into a set of orthogonal vectors and the refined mesh which passes the refinement criteria for all the vectors can satisfy the refinement criteria for the solution, the Ritz vectors are used as sources to discretize the continuous spatial domain. An a posteriori energy norm of residual error serves as the error measure. Finally, the performance and the efficiency of the proposed technique is demonstrated by solving several examples.