The paper proves isoperimetric regions in specific manifolds cannot escape to infinity.
problem Exploring isoperimetric regions in asymptotically hyperbolic manifolds.
method Analyzing scalar curvature and Hawking mass to prove region exhaustivity.
result Isoperimetric regions with scalar curvature ≥ -6 cannot escape to infinity.
Study predicts evolution patterns for pretzel knots, revealing abrupt transitions and hidden non-linearity.
problem Predicting evolution of Khovanov polynomials for pretzel knots.
method Conjectured explicit evolution formulas, revealed abrupt transitions, and identified additional Lyapunov exponents.
result Abrupt transitions and hidden non-linearity in evolution of Khovanov polynomials for thick knots.
We present a sparse knowledge gradient (SpKG) algorithm for adaptively selecting the targeted regions within a large RNA molecule to identify which regions are most amenable to interactions with other molecules. Experimentally, such regions can be inferred from fluorescence measurements obtained by binding a complement…
By employing exhaustive lists of large firms in European countries, we show that the upper-tail of the distribution of firm size can be fitted with a power-law (Pareto-Zipf law), and that in this region the growth rate of each firm is independent of the firm's size (Gibrat's law of proportionate effect). We also find t…
Study examines money flow network among firms' accounts in a Japanese region.
problem Understanding the relationship between money flow and economic activities of firms.
method Employed exhaustive bank transfer data, network statistics, Hodge decomposition, and non-negative matrix factorization.
result Identified a 'walnut' structure with core and upstream/downstream components, correlated with economic activities.
Compactness theorem for Riemannian manifolds with volume and curvature bounds.
problem Investigating the regularity of limit spaces of Riemannian manifolds.
method Local volume growth condition, compactness theorem, different convergence notion.
result Compactness theorem for Riemannian manifolds with Lp curvature bounds and volume growth assumption. 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. 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.
Novel graph-based framework for hyperspectral image classification using superpixels.
problem High classification accuracy with limited labelled data in hyperspectral images.
method Superpixel method for defining local regions, spectral and spatial features extraction, contracted graph representation, semi-supervised classifier.
result Our approach produces accurate classifications with minimal labelled data, outperforming state-of-the-art techniques.
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.
AntBO optimizes antibody design using Bayesian optimization for efficient and effective CDRH3 sequence generation.
problem Designing optimal antigen-specific CDRH3 regions in antibody design due to combinatorial sequence space.
method Combinatorial Bayesian optimization framework with trust region for developability.
result AntBO designs CDRH3 regions with diverse biophysical properties and outperforms existing methods.
Deep feature fusion improves mitosis counting accuracy.
problem Manual mitosis counting by pathologists is time-consuming and inconsistent.
method Combines Faster R-CNN for object detection with UNet segmentation features and RGB image features.
result Achieved an F-score of 0.508 on mitosis counting challenge dataset, outperforming state-of-the-art methods.
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.
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.
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.
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.
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.
MA-COPP predicts multi-agent system outcomes using data from a different policy, with probabilistic guarantees.
problem Predicting outcomes in multi-agent systems using data from a different policy.
method Conformal prediction framework applied to multi-agent systems, avoiding exhaustive search.
result Achieves probabilistic guarantees for multi-agent system predictions.
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.
New distances defined between space-times, proving some definite.
problem Defining distances between space-times.
method Introducing causal-null-compactifiable space-times and using cosmological time and null distance.
result Various definite distances defined, proving convergence of space-times.
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.
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. 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.
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. HRFs adaptively linearize kernels for accurate approximations.
problem Linearizing softmax and Gaussian kernels for machine learning applications.
method Generalizes Bochner's Theorem for kernels, uses random features for compositional kernels.
result Strong theoretical guarantees and unbiased approximation with smaller relative errors.
New mass definition linked to ADM mass for general metrics.
problem Defining mass for metrics with low regularity.
method Using isocapacitary inequality to define total mass.
result Inequality between new mass and ADM mass proved.
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…
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 …
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.
Automates verifying deep neural networks' safety against minor image changes.
problem Deep neural networks can be unstable to small image perturbations.
method SMT-based automated verification framework for neural networks.
result Guaranteed discovery of adversarial examples for image classification.
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 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…
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…
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
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.
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…
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 …
Following a purely algebraic procedure, we provide an exhaustive classification of local Weyl-invariant scalar densities in dimension D=8.
Interactive framework improves understanding of deep neural networks.
problem False sense of comprehension from static explanation methods.
method Interactive framework allowing exhaustive inspection and testing of decisions.
result Interactive approach leads to better understanding of complex decision boundaries.
Pattern sampling reduces time series classification complexity.
problem High computational complexity of exhaustive search for shapelets.
method Pattern sampling using a weighted trie to extract discriminative patterns.
result Significant reduction in computational and memory resources.
This paper improves image super-resolution by integrating cross-scale non-local attention.
problem Improving image super-resolution by leveraging long-range and cross-scale feature correlations.
method Proposes a Cross-Scale Non-Local (CS-NL) attention module integrated into a recurrent neural network.
result Significantly improved performance on SISR benchmarks.