Spatial Subdomains Research Articles

Killing versus branching: Unexplored facets of diffusive relaxation.

We analyze the relaxation dynamics of Feynman-Kac path integral kernel functions, in terms of branching diffusion processes with killing. This amounts to the killing versus branching approach to path integration, which seems to be a novelty in the pathwise description of conditioned Brownian motions and diffusion processes with absorbing boundaries. There, Feynman-Kac kernels appear as building blocks of inferred (Fokker-Planck) transition probability density functions. A consistent probabilistic meaning is hereby provided (killing versus branching time rate) to bounded from below Feynman-Kac potential functions, which instead of being positive-definite (a standard killing paradigm), may take negative values on bounded spatial subdomains (that inflicts trajectory branching).

Embodied semantic parameters for the lexical representation of spatial relational categories

Abstract This paper proposes an explanatory model for the lexical representation of the native speakers’ lexical knowledge of English prepositions. Lexical knowledge of prepositions as relational predicates includes argument structure (trajector-landmark) as in Cognitive Grammar, situation types (position vs state) as in Functional Grammar, lexical hierarchies (spatial subdomains) based on semantic primitives, as in Natural Semantic Metalanguage, and embodied perceptual parameters configured in four dimensions, namely, geometry, topology, force-dynamics and function (from Cognitive Linguistics). This model is illustrated here by expounding three lexical templates compatible with constructional templates in the Lexical Constructional Model, representing the semantic decomposition of English prepositions at, on and in.

Domain Decomposition Strategy for Combining Nonlinear and Linear Reduced-Order Models

Increasingly ubiquitous reliance on expensive, high-fidelity numerical simulations has led to the emergence of reduced-order modeling as an effective method to predict high-dimensional, spatially discretized field outputs in an efficient manner. This study presents a method to construct parametric, nonintrusive reduced-order models (ROMs) by leveraging domain decomposition (DD) to enable using multiple dimension reduction (DR) techniques within different spatial subdomains of the field to construct a single predictive ROM. To enforce smoothness of solutions across subdomains, points at domain interfaces are reconstructed using the data-driven gappy proper orthogonal decomposition method. The method is assessed on three high-dimensional test cases with shocks, including one with two-dimensional turbulent flow around the RAE2822. Results show that fully nonlinear ROMs predict fields more accurately in the vicinity of discontinuous features compared to their linear counterparts, which are more accurate in regions that are far from these discontinuities. Furthermore, irrespective of the DR method, DD-based ROMs outperformed their global counterparts in all test cases. Finally, models that used a combination of DR methods simultaneously showed superior performance near shockwaves and a significant improvement in total error compared to existing approaches that employ a single DR method in all subdomains.

Nonlinear transient heat transfer analysis of multilayered thermal protection systems by incremental differential quadrature element method

As a first attempt, the incremental differential quadrature element method (IDQEM) is used for the one-dimensional nonlinear transient heat transfer analysis of multilayered thermal protection systems (TPSs) under time-dependent aerodynamic heating. All thermophysical properties are considered to be temperature-dependent (TD). Based on the IDQEM, the multilayered TPS is divided into several spatial sub-domains along the layer interfaces, and the entire heating process is also divided into several temporal sub-domains. For each temporal sub-domain, the governing equations are discretized by the differential quadrature method and then solved by the Newton-Raphson method. The initial condition of each temporal sub-domain is defined by the temperature results at the end of the previous sub-domain. The temperature profile of the TPS during the entire heating process can be obtained by repeating the calculation procedure from the first temporal sub-domain to the last one. Convergence and accuracy of the method are confirmed. Numerical examples are carried out to show the effects of TD thermophysical properties, thermal boundary, and layer thickness on the temperature profile of a three-layer TPS. The results show that the temperature dependency of thermophysical properties is worthy of consideration in predicting the temperature profile of the TPSs.

The accuracy of pollutant concentration calculations on the microscale using a modified Lagrangian advanced micro-scale model

The influence of data determining the initial wind field in a diagnostic wind model with spatial subdomains on the accuracy of concentrations calculated by Lagrangian Advanced Micro-scale Model was analysed. Calculations were carried out for an idealised built environment. Three input datasets were considered: (I) a single inlet wind profile, (II) a single inlet wind profile with additional parametrisation of wind flow around buildings and (III) full wind tunnel wind data. Results show that: in case (I) it is not possible to properly map the position of the pollutant plume; in case (II) the application of additional parametrisation leads to increased accuracy of the mapping of the position of the pollutant plume, in particular in the close vicinity of the source; in case (III) correct mapping of the shape and location of the plume within the entire area was achieved.

Spatial abilities in Down syndrome: Characterising the profile of spatial skills and models of spatial development

Evidence shows that spatial interventions are successful in typical development. However, the potential of spatial interventions for Down syndrome (DS) populations is hindered by the lack of literature on spatial skills and their development in this group. This paper investigates (a) the profile of strengths and weaknesses in spatial abilities, and (b) the cross-sectional developmental trajectories of spatial skills, in DS relative to typical development. Participants included 33 individuals with DS (58% male; 10–35 years) and 131 typically developing (TD) children (53% male; 4–11 years) who completed spatial tasks assessing two spatial sub-domains. Despite weaknesses in spatial skill, the DS spatial profile aligned closely with that of mental-age matched TD children. Cross-sectional developmental trajectories revealed slower rates of spatial development for those with DS, relative to TD children. Collectively, these results indicate potential for improving spatial skills in DS through intervention.

Implementation and optimization of hybrid parallel strategy in HNET

For the self-developed three-dimensional whole-core High-fidelity NEutron Transport calculation program HNET, although the numerical acceleration algorithms can improve the computation performance of high-fidelity neutron transport in terms of algorithms and models, it still faces some critical issues such as long computing time and enormous memory requirement. The rapid development of high-performance clusters provides a foundation for the application of massively parallel computing. Most current MOC programs are based on a single-type variable to achieve efficient parallelism, and spatial domain decomposition methods are the most common parallel schemes. However, its parallelism is limited and cannot fully utilize the current state-of-the-art computer resources. To solve this problem, hybrid parallel strategies are implemented in HNET to further expand the parallel degree, improve the speed of computation, and reduce the memory requirement. A hybrid MPI/OpenMP method based on domain decomposition and characteristic rays is proposed for the method of characteristics (MOC). For domain decomposition, the simulation domain is divided into spatial subdomains, with each subdomain handled by different processes. On this basis, the characteristic ray parallelism is implemented taking advantage of the inherent parallelism of the characteristic rays. Meanwhile, the optimization of the hybrid parallel strategy further improves the computation speed by eliminating atomic operations and using private pointer arrays and other techniques. In addition, in the framework of generalized equivalence theory (GET) based two-level coarse mesh finite difference method (CMFD), there is also a certain time consumption in solving CMFD linear system. Hence, for CMFD, a hybrid MPI/OpenMP method based on domain decomposition and secondary domain decomposition can be used. Using the secondary domain decomposition method, each subdomain is divided into sub-subdomains, with each sub-subdomain handled by threads, which allows CMFD to utilize the resources of characteristic ray parallelism in MOC, and also increases the speed of CMFD computation. Numerical results show that for both steady-state and transient calculations, the hybrid MPI/OpenMP in HNET can further expand the parallelism and accelerate the computation. It can take full use of parallel resources and achieve large-scale parallelism.

Giving voice to space: the grammar of Northern Alta spatial roots

Abstract Recent cross-linguistic studies on spatial language reveal a great diversity in the way languages encode spatial information. Yet, given that there are not many spatial studies that have systematically targeted languages with a Philippine-type voice system, it is not clear how spatial expression is structured in such languages. The aim of this study is to address this knowledge gap through an in-depth investigation of Northern Alta, a language presenting such a voice system. The study combines data from stimulus-based tasks with a modern documentation corpus of the language and elicited data to examine the linguistic strategies deployed in four different spatial subdomains: location, disposition, orientation, and routes. The results show that each subdomain favors a distinct set of derivational affixes and a particular set of lexical roots. It is argued that the morphological system of the language plays a crucial role in the structuring of spatial expression. It allows roots with spatial meanings such as ‘front’, ‘side’, ‘top’, and ‘back’ to derive a variety of spatial verbs that are key in several spatial domains. The study also shows that Philippine-type languages have important information to contribute to cross-linguistic studies of spatial language.

Distinct regulatory states control the elongation of individual skeletal rods in the sea urchin embryo.

BackgroundUnderstanding how gene regulatory networks (GRNs) control developmental progression is a key to the mechanistic understanding of morphogenesis. The sea urchin larval skeletogenesis provides an excellent platform to tackle this question. In the early stages of sea urchin skeletogenesis, skeletogenic genes are uniformly expressed in the skeletogenic lineage. Yet, during skeletal elongation, skeletogenic genes are expressed in distinct spatial sub‐domains. The regulation of differential gene expression during late skeletogenesis is not well understood.ResultsHere we reveal the dynamic expression of the skeletogenic regulatory genes that define a specific regulatory state for each pair of skeletal rods, in the sea urchin Paracentrotus lividus. The vascular endothelial growth factor (VEGF) signaling, essential for skeleton formation, specifically controls the migration of cells that form the postoral and distal anterolateral skeletogenic rods. VEGF signaling also controls the expression of regulatory genes in cells at the tips of the postoral rods, including the transcription factors Pitx1 and MyoD1. Pitx1 activity is required for normal skeletal elongation and for the expression of some of VEGF target genes.ConclusionsOur study illuminates the fine‐tuning of the regulatory system during the transition from early to late skeletogenesis that gives rise to rod‐specific regulatory states.

Transcriptional heterogeneity of ventricular zone cells in the ganglionic eminences of the mouse forebrain.

The ventricular zone (VZ) of the nervous system contains radial glia cells that were originally considered relatively homogenous in their gene expression, but a detailed characterization of transcriptional diversity in these VZ cells has not been reported. Here, we performed single-cell RNA sequencing to characterize transcriptional heterogeneity of neural progenitors within the VZ and subventricular zone (SVZ) of the ganglionic eminences (GEs), the source of all forebrain GABAergic neurons. By using a transgenic mouse line to enrich for VZ cells, we characterize significant transcriptional heterogeneity, both between GEs and within spatial subdomains of specific GEs. Additionally, we observe differential gene expression between E12.5 and E14.5 VZ cells, which could provide insights into temporal changes in cell fate. Together, our results reveal a previously unknown spatial and temporal genetic diversity of VZ cells in the ventral forebrain that will aid our understanding of initial fate decisions in the forebrain.

Stress Orientations and Driving Forces in the Indo-Burma Plate Boundary Zone

ABSTRACT The Indo-Burma range (IBR) is the forearc of an oblique subduction zone where the Indian slab obliquely converges with the Burma microplate. In this study, we consider earthquake focal mechanisms to help elucidate the tectonic behavior of the region. Toward this end, we examine the spatially variable stress orientations across the IBR and in the downgoing plate to better understand the associated plate driving forces and subduction dynamics. We combined earthquake focal mechanisms from 1 January 1950 until 31 December 2019 from a number of available catalogs and published studies, and divided the total of 189 events into spatial subdomains before performing stress inversions to document the spatial variability of the stress tensor. Generally, the maximum principal stress (S1) is oriented approximately north–south in all domains, subparallel to the subducting slab. The intermediate principal stress (S2) is plunging westward at variable angles. In contrast, the minimum principal stress (S3) is plunging to the east roughly following the dip of the subducting plate, indicative of down-dip tension in the slab. We do not observe a significant variation of the S1 orientation with depth, suggesting that north–south compression is due to the slab pushing northward through the mantle. Due to the well-defined slab-dip-parallel S3 direction for the megathrust and upper plate catalogs, the primary driving force of this subduction region is likely to be a net slab pull. Based on the seismic activity of the region, the consistency of focal mechanism-based stress and regional tectonic driving forces, as well as the S3 evidence for slab-pull forces, the possibility that the IBR can produce large earthquakes cannot be ruled out.

Intrinsic winding of braided vector fields in tubular subdomains

Braided vector fields on spatial subdomains which are homeomorphic to the cylinder play a crucial role in applications such as solar and plasma physics, relativistic astrophysics, fluid and vortex dynamics, elasticity, and bio-elasticity. Often the vector field’s topology—the entanglement of its field lines—is non-trivial, and can play a significant role in the vector field’s evolution. We present a complete topological characterisation of such vector fields (up to isotopy) using a quantity called field line winding. This measures the entanglement of each field line with all other field lines of the vector field, and may be defined for an arbitrary tubular subdomain by prescribing a minimally distorted coordinate system. We propose how to define such coordinates, and prove that the resulting field line winding distribution uniquely classifies the topology of a braided vector field. The field line winding is similar to the field line helicity considered previously for magnetic (solenoidal) fields, but is a more fundamental measure of the field line topology because it does not conflate linking information with field strength.

The method of images in thermoelasticity with an application to wafer heating

The well-known method of images relates the solution of the heat equation on (typically n = 2 or n = 3) to the solution of the heat equation on certain spatial subdomains Ω of By reformulating the method of images in terms of a convolution kernel, two novel extensions are obtained in this paper. First, the method of images is extended from thermal problems to thermoelastic problems, that is, it is demonstrated how the heat-induced deformations on can be related to the heat-induced deformations on certain subdomains Ω of Secondly, an explicit expression for the convolution kernel for the disk is obtained. This enables the application of the method of images to circular domains to which it could not be applied before. The two obtained extensions lead to a computationally efficient simulation method for repetitive heat loads on a disk. In a representative simulation example of wafer heating, the proposed method is more than ten times faster than a conventional Finite Element approach.

Modelling a targeted use of pesticide procedure for pest populations with heterogeneous spatial distributions

Commercial and environmental considerations have led to increased pressure to reduce pesticide use in agricultural crops resulting in a growing interest in development of pesticide application protocols that allow for their targeted use. In this paper, we revisit a standard decision-making protocol for pesticide application and introduce protocol modifications to apply pesticide to selected spatial sub-domains in the agricultural field. The baseline case we consider is the control of populations of the grey field slug (Deroceras reticulatum) in commercial fields. It is well known that slugs have strongly heterogeneous (patchy) spatial distribution and we show that targeting patches with higher slug density only, may offer significant potential for reducing the use of pesticides. An approach to incorporating targeted application of pesticide into a control protocol with treatment decisions based on a threshold population abundance will be discussed. The benefits of the targeted use of pesticides will be clearly demonstrated using data on slug abundance collected in commercial fields.We then argue that employing a single threshold for decision-making in the pesticide application protocol is not the most efficient way to assess risks associated with the population abundance when pesticide is applied selectively. It will be shown that a protocol for targeted use of pesticides depends heavily on the definition of a spatial density patch in heterogeneous spatial distribution, and a single decision-making parameter such as the population threshold cannot accommodate important information about the patch size. Hence an alternative is to introduce two controlling parameters into the protocol in order to quantify the pest abundance in each patch and patch size separately and we discuss this approach in the paper.

The spatial and angular domain decomposition method for radiation heat transfer in 2D rectangular enclosures with discontinuous boundary conditions

To remedy discontinuous boundary conditions, we propose the spatial and angular domain decomposition approach for the solution of radiative transfer equation (RTE) in a two-dimensional rectangular enclosure. The RTE is angularly and spatially discretized. For each spatial node, the total solid angle 4π is decomposed into several angular sub-domains according to the distribution of discontinuous boundaries, and the quadrature weighting factors are recalculated for each angular sub-domain by using the compound trapezoidal integral scheme. For each angularly-discretized direction, the spatial domain is decomposed into a few spatial sub-domains according to the distribution of discontinuous boundaries. In each spatial sub-domain the distribution of radiative intensity is continuous, and the angularly-discretized RTE is solved for each spatial sub-domain. Two examples are employed to verify the performance of the domain decomposition method, and the results confirm its suitability and advantage for treating radiative transfer problem with discontinuous boundary conditions.

Anomaly detection in scientific data using joint statistical moments

We propose an anomaly detection method for multi-variate scientific data based on analysis of high-order joint moments. Using kurtosis as a reliable measure of outliers, we suggest that principal kurtosis vectors, by analogy to principal component analysis (PCA) vectors, signify the principal directions along which outliers appear. The inception of an anomaly, then, manifests as a change in the principal values and vectors of kurtosis. Obtaining the principal kurtosis vectors requires decomposing a fourth order joint cumulant tensor for which we use a simple, computationally less expensive approach that involves performing a singular value decomposition (SVD) over the matricized tensor. We demonstrate the efficacy of this approach on synthetic data, and develop an algorithm to identify the occurrence of a spatial and/or temporal anomalous event in scientific phenomena. The algorithm decomposes the data into several spatial sub-domains and time steps to identify regions with such events. Feature moment metrics, based on the alignments of the principal kurtosis vectors, are computed at each sub-domain and time step for all features to quantify their relative importance towards the overall kurtosis in the data. Accordingly, spatial and temporal anomaly metrics for each sub-domain are proposed using the Hellinger distance of the feature moment metric distribution from a suitable nominal distribution. We apply the algorithm to two turbulent auto-ignition combustion cases and demonstrate that the anomaly metrics reliably capture the occurrence of auto-ignition in relevant spatial sub-domains at the right time steps.

The developmental relations between spatial cognition and mathematics in primary school children

Spatial thinking is an important predictor of mathematics. However, existing data do not determine whether all spatial sub-domains are equally important for mathematics outcomes nor whether mathematics-spatial associations vary through development. This study addresses these questions by exploring the developmental relations between mathematics and spatial skills in children aged 6-10years (N=155). We extend previous findings by assessing and comparing performance across Uttal etal.'s (2013), four spatial sub-domains. Overall spatial skills explained 5%-14% of the variation across three mathematics performance measures (standardized mathematics skills, approximate number sense and number line estimation skills), beyond other known predictors of mathematics including vocabulary and gender. Spatial scaling (extrinsic-static sub-domain) was a significant predictor of all mathematics outcomes, across all ages, highlighting its importance for mathematics in middle childhood. Other spatial sub-domains were differentially associated with mathematics in a task- and age-dependent manner. Mental rotation (intrinsic-dynamic skills) was a significant predictor of mathematics at 6 and 7years only which suggests that at approximately 8years of age there is a transition period regarding the spatial skills that are important for mathematics. Taken together, the results support the investigation of spatial training, particularly targeting spatial scaling, as a means of improving both spatial and mathematical thinking.

Emergence of form in embryogenesis.

The development of form in an embryo is the result of a series of topological and informational symmetry breakings. We introduce the vector–reaction–diffusion–drift (VRDD) system where the limit cycle of spatial dynamics is morphogen concentrations with Dirac delta-type distributions. This is fundamentally different from the Turing reaction–diffusion system, as VRDD generates system-wide broken symmetry. We developed ‘fundamental forms’ from spherical blastula with a single organizing axis (rotational symmetry), double axis (mirror symmetry) and triple axis (no symmetry operator in three dimensions). We then introduced dynamics for cell differentiation, where genetic regulatory states are modelled as a finite-state machine (FSM). The state switching of an FSM is based on local morphogen concentrations as epigenetic information that changes dynamically. We grow complicated forms hierarchically in spatial subdomains using the FSM model coupled with the VRDD system. Using our integrated simulation model with four layers (topological, physical, chemical and regulatory), we generated life-like forms such as hydra. Genotype–phenotype mapping was investigated with continuous and jump mutations. Our study can have applications in morphogenetic engineering, soft robotics and biomimetic design.

A hybrid method for calculating seismic wave first-arrival traveltimes in two-dimensional models with an irregular surface

A hybrid method is developed for the calculation of seismic wave first-arrival traveltimes in two-dimensional models with an irregular free surface. The method is based on a combination of the classical eikonal equation (CEE) and the topography-dependent eikonal equation (TDEE); the latter applies only to the part of the explored domain that includes the non-flat surface, while the first equation applies anywhere outside this domain. CEE is solved using a fast-sweeping method, and TDEE is solved after discretizing the numerical Hamiltonian using the Legendre transform and applying the upwind fast-sweeping method. For the implementation of the hybrid method and the appropriate application of CEE and TDEE, we sort the contact mode between spatial sub-domains into three types and give an explanation about the working routine adopted for each one. Several numerical experiments considering different models, mesh sizes, seismic source positions and partition styles demonstrate that the proposed hybrid method can effectively address seismic modeling problems involving undulated free surfaces, keeping the same precision as TDEE but with a fairly rapid convergence. This proves that the hybrid method is a powerful tool for practical applications aimed at obtaining high-quality images of earth structures.

Overlapping but distinct topology for zebrafish V2R-like olfactory receptors reminiscent of odorant receptor spatial expression zones

BackgroundThe sense of smell is unrivaled in terms of molecular complexity of its input channels. Even zebrafish, a model vertebrate system in many research fields including olfaction, possesses several hundred different olfactory receptor genes, organized in four different gene families. For one of these families, the initially discovered odorant receptors proper, segregation of expression into distinct spatial subdomains within a common sensory surface has been observed both in teleost fish and in mammals. However, for the remaining three families, little to nothing was known about their spatial coding logic. Here we wished to investigate, whether the principle of spatial segregation observed for odorant receptors extends to another olfactory receptor family, the V2R-related OlfC genes. Furthermore we thought to examine, how expression of OlfC genes is integrated into expression zones of odorant receptor genes, which in fish share a single sensory surface with OlfC genes.ResultsTo select representative genes, we performed a comprehensive phylogenetic study of the zebrafish OlfC family, which identified a novel OlfC gene, reduced the number of pseudogenes to 1, and brought the total family size to 60 intact OlfC receptors. We analyzed the spatial pattern of OlfC-expressing cells for seven representative receptors in three dimensions (height within the epithelial layer, horizontal distance from the center of the olfactory organ, and height within the olfactory organ). We report non-random distributions of labeled neurons for all OlfC genes analysed. Distributions for sparsely expressed OlfC genes are significantly different from each other in nearly all cases, broad overlap notwithstanding. For two of the three coordinates analyzed, OlfC expression zones are intercalated with those of odorant receptor zones, whereas in the third dimension some segregation is observed.ConclusionOur results show that V2R-related OlfC genes follow the same spatial logic of expression as odorant receptors and their expression zones intermingle with those of odorant receptor genes. Thus, distinctly different expression zones for individual receptor genes constitute a general feature shared by teleost and tetrapod V2R/OlfC and odorant receptor families alike.