Proves rotational symmetry for Serrin-type problems in doubly connected domains.
problem Proving symmetry in Serrin-type problems for doubly connected domains.
method Employing the technique from arXiv:2109.11255 and comparing with the classical moving plane method.
result Rotational symmetry results for Serrin-type problems in doubly connected domains.
The concept of a conformal deformation has two natural extensions: quasiconformal and harmonic mappings. Both classes do not preserve the conformal type of the domain, however they cannot change it in an arbitrary way. Doubly connected domains are where one first observes nontrivial conformal invariants. Herbert Groetz…
Let N=(Ω,σ) and M=(Ω∗,ρ) be doubly connected Riemann surfaces and assume that ρ is a smooth metric with bounded Gauss curvature K and finite area. The paper establishes the existence of homeomorphisms between Ω and Ω∗ that minimize the Dirichlet energy. In the class of all homeomorphisms $f \col…
Formula for squeezing function on annuli disproves conjecture.
problem Proving squeezing function formula for annuli.
method Schottky-Klein prime function and Loewner differential equation.
result Formula for squeezing function on annuli established.
Commentary on Teichmüller's 1938 paper on conformal and quasiconformal mappings.
problem Investigations into conformal and quasiconformal mappings and their applications.
method Detailed development of conformal invariants and applications in value distribution theory.
result Insures the almost circularity of certain loci and the circularity near infinity of quasiconformal maps.
Eigenvalue problems for Laplacian in specific domains are studied, showing maximum eigenvalues occur under certain conditions.
problem Eigenvalue problems for Laplacian in doubly connected domains and geodesically symmetric spaces.
method Analytical study of boundary value problems for Laplacian.
result Maximum eigenvalues occur when domains are concentric or geodesic balls.
The paper examines Einstein doubly warped product manifolds with a semi-symmetric metric connection.
problem Characterizing Einstein doubly warped product manifolds with a semi-symmetric metric connection.
method Deriving curvature formulas and proving necessary and sufficient conditions for a manifold to be a warped product.
result Obtained results for Einstein doubly warped product manifolds and Einstein-like doubly warped product manifolds.
Solves a Dirichlet problem for flat metrics on Riemann surfaces with boundary.
problem Solving a Dirichlet problem for flat hermitian metrics on Hilbert bundles over compact Riemann surfaces with boundary.
method Proves solvability using flat hermitian metrics and factorization results.
result Solves the Dirichlet problem for flat metrics on Riemann surfaces with boundary.
The study explores special submanifolds in the probability simplex with unique geometric properties.
problem Exploring special submanifolds in the probability simplex.
method Algebraic characterization and classification of doubly autoparallel submanifolds.
result Characterization and classification of doubly autoparallel submanifolds on the probability simplex.
Hamiltonian cycles found in toroidal maps.
problem Hamiltonicity of doubly semi-equivelar maps on the torus.
method Analyzing 2-uniform tilings of the plane to derive Hamiltonian cycles.
result Every doubly semi-equivelar map on the torus contains a Hamiltonian cycle.
Characterizes spacetimes using doubly torqued vectors.
problem Classifying spacetimes based on their geometric properties.
method Characterization through doubly torqued vectors and their properties.
result Doubly twisted and Kundt spacetimes can be characterized.
Geometric approach for unsupervised word embedding alignment.
problem Learning alignment between word embeddings of source and target languages.
method Formulates alignment as domain adaptation on the manifold of doubly stochastic matrices, employing Riemannian conjugate gradient algorithm.
result Empirically outperforms state-of-the-art methods on bilingual lexicon induction tasks.
We show that if the connected sum of two knots with coprime Alexander polynomials is doubly slice, then the Ozsváth-Szabó correction terms as smooth double sliceness obstructions vanish for both knots. Recently, Jeffrey Meier gave smoothly slice knots that are topologically doubly slice, but not smoothly doubly slice. …
The paper extends a method for numerical conformal mappings to surfaces using Laplace-Beltrami equations.
problem Computing conformal mappings between Riemannian surfaces.
method Adapting the conjugate function method to Riemannian surfaces using hp-adaptive finite element methods. result Highly accurate numerical computations of conformal mappings on surfaces, including complex geometries.
The study finds lower bounds for the first eigenvalue of the Laplacian in planar domains with magnetic fields.
problem Finding lower bounds for the first eigenvalue of the Laplacian in planar domains with magnetic fields.
method Analyzing the spectrum of the Laplacian with magnetic Neumann boundary conditions, focusing on multiply connected domains with convex curves. Lower bounds are derived based on geometric invariants such as area, perimeter, diameter, and fluxes around inner holes.
result Sharp lower bounds for the first eigenvalue are derived for doubly connected domains and domains with an arbitrary number of holes, and a lower bound is obtained for Aharonov-Bohm operators with an arbitrary number of poles when holes shrink to points.
This paper extends ResNet theory to infinitely deep networks, linking them to diffusion processes.
problem Training infinitely deep ResNets with i.i.d. initializations leads to undesirable properties.
method Introduced doubly infinite ResNets with i.i.d. initializations, linking to diffusion processes.
result The dynamics of quantities of interest converge to deterministic limits in the limit of infinite depth.
New restrictions found on triple linking numbers of knot derivatives.
problem Understanding triple linking numbers of knot derivatives.
method Defined a new obstruction for Z[Z]-homology ribbon knots.
result New non-doubly slice knots discovered.
Let B1 be a ball of radius r1 in $S^n(\Hy^n)$, and let B0 be a smaller ball of radius r0 such that B0ˉ⊂B1. For Sn we consider r1<π. Let u be a solution of the problem $-\La u =1$ in $\Om := B_1\setminus \bar{B_0}$ vanishing on the boundary. It is shown that the associated functional…
A knot in the 3-sphere is called doubly slice if it is a slice of an unknotted 2-sphere in the 4-sphere. We give a bi-sequence of new obstructions for a knot being doubly slice. We construct it following the idea of Cochran-Orr-Teichner's filtration of the classical knot concordance group. This yields a bi-filtration o…
We propose an efficient method for estimating covariate effects in doubly-stochastic spatial models.
problem Computational demands and restrictive assumptions in existing doubly-stochastic spatial models.
method Penalized regression method for estimating covariate effects in doubly-stochastic point processes.
result Consistency and asymptotic normality of the covariate effect estimates achieved despite model misspecification.
A new algorithm speeds up optimal transport for machine learning.
problem Optimal transport for machine learning with additional terms.
method Forward-backward splitting algorithm based on Bregman distances.
result Significant improvement in speed and performance for domain adaptation.
We investigate manifolds obtained as a quotient of a doubly warped product. We show that they are always covered by the product of two suitable leaves. This allows us to prove, under regularity hypothesis, that these manifolds are a doubly warped product up to a zero measure subset formed by an union of leaves. We also…
CPME embeds counterfactual outcomes in RKHS for flexible policy evaluation.
problem Estimating counterfactual policy outcomes for decision-making.
method Counterfactual Policy Mean Embedding (CPME) framework in RKHS, plug-in and doubly robust estimators, kernel test statistic.
result Doubly robust estimator improves convergence rates and asymptotic normality.
Our goal is to provide a novel method of representing 2D shapes, where each shape will be assigned a unique fingerprint - a computable approximation to a conformal map of the given shape to a canonical shape in 2D or 3D space (see page 22 for a few examples). In this paper, we make the first significant step in this pr…
Lipschitz mappings found between Riemann surfaces with specific properties.
problem Finding globally Lipschitz mappings between doubly connected Riemann surfaces.
method Using a result from Iwaniec, Kovalev, and Onninen, the minimizer of the energy functional is shown to be locally Lipschitz and globally Lipschitz.
result The minimizer of the energy functional is a globally Lipschitz mapping.
We prove the existence of Cannon-Thurston maps for simply and doubly degenerate surface Kleinian groups. As a consequence we prove that connected limit sets of finitely generated Kleinian groups are locally connected.
For every g∈N0 and ε>0, we construct a smooth genus g surface embedded into the unit ball with area 8π and Willmore energy smaller than 8π+ε. From this we deduce that a minimising sequence for Willmore's energy in the class of genus g surfaces embedded in the unit ball with area 8π converges …
Natural experiment dataset reveals inconsistent treatment effect estimators.
problem Inconsistent results from over 20 estimators on a new dataset.
method Created a benchmark to evaluate estimator accuracy, derived variance formula, introduced new estimator.
result Doubly robust estimators outperform others by orders of magnitude.
(This is a revised version of the paper) - In the present paper we study the geometry of doubly extended Lie groups with their natural biinvariant metric. We describe the curvature, the holonomy and the space of parallel spinors. This is completely done for all simply connected groups with biinvariantmetric of Lorentzi…
Let A⊂R2 be a smooth doubly connected domain. We consider the Dirichlet energy E(u)=∫A∣∇u∣2, where u:A→C, and look for critical points of this energy with prescribed modulus ∣u∣=1 on ∂A and with prescribed degrees on the two connected components o…
Estimates exponential family distributions using a novel doubly dual embedding technique.
problem Estimating exponential family distributions with smoothness and efficiency.
method Doubly dual embedding for avoiding partition function computation and flexible sampling.
result Improves memory and time efficiency while offering stronger statistical properties.
This paper establishes non-asymptotic learning bounds for the DR covariate shift adaptation.
problem Distribution shift between training and test domains in machine learning.
method Doubly-robust (DR) estimator combining density ratio estimation and pilot regression model.
result First non-asymptotic learning bounds for DR covariate shift adaptation.
The paper extends knot theory to 4-manifolds, defining new genera and obstructions.
problem Understanding embeddings of 3-manifolds into 4-manifolds with specific properties.
method New L2-signature obstructions and extensions of knot genera. result Existence of knots with arbitrarily large generalized superslice genera and double stabilizing numbers.
Proposes SDRG to adjust missingness in machine learning models.
problem Systemic missingness in observational data leads to biased parameter estimation.
method Introduces SDRG using two models: weight-corrected gradients and per-covariate control variates.
result Empirically demonstrates convergence in training image classifiers with missing data.
We construct finite energy instanton connection on R4 which are periodic in two directions via an analogue of the Nahm transform for certain singular solutions of Hitchin's equations defined over a 2-torus.
Accelerates Birkhoff projection for manifold-constrained hyper-connections with high accuracy and speed.
problem Inaccurate and slow Birkhoff projection in mHC implementations.
method Dual formulation, Newton's method, implicit differentiation, warp-level CUDA kernel.
result Substantial speedups and accuracy improvements in doubly stochastic projections.
This work concerns the study of certain finite-energy solutions of the anti-self-dual Yang-Mills equations on Euclidean 4-dimensional space which are periodic in two directions, so-called doubly-periodic instantons. We establish a circle of ideas involving equivalent analytical and algebraic-geometric descriptions of t…
The paper connects minimal surfaces to cones in a ball.
problem Understanding minimal surfaces with free boundaries.
method Establishing a connection between minimal surfaces and cones.
result Doubly connected minimal surfaces in a ball are catenoids.
New invariant measures doubly slice links, disproving previous bounds.
problem Understanding doubly slice links and their invariants.
method Introduced new invariant gst to measure doubly slice links and disproved previous bounds. result Examples of links with large doubly slice genus but gst=1. Framework combines HMM and MTGCN for spatiotemporal causal inference in clinical data.
problem Challenges in observing direct treatment effects in clinical domains.
method Integrates Hidden Markov Model and Multi Task and Multi Graph Convolutional Network for spatiotemporal data.
result Advances predictive causal inference by structurally adapting to spatiotemporal complexities.
An almost-Fuchsian group is a quasi-Fuchsian group such that the quotient hyperbolic manifold contains a closed incompressible minimal surface with principal curvatures contained in (-1,1). We show that the domain of discontinuity of an almost-Fuchsian group contains many balls of a fixed spherical radius in the visual…
Characterizes a specific type of spacetime using vector fields.
problem Classifying a specific type of spacetime.
method Using vector fields to characterize 1+n doubly twisted spacetimes.
result Simple classification of 1+n doubly-twisted spacetimes.
Characterizes and examines gradient solitons on doubly warped product manifolds.
problem Understanding gradient solitons on specific manifold structures.
method Characterizations and examinations of various types of gradient solitons on doubly warped product manifolds.
result Effects of gradient solitons on factor manifolds and specific curvature properties of doubly warped products.
DNNet slices network for efficient inference.
problem Resource constraints in inference.
method Doubly nested network with channel-wise nesting and channel-causal convolutions.
result Resource-efficient inference with sub-models.
The article enumerates doubly symmetric diagrams for knots up to 18 crossings.
problem Enumerating doubly symmetric diagrams for knots.
method Developed an enumeration strategy for prime knots given by doubly symmetric diagrams.
result Determined all cases of doubly symmetric diagrams up to 18 crossings.
Proposes DR-ACI for causal effect intervals with temporal dependence.
problem Causal effect intervals under temporal dependence.
method Doubly robust adaptive conformal inference (DR-ACI).
result Constructs prediction intervals for causal effects.
Proves conditions for odd pretzel knots to be doubly slice.
problem Identifying conditions for odd pretzel knots to be doubly slice.
method Analyzes knots with specific twist parameters and odd integers.
result Identifies all doubly slice odd pretzel knots.
Simplified tutorial on doubly robust learning for causal inference.
problem Challenges in applying doubly robust methods due to complexity and software barriers.
method Combines propensity score and outcome modeling for robust causal inference.
result Makes doubly robust learning accessible through simplified methodology and practical examples.