arXiv research

In many signal processing problems, it may be fruitful to represent the signal under study in a frame. If a probabilistic approach is adopted, it becomes then necessary to estimate the hyper-parameters characterizing the probability distribution of the frame coefficients. This problem is difficult since in general the …

Study evaluates how framing affects machine learning models for sepsis prediction.

Stochastic video prediction models take in a sequence of image frames, and generate a sequence of consecutive future image frames. These models typically generate future frames in an autoregressive fashion, which is slow and requires the input and output frames to be consecutive. We introduce a model that overcomes the…

Clarifies Einstein-Cartan gravitation with Dirac spinor on generalized frame bundle.

PyTorch Frame simplifies multi-modal tabular learning with modular data and model handling.

A semi-recurrent hybrid VAE-GAN model for generating sequential data is introduced. In order to consider the spatial correlation of the data in each frame of the generated sequence, CNNs are utilized in the encoder, generator, and discriminator. The subsequent frames are sampled from the latent distributions obtained b…

In deep reinforcement learning (RL) tasks, an efficient exploration mechanism should be able to encourage an agent to take actions that lead to less frequent states which may yield higher accumulative future return. However, both knowing about the future and evaluating the frequentness of states are non-trivial tasks, …

Bertrand framed surfaces defined in Euclidean 3-space with applications.

Quaternionic frames' admissibility and homotopy proven.

New kinematic model for a spin-rolling sphere using Darboux frame.

Introduces hyperbolic generalized framed surfaces and their properties.

This paper presents a generalization of symplectic geometry to a principal bundle over the configuration space of a classical field. This bundle, the vertically adapted linear frame bundle, is obtained by breaking the symmetry of the full linear frame bundle of the field configuration space, and it inherits a generaliz…

Study of generalized Bishop frames on curves in 4D space.

Dual frame-rate system improves real-time perception for autonomous vehicles.

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 …

New framed moves extend classical knot theory results.

Study on Bertrand lightcone framed curves in Lorentz-Minkowski 3-space.

The paper extends BPS invariants for framed knots and links.

Simply connected spaces of tight frames identified.

Gradient descent constructs tight fusion frames.

This paper improves ASR performance by aligning frames more accurately.

New invariants defined for framed knots and links.

Study reveals LLM personas have two distinct components: frame-robust aggregated traits and frame-dependent geometric features.

Higher-dimensional Milnor frames are characterized and contrasted with 3D Heisenberg and 4D nilpotent Lie algebras.

Generating video frames that accurately predict future world states is challenging. Existing approaches either fail to capture the full distribution of outcomes, or yield blurry generations, or both. In this paper we introduce an unsupervised video generation model that learns a prior model of uncertainty in a given en…

Canonical framings and stable framings for the tangent bundle of a spin 3-manifold are introduced, and illustrated by a number of familiar examples. Methods for constructing canonical framings, and for comparing them with other naturally defined framings, are discussed.

Study on focal surfaces of lightcone framed surfaces in Lorentz-Minkowski 3-space.

The paper shows that random frames have full spark with high probability.

The paper connects hyperbolic spinors to non-null framed curves in Minkowski 3-space.

This note is dedicated to the study of a Hopf module structures on the space of framed chord diagrams and framed graphs. We also introduce a framed version of the chromatic polynomial and propose two methods to construct framed weight systems.

We discuss the geometric foundation behind the use of stochastic processes in the frame bundle of a smooth manifold to build stochastic models with applications in statistical analysis of non-linear data. The transition densities for the projection to the manifold of Brownian motions developed in the frame bundle lead …

Paper revisits FRAME model, explaining instability and proposing a new metric.

Introduces formal frames for manifolds and their properties.

Kirchhoff energy is a classical functional on the space of arclength-parameterized framed curves whose critical points approximate configurations of springy elastic rods. We introduce a generalized functional on the space of framed curves of arbitrary parameterization, which model rods with axial stretch or cross-secti…

Generalized Frenet frames for singular space curves

Frame-spun knots are constructed by spinning a knot of lower dimension about a framed submanifold of S^n. We show that all frame-spun knots are slice (null-cobordant).

Study of lightcone framed surfaces in Lorentz-Minkowski 3-space, focusing on curvature behavior.

Proposes SE(3) equivariant graph neural networks with local frames for efficient geometric approximation.

Modified knotoids with framing and coframing for quantum invariants.

The paper studies circular evolutes and involutes of framed curves in Euclidean space.

The generic singularities and bifurcations are classified for one-parameter families of curves with frames in a space form, the Euclidean space, the elliptic space or the hyperbolic space via projective geometry. Two kinds of frames are considered, adapted frames and osculating frames, in terms of certain differential …

The paper explores Parseval frames on vector bundles, proving their existence for certain cases.

We introduce and study the writhe of a permutation, a circular variant of the well-known inversion number. This simple permutation statistics has several interpretations, which lead to some interesting properties. For a permutation sampled uniformly at random, we study the asymptotics of the writhe, and obtain a non-Ga…

In this paper we present a new method for motion tracking of tumors in liver ultrasound image sequences. Our algorithm has two main steps. In the first step, we apply mean shift algorithm with multiple features to estimate the center of the target in each frame. Target in the first frame is defined using an ellipse. Ed…

Quantizes neural networks using frame theory for improved accuracy.

Paper defends against adversarial videos by detecting and reducing imperceptible perturbations.

Using a model for the bundle $\hat{\mathcal F}^2M$ of semi-holonomic second order frames of a manifold $M$ as an extension of the bundle ${\mathcal F}^2M$ of holonomic second order frames of $M$, we introduce in $\hat{\mathcal F}^2M$ a principal bundle structure over ${\mathcal F}^2M$, the structure group being the add…

It is well-known that a knot in a contact manifold $(M,C)$ transverse to a trivialized contact structure possesses the natural framing given by the first of the trivialization vectors along the knot. If the Euler class $e_C\in H^2(M)$ of $C$ is nonzero, then $C$ is nontrvivializable and the natural framing of transvers…