Researchers create a new moduli space for Fano manifolds with special geometric properties.
problem Constructing a new moduli space for Fano manifolds with Kähler-Ricci solitons.
method Developed a moment map picture and used complex analytic charts to construct the moduli space.
result Created a larger moduli space that includes Fano manifolds with Kähler-Einstein metrics.
Unified framework for singular statistical models using observable charts.
problem Non-identifiability and breakdown of classical asymptotic theory in singular models.
method Invariant framework based on observable charts to define local coordinate systems in model space.
result Observable order provides a lower bound on KL divergence vanishing rate in singular models.
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.
Analyzes when vector fields can be real analytic in coordinates.
problem When can vector fields be represented by real analytic functions in coordinates?
method Provides necessary and sufficient conditions for real analytic coordinates.
result Necessary and sufficient conditions for real analytic coordinates exist.
Deep learning predicts stock market trends using candlestick charts.
problem Predicting stock market prices with multiple influencing factors.
method Used Deep Convolutional Neural Networks and candlestick charts.
result 92.2% and 92.1% accuracy for Taiwan and Indonesian stock markets.
No minimal charts with exactly seven white vertices found.
problem Finding minimal charts with specific vertex counts.
method Investigating charts representing embedded surfaces in 4-space.
result No minimal chart with exactly seven white vertices exists.
The projective hull X^ of a subset X in complex projective space P^n is an analogue of the classical polynomial hull of a set in C^n. If X is contained in an affine chart C^n on P^n, then the affine part of X^ is the set of points x in C^n for which there exists a constant M=M_x so that |p(x)| < M^d sup{|p(y)| : y in X…
This paper studies minimal charts of a specific type to understand embedded surfaces in 4-space.
problem Investigating minimal charts of a specific type to understand embedded surfaces in 4-space.
method Analyzing charts of type (5,2) to find a minimal chart.
result Identified a minimal chart of type (5,2) representing an embedded surface in 4-space.
In this paper, we give definitions of three kinds of minimal charts, and we investigate properties of minimal charts and establish fundamental theorems characterizing minimal charts. To classify charts with two or three crossings we use the fundamental theorems. In the future paper, we give an numeration of the charts …
No minimal chart of type (7) exists.
problem Characterizing minimal charts of specific types.
method Analyzing charts based on edge labels and white vertex counts.
result There is no minimal chart of type (7).
Critical points of scale-invariant curvature energies in 4D are analytic.
problem Analyzing critical points of curvature energies in 4D manifolds.
method Applying Noether's theorem to identify conservation laws and lower order elliptic system of PDEs, then using integrability by compensation and interpolation theory.
result Critical points of scale-invariant curvature energies in 4D are analytic.
No minimal chart of type (4,3) exists in 4-space.
problem Existence of minimal charts of specific type in 4-space.
method Investigation of charts and their properties in 4-space.
result No minimal chart of type (4,3) exists.
Optimizes coordinate charts for smooth elliptic structures.
problem Achieving optimal regularity for coordinate charts of smooth elliptic structures.
method Generalizing Malgrange's proof of the Newlander-Nirenberg Theorem to this setting.
result Optimal regularity for coordinate charts of smooth elliptic structures.
Paper classifies surface-links using charts with specific properties.
problem Classifying surface-links with specific charts.
method Using quandle colorings to differentiate charts representing different surface-links.
result Charts in the second class represent different surface-links.
The paper studies 4-charts with three crossings and their equivalence to a specific knot.
problem Investigating the structure and equivalence of 4-charts with three crossings.
method Examining charts as oriented labeled graphs in a disk, focusing on acyclic components and equivalence through label-orientation-reflection.
result Any linear minimal 4-chart with three crossings is equivalent to a 2-twist spun trefoil knot.
No minimal chart of type (2,3,2) exists.
problem Characterizing minimal charts of specific types.
method Analyzing charts with given edge label constraints.
result No minimal chart of type (2,3,2) exists.
No minimal chart of type (3,2,2) exists.
problem Characterizing minimal charts of specific types.
method Analyzing charts of type (3,2,2) and proving non-existence.
result There is no minimal chart of type (3,2,2).
A new SVDD-based control chart for high-frequency multivariate data.
problem Challenges in interpreting kernel distance plots for high-frequency multivariate data.
method Proposes a new SVDD-based control chart, KT chart, to track process variation and central tendency. result Demonstrates successful use of KT chart on the Tennessee Eastman process data. Minimal charts of specific type contain unique subgraphs.
problem Characterizing minimal charts of type (m;2,3,2). method Analyzing the structure of charts and their subgraphs.
result Each of Γm+1 and Γm+2 contains one of three specific subgraphs. Simplifies surface-knots using chart moves involving black vertices.
problem Simplifying branched covering surface-knots.
method Chart moves involving black vertices to simplify surface-knots.
result Properties of simplified branched covering surface-knots with branch points.
In this paper, we shall show a condition for that a chart is C-move equivalent to the product of two charts, the union of two charts Γ∗ and Γ∗∗ which are contained in disks D∗ and D∗∗ with D∗∩D∗∗=∅.
Simplifies surface-knots by adding 1-handles with chart loops.
problem Complexity of branched covering surface-knots.
method Adding 1-handles with chart loops to simplify charts.
result Properties of simplified charts are investigated.
Minimal charts of type (3,3) are equivalent to a specific subchart.
problem Characterizing minimal charts of type (3,3).
method Analyzing subgraphs and C-move equivalence.
result Minimal charts of type (3,3) are equivalent to a specific subchart.
Sharp conditions found for coordinates adapted to vector fields.
problem Finding coordinates adapted to vector fields with specific smoothness.
method Coordinate-free conditions and quantitative study.
result Necessary and sufficient conditions for Cs+1 coordinates. Sharp Hölder regularity found for complex Frobenius theorem coordinates.
problem Finding optimal Hölder-Zygmund regularity for complex Frobenius theorem coordinates.
method Analyzing necessary and sufficient conditions for coordinate charts achieving the theorem's structure.
result The optimal Hölder-Zygmund regularity for coordinate charts is shown to be α. This paper studies the structure of a specific neighborhood in minimal 2-crossing charts.
problem Understanding the structure of a minimal 2-crossing chart with specific neighborhoods.
method Analyzes the neighborhoods of Γα∪Γβ and proposes a normal form for 2-crossing minimal n-charts. result Proposes a normal form for 2-crossing minimal n-charts. A method to fix radius distortion in generative models on curved spaces.
problem Distortion in geodesic radius measurements across different charts on Riemannian manifolds.
method Radial Compensation (RC) adjusts the tangent-space base distribution to match the geodesic radius law, improving model stability and interpretability.
result RC ensures that the model's geodesic radius matches the intended distribution, improving numerical stability and curvature interpretation.
DDR game charts generated from raw audio tracks.
problem Creating new step charts for songs without existing charts.
method Combining recurrent and convolutional neural networks for step placement and a conditional LSTM for step selection.
result Improved step charts generated from raw audio tracks.
Paper improves channel charting using autoencoders with spatial constraints.
problem Improving logical positioning of UEs using channel-state information.
method Representation-constrained autoencoders to enhance channel charts.
result Improved quality of learned channel charts for UE positioning.
Criteria ensure manifold triangulation without differentiable structure.
problem Ensuring a manifold can be triangulated without differentiable structure.
method Local coordinate chart criteria for homeomorphism verification.
result Criteria guarantee triangulation of manifolds without Delaunay property.
Study uses CNN and LSTM to recognize stock chart patterns.
problem Recognizing stock chart patterns for trading.
method Used CNN and LSTM neural networks on historical stock data.
result Obtained accuracies for recognizing two common chart patterns.
A 2-dimensional braid over an oriented surface-knot F is presented by a graph called a chart on a surface diagram of F. We consider 2-dimensional braids obtained by an addition of 1-handles equipped with chart loops. We introduce moves of 1-handles with chart loops, called 1-handle moves, and we investigate how muc…
The classification of even-homogeneous complex supermanifolds of dimension 1|m, m\leq 3, on CP^1 up to isomorphism is given. An explicit description of such supermanifolds in terms of local charts and coordinates is obtained.
Efficient online kernel CUSUM detects changes quickly and accurately.
problem Detecting changes in online data streams efficiently.
method Online kernel CUSUM using maximum kernel statistics.
result Increased sensitivity to small changes compared to existing methods.
Study the structure of a minimal chart with two crossings.
problem Enumerate minimal charts with two crossings.
method Analyze a disk not containing crossings but intersecting specific edge labels.
result Two crossings are contained in the intersection of specific edge labels.
Study projective structures with poles, mapping them to local systems.
problem Understanding projective structures with poles on surfaces.
method Define a monodromy map from parameter space to framed local systems, proving containment in cluster chart domains.
result The image of the monodromy map is contained in the union of cluster chart domains.
New surfaces in 4-ball constructed from knits, described by charts.
problem Constructing surfaces in 4-ball from knits.
method Introducing knitted surfaces, describing them with BMW charts.
result Every compact surface in 4-ball is ambiently isotopic to a knitted surface.
Chart autoencoders learn latent features preserving manifold topology and geometry, with robust denoising capabilities.
problem Learning low-dimensional latent features of high-dimensional data sampled near a manifold.
method Chart autoencoders encode data into latent features on charts, preserving manifold topology and geometry.
result Chart autoencoders achieve a squared generalization error of n−d+22log4n under proper network architectures. Chart descriptions are a graphic method to describe monodromy representations of various topological objects. Here we introduce a chart description for hyperelliptic Lefschetz fibrations, and show that any hyperelliptic Lefschetz fibration can be stabilized by fiber-sum with certain basic Lefschetz fibrations.
We investigate minimal charts with loops, a simple closed curve consisting of edges of label m containing exactly one white vertex. We shall show that there does not exist any loop in a minimal chart with exactly seven white vertices in this paper.
CAE models learn complex manifold structures in data.
problem Flat latent spaces in auto-encoders fail to capture manifold structures.
method Proposes Chart Auto-Encoders (CAE) with a multi-chart latent space.
result CAE provides better data representation with manifold properties.
CC charts radio geometry for user localization.
problem Locating users in radio environments.
method Unsupervised learning from passive CSI.
result Extracts channel features for spatial comparison.
Introduces Hurewicz fibrations for embedding maps of orbifold charts.
problem No specific problem stated; focuses on new concept definition.
method Defines E-fibration embedding and studies its properties.
result Introduces and studies properties of E-fibration embedding.
Chart descriptions are a graphic method to describe monodromy representations of various topological objects. Here we introduce a chart description for genus-two Lefschetz fibrations, and show that any genus-two Lefschetz fibration can be stabilized by fiber-sum with certain basic Lefschetz fibrations.
We give a combinatorial description of closed curves on oriented surfaces in terms of certain permutations, called charts. We describe automorphisms of curves in terms of charts and compute the total number of curves counted with appropriate weights. We also discuss relations between curves, Grothendieck dessins d'enfa…
Generative mixture models of VAEs learn manifolds for inverse problems.
problem Representing high-dimensional data manifolds efficiently and accurately.
method Mixture model of variational autoencoders (VAEs) with Riemannian gradient descent.
result Learned manifold enables solving inverse problems with data fidelity.
The paper classifies Poisson structures on toric manifolds and computes their cohomology.
problem Classifying real Poisson structures on complex toric manifolds of type (1,1) and computing their cohomology. method Investigates algebraic and differential Poisson structures, focusing on smooth and generically non-degenerate cases.
result Computes the first two cohomology groups for algebraic Poisson structures.
Unified Siamese network for wireless positioning and channel charting.
problem Wireless positioning and channel charting using CSI.
method Unified Siamese neural network architecture for both supervised and unsupervised learning.
result Siamese networks achieve similar or better performance than existing methods.