Deep learning predicts AF recurrence from MRI images without pre-processing.
problem Estimating AF recurrence from MRI images efficiently and accurately.
method Deep learning approach to predict shape descriptors directly from MRI images.
result Deep learning method produces similar outcomes to state-of-the-art methods.
The paper proves the existence of area-minimizing hypersurfaces in AF manifolds of higher dimensions.
problem Existence of area-minimizing hypersurfaces in AF manifolds with arbitrary dimension and ends.
method Positive mass theorem for AF manifolds with arbitrary ends and global behavior for hypersurfaces in AF manifolds of dimension ≤ 8.
result Existence and behavior of area-minimizing hypersurfaces in AF manifolds of higher dimensions.
FunBO uses LLMs to discover effective acquisition functions for Bayesian optimization.
problem Designing optimal acquisition functions for Bayesian optimization across diverse problems.
method FunBO leverages FunSearch, an LLM, to learn and evaluate new acquisition functions.
result FunBO discovers acquisition functions that generalize well and outperform existing methods.
New method improves BO's AF maximizer initialization for high-dimensional problems.
problem Challenges in maximizing acquisition functions in high-dimensional Bayesian optimization.
method Proposes a heuristic optimizer-based initialization approach to improve AF maximizer performance.
result Our approach significantly enhances BO performance in most test cases.
AF improves sampling from high-dimensional, multi-modal distributions.
problem Sampling from high-dimensional, multi-modal distributions is challenging.
method Annealing Flow (AF) using Continuous Normalizing Flow (CNF) with dynamic Optimal Transport (OT) objective and annealing procedures.
result AF significantly improves training efficiency and stability, outperforming state-of-the-art methods.
AFS-BM improves model accuracy by dynamically selecting features.
problem Feature selection challenges in ML, especially scalability and adaptability.
method Joint optimization for feature selection and model training with binary masking.
result AFS-BM achieves significant improvements in model accuracy and computational efficiency.
Bayesian optimization tackles expensive discrete and mixed parameter spaces.
problem Optimizing expensive functions with discrete and mixed parameters.
method Probabilistic reparameterization to maximize expectation of AF over continuous parameters.
result Our approach provably converges to a maximizer of the AF and enjoys the same regret bounds as standard BO.
We construct a functor which maps conjugate pseudo-Anosov automorphisms of a surface to the so-called stably isomorphic stationary AF-algebras; the functor gives new topological invariants of three dimensional manifolds coming from the known invariants of the AF-algebras. The main invariant is a triple (L, [I], K), whe…
This paper tackles few-shot AF learning for BO, improving performance across various functions.
problem Designing a single AF that performs well across different types of black-box functions.
method Integrates Q-functions and DQN, using Bayesian model-agnostic meta-learning and Kullback-Leibler regularization.
result FSAF achieves comparable or better performance than state-of-the-art benchmarks.
New test assesses reliability of auto-generated features.
problem Lack of reliable assessment for auto-generated features.
method Selective inference framework for statistical testing.
result Proposes a statistical test for auto-generated features in linear models.
Optimal AFs minimize RFR test error and sensitivity.
problem Finding optimal AFs for RFR to minimize test error and sensitivity.
method Closed-form solution for AFs minimizing test error and sensitivity under different functional parsimony.
result Optimal AFs can be linear, saturated linear, or Hermite polynomial expressions.
AF improves classification models by adaptively weighting trees.
problem Improving classification model performance.
method AF combines OP2T for input-dependent weights and MIO for dynamic refinement.
result AF consistently outperforms RF, XGBoost, and other weighted RF.
Study shows GAN and GMM data augmentation improves AF signal classification accuracy.
problem Class imbalance in atrial fibrillation ECG datasets.
method Investigated various data augmentation techniques (oversampling, GMMs, GANs).
result GAN and GMM data augmentation lead to better AF signal classification accuracy.
Paper proposes a DNN-driven AF framework for improved generalization.
problem Generalization challenge in adaptive filtering.
method Structural embedding of DNN into AF system, using maximum likelihood as implicit cost function.
result Demonstrates improved generalization capability through extensive experiments.
In a recent paper, Alfonsi, Fruth and Schied (AFS) propose a simple order book based model for the impact of large orders on stock prices. They use this model to derive optimal strategies for the execution of large orders. We apply these strategies to an agent-based stochastic order book model that was recently propose…
Novel ECG classification for AF using spectro-temporal Kalman filtering and deep CNN.
problem Atrial fibrillation (AF) detection in ECG signals.
method Spectro-temporal representation using Kalman filter and deep convolutional neural networks.
result Proposed method achieves an overall F1 score of 80.2% on the PhysioNet/Computing in Cardiology (CinC) 2017 dataset.
Proves positive mass theorem for AF spin manifolds with conical singularities.
problem Proving the positive mass theorem for singular metrics on AF manifolds.
method Analyzes AF spin manifolds with isolated conical singularities, allowing topological singularities.
result Proves the positive mass theorem for AF spin manifolds with conical singularities.
AFS uses attention to select features efficiently.
problem Efficiently selecting features from high-dimensional data.
method AFS combines an attention module and a learning module to address feature selection challenges.
result AFS outperforms state-of-the-art feature selection algorithms in accuracy and stability.
Given a Riemannian 3-ball (Bˉ,g) of non-negative scalar curvature, Bartnik conjectured that (Bˉ,g) admits an asymptotically flat (AF) extension (without horizons) of the least possible ADM mass, and that such a mass-minimizer is an AF solution to the static vacuum Einstein equations, uniquely determined b…
Proves mass theorem for AF manifolds with conical singularities.
problem Proving the positive mass theorem for specific types of manifolds.
method Conformal blow up technique applied to AF manifolds with isolated conical singularities.
result Positive mass theorem proven for the specified manifolds.
We give some lower estimates of the ADM mass of an asymptotically flat (AF) Riemannian manifold without assuming that the scalar curvature of the manifold is nonnegative. Some sufficient conditions for an AF manifold to have nonnegative ADM mass are obtained. We also give some lower estimates of the Brown-York mass of …
L*ReLU improves deep learning for fine-grained image classification.
problem Fine-grained image classification requires specific AFs.
method Proposes L*ReLU, piece-wise linear AFs for deep learning.
result L*ReLU achieves superior results on FGVC datasets.
Paper improves PINNs' extrapolation by TL and adaptive AFs.
problem PINNs' poor extrapolation performance and sensitivity to AFs.
method Transfer learning within an extended domain and adaptive activation functions.
result Average 40% reduction in relative L2 error and 50% in mean absolute error in extrapolation domain.
Classifies instantons on a specific gravitational instanton and computes partition functions.
problem Classifying finite energy harmonic 2-forms and anti-self-dual Yang-Mills instantons.
method Analyzes U(1)-bundles and computes instantons explicitly. result Unique anti-self-dual Yang-Mills instantons exist and are described explicitly.
The conjugacy problem for the pseudo-Anosov automorphisms of a compact surface is studied. To each pseudo-Anosov automorphism f, we assign an AF-algebra A(f) (an operator algebra). It is proved that the assignment is functorial, i.e. every f', conjugate to f, maps to an AF-algebra A(f'), which is stably isomorphic to A…
Proves effective positive mass theorem for AF manifolds and singular spaces.
problem Proves positive mass theorem for AF manifolds with singularities.
method Dimension reduction techniques, bypassing N. Smale's regularity theorem.
result Effective positive mass theorem for AF manifolds of dimension n≤8 with singularities. In this paper, we study two aspects of the variational autoencoder (VAE): the prior distribution over the latent variables and its corresponding posterior. First, we decompose the learning of VAEs into layerwise density estimation, and argue that having a flexible prior is beneficial to both sample generation and infer…
A complete characterization is obtained of the asymptotic behavior of solutions of the static vacuum Einstein equations which have a (pseudo)-compact horizon or boundary and are complete away from the boundary. It is proved that the time-symmetric space-like hypersurface has only finitely many ends, each of which is ei…
Meta-learning AFs for transfer learning in Bayesian optimization improves data-efficiency.
problem Improving data-efficiency in global black-box optimization.
method Meta-learning acquisition functions using reinforcement learning to meta-train on related tasks.
result The method learns to extract structural information and improves data-efficiency across various tasks.
New method for explaining neural network activation functions.
problem Transparency in black-box deep learning algorithms.
method Symbolic explanation of activation functions using adaptive Gaussian Processes.
result Achieved partially explainable learning model with scalable topology.
Study K-theory of Etesi C∗-algebras to understand smooth manifolds.
problem Understanding smooth manifolds through K-theory of Etesi C∗-algebras. method Calculate topological and smooth invariants of manifolds using K-theory of Etesi C∗-algebras. result Smoothings of a manifold form a torsion abelian group isomorphic to the Brauer group of a number field.
The development of new technology such as wearables that record high-quality single channel ECG, provides an opportunity for ECG screening in a larger population, especially for atrial fibrillation screening. The main goal of this study is to develop an automatic classification algorithm for normal sinus rhythm (NSR), …
The paper studies global Yamabe flow on AF manifolds, preserving ADM mass.
problem Existence and behavior of Yamabe flow on AF manifolds.
method New local existence theorem and maximum principle for parabolic equations.
result Global existence of Yamabe flow on AF manifolds with non-negative scalar curvature.
Study improves estimation of functions from noisy data using convex penalties.
problem Estimating functions from noisy point evaluations of linear operators.
method Tikhonov regularization with convex and p-homogeneous penalty functionals. result Derives concentration rates for regularized solutions in symmetric Bregman distance.
Mathematical model audits social media algorithms to prevent bias.
problem Algorithmic filtering can bias users' decisions and societal norms.
method Formalized mathematical framework for auditing social media algorithms.
result Data-driven statistical auditing procedure to regulate algorithmic bias.
It is well-know that Hawking mass is nonnegative for a stable constant mean curvature (CMC) sphere in three manifold of nonnegative scalar curvature. R. Bartnik proposed the rigidity problem of Hawking mass of stable CMC spheres. In this paper, we show partial rigidity results of Hawking mass for stable CMC spher…
It is shown, that the mapping class group of a surface of the genus g > 1 admits a faithful representation into the matrix group GL (6g-6, Z). The proof is based on a categorical correspondence between the Riemann surfaces and the so-called toric AF-algebras.
The paper solves a problem related to scalar curvature and boundary metrics.
problem Proving the extensibility of boundary metrics to positive scalar curvature metrics.
method Introducing a fill-in invariant and proving relationships with positive mass theorems.
result The positive mass theorem for asymptotically hyperbolic manifolds implies the same for asymptotically flat manifolds.
HCNAF models complex conditional distributions for probabilistic occupancy forecasting.
problem Modeling complex conditional probability density functions for occupancy forecasting.
method Hyper-Conditioned Neural Autoregressive Flow (HCNAF) combining AF and hyper-network.
result HCNAF achieves state-of-the-art performance in self-driving datasets.
In this paper, we study local solutions F=(F1,..,Fn) of a general functional equation of the form F1(U1(x,y))+....+Fn(Un(x,y))=0. A such equation will be called an ``abelian functional equation'' (Afe). We will restrict ourselves to the case when the inner functions Ui's are real rational functions. First we prove that…
Convolutional neural network localizes OD and fovea in UWFoV-SLO images.
problem Localizing optic disc and fovea centers in ultra-widefield retinal images.
method Convolutional neural network trained on reflectance and autofluorescence images.
result 99.4% OD localisation accuracy and 99.1% fovea localisation accuracy.
This paper improves Bayesian optimization methods with tighter regret bounds and practical solutions.
problem Improving Bayesian optimization methods with tighter regret bounds and practical solutions.
method The paper analyzes and compares different acquisition functions (GP-UCB, TS, PIMS) to achieve tighter Bayesian cumulative regret bounds and address practical issues.
result PIMS achieves the tighter BCR bound and avoids hyperparameter tuning, unlike GP-UCB and TS.
We study solutions to the static vacuum Einstein equations on exterior domains with prescribed metric and mean curvature on the inner boundary. It is proved that for any such boundary data near the standard round boundary data in Euclidean space, there exists a unique AF solution to the static vacuum equations realizin…
DeepBeat uses deep learning to assess signal quality and detect arrhythmia in wearable devices.
problem Detecting atrial fibrillation from wearable devices with noise.
method Multi-task deep learning approach using convolutional denoising autoencoders.
result Significantly improved AF detection accuracy compared to traditional methods.
This technical note considers the problems of blind sparse learning and inference of electrogram (EGM) signals under atrial fibrillation (AF) conditions. First of all we introduce a mathematical model for the observed signals that takes into account the multiple foci typically appearing inside the heart during AF. Then…
Under suitable conditions near infinity and assuming boundedness of curvature tensor, we prove a no breathers theorem in the spirit of Ivey-Perelman for some noncompact Ricci flows. These include Ricci flows on asymptotically flat (AF) manifolds with positive scalar curvature. Since the method for the compact case face…
In this paper, we introduce a non linear ODE method to construct CMC surfaces in Riemannian manifolds with symmetry. As an application we construct unstable CMC spheres and outlying CMC spheres in asymptotically Schwarzschild manifolds with metrics like gij=(1+l1)2δij+O(l−2). The existence of uns…
Maps between automorphism groups are isomorphisms for free factor complexes.
problem Understanding the structure of automorphism groups of free factor complexes.
method Establishing isomorphisms between automorphism groups and automorphism groups of free factor complexes.
result Natural maps from mAut(Fn) to the automorphism group of the free-factor complex AFn are isomorphisms.