## What is/are Two Spatial?

Two Spatial - We employ the active PFC model to study the occurrence of localized and periodic active crystals in two spatial dimensions.^{[1]}Also, two spatial clusters of seropositivity were found within a significant area by Scan, and a probable relationship between the Scan result and the livestock concentration by area was found.

^{[2]}As the frequency domain encryption section is a sandwich between the two spatial domain encryption sections, we called it a ”sandwich encryption.

^{[3]}When considering the hydrodynamic flow characteristics, it can be stated that two spatial derivative schemes perform very similarly.

^{[4]}We note that superfluid vortices form a Hamiltonian system that conserves total dipole moment and trace of the quadrupole moment of vorticity; thereby establishing a relation to a traceless scalar charge theory in two spatial dimensions.

^{[5]}The methodology proposed is based on two spatial levels: the district level, where the territory of mapping is the municipal districts of Volgograd region, and the object is rural settlements; the regional level covering the entire territory of the region.

^{[6]}Common bean intercropped with maize at three planting dates (simultaneously with maize, at emergence and knee height of maize) in two spatial arrangements (alternate and paired arrangements).

^{[7]}Global soil organic carbon (SOC) and clay content maps from S-World were studied at two spatial resolutions in three steps.

^{[8]}We investigated the epizootiology of the SCTLD outbreak in the lower Florida Keys at two spatial scales (among reefs ∼1 km and within reefs <10 m) over a 19 month period.

^{[9]}We compared signatures of local adaptation across the genome of mountain ash (Eucalyptus regnans) at two spatial scales: A species‐wide data set and a topographically‐complex subregional data set.

^{[10]}Twenty sheep received two fortnightly infusions of either bleomycin (3U), or saline (control) into two spatially separate lung segments.

^{[11]}I select two spatial planning sites from urban fringe Australia, both of which involve significant transformation of (semi-)riparian habitat.

^{[12]}Either 2 (young adult) or 12–14 (middle-age) months post exposure, rats were tested on two spatial tasks: spontaneous alternation and novel object in place.

^{[13]}This paper presents two spatial ability trainer apps exploring the latest mobile technologies: augmented reality and virtual reality.

^{[14]}The implications of spatial and temporal discretization are discussed, and an extension of the Arbitrary Lagrangian–Eulerian finite element method is proposed to enforce the resulting balance laws on the grown/resorbed body in two spatial dimensions.

^{[15]}It employs two spatial analysis methods, quadrat density analysis and negative binomial regression analysis, to describe the location patterns of NMTC projects and their relationship to two variables known to correlate with gentrification: high vacancy rates and increasing rental rates.

^{[16]}The analysis is performed in two spatial dimensions however the results are valid in three spatial dimensions as well.

^{[17]}We demonstrate that the rapidity and robustness of slow contraction in homogenizing and flattening the universe found in simulations in which the initial conditions were restricted to non-perturbative variations described by a single fourier mode along only a single spatial direction are in general enhanced if the initial variations are along two spatial directions, include multiple modes, and thereby have reduced symmetry.

^{[18]}The design developed here provides a novel, pseudo-experimental approach for assessing the response of mobile species to gradients of management at two spatial scales.

^{[19]}We present the Code SkyAx solving the Hartree–Fock equations in two spatial dimensions assuming axial symmetry.

^{[20]}Iterative regression analyses were carried out for two spatial extents: the entire Colombian Amazon and a subset area which was most affected by deforestation.

^{[21]}Radial scans of the ion velocity show that a continuous control of the rotation profile may be obtained using two spatial configurations for the locations of the emissive cathodes (either in the centre or at the edge of the plasma column).

^{[22]}The existence and uniqueness of weak solutions of dynamical low-rank evolution for parabolic partial differential equations in two spatial dimensions is shown, covering also non-diagonal diffusion in the elliptic part.

^{[23]}Forests were evaluated on two spatial scales.

^{[24]}We examine this question at two spatial resolutions: (1) at the municipal landscape scale to capture broadscale change regardless of land tenure; and (2) at the scale of designated public open spaces within the municipalities to investigate the extent to which the loss of vegetation has occurred on lands that are intended to provide public access to vegetated areas in the city.

^{[25]}The device functions by the ambipolar transport of charge carriers between two spatially isolated poly(dimethylsiloxane) (PDMS) microwells through an underlying multi-walled carbon nanotube (MWCNT) mat.

^{[26]}Here, we report two spatially resolved methods for measuring growth rates in bacterial colonies.

^{[27]}Two spatial data sets are considered to be similar if they originate from the same stochastic process in terms of their spatial structure.

^{[28]}Interrogating two cases, Sealed Off and Miss Sophia’s Diary, this paper seeks to apply spatial narrative theories to extract two spatial dimensions, namely physical-space and subjective-space, and interpret the authoresses’ feminist positions based on their deliberate writing on intricate feminine consciousness and psychology that male writers would not be able to experience.

^{[29]}Linear models were used to assess the effect of population and individual traits on dispersal distance at two spatial scales.

^{[30]}Specifically, the GCA module is composed of two key components, where the global feature aggregation module achieves mutual reinforcement of salient feature embeddings from any two spatial locations, and the cascaded pyramid attention module tackles the scale variation issue by building up a cascaded pyramid framework to progressively refine the attention map in a coarse-to-fine manner.

^{[31]}In this study, a custom system that is capable of switching between two spatially offset Raman excitation modes, namely inverse (iSORS, ring) and diffuse (dSORS, enlarged flat-top circle), were compared at the same power for depth-probing Raman spectroscopy applications.

^{[32]}Testing whether two spatial point processes have the same spatial distribution is an important task that can be addressed from different perspectives.

^{[33]}We employed two spatial analyses—bivariate maps and local indicator of spatial association (LISA)—to identify and prioritize sub-basin clusters based on multiple biodiversity and conservation metrics in addition to species richness.

^{[34]}Including 3D prints allowed a direct comparison of two spatially resolved display methods.

^{[35]}Specifically, two spatial models, Spatial Error Model and Spatial Lag Model, are estimated for boarding and alighting separately by employing several exogenous variables including stop-level attributes, transportation and transit infrastructure variables, built environment and land use attributes, and sociodemographic and socioeconomic variables in the vicinity of the stop along with spatial and spatiotemporal lagged variables.

^{[36]}A symmetric binary phase grating and condenser lens system forms two spatially separated, focused probes at the sample which can be scanned while maintaining alignment.

^{[37]}A speech-in-noise test was also performed unaided and aided for two spatial configurations (S0N90; implanted side; S0N90; nonimplanted side).

^{[38]}Two spatially-resolved areas on the dual-disk glassy carbon electrode (DDGCE) were modified with a AuNPs film by electrodeposition to improve the conductivity of the sensing interface.

^{[39]}Forests were evaluated on two spatial scales.

^{[40]}We derive a complete classification of Floquet phases of interacting bosons and fermions with $U(1)$ symmetry in two spatial dimensions.

^{[41]}The focus lies on the first time-step and on situations where only one slip system is active, in two spatial dimensions.

^{[42]}We analyze a large data set of 58 self-assembled monolayers (SAMs) containing ligands with nonpolar and polar end groups of different chemical identity (amine, amide, and hydroxyl) in five mole fractions, two spatial patterns, and with scaled partial charges.

^{[43]}Using the current landscape without artificial firebreaks as the baseline, we assessed the BP changes for 49 simulated firebreak scenarios that included combinations of eleven densities, three widths, and two spatial patterns.

^{[44]}Here, we demonstrate intrinsic coupling between two spatially-separated surface states in the Weyl orbits by measuring a dual-gate device of a Dirac semimetal film.

^{[45]}In this paper, we attempted to review the erosion in the Ouergha watershed by applying two spatial approaches.

^{[46]}We find strong evidence for two spatially confined regions over North America and Australia that exhibit increased cosmic ray particle fluxes at the 5σ level.

^{[47]}After that, in order to integrate the two spatial properties, the multidirectional improved top-hat filter (MITHF) is proposed by fusing LIDM and LGSM to highlight potential small targets and suppress strong structural edge clutters.

^{[48]}Finally, the feasibility and generality of these new indices are demonstrated by the performance analysis of three ROPMs, including one planar case and two spatial cases.

^{[49]}We investigate nonequilibrium dynamics after rapid quenches in a many-body system composed of 3 to 200 strongly interacting qubits in one and two spatial dimensions.

^{[50]}

## Identify Two Spatial

(2020a) identify two spatially separated α3β1-dependent signaling branches fostering skin tumor outgrowth.^{[1]}Based on long-slit spectroscopy and narrow band imaging centered on the Lyα emission, we identify two spatial components: a “compact component” with high velocity dispersion (∼ 1500 km s−1) seen in all three lines, and an “extended component”, having low velocity dispersion (i.

^{[2]}We identify two spatially intermingled glutamatergic populations separable by axonal projections, mouse genetics, neuronal activity profiles, and motor functions.

^{[3]}

## Report Two Spatial

Here, we report two spatially resolved methods for measuring growth rates in bacterial colonies.^{[1]}Here, we report two spatially resolved methods for measuring growth rates in bacterial colonies.

^{[2]}

## Following Two Spatial

First, we describe the following two spatial reasoning IQ tests: rotation and shape composition.^{[1]}Finally, the tensors obtained after the above steps are respectively input into the following two spatial convolutional neural network architectures to perform classification, one is a simple CNN structure, which has only two convolution layers, one dense layer and one softmax layer.

^{[2]}

## two spatial dimension

We employ the active PFC model to study the occurrence of localized and periodic active crystals in two spatial dimensions.^{[1]}We note that superfluid vortices form a Hamiltonian system that conserves total dipole moment and trace of the quadrupole moment of vorticity; thereby establishing a relation to a traceless scalar charge theory in two spatial dimensions.

^{[2]}The implications of spatial and temporal discretization are discussed, and an extension of the Arbitrary Lagrangian–Eulerian finite element method is proposed to enforce the resulting balance laws on the grown/resorbed body in two spatial dimensions.

^{[3]}The analysis is performed in two spatial dimensions however the results are valid in three spatial dimensions as well.

^{[4]}We present the Code SkyAx solving the Hartree–Fock equations in two spatial dimensions assuming axial symmetry.

^{[5]}The existence and uniqueness of weak solutions of dynamical low-rank evolution for parabolic partial differential equations in two spatial dimensions is shown, covering also non-diagonal diffusion in the elliptic part.

^{[6]}Interrogating two cases, Sealed Off and Miss Sophia’s Diary, this paper seeks to apply spatial narrative theories to extract two spatial dimensions, namely physical-space and subjective-space, and interpret the authoresses’ feminist positions based on their deliberate writing on intricate feminine consciousness and psychology that male writers would not be able to experience.

^{[7]}We derive a complete classification of Floquet phases of interacting bosons and fermions with $U(1)$ symmetry in two spatial dimensions.

^{[8]}The focus lies on the first time-step and on situations where only one slip system is active, in two spatial dimensions.

^{[9]}We investigate nonequilibrium dynamics after rapid quenches in a many-body system composed of 3 to 200 strongly interacting qubits in one and two spatial dimensions.

^{[10]}This is described by a confinement transition of quantum electrodynamics in two spatial dimensions (QED3 Gross–Neveu theories).

^{[11]}The trial state used in the upper bound yields an analogous estimate also in the case of two spatial dimensions, which is believed to be sharp at low temperature.

^{[12]}It is known that global smooth solutions exist in one and two spatial dimensions, subject to sub-critical initial data.

^{[13]}Its main features are as follows: a free software with an open source, it solves the neutron transport equation to a few steady-state groups on a grid structured in one or two spatial dimensions with an isotropic and anisotropic dispersion source, and any new calculation method and algorithm would be easy to implement in this proposed code.

^{[14]}First of all, the observed and predicted counts are binned in three dimensions (two spatial dimensions and one energy dimension) and comparing two 3D maps is not straightforward.

^{[15]}The initial boundary value problem for a nonlinear system of equations modeling the chevron patterns is studied in one and two spatial dimensions.

^{[16]}We trace what happens with asymptotically free behavior of the running coupling in φ3 theory in six-dimensional spacetime, if to compactify two spatial dimensions on a 2D closed manifold.

^{[17]}The analysis is restricted to two spatial dimensions for simplicity.

^{[18]}Moreover, the architecture is based on two-dimensional integrated photonic chips used to produce a qubit cluster state in one temporal and two spatial dimensions.

^{[19]}We present a study in two spatial dimensions and time, focussing on the fast and linear regime, and show how fast flavor oscillations depend on the ELN and its crossings.

^{[20]}We derive a mode-coupling theory (MCT) to describe the dynamics of tracer particles in dense, glass-forming systems of active Brownian particles (ABP) in two spatial dimensions.

^{[21]}We study the ground-state entanglement of gapped domain walls between topologically ordered systems in two spatial dimensions.

^{[22]}We examine some leading-order flow and stability properties of smectic A (SmA) liquid crystals (LCs) in two spatial dimensions by analysing a fully nonlinear continuum theory of these materials.

^{[23]}Under the assumption of quadratic decay of predator, we prove the global existence and uniform boundedness of classical solutions up to two spatial dimensions.

^{[24]}We propose a scalable analog quantum simulator for quantum electrodynamics in two spatial dimensions.

^{[25]}Results are demonstrated on linear and nonlinear scalar conservation laws in two spatial dimensions.

^{[26]}Topological spin liquids in two spatial dimensions are stable phases in the presence of a small magnetic field, but may give way to field-induced phenomena at intermediate field strengths.

^{[27]}We describe the large-N saddle point, and the structure of fluctuations about the saddle point, of a theory containing a sharp, critical Fermi surface in two spatial dimensions.

^{[28]}The existence of soliton families in non-parity-time-symmetric complex potentials remains poorly understood, especially in two spatial dimensions.

^{[29]}, two spatial dimensions for the image frames and the third dimension for time).

^{[30]}These plaquettes are in two spatial dimensions and calculations use the Hamiltonian formulation where time is not discretized.

^{[31]}Finally, numerical results in one and two spatial dimensions are presented to corroborate our theoretical observations.

^{[32]}The simulation is carried out in two spatial dimensions and the algorithm used is generalized for n-spatial dimensions.

^{[33]}As a particular example, we discuss time-reversal symmetric boundary unitary operators in one and two spatial dimensions, where the anomaly emerges as we gauge the so-called Kubo-Martin-Schwinger (KMS) symmetry.

^{[34]}This function and its velocity fields build a nonlinear dynamic system in two spatial dimensions.

^{[35]}We introduce a method to estimate continuum percolation thresholds and illustrate its usefulness by investigating geometric percolation of noninteracting line segments and disks in two spatial dimensions.

^{[36]}The result is a 3D data cube with two spatial dimensions and a wavelength dimension, composed of hundreds of co-registered images containing information on the spectral signature of the materials present in the field of view of the sensor at the time of capture.

^{[37]}Robustness, accuracy, and computational efficiency of the proposed algorithm are illustrated for some relevant pattern-forming systems, in both one and two spatial dimensions, exhibiting solutions with a rich spatio-temporal structure.

^{[38]}A general form of the solutions, using Fourier-Laplace transforms and asymptotic analysis, is developed for several spatially infinite regular lattices in one and two spatial dimensions, and the theory is developed for the analysis of transport and internal state changes on general graphs.

^{[39]}Here, we consider a gapless U(1) spin liquid with spinon Fermi pockets in two spatial dimensions.

^{[40]}We investigate the mechanical response of jammed packings of circulo-lines in two spatial dimensions, interacting via purely repulsive, linear spring forces, as a function of pressure P during athermal, quasistatic isotropic compression.

^{[41]}We study a rock–paper–scissors model for competing populations that exhibits travelling waves in one spatial dimension and spiral waves in two spatial dimensions.

^{[42]}We show that also genuinely interacting systems in two spatial dimensions can become nonergodic as a consequence of this mechanism.

^{[43]}We present OpenMP version of a Fortran program for solving the Gross–Pitaevskii equation for a harmonically trapped three-component rotating spin-1 spinor Bose–Einstein condensate (BEC) in two spatial dimensions with or without spin–orbit (SO) and Rabi couplings.

^{[44]}The model is then numerically solved in two spatial dimensions.

^{[45]}We prove resolvent estimates in $L^p$-spaces for time-harmonic Maxwell’s equations in two spatial dimensions and in three dimensions in the partially anisotropic case.

^{[46]}We call this architecture Blended inverse-PDE networks (hereby dubbed BiPDE networks) and demonstrate its applicability on recovering the variable diffusion coefficient in Poisson problems in one and two spatial dimensions, as well as the diffusion coefficient in the time-dependent and nonlinear Burgers' equation in one dimension.

^{[47]}Finally, we illustrate our theoretical findings through several numerical experiments in one and two spatial dimensions that highlight the differences in features of local and nonlocal solutions and also the sharp interface properties of the nonlocal model.

^{[48]}Nature of problem: The present Open Multi-Processing (OpenMP) FORTRAN programs solve the time-dependent nonlinear partial differential Gross–Pitaevskii (GP) equation for a trapped spinor Bose–Einstein condensate, with or without spin–orbit coupling, in one and two spatial dimensions.

^{[49]}Numerical results in one and two spatial dimensions for both scalar equations and systems are presented, supporting our theoretical analysis.

^{[50]}

## two spatial scale

We investigated the epizootiology of the SCTLD outbreak in the lower Florida Keys at two spatial scales (among reefs ∼1 km and within reefs <10 m) over a 19 month period.^{[1]}We compared signatures of local adaptation across the genome of mountain ash (Eucalyptus regnans) at two spatial scales: A species‐wide data set and a topographically‐complex subregional data set.

^{[2]}The design developed here provides a novel, pseudo-experimental approach for assessing the response of mobile species to gradients of management at two spatial scales.

^{[3]}Forests were evaluated on two spatial scales.

^{[4]}Linear models were used to assess the effect of population and individual traits on dispersal distance at two spatial scales.

^{[5]}Forests were evaluated on two spatial scales.

^{[6]}Comparisons were conducted at two spatial scales by partitioning the RS-ET into two scales, while streamflow comparisons were only conducted at one scale.

^{[7]}We show that these findings result from the interplay of the two spatial scales of the correlation structures associated with the temperature field and with the noise generated by precipitation intermittency.

^{[8]}To infer whether (a) niche-based or dispersal-based processes play the main role in the assembly of flea communities parasitic on small mammals and whether (b) the main processes of flea community assembly are scale-dependent, we applied a novel permutation-based algorithm (PER-SIMPER) and the dispersal-niche continuum index (DNCI), to data on the species incidence of fleas and their hosts at two spatial scales.

^{[9]}Redundancy analysis (RDA) was used to detect candidate markers across two spatial scales (entire study area and within subregions).

^{[10]}Estimates were compared with those from concurrent surveys for two spatial scales corresponding to the fishery and the three pink snapper stocks within the fishery.

^{[11]}Body size, diet (stomach fullness and eukaryotic 18S ribosomal sequencing), nutritional condition (RNA:DNA) and gut microbiota (16S prokaryotic ribosomal sequencing) were compared in fish at two spatial scales: between beaches separated by 10s of kilometres and between sites at different depths on the same beach, separated by 10s of metres.

^{[12]}We test the thermal adaptation and thermal niche asymmetry hypotheses to explain interspecific patterns of thermal tolerance at these two spatial scales.

^{[13]}arrecta in the Guaraguacu River, a subtropical tidal river in South Brazil, to analyze effects that this invasive grass has on the biodiversity of native macrophytes at two spatial scales.

^{[14]}We use hand-fishing-nets and fishing funnel traps to record turtles in 18 distinct sites and analyze habitat preferences by species at two spatial scales.

^{[15]}Abiotic factors were evaluated during two seasons, spring and autumn, and at two spatial scales.

^{[16]}In this study, we tested hypotheses about drivers of introgression at two spatial scales within the Saltmarsh Sparrow ( Ammospiza caudacuta ) and Nelson’s Sparrow ( A.

^{[17]}Applying stable isotope analysis and mixing models, we made comparisons at two spatial scales: (1) a large scale, comparing intertidal flats with (mangrove sites) and without (control sites) adjacent mangrove forests regarding the carbon isotopic signature of macrozoobenthos and sediment organic matter (SOM), and the relative importance of potential primary food sources in sustaining macrozoobenthos, and (2) a fine scale, performing stable carbon isotope measurements along 200 m transects from the coastline out to open intertidal flats, to trace mangrove carbon in macrozoobenthos and in the SOM.

^{[18]}We measured hydraulic variables for each 500‐m reach, and landscape stressors at two spatial scales (subcatchment and riparian buffer forest).

^{[19]}Two spatial scales were considered in the analysis, with water quality parameters (temperature, salinity, dissolved oxygen, turbidity, water residence times, N, P and chlorophyll-a concentrations) being measured at a fine, fyke-net scale and morphological (average bottom elevation and sediment grain size) and habitat features (habitat proportion, diversity and complexity) being measured at a broader, seascape scale.

^{[20]}We evaluated the beta diversity patterns of aquatic macroinvertebrate assemblages at two spatial scales in streams in the Eastern Amazon, as well as tested whether environmental and spatial factors affected these assemblage patterns differently for non-flying (i.

^{[21]}We paired CTs from a permanent camera-trapping grid (with 38 CTs) targeted at monitoring Eurasian lynx (Lynx lynx) in Innlandet County, Norway, with additional randomly placed CTs at two spatial scales (38 CTs within the same habitat patch and 38 CTs within the same 50-km2 grid cell as the lynx-targeted CTs) for three months.

^{[22]}Taking the entire Yangtze River Delta Urban Agglomerations (YRD) as a study area, we applied the LAdI for individual landscape classes (Vi) and landscape level (LV) to quantitatively assess change over time in the ecological stress of YRD from 1990 to 2015 at two spatial scales: municipal scale and 5 km-grid scale.

^{[23]}We examine free-space propagation of soft apertured realizations of the proposed beams and show that their evolution is governed by two spatial scales: the coherence width of the background and the aperture size.

^{[24]}Here, we mathematically model the subcircuits of the outer plexiform layer of the retina on two spatial scales: that of an individual synapse and that of the scale of the receptive field (hundreds to thousands of synapses).

^{[25]}Our analysis incorporated two spatial scales, a smaller scale focused on roost counting areas and food available to birds in these areas and a larger spatial scale of tidal basins.

^{[26]}Here, we assessed the importance of anthropogenic, biotic, and abiotic factors at two spatial scales as drivers of plant invasions along three roads in south-central Chile.

^{[27]}We performed botanical and habitat surveys (topography and soil measures, vegetation structure, composition and biomass, fodder quality) at two spatial scales, in 1x1 m and 4x4 m plots.

^{[28]}Turbulence bridges these two spatial scales and results in an energy cascade through the wavenumbers.

^{[29]}This study describes an approach guided by spatial mapping to quantify and predict antimicrobials and ARG in Minnesota’s waterbodies in water and sediment at two spatial scales: macro, throughout the state, and micro, in specific waterbodies.

^{[30]}The study was conducted on the example of Poland in two spatial scales: regional (province) and local (community).

^{[31]}Light microscopy (LM) has the potential to bridge the above two spatial scales, with a resolution ranging from a few hundred nanometers to a few micrometers.

^{[32]}Assembly patterns at the two spatial scales were similar.

^{[33]}We used mixed-effects logistic regression to test 14 a priori hypotheses represented by statistical models formulated at two spatial scales (100 and 1000 m), with four categories of explanatory factors: sampling bias, forest structure, topography, and human disturbance.

^{[34]}Specifically, we investigated the spectral shift resulting from GWC and manure application at two spatial scales, satellite and proximal.

^{[35]}In this study, we quantified groundwater storage changes in California's Central Valley at two spatial scales for the period 2002 through 2020 using remote sensing data and an ensemble water balance method.

^{[36]}We focused on assessing the reproducibility of multi-frequency multilayer topologies exploring the effect of two filtering methods for extracting frequencies from BOLD activity, three connectivity estimators, with or without a topological filtering scheme, and two spatial scales.

^{[37]}The research’s spatial scope covers Poland’s territory on two spatial scales: the system of regions (16 NUTS2 units) and poviats (314 LAU level 1 units).

^{[38]}MethodsData from 152 multi-stage cluster random trachoma surveys were used to understand the degree of clustering of trachoma on two spatial scales (district and village) in Amhara using a geographical information system and the Getis-Ord Gi* (d) statistic for local clustering.

^{[39]}We aimed to examine the (1) relationships between vein densities at two spatial scales (lower- vs.

^{[40]}The method was tested at two spatial scales (a 125 km2 catchment and a 4 km2 sub-area of that catchment) in a region in Western Kenya characterized by smallholder farming.

^{[41]}In particular, through the lens of both classical and distributional convergence frameworks, two spatial scales are contrasted: municipalities and states.

^{[42]}We quantified variability and synchrony at two levels of organization (population and community) and two spatial scales (local plots and region) and quantified the strength of species and spatial insurance by comparing observed variability and synchrony in aggregate biomass to null models of independent species or spatial dynamics based on cyclic-shift permutation.

^{[43]}METHODS: We designed two structural equation models integrating relationships between biotic and abiotic variables at two spatial scales, local and regional.

^{[44]}” We contend that the organization of such Schumpeterian entrepreneurship occurs at two spatial scales.

^{[45]}ABSTRACT To demonstrate the dynamics of forest patches in the Mongolian forest-steppe ecotone and examine how forest structure changes with distance from the forest edge, we investigated forest structure and tree age according to two spatial scales: transects and quadrats within transects.

^{[46]}

## two spatial variable

Their local dynamics determines the behavior of solutions of the original boundary value problems with two spatial variables.^{[1]}We consider the Cahn–Hilliard equation in the case where its solution depends on two spatial variables, with homogeneous Dirichlet and Neumann boundary conditions, and also periodic boundary conditions.

^{[2]}An algorithm for reducing the input problem to a study of special nonlinear equations of the parabolic type with one or two spatial variables is developed.

^{[3]}The starting point is Taylor expansions about the mean-line in curvilinear coordinates, and the goal is to eliminate the two spatial variables in the cross section in a pointwise manner in order to obtain a closed system for the displacement coefficients.

^{[4]}Our wave equation includes one second-order temporal derivative and two spatial variable-order fractional Laplacian operators.

^{[5]}5-m spatial resolution, 13 spectral indices and reflectance from SENTINEL-2 satellite (MSIsensor), and five soil properties and two spatial variables of latitude and longitude were used as covariates for digital mapping of topsoil total nitrogen.

^{[6]}In some of the most interesting cases, the obtained equations of the first approximation contain two spatial variables; therefore, it is natural to expect the appearance of complex dynamic effects.

^{[7]}

## two spatial resolution

Global soil organic carbon (SOC) and clay content maps from S-World were studied at two spatial resolutions in three steps.^{[1]}We examine this question at two spatial resolutions: (1) at the municipal landscape scale to capture broadscale change regardless of land tenure; and (2) at the scale of designated public open spaces within the municipalities to investigate the extent to which the loss of vegetation has occurred on lands that are intended to provide public access to vegetated areas in the city.

^{[2]}The performance of red-green-blue (RGB) images were assessed at two spatial resolutions 3 cm/pixel and 13 cm/pixel, while NDVI and GNDV images were only at 13 cm/pixel.

^{[3]}Cerebrovascular relative pressures were also derived in 4D Flow MRI from healthy volunteers ( n = 8 ), acquired at two spatial resolutions (dx = 1.

^{[4]}The brightness temperature of SMAP available at two spatial resolutions (36 and 9 km) was used for two seasons intended for SM assessment.

^{[5]}We compare the performance of the proposed control algorithms assuming the availability of occupancy data with two spatial resolutions, and confirm through experiments that a better trade-off can be achieved should zone-level occupancy information become available.

^{[6]}

## two spatial direction

We demonstrate that the rapidity and robustness of slow contraction in homogenizing and flattening the universe found in simulations in which the initial conditions were restricted to non-perturbative variations described by a single fourier mode along only a single spatial direction are in general enhanced if the initial variations are along two spatial directions, include multiple modes, and thereby have reduced symmetry.^{[1]}To increase the efficiency of parallel calculations, the decomposition of the calculated spatial grid and all grid data in one or two spatial directions - in horizontal directions-is also performed.

^{[2]}, two spatial directions and one temporal direction) to prepare a training data set.

^{[3]}The model can be rotated in two spatial directions to vary the local relevance of sedimentation for aerosol deposition.

^{[4]}A novel method for three-direction decomposition of hyperspectral change tensors is proposed—change tensor is decomposed along the spectral direction and two spatial directions to get a single tensor containing the spectral information and two kinds of tensors containing the spectral–spatial information.

^{[5]}In the ansatzes for the metric, dilaton and electromagnetic fields, we consider dependence on time and two spatial directions.

^{[6]}

## two spatial cluster

Also, two spatial clusters of seropositivity were found within a significant area by Scan, and a probable relationship between the Scan result and the livestock concentration by area was found.^{[1]}Experimental stimuli were images of real-world objects arranged in either one or two spatial clusters.

^{[2]}The results of the applied cluster analysis are the indicators of the existance of two spatial clusters.

^{[3]}Water quality analysis was conducted in three interannual (IA) groups: IA I (1991–1993, 1995), IA II (1994, 1996–2000, 2002–2006), and IA III (2001, 2007–2011); two seasonal clusters: non-flood season (NF, November–December and January–April) and flood season (FL, May–October); and two spatial clusters (MP-main part of Kuxi and Kudong and NH-Neihu), based on spatial I (I-Kudong, I-Kuxi, and I-Neihu), spatial II (II-Kudong, II-Kuxi, and II-Neihu), spatial III (III-Kudong, III-Kuxi, and III-Neihu), spatial NF (NF-Kudong, NF-Kuxi, and NF-Neihu), and spatial FL (FL-Kudong, FL-Kuxi, and FL-Neihu).

^{[4]}Two spatial clusters were detected for all-age malaria mortality with only the primary cluster (RR = 1.

^{[5]}

## two spatial configuration

Radial scans of the ion velocity show that a continuous control of the rotation profile may be obtained using two spatial configurations for the locations of the emissive cathodes (either in the centre or at the edge of the plasma column).^{[1]}A speech-in-noise test was also performed unaided and aided for two spatial configurations (S0N90; implanted side; S0N90; nonimplanted side).

^{[2]}Speech reception thresholds (SRTs) were measured by means of a matrix sentence test in five acoustic environments that included different noise conditions (amplitude modulated and continuous), two spatial configurations, and reverberation.

^{[3]}We first identified two spatial configurations of river networks based on the river density: river cluster patches and river corridors, which were each divided into four spatial levels.

^{[4]}Using the experiment data, we formulate and evaluate a new Fitts’ model combining two spatial configurations in a SAR pointing task to capture key characteristics, initial target occlusion, target view angle, and user movement.

^{[5]}

## two spatial level

The methodology proposed is based on two spatial levels: the district level, where the territory of mapping is the municipal districts of Volgograd region, and the object is rural settlements; the regional level covering the entire territory of the region.^{[1]}It maps out possible reasons for expected similarities between the two spatial levels in the degree redistribution is supported and also the underlying mechanisms that foster support rates.

^{[2]}Secondly, we show that the prevalence of the virus in the respective reservoir hosts was associated with habitat composition at two spatial levels, independent of resource addition, supporting previous findings that habitat composition is a primary driver of the prevalence of hantaviruses in the neotropics.

^{[3]}those native to part but not all of Great Britain (GB), were assessed with the Aquatic Species Invasiveness Screening Kit (AS-ISK) at two spatial levels (River Basin District [RBD] and GB overall), the outcome scores calibrated and analysed to determine the relevance of geographical scale (GB, RBD and freshwater ecoregion) on AS-ISK outcome score rankings.

^{[4]}

## two spatial model

Specifically, two spatial models, Spatial Error Model and Spatial Lag Model, are estimated for boarding and alighting separately by employing several exogenous variables including stop-level attributes, transportation and transit infrastructure variables, built environment and land use attributes, and sociodemographic and socioeconomic variables in the vicinity of the stop along with spatial and spatiotemporal lagged variables.^{[1]}Two spatial models, i.

^{[2]}Two spatial models, geographic detector and geographic weighted regression (GWR), were employed to assess the global effects and the local effects of the driving factors for ecological land change, respectively.

^{[3]}For this purpose, two spatial models will be considered: the spatial error model and spatial lag model.

^{[4]}

## two spatial mode

We demonstrate a source for correlated pairs of atoms characterized by two opposite momenta and two spatial modes forming a Bell state only involving external degrees of freedom.^{[1]}We encode qubits in a superposition of two spatial modes on a photonic Lieb lattice.

^{[2]}Each similarity group can constitute a 4-D tensor, including two spatial modes, a spectral mode and a non-local similarity mode, which has strong low-rank properties.

^{[3]}Here, assisted by diamond nitrogen-vacancy (NV) centers inside single-sided optical cavities, we first introduce the single-photon quantum routing operation, with which a single-photon polarization qubit can be coherently routed to the superposition of two spatial modes according to the state of the other polarization qubit.

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## two spatial frequency

At 1 and 3mo postoperatively, under scotopic conditions without glare and scotopic conditions with glare, FS-LASIK-CV group showed more improvement in logCS at two spatial frequencies (12.^{[1]}It has been shown that the use of more than two spatial frequencies (multi-fx ) can vastly improve measurement accuracy and reduce chromophore estimation uncertainties, but real-time multi-fx SFDI for chromophore monitoring has been limited in practice due to the slow speed of available chromophore inversion algorithms.

^{[2]}In this study, we used phase-shift discrimination and motion-direction discrimination tasks to measure motion spatial suppression induced by stimuli of two spatial frequencies (0.

^{[3]}The models are trained on labelled datasets and evaluated at various flux levels and for two spatial frequency contents (20 and 100 Zernike modes).

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## two spatial domain

As the frequency domain encryption section is a sandwich between the two spatial domain encryption sections, we called it a ”sandwich encryption.^{[1]}Furthermore, for creating a multimodal fusion framework and to exploit activity images, we made each type of activity images multimodal by convolving with two spatial domain filters: Prewitt filter and High-boost filter.

^{[2]}EUHFORIA consists of two parts, covering two spatial domains; the solar corona and the inner heliosphere.

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## two spatial analysi

It employs two spatial analysis methods, quadrat density analysis and negative binomial regression analysis, to describe the location patterns of NMTC projects and their relationship to two variables known to correlate with gentrification: high vacancy rates and increasing rental rates.^{[1]}Therefore, two spatial analysis software namely Arc GIS and Erdas Imagine have been used to identify the amount of land cover change and variation in land surface temperature through supervised image classification and spectral radiance calculation methods on Landsat satellite images (1998.

^{[2]}In this research, we analyzed COVID-19 distribution patterns based on hotspots and space–time cubes (STC) in East Java, Indonesia The data were collected based on the East Java COVID-19 Radar report results from a four-month period, namely March, April, May, and June 2020 Hour, day, and date information were used as the basis of the analysis We used two spatial analysis models: the emerging hotspot analysis and STC Both techniques allow us to identify the hotspot cluster temporally Three-dimensional visualizations can be used to determine the direction of spread of COVID-19 hotspots The results showed that the spread of COVID-19 throughout East Java was centered in Surabaya, then mostly spread towards suburban areas and other cities An emerging hotspot analysis was carried out to identify the patterns of COVID-19 hotspots in each bin Both cities featured oscillating patterns and sporadic hotspots that accumulated over four months This pattern indicates that newly infected patients always follow the recovery of previous COVID-19 patients and that the increase in the number of positive patients is higher when compared to patients who recover The monthly hotspot analysis results yielded detailed COVID-19 spatiotemporal information and facilitated more in-depth analysis of events and policies in each location/time bin The COVID-19 hotspot pattern in East Java, visually speaking, has an amoeba-like pattern Many positive cases tend to be close to the city, in places with high road density, near trade and business facilities, financial storage, transportation, entertainment, and food venues Determining the spatial and temporal resolution for the STC model is crucial because it affects the level of detail for the information of endemic disease distribution and is important for the emerging hotspot analysis results We believe that similar research is still rare in Indonesia, although it has been done elsewhere, in different contexts and focuses.

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## two spatial datum

Two spatial data sets are considered to be similar if they originate from the same stochastic process in terms of their spatial structure.^{[1]}Two spatial data sets with information on the construction period of residential buildings, aggregated on municipality sections and hectare grid cells, are used to show how census-based spatial data sets can enhance the approach.

^{[2]}Two spatial data analyses were carried out: a buffer analysis near the healthcare facilities and an advertisement hotspot analysis using ArcMap 10.

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## two spatial orientation

The teeth were individually placed in a phantom composed of a human skull and mandible, which was CBCT scanned in two spatial orientations: conventional (with the Frankfurt plane parallel to the floor) and angled acquisition (tilted 90 degrees backward).^{[1]}Concretely, we first employ four directed recurrent neural networks (RNNs) based on two spatial orientations to traverse electrode signals on two separate brain regions.

^{[2]}METHODS We adapted two spatial orientation tasks to immersive virtual environments: a "survey to route" task in which participants had to transfer information from a map to their body position within a maze [Spatial Orientation in Immersive Virtual Environment Test (SOIVET) Maze], and an allocentric-type, route learning task, with well-established topographic landmarks (SOIVET Route).

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## two spatial clustering

The results revealed that, first, China’s air pollution showed two spatial clustering areas: the eastern coastal area (e.^{[1]}In this study, two spatial clustering techniques of Getis-Ord Gi* statistic and K-means clustering analysis were performed on 15 PTEs in 6,862 topsoil samples from the Tellus datasets of Northern Ireland to investigate the hidden spatial patterns and association with their controlling factors.

^{[2]}In this research traffic accident hotspots are identified using two spatial clustering analysis methods namely Getis-Ord Gi* and Nearest Neighborhood Hierarchy (NNH).

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## two spatial light

The system is implemented based on two spatial light modulators (SLMs), one of which forms a multiplexed signal on the transmitting side, and the other implements a multichannel DOE for separating the vortex beams on the receiving side.^{[1]}This paper proposes a novel image data augmentation method based on the 4F optical diffuser system with two spatial light modulators.

^{[2]}Two spatial light modulators (SLMs) are used in the system, one of which is used for beam shaping, and the other is used for reproducing the image.

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## two spatial task

Either 2 (young adult) or 12–14 (middle-age) months post exposure, rats were tested on two spatial tasks: spontaneous alternation and novel object in place.^{[1]}We administered two spatial tasks and a math task to 312 first- through third-grade students who were tested in the spring for three consecutive school years.

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## two spatial component

Based on long-slit spectroscopy and narrow band imaging centered on the Lyα emission, we identify two spatial components: a “compact component” with high velocity dispersion (∼ 1500 km s−1) seen in all three lines, and an “extended component”, having low velocity dispersion (i.^{[1]}Additionally, to better integrate the spatial information, BLR has two spatial components, a user-based spatial component to find the spatial preferences of the user, and a behavior-based spatial component to find locations of interest for different behaviors.

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## two spatial derivative

When considering the hydrodynamic flow characteristics, it can be stated that two spatial derivative schemes perform very similarly.^{[1]}, 2019), we show how to integrate the potential term by losing two spatial derivatives.

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## two spatial planning

I select two spatial planning sites from urban fringe Australia, both of which involve significant transformation of (semi-)riparian habitat.^{[1]}According to the LUFs clustering results, we proposed two spatial planning-zoning schemes based on the land use function and human utilization intensity.

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