Paper finds new cscK metrics on orbifold resolutions.
problem Existence of cscK metrics on orbifold resolutions.
method Computes Futaki invariant of Kaehler classes on resolutions.
result New existence and non-existence results for cscK metrics.
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48 results for “resolution invariance”
When the signed weighted resolution set was defined as an invariant of pseudoknots, it was unknown whether this invariant was complete. Using the Gauss-diagrammatic invariants of pseudoknots introduced by Dorais et al, we show that the signed were-set cannot distinguish all non-equivalent pseudoknots. This goal is achi…
Extends results on Futaki invariant for Kaehler metrics on algebraic manifolds.
problem Existence of Kaehler metrics with constant scalar curvature.
method Revisits and extends classical and recent results on Futaki invariant.
result Extensions and applications of Futaki invariant in Kaehler geometry.
This paper considers the invariance of knot Floer homology in a purely algebraic setting, without reference to Heegaard diagrams, holomorphic disks, or grid diagrams. We show that (a small modification of) Ozsváth and Szabó's cube of resolutions for knot Floer homology, which is assigned to a braid presentation with a …
Study symplectic cohomology of certain singularities using homological mirror symmetry.
problem Compute symplectic cohomology for specific singularities.
method Use homological mirror symmetry to compute symplectic cohomology.
result Suggests a new conjecture about the relationship between small resolutions and symplectic cohomology.
DFMs generalize neural networks for topological layer design.
problem Designing neural networks that can handle high-resolution data without parameter dependence.
method Introducing deep function machines (DFMs) that are invariant to input dimensionality.
result DFMs can approximate bounded non-linear operators between function spaces.
Paper constructs a HOMFLYPT-type invariant for pseudo links.
problem Inability to construct polynomial invariants for pseudo links using Hecke algebra techniques.
method Using a resolution homomorphism and pseudo Hecke algebra of type \(A\), the paper constructs a HOMFLYPT-type invariant for oriented pseudo links.
result The constructed invariant satisfies a natural pseudo skein relation and admits a state-sum formulation.
Computes -algebroid for linear foliations on vector spaces.
problem Invariants of singular foliations on vector spaces induced by Lie subalgebras.
method Explicitly constructs projective resolutions and computes -algebroid structure.
result Provides invariants and constant-rank replacements of singular foliations.
New invariant for tied links connects states without resolution dependence.
problem Understanding the Kauffman-like states for tied links.
method Defined Aicardi-Juyumaya states and showed their contribution to the invariant is independent of resolution.
result The double bracket of a tied link diagram can be computed and used to find linked but differently polynomial tied links.
This paper is devoted to the study of geometric structures modeled on homogeneous spaces G/P, where G is a real or complex semisimple Lie group and is a parabolic subgroup. We use methods from differential geometry and very elementary finite-dimensional representation theory to construct sequences of invar…
Knot lattice homology invariant of smooth knot type in rational homology spheres.
problem Invariance of knot lattice homology in rational homology spheres.
method Proving knot lattice homology invariant through doubly-filtered homotopy type.
result Knot lattice homology invariant of smooth knot type in rational homology spheres.
Proves invariance of weighted extremal Kähler metrics under smooth blowups.
problem Invariance of weighted extremal Kähler metrics under smooth blowups.
method Uniform coercivity estimate for the (relative, weighted) Mabuchi energy on blowups.
result Invariance of weighted extremal Kähler metrics under smooth blowups.
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.
Bialynicki-Birula theory, Morse-Bott theory, and resolution of singularities for analytic spacesmath.CV
Develops Bialynicki-Birula and Morse-Bott theory for complex analytic spaces.
problem Extending classical theories to complex analytic spaces with holomorphic actions.
method Extends Bialynicki-Birula and Morse-Bott theories to non-compact complex manifolds and analytic spaces, proving existence and deriving geometric consequences.
result Existence of Bialynicki-Birula decompositions for -invariant subspaces in complex manifolds.
Characterizes values of slice-torus invariants related to knot genus.
problem Understanding the values of slice-torus invariants for knots.
method Characterization based on stable smooth slice genus.
result Existence of slice torus invariants without explicit constructions.
Seiberg-Witten invariants and surface singularities II. Singularities with good $\C^*$-actionmath.AG
This is a continuation of our paper math.AG/0111298. We prove an explicit formula for the geometric genus p_g of a quasihomogeneous isolated surface singularity in terms of the Seiberg-Witten invariant of the link and other topological data which can be read from a resolution graph of the singularity. Moreover, we also…
Simplified Khovanov-Rozansky operators for link invariants.
problem Complexity in Khovanov-Rozansky knot invariants.
method Substituted matrix factorization with simple operators and conjugations.
result Global reductions for simplifying link invariants.
A physically natural potential energy for simple closed curves in is shown to be invariant under Möbius transformations. This leads to the rapid resolution of several open problems: round circles are precisely the absolute minima for energy; there is a minimum energy threshold below which knotting cannot oc…
A new dynamical approach connects resolution cohomology to group representations.
problem Establishing a bijection between resolution cohomology and group representations.
method Gauge-theoretic Morse flow on the minimal resolution.
result The flow converges to specific irreducible representations of the group.
Probabilistic pseudo knots model uncertain knot diagrams.
problem Modeling knots with unresolved crossings.
method Assign probabilities to undetermined crossings; define probabilistic equivalence and extend classical knot invariants.
result Capture uncertainty in physical, biological, and computational contexts.
This is the last in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of ``global conformal invariants''; these are defined to be conformally invariant integrals of geometric scalars. The conjecture asserts that the integrand of any such integral can be expressed as…
Study symmetries in smoothed polygonal links.
problem Computing Khovanov homology and link invariants.
method Cube of resolutions with combinatorial structure.
result New group-theoretic invariants of links.
Researchers create exact sequences for isotropic 2-Grassmannian.
problem Constructing exact sequences for isotropic 2-Grassmannian.
method Using Penrose transform over a double fibration.
result The constructed sequences are analogues of the Bernstein-Gelfand-Gelfand resolutions.
Extends Adams' theorem to periodic cohomology.
problem Proving Adams' theorem for periodic cohomology.
method Adapting Adams' approach to periodic cohomology.
result Conjecture proven in a special case.
Mapping Low-Resolution Images To Multiple High-Resolution Images Using Non-Adversarial Mappingeess.IV
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.
A Categorification of the HOMFLY-PT Polynomial with a Spectral Sequence to Knot Floer Homologymath.GT
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.
DICOD creates efficient shift-invariant representations for long signals.
problem Creating efficient shift-invariant representations for long signals.
method DICOD is a distributed convolutional sparse coding algorithm based on coordinate descent with locally greedy updates.
result DICOD achieves super-linear computational speed-up in a distributed setting.
Floer theory constructs filtrations on quantum cohomology for symplectic manifolds.
problem Quantum cohomology of symplectic manifolds with -actions.
method Floer theory applied to -actions on symplectic manifolds.
result Constructs a family of filtrations on quantum cohomology for Conical Symplectic Resolutions.
Twisted skein homologymath.GT
We apply the techniques of totally twisted Khovanov homology to the constructions by M. Asaeda, J. Przytycki, and A. Sikora of Khovanov type homologies for links and tangles in I-bundles over (orientable) surfaces. As a result we describe an invariant chain complex built out of resolutions with only non-contractible ci…
Researchers link tangle invariants for Khovanov and knot Floer homologies.
problem Relating tangle invariants for Khovanov and knot Floer homologies.
method Constructing algebraic DA bimodules for tangles and open braids, showing homotopy equivalence to Ozsvath-Szabo bimodules.
result Homotopy equivalence of DA bimodules for tangles and knot Floer homology.
The paper proposes a method to improve fine-resolution predictions using coarse-resolution data.
problem Limited supervision for fine-resolution predictions with scarce data.
method Attention-based regularization on multi-view coarse-resolution data.
result The method improves fine-resolution predictions using coarse-resolution data.
Super-resolution improves MRI resolution and accuracy for biomarker assessment.
problem Inadequate SNR for accurate quantification in high-resolution MRI.
method Utilized deep learning super-resolution to maintain SNR for T2 relaxation time biomarkers while generating high-resolution images.
result Super-resolution successfully maintains high-resolution and accurate biomarkers for MRI.
The Theory of Pseudoknotsmath.GT
Classical knots in can be represented by diagrams in the plane. These diagrams are formed by curves with a finite number of transverse crossings, where each crossing is decorated to indicate which strand of the knot passes over at that point. A pseudodiagram is a knot diagram that may be missing crossing…
This study prioritizes temporal resolution over spatial in energy systems models due to higher influence.
problem The impact of spatial and temporal resolution on energy system models.
method Global sensitivity analysis to compare structural aspects, spatial, and temporal resolution.
result Temporal resolution has a higher influence on all results parameters compared to spatial resolution.
Deep learning improves 3D microscopy resolution without matched target images.
problem Anisotropic resolution in volumetric fluorescence microscopy.
method Cycle-consistent generative adversarial network trained on unpaired 2D images.
result Enhanced axial resolution and restored details between imaging planes.
There are 2^n possible resolutions of a smooth pseudodiagram with n precrossings. If we consider piecewise-linear (PL) pseudodiagrams and resolutions that themselves are PL, certain resolutions of the pseudodiagram may not exist in three-space. We investigate this situation and its impact on the weighted resolution set…
This is a survey article about knot Floer homology. We present three constructions of this invariant: the original one using holomorphic disks, a combinatorial description using grid diagrams, and a combinatorial description in terms of the cube of resolutions. We discuss the geometric information carried by knot Floer…
Recently M. Kreck introduced a class of stratified spaces called p-stratifolds [M. Kreck, Stratifolds, Preprint]. He defined and investigated resolutions of p-stratifolds analogously to resolutions of algebraic varieties. In this note we study a very special case of resolutions, so called optimal resolutions, for p-str…
High-resolution signal recovery via generalized sampling and functional principal component analysismath.ST
The paper presents a method to recover high-resolution signals from low-resolution measurements.
problem Recovering high-resolution signals from low-resolution indirect measurements.
method Combining generalized sampling and functional principal component analysis.
result High-resolution recovery is possible under certain conditions and with a sufficiently large training set.
A resolution of the St. Petersburg paradox is presented. In contrast to the standard resolution, utility is not required. Instead, the time-average performance of the lottery is computed. The final result can be phrased mathematically identically to Daniel Bernoulli's resolution, which uses logarithmic utility, but is …
The `Folk Theorem' that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type is proved in the context of manifolds with corners. This procedure is shown to capture the simultaneous resolution of all isotropy types in a `resolution tower' which projects …
Enhanced coloring invariant distinguishes folded molecular chain topologies.
problem Apparent indistinguishability of folded chain topologies using current coloring invariants.
method Introduced Boltzmann weights to improve the resolving power of quandle colorings.
result Improved resolution in distinguishing folded chain topologies.
DeepDownscale uses deep learning to upscale weather forecasts.
problem Computational expense of high-resolution weather models limits their use.
method Supervised deep learning to learn high-resolution from low-resolution forecasts.
result Significant improvement in weather forecast quality.
Develops a multi-resolution multi-task framework for integrating noisy, varying data.
problem Integrating evidence from multiple observation processes with varying resolutions and noise levels.
method Multi-resolution Multi-task Gaussian Processes (MRGP) framework, shallow and deep Gaussian Process mixtures.
result Generalizes and outperforms state-of-the-art GP compositions, offering efficient corrections and approximations.
Study contact resolutions for Jacobi structures, providing examples and impossibility results.
problem Understanding contact resolutions of Jacobi structures.
method Examining various classes of Jacobi structures and their contact properties.
result Identified conditions under which contact resolutions exist and those where they do not.
Study proposes CNN for reconstructing high-res urban DEMs.
problem Lack of high-res urban DEM datasets for flood modeling.
method Multi-scale CNN model trained on urban DEMs of varying resolutions.
result CNN-based method produces superior high-res urban DEMs.
Word embeddings may not be uniquely defined due to incompatibility between invariant classes of transformations.
problem Incompatibility between word embeddings and evaluation functions leads to performance discrepancies.
method Formal treatment of identifiability issue, numerical examples, and proposed resolutions.
result Word embeddings are not unique and performance differences may be due to arbitrary elements.