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.
Constructing Einstein analogues with a non-zero cosmological constant
problem Constructing an Einstein analogue with a non-zero cosmological constant
method Proving the solution is either the Plebański-Demiański metric or has an anti-self-dual Weyl tensor
result For λ < 0, there is a conformal infinity separating two asymptotically hyperbolic metrics; one is globally conformal to an ALE scalar-flat Kähler metric; gravitational instantons with different topologies are constructed; the geometry is a 4-pole solution in the Calderbank-Pedersen classification
Study classifies gravitational instantons based on their asymptotic geometry.
problem Classifying gravitational instantons based on their asymptotic properties.
method Investigation of asymptotic geometry of Hermitian non-Kähler Ricci-flat metrics.
result All Hermitian non-Kähler gravitational instantons can be compactified to log del Pezzo surfaces.
Gravitational instantons are non-Kähler, providing a counterexample to Euclidean Black Hole Uniqueness.
problem Classical Euclidean Black Hole Uniqueness conjecture
method Analyzing the Chen-Teo gravitational instanton
result The Chen-Teo instanton is Hermitian and non-Kähler
New instantons show Einstein-Maxwell fields are more complex.
problem Disprove Euclidean Einstein-Maxwell black hole uniqueness.
method Explicit construction of new three-parameter family of asymptotically flat instantons.
result Demonstrate subtle properties of coupled gravitational and electromagnetic fields.
Study describes ALF instantons with conical singularities.
problem Understanding ALF instantons with conical singularities.
method Applied techniques from previous work.
result Only 4D subfamilies can be smoothly compactified with conical singularities.
Researchers construct explicit bundles for ALF metrics, revealing rational patching matrices for gravitational instantons.
problem Constructing explicit toric Ricci-flat metrics and their associated bundles.
method Explicit construction of patching matrices for ALF metrics and gravitational instantons.
result Rational form of patching matrices for gravitational instantons in the Chen--Teo family.
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.
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 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…
Researchers solve field equations for special gravitational instantons.
problem Solving field equations for conformally Kähler Riemannian four-manifolds.
method Developed a framework to solve the field equations for generalised gravitational instantons using conformal self-duality and cosmological Einstein-Maxwell.
result Found conformally self-dual and Einstein-Maxwell generalisations of specific geometries.
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.
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. 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.
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…
Cardiovascular diseases are the most common cause of mortality worldwide. Detection of atrial fibrillation (AF) in the asymptomatic stage can help prevent strokes. It also improves clinical decision making through the delivery of suitable treatment such as, anticoagulant therapy, in a timely manner. The clinical signif…
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.
In this article, we propose a novel ECG classification framework for atrial fibrillation (AF) detection using spectro-temporal representation (i.e., time varying spectrum) and deep convolutional networks. In the first step we use a Bayesian spectro-temporal representation based on the estimation of time-varying coeffic…
Deep neural networks paved the way for significant improvements in image visual categorization during the last years. However, even though the tasks are highly varying, differing in complexity and difficulty, existing solutions mostly build on the same architectural decisions. This also applies to the selection of acti…
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 …
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.
As an effective data preprocessing step, feature selection has shown its effectiveness to prepare high-dimensional data for many machine learning tasks. The proliferation of high di-mension and huge volume big data, however, has brought major challenges, e.g. computation complexity and stability on noisy data, upon exi…
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…
Classifies 4D toric Hermitian ALF metrics with conical singularities.
problem Classifying specific types of 4D Riemannian metrics.
method Explicit formulas provided for classification.
result Examples of metrics with conical singularities have infinitely many distinct topologies.
Left atrium shape has been shown to be an independent predictor of recurrence after atrial fibrillation (AF) ablation. Shape-based representation is imperative to such an estimation process, where correspondence-based representation offers the most flexibility and ease-of-computation for population-level shape statisti…
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…
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.
We introduce Hyper-Conditioned Neural Autoregressive Flow (HCNAF); a powerful universal distribution approximator designed to model arbitrarily complex conditional probability density functions. HCNAF consists of a neural-net based conditional autoregressive flow (AF) and a hyper-network that can take large conditions …
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…
Proves uniqueness of certain S1-symmetric gravitational instantons.
problem Proving uniqueness of S1-symmetric gravitational instantons. method Using a divergence identity and results from the G-signature theorem. result Proof of the S1-symmetric Euclidean Black Hole Uniqueness conjecture. 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.