Survey of recent progress in Sasakian geometry.
problem Topological properties and existence of Sasakian structures.
method Review of recent research findings.
result Recent progress in Sasakian geometry.
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arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
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48 results for “recent progress”
Survey of recent austere submanifold results.
problem Understanding austere submanifolds.
method Review of existing papers [24,25].
result Recent progress in the field of austere submanifolds.
We give a short review of recent progress on the positive energy theorem in general relativity, especially for spacetimes with nonzero cosmological constant.
In recent years, there are many progress made in Kähler geometry. In particular, the topics related to the problems of the existence and uniqueness of extremal Kähler metrics, as well as obstructions to the existence of such metrics in general Kähler manifold. In this talk, we will report some recent developments in th…
Weil-Petersson perspectivesmath.DG
We highlight recent progresses in the study of the Weil-Petersson (WP) geometry of finite dimensional Teichmüller spaces. For recent progress on and the understanding of infinite dimensional Teichmüller spaces the reader is directed to the recent work of Teo-Takhtajan. As part of the highlight, we also present possible…
This paper gives a survey of recent progress in isoparametric functions and isoparametric hypersurfaces, mainly in two directions. (1) Isoparametric functions on Riemannian manifolds, including exotic spheres. The existences and non-existences will be considered. (2) The Yau conjecture on the first eigenvalues of the e…
Ricci solitons are natural generalizations of Einstein metrics. They are also special solutions to Hamilton's Ricci flow and play important roles in the singularity study of the Ricci flow. In this paper, we survey some of the recent progress on Ricci solitons.
In this note, we give a brief survey on some recent developments of biharmonic submanifolds. After reviewing some recent progress on Chen's biharmonic conjecture, the Generalized Chen's conjecture on biharmonic submanifolds of non-positively curved manifolds, and some classifications of biharmonic submanifolds of spher…
We survey recent progress in the problem of recovering a tensor field from its integrals along geodesics. We also propose several open problems.
This paper surveys recent progress on issues related to the Bartnik quasi-local mass . In addition, we formulate a number of new problems and conjectures regarding foundational properties of the mass . This work is dedicated with pleasure to Robert Bartnik in honor of his 60th birthday.
Survey of recent progress in gravitational instantons
problem Classification of hyperkähler and Hermitian gravitational instantons
method Survey of recent progress in gravitational instantons
result Survey of recent progress in gravitational instantons
New progress on frame flow ergodicity for nearly pinched manifolds.
problem Ergodicity of frame flow on negatively-curved manifolds.
method New ideas leading to ergodicity for nearly 0.25-pinched manifolds.
result Achieved progress towards Brin's conjecture.
New algorithm outperforms existing ones by focusing on mastering rate.
problem Low sample efficiency in learning progress-based algorithms.
method Proposes a new algorithm based on mastering rate.
result Significantly outperforms learning progress-based algorithms.
Recent anomaly detection benchmarks are flawed, potentially misleading progress.
problem Flawed benchmark datasets create misleading progress reports.
method Identified four flaws in benchmark datasets and introduced a new archive.
result Published comparisons may be unreliable due to flaws in benchmark datasets.
Lie groups applied to tech progress in economic growth.
problem Understanding the impact of technical progress on economic growth.
method Application of Lie theory and economic modeling.
result Estimation of GDP function for Viet Nam, highlighting tech progress impact.
Summarizes key algorithmic trading problems and recent advances.
problem Optimal execution, placement, and price impact in algorithmic trading.
method Discusses recent advances in algorithmic trading using Machine Learning techniques.
result Recent progress in algorithmic trading includes the use of Deep Learning, Reinforcement Learning, and Generative Adversarial Networks.
Surveying recent progress on flows of -structures on 7-manifolds.
problem Preserving metrics while modifying -structures on 7-manifolds.
method Heat flows and other approaches in terms of -forms, octonions, vector fields, and geometric structures.
result Comparison of different perspectives on -structure flows.
This paper can be viewed as a sequel to the author's long survey on the Zimmer program \cite{F11} published in 2011. The sequel focuses on recent rapid progress on certain aspects of the program particularly concerning rigidity of Anosov actions and Zimmer's conjecture that there are no actions in low dimensions. Some …
Surveying progress on deformed Hermitian-Yang-Mills equation and its connections to stability.
problem Solvability of the deformed Hermitian-Yang-Mills equation and its relation to geometric stability.
method Utilizing geometric invariant theory (GIT) and Bridgeland stability theory to analyze the equation.
result On the blow-up of \(\mathbb{P}^2\), line bundles admitting a solution of the deformed Hermitian-Yang-Mills equation are Bridgeland stable, but not conversely.
Deep learning's success requires vast computing power, making future progress unsustainable.
problem Deep learning's success is heavily dependent on computing power, making future progress unsustainable.
method Cataloging and extrapolating the dependency on computing power for various deep learning applications.
result Continued progress in deep learning applications will require more computationally-efficient methods.
We propose Progressive Structure-conditional Generative Adversarial Networks (PSGAN), a new framework that can generate full-body and high-resolution character images based on structural information. Recent progress in generative adversarial networks with progressive training has made it possible to generate high-resol…
The aim of this paper is to report on recent development on the conformal fractional Laplacian, both from the analytic and geometric points of view, but especially towards the PDE community.
This is a survey paper on our recent works concerning the classification of positively curved homogeneous Finsler spaces, and some related topics. At the final part, we present some open problems in this field.
In this note, we discuss the interactions between differential topology and isoparametric foliations, surveying some recent progress and open problems.
Deep neural networks solve Raven's Progressive Matrices with high accuracy.
problem Testing relational reasoning in machine learning systems.
method Combining Wild Relation Networks with Multi-Layer Relation Networks and introducing Magnitude Encoding.
result Deep neural networks achieve 98.0 percent accuracy, significantly improving over previous methods.
We introduce a novel approach for predicting the progression of adolescent idiopathic scoliosis from 3D spine models reconstructed from biplanar X-ray images. Recent progress in machine learning have allowed to improve classification and prognosis rates, but lack a probabilistic framework to measure uncertainty in the …
Alzheimer's disease (AD) is a degenerative brain disease impairing a person's ability to perform day to day activities. The clinical manifestations of Alzheimer's disease are characterized by heterogeneity in age, disease span, progression rate, impairment of memory and cognitive abilities. Due to these variabilities, …
We discuss some open problems and recent progress related to the 4th order Paneitz operator and Q curvature in dimensions other than 4.
We give an elementary introduction to our papers relating the geometry of rational homogeneous varieties to representation theory. We also describe related work and recent progress.
We introduce a novel generative autoencoder network model that learns to encode and reconstruct images with high quality and resolution, and supports smooth random sampling from the latent space of the encoder. Generative adversarial networks (GANs) are known for their ability to simulate random high-quality images, bu…
Deep nearest neighbors outperform self-supervised methods in anomaly detection.
problem Anomaly detection using self-supervised deep methods.
method Simple nearest-neighbor approach on Imagenet pretrained features.
result Nearest-neighbor method outperforms self-supervised methods in accuracy, few shot generalization, training time, and noise robustness.
We survey some of the state of the art regarding singularities in Lagrangian mean curvature flow. Some open problems are suggested at the end.
Surveying recent progress on hyperbolic 3-manifold rigidity.
problem Profinite rigidity of hyperbolic 3-manifolds.
method Review of profinite completion and rigidity of groups, evidence from other types of 3-manifolds, and existing ideas.
result Positive evidence for profinite rigidity in hyperbolic 3-manifolds.
This is a survey article of the recent progresses on the metric behaviour of Ricci-flat Kähler-Einstein metrics along degenerations of Calabi-Yau manifolds.
Survey explores how transfer learning improves deep reinforcement learning.
problem Challenges in reinforcement learning efficiency and effectiveness.
method Categorizes and analyzes transfer learning approaches.
result Transfer learning enhances reinforcement learning performance.
Abstract reviews recent Lagrangian analysis on immersions into higher dimensions.
problem Analyzing Lagrangians on immersions into higher dimensions.
method Reviews recent progress on Lagrangians on immersions with first and second fundamental forms and their derivatives.
result Recent progress in the analysis of Lagrangians on immersions into higher dimensions.
We give a survey of various compactness and non-compactness results for the Yamabe equation. We also discuss a conjecture of Hamilton concerning the asymptotic behavior of the parabolic Yamabe flow.
Non-Euclidean Analysismath.DG
This paper deals with various topics in analysis on hyperbolic spaces. It surveys some recent progress in non-Euclidean Fourier Analysis and proves some new results for the geodesic Radon transform on hyperbolic spaces.
This article is a short nontechnical survey of recent progresses in fluid dynamics and differential geometry, relating a conjecture of Lars Onsager to the work of Nash on isometric embeddings.
Adversarial images are designed to mislead deep neural networks (DNNs), attracting great attention in recent years. Although several defense strategies achieved encouraging robustness against adversarial samples, most of them fail to improve the robustness on common corruptions such as noise, blur, and weather/digital …
The paper argues against the inefficiency of explaining deep learning phenomena.
problem Explaining deep learning phenomena often leads to ad hoc hypotheses.
method Analyzing recent literature to assess the relevance of these phenomena.
result Many phenomena do not appear in real-world applications and may be inefficient.
Recent progress in portfolio choice has made a wide class of problems involving transaction costs tractable. We review the basic approach to these problems, and outline some directions for future research.
We survey some recent topics on singularities, with a focus on their connection to the minimal model program. This includes the construction and properties of dual complexes, the proof of the ACC conjecture for log canonical thresholds and the recent progress on the `local stability theory' of an arbitrary Kawamata log…
Arguably, unsupervised learning plays a crucial role in the majority of algorithms for processing brain imaging. A recently introduced unsupervised approach Deep InfoMax (DIM) is a promising tool for exploring brain structure in a flexible non-linear way. In this paper, we investigate the use of variants of DIM in a se…
A short survey on the type numbers of closed geodesics, on applications of the Morse theory to proving the existence of closed geodesics and on the recent progress in applying variational methods to the periodic problem for Finsler and magnetic geodesics
Study on hyperbolic manifolds and their boundary data, focusing on volume functions.
problem Determining the hyperbolic metric from boundary data of convex co-compact hyperbolic manifolds.
method Analysis of volume functions and their relation to boundary data, using first variations.
result New connections with physics and probability theory, with open questions remaining.
Prediction of the progression of subcortical brain structures in Alzheimer's disease from baselinecs.CV
We propose a method to predict the subject-specific longitudinal progression of brain structures extracted from baseline MRI, and evaluate its performance on Alzheimer's disease data. The disease progression is modeled as a trajectory on a group of diffeomorphisms in the context of large deformation diffeomorphic metri…
We discuss the issue of branching in quasiregular mapping, and in particular the relation between branching and the problem of finding geometric parametrizations for topological manifolds. Other recent progress and open problems of a more function theoretic nature are also presented.