Let and be a conformal map from into , with . Then with and is a moving frame on . It satisfies the following equation $$d\s…
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48 results for “partial frames”
On partially hyperbolic diffeomorphisms in dimension three via a notion of autonomous dynamicsmath.DS
Proves rigidity of 3D partially hyperbolic systems via autonomous dynamics.
problem Rigidity of partially hyperbolic diffeomorphisms in 3D.
method Introducing autonomous dynamical systems to prove rigidity.
result Rigidity of partially hyperbolic diffeomorphisms on 3-manifolds.
Generalizes abelianization for framed local systems over surfaces.
problem Understanding framed local systems over punctured surfaces for various groups.
method Analysis of spectral networks, triangulations, and matrix reinterpretation of path lifting rules.
result Parametrizations of moduli spaces of decorated and framed local systems.
The paper studies posets from decompositions in symmetric monoidal categories.
problem Understanding posets from decompositions in symmetric monoidal categories.
method Defining decompositions and partial decompositions, complexes of frames, partial bases, and ordered versions.
result Unified approach to combinatorics and homotopy type of posets and complexes.
Describes maps with prescribed eigenvectors of Jacobian matrices.
problem Maps with specific eigenvectors of Jacobian matrices.
method Coordinate-independent definition of Jacobian, Frobenius integrability theorems, rich partial frames.
result Complete analysis for rich partial frames, partial results for non-rich and non-involutive cases.
The paper classifies time-like surfaces in a static space-time.
problem Classifying time-like surfaces in a static space-time.
method Constructing a pseudo-orthonormal frame field and analyzing invariants.
result Complete classification theorem for class~ surfaces.
Study inextensible flows of curves in 4D pseudo-Galilean space and defines energy functions.
problem Analyzing inextensible flows and energy of curves in 4D pseudo-Galilean space.
method Expressed inextensible flows as partial differential equations, defined directional derivatives, and expressed bending elastic energy functions.
result Necessary and sufficient conditions for inextensible flows are given as partial differential equations.
Via Gauge theory, we give a new proof of partial regularity for harmonic maps in dimension m>2 into arbitrary targets. This proof avoids the use of adapted frames and permits to consider targets of "minimal" C^2 regularity. The proof we present moreover extends to a large class of elliptic systems of quadratic growth.
In the paper we study the algebroid A of the groupoid of partially invertible elements over the lattice of orthogonal projections of a -algebra. In particular the complex analytic manifold structure of these objects is investigated. The expressions on the Lie brackets for A and related algebroids are given in nonc…
Novel method controls complex physical systems over long time frames.
problem Controlling complex nonlinear physical systems over long time frames.
method Hierarchical predictor-corrector scheme with separate planning and control networks.
result Successfully controls complex physical systems like incompressible Navier-Stokes equations.
Neural architectures learn belief representations for partially observable environments.
problem Learning belief states in partially observable domains.
method One-step frame prediction and contrastive predictive coding (CPC) as objective functions.
result Neural architectures can learn belief representations, encoding both state information and uncertainty.
We study the problem of finding the minimal (maximal) genus for a surface where a given four-valent graph with fixed opposite edge structure can be embedded into. We find several partial relations and give new reformulations in combinatorial and knot theoretic languages.
We show how pairs of isothermic surfaces are given by curved flats in a pseudo Riemannian symmetric space and vice versa. Calapso's fourth order partial differential equation is derived and, using a solution of this equation, a Möbius invariant frame for an isothermic surface is built.
We prove that the Einstein equations can be solved in a very general form for arbitrary spacetime dimensions and various types of vacuum and non-vacuum cases following a geometric method of anholonomic frame deformations for constructing exact solutions in gravity. The main idea of this method is to introduce on (pseud…
This work frames active inference through control as inference, offering robust control algorithms.
problem Active inference framework lacks practical sensorimotor control algorithms.
method Frame active inference through control as inference, presenting trajectory optimization as inference.
result AI may be framed as partially-observed CaI when the cost function is defined in observation states.
We present two families of exterior differential systems (EDS) for non-isometric embeddings of orthonormal frame bundles over Riemannian spaces of dimension q = 2, 3, 4, 5.... into orthonormal frame bundles over flat spaces of sufficiently higher dimension. We have calculated Cartan characters showing that these EDS sa…
Analyzes soap films using BV functions and covering spaces.
problem Solving Plateau's problem with soap films.
method Covering space method with constrained BV functions.
result Examples of soap films not modelable with Reifenberg method.
The smoothing theory is revised to generalize to different disc embedding spaces.
problem Generalizing the smoothing theory to various disc embedding spaces.
method Revising the Morlet-Burghelea-Lashof-Kirby-Siebenmann theorem to apply to different versions of disc smooth embedding spaces.
result The delooping of disc embedding spaces is shown to be compatible with the Hatcher and Budney actions.
Researchers adapt Newstead's method to compute betti numbers in characteristic 2.
problem Computing betti numbers of framed moduli spaces in characteristic 2.
method Adaptation of Newstead's Mayer-Vietoris argument in characteristic 2.
result Conjectural recursive formulae for mod two betti numbers verified partially.
For each integer q>0 there is a cohomology theory such that the zero cohomology group of a manifold N of dimension n is a certain group of cobordism classes of proper fold maps of manifolds of dimension n+q into N. We prove a splitting theorem for the spectrum representing the cohomology theory of fold maps. For even q…
The paper introduces new metric structures on -foliations and uses a flow to deform them.
problem Developing new flexible metric structures on -foliations.
method Introducing new metric structures and using the partial Ricci flow to deform them.
result Deformation retraction of new structures with positive partial Ricci curvature onto classical structures.
A new reinforcement learning method for medical decisions with limited data.
problem Learning high-performing policies from partially observed data in healthcare.
method Optimization objective that combines policy and generative model quality, suitable for batch off-policy settings.
result Demonstrated improved performance on synthetic and medical decision-making problems.
SQAIR generates videos of moving objects, tracking and predicting them reliably.
problem Generating videos of moving objects with reliable object tracking and prediction.
method Explicitly encoding object presence, locations, and appearances in latent variables.
result SQAIR reliably discovers and tracks objects throughout sequences of frames and generates future frames.
Geometric invariants of fold maps and their signatures.
problem Characterizing cobordism groups of fold maps.
method Combining immersion data and stable partial framings.
result A Poincare-Hopf type formula for the signature of manifolds.
Paper connects Turaev cobracket to Kashiwara--Vergne problem via Hodge theory.
problem Solving the Kashiwara--Vergne problem in algebraic geometry.
method Combining Turaev cobracket and Goldman bracket results, constructing torsors of solutions.
result Found a torsor of solutions to the Kashiwara--Vergne problem that depends only on topology.
Bayesian model captures spatial correlations in data.
problem Modeling spatial correlations in high-dimensional data.
method Structured Bayesian Gaussian process latent variable model with parameterized spatial kernel and structure-exploiting algebra.
result Inference is tractable with computational complexity similar to traditional Bayesian GP-LVM.
We propose a method for explicit computation of the Chern character form of a holomorphic Hermitian vector bundle over a complex manifold in a local holomorphic frame. First, we use the descent equations arising in the double complex of -forms on and find explicit degree decomposition of the Cher…
Paper tackles fall detection using adversarial learning.
problem Detecting falls in the absence of training data due to class imbalance.
method Adversarial learning framework with spatio-temporal autoencoder and convolution network.
result Proposed framework outperformed baseline methods on publicly available datasets.
New method for classifying disk embeddings in 4-manifolds.
problem Classifying smooth isotopy classes of neat embeddings of 2-disks in 4-manifolds.
method Using an invariant going back to Dax, constructing a group structure, and relating to mapping class groups.
result The group structure on isotopy classes of neat embeddings is usually not abelian or finitely generated.
New method estimates model performance bounds without ground truth labels.
problem Evaluation of weakly supervised models without direct access to ground truth labels.
method Formulates model evaluation as a partial identification problem and uses Fréchet bounds for performance estimation.
result Derives accurate and computationally efficient bounds for key metrics like accuracy, precision, recall, and F1-score.
We develop an invariant local theory of Lorentz surfaces in pseudo-Euclidean 4-space by use of a linear map of Weingarten type. We find a geometrically determined moving frame field at each point of the surface and obtain a system of geometric functions. We prove a fundamental existence and uniqueness theorem in terms …
We introduce an approach based on moving frames for polygon recognition and symmetry detection. We present detailed algorithms for recognition of polygons modulo the special Euclidean, Euclidean, equi-affine, skewed-affine and similarity Lie groups, and explain the procedure for a generic Lie group. The time complexity…
The description of invariants of surfaces with respect to the motion groups is reduced to the description of invariants of parameterized surfaces with respect to the motion groups. Existence of a commuting system of invariant partial differential operators (derivatives) and a finite system of invariants, such that any …
Conditional Independence Testing with Heteroskedastic Data and Applications to Causal Discoverystat.ME
Improved CI test for heteroskedastic data enhances causal discovery.
problem CI testing assumptions fail in heteroskedastic data.
method Adapted partial correlation CI test for heteroskedastic noise.
result The adapted test outperforms standard CI test in heteroskedastic cases.
Bertrand framed surfaces defined in Euclidean 3-space with applications.
problem Defining and characterizing Bertrand framed surfaces.
method Using moving frames to define Bertrand framed surfaces and analyzing their caustics and involutes.
result Conditions for caustics and involutes to be inverse operations of framed surfaces.
Quaternionic frames' admissibility and homotopy proven.
problem Existence and interpolation of quaternionic frames.
method Interpreting frames as adjoint orbits.
result Spaces of quaternionic frames are path-connected.
Introduces hyperbolic generalized framed surfaces and their properties.
problem None explicitly stated; focuses on introducing new geometric objects.
method Generalization of hyperbolic framed surfaces and curves.
result Established conditions for a surface to be a hyperbolic generalized framed base surface and explored their singularities.
Study of generalized Bishop frames on curves in 4D space.
problem Understanding frames on curves in 4D space.
method Introducing and studying four types of generalized Bishop frames on curves in .
result Every regular curve in admits all four types of generalized Bishop frames.
The main drawback of the Frenet frame is that it is undefined at those points where the curvature is zero. Further- more, in the case of planar curves, the Frenet frame does not agree with the standard framing of curves in the plane. The main drawback of the Bishop frame is that the principle normal vector N is not in …
Framed Braid Equivalencesmath.GT
New framed moves extend classical knot theory results.
problem Extending classical knot theory to framed braids.
method Introduced framed versions of L-moves, Hilden, Pure Hilden groups, and framed versions of the Birman theorem.
result Proved a framed version of the Birman theorem for framed links in plat representation.
Study on Bertrand lightcone framed curves in Lorentz-Minkowski 3-space.
problem Analyzing mixed types of curves with singular points in Lorentz-Minkowski 3-space.
method Using lightcone frame to consider Bertrand types for lightcone framed curves.
result Existence conditions of Bertrand lightcone framed curves in all cases.
The paper extends BPS invariants for framed knots and links.
problem Investigating BPS invariants for framed knots and links.
method Using the dual A-polynomial and framing change formula, the paper extends the relationship between algebraic curves and BPS invariants to framed knots and links.
result Explicit formulas for extremal A-polynomials and BPS invariants of framed knots, and numerical calculations for framed Whitehead links and Borromean rings.
Gradient descent constructs tight fusion frames.
problem Constructing tight fusion frames from prescribed subspaces.
method Gradient descent and symplectic geometry.
result Gradient descent can be used to construct tight fusion frames.
Simply connected spaces of tight frames identified.
problem Understanding the connectivity of spaces of tight frames.
method Viewing tight frames as elements of Stiefel manifolds and identifying simply connected spaces.
result Spaces of tight frames, including finite unit-norm tight frames, are simply connected.
TrackNet: A Deep Learning Network for Tracking High-speed and Tiny Objects in Sports Applicationscs.LG
TrackNet tracks tiny balls in sports videos with high precision.
problem Accurately tracking tiny and fast-moving objects like tennis balls in sports videos.
method Developed a heatmap-based deep learning network, TrackNet, trained on public and additional labeled videos.
result Achieved high precision (99.7%) in ball tracking on public domain videos.
New invariants defined for framed knots and links.
problem Defining invariants for framed knots and links.
method Introducing birack brackets and categorifying their multiset.
result Quiver-valued invariant defined for framed knots and links.
Study reveals LLM personas have two distinct components: frame-robust aggregated traits and frame-dependent geometric features.
problem Evaluation of LLM personas via psychometric questionnaires discards within-instance correlation structure.
method Constructed within-instance correlation matrices from IPIP-50 responses and analyzed geometry on SPD manifolds under manipulated question orderings.
result Persona expression comprises two dissociable components: aggregated features (Big Five scores) and geometric features (SPD manifold).
Higher-dimensional Milnor frames are characterized and contrasted with 3D Heisenberg and 4D nilpotent Lie algebras.
problem Characterizing higher-dimensional Milnor frames and their properties.
method Definition and classification of higher-dimensional Milnor frames and their relationship to known Lie algebras.
result Higher-dimensional Milnor frames are isomorphic to direct sums of 3D Heisenberg and 4D nilpotent Lie algebras and an abelian Lie algebra.