A Smale flow is a structurally stable flow with one dimensional invariant sets. We use information from homology and template theory to construct, visualize and in some cases, classify, nonsingular Smale flows in the 3-sphere.
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48 results for “flow visualization”
We present numerical visualizations of Ricci Flow of surfaces and 3-dimensional manifolds of revolution. Ricci_rot is an educational tool which visualizes surfaces of revolution moving under Ricci flow. That these surfaces tend to remain embedded in R3 is what makes direct visualization possible. The numerical lessons …
Combining visual attention with deep reinforcement learning improves sample efficiency.
problem Improving sample efficiency in deep reinforcement learning.
method Visual selective attention mechanism implemented using optical flow and batch normalization.
result Visual selective attention leads to improvements in sample efficiency on Atari games.
Visualizes information flow in ML systems for better understanding and analysis.
problem Understanding the flow of information in complex ML systems.
method Proposes a visual approach using Sankey Diagrams to analyze flow of information.
result Demonstrates the effectiveness of the proposed technique in diagnosing model performance.
We introduce a new, systematic framework for visualizing information flow in deep networks. Specifically, given any trained deep convolutional network model and a given test image, our method produces a compact support in the image domain that corresponds to a (high-resolution) feature that contributes to the given exp…
Efficiently visualizes uncertainty in local divergence of 2D vector fields.
problem Uncertainty in vector field data leads to inaccurate divergence computations.
method Closed-form approach for highly efficient and accurate uncertainty visualization of local divergence, assuming independently Gaussian-distributed vector uncertainties.
result Significantly enhanced efficiency and accuracy of our algorithms over classical MC approach.
InstanceFlow visualizes classifier confusion over training epochs.
problem Limited model interpretability through aggregate performance measures.
method Dual-view visualization tool showing instance-level learning behavior.
result Allows temporal analysis of training process and instance-level performance.
HFM uses deep learning to infer fluid dynamics from visual data.
problem Data assimilation of fluid dynamics from flow visualizations.
method Physics-informed deep learning framework based on Navier-Stokes equations.
result Accurate predictions of velocity and pressure fields in complex flows.
We consider the evolution of a compact segment of an analytic curve on the unit tangent bundle of a finite volume hyperbolic -manifold under the geodesic flow. Suppose that the curve is not contained in a stable leaf of the flow. It is shown that under the geodesic flow, the normalized parameter measure on the curve…
Study shows how brain completes missing parts of curves and constructs surfaces of negative curvature.
problem How the brain completes missing parts of curves and constructs surfaces of negative curvature.
method Solving variational problems to find sub-Riemannian geodesics and constructing surfaces of constant negative curvature.
result There is a one-to-one correspondence between sub-Riemannian geodesics used by the brain and rotational surfaces of constant negative curvature.
Visuals in scientific papers are used to express complex ideas; this study uses them to identify knowledge domains.
problem Scientific figures are underutilized in literature analysis.
method Encoded scientific figures into visual signatures and used distances between signatures to compare communities of practice.
result Figures can differentiate knowledge domains as effectively as text or citation patterns.
We study curvature flows in the locally homogeneous case (e.g. compact quotients of Lie groups, solvmanifolds, nilmanifolds) in a unified way, by considering a generic flow under just a few natural conditions on the broad class of almost-hermitian structures. As a main tool, we use an ODE system defined on the variety …
The paper develops a neural network to predict wind speed from visual observations.
problem Accurate wind speed prediction for renewable energy and weather forecasting.
method Coupled Convolutional and Recurrent Neural Network architecture trained on visual flow-structure interactions.
result The model accurately predicts wind speeds with low error compared to cup anemometer measurements.
The in-game economies of massively multi-player online games (MMOGs) are complex systems that have to be carefully designed and managed. This paper presents the results of an analysis of auction house data from the MMOG Glitch, across a 14 month time period, the entire lifetime of the game. The data comprise almost 3 m…
In this paper, we consider the interpretability of the foundational Laplacian-based semi-supervised learning approaches on graphs. We introduce a novel flow-based learning framework that subsumes the foundational approaches and additionally provides a detailed, transparent, and easily understood expression of the learn…
DSM improves visual quality of fetoscopic videos by mosaicking.
problem Challenges in identifying all vascular connections during fetoscopy due to low visual quality and drift.
method Proposes a Deep Sequential Mosaicking (DSM) framework using deep learning techniques to handle visual variations and reduce drift.
result DSM framework reduces accumulated drift and improves visual quality of fetoscopic videos.
Analysis of flow cytometry data is an essential tool for clinical diagnosis of hematological and immunological conditions. Current clinical workflows rely on a manual process called gating to classify cells into their canonical types. This dependence on human annotation limits the rate, reproducibility, and complexity …
Proposes a neural network method to improve consistencies in high dimensional data analysis.
problem Inconsistencies among dimensionality reduction, clustering, and visualization tasks in high dimensional data analysis.
method Consistent Representation Learning (CRL) neural network that performs NLDR transformations to satisfy LGP constraints.
result Improves consistencies in data interpretation through end-to-end task execution.
Classifies Morse flows on 3-sphere with specific saddle connections.
problem Classifying Morse-Smale flows on a 3-sphere with specific saddle connections.
method Used generalized Heegaard diagrams (Pr-diagrams) to classify flows.
result Found all possible, up to homeomorphism, ways to embed two circles in a 2-sphere with no more than 10 points of transversal intersection.
We develop a general approach to study geometric flows on homogeneous spaces. Our main tool will be a dynamical system defined on the variety of Lie algebras called the bracket flow, which coincides with the original geometric flow after a natural change of variables. The advantage of using this method relies on the fa…
Optical flow refers to the visual motion observed between two consecutive images. Since the degree of freedom is typically much larger than the constraints imposed by the image observations, the straightforward formulation of optical flow as an inverse problem is ill-posed. Standard approaches to determine optical flow…
Recent progress on automatic generation of image captions has shown that it is possible to describe the most salient information conveyed by images with accurate and meaningful sentences. In this paper, we propose an image caption system that exploits the parallel structures between images and sentences. In our model, …
FlowGMM uses normalizing flows for semi-supervised learning, showing promising results across various data types.
problem Semi-supervised learning with limited labeled data.
method Normalizing flows combined with latent Gaussian mixture models for generative modeling.
result FlowGMM achieves promising results on multiple data types, including text and tabular data.
Improved GAN performance with a novel local attention mechanism.
problem Enhancing the performance of Generative Adversarial Networks (GANs).
method Introducing a two-dimensional local attention mechanism that preserves geometry and locality, and using information flow graphs for design.
result Significant improvements in FID and Inception scores, from 18.65 to 15.94 on ImageNet.
This paper improves normalizing flows by combining MLE and sliced-Wasserstein distance for better data fidelity.
problem Normalizing flows struggle with generating realistic data and detecting out-of-distribution data.
method Proposes a hybrid objective function combining MLE and sliced-Wasserstein distance.
result Shows better generative abilities and lower likelihood of out-of-distribution data.
We define a class of Euclidean distances on weighted graphs, enabling to perform thermodynamic soft graph clustering. The class can be constructed form the "raw coordinates" encountered in spectral clustering, and can be extended by means of higher-dimensional embeddings (Schoenberg transformations). Geographical flow …
For decades, the sphere eversion has been a classic subject for mathematical visualization. The 1998 video "The Optiverse" shows geometrically optimal eversions created by minimizing elastic bending energy. We contrast these minimax eversions with earlier ones, including those by Morin, Phillips, Max, and Thurston. The…
Generative model for set-valued data using permutation invariant flows.
problem Modeling set-valued data with conditional generative models.
method Conditional generative probabilistic model using continuous normalizing flows with permutation equivariant dynamics.
result Significantly outperforms non-permutation invariant baselines in log likelihood and domain-specific metrics.
RG-Flow: A hierarchical and explainable flow model based on renormalization group and sparse priorcs.LG
RG-Flow combines RG and sparse priors for hierarchical image disentanglement.
problem Disentangling and manipulating image representations at different scales.
method Hierarchical flow model using RG and sparse prior distributions.
result RG-Flow enables semantic manipulation and style mixing at different image scales.
Graphs model human mobility patterns, reducing errors in data matching.
problem Lack of high-quality data and computational resources for graph-based mobility analysis.
method Embedding graphs into a continuous space to address matching, modeling, and visualization challenges.
result Approx 40% decrease in error on average in matched graphs vs unmatched ones.
GraphQ system uses GNNs to search for subgraph patterns in graphs.
problem Efficiently identifying and matching subgraph patterns in graph data.
method Graph neural networks (GNNs) for encoding graph data and NeuroAlign for node alignment.
result NeuroAlign improves node-alignment accuracy by 19-29% compared to baseline GNNs.
NOFIS uses normalizing flows to estimate rare event probabilities more efficiently.
problem Accurate estimation of rare event probabilities using conventional methods is inefficient and resource-intensive.
method NOFIS learns a sequence of proposal distributions by minimizing KL divergence losses and estimates rare event probability using importance sampling.
result NOFIS outperforms baseline approaches in estimating rare event probabilities across 10 distinct test cases.
Cohomology fractals illustrate complex 3-manifold properties.
problem Visualizing complex cohomology classes in hyperbolic 3-manifolds.
method Ray-tracing cohomology fractals and proving their distribution.
result Cohomology fractals converge to a distribution on the sphere at infinity.
Neural production systems learn visual dynamics by applying rule templates to entities.
problem Modeling interactions among entities in structured visual environments.
method Inspired by production systems, the paper uses rule templates to bind placeholder variables to specific entities, scoring and applying the best fitting rules to update entity properties.
result The architecture achieves robust future-state prediction and extrapolation from simple to complex environments, outperforming GNNs.
New network distance based on Laplacian flow captures structure.
problem Measuring similarity between network objects.
method Introducing Laplacian flow to define a new diffusion distance.
result Demonstrated utility and advantage over existing distances.
We present in this paper a general approach to study the Ricci flow on homogeneous manifolds. Our main tool is a dynamical system defined on a subset H(q,n) of the variety of (q+n)-dimensional Lie algebras, parameterizing the space of all simply connected homogeneous spaces of dimension n with a q-dimensional isotropy,…
MAGIC-Flow: Multiscale Adaptive Conditional Flows for Generation and Interpretable Classificationcs.LG
MAGIC-Flow generates and classifies medical images with interpretability.
problem Challenges in generative modeling for medical imaging.
method Conditional multiscale normalizing flow architecture.
result MAGIC-Flow creates realistic, diverse samples and improves classification.
FIS-GAN uses importance sampling in GANs to speed up training.
problem Efficiency in GAN training by focusing on hard-to-generate examples.
method Adapting importance sampling into GANs using normalizing flows.
result Significant acceleration in GAN optimization with improved fidelity.
In the first part of this dissertation, we give a new definition of a Laplace operator for Finsler metric as an average, with regard to an angle measure, of the second directional derivatives. This operator is elliptic, symmetric with respect to the Holmes-Thompson volume, and coincides with the usual Laplace--Beltrami…
Adversarial learning of probabilistic models has recently emerged as a promising alternative to maximum likelihood. Implicit models such as generative adversarial networks (GAN) often generate better samples compared to explicit models trained by maximum likelihood. Yet, GANs sidestep the characterization of an explici…
One of the key challenges of visual perception is to extract abstract models of 3D objects and object categories from visual measurements, which are affected by complex nuisance factors such as viewpoint, occlusion, motion, and deformations. Starting from the recent idea of viewpoint factorization, we propose a new app…
Notes on Morse Homology, focusing on gradient flow lines and semi-infinite dimensional cases.
problem Exploring Morse Homology and its applications in semi-infinite dimensional spaces.
method Presentation of concepts in finite dimensional Morse Homology, with an eye towards generalization to semi-infinite dimensions.
result Intuition for Floer homology through finite dimensional Morse Homology concepts.
We define an ending lamination for a Weil-Petersson geodesic ray. Despite the lack of a natural visual boundary for the Weil-Petersson metric, these ending laminations provide an effective boundary theory that encodes much of its asymptotic CAT(0) geometry. In particular, we prove an ending lamination theorem (Theorem …
Survey on robust data representation learning from a knowledge flow perspective.
problem Learning robust visual representation from noisy, incomplete or mismatched data.
method Low-rank modeling for robust knowledge recovery, transfer, and fusion.
result Unified formulation for robust knowledge discovery and transfer/fusion.
GIFsentiment predicts stock market returns and investor sentiment from social media GIFs.
problem Understanding investor sentiment in the stock market.
method Constructing a sentiment index from social media GIFs and analyzing its correlation with market returns and volume.
result GIFsentiment positively predicts stock market returns and negatively predicts returns for up to four weeks.
Curvature flow and inverse curvature flow solutions on 2D light cone identified.
problem Identifying self-similar solutions to curvature flow and inverse curvature flow on 2D light cone.
method Proved correspondence between CF and ICF solutions, analyzed ellipses and hyperboles, and characterized self-similar solutions.
result Ellipses and hyperboles are the only curves evolving under homotheties on the 2D light cone.
Flow cytometry is often used to characterize the malignant cells in leukemia and lymphoma patients, traced to the level of the individual cell. Typically, flow cytometric data analysis is performed through a series of 2-dimensional projections onto the axes of the data set. Through the years, clinicians have determined…
Generative adversarial networks improve stochastic input parametrization in subsurface flow simulations.
problem Effective parametrization of high-dimensional, correlated stochastic inputs in subsurface flow simulations.
method Training a generative adversarial network to emulate the data generating process of stochastic inputs.
result Generative adversarial networks preserve both visual realism and high-order statistics of flow responses, achieving a significant dimensionality reduction.