New statistical tests detect mRNA and protein subcellular patterns.
problem Detecting spatial patterns in mRNA and protein subcellular localization.
method Developed generalized estimators for spatial statistics on arbitrary random measures.
result Identified correlated mRNA and protein subcellular patterns.
Paper predicts spatial variation data from few samples using tensor methods.
problem Predict spatial variation data from limited samples in high-dimensional data.
method Bayesian tensor completion exploiting hidden low-rank property.
result Predicts spatial variation data efficiently from few samples.
Study on linking numbers in random book embeddings of complete graphs.
problem Distribution and mean of linking numbers in random book embeddings of complete graphs.
method Analyzes a family of two-component links arising from random embeddings of complete graphs, using Eulerian numbers and linear growth in mean linking number.
result Mean of squared linking number over all random embeddings is $ rac{i}{6}$, where i is the number of interior edges. Image-to-image networks speed up SAR model parameter estimation.
problem Computational infeasibility of MLE for large, non-stationary spatial fields.
method Used image-to-image networks to estimate SAR model parameters.
result Image-to-image networks enable faster and more accurate parameter estimation.
Complete classification of links and spatial graphs with finite N-quandles.
problem Classifying links and spatial graphs with finite N-quandles.
method Extending fundamental quandle relationships to N-quandles of links and spatial graphs.
result Complete list of links and partial list of spatial graphs with finite N-quandles.
The paper generalizes linking number properties for complete graphs.
problem Understanding linking numbers in spatial complete graphs.
method Analyzing the sum of square linking numbers and triangle-triangle links.
result Explicit formula for the sum of square linking numbers in large complete graphs.
Proposes a method to make statistical inferences robust in spatially dependent settings with missing at random labels.
problem Statistical inference challenges with missing at random labels and spatial dependence.
method Doubly robust estimator with cross-fit nuisances and jackknife spatial HAC variance correction.
result Asymptotically valid confidence intervals with improved finite-sample calibration.
Paper defines spatial risk measures for analyzing extreme events.
problem Risk assessment of extreme environmental events.
method Introduces spatial risk measures and axioms, investigates conditions for asymptotic spatial homogeneity.
result Conditions for spatial risk measures to satisfy asymptotic spatial homogeneity are provided.
A new method clusters hyperspectral images using spatially regularized diffusion.
problem Clustering hyperspectral images effectively.
method Spatially regularized random walks and diffusion geometry.
result The method outperforms state-of-the-art algorithms on real data.
Study on spatial graphs and their constituent knots, linking polynomial invariants.
problem Understanding the polynomial invariants of spatial graphs and their constituent knots.
method Analyzing spatial K4 graphs, constructing band surfaces, and relating polynomials. result Relations between Yamada/Jaeger polynomials and Jones polynomials of constituent knots and associated links.
STICC clusters geographic objects considering both spatial contiguity and attributes.
problem Discovering repeated geographic patterns with spatial contiguity.
method Spatial Toeplitz Inverse Covariance-Based Clustering (STICC) method.
result STICC significantly outperforms baseline methods in adjusted rand index and macro-F1 score.
A scalable framework for clustering large graphs using randomized sketching.
problem Clustering large partially observed graphs efficiently.
method Randomized graph sketching, correlation-based retrieval, uniform and degree-based node sampling.
result Improved phase transitions for clustering with reduced computational complexity and minimum cluster size.
S-SIRUS explains RF for spatial data, improving accuracy and interpretability.
problem Non-interpretable nature of Random Forest in spatially dependent data.
method Proposes S-SIRUS, a spatial extension of SIRUS for extracting interpretable rules.
result S-SIRUS outperforms SIRUS in spatially dependent data, offering higher predictive accuracy and shorter rule lists.
Gradient boosting algorithm for spatial panel models improves estimation in high-dimensional settings.
problem Estimation failure in high-dimensional spatial panel models.
method Model-based gradient boosting algorithm for spatial panel models with random and fixed effects.
result Feasibility and interpretability in both low- and high-dimensional settings.
An ordered and oriented 2-component link L in the 3-sphere is said to be achiral if it is ambient isotopic to its mirror image ignoring the orientation and ordering of the components. Kirk-Livingston showed that if L is achiral then the linking number of L is not congruent to 2 modulo 4. In this paper we study orientat…
New algorithm combines Geostatistics and Quantile Random Forests for non-stationary spatial modelling.
problem Non-stationary spatial modelling with multiple secondary variables.
method Combines Geostatistics and Quantile Random Forests to estimate conditional distributions and simulate spatial data.
result Consistent results similar to geostatistical and Quantile Random Forests, allowing for embedding simpler interpolation techniques.
Spatial variable selection is crucial for reliable spatial predictions in machine learning.
problem Spatial autocorrelation leads to overfitting and poor spatial predictions.
method Used Random Forests with non-spatial and spatial cross-validation strategies.
result Spatial variable selection is essential for reliable spatial predictions.
The paper develops a new model for high-dimensional spatial arbitrage pricing.
problem Estimating spatial interactions in high-dimensional asset pricing.
method Integrates spatial interactions with multi-factor analysis using generalized shrinkage Yule-Walker (SYW) estimation.
result Established asymptotic properties for high-dimensional spatial arbitrage pricing models.
This paper explores the trade-off between spatial and adversarial robustness in neural networks.
problem Understanding the trade-off between spatial and adversarial robustness in neural networks.
method Quantitative analysis and empirical testing with curriculum learning.
result Spatial robustness and adversarial robustness are quantitatively related and can be improved simultaneously.
In 1983, Conway-Gordon showed that for every spatial complete graph on 6 vertices, the sum of the linking numbers over all of the constituent 2-component links is congruent to 1 modulo 2, and for every spatial complete graph on 7 vertices, the sum of the Arf invariants over all of the Hamiltonian knots is also congruen…
A new graph-based clustering method for moderate-dimensional data.
problem Performance degradation of existing graph-based clustering methods in high dimensions.
method Introduces UN-CCDs using NND-based MC-SRT for covering radii determination.
result UN-CCDs provide stable and competitive performance in moderate-sized datasets.
This work classifies strategies to incorporate spatial dependence in Random Forest models.
problem Spatial and temporal dependence in environmental data not adequately modeled by standard Random Forest.
method Taxonomy and systematic review of strategies to adjust Random Forest for spatially dependent data.
result 32 scientific documents reviewed, providing a comprehensive classification of strategies.
A new stochastic solver improves Convolutional Sparse Coding efficiency.
problem Efficiency and sparsity in Convolutional Sparse Coding.
method Randomized subsampling strategy in spatial domain for online learning.
result Improved execution time with no loss in learning quality.
Model place cells as spatial embeddings for efficient path planning and cognitive map construction.
problem Encoding spatial navigation in the hippocampus.
method Model place cells using spectral decomposition of multi-step random walk transition kernels, inducing sparsity and adjacency.
result Place cells encode spatial information through non-negativity and inner-product structure, forming a cognitive map.
RFN models urban mobility demand by separating temporal and spatial variability.
problem Aligning supply and demand in MoD systems for efficient transportation.
method Recurrent flow networks with latent variables and normalizing flows.
result RFN models explicitly disentangle temporal and spatial variability in urban mobility.
Complete invariant for surfaces in 3-sphere derived from diagrams of fundamental groups.
problem Constructing a complete invariant for closed surfaces in the three-sphere.
method Diagram of fundamental groups, generalization of Kneser conjecture, extensions of Waldhausen's theorem.
result Proves the diagram of fundamental groups is a complete invariant for closed surfaces in the three-sphere.
The study optimizes sampling in complex systems with probabilistic response distributions.
problem Calibrating and optimizing complex systems with probabilistic response distributions.
method Non-parametric Bayesian approach to modeling spatial fields of probability distributions, introducing adaptive sampling strategies.
result Adaptive sampling strategies improve system evaluations by guiding focus towards key features.
Generalizations of Conway-Gordon theorems for complete graphs with new key results.
problem Understanding intrinsic knotting in complete graphs.
method Integral lifts and square of linking numbers for complete graphs with arbitrary vertices.
result Sum of second coefficients of Conway polynomials is determined for rectilinear complete graphs.
New theorem shows every integer can be represented by knot summation.
problem Understanding the summation of knot coefficients.
method Analyzing spatial complete graphs and Hamiltonian knots.
result Every integer can be represented by knot summation.
Deep GMRFs improve spatial data modeling and prediction.
problem Modeling spatial dependencies in data.
method Established connection between GMRFs and CNNs, allowing for multi-layer architectures.
result Deep GMRFs outperform state-of-the-art models in satellite temperature prediction.
We give a Conway-Gordon type formula for invariants of knots and links in a spatial complete four-partite graph K3,3,1,1 in terms of the square of the linking number and the second coefficient of the Conway polynomial. As an application, we show that every rectilinear spatial K3,3,1,1 contains a nontrivial Ha…
2DSCNs improve image data analytics by extending SCN to handle spatial information.
problem Limitation of 1D SCNs in preserving spatial information of images.
method Extend SCN to 2DSCNs by stochastically configuring hidden nodes in a matrix-inputs framework.
result 2DSCNs outperform 1D SCNs in image data analytics tasks.
In this article we study self-gravitating static solutions of the Einstein-ScalarField system in arbitrary dimensions. We discuss the existence and the non-existence of geodesically complete solutions depending on the form of the scalar field potential V(φ), and provide full global geometric estimates when the soluti…
Improved spatial prediction for massive datasets using SME model.
problem Efficiently estimating parameters in massive spatial datasets.
method Spatial Mixed Effects (SME) model with AECM algorithm for flexibility.
result Improved estimation without sacrificing prediction accuracy.
Conway-Gordon proved that for every spatial complete graph on 6 vertices, the sum of the linking numbers over all of the constituent 2-component links is congruent to 1 modulo 2, and for every spatial complete graph on 7 vertices, the sum of the Arf invariants over all of the Hamiltonian knots is also congruent to 1 mo…
Paper generalizes pretzel links using spatial graphs.
problem Classical pretzel links need a generalization.
method Introduces graph-pretzel links based on spatial graph projections.
result Constructs an infinite family of distinct ribbon knots.
In 2+1 dimensions, all complete spacetimes are cylindrical.
problem Understanding rigidity of Ricci flow spacetimes in (2+1) dimensions. method Analyzing complete and sufficiently regular spacetimes, showing they must be cylindrical.
result Every spatial slice is diffeomorphic to a fixed surface, and the spacetime is isometric to a classical Ricci flow.
Paper finds unique maximal hypersurfaces in open spacetimes.
problem Finding unique maximal hypersurfaces in open spacetimes.
method Natural geometric and physical assumptions applied to spatially open Robertson-Walker spacetimes with flat fiber.
result New uniqueness and non-existence results for complete maximal hypersurfaces.
Study quantifies risk of extreme wind events using spatial risk measures.
problem Assessing risk of impacts from extreme wind events.
method Spatial risk measure axioms, Brown-Resnick max-stable random fields, powers of max-stable random fields.
result Spatial risk measures associated with extreme wind speeds satisfy risk measure axioms.
Forest-guided smoothing uses random forest outputs for interpretable local smoothers.
problem Creating interpretable local smoothers from complex random forest outputs.
method Uses random forest outputs to define spatially adaptive bandwidth matrices for a linear smoother.
result Improves interpretability and applicability of random forest outputs for various analyses.
New method estimates spatial weights matrix for lattice data, improving prediction accuracy.
problem Estimating spatial dependence structure for regular lattice data.
method Adaptive lasso with cross-sectional resampling to estimate sparse spatial weights matrix.
result Improves prediction accuracy of nitrogen dioxide concentrations.
Efficiently infers gene regulatory networks from spatial data.
problem Inferring spatially-varying gene regulatory networks.
method Proposed an efficient optimization problem for SV-GMRFs.
result Solves large-scale SV-GMRF problems in minutes.
A neighborhood homotopy is an equivalence relation on spatial graphs which is generated by crossing changes on the same component and neighborhood equivalence. We give a complete classification of all 2-component spatial graphs up to neighborhood homotopy by the elementary divisor of a linking matrix with respect to th…
New configuration space accounts for spatial linkages and collisions.
problem Modeling spatial linkages considering collisions.
method Constructed completed and simplified configuration spaces.
result New configuration spaces account for linkages touching each other.
CNNs predict spatial fields from sparse data.
problem Predicting complete spatial fields from limited observations.
method Convolutional Neural Networks (CNNs) trained on a single partially observed field.
result CNNs can flexibly capture local spatial patterns without explicit covariance modeling.
New RL framework learns task completion without prior knowledge.
problem Learning task completion without linguistic or perceptual knowledge.
method Sequentially imagining visual goals and choosing actions.
result Framework outperforms flat and hierarchical architectures.
Dual random fields improve mineral potential predictions.
problem Limited understanding of multi-dimensional causalities and dependencies.
method Introduces dual random fields to pool response functions across the domain.
result Spatial inference and uncertainty assessment of response models and predictions.
Paper proposes efficient multivariate spatial Fay-Herriot models using variational autoencoders.
problem Estimating population characteristics in small areas with limited data.
method Integrates multivariate spatial Fay-Herriot model with variational autoencoders to leverage spatial structure efficiently.
result Significant computational efficiency improvements for high-dimensional datasets.