2-stein submanifolds in space forms have constant curvature if normal connection is flat or codimension is 2.
problem Characterizing submanifolds with constant curvature in space forms.
method Analyzing submanifolds with flat normal connection or codimension 2.
result 2-stein submanifolds have constant curvature under specified conditions.
The paper finds charts for Legendrian curves in complex contact manifolds.
problem Finding charts for Legendrian curves in complex contact manifolds.
method Holomorphic Darboux charts and approximations of Legendrian immersions.
result Holomorphic Legendrian immersions can be approximated by embeddings.
Classifies totally geodesic submanifolds in specific spaces and finds Einstein hypersurfaces.
problem Classifying totally geodesic submanifolds in Damek-Ricci spaces and Cayley projective plane.
method Analyzing properties of harmonic manifolds, using curvature conditions, and applying classification techniques.
result Characterizes totally geodesic submanifolds and Einstein hypersurfaces in specific spaces.
The paper confirms conjectures about Stein manifolds formed by quotients of the ball.
problem Characterizing Stein manifolds formed by quotients of the ball.
method Analyzing discrete subgroups of PU(n,1) and their quotients.
result The quotient of the ball by geometrically finite groups is Stein.
This paper removes the log loss for eigenfunction restrictions to certain submanifolds.
problem Removing the log loss in L2 estimates for eigenfunctions restricted to submanifolds of codimension 2. method Generalizing Chen and Sogge's method to higher dimensions and studying specific curves.
result Log loss can be removed for totally geodesic submanifolds of codimension 2 and certain curves.
The study translates Weinstein structures to Legendrian handlebodies for symplectic topology.
problem Detecting flexibility and rigidity in Weinstein manifolds.
method Systematic recipe for translating Weinstein Lefschetz fibrations to Legendrian handlebodies.
result Verification of Stein deformation equivalence and existence of closed exact Lagrangian submanifolds.
We show that every smooth closed oriented four-manifold admits a decomposition into two co- dimension zero submanifolds with common boundary. Each of these submanifolds carries a structure of a symplectic manifold with pseudo-convex boundary. This imply, in particular, that every smooth closed simply-connected four-man…
We show that, for any two orientable smooth open 4-manifolds X0,X1 which are homeomorphic, their cotangent bundles T∗X0,T∗X1 are symplectomorphic with their canonical symplectic structure. In particular, for any smooth manifold R homeomorphic to R4, the standard Stein structure on T∗R is Stei…
Given a 4-manifold X and an imbedding of T^{2} x B^2 into X, we describe an algorithm X --> X_{p,q} for drawing the handlebody of the 4-manifold obtained from X by (p,q)-logarithmic transforms along the parallel tori. By using this algorithm, we obtain a simple handle picture of the Dolgachev surface E(1)_{p,q}, from t…
We study exotic smoothings of open 4-manifolds using the minimal genus function and its analog for end homology. While traditional techniques in open 4-manifold smoothing theory give no control of minimal genera, we make progress by using the adjunction inequality for Stein surfaces. Smoothings can be constructed with …
It is known that every compact Stein 4-manifolds can be embedded into a simply connected, minimal, closed, symplectic 4-manifold. By using this property, we discuss a new method of constructing corks. This method generates a large class of new corks including all the previously known ones. We prove that every one of th…
Stein's method improves probabilistic inference and learning.
problem Improving probabilistic inference and learning methods.
method Constructing Stein discrepancies from Stein operators and Stein sets, discussing their properties.
result Connection between Stein operators and Stein variational gradient descent.
It is known that every exotic smooth structure on a simply connected closed 4-manifold is determined by a codimention zero compact contractible Stein submanifold and an involution on its boundary. Such a pair is called a cork. In this paper, we construct infinitely many knotted imbeddings of corks in 4-manifolds such t…
Holomorphic bundles on complex manifolds with boundary are studied, extending results from Donaldson's work.
problem Extending holomorphic structures to complex manifolds with boundary.
method Analyzing formally integrable almost complex structures and their extensions to holomorphic structures.
result Holomorphic structures can be extended to a neighborhood of a strictly pseudoconvex boundary.
GC Stein manifolds characterized with embeddings and functions.
problem Characterize GC Stein manifolds using embeddings and functions.
method Extended Cartan's Theorem A and B, defined L-plurisubharmonic functions, established GH embeddings. result Characterized GC Stein manifolds via L-plurisubharmonic exhaustion functions and GH embeddings. Survey on Stein manifolds embeddings and immersions, including a new result.
problem Existence of holomorphic embeddings and immersions of Stein manifolds.
method Survey and inclusion of a new result involving homotopy and Stein structures.
result Every continuous map between Stein manifolds is homotopic to a proper holomorphic embedding under certain conditions.
Stochastic Stein Discrepancies improve inference efficiency.
problem Intractable computation of Stein discrepancies.
method Subsampled approximations of Stein operators.
result Stochastic Stein Discrepancies inherit convergence properties of standard SDs.
Extends Stein's lemma to exponential-family mixtures for gradient computation.
problem Computing gradients for complex distributions with weak assumptions.
method Generalizes Stein's lemma to exponential-family mixtures and applies it to reparameterization trick.
result Derives new gradient identities for various distributions.
We give a bordism-theoretic characterisation of those closed almost contact (2q+1)-manifolds (with q > 2) which admit a Stein fillable contact structure. Our method is to apply Eliashberg's h-principle for Stein manifolds in the setting of Kreck's modified surgery. As an application, we show that any simply connected a…
Improved sampling method using regularized Stein Variational Gradient Flow.
problem Improving the accuracy of sampling methods in machine learning.
method Proposed Regularized Stein Variational Gradient Flow to interpolate between SVGD and Wasserstein Gradient Flow.
result Established theoretical properties and provided preliminary numerical evidence of improved performance.
Develops Stein's method for Riemannian manifolds using diffusion.
problem Bounding integral metrics on probability measures on Riemannian manifolds.
method Exploits the relationship between diffusion generators and Stein operators to derive Stein factors.
result Derives curvature-dependent Stein factors that generalize existing results for Euclidean spaces.
Regularized Stein thinning improves MCMC output approximations.
problem Pathologies in Stein thinning leading to poor approximations.
method Theoretical analysis and regularization to improve KSD.
result Regularized Stein thinning alleviates pathologies and improves efficiency.
Study Stein and Milnor fillings of links from surface singularities.
problem Comparing Stein and Milnor fillings of links from surface singularities.
method Analyzing the topology and obstructions of Stein fillings and Milnor fillings.
result Milnor fillings have bounded topology, while Stein fillings can be more varied.
It is shown that every subcritical Stein manifold is deformation equivalent to the product of a Stein manifold with $\C$.
New contact manifolds have many ways to be filled.
problem Understanding infinitely many ways to fill contact manifolds.
method Constructing specific contact manifolds and proving they have many Stein fillings.
result Contact manifolds have infinitely many ways to be filled.
Stein transport improves Bayesian inference with faster convergence and reduced variance.
problem Efficiently approximating posterior distributions in Bayesian inference.
method A novel Bayesian inference method using Stein transport, which pushes particles along a curve of tempered distributions.
result Stein transport reaches posterior approximations faster and more accurately than Stein variational gradient descent (SVGD).
The paper improves Stein importance sampling for Markov chain samples.
problem Improving the accuracy of sampling from complex distributions.
method Reproducing Stein kernels approach for post-hoc correction.
result Consistent estimators for target distributions using geometrically ergodic Markov chains.
Counterexample found for Stein property of certain solvable Lie groups.
problem Stein property of simply connected unimodular solvable Lie groups with left-invariant complex structures.
method Constructing a solvable Lie group with specific properties.
result A simply connected solvable Lie group with a left-invariant complex structure whose universal cover is not Stein.
Stein Points improve posterior approximation with minimal points.
problem Approximating posterior distributions with limited points.
method Greedy or conditional gradient method to minimize kernel Stein discrepancy.
result Stein Points enable accurate approximation at low computational cost.
SVGD uses particle transport to approximate distributions, with theoretical guarantees.
problem Approximating complex distributions efficiently.
method Iterative particle transport guided by gradient of KL divergence.
result SVGD's asymptotic behavior is a gradient flow under a new metric.
A new framework improves kernel Stein discrepancy tests for validating distributions.
problem Improving goodness-of-fit testing for non-normal distributions.
method Introducing Sf-KSD, a unifying framework for studying Stein operators in KSD-based tests.
result Sf-KSD guides the development of new tests and outperforms existing methods.
Let M be a real analytic Riemannian manifold. An adapted complex structure on TM is a complex structure on a neighborhood of the zero section such that the leaves of the Riemann foliation are complex submanifolds. This structure is called entire if it may be extended to the whole of TM. We prove here that the only …
We show that, under a certain condition, contact 5-manifolds can `coarsely' distinguish smooth structures on compact Stein 4-manifolds via contact open books. We also give a simple sufficient condition for an infinite family of Stein 4-manifolds to have an infinite subfamily of pairwise non-diffeomorphic Stein 4-manifo…
New KCC-SDs improve distribution comparison in high dimensions.
problem Challenges in high-dimensional Stein discrepancies.
method Kernelized complete conditional Stein discrepancies (KCC-SDs).
result KCC-SDs outperform baselines in distinguishing distributions.
Sliced kernelized Stein discrepancy improves goodness-of-fit tests and model learning in high dimensions.
problem The curse-of-dimensionality in kernelized Stein discrepancy (KSD).
method Sliced Stein discrepancy and its scalable variants using optimal one-dimensional projections.
result Significantly outperforms KSD and baselines in goodness-of-fit tests and improves model learning.
The study finds knots with Stein structures beyond the typical upper bound.
problem Finding knots with Stein structures beyond the known upper bound.
method Constructing specific knots and framings to demonstrate Stein structures.
result The largest framing for which a knot admits a Stein structure can be arbitrarily larger than the usual upper bound.
We give an algorithm which produces infinitely many pairwise exotic Stein fillings of the same contact 3-manifolds, applying positive allowable Lefschetz fibrations over the disk. As a corollary, for a large class of Stein fillings, we realize the topological invariants (i.e. fundamental group, homology group, homology…
The square root of Fredholm determinants causes numerical instabilities in option pricing models.
problem Numerical instabilities in Fourier-based option pricing for the Volterra Stein-Stein model.
method Characterization of determinant crossing behavior, derivation of transform to handle crossings, efficient algorithms.
result Significant improvement in accuracy and reduction in computational cost for Fourier-based pricing.
Stein Variational Gradient Descent optimizes particle sets to match distribution expectations.
problem Efficiently approximating complex distributions in machine learning.
method Evolve particle sets to match the expectations of a given distribution using Stein operators and kernels.
result Particles can be used to exactly estimate expectations of functions on distributions, providing insights into kernel choice.
Study Stein fillings of planar contact 3-manifolds with relative trisection genus 2.
problem Classify Stein fillings of planar contact 3-manifolds under constraints on their relative trisections.
method Partial classification of diffeomorphism types of fillings with relative trisections of genus at most 2.
result Partially classify the diffeomorphism types of Stein fillings with relative trisections of genus at most 2.
Improving scalability and stability of Stein discrepancies for scalable goodness-of-fit testing
problem Improving scalability and stability of Stein discrepancies for scalable goodness-of-fit testing
method Reformulating Stein discrepancy construction as an explicit SNR^2 maximisation problem
result Avoiding exponential SNR^2 collapse and achieving stable SNR^2
Study continuity and Hölder estimates for solutions on Stein spaces.
problem Continuity and Hölder estimates for solutions to degenerate complex Monge-Ampère equations.
method Prove continuity up to the boundary and local Hölder estimates on the regular locus.
result Local Hölder estimates on the regular locus for solutions to degenerate complex Monge-Ampère equations.
Complete negative Kähler-Einstein metric found on Stein manifolds.
problem Existence of complete Kähler-Einstein metrics on Stein manifolds with negative curvature.
method Normalized Kähler-Ricci flow to deform metrics to complete negative Kähler-Einstein metric.
result Existence of complete negative Kähler-Einstein metric on Stein manifolds with negatively pinched holomorphic sectional curvature.
Paper proves existence of compatible Lefschetz fibrations on 6-ball and Stein domains.
problem Existence of compatible Lefschetz fibrations on Stein domains.
method Topological proof for 6-ball fibrations, construction of relative Stein pairs.
result Existence of compatible Lefschetz fibrations on Stein domains of dimension six.
Stein Variational Gradient Descent optimizes Bayesian inference efficiently.
problem Efficient Bayesian inference for complex models.
method Iteratively transports particles to match target distribution using KL divergence minimization.
result Competitive with state-of-the-art methods on various real-world models.
New Stein operator improves robustness in model inference.
problem Improving robustness in inference for unnormalized models.
method Density-power weighted Stein operator (γ-Stein operator). result Robust methods for goodness-of-fit testing and posterior approximation.
Characterizes Stein surfaces with finite homotopy rank-sum.
problem Finite homotopy rank-sum in Stein spaces.
method Rational homotopy theory, classification of Stein surfaces.
result Affine Stein surfaces with finite fundamental group are either simply connected or of order 2.
A new method reduces complexity and uncertainty in neural networks.
problem Uncertainty quantification in complex neural networks.
method Condensed Stein Variational Gradient Descent (cSVGD) method.
result Condensed SVGD provides uncertainty quantification on parameters.