We recast the Calabi flow in DeGiorgi's language of minimizing movements. We establish the long time existence of minimizing movements for K-energy with arbitrary initial condition. Furthermore we establish some a priori regularity of these solutions, and that sufficiently regular minimizing movements are smooth soluti…
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48 results for “Minimizing Movement”
Paper proves minimizing movements match smooth droplet flow in 3D.
problem Consistency of minimizing movements with smooth mean curvature flow.
method Proved minimizing movements coincide with smooth droplet flow.
result Minimizing movements and smooth mean curvature flow are consistent in 3D.
Study on droplet flow on uneven surfaces, proving existence and properties.
problem Understanding droplet movement on irregular surfaces.
method Existence of smooth flow and 1/2-Hölder continuous minimizing movement solutions.
result Properties of minimizing movements including comparison principles and uniform boundedness.
Alternative proof of weak solutions to mean curvature flow using minimizing movements.
problem Existence of weak solutions to mean curvature flow and volume preserving mean curvature flow.
method Proposes a new existence proof using a minimizing movements scheme and a novel proxy for distance.
result Unconditional convergence towards a De Giorgi solution for the minimizing movements scheme.
We show that K-energy minimizing movements agree with smooth solutions to Calabi flow as long as the latter exist. As corollaries we conclude that in a general Kahler class long time solutions of Calabi flow minimize both K-energy and Calabi energy. Lastly, by applying convergence results from the theory of minimizing …
Paper proves existence of solutions for complex surface diffusion equation.
problem Existence of solutions for anisotropic surface diffusion with elasticity.
method Cahn-Taylor minimizing movement scheme for three-dimensional analysis.
result Proves existence of classical solutions without curvature regularization.
Scheme minimizes -elastic energy of curves over time.
problem Minimizing -elastic energy of curves over time.
method Minimizing movement scheme with approximate normal graphs.
result Short-time existence and lower bound on solution's lifetime.
New method for evolving surfaces using generalized power mean curvature flow.
problem Evolve surfaces with volume penalization replaced by a generalized term.
method Generalized minimizing movement scheme converging to geometric evolution equation.
result Minimizing movements coincide with smooth classical solutions and preserve mean convexity.
Study a flow for curve energy, proving existence for various p.
problem Evolution of closed curves under energy minimization.
method Second order flow decreasing p-elastic energy, proving existence via minimizing movements.
result Existence of solutions for , long-time existence for .
Study finds weak solutions for complex map flows with optimal lifespan.
problem Existence of weak solutions for two-phase matrix-valued harmonic map flows.
method Modified minimizing movement scheme, discretizing time and interpolating solutions.
result Existence of weak solutions with optimal lifespan for the limiting system.
New algorithm reduces costs in wind energy systems by minimizing decision changes.
problem Costs associated with decision changes in wind energy systems.
method Episodic CBO with movement costs using Gaussian Process and mirror descent.
result Our algorithm consistently outperforms standard CBO in altitude optimization.
NoTMF forecasts sparse urban road movement speeds with nonstationary temporal matrix factorization.
problem Sparse and nonstationary movement speed data from urban roads.
method Nonstationary Temporal Matrix Factorization (NoTMF) model.
result NoTMF outperforms baseline models in forecasting urban road movement speeds.
Smartwatch HRV measurements improved with machine learning.
problem Systematic error in HRV measurements from consumer smartwatches.
method Explanatory and predictive modeling using accelerometer data.
result Error in HRV measurements can be minimized by machine learning.
A new method reduces data movement in neural network training.
problem Large data movement during neural network training.
method Streaming batch principal component analysis for low-rank updates.
result Effective training of convolutional neural networks with low overhead.
A deep implicit-explicit minimizing movement method for option pricing in jump-diffusion modelsq-fin.CP
New deep learning method for option pricing in jump-diffusion models.
problem Option pricing in jump-diffusion models with high-dimensional assets.
method Implicit-explicit minimizing movement time-stepping approach using deep ANNs.
result Consistent and asymptotically correct solutions for large underlyings.
Gradient flows and Evolution Variational Inequalities in metric spaces. I: structural propertiesmath.FA
Analyzes gradient flows and EVI in metric spaces with structural properties and convergence results.
problem Characterizing and analyzing gradient flows and Evolution Variational Inequalities in metric spaces.
method Study of structural properties, equivalence with maximal slope curves, convergence of Minimizing Movement-JKO scheme.
result Equivalence with maximal slope curves and uniform convergence of Minimizing Movement-JKO scheme.
Strong convergence of the thresholding scheme for the mean curvature flow of mean convex setsmath.AP
Study shows thresholding scheme converges for mean curvature flow of convex sets.
problem Analyzing convergence of thresholding scheme for mean curvature flow.
method Time discretization using Merriman, Bence and Osher's scheme, focusing on two-phase mean convex settings.
result Time-integrated energy of approximation converges to limit's energy in minimizing movements interpretation.
We derive generalization error bounds for stationary univariate autoregressive (AR) models. We show that imposing stationarity is enough to control the Gaussian complexity without further regularization. This lets us use structural risk minimization for model selection. We demonstrate our methods by predicting interest…
Framework uses optimal transport for neural architecture search.
problem Optimizing neural architectures in deep learning.
method Semi-discrete optimization using optimal transport.
result Gradient flow and minimizing movement scheme converge to reaction-diffusion equations.
Quantitative Alexandrov theorem and asymptotic behavior of the volume preserving mean curvature flowmath.AP
New theorem shows shapes close to balls, flow converges to balls in 2D and 3D.
problem Understanding the asymptotic behavior of volume-preserving mean curvature flow.
method Proved a new quantitative Alexandrov theorem and used it to show flow convergence.
result Weak solutions of volume-preserving mean curvature flow converge to disjoint balls in R^2 and R^3.
Unified online algorithm for both competitive ratio and regret minimization.
problem Achieving both competitive ratio and regret minimization in online algorithms.
method Extending a regret minimization algorithm to handle movement cost and combining it with a base algorithm.
result Unified online algorithm that guarantees both competitive ratio and small regret over any time interval.
Wearable smart suit tracks infant movements with high accuracy.
problem Early detection of atypical motor development in infants.
method Developed a multi-sensor smart suit for data collection, trained a deep CNN algorithm for automatic posture and movement classification.
result Setup achieves human equivalent accuracy in infant posture and movement classification.
Paper reduces movement primitive dimensionality in parameter space.
problem High dimensionality of movement primitives makes policy optimization expensive.
method Investigates dimensionality reduction in parameter space, identifying principal movements.
result Dimensionality reduction in parameter space is more effective than in configuration space.
Deep convolutional architecture identifies eye movements for biometric faster and more accurately.
problem Biometric identification of eye movements for authentication.
method Developed a deep convolutional architecture to process raw eye-tracking signals.
result Achieved a lower error rate by one order of magnitude and faster identification time by two orders of magnitude.
New algorithms achieve optimal performance in online convex optimization with strong convexity and squared norms.
problem Optimal performance in online convex optimization with specific cost structures.
method Proposed and analyzed new algorithms (G-OBD, R-OBD) with theoretical guarantees.
result G-OBD and R-OBD achieve optimal competitive ratios of under specific conditions.
Survey reviews machine learning for automatic movement generation.
problem Need for automatic movement animation in interactive media.
method Machine learning techniques and motion capture data.
result Discussion of research gaps and challenges for future work.
Hedging Extreme Co-Movementscond-mat.stat-mech
Based on a recent theorem due to the authors, it is shown how the extreme tail dependence between an asset and a factor or index or between two assets can be easily calibrated. Portfolios constructed with stocks with minimal tail dependence with the market exhibit a remarkable degree of decorrelation with the market at…
Taureau uses Twitter sentiment analysis to predict stock market movement.
problem Predicting stock market movement using public opinion on Twitter.
method Obtained historical tweets, filtered and labeled, generated word embeddings, assessed sentiment scores, correlated with stock price movement, designed and evaluated predictive model.
result Taureau can predict stock price movement from lagged sentiment scores.
The study models market price movement based on investors' expectations.
problem Understanding the dynamics of investors' expectations and market price movement.
method Developed a non-linear evolutionary equation linking investors' expectations and market asset price movement.
result Model predictions co-integrated with asset time series, suggesting potential for price movement forecasting.
Neural nets predict user attention from mouse movements.
problem Predicting user attention from mouse cursor movements.
method Investigated different mouse movement representations and trained neural networks.
result Neural networks outperform handcrafted features for predicting user attention.
In this article we discuss the distribution of asset price movements by the market potential function. From the principle of free energy minimization we analyze two different kinds of market potentials. We obtain a U-shaped potential when market reversion (i.e. contrarian investors) is dominant. On the other hand, if t…
MPANF improves naive forecast by incorporating directional information.
problem Challenging to surpass naive forecast in financial time series.
method Combines naive forecast with movement prediction and accuracy.
result MPANF generally outperforms common benchmarks.
Framework infers coordination strategies from movement data.
problem Inferring individual movement strategies from group data.
method Formalizes Coordination Strategy Inference Problem; provides methodology to infer strategies.
result Framework accurately infers strategies in simulated and real-world datasets.
Neuroscientific studies of drawing-like movements usually analyze neural representation of either geometric (eg. direction, shape) or temporal (eg. speed) features of trajectories rather than trajectory's representation as a whole. This work is about empirically supported mathematical ideas behind splitting and merging…
Study identifies key trades predicting market movements.
problem Predicting future market price movements.
method Optimized neural network predictor to identify influential trades.
result Trades with specific characteristics significantly impact future price predictions.
The study introduces a new stickiness parameter for stock prices using a non-linear model.
problem Understanding how closely individual stocks follow a stock index's price movements.
method Developed a non-linear pricing model inspired by tectonic plate movements to measure stickiness.
result Defined a stickiness parameter for stock price returns using a novel model.
This paper uses GAN and ERMSE to improve stock price movement prediction accuracy.
problem Predicting stock price movement direction is challenging due to complex, incomplete, and fuzzy information.
method The paper proposes a deep learning model using GAN and ERMSE to forecast stock market trends.
result The GAN model outperformed LSTM in predicting stock price movement direction with a 4.35% improvement.
Bayesian method infers local rules for collective animal movement.
problem Learn local rules governing long-term group behaviors.
method Bayesian Inverse Reinforcement Learning with Linearly-Solvable Markov Decision Process.
result Recover true costs and find value of collective movement.
Optimizing data movement significantly improves transformer training efficiency.
problem Data movement is a major bottleneck in training transformers.
method Developed a recipe to globally optimize data movement in transformers.
result Achieved up to 1.30x performance improvement over state-of-the-art frameworks.
Study on pseudo-Riemannian Bertrand manifolds finds no closed movement systems.
problem Exploring properties of pseudo-Riemannian Bertrand manifolds.
method Proof of properties and discussion of the theory.
result No pseudo-Riemannian completely Bertrand systems exist.
Study identifies personality traits from dance movements in music.
problem Predicting individual differences from music-induced movement.
method Identified Big Five personality traits and EQ/SQ scores from dance movements.
result Successfully explored unseen space for personality and EQ/SQ.
The paper supports task classification from eye movements, achieving 95.4% accuracy.
problem Decoding the observer's task from eye movements.
method Exploratory analysis, feature projection, feature elimination, SVM and Ada Boosting classifier training.
result Achieved 95.4% accuracy in task classification.
New algorithm reduces dynamic regret in time-varying movement costs.
problem Dynamic regret in online convex optimization with time-varying movement costs.
method Introduced a novel algorithm for time-varying movement costs, achieving comparator-adaptive dynamic regret bound.
result Established first comparator-adaptive dynamic regret bound of .
Stock selection improved with a novel neural model capturing continuous stock dynamics.
problem Lack of continuous stock dynamics prediction and implicit cross-domain dependencies.
method StockODE, a latent variable model with NRODEs and hierarchical hypergraph for continuous stock volatility and inter-domain dependencies.
result Significantly outperforms baselines, improving Sharpe Ratio by up to 18.57%.
Generically learns movement control policies from exploration data.
problem Movement optimization in physically based characters.
method Parameterizes actions as target states, learns low-level control policy.
result Improves movement optimization across multiple tasks and algorithms.
Paper adapts and learns movement primitives robustly with probabilistic models.
problem Learning and adapting movement primitives with variability and correlations.
method Prior distributions and general purpose operators for robust parameter estimation and adaptation.
result Robust learning and adaptation achieved with fewer training instances and task-specific heuristics.
DeepMove learns place representations from large movement data.
problem Lack of movement context in traditional place representations.
method Directly models movements between places using deep learning.
result DeepMove outperforms state-of-the-art methods in place categorization and clustering.
Automated GMA using accelerometers detects abnormal infant movements with human-level accuracy.
problem Undetected perinatal stroke leads to lifelong disability.
method Wearable accelerometers and Discriminative Pattern Discovery (DPD) for automated GMA.
result Automated method correctly identifies abnormal movements with human-level accuracy.