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.
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48 results for “Koszul-Tate resolution”
Constructs a new graded variety from algebraic data.
problem Creating a -graded extension of differential varieties.
method Algorithm using homotopy retract data of Koszul-Tate resolution.
result Significantly reduced number of homological computations.
Normal forms for Q-structures on graded manifolds explained.
problem Understanding structures of Q-manifolds on graded manifolds.
method Local and global normal forms results for Q-structures.
result Structures are concentrated along the zero-locus of curvatures.
Given a generic Lagrangian system, its Euler-Lagrange operator obeys Noether identities which need not be independent, but satisfy first-stage Noether identities, and so on. This construction is generalized to arbitrary differential operators on a smooth fiber bundle. Namely, if a certain necessary and sufficient condi…
A generic degenerate Lagrangian system of even and odd variables on an arbitrary smooth manifold is examined in terms of the Grassmann-graded variational bicomplex. Its Euler-Lagrange operator obeys Noether identities which need not be independent, but satisfy first-stage Noether identities, and so on. However, non-tri…
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.
Background: Three-dimensional, whole heart, balanced steady state free precession (WH-bSSFP) sequences provide delineation of intra-cardiac and vascular anatomy. However, they have long acquisition times. Here, we propose significant speed ups using a deep learning single volume super resolution reconstruction, to reco…
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…
Many real-world phenomena are observed at multiple resolutions. Predictive models designed to predict these phenomena typically consider different resolutions separately. This approach might be limiting in applications where predictions are desired at fine resolutions but available training data is scarce. In this pape…
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…
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 …
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.
Running high-resolution physical models is computationally expensive and essential for many disciplines. Agriculture, transportation, and energy are sectors that depend on high-resolution weather models, which typically consume many hours of large High Performance Computing (HPC) systems to deliver timely results. Many…
WrapNet optimizes inference for low-resolution neural networks by using 8-bit additions.
problem Reducing multiplication complexity in low-resolution neural networks.
method Adapting neural networks to use low-resolution (8-bit) additions in accumulators, with a cyclic activation layer and overflow penalty regularizer.
result Achieves comparable classification accuracy to 32-bit counterparts using low-resolution additions.
This paper simplifies diffusion models for high resolution images.
problem Applying diffusion models to high resolution images is challenging.
method Adjust noise schedule, scale specific parts, add dropout, and use downsampling.
result Achieved state-of-the-art image generation performance.
A refined form of 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 was established by the authors in the context of manifolds with corners; the canonical construction induces fibrations on the boundary faces of the resolution…
Some Poisson structures do admit resolutions by symplectic manifolds of the same dimension. We give examples and simple conditions under which such resolutions can not exist.
The shortage of high-resolution urban digital elevation model (DEM) datasets has been a challenge for modelling urban flood and managing its risk. A solution is to develop effective approaches to reconstruct high-resolution DEMs from their low-resolution equivalents that are more widely available. However, the current …
New deep learning method improves 4D Flow MRI super-resolution under domain shift.
problem Domain shift in low-resolution 4D Flow MRI data.
method Distributional deep learning framework for domain generalization.
result Framework significantly outperforms traditional methods in real data applications.
Training a deep neural network for classification constitutes a major problem in remote sensing due to the lack of adequate field data. Acquiring high-resolution ground truth (GT) by human interpretation is both cost-ineffective and inconsistent. We propose, instead, to utilize high-resolution, hyperspectral images for…
Obtaining magnetic resonance images (MRI) with high resolution and generating quantitative image-based biomarkers for assessing tissue biochemistry is crucial in clinical and research applications. How- ever, acquiring quantitative biomarkers requires high signal-to-noise ratio (SNR), which is at odds with high-resolut…
A refined form of 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 stru…
In the paper titled "Bockstein basis and resolution theorems in extension theory" (arXiv:0907.0491v2), we stated a theorem that we claimed to be a generalization of the Edwards-Walsh resolution theorem. The goal of this note is to show that the main theorem from (arXiv:0907.0491v2) is in fact equivalent to the Edwards-…
MeshfreeFlowNet generates high-resolution spatio-temporal solutions from low-resolution inputs.
problem Generating high-resolution spatio-temporal solutions from low-resolution inputs.
method Physics-constrained deep learning framework using fully convolutional encoders.
result Significantly outperforms existing baselines in super-resolution of turbulent flows.
Constant Scalar Curvature Kähler Metrics on Resolutions of an Orbifold Singularity of Depth 1math.DG
New metrics found on orbifold resolutions with specific curvature.
problem Finding metrics with constant scalar curvature on orbifolds.
method Constructing metrics on resolutions of orbifolds with type I singularities.
result Constant scalar curvature Kähler metrics constructed on resolutions.
A Monte Carlo k-nearest neighbours (KNN) and a multi-resolution convolutional neural network (CNN) were developed to detect the presences of multiple gasses in near infrared (IR) spectrums. High Resolution Transmission database was used to synthesize the near IR spectrums. Monte Carlo KNN determined the optimal kernel …
Method fuses low and high-resolution data for better health estimates.
problem Improving high-resolution health estimates from mixed data sources.
method Fusion of unbiased low-resolution and potentially biased high-resolution data, learning a distribution consistent with sampling bias.
result Significant reduction in bias in high-resolution estimates.
Generative adversarial networks generate realistic, time-evolving high-resolution atmospheric fields.
problem Improving spatial resolution of low-resolution atmospheric images.
method Recurrent, stochastic super-resolution GAN for generating ensembles of time-evolving high-resolution atmospheric fields.
result The GAN produces realistic, temporally consistent super-resolution sequences for radar-measured precipitation and cloud optical thickness.
High-Resolution Peak Demand Estimation Using Generalized Additive Models and Deep Neural Networkscs.LG
Paper proposes combining GAM and DNN for accurate peak demand estimation from lower-resolution data.
problem Predicting high-resolution peak demand from limited lower-resolution data.
method Combines generalized additive models (GAM) and deep neural networks (DNN) for half-hourly load forecasting.
result Proposed method reduces out-of-sample RMSE by 57.4% compared to benchmark.
High-resolution signal recovery via generalized sampling and functional principal component analysismath.ST
In this paper, we introduce a computational framework for recovering a high-resolution approximation of an unknown function from its low-resolution indirect measurements as well as high-resolution training observations by merging the frameworks of generalized sampling and functional principal component analysis. In par…
Study shows zero-shot super-resolution in neural operators is impossible in many cases.
problem Understanding the theoretical limits of zero-shot super-resolution in neural operators.
method Systematic theoretical study including information-theoretic and generalization bounds analysis.
result Zero-shot super-resolution is information-theoretically impossible in many settings.
Resolves singular fibers of a 5-manifold with action.
problem Discrete singular fibers of a closed 5-manifold with action.
method Construction of resolution compatible with cyclic surface singularities.
result Compatibility proved between resolution and cyclic surface singularities.
We present a method of generating high resolution 3D shapes from natural language descriptions. To achieve this goal, we propose two steps that generating low resolution shapes which roughly reflect texts and generating high resolution shapes which reflect the detail of texts. In a previous paper, the authors have show…
Pixel-space diffusion models outperform latent models on high-resolution image synthesis.
problem Efficiency and quality trade-off in high-resolution image synthesis.
method Sigmoid loss-weighting, simplified architecture, and resolution scaling.
result Achieved 1.5 FID on ImageNet512, new SOTA results on other datasets.
One significant challenge to scaling entity resolution algorithms to massive datasets is understanding how performance changes after moving beyond the realm of small, manually labeled reference datasets. Unlike traditional machine learning tasks, when an entity resolution algorithm performs well on small hold-out datas…
StyleNeRF generates high-resolution images with 3D consistency and style control.
problem Generating high-resolution images with fine details and 3D consistency.
method Integrates NeRF into a style-based generator for efficient high-resolution image synthesis.
result Synthesizes high-resolution images at interactive rates with high 3D consistency and style control.
Spin(7)-Orbifold Resolutionsmath.DG
We resolve Spin(7)-orbifolds using algebraic and symplectic techniques.
problem Resolving Spin(7)-orbifolds in exceptional holonomy metrics.
method Combines algebraic and symplectic techniques with analytic gluing methods.
result Existence of torsion-free Spin(7)-structures extending Joyce's theorem.
Determined the balanced cone of a specific geometric space.
problem Determining the balanced cone of the small resolution of the quintic conifold.
method Intersection number method to explicitly determine the cone.
result Explicitly determined the balanced cone of the small resolution of the quintic conifold.
Digital Rock Imaging is constrained by detector hardware, and a trade-off between the image field of view (FOV) and the image resolution must be made. This can be compensated for with super resolution (SR) techniques that take a wide FOV, low resolution (LR) image, and super resolve a high resolution (HR), high FOV ima…
Construct -instantons on orbifold resolutions using specific geometric ingredients.
problem Constructing -instantons on orbifold resolutions.
method Combining -instantons on orbifolds with Fueter sections over singular sets.
result Construction of numerous -instantons on resolutions of .
Land use classification of low resolution spatial imagery is one of the most extensively researched fields in remote sensing. Despite significant advancements in satellite technology, high resolution imagery lacks global coverage and can be prohibitively expensive to procure for extended time periods. Accurately classi…
Probabilistic SR method speeds up high-fidelity simulations with reliable uncertainty estimates.
problem Lack of reliable uncertainty quantification in deep-learning based SR methods.
method Statistical Finite Element Method and energy-based generative modeling.
result Efficient high-resolution predictions with inherent uncertainty estimates.
Defines products for fibered corners manifolds, generalizing resolutions.
problem Resolving fibered corners manifolds.
method Introduces a category of fibered corners manifolds with products and transverse fiber products, defining the 'ordered product' for wedge metrics.
result The 'ordered product' is a natural product for wedge metrics.
A central problem in neuroscience is reconstructing neuronal circuits on the synapse level. Due to a wide range of scales in brain architecture such reconstruction requires imaging that is both high-resolution and high-throughput. Existing electron microscopy (EM) techniques possess required resolution in the lateral p…
Method resolves 4D symplectic orbifolds using complex geometry.
problem Resolving symplectic orbifolds in 4 dimensions.
method Combining complex geometry techniques with symplectic form gluing.
result Examples of 4D symplectic orbifolds successfully resolved.