Diagonal Neighbors Research Articles

Magnetic monopole free motion in two-dimensional artificial spin ice

Magnetic monopole motion (without its partner in a pair) as a function of external magnetic fields is presented as a fingerprint of freedom of these emergent quasi-particles in a two-dimensional artificial spin ice material. Such freedom, required, for example, for further application in magnetricity, is only possible due to ground-state degeneracy, which causes an anisotropic string energy reduction in rectangular ice geometries, designed to allow highest equidistance among lateral and diagonal neighbor nanomagnets. By measurements of magnetic force microscopy, we observe magnetic monopole creation, transport, and annihilation in such an arrangement, where monopoles are free to move throughout large regions of the sample, since they are not permanently bound by the string bonds, as commonly observed in conventional artificial spin ice systems. Instead, monopoles leave a wake of elongated tensionless string, which is connected to superficial charges or charges pinned to the array borders.

Self-organization of channels and hillslopes in models of fluvial landform evolution and its potential for solving scaling issues

Abstract. Including hillslope processes in models of fluvial landform evolution is still challenging. Since applying the respective models for fluvial and hillslope processes to the entire domain causes scaling problems and makes the results dependent on the spatial resolution, the domain is explicitly subdivided into channels and hillslopes in some models. The transition from hillslopes to channels is typically attributed to a given threshold catchment size as a proxy for a minimum required discharge. Here we propose a complementary approach for delineating channels based on the discrete representation of the topography. We assume that sites with only one lower neighbor are channelized. In combination with a suitable model for hillslope processes, this concept initiates the self-organization of channels and hillslopes. A numerical analysis with a simple model for hillslope dynamics reveals no scaling issues, so the results appear to be independent of the spatial resolution. The approach predicts a break in slope in the sense that all channels are distinctly less steep than hillslopes. On a regular lattice, the simple D8 flow-routing scheme (steepest descent among the eight nearest and diagonal neighbors) harmonizes well with the concept proposed here. The D8 scheme works well even when applied to the hillslopes. This property simplifies the numerical implementation and increases its efficiency.

A Framework to Create a Deep Learning Detector from a Small Dataset: A Case of Parawood Pith Estimation

A deep learning-based object detector has been successfully applied to all application areas. It has high immunity to variations in illumination and deviations among objects. One weakness of the detector is that it requires a huge, undefinable dataset for training the detector to avoid overtraining and make it deployable. This research proposes a framework to create a deep learning-based object detector with a limited-sized dataset. The framework is based on training the detector with the regions surrounding an object that typically contain various features over a more extensive area than the object itself. Our proposed algorithm further post-processes the detection results to identify the object. The framework is applied to the problem of wood pith approximation. The YOLO v3 framework was employed to create the detector with all default hyperparameters based on the transfer learning approach. A wood pith dataset with only 150 images is used to create the detector with a ratio between training to testing of 90:10. Several experiments were performed to compare the detection results from different approaches to preparing the regions surrounding a pith, i.e., all regions, only close neighbors, and only diagonal neighbors around a pith. The best experiment result shows that the framework outperforms the typical approach to create the detector with approximately twice the detection precision at a relative average error. Doi: 10.28991/ESJ-2023-07-01-017 Full Text: PDF

Local neighborhood gradient pattern: A feature descriptor for content based image retrieval

Local feature descriptors are efficient encoders for capturing repeated local patterns in many of the computer vision applications. Majority of such descriptors consider only limited local neighborhood pixels to encode a pattern. One of the major issues while considering more number of neighborhood pixels is that it increases the dimensionality of the feature descriptor. The proposed descriptor addresses these issues by describing an effective encoding pattern with optimal feature vector length. In this paper, we have proposed Local Neighborhood Gradient Pattern (LNGP) for Content-Based Image Retrieval (CBIR) in which the relationship between a set of neighbours and the centre pixel is considered to obtain a compact 8-bit pattern in the respective pixel position. The relationship of the gradient information of immediate, next-immediate, and diagonal neighbours with the centre pixel is considered for pattern formation, and thus the local information based on pixels in three directions are captured. The experiments are conducted on benchmarked image retrieval datasets such as Wang’s 1K, Corel 5K, Corel 10K, Salzburg (Stex), MIT-Vistex, AT & T, and FEI datasets and it is observed that the proposed descriptor yields average precision of 71.88%, 54.57%, 40.66%, 71.85%, 86.12%, 82.54%, and 68.54% respectively in the mentioned datasets. The comparative analysis of the recent descriptors indicates that the proposed descriptor performs efficiently in CBIR applications.

Optimal surface-tension isotropy in the Rothman-Keller color-gradient lattice Boltzmann method for multiphase flow.

The Rothman-Keller color-gradient (CG) lattice Boltzmann method is a popular method to simulate two-phase flow because of its ability to deal with fluids with large viscosity contrasts and a wide range of interfacial tensions. Two fluids are labeled red and blue, and the gradient in the color difference is used to compute the effect of interfacial tension. It is well known that finite-difference errors in the color-gradient calculation lead to anisotropy of interfacial tension and errors such as spurious currents. Here, we investigate the accuracy of the CG calculation for interfaces between fluids with several radii of curvature and find that the standard CG calculations lead to significant inaccuracy. Specifically, we observe significant anisotropy of the color gradient of order 7% for high curvature of an interface such as when a pinchout occurs. We derive a second order accurate color gradient and find that the diagonal nearest neighbors can be weighted differently than in the usual color-gradient calculation such that anisotropy is minimized to a fraction of a percent. The optimal weights that minimize anisotropy for the smallest radius of curvature interface are found to be w=(0.298,0.284,0.275) for diagonal nearest neighbors for the cases of the interface smoothing parameter β=(0.5,0.7,0.99), somewhat higher than the w=0.25 value derived by Leclaire etal. [Leclaire, Reggio, and Trepanier, Computers and Fluids 48, 98 (2011)CPFLBI0045-793010.1016/j.compfluid.2011.04.001] based on obtaining isotropic errors to second order. We find that use of these optimal w values yields over a factor of 10 decrease in anisotropy and over a factor of 30 decrease in mean anisotropy relative to using the standard w=1 value. And we find a factor of about 2 decrease in the anisotropic error and up to factor 15 decrease in mean anisotropic error relative to the choice of w=0.25 for small radius of curvature interfaces. The improved CG calculations will allow the method to be more reliably applied to studies of phenomenology and pore scale processes such as viscous and capillary fingering, and droplet formation where surface-tension isotropy of narrow fingers and small droplets plays a crucial role in correctly capturing phenomenology. We present an example illustrating how different phenomena can be captured using the improved color-gradient method. Namely, we present simulations of a wetting fluid invading a fluid filled pipe where the viscosity ratio of fluids is unity in which droplets form at the transition to fingering using the improved CG calculations that are not captured using the standard CG calculations. We present an explanation of why this is so which relates to anisotropy of the surface tension, which inhibits the pinchouts needed to form droplets.

A novel approach for facial expression recognition using local binary pattern with adaptive window

Facial Expression Recognition (FER) is an important area in human computer interaction. FER has different applications such as analysis of student behaviour in virtual class room, driver mood detection, security systems, and medicine. The analysis of facial expressions is an interesting and exciting problem. Feature extraction plays important role in any FER system. Local Binary Pattern (LBP) and its variants are popular for feature extraction due to simplicity in computation and monotonic illumination invariant property. However, the performance of LBP is poor in the presence of noise. This work proposes a novel approach for feature extraction to improve the performance of the FER. In this approach, the LBP is calculated considering 4-neighbors and diagonal neighbours separately. Further, for affective feature description, the concept of adaptive window and averaging in radial directions is introduced. This approach reduces the length of the feature vector as well as immune to noise. Support Vector Machine (SVM) is considered for classification. Recognition rate and confusion matrix are used to assess the performance of the proposed algorithm. Extensive experimental results on JAFFE, CK, FERG and FEI face databases show significant improvement in recognition rate compared to the available techniques both in noise free and noisy conditions.

Performance of Predictive Coders for Wireless Capsule Endoscopy Image Compression

Wireless capsule endoscopy is a medical diagnostic technique developed for the endoscopic examination of the small bowel. The encoder module is the core of the wireless capsule endoscopic system impacting on power and area requirement for the hardware implementation of the capsule. One of the remarkable features of the endoscopic image is that the neighboring pixels are highly correlated. Two predictive coding techniques are considered in this work exploiting the above fact. The first predictive coder i.e., DPCM coder is based on previous horizontal neighboring pixel, whereas the second predictive coder is based on adjacent horizontal and diagonal neighbors. The performance of the predictive coders is tested with 41 small bowel type endoscopic images available in the Gastrolab dataset. The results show that the average compression rate and peak signal to noise ratio attained by DPCM coder and newly tested predictive coder are 66.37 % & 73.03 % and 32.17 dB & 35.55 dB, respectively.

Thermal Crosstalk Measurements and Simulations for an X-ray Microcalorimeter Array

Arrays of high-density microcalorimeters require careful heat sinking in order to minimize the thermal crosstalk between nearby pixels. For the array of microcalorimeters developed for the Athena X-ray Integral Field Unit instrument, which has more than 3000 pixels on a 275 µm pitch, it is essential to address this problem in order to meet the energy-resolution requirements. The instrument’s energy-resolution budget requires that the impact of the thermal crosstalk on the energy resolution be a contribution that, added in quadrature to other energy-resolution contributions, is less than 0.2 eV. This value results in a derived requirement that the ratio between the amplitude of the crosstalk signal to an X-ray pulse (for example at 6 keV) is less than 1 × 10−3 (for the first neighbor), less than 4 × 10−4 (for the diagonal neighbor) and less than 8 × 10−5 (for the second nearest neighbor). We have measured the thermal crosstalk levels between pixels in various geometries and configurations. The results show a crosstalk ratio which is at least a factor of 4 lower than the derived requirement. We also developed a finite element (FEM) 2D thermal model to predict the thermal behavior of large-scale arrays. This model successfully simulates the measured data in terms of pulse amplitude and time constants.

Asymptotic analysis of breather modes in a two-dimensional mechanical lattice

We consider a two-dimensional square lattice in which each node is restricted to the plane of the lattice, but is permitted to move in both directions of the lattice. We assume nodes are connected to nearest neighbours along the lattice directions with nonlinear springs, and to diagonal neighbours with linear springs. We consider a generalised Klein–Gordon system, that is, where there is an onsite potential at each node in addition to the (nonlinear) nearest-neighbour interactions. We derive the equations of motion for the displacements from the Hamiltonian. We use asymptotic techniques to derive the form of small amplitude breather solutions, and find necessary conditions required for their existence. We find two types of mode, which we term ‘optical’ and ‘acoustic’, based on the analysis of other lattices which support dispersion relations with multiple branches. In addition to the usual inequality on the sign of the nonlinearity in order for the NLS to be of the focusing type, we obtain an additional ellipticity constraint, that is a restriction in the two-dimensional wavenumber space, required for the spatial differential operator to be elliptic.

Elliptical local binary co-occurrence pattern for face image retrieval

Face image retrieval is considered as an active research field in computer vision. This paper describes a novel feature descriptor called elliptical local binary co-occurrence pattern (ELBCoP) for face image retrieval. This descriptor employs a combination of sparse elliptical local binary pattern (ELBP) and grey level co-occurrence matrix (GLCM). Unlike previous approaches, the sparse ELBP consider only 4 horizontal and 4 vertical neighbors from the elliptic shaped neighborhood, and uses 4 simple diagonal neighbors. Then the co-occurrence of pixel pairs, in the three local pattern maps obtained using sparse ELBP, are calculated using GLCM in two selected directions. These two directions of GLCM are selected according to the shape of the elliptic neighborhood. Through GLCM, the proposed ELBCoP extracts the frequency details and also the spatial relationship between the local pattern pairs very effectively. It is also shown that a properly selected subset of ELBCoP can still provide a robust and efficient description of face images, with significant reduction in feature vector dimensions. Experimental results on two benchmark face image databases show superior retrieval performance of ELBCoP and also subset of ELBCoP, when compared to various state of the art methods including a few very recent ones.

Medical image rigid registration using a novel binary feature descriptor and modified affine transform

Robust and reliable features with noise immunity, rotation-invariance, and low-dimensionality are the challenging aspects of pattern recognition. In this study, the authors presented a novel low-dimensional binary feature descriptor local diagonal Laplacian pattern (LDLP) for medical image registration. LDLP method is developed by defining the local relationship between a centre pixel and its diagonal neighbours and encoding it to a binary feature vector. The idea of centre-diagonal pixel correlation has drastically reduced the length of the feature vector without compromising the quality of local texture analysis. In the proposed work, first, the LDLP feature histograms of computed tomography (CT), magnetic resonance (MR), and ultrasound images are obtained. Further, these LDLP features of individual medical images are considered as target/fixed objects while their corresponding rotated and noisy features are considered as moving/floating objects to perform mono-modal rigid registration using an improved Procrustes analysis-based affine transform. The registration quality is examined by calculating the squared intensity error and the results are compared with the existing binary patterns such as local binary patterns, local tetra patterns, and local diagonal extrema patterns. The proposed LDLP feature descriptor-based rigid registration has attained relatively better performance in terms of registration accuracy and computational complexity.

Local diagonal extrema number pattern: A new feature descriptor for face recognition

This paper proposes a simple and novel feature descriptor for face recognition called local diagonal extrema number pattern (LDENP). LDENP produces a compact code of facial features which is obtained by encoding the directional information of the face image. Further, LDENP micro-patterns are created using values and indices of the local diagonal extremas (i.e. minima and maxima) using first order local diagonal derivatives that extract the directional information. Moreover, the proposed algorithm partitions the face into several regions to facilitate extraction of features from each region individually. Consequently, the extracted features are concatenated into a single feature vector which is used as a face descriptor. In this work, only the diagonal neighbours are considered, hence, the dimension of the feature, and the computation time to recognize the face are reduced. Therefore, the curse of dimensionality problem is solved. Experimental results are carried out on standard benchmark databases like FERET, Extended YALE-B, ORL and LFW-a. Moreover, efficiency of LDENP descriptor is asserted by comparing recognition rates of the proposed method with other existing local-descriptor based methods.

RVB states in doped band insulators from Coulomb forces: theory and a case study of superconductivity in BiS2 layers

Doped band insulators, HfNCl, WO3, diamond, Bi2Se3, BiS2 families, STO/LAO interface, gate doped SrTiO3, MoS2 and so on are unusual superconductors. With an aim to build a general theory for superconductivity in doped band insulators, we focus on the BiS2 family which was discovered by Mizuguchi et al in 2012. While maximum Tc is only ∼11 K in , a number of experimental results are puzzling and anomalous in the sense that they resemble high Tc and unconventional superconductors. Using a two orbital model of Usui, Suzuki and Kuroki, we show that the uniform low density free Fermi sea in is unstable towards formation of the next nearest neighbor Bi-S-Bi diagonal valence bond (charged −2e Cooper pair) and their Wigner crystallization. Instability to this novel state of matter is caused by unscreened nearest neighbor coulomb repulsions (V ∼ 1 eV) and a hopping pattern with sulfur mediated diagonal next nearest neighbor Bi-S-Bi hopping t’ ∼ 0.88 eV, as well as larger than nearest neighbor Bi-Bi hopping, t ∼ 0.16 eV. Wigner crystals of Cooper pairs quantum melt for doping around x = 0.5 and stabilize certain resonating valence bond states and superconductivity. We study a few variational RVB states and suggest that BiS2 family members are latent high Tc superconductors, but challenged by competing orders and the fragile nature of many body states sustained by unscreened Coulomb forces. One of our superconducting states has dXY symmetry and a gap. We also predict a 2d Bose metal or vortex liquid normal state, as charged −2e valence bonds survive in the normal state.

Root Activity Distribution and Inter-plant Root Competition in 'Robusta' Banana (Musa Sp., 'AAA') under High-Density Planting Determined by Tracer Technique

By applying soil injection technique using carrier-free 32P as a tracer in 'Robusta' banana (Musa sp. 'AAA') planted at 1.5m x 1.5m spacing, during the 8th leaf stage of growth, 52.04 and 62.96% of active roots were present at 25cm across and 15cm depth, respectively. At the 16th leaf stage, only 40.5% of active roots were traced at 25cm across, and root activity increased at wider distances and deeper layers. At flower-initiation stage, a significant gain in root activity was seen at 45cm depth. Distance-wise distribution, however, did not change appreciably. At the shooting stage, 46.89% and 43.98% of the active roots were present closest to the pseudostem (25cm distance) and soil surface (15cm), respectively. However, the greatest depth (45cm) gained active roots (38.51%) at shooting-stage, creating an hour-glass pattern of root distribution, mainly owing to migration of roots from the surface (15cm deep) soil. However, a strong presence of active roots persisted close to the base of the plant, and in the surface-soil. A small proportion (>1%) of phosphorus applied to the main plant was absorbed by the orthogonal neighbour located at 1.5m distance, indicating practically insignificant competition with its closest neighbour. None of the diagonal neighbours located farthest (at 2.1m distance from the main plant) showed any activity of the tracer indicating that the root competition with the main plant was absent. Results indicate that a spacing of 1.5m × 1.5m in high-density planting of 'Robusta' banana raised in sandy-loam is optimum, with practically no untoward competition from the root for nutrients applied to each plant.

Local Diagonal Extrema Pattern: A New and Efficient Feature Descriptor for CT Image Retrieval

The medical image retrieval plays an important role in medical diagnosis where a physician can retrieve most similar images from template images against a query image of a particular patient. In this letter, a new and efficient image features descriptor based on the local diagonal extrema pattern (LDEP) is proposed for CT image retrieval. The proposed approach finds the values and indexes of the local diagonal extremas to exploit the relationship among the diagonal neighbors of any center pixel of the image using first-order local diagonal derivatives. The intensity values of the local diagonal extremas are compared with the intensity value of the center pixel to utilize the relationship of central pixel with its neighbors. Finally, the descriptor is formed on the basis of the indexes and comparison of center pixel and local diagonal extremas. The consideration of only diagonal neighbors greatly reduces the dimension of the feature vector which speeds up the image retrieval task and solves the “Curse of dimensionality” problem also. The LDEP is tested for CT image retrieval over Emphysema-CT and NEMA-CT databases and compared with the existing approaches. The superiority in terms of performance and efficiency in terms of speedup of the proposed method are confirmed by the experiments.

Data Processing for a High Resolution Preclinical PET Detector Based on Philips DPC Digital SiPMs

In positron emission tomography (PET) systems, light sharing techniques are commonly used to readout scintillator arrays consisting of scintillation elements, which are smaller than the optical sensors. The scintillating element is then identified evaluating the signal heights in the readout channels using statistical algorithms, the center of gravity (COG) algorithm being the simplest and mostly used one. We propose a COG algorithm with a fixed number of input channels in order to guarantee a stable calculation of the position. The algorithm is implemented and tested with the raw detector data obtained with the Hyperion-II $^{\rm D}$ preclinical PET insert which uses Philips Digital Photon Counting’s (PDPC) digitial SiPMs. The gamma detectors use LYSO scintillator arrays with $30 \times 30$ crystals of $1 \times 1 \times 12~\hbox{mm}^3$ in size coupled to $4 \times 4$ PDPC DPC 3200-22 sensors (DPC) via a 2-mm-thick light guide. These self-triggering sensors are made up of $2 \times 2$ pixels resulting in a total of 64 readout channels. We restrict the COG calculation to a main pixel, which captures most of the scintillation light from a crystal, and its (direct and diagonal) neighboring pixels and reject single events in which this data is not fully available. This results in stable COG positions for a crystal element and enables high spatial image resolution. Due to the sensor layout, for some crystals it is very likely that a single diagonal neighbor pixel is missing as a result of the low light level on the corresponding DPC. This leads to a loss of sensitivity, if these events are rejected. An enhancement of the COG algorithm is proposed which handles the potentially missing pixel separately both for the crystal identification and the energy calculation. Using this advancement, we show that the sensitivity of the Hyperion-II $^{\rm D}$ insert using the described scintillator configuration can be improved by 20–100% for practical useful readout thresholds of a single DPC pixel ranging from 17–52 photons. Furthermore, we show that the energy resolution of the scanner is superior for all readout thresholds if singles with a single missing pixel are accepted and correctly handled compared to the COG method only accepting singles with all neighbors present by 0–1.6% (relative difference). The presented methods can not only be applied to gamma detectors employing DPC sensors, but can be generalized to other similarly structured and self-triggering detectors, using light sharing techniques, as well.

Spatial Discrete Soliton in Homogeneous Two Dimensional Waveguide Arrays with Kerr Medium

Behaviors of discrete spatial solitons in nonlinear mediums have recently received a plenty of research interest. In this study, for the first time, the effects of diagonal neighbors on spatial discrete solitons in a two dimensional waveguide with Kerr medium are investigated. A numerical model for propagation of the Gaussian beam through a two dimensional waveguides array is proposed. The waveguide contains medium with Kerr nonlinearity considering coupling to vertical, horizontal and diagonal neighbor through light electric field. Different values of intensity, nonlinear coefficient Kerr and Gaussian beam width of incident Gaussian beam are examined and finally suitable parameters for providing central spatial solutions are obtained.

Depixelizing pixel art

We describe a novel algorithm for extracting a resolution-independent vector representation from pixel art images, which enables magnifying the results by an arbitrary amount without image degradation. Our algorithm resolves pixel-scale features in the input and converts them into regions with smoothly varying shading that are crisply separated by piecewise-smooth contour curves. In the original image, pixels are represented on a square pixel lattice, where diagonal neighbors are only connected through a single point. This causes thin features to become visually disconnected under magnification by conventional means, and creates ambiguities in the connectedness and separation of diagonal neighbors. The key to our algorithm is in resolving these ambiguities. This enables us to reshape the pixel cells so that neighboring pixels belonging to the same feature are connected through edges, thereby preserving the feature connectivity under magnification. We reduce pixel aliasing artifacts and improve smoothness by fitting spline curves to contours in the image and optimizing their control points.

On the Degradation of Cell-Centered Diffusive Preconditioners for Accelerating SN Transport Calculations in the Periodic Horizontal Interface Configuration

We investigate the degraded effectiveness of diffusion-based acceleration schemes in terms of the adjacent-cell preconditioner (AP) in a periodically heterogeneous limit devised for the two-dimensional (2-D) periodic horizontal interface (PHI) configuration. Specifically, we demonstrate that the diffusive low-order operator employed in the AP scheme lacks the structure of the integral transport operator in the above asymptotic limit since it (1) ignores cross-derivative coupling and (2) incorrectly estimates the strength of intra-layer coupling in the optically thin layers. In order to prove propositions 1 and 2, we derive expressions for the elements of the matrix representing a certain angular (SN) and spatially discretized form of the 2-D neutron transport integral operator. This is the transport operator that produces the full scalar flux solution if it is directly inverted on the once-collided particle source. The properties of this operator’s elements are then investigated in the asymptotic limit for PHI. The results of the asymptotic analysis point to a sparse but nonlocal matrix structure due to long-range coupling of a cell’s average flux with its neighboring cells, independent of the distance between the cells in the spatial mesh. In particular, for a cell in a thin layer, cross-derivative coupling of the cell’s flux to its diagonal neighbors is of the same asymptotic order as self-coupling and coupling with its north/south Cartesian neighbors. Similarly, its coupling with the fluxes in the same thin layer is of the same order, independent of the distance between the cells in the layer, as the coupling with the east/west Cartesian neighbors.We also show that modifying the standard diffusion-based AP can lead to effective acceleration in PHI. Specifically, we devise three novel acceleration schemes, named APB, Optimized-AP (OAP), and Hybrid-AP (HAP), obtained by modifying the original AP formalism in 2-D. In the APB the five-point AP operator is extended to a nine-point stencil that accounts for cross-derivative coupling by including the matrix elements of the integral transport operator B, which couple a cell-averaged scalar flux to its first diagonal neighbors. In the OAP the five-point stencil of the original AP operator is retained while optimizing the value of the elements in the preconditioner that affect the coupling of a cell with its east/west Cartesian neighbors. Specifically, the optimum elements are obtained by minimizing the iteration’s spectral radius and offer a more correct estimate of the strength of intra-layer coupling in a thin layer. Finally, the nine-point HAP operator represents a “hybrid” of the APB and OAP approaches, in the sense that the spectral properties of the optimized five-point OAP are further improved via the inclusion of cross-derivative terms. Fourier analysis of the novel acceleration schemes indicates that robustness of the accelerated iterations can be recovered, in spite of sharp material discontinuities, by accounting for cross-derivative coupling and by optimizing the preconditioner elements. The new acceleration schemes have also been implemented in a 2-D transport code, and numerical tests successfully verify the predictions of the Fourier analysis. However, it is important to emphasize that the modifications attempted in this work are specific to the selected asymptotic limit for PHI and do not translate into new low-order operators for the general heterogeneous-material case. Rather, the above modified operators suggest that it may be possible to eventually derive such a general low-order unconditionally robust operator.

Monte Carlo integration over stepping stone models for spatial genetic inference using approximate Bayesian computation

Approximate Bayesian computation (ABC) substitutes simulation for analytic models in Bayesian inference. Simulating evolutionary scenarios under Kimura's stepping stone model (KSS) might therefore allow inference over spatial genetic process where analytical results are difficult to obtain. ABC first creates a reference set of simulations and would proceed by comparing summary statistics over KSS simulations to summary statistics from localities sampled in the field, but: comparison of which localities and stepping stones? Identical stepping stones can be arranged so two localities fall in the same stepping stone, nearest or diagonal neighbours, or without contact. None is intrinsically correct, yet some choice must be made and this affects inference. We explore a Bayesian strategy for mapping field observations onto discrete stepping stones. We make Sundial, for projecting field data onto the plane, available. We generalize KSS over regular tilings of the plane. We show Bayesian averaging over the mapping between a continuous field area and discrete stepping stones improves the fit between KSS and isolation by distance expectations. We make Tiler Durden available for carrying out this Bayesian averaging. We describe a novel parameterization of KSS based on Wright's neighbourhood size, placing an upper bound on the geographic area represented by a stepping stone and make it available as m Vector. We generalize spatial coalescence recursions to continuous and discrete space cases and use these to numerically solve for KSS coalescence previously examined only using simulation. We thus provide applied and analytical resources for comparison of stepping stone simulations with field observations.