SC-Net learns interpretable filters for inverse problems, achieving optimal convergence and super-resolution.
problem Solving ill-posed inverse problems with effective regularization and interpretability.
method SC-Net operates in the spectral domain, learning a pointwise adaptive filter function based on signal-to-noise ratio.
result SC-Net achieves optimal convergence rate and zero-shot super-resolution, matching theoretical bounds.
Hyperspectral remote sensing images (HSIs) usually have high spectral resolution and low spatial resolution. Conversely, multispectral images (MSIs) usually have low spectral and high spatial resolutions. The problem of inferring images which combine the high spectral and high spatial resolutions of HSIs and MSIs, resp…
The Koszul-Tate resolution is described in the context of the geometry of jet spaces and differential equations. The application due to Barnich, Brandt, and Henneaux of this resolution to computing the horizontal cohomology is analyzed. Relations with the Vinogradov spectral sequence are discussed.
Study of Dirac operators on S3 and S2 spheres.
problem Analyzing Dirac operators on specific spheres.
method Using Kähler's formalism, spectral resolution of eigenspinors.
result Complete spectral resolution of Dirac operators on S3 and S2.
Hyperspectral remote sensing images (HSIs) are characterized by having a low spatial resolution and a high spectral resolution, whereas multispectral images (MSIs) are characterized by low spectral and high spatial resolutions. These complementary characteristics have stimulated active research in the inference of imag…
Proves a rank inequality between Khovanov and knot Floer homologies.
problem Rank inequality between Khovanov and knot Floer homologies for knots.
method Oriented cube of resolutions construction for knot Floer homology.
result Proves Rasmussen's conjecture about Khovanov and knot Floer ranks.
Combines BTEM and T-PLS for accurate spectral recovery and calibration.
problem Calibrating pure spectra of minority components in mixtures without prior knowledge.
method Band target entropy minimization (BTEM) and target partial least squares (T-PLS).
result Estimated amounts from BTEM-T-PLS similar to MCR-ALS on simple mixtures, superior on complex ones.
Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution ena…
New method reconstructs moving parts of proteins in cryo-EM.
problem Reconstructing non-rigid molecules with moving parts in cryo-EM.
method Graph Laplacian construction from multiple projection images, followed by spectral volume expansion.
result High-resolution visualization of molecular dynamics using spectral volumes.
Spectral sequence links knot Floer homology to HOMFLY-PT polynomial.
problem Connecting knot Floer homology to HOMFLY-PT polynomial.
method Constructing a spectral sequence from cube of resolutions.
result Spectral sequence converges to knot Floer homology and ranks HOMFLY-PT homology.
A new method estimates nonhomogeneous Poisson process intensities with super-resolution.
problem Estimating cyclic arrival rates of nonhomogeneous Poisson processes.
method Super-resolution estimation using sinusoidal waves with unknown parameters.
result Finite sample guarantees for super-resolution estimation under suitable conditions.
Study spectral sequences in smooth generalized cohomology theories.
problem Systematic study of torsion in differential cohomology.
method Use Atiyah-Hirzebruch spectral sequences with filtrations by Cech resolutions.
result Explicit identification of differentials in spectral sequences for various theories.
Analytic lattice cohomology defined for isolated singularities, linking to Heegaard Floer cohomology.
problem Defining and analyzing analytic lattice cohomology for isolated singularities.
method Using a good resolution of the singularity, proving independence of resolution choice, and relating to Hodge spectral numbers.
result Independence of analytic lattice cohomology from the choice of resolution and connection to Hodge spectral numbers.
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency, thereby resulting in a coherent design. The popular convex compressed sensing methods…
Khovanov homology for links in S^3 via 1-tangle diagrams in annulus.
problem Computing Khovanov homology for links in S^3.
method Constructing a chain complex from a 1-tangle diagram in the annulus, using a cube of resolutions.
result A spectral sequence converging to reduced Khovanov homology.
In this paper we define a new convergence called "asymptotically conic convergence" in which a smooth family of Riemannian metrics on a fixed compact manifold degenerate to a metric with isolated conic singularity. Our results are: convergence of the spectrum of the geometric Laplacians and uniform convergence of the c…
Ozsvath and Szabo gave a combinatorial description of knot Floer homology based on a cube of resolutions, which uses maps with twisted coefficients. We study the t=1 specialization of their construction. The associated spectral sequence converges to knot Floer homology, and we conjecture that its E_1 page is isomorphic…
New non-Kähler manifolds constructed with specific properties.
problem Creating non-Kähler manifolds with cohomological properties.
method Four constructions using quotient singularities and spectral sequences.
result Disproved a conjecture by Popovici.
Detects and maps informal settlements in developing countries using satellite imagery.
problem Mapping informal settlements for aid delivery.
method Two methods: LR Sentinel-2 imagery and VHR satellite imagery.
result Successfully mapped informal settlements with LR satellite imagery.
Spectral representations improve CNNs without changing the model.
problem Efficient computation and model flexibility in CNNs.
method Spectral pooling, stochastic regularization, complex-coefficient spectral parameterization.
result Spectral representations lead to faster convergence and competitive performance.
SAGAN improves image generation by leveraging attention across feature locations.
problem Traditional GANs generate details only from local feature maps, limiting image quality.
method SAGAN uses self-attention to model long-range dependencies and spectral normalization for better training.
result SAGAN achieves state-of-the-art results, boosting Inception score and reducing Frechet Inception distance.
The paper proposes using CWT and STFT for training neural speech models.
problem Training high-quality neural speech models.
method Proposes spectral amplitude and phase losses from STFT and CWT for training.
result Shows that CWT spectral loss can train a high-quality model as good as STFT-based loss.
We prove the existence of a spectral sequence for Lagrangian Floer homology which converges to the Floer homology of the image of a Lagrangian submanifold under multiple fibred Dehn twists. The E1 term of the sequence is given by the hypercube of "resolutions" of the Dehn twists involved. The proof relies on the exa…
New symplectic annular Khovanov homology connects knot theory to Floer homology.
problem Understanding the relationship between knot theory and Floer homology.
method Introducing a new version of symplectic annular Khovanov homology and establishing spectral sequences.
result Established spectral sequences linking different knot homologies.
New method compresses non-Gaussian distributions exponentially.
problem Efficiently representing and computing non-Gaussian probability distributions.
method Tensor-Network Fourier Methods using QTT representation.
result Exponential compression of non-Gaussian distributions.
This paper proves a conjecture about knot homologies.
problem Proving a spectral sequence from reduced triply graded homology to knot Floer homology.
method Constructing a bigraded spectral sequence from gl0 homology to knot Floer homology. result Proof of the Dunfield-Gukov-Rasmussen conjecture.
SPECTRA improves probabilistic energy forecasting by separating trends and uncertainties.
problem Interacting uncertainties from renewable intermittency, demand flexibility, market volatility, and weather impact probabilistic forecasts.
method Adaptive state-space exogenous context and temporal-frequency resolution architecture.
result Achieved best CRPS in 14 out of 18 settings, reducing CRPS by 5.74% and upper-tail quantile risk by 7.27%.
This article addresses the two significant aspects of Ozsváth and Szabó's knot Floer cube of resolutions that differentiate it from Khovanov and Rozansky's HOMFLY-PT chain complex: (1) the use of twisted coefficients and (2) the appearance of a mysterious non-local ideal. Our goal is to facilitate progress on Rasmussen…
Proves a conjecture linking knot Floer homology and HOMFLY-PT homology for singular knots.
problem Proving a conjecture about the relationship between knot Floer homology and HOMFLY-PT homology for singular knots.
method Using a basepoint filtration, a recursion formula, and additional sln-like differentials, the authors prove the conjecture. result The conjecture linking knot Floer homology and HOMFLY-PT homology for singular knots is proven.
HSSE framework embeds single-cell RNA-seq data at multiple scales.
problem Capturing heterogeneous local structure in single-cell RNA-seq data.
method Hierarchical sheaf spectral embedding (HSSE) framework.
result HSSE achieves competitive or improved performance in single-cell RNA-seq data representation learning.
Paper combines geometry and time-series analysis for spatiotemporal data.
problem Multivariate time-series data from multiple sensors.
method Combines manifold learning, Riemannian geometry, and spectral analysis.
result Proposes Riemannian multi-resolution analysis (RMRA) for dynamic mode extraction.
New machine learning model detects informal settlements in developing countries using low-res satellite data.
problem Lack of detailed maps for vulnerable populations in developing countries.
method Developed a new machine learning data set and demonstrated effective classification schemes for low-resolution satellite imagery.
result It is possible to detect informal settlements using low-resolution satellite data, making it more accessible for NGOs.
Proposes a parsimonious graph spectral method for time series data.
problem Efficiently transmitting multivariate time series data.
method Graph spectral embedding with unsupervised, parsimonious encoding.
result Near-linear computational complexity and interpretable event structure.
Geodesic rays and chordal distances link algebraic and geometric properties of positive metrics.
problem Understanding the geometry of the space of positive metrics at infinity.
method Using Monge-Ampère equations and test configurations, algebraic descriptions of geodesic rays and chordal distances are derived.
result The Mabuchi chordal distance between geodesic rays associated with ample test configurations equals the spectral distance between their filtrations.
A 3-stage method enhances hyperspectral image classification accuracy.
problem Classifying detailed classes in hyperspectral images with limited labeled data.
method Uses Nested Sliding Window and PCA for spatial consistency, SVM for spectral estimation, and TV model for spatial smoothing.
result Our method outperforms state-of-the-art algorithms, especially in scenarios with small training sets.
The paper computes the cohomology of cubic surfaces and their lines.
problem Understanding the cohomology of cubic surfaces and their lines.
method Spectral sequence in the method of simplicial resolution developed by Vassiliev.
result The cohomology ring of the space of lines on cubic surfaces is isomorphic to that of PGL(4,C). New method tackles nonlinear, infinite-dimensional signal processing problems.
problem Nonlinear, infinite-dimensional signal processing challenges.
method Directly addresses continuous, nonlinear problems as sparse functional optimization.
result Proves no duality gap for non-atomic problems, allowing efficient solution.
Detects and maps informal settlements using satellite data.
problem Mapping informal settlements for aid distribution.
method Combining satellite data and machine learning for roofing material detection.
result Effective aid distribution through accurate settlement mapping.
A hybrid model combines diffusion and neural operator methods for stress prediction in hyperelastic materials.
problem Challenges in predicting stress fields in hyperelastic materials with complex microstructures.
method A hybrid surrogate framework combining a conditional denoising diffusion probabilistic model (cDDPM) and a modified DeepONet.
result The hybrid model consistently outperforms traditional methods by one to two orders of magnitude.
Optimizes maps with controlled distortion for geometric tasks.
problem Free-boundary diffeomorphism optimization in geometric modeling.
method Least-squares quasiconformal (LSQC) operator and Spectral Beltrami Network (SBN).
result LSQC minimizer well-posed under mild conditions, stable under mesh refinement.
Deep learning classifies land use from high-resolution aerial imagery.
problem Variations in land features in aerial imagery due to sensor settings and context.
method Used deep convolutional neural networks to classify land use from VHR orthophoto mosaics.
result Deep learning can accurately classify land use from high-resolution visible band multispectral imagery.
SR-NAM maps low-res images to multiple high-res images realistically.
problem Mapping low-resolution images to multiple high-resolution images realistically.
method SR-NAM using Non-Adversarial Mapping (NAM) technique and a degradation model.
result Realistic degradation and down-sampling of high-resolution images.
Deep learning speeds up whole heart MRI to 30 seconds.
problem Long acquisition times in whole heart MRI.
method Deep learning, specifically a 3D residual U-Net, to reconstruct high-resolution images from low-resolution data.
result Super-resolution images show better edge sharpness and fewer artefacts than low-resolution images.
pAElla detects malware in DCs/SCs with high accuracy.
problem Real-time malware detection in high-resolution data centers.
method AI-powered edge computing with IoT-based monitoring and Power Spectral Density.
result pAElla achieves F1-score close to 1 with low false alarm and malware miss rates.
Novel neural operator predicts complex spatiotemporal dynamics from partial observations.
problem Capturing complex operator dynamics in infinite-dimensional function spaces.
method Integrates Koopman operator theory with deep neural networks to approximate nonlinear operators between Banach spaces.
result BNO achieves robust zero-shot super-resolution in unsteady flow prediction and outperforms conventional methods.
TMSCD detects multi-scale communities in temporal networks automatically.
problem Discovering multi-scale communities in large, evolving networks.
method Spectral multilayer formulation of MM method with automatic parameter selection.
result Automatic detection of multi-scale communities without manual parameter selection.
Paper introduces a new algebraic link invariant related to knot Floer and Khovanov homologies.
problem Developing a new algebraic link invariant related to knot homologies.
method Constructing a chain complex C1±1(D) from plat braid diagrams, showing it is isomorphic to Khovanov homology and conjecturing it is a link invariant. result The total homology of the constructed complex is a link invariant, and it is conjectured to be isomorphic to δ-graded knot Floer homology.
A neural network improves DOA estimation from a single snapshot.
problem Estimating DOAs from a single snapshot with limited aperture.
method Deep learning architecture trained to generate high-resolution spatial spectrum.
result Our (SP)2-Net outperforms classical methods.