Higgs bundles used in new applications.
problem None explicitly stated in the abstract.
method Overview of recent applications.
result Applications of Higgs bundles.
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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 applications”
This article reports recent developments of the research on Hamilton's Ricci flow and its applications.
Survey on broken ray transforms and open problems.
problem Understanding broken ray transforms and their applications.
method Survey of recent developments and open problems.
result Discussion of open problems in broken ray transforms.
An overview of some of the recent developments in the theory of valuations on convex sets and its generalizations to manifolds is given. The exposition is focused towards applications to integral geometry; several of such applications are discussed.
Deep Reinforcement Learning has made significant progress in multi-agent systems in recent years. In this review article, we have focused on presenting recent approaches on Multi-Agent Reinforcement Learning (MARL) algorithms. In particular, we have focused on five common approaches on modeling and solving cooperative …
Survey of advances in non-convex min-max optimization for applications.
problem Finding optimal solutions in non-convex, non-concave min-max problems.
method Selective review of theoretical and algorithmic advances.
result Exciting recent advances in solving non-convex min-max problems.
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…
In recent years, multi-armed bandit (MAB) framework has attracted a lot of attention in various applications, from recommender systems and information retrieval to healthcare and finance, due to its stellar performance combined with certain attractive properties, such as learning from less feedback. The multi-armed ban…
Survey on factor models and their applications in econometrics.
problem Estimating low-rank structures in high-dimensional models.
method Low-rank recovery techniques for factor model estimation.
result New insights into factor model applications in econometrics.
We review recent probabilistic results on covariant Schrödinger operators on vector bundles over (possibly locally infinite) weighted graphs, and explain applications like semiclassical limits. We also clarify the relationship between these results and their formal analogues on smooth (possibly noncompact) Riemannian m…
The Novikov Conjecturemath.GT
We give a survey on recent development of the Novikov conjecture and its applications to topological rigidity and non-rigidity. .
Survey on strong convergence in random matrices and its applications.
problem Understanding convergence of random matrices to operators.
method Analysis of operator norms of noncommutative polynomials.
result New insights and applications in random graphs, geometry, and operator algebras.
Nonlinear analysis has played a prominent role in the recent developments in geometry and topology. The study of the Yang-Mills equation and its cousins gave rise to the Donaldson invariants and more recently, the Seiberg-Witten invariants. Those invariants have enabled us to prove a number of striking results for low …
The application of stochastic variance reduction to optimization has shown remarkable recent theoretical and practical success. The applicability of these techniques to the hard non-convex optimization problems encountered during training of modern deep neural networks is an open problem. We show that naive application…
Machine learning techniques are being applied to scientific fields, showing promise and challenges.
problem Applying machine learning to scientific data poses challenges in universality and robustness.
method Critical analysis of anomaly detection techniques, focusing on data universality, robustness, and transferability.
result Machine learning techniques show potential but also present domain-specific challenges.
Study smooth manifolds using disc-presheaves.
problem Understanding smooth manifolds.
method Using presheaves on a category of discs.
result Disc-presheaves have desirable properties and strong applications.
Looking for associations among multiple variables is a topical issue in statistics due to the increasing amount of data encountered in biology, medicine and many other domains involving statistical applications. Graphical models have recently gained popularity for this purpose in the statistical literature. Following t…
Discussing new econophysics methods for volatility and probability density estimation.
problem Estimating volatility and probability densities in econophysics.
method Reviewing recent methods for volatility and probability density estimation.
result Pioneering methods for volatility and probability density estimation in econophysics.
Some recent work in Frechet geometry is briefly reviewed. In particular an earlier result on the structure of second tangent bundles in the finite dimensional case was extended to infinite dimensional Banach manifolds and Frechet manifolds that could be represented as projective limits of Banach manifolds. This led to …
In this paper we describe some recent applications of the barycenter method in geometry. This method was first used by Duady-Earle and later greatly extended by Besson-Courtois-Gallot in their solution of a number of long-standing problems, in particular in their proof of entropy rigidity for closed, negatively curved …
The sharp decline in Ireland's economic performance in recent years has coincided with a recent fall in asylum applications. Simultaneously countries such as Switzerland are seeing increases in asylum numbers with evidence for greater numbers of Nigerian applicants, a group that have for some time been the largest nati…
Marden's Tameness Conjecture predicts that every hyperbolic 3-manifold with finitely generated fundamental group is homeomorphic to the interior of a compact 3-manifold. It was recently established by Agol and Calegari-Gabai. We will survey the history of work on this conjecture and discuss its many applications.
RL applied to finance tasks, highlighting challenges and future directions.
problem Decision-making tasks in finance using RL.
method Meta-analysis of RL applications, identifying challenges and proposing future directions.
result Challenges in RL performance and future research directions.
In this paper we survey the recent developments of the Ricci flows on complete noncompact Kähler manifolds and their applications in geometry.
Survey on understanding neural networks for medical applications.
problem Black-box nature of deep neural networks hinders their use in critical applications.
method Comprehensive review of interpretability studies in neural networks.
result Interpretability research is crucial for the acceptance of neural networks in medical diagnosis.
Study continuity of complex Sobolev functions, with applications to Kaehler metrics.
problem Continuity of functions in complex Sobolev spaces.
method Analysis of function regularity in Sobolev spaces, with applications to Kaehler metrics.
result Hermitian generalizations of recent results on Kaehler metrics.
We show that if a knot has a minimal spanning surface that admits certain Gabai disks, then this knot has Property P. As one of the applications we extend and simplify a recent result of Menasco and Zhang that closed 3-braid knots have Property P. Other applications are given.
Explosive growth in data and availability of cheap computing resources have sparked increasing interest in Big learning, an emerging subfield that studies scalable machine learning algorithms, systems, and applications with Big Data. Bayesian methods represent one important class of statistic methods for machine learni…
Survey on spectral embeddings for data analysis.
problem None explicitly stated in the abstract.
method Presentation of spectral embeddings from Riemannian geometry to data analysis.
result Survey of spectral embeddings and their applications.
The goal of this note is to illustrate the impact of a self-financing condition recently introduced by the authors. We present the analyses of two specific applications usually considered in more traditional models in financial mathematics. They include hedging European options with limit orders and the optimal behavio…
To study a noncompact Riemannian manifold, it is often useful to find a compactification. We discuss several common compactifications and survey some recent results.
In this short note we discuss some recent results about two-positive Ricci curvature and their applications to positive Einstein curvature.
Survey recent constructions of cyclic cocycles for Lie groups.
problem Higher index theory for proper cocompact -actions.
method Constructions of cyclic cocycles on Harish-Chandra Schwartz algebra.
result Applications to higher index theory.
We survey some recent developments in the quest for global surfaces of section for Reeb flows in dimension three using methods from Symplectic Topology. We focus on applications to geometry, including existence of closed geodesics and sharp systolic inequalities. Applications to topology and celestial mechanics are als…
We compute a recently introduced geometric invariant of stricly pseudoconvex CR 3-manifolds for certain circle invariant spherical CR structures on Seifert manifolds. We give applications to the problem of filling the CR manifold by a complex hyperbolic manifold, and more generally by a Kaehler-Einstein or an Einstein …
Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as a powerful discrepancy measure for probability distributions. The recent developments on alternative formulations of the optimal transport have allowed for faster solutio…
We review recent results about heat kernel estimates based on Kato conditions on the negative part of the Ricci curvature.
Algebraic integral geometrymath.DG
A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.
Low-rank modeling generally refers to a class of methods that solve problems by representing variables of interest as low-rank matrices. It has achieved great success in various fields including computer vision, data mining, signal processing and bioinformatics. Recently, much progress has been made in theories, algori…
Machine learning methods have been remarkably successful for a wide range of application areas in the extraction of essential information from data. An exciting and relatively recent development is the uptake of machine learning in the natural sciences, where the major goal is to obtain novel scientific insights and di…
Fuzzing has played an important role in improving software development and testing over the course of several decades. Recent research in fuzzing has focused on applications of machine learning (ML), offering useful tools to overcome challenges in the fuzzing process. This review surveys the current research in applyin…
We summarize the main results of our recent investigation of bundles of real Clifford modules and briefly touch on some applications to string theory and supergravity.
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.
Develops an algorithm for bilevel optimization with coupled constraints.
problem Challenges in bilevel optimization with coupled constraints.
method Primal-dual-assisted penalty approach and a fully first-order algorithm (BLOCC).
result Established rigorous convergence theory and demonstrated effectiveness on real-world applications.
Granger causality reviewed and advanced for complex data.
problem Validity of inferring causal relationships from time series data.
method Recent advances in models for high-dimensional time series, accounting for nonlinear and non-Gaussian observations, and sub-sampled data.
result Improved computational tools for Granger causality.
We survey recent results on the existence of Kähler-Einstein metrics on certain smoothable Fano varieties, focusing on the importance of such metrics in the construction of compact algebraic moduli spaces of K-polystable Fano varieties. Moreover, we give some applications and we discuss some natural problems which dese…
Interactive Machine Learning (IML) is an iterative learning process that tightly couples a human with a machine learner, which is widely used by researchers and practitioners to effectively solve a wide variety of real-world application problems. Although recent years have witnessed the proliferation of IML in the fiel…
We shall define the relative $\dbar$-complex and study the curvature properties of the associated vector bundles. As an application, we shall prove that Yamaguchi's theory on subharmonicity of the Green operator can be seen as a curvature property of the quotient bundle. A short survey of other recent applications will…