Newly discovered 5 triangle-free intrinsically knotted graphs with 22 edges.
problem Identifying intrinsically knotted graphs with specific properties.
method Analyzing graphs with 22 edges, using specific graph operations and properties.
result There are exactly five triangle-free intrinsically knotted graphs with 22 edges.
A graph is intrinsically knotted if every embedding contains a knotted cycle. It is known that intrinsically knotted graphs have at least 21 edges and that the KS graphs, K7 and the 13 graphs obtained from K7 by ∇Y moves, are the only minor minimal intrinsically knotted graphs with 21 edges. This set incl…
A graph is called intrinsically knotted if every embedding of the graph contains a knotted cycle. Johnson, Kidwell and Michael showed that intrinsically knotted graphs have at least 21 edges. Recently Lee, Kim, Lee and Oh, and, independently, Barsotti and Mattman, showed that K7 and the 13 graphs obtained from K7…
Maximal knotless graphs have at least 74% of their vertices' edges.
problem Characterizing maximal knotless graphs and understanding their edge constraints.
method Analyzing edge maximality and constructing graphs to meet constraints.
result There exists an infinite family of maximal knotless graphs with fewer edges than previously thought.
New research finds six bipartite intrinsically knotted graphs with 23 edges.
problem Identifying intrinsically knotted bipartite graphs with 23 edges.
method Analyzing embeddings and graph minors to find minimal intrinsically knotted graphs.
result No minor minimal intrinsically knotted bipartite graph exists with 23 edges.
Defines a new version of Turaev-Viro invariants for 3-manifolds with boundaries.
problem Computing the volume of hyperbolic polyhedral 3-manifolds.
method Introduces a relative version of Turaev-Viro invariants for ideally triangulated compact 3-manifolds with boundaries and a coloring on edges.
result Proves the Volume Conjecture for these invariants, suggesting a method to solve the conjecture for hyperbolic 3-manifolds with totally geodesic boundary.
New algorithm estimates edge density of random graphs robustly, achieving optimal breakdown point.
problem Estimating edge density of Erdős-Rényi graphs under adversarial edge manipulation.
method Sum-of-Squares (SoS) hierarchy, constructing constant-degree certificates for concentration.
result First polynomial-time algorithm with optimal breakdown point and matching error guarantees.
Study finds no statistically significant trading edge in MNQ futures signals from OHLCV data.
problem Testing intraday momentum signals from OHLCV data in MNQ futures under realistic execution constraints.
method 947 trading days of five-minute data, 14 signal families evaluated, strict institutional criteria applied.
result No signal satisfies all criteria simultaneously, gross edge insufficient to overcome costs.
Paper proposes MAMRL for efficient energy dispatch in self-powered edge computing systems.
problem High energy consumption in self-powered edge computing systems.
method Developed a semi-distributed data-driven MAMRL framework to solve a two-stage linear stochastic programming problem.
result The proposed MAMRL framework reduces up to 11% non-renewable energy usage and 22.4% energy cost.
Experimentally identified 22 L-space knots with tunnel number >1, some having high genus and braid index.
problem Identifying L-space knots with tunnel number greater than 1.
method Cataloging hyperbolic manifolds, using SnapPy and KLO to find knot presentations as closures of positive braids.
result Found 9 asymmetric L-space knot complements with tunnel number 2, and 22 with tunnel number 1.
New research confirms Kähler-Einstein metrics for all Fano threefolds of degree 22.
problem Identifying Fano threefolds of degree 22 with Kähler-Einstein metrics.
method Analyzing the structure and properties of Fano threefolds of Picard rank one with anti-canonical degree 22.
result All remaining Fano threefolds of degree 22 admit Kähler-Einstein metrics.
We give a rigorous geometric proof of the Murakami-Yano formula for the volume of a hyperbolic tetrahedron. In doing so, we are led to consider generalized hyperbolic tetrahedra, which are allowed to be non-convex, and have vertices `beyond infinity'; and we uncover a group, which we call 22.5K, of 23040 scissors-class…
The paper analyzes the emergence of almost-honeycomb structures in low-energy planar clusters.
problem Understanding the formation of shapes resembling honeycombs in low-energy configurations.
method Detailed quantitative estimates and a revision of the global isoperimetric principle for honeycomb clusters.
result The majority of chambers in low-energy planar clusters are generalized hexagons, closely resembling regular hexagons.
Study of K-moduli of prime Fano threefolds of genus twelve, proving boundary purely divisorial.
problem Understanding the boundary of K-moduli of prime Fano threefolds of genus twelve.
method Developed a modular relation between Fano threefolds and their anticanonical K3 surfaces, proving forgetful morphism is an open immersion.
result Proved the boundary of K-moduli of V22 is purely divisorial and consists of four irreducible components. Study proves most Fano threefolds are Kähler-Einstein.
problem Existence of Kähler-Einstein metrics on smooth Fano threefolds.
method Investigated smooth Fano threefolds of Picard rank one and anticanonical degree 22 with C∗ action. result Proved existence of Kähler-Einstein metrics on most such threefolds, except possibly two cases.
DAFL learns efficient neural networks without training data.
problem Training data unavailable for deep networks.
method Generative adversarial networks (GANs) to create training samples.
result Achieves high accuracy (92.22%) on CIFAR-10 dataset.
We proved by computer enumeration that the Jones polynomial distinguishes the unknot for knots up to 22 crossings. Following an approach of Yamada, we generated knot diagrams by inserting algebraic tangles into Conway polyhedra, computed their Jones polynomials by a divide-and-conquer method, and tested those with triv…
We show that the only parameter prior for complete Gaussian DAG models that satisfies global parameter independence, complete model equivalence, and some weak regularity assumptions, is the normal-Wishart distribution. Our analysis is based on the following new characterization of the Wishart distribution: let W be an …
We give new counterexamples to a question of Karsten Grove, whether there are only finitely many rational homotopy types among simply connected manifolds satisfying the assumptions of Gromov's Betti number theorem. Our counterexamples are homogeneous Riemannian manifolds, in contrast to previous ones. They consist of t…
New solutions found for complex structures on specific manifolds.
problem Constructing smooth solutions to the Hull-Strominger system.
method Using fibrations over K3 orbisurfaces.
result Proved existence of solutions for certain manifolds.
New solutions found for Hull-Strominger system on torus bundles.
problem Finding solutions to the Hull-Strominger system with torus symmetry.
method Constructing solutions on torus bundles over K3 orbifolds.
result Smooth manifolds with complex structures have solutions to the Hull-Strominger system.
Develops methods for constructing parameter priors in DAG models.
problem Constructing parameter priors for model choice among DAG models.
method Introduces assumptions and methods for parameter priors construction and marginal likelihood computation.
result The only parameter prior for complete Gaussian DAG models that satisfies assumptions is the normal-Wishart distribution.
Corrects errors in previous work on spectral asymptotics in elasticity.
problem Two-term asymptotics of elastic eigenvalues on Riemannian manifolds.
method Strongly continuous semigroups and pseudodifferential operators.
result Theorem 1.1 in \cite{Liu-21} is rigorously proven.
Reduced-channel EEG systems struggle with artifact detection, highlighting the importance of referential channels.
problem Artifact detection in EEG signals with fewer channels.
method Investigated a deep learning algorithm, CNN-LSTM, on various channel configurations.
result False alarms increase dramatically when fewer channels are used, emphasizing the importance of referential channels.
The study examines stable minimal hypersurfaces in higher dimensions.
problem Characterizing stable minimal hypersurfaces in Rn+1. method Analyzing volume growth and stability conditions.
result Conditions for complete two-sided δ-stable minimal hypersurfaces to be the hyperplane. This article was originally published in Topology 22 (1983). The present hyperTeXed redaction includes references to post-1983 results as Addenda, and corrects a few typographical errors. (See math.GT/0411115 for a more comprehensive overview of the subject as it appears 21 years later.)
Paper compares two entropy concepts for finite presentation groups.
problem Comparing two entropy concepts for groups of finite presentation.
method Analyzes and contrasts minimum volume entropy for geometrically finite groups.
result Two entropy concepts coincide in dimension 1 but differ in others.
These notes briefly summarize the lectures for the Summer School "Optimal transportation: Theory and applications" held by the second author in Grenoble during the week of June 22-26, 2009. Their goal is to describe some recent results on Brenier's variational models for incompressible Euler equation.
These notes are based on a lecture course given by the first author in the Sedano Winter School on K-theory held in Sedano, Spain, on January 22-27th of 2007. They aim at introducing K-theory of C^*-algebras, equivariant K-homology and KK-theory in the context of the Baum-Connes conjecture.
Catch22 reduces time series feature space to 22 canonical characteristics for efficient analysis.
problem Efficiently capturing and comparing time series properties for diverse applications.
method Inference of minimal sets of time-series features from a comprehensive library.
result Catch22 (22 canonical characteristics) reduces computation time and complexity.
These notes are the first half of the contents of the course given by the second author at the Bachelier Seminar (February 8-15-22 2008) at IHP. They also correspond to topics studied by the first author for her Ph.D.thesis.
Training neural networks is hard in fixed dimensions.
problem Training two-layer neural networks is computationally hard in fixed dimensions.
method Parameterized complexity analysis considering dimension and number of neurons.
result Training two-layer neural networks is NP-hard for two dimensions.
Summary of tensor tomography proofs on manifolds with boundaries.
problem Proving injectivity of tensor tomography on compact Riemannian manifolds with boundaries.
method Summarized proofs from previous studies.
result Summary of proofs for s-injectivity.
We describe a minimal global coordinate system of order 30 on the SL(4,C)-character variety of a rank 2 free group. Using symmetry within this system, we obtain a smaller collection of 22 coordinates subject to 5 further real relations that determine conjugation classes of generic pairs of matrices in SU(3,1).
We classify non-dilatonic NS-NS type II supergravity backgrounds admitting a consistent absolute parallelism. They are all given by parallelised Lie groups admitting scalar flat bi-invariant lorentzian metrics. There are seven different classes, some of them containing moduli. For each class we determine the amount of …
Paper detects anomalous edges in social networks using edge exchangeability.
problem Detecting anomalous edges in directed social networks.
method Exploits edge exchangeability and uses conformal prediction theory.
result Proposed anomaly detector has a guaranteed upper bound for false positives.
Study resolves conjecture on overparameterized linear models' generalization.
problem Asymptotic generalization of multiclass classification with overparameterized models.
method Gaussian covariates bi-level model, Hanson-Wright inequality variant.
result Min-norm interpolating classifier can be suboptimal compared to noninterpolating classifiers.
In this short note, we present a construction of new symplectic 4-manifolds with non-negative signature using the complex surfaces on Bogomolov-Miyaoka-Yau line c12=9χh, the fake projective planes and Cartwright-Steger surfaces. Our construction yields an infinite family of fake rational homology $(2n-1)\CP#(2n-…
TGR rewires temporal graphs to improve TGNN performance.
problem Temporal graphs in evolving networks can suffer from under-reaching and over-squashing issues.
method TGR uses expander graph propagation to create message-passing highways between temporally distant nodes.
result TGR achieves state-of-the-art results on temporal graph benchmarks.
We present a short overview on the strongest variational formulation for gradient flows of geodesically λ-convex functionals in metric spaces, with applications to diffusion equations in Wasserstein spaces of probability measures. These notes are based on a series of lectures given by the second author for the Summer…
Generators for invariants of geometric mappings are derived.
problem Finding invariants of geometric mappings.
method Generalizing Thomas projective parameter and Weyl projective tensor, obtaining generators for vector spaces of invariants.
result Generators for vector spaces of invariants of geometric mappings are obtained.
We perform return interval analysis of 1-min {\em{realized volatility}} defined by the sum of absolute high-frequency intraday returns for the Shanghai Stock Exchange Composite Index (SSEC) and 22 constituent stocks of SSEC. The scaling behavior and memory effect of the return intervals between successive realized vola…
The paper characterizes chordal graphs via edge deletions and finds a local minimum spanning tree algorithm.
problem Characterizing chordal graphs and finding efficient minimum spanning trees.
method Focus on exposed edges, characterize chordal graphs via deletions, and use local properties to modify Kruskal's algorithm.
result A modified Kruskal's algorithm for weighted chordal graphs is local and efficient.
Deep Claim predicts payer responses from claims data using deep learning.
problem Predicting payer responses from claims data to improve healthcare performance.
method Learning complex dependencies in claim inputs to create a compact representation, then using deep learning to predict responses.
result Deep Claim improves claim denial prediction by 22.21%.
Algorithm estimates covariance from noisy data efficiently.
problem Estimating covariance from a noisy set of points.
method Spectral techniques for list-decodable covariance estimation.
result Efficient algorithm with poly(1/α) sample and time complexity.
Extends duality preserving singular set images and first fundamental forms to generalized cuspidal edges.
problem Preserving singular set images and first fundamental forms on generalized cuspidal edges.
method Extends previous isometric duality to generalized cuspidal edges including cuspidal cross caps and 5/2-cuspidal edges.
result New geometric insights on the duality.
We study parallel surfaces and dual surfaces of cuspidal edges. We give concrete forms of principal curvature and principal direction for cuspidal edges. Moreover, we define ridge points for cuspidal edges by using those. We clarify relations between singularities of parallel and dual surfaces and differential geometri…
OL4EL optimizes edge learning on resource-constrained servers.
problem Resource constraints on edge servers hinder effective distributed machine learning.
method Online Learning for EL (OL4EL) framework using budget-limited multi-armed bandit model.
result OL4EL significantly improves learning performance while conserving resources.