Proves existence of functions for Ricci flow and Yau's conjecture.
problem Existence of exhaustion functions for Ricci flow and Yau's conjecture.
method Adapting L.-F. Tam's method for proving existence.
result Short-time existence of Ricci flow and uniformization of surfaces.
By a theorem of Greene and Wu, a noncompact connected Riemannian manifold admits a smooth strictly subharmonic exhaustion function. Demailly provided an elementary proof of this fact. A further simplification of Demailly's proof and some (mostly known) applications are described. Applications include the fact that the …
The paper studies Kähler metrics from finite Monge-Ampère mass exhaustion functions.
problem Investigating the spectrum of complete Kähler metrics from finite Monge-Ampère mass exhaustion functions.
method Analyzing logarithmic potentials and the associated complete Kähler metrics, proving bounds on the spectrum using the finite Monge-Ampère mass condition.
result The lower bound of the spectrum of the Laplace-Beltrami operator is n2 under the finite Monge-Ampère mass condition. The study proves regularity of metrics on complex domains.
problem Regularity of metrics on complex domains.
method Abstract complex manifold theorem with Monge-Ampère exhaustions of Ck regularity. result Existence of bounded open neighborhoods with smooth metrics.
We generalize A. Borbély's condition for the conclusion of the Omori-Yau maximum principle for the Laplace operator on a complete Riemannian manifold to a second-order linear semi-elliptic operator L with bounded coefficients and no zeroth order term. Also, we consider a new sufficient condition for the existence of …
Study exhausts curve complex on nonorientable surfaces using finite rigid sets.
problem Exhausting curve complexes on nonorientable surfaces.
method Using finite rigid sets to exhaust curve complex.
result Improves exhaustion result for (g,n)=(3,0) or g+n≥5. The paper explores uniform perfectness and centers in Morse boundaries.
problem Detecting κ-center exhaustivity in uniformly perfect Morse boundaries. method Analyzes CAT(0) and geodesic spaces, using visual boundary data and metric transforms.
result Fixed-basepoint uniform perfectness is insufficient for κ-center exhaustivity. For nonorientable surfaces, curve complexes can be exhausted by finite superrigid sets.
problem Exhausting curve complexes on nonorientable surfaces.
method Using finite superrigid sets for exhaustion.
result An exhaustion of curve complexes by finite superrigid sets for (g,n)eq(1,2) and g+neq4. This paper exhausts curve complexes on non-orientable surfaces.
problem Proving exhaustion of curve complexes on non-orientable surfaces.
method Proving exhaustion via rigid expansions and graph endomorphisms.
result Any graph endomorphism of curve complexes whose restriction to a finite rigid set is injective is induced by a homeomorphism.
A compact real analytic Riemannian manifold M admits a canonical complexification with plurisubharmonic exhaustion function satisfying the homogeneous complex Monge-Ampere equation, called a Grauert tube. From the point of view of complex analysis, several authors have considered whether a given complex manifold can ar…
Constructs uniformly positive scalar curvature metrics on open manifolds
problem Finding uniformly positive scalar curvature metrics on open manifolds
method Using Morse functions and exhaustion
result Proving the existence of uniformly positive scalar curvature metrics
Proposes methods for selecting sparse variables in linear regression.
problem Selecting sparse variables in linear regression models.
method K-sparse exhaustive search (ES-K) and K-sparse approximate exhaustive search (AES-K) methods.
result AES-K method effectively reconstructs density of states for large problems.
Probabilistic model for exhaustion in infinite-genus curve complexes.
problem Action rigidity in infinite-genus curve complexes.
method Costa and Farber's model for random simplicial complexes.
result Probabilistic evidence for exhaustion via rigid expansions.
The paper explores different smooth map notions on convex sets and their relationships.
problem Exploring and comparing different smooth map notions on convex sets.
method Constructing a function that doesn't extend to a smooth function on any open neighborhood but does for Ck functions. result Diffeological and Sikorski smoothness notions do not coincide for all convex sets.
grangersearch tests causal relationships in time series data.
problem Testing causal relationships between multiple time series.
method Exhaustive pairwise search, automatic lag order optimization, tidyverse integration.
result Automated Granger causality testing simplifies causal analysis.
Let M be a complete Riemannian manifold possessing a strictly convex Lipschitz continuous exhaustion function. We show that the isoperimetric profile of M is a continuous and non-decreasing function. Particular cases are Hadamard manifolds and complete non-compact manifolds with strictly positive sectional curvatur…
Researchers solved a model of an exhaustible resource with stochastic discoveries.
problem Optimal exploration of an exhaustible resource with uncertain discoveries.
method Impulse control and Poisson process of new discoveries.
result A frontier of critical levels of proven reserves exists, above which exploration is stopped.
Let S be a connected orientable surface of finite topological type. We prove that there is an exhaustion of the curve complex C(S) by a sequence of finite rigid sets.
Study exhaustions for complex orbits in almost homogeneous manifolds.
problem Complex orbits in almost homogeneous manifolds.
method Complex homogeneous Monge-Ampère equations.
result Rigidity results on complex spaces.
Researchers exhaustively cover pants graphs of spheres with punctures using finite rigid sets.
problem Covering all pants graphs of punctured spheres efficiently.
method Constructing a sequence of finite rigid sets in the pants graph.
result The union of these sets covers the entire pants graph of the punctured sphere.
Paper proposes a new co-clustering method for overlapping clusters and outliers.
problem Real-world datasets often contain overlaps and outliers in co-clusters.
method Formulated Non-Exhaustive, Overlapping Co-Clustering problem and developed NEO-CC algorithm.
result NEO-CC algorithm effectively captures underlying co-clustering structure of real-world data.
Researchers exhaust curve graph using rigid expansions on surfaces.
problem Exhausting the curve graph of surfaces with genus ≥ 3.
method Constructing a finite set of curves and using iterated rigid expansions.
result The constructed set exhausts the curve graph via rigid expansions.
Deep learning improves demosaicing but edge devices struggle.
problem Edge devices struggle with deep learning-based demosaicing.
method Exhaustive search of deep neural network architectures to find the best balance between performance and model complexity.
result Found architectures that outperform state-of-the-art demosaicing models on edge devices.
Study on 3-manifolds with nonnegative scalar curvature and positive harmonic functions.
problem Characterizing 3-manifolds with nonnegative scalar curvature.
method Exhaustions by level sets of harmonic functions and refined average gradient estimates.
result Contractible 3-manifolds are diffeomorphic to R^3, and handlebodies have genus at most 1.
The paper examines eigenvalues and inequalities on Riemannian manifolds.
problem Eigenvalue behavior and volume growth on Riemannian manifolds.
method Analyzes the asymptotic behavior of the first eigenvalues of balls on Riemannian manifolds.
result Sharp estimates of volume growth and Hardy inequalities under spectral conditions.
In this thesis, we study cohomological properties of non-Kähler manifolds. In particular, we are concerned in investigating the cohomology of compact (almost-)complex manifolds, and of manifolds endowed with special structures, e.g., symplectic structures, D-complex structures in the sense of F. R. Harvey and H. B. Law…
Bayesian model adapts to changing classes in machine learning.
problem Non-stationary environments with incomplete class information.
method Doubly non-parametric Bayesian Gaussian mixture model.
result Model can grow to accommodate any number of classes.
Proposes a taxonomy for economic policies.
problem Lack of a standardized list of economic policies.
method Develops a tree taxonomy to categorize economic policies.
result Constructs an exhaustive list of economic policies.
Using the stress energy tensor, we establish some monotonicity formulae for vector bundle-valued p-forms satisfying the conservation law, provided that the base Riemannian (resp. Kähler) manifolds poss some real (resp. complex) p-exhaustion functions. Vanishing theorems follow immediately from the monotonicity formulae…
In this paper, aimed at exploring the fundamental properties of isoperimetric region in 3-manifold (M3,g) which is asymptotic to Anti-de Sitter-Schwarzschild manifold with scalar curvature R≥−6, we prove that connected isoperimetric region {Di} with Hg3(Di)≥δ0>0 cannot slide off to …
Regularity properties of intrinsic objects for a large class of Stein Manifolds, namely of Monge-Ampère exhaustions and Kobayashi distance, is interpreted in terms of modular data. The results lead to a construction of an infinite dimensional family of convex domains with squared Kobayashi distance of prescribed regula…
Paper proposes using pairwise feature comparisons to infer modification costs for user recourse.
problem Learning and inferring user preferences for modifying features in black-box models.
method Bradley-Terry model for inferring feature-wise costs from non-exhaustive human comparison surveys.
result Non-exhaustive human surveys can efficiently learn feature costs, enabling recourse finding.
Neurally-Guided Structure Inference combines search and data-driven methods for efficient, robust structure inference.
problem Combining the advantages of exhaustive search and data-driven methods for structure inference.
method Neurally-Guided Structure Inference (NG-SI) uses a neural network to guide hierarchical search over structures.
result NG-SI outperforms search-based and data-driven methods on probabilistic matrix decomposition and symbolic program parsing.
Efficiency criteria improve conformal predictors' performance.
problem Improving the performance of conformal predictors.
method Learning classifiers by minimizing observed fuzziness as a training objective function.
result Conformal predictors trained by minimizing observed fuzziness perform better than traditional ones.
In this paper we prove the following result: if two 2-dimensional 2-homogeneous rational vector fields commute, then either both vector fields can be explicitly integrated to produce rational flows with orbits being lines through the origin, or both flows can be explicitly integrated in terms of algebraic functions. In…
We study infinite-type 3-manifolds with compact hyperbolizable pieces.
problem Characterizing infinite-type 3-manifolds with hyperbolizable pieces.
method Compact exhaustion and topological conditions for hyperbolic metrics.
result Necessary and sufficient conditions for complete hyperbolic metrics.
In this paper, we prove that the L^2 Betti numbers of an amenable covering space can be approximated by the average Betti numbers of a regular exhaustion, under some hypotheses. We also prove that some L^2 spectral invariants can be approximated by the corresponding average spectral invariants of a regular exhaustion. …
Generalizes Nakano-positivity to Hilbert space fields.
problem Extending Nakano-positivity to Hilbert space fields.
method Exhaustion arguments to generalize the theorem.
result Log-plurisubharmonic variation results for Stein manifolds.
A finitely presented group is weakly geometrically simply connected (wgsc) if it is the fundamental group of some compact polyhedron whose universal covering is wgsc i.e. it has an exhaustion by compact connected and simply connected sub-polyhedra. We show that this condition is almost-equivalent to Brick's qsf propert…
We construct exhaustion and cut-off functions with controlled gradient and Laplacian on manifolds with Ricci curvature bounded from below by a (possibly unbounded) nonpositive function of the distance from a fixed reference point, without any assumptions on the topology or the injectivity radius. Along the way we prove…
New research shows IBM's GDX algorithm outperforms Vytelingum's Adaptive-Aggressive strategy in market simulations.
problem Comparing the performance of adaptive-aggressive trading algorithms in various market scenarios.
method Exhaustive testing across a wide range of market environments using large-scale compute facilities.
result Vytelingum's Adaptive-Aggressive strategy is consistently outperformed by IBM's GDX algorithm in simple market conditions.
This research extends quasiplurisubharmonic functions on compact Kähler manifolds.
problem Extending quasiplurisubharmonic functions on compact Kähler manifolds.
method Using a cover of Zariski-open Stein sets with strictly plurisubharmonic potentials, the authors prove extension properties for plurisubharmonic functions.
result Any ω|_X-plurisubharmonic function on an analytic subvariety X of a compact Kähler manifold V extends to a ω-plurisubharmonic function on V.
The jet bundle description of time-dependent mechanics is revisited. The constraint algorithm for singular Lagrangians is discussed and an exhaustive description of the constraint functions is given. By means of auxiliary connections we give a basis of constraint functions in the Lagrangian and Hamiltonian sides. An ad…
In this paper we study the Sasakian geometry on S^3-bundles over a Riemann surface of genus g>0 with emphasis on extremal Sasaki metrics. We prove the existence of a countably infinite number of inequivalent contact structures on the total space of such bundles that admit 2-dimensional Sasaki cones each with a Sasaki m…
Investigates properties of a pseudometric on domains in Euclidean space, linking it to hyperbolic geometry.
problem Defines and analyzes a pseudometric on domains in Rn to understand their hyperbolic properties. method Introduces a pseudometric based on conformal harmonic discs and studies its properties and conditions for hyperbolicity.
result Characterizes domains as hyperbolic based on their geometric properties and provides sufficient conditions for hyperbolicity.
Following a purely algebraic procedure, we provide an exhaustive classification of local Weyl-invariant scalar densities in dimension D=8.
Linear invariants of complex manifolds preserved by biholomorphisms.
problem Identifying biholomorphic mappings between complex manifolds using holomorphic function spaces.
method Proving biholomorphic equivalence of domains via linear isometries of Lp-integrable holomorphic functions. result Linear isometries between Ap spaces imply biholomorphic equivalence of domains, with conditions on p and domain properties. New framework for Seiberg-Witten map on non-compact 4-manifolds.
problem L^2 self-dual forms on non-compact 4-manifolds cannot exhaust d^+ images.
method Functional analytic framework for Seiberg-Witten map.
result Construction of new functional analytic framework.