New method finds grid diagrams for many fibered knots.
problem Detecting fibered knots using grid diagrams.
method Developed an efficient method to identify grid diagrams with unique maximal Alexander grading states.
result Found suitable grid diagrams for 5385 of 5397 fibered prime knots with crossing number ≤ 13.
New method constructs moduli spaces of Lagrangian surfaces in CP^2 from grid diagrams.
problem Constructing explicit examples of triple grid diagrams for Lagrangian surfaces in CP^2.
method Elegant geometric construction reducing to linear algebra.
result Explicit construction of moduli space of triple grid diagrams.
This paper proposes a multi-grid method for learning energy-based generative ConvNet models of images. For each grid, we learn an energy-based probabilistic model where the energy function is defined by a bottom-up convolutional neural network (ConvNet or CNN). Learning such a model requires generating synthesized exam…
Computes elastic grids that approximate 3D surfaces without physical simulations.
problem Creating planar grids that fit complex 3D surfaces efficiently.
method Uses differential geometry to minimize bending energy and nestle to the surface.
result Elastic grids can approximate 3D surfaces without physical simulations.
Direction of arrival (DOA) estimation is a classical problem in signal processing with many practical applications. Its research has recently been advanced owing to the development of methods based on sparse signal reconstruction. While these methods have shown advantages over conventional ones, there are still difficu…
For low-dimensional data sets with a large amount of data points, standard kernel methods are usually not feasible for regression anymore. Besides simple linear models or involved heuristic deep learning models, grid-based discretizations of larger (kernel) model classes lead to algorithms, which naturally scale linear…
The segmentation of large scale power grids into zones is crucial for control room operators when managing the grid complexity near real time. In this paper we propose a new method in two steps which is able to automatically do this segmentation, while taking into account the real time context, in order to help them ha…
Survey of RL methods for optimizing power grid topologies.
problem Optimizing power grid operation with adaptive control strategies.
method Reinforcement Learning (RL) for dynamic and uncertain environments.
result Comprehensive evaluation of RL-based methods for power grid topology optimization.
New method solves elliptic equations on manifolds without grids.
problem Solving elliptic equations on complex manifolds.
method Numerical domain decomposition method avoiding global grids.
result Method validated on specific 4D manifolds.
New method identifies distribution grid outages using smart meter data.
problem Outages in urban distribution grids due to DERs and smart meters' last gasp signals.
method Data-driven approach based on stochastic time series analysis and maximum likelihood estimation.
result Proves optimal performance in identifying distribution grid outages using smart meter data.
Power grids are one of the most important components of infrastructure in today's world. Every nation is dependent on the security and stability of its own power grid to provide electricity to the households and industries. A malfunction of even a small part of a power grid can cause loss of productivity, revenue and i…
The increasing penetration of distributed energy resources poses numerous reliability issues to the urban distribution grid. The topology estimation is a critical step to ensure the robustness of distribution grid operation. However, the bus connectivity and grid topology estimation are usually hard in distribution gri…
We present a grid diagram analogue of Carter, Rieger and Saito's smooth movie theorem. Specifically, we give definitions for grid movies, grid movie isotopies and present a definition of grid planar isotopy as a particular subset of the grid diagram moves: stabilization, destabilization and commutation. We show that gr…
PhI-GPR improves power grid state estimation and forecasting.
problem Accurate state estimation and forecasting in power grids with sparse measurements.
method Physics-informed Gaussian process regression (PhI-GPR) for stochastic differential equations.
result PhI-GPR provides more accurate forecasts and estimates of power grid states compared to ARIMA.
Paper proposes a learning-based sparse Bayesian method for accurate off-grid DOA estimation.
problem One-bit off-grid direction of arrival (DOA) estimation in a single snapshot scenario.
method Formulated off-grid DOA estimation model, used Sparse Bayesian framework, proposed Learning-based Sparse Bayesian approach.
result Improved computational efficiency and accuracy in off-grid DOA estimation.
New model solves PDEs using probabilistic random grids.
problem Solving parametric PDEs with probabilistic collocation grids.
method Random Grid Neural Processes (RGNPs) with GICNets.
result Significant computational advantages and improved predictive capabilities.
Graph convolutional networks (GCNs) suffer from the irregularity of graphs, while more widely-used convolutional neural networks (CNNs) benefit from regular grids. To bridge the gap between GCN and CNN, in contrast to previous works on generalizing the basic operations in CNNs to graph data, in this paper we address th…
The paper introduces triple grid diagrams to construct Lagrangian surfaces in complex projective space.
problem Constructing Lagrangian surfaces in complex projective space.
method Defining and analyzing triple grid diagrams to determine Lagrangian caps and surfaces.
result Triple grid diagrams can determine closed Lagrangian surfaces in CP2 under certain conditions. New method uses tensor networks to price multi-asset options efficiently.
problem Pricing multi-asset options via classical full-grid solvers is computationally infeasible due to the curse of dimensionality.
method Quantized tensor trains (QTT) transform the d-asset Black-Scholes PDE into a tractable high-dimensional problem.
result Full-grid prices and Greeks for correlated basket and max-min options in three to five dimensions can be computed with high accuracy.
Proposes learning regularization strength directly from data.
problem Computational expense and data reduction in grid search for deep learning hyperparameters.
method Modified Evidence Lower Bound (ELBo) objective for model selection on full training set.
result Comparable heldout accuracy to grid search with less compute time.
Improved tracking of tangled point sources using Riemannian metrics.
problem Tangled point source trajectories in temporal stacks.
method Lifting to higher-dimensional space of roto-translation group, new regularisation based on relaxed Reeds-Shepp metric.
result Reconstruction and untangling of trajectories even from numerical standpoint.
AI model enhances grid monitoring with synchro-waveform tech.
problem Dynamic, stochastic, low-inertia future grids need advanced monitoring.
method AI Foundation Model with synchro-waveform tech.
result Significantly improved fault detection accuracy and speed.
Context: One of the black arts of data mining is learning the magic parameters which control the learners. In software analytics, at least for defect prediction, several methods, like grid search and differential evolution (DE), have been proposed to learn these parameters, which has been proved to be able to improve t…
Half grid diagrams prove every link can be represented by a special type of grid diagram.
problem Representing links using grid diagrams and related invariants.
method Defining half grid diagrams and constructing canonical pairs, proving equivalence to Jones' construction, relating to classical link invariants.
result Established a new method to relate the oriented Thompson index to classical link invariants and provided bounds for knot invariants.
The paper compares inserting and stretching points for grid refinement near critical points.
problem Decreased accuracy of finite difference methods near discontinuities.
method Comparison of inserting and stretching points for grid refinement near critical points.
result Proposes a new fast and simple stretching function.
Grid homology confirms the Upsilon invariant in knot theory.
problem Verifying the equivalence of Upsilon invariants in knot theory.
method Reconstructed Upsilon invariant using grid homology and proved equivalence.
result Upsilon invariants in knot Floer and grid homology are equivalent.
GridPyM handles grid diagrams for knot theory.
problem Handling grid diagrams for knot theory.
method Generates and simplifies grids, models local transformations.
result Models local transformations between grid diagrams.
Grid homology theory for spatial graphs extends skein sequence.
problem No specific problem stated; focuses on extending a sequence.
method Defined grid homology theory for spatial graphs and extended skein sequence.
result Skein exact sequence extended to grid homology for spatial graphs.
Extends knot invariant to filtered grid complexes.
problem Knot invariants and grid complexes.
method Combining Ozsváth-Szabó-Stipsicz crossing-change maps with Alishahi-Eftekhary l(K) invariant.
result Combinatorial formulation of knot invariant.
Grid homology properties for MOY graphs studied.
problem Defining and studying properties of grid homology for MOY graphs.
method Defined grid homology from Harvey and O'Donnol's work. Studied properties using oriented skein relation, edge contraction, and parallel edge unification.
result Properties of grid homology for MOY graphs were studied and defined.
A new method uses SVM classification to efficiently compute confidence sets.
problem Computing confidence sets for moment inequalities is computationally intensive.
method Converts confidence set construction into a classification problem using SVM.
result Asymptotically reproduces the test in the confidence set using SVM classification.
Graph neural networks improve topology control of power grids.
problem Grid congestion due to renewable energy and electrification.
method Investigated the effect of graph representation on GNN effectiveness for topology control.
result Heterogeneous graph representation outperforms homogeneous in topology control tasks.
Grid homology invariant proved for lens space links.
problem Proving combinatorial invariance of grid homology for lens space links.
method Combining combinatorial methods with sign assignments to prove invariance.
result Grid homology is a link invariant for lens space links.
New trading strategy beats traditional grid in crypto markets.
problem Low expected return of traditional grid trading strategy.
method Dynamic Grid Trading (DGT) strategy that adapts to market conditions.
result DGT strategy outperforms traditional grid and buy-and-hold strategies.
We introduce elastic geodesic grids for easy-to-fabricate, deployable structures.
problem Approximating freeform surfaces with deployable structures.
method Geodesic curves on target surfaces, kinematic mechanism, differential geometry.
result Elastic geodesic grids can approximate freeform surfaces easily and deployably.
Develops equivariant grid homology for strongly invertible knots.
problem Invariants of strongly invertible knots.
method Equivariant grid diagrams and mapping cones.
result Equivariant unknotting numbers and genus bounds.
Paper proposes a method to locate power grid recordings using ENF sequences.
problem Locating power grid recordings without concurrent power signals.
method Extract ENF sequences from power and audio recordings, develop multi-class SVM model.
result Validation of location authenticity of recordings using ENF sequences.
Computes homology of an obstruction chain complex in grid homology.
problem Computing the homology of an obstruction chain complex in grid homology.
method Defined and computed the homology of the obstruction chain complex of the full grid.
result Results about the existence of sign assignments in grid homology.
Grid homology shows knot unknotting lower bound.
problem Knot unknotting number determination
method Grid homology analysis
result Torsion homology classes order bounds unknotting number
SKI accelerates GP inference with sparse grids to handle higher dimensions.
problem SKI scales poorly in high dimensions due to dense grid size.
method Sparse grids within SKI framework, novel matrix-vector multiplication algorithm.
result SKI can be scaled to higher dimensions while maintaining accuracy.
Efficiently prices American options with multiple assets using sparse grids.
problem Pricing American options with multiple underlying assets efficiently.
method Dynamic programming formulation followed by sparse grid interpolation.
result Sparse grids reduce the number of interpolation points and maintain function smoothness.
The least squares Monte Carlo algorithm has become popular for solving portfolio optimization problems. A simple approach is to approximate the value functions on a discrete grid of portfolio weights, then use control regression to generalize the discrete estimates. However, the classical global control regression can …
Paper tackles RL for power grid topology optimization.
problem Managing large action spaces in growing power networks.
method Hierarchical multi-agent reinforcement learning (MARL) framework.
result MARL framework outperforms single-agent RL methods.
Scalable algorithm for sampling Gaussian processes using sparse grids and preconditioners.
problem Generating high-dimensional Gaussian random vectors for GP sampling is computationally challenging.
method Proposes a scalable algorithm using inducing points approximation with sparse grids and additive Schwarz preconditioners.
result Demonstrates the efficacy and accuracy of the proposed method through experiments and comparisons.
The paper studies grid homology for spatial graphs and proves a Künneth formula for connected sums.
problem Understanding grid homology for spatial graphs with various types of edges.
method Developed grid homology for spatial graphs with cut edges and applied it to prove a Künneth formula for connected sums.
result A Künneth formula for knot Floer homology of connected sums is proven using grid homology.
New method selects critical DER scenarios for distribution grid investment planning.
problem Determining critical DER adoption scenarios for risk assessment in distribution grids.
method Bayesian Optimization framework using Gaussian Process surrogates and Pareto-critical acquisition function.
result Statistical guarantee and significant speed-up over exhaustive search in selecting critical DER scenarios.
A simpler edge-based discretization method without dual volumes.
problem Efficiently computing edge-based discretization vectors without forming dual volumes.
method Directly compute edge-midpoint vectors and reduce dual volume formation.
result Significant reduction in computing time for tetrahedral grids.
Improved weather forecasting with gridded pseudo-token TNPs.
problem Handling large-scale, unstructured spatio-temporal data in weather forecasting.
method Introducing gridded pseudo-token transformer neural processes (TNPs) with efficient attention mechanisms.
result Consistently outperforms baselines on various synthetic and real-world regression tasks involving large-scale data.