MT-VAE learns motion transitions for generating diverse future motions.
problem Learning long-term human motion sequences with transitions.
method Jointly learns motion mode embeddings and transitions using Variational Auto-Encoders.
result Generates multiple plausible future motion sequences from input.
Study of Schrödinger flows on S6 using octonions.
problem Schrödinger flows on S6 and related geometric properties. method Using G2-structure on O, study of G2-binormal motion of curves in R7. result Equivalence of G2-binormal motion to Schrödinger flows and nonlinear Schrödinger-type system. New equations for Cosserat media motions derived from bundle automorphisms.
problem Modeling deformations in Cosserat media.
method Euler-type equations derived from SO(3)-bundle automorphisms.
result Presented new equations for Cosserat media motions.
We expose some ideas from mathematical logics, i.e. the background of the theory of o-minimal structures, and demonstrate how they lead to the notion of a tame integral of motion and some extensions and clarifications of previous results on obstructions to integrability of geodesic flows.
New minimal surfaces derived from helicoids.
problem Existence of minimal surfaces with specific symmetries.
method Balance equations and nodal limit analysis.
result Existence of new screw motion invariant minimal surfaces.
Sprays get Hamiltonian description using Dirac structures.
problem Finding Hamiltonian descriptions for sprays.
method Using Dirac structures and gauge transformations to find constants of motion.
result Sprays can have Hamiltonian descriptions.
It is common for CCTV operators to overlook inter- esting events taking place within the crowd due to large number of people in the crowded scene (i.e. marathon, rally). Thus, there is a dire need to automate the detection of salient crowd regions acquiring immediate attention for a more effective and proactive surveil…
We present a robust multiple manifolds structure learning (RMMSL) scheme to robustly estimate data structures under the multiple low intrinsic dimensional manifolds assumption. In the local learning stage, RMMSL efficiently estimates local tangent space by weighted low-rank matrix factorization. In the global learning …
This paper learns motion primitives from driving data to improve vehicle path-tracking.
problem Improving vehicle path-tracking accuracy through learned motion primitives.
method Two-level structure with path segmentation and clustering; Gaussian Mixture Model (GMM) and Gaussian Mixture Regression (GMR).
result The model predicts future lateral control commands with high accuracy.
Finsler space is differentiable manifold for which Minkowski space is the fiber of the tangent bundle. To understand structure of the reference frame in Finsler space, we need to understand the structure of orthonormal basis in Minkowski space. In this paper, I considered the definition of orthonormal basis in Minkowsk…
End-to-end machine learning identifies and classifies ciliary motion.
problem Manual ciliary motion analysis is laborious, error-prone, and unscaleable.
method Convolutional LSTM networks for automatic ciliary segmentation and classification.
result 90% accuracy achieved with few hundred training epochs.
Computes group of ring motions for a specific link structure.
problem Computing the group of motions for a specific type of link.
method Study of a short exact sequence of groups of ring motions for general ring links in R^3.
result Builds a presentation for the group of motions of H-trivial links with an arbitrary number of components.
Study constructs balanced datasets for seismic failure prediction.
problem Imbalanced datasets limit machine learning performance in seismic failure prediction.
method Framework with three steps: GMF identification, probability density estimation, and sample transformation.
result Framework improves machine learning performance in seismic failure mode prediction.
We rephrase the problem of 3D reconstruction from images in terms of intersections of projections of orbits of custom built Lie groups actions. We then use an algorithmic method based on moving frames "a la Fels-Olver" to obtain a fundamental set of invariants of these groups actions. The invariants are used to define …
Innovative ball bearing converts rotary to reciprocating motion.
problem Designing efficient motion conversion mechanisms.
method Closed curve envelopment theory and diameter-stroke ratio concept.
result Compact and vibration-reduced ball bearing design.
In this paper we show that Galilean group is a matrix Lie group and find its structure. Then provide the invariants of special Galilean geometry of motions, by Olver's method of moving coframes, we also find the corresponding {e}−structure.
Abstract: Study Hamiltonian systems on almost cosymplectic manifolds, extending contact Hamiltonian systems.
problem Extend Hamiltonian systems to almost cosymplectic manifolds.
method Determine Hamiltonian vector field on odd-dimensional almost cosymplectic manifolds.
result Extend equations of motion to generalized transitive almost cosymplectic structures.
Study of motion constraints and path-following on 3D space.
problem Path-following with non-holonomic constraints on R3. method Exploration of geometric structure and construction of guiding vector fields.
result General principles for constructing guiding vector fields for path-following.
A CNN-based method improves DTI of the human heart, compensating for motion.
problem Signal loss due to heart motion in DTI.
method Invertible Wavelet Scattering using CNN.
result Effective motion compensation and improved fiber structures.
Unified framework for human motion generation on Riemannian manifolds.
problem Learning valid human motion in Euclidean spaces.
method Riemannian Motion Generation (RMG) on product manifolds, Riemannian flow matching.
result Achieves state-of-the-art FID (0.043) on HumanML3D and surpasses strong baselines on MotionMillion.
Generative adversarial networks model and generate physical therapy exercises.
problem Mathematical modeling of human movements in physical therapy.
method Generative adversarial network structure with discriminative and generative models trained concurrently.
result Ability to classify and generate motion examples that resemble recorded sequences.
Survey on manifold complexities and motion planning in robotics.
problem Understanding topological complexities of manifolds in robotic motion planning.
method Overview of topological complexities, geodesic motion planning, and connections to critical point theory.
result Estimation of motion planning complexity using Riemannian geometry and critical point theory.
SL(N,C) is the phase space of the Poisson SU(N). We calculate explicitly the symplectic structure of SL(N,C), define an analogue of the Hamiltonian of the free motion on SU(N) and solve the corresponding equations of motion. Velocity is related to the momentum by a non-linear Legendre transformation.
The paper models term structures under volatility uncertainty using G-Brownian motion.
problem Modeling term structures with volatility uncertainty.
method Modeling instantaneous forward rates as a diffusion process driven by G-Brownian motion.
result Derives a sufficient condition for the absence of arbitrage under volatility uncertainty.
New method separates market motion from stock correlations.
problem Understanding the dynamics of stock correlations relative to market motion.
method Cluster reduced-rank correlation matrices by subtracting the largest eigenvalue.
result Extracted market states are quasi-stationary over long periods.
Paper proposes incorporating road rules as a loss function for better motion planning.
problem Lack of structured priors in perception and motion forecasting methods.
method Integrates road rules as a loss function in a probabilistic model using REINFORCE.
result Motion forecasts result in safer plans for self-driving vehicles.
Kinetic theory explains financial Brownian motion from trader dynamics.
problem Understanding financial Brownian motion from high-frequency trading dynamics.
method Deriving time-evolution equations, Bogoliubov-Born-Green-Kirkwood-Yvon hierarchies, Boltzmann-like and Langevin-like equations.
result Mathematical foundation for financial Brownian motion parallels physical Brownian motion.
A new model captures option price dynamics using sub-fractional Brownian motion.
problem Capturing the complex price dynamics of financial options.
method Developed a CEV model driven by a mixed sub-fractional Brownian motion.
result Empirical tests show the model effectively captures option price dynamics.
Geometric model for flag waving motion.
problem Modeling the motion of a physical flag.
method Isometric immersion of a square into 3D space with boundary conditions.
result The space of flags is an infinite dimensional manifold.
FDBM models use fractional Brownian motion to model complex stochastic processes.
problem Capturing memory effects and long-range dependencies in stochastic processes.
method Developed a generative diffusion bridge framework using a Markovian approximation of fractional Brownian motion.
result FDBM outperforms standard models in predicting future states and unpaired data translation.
Researchers derive a formula for Brownian motion transition probability in a specific octant.
problem Computing default probabilities and credit valuation adjustments in structural credit models.
method Semi-analytic formula derived using separation of variables in spherical coordinates, followed by numerical methods to solve the resulting eigenvalue problem.
result A solution to the transition probability problem expressed as an expansion into special functions and an eigenvalue.
In this paper we study a notion of topological complexity for the motion planning problem. The topological complexity is a number which measures discontinuity of the process of motion planning in the configuration space X. More precisely, it is the minimal number k such that there are k different motion planning rules,…
Programmatic Motion Concepts learn human actions from paired videos.
problem Learning motion concepts from paired video and action sequences.
method Semi-supervised learning architecture for hierarchical motion representation.
result Outperforms established baselines, especially in small data settings.
Deformational structures, in many aspects generalizing standard elasticity theory, are investigated in abstract form. Within free deformational structures we define algebra of deformations, classify them by its special properties, define motions and conformal motions together with deformational decomposition of manifol…
Introduces Motion Programs for better video analysis of human motion.
problem Current video analysis focuses on raw pixels or keypoints, missing higher-level motion primitives.
method Introduces Motion Programs as a neuro-symbolic representation of motions as a composition of high-level primitives.
result Motion Programs accurately describe diverse human motions and improve downstream tasks.
Paper introduces new motion synthesis model using normalizing flows.
problem Data-driven motion synthesis with probabilistic and controllable models.
method Probabilistic, generative, autoregressive model using normalizing flows and LSTMs.
result Randomly sampled motion from the model outperforms task-agnostic baselines.
Modular method predicts motion in crowded scenes using learned environment models.
problem Predicting motion in dynamic, crowded environments.
method Modular model of spatial and dynamic aspects, unsupervised adaptation to new tasks.
result Comparable performance to state-of-the-art, transferable across tasks.
We derive an equation of motion for interest-rate yield curves by applying a minimum Fisher information variational approach to the implied probability density. By construction, solutions to the equation of motion recover observed bond prices. More significantly, the form of the resulting equation explains the success …
Study on determinants of unitary Brownian motion and their asymptotic laws.
problem Understanding determinants of unitary Brownian motion and their behavior over time.
method Using Stiefel fibration and skew-product decomposition of the Stiefel Brownian motion.
result Prove asymptotic laws for determinants of block entries of unitary Brownian motion.
New deep architecture improves head motion prediction in 360° videos.
problem Predicting user head motion in 360-degree videos using past positions and video content.
method Re-examined existing deep-learning approaches, identified flaws, and designed a new TRACK architecture.
result TRACK achieves state-of-the-art performance, outperforming competitors by up to 20 percent.
New process from fractional BM and OU process yields simpler variance.
problem Simpler model for autocovariance structure.
method Construct new process using fractional BM and OU process, analyze increments.
result Variance of new process easier to compute than FARIMA.
Generative model learns motion to language and vice versa using deep RNNs.
problem Linking human motion and natural language for semantic representations and robot behaviors.
method Bidirectional mapping between motion and language using deep recurrent neural networks (RNNs) and sequence-to-sequence learning.
result Model generates realistic motions from natural language descriptions and vice versa.
Deep neural nets predict vortex-induced vibrations from limited flow data.
problem Predicting lift and drag forces on structures from scattered velocity field data.
method Extended deep neural networks solving coupled Navier-Stokes and structural dynamics equations.
result Deep neural networks can accurately infer structural parameters, pressure field, and velocity field from limited flow data.
A new method learns object representations from motion in slot representations.
problem Unsupervised object extraction from low-level visual data.
method Contrastive learning in slot representations, focusing on moving objects and distinct entities.
result Introduced a new evaluation metric to measure diversity of slot vectors.
Diffusion Variational Autoencoders capture topological properties of datasets.
problem Standard VAEs struggle with topological properties of certain datasets.
method Introduces Diffusion VAEs with transition kernels of Brownian motion on arbitrary manifolds.
result Diffusion VAEs can capture topological properties of synthetic datasets.
Equations for minimal surfaces from rigid motions in high dimensions.
problem Finding minimal surfaces from rigid motions in RN. method Derives equations for minimal surfaces using rigid motions in RN. result Equations for minimal surfaces in RN. Motivated by the interplay between structural and reduced form credit models, we propose to model the firm value process as a time-changed Brownian motion that may include jumps and stochastic volatility effects, and to study the first passage problem for such processes. We are lead to consider modifying the standard f…
Study geodesic complexity in homogeneous Riemannian manifolds.
problem Geodesic motion planning and complexity in homogeneous Riemannian manifolds.
method Riemannian geometry, stratifications of cut loci, and properties of homogeneous manifolds.
result Established new bounds on geodesic complexity and computed its value for homogeneous Riemannian manifolds.