The canonical components of SL_2-character varieties of arithmetic two bridge link groups are determined.
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48 results for “canonical component”
In this paper we determine topologically the canonical component of the character variety of the Whitehead link complement.
Proves freely 2-periodic knots have two canonical components in their character variety.
problem Identifying freely 2-periodic knots in character varieties.
method Analyzes SL(2, C) character variety and hyperbolic torsion polynomial.
result Character variety has two canonical components for freely 2-periodic knots.
Canonical maps connect complex structures to Hitchin components.
problem Connecting higher complex structures to Hitchin components.
method Equivariant vector bundle construction and canonical isomorphisms.
result Canonical diffeomorphisms between spaces of higher complex structures and Hitchin components.
Let M be a two cusped hyperbolic 3-manifold and let M(r) be the result of r Dehn filling of a fixed cusp of M. We study canonical components of the SL(2,C) character varieties of M(r). We show that the gonality of these sets is bounded, independent of the filling parameter. We also obtain bounds, depending on r, for th…
Symplectic coordinates found on a Hitchin component for a hyperbolic surface.
problem Parametrizing the -Hitchin component with canonical coordinates.
method Proved global Darboux coordinates with half canonical Goldman coordinates.
result Global Darboux coordinates exist for the -Hitchin component.
We compute both natural and smooth models for the character varieties of the two component double twist links, an infinite family of two-bridge links indexed as . For each , the component(s) of the character variety containing characters of irreducible representations are birational to…
The paper uses algebraic geometry tools to study knot invariants and Dehn surgeries.
problem Understanding algebraic and number theoretic properties of canonical components of character varieties.
method Utilizes quaternion Azumaya algebras and Brauer groups of curves over number fields.
result Constructs new knot invariants using algebraic geometry.
Study on knot surgeries reveals infinite residue characteristics and infinite order points.
problem Arithmetic properties of Dehn surgery points on knot .
method Analyzing the canonical component of the -character variety.
result Infinite set of ramified places and infinite order points in the Mordell-Weil group.
Study shows boundedness of klt singularities in 3D or with bounded Kollár components.
problem Boundedness of klt singularities in algebraic geometry.
method Analysis of Kollár components and local volumes.
result Minimal log discrepancies of Kollár components are bounded in dimension 3.
Constructs a new geometric structure on surfaces to generalize Teichmüller theory.
problem Exploring new geometric structures in Teichmüller theory.
method Uses the punctual Hilbert scheme of the plane to construct a higher complex structure and explores its properties.
result Establishes a canonical diffeomorphism between the moduli space of higher complex structures and Hitchin's component.
A new method for real-time CCA on streaming data.
problem Finding correlated features in online data streams.
method Sliding Window Informative Canonical Correlation Analysis (SWICCA) using streaming PCA.
result SWICCA provides real-time CCA components in high dimensions with theoretical guarantees.
The study of Euclidean submanifolds with incompressible canonical vector fields.
problem Characterizing Euclidean submanifolds with incompressible canonical vector fields.
method Analyzing the canonical vector field properties and conditions for incompressibility.
result Necessary and sufficient conditions for the canonical vector field of a Euclidean submanifold to be incompressible.
In this paper we show that there exists a family of simply connected, symplectic 4-manifolds such that the (Poincare dual of the) canonical class admits both connected and disconnected symplectic representatives. This answers a question raised by Fintushel and Stern.
It is proved that the Hasse-Weil zeta functions of the canonical components of the ()-character varieties of closed orientable complete hyperbolic -manifolds of finite volume are equal to the Dedekind zeta functions of their trace fields (invariant trace fields). When the closed -manifol…
Classifies prime algebraic tangles up to 14 crossings.
problem Classifying prime algebraic tangles systematically.
method Developed a novel canonical representation to distinguish mutant tangles.
result Increased classification of prime tangles up to 14 crossings.
The study characterizes Euclidean submanifolds with a conformal canonical vector field.
problem Characterizing Euclidean submanifolds with a specific vector field property.
method Investigating properties of the canonical vector field and its conformal nature.
result Characterization of Euclidean submanifolds with conformal canonical vector fields.
New method improves deep CCA by modeling private components conditionally independent of common factors.
problem Discovering latent co-variation in multiview datasets with weak common factors.
method Proposes a novel formulation that models private components conditionally independent of common factors.
result Validates the approach with synthetic and real datasets, showing improved identification of common factors.
We extend the result in J. Reine Angew. Math. 664, 29-53, to the non-compact case. Namely, we prove that the canonical connection on a simply connected and irreducible naturally reductive space is unique, provided the space is not a sphere, a compact Lie group with a bi-invariant metric or its symmetric dual. In partic…
To a system of second order ordinary differential equations (SODE) one can assign a canonical nonlinear connection that describes the geometry of the system. In this work we develop a geometric setting that allows us to assign a canonical nonlinear connection also to a system of higher order ordinary differential equat…
Functional Generalized Canonical Correlation Analysis for studying multiple longitudinal variablesstat.ME
New method for analyzing multiple longitudinal data processes.
problem Exploring associations between multiple random processes observed jointly.
method Functional Generalized Canonical Correlation Analysis (FGCCA) based on multiblock Regularized Generalized Canonical Correlation Analysis (RGCCA).
result FGCCA framework is robust to sparsely and irregularly observed data.
Efficient algorithm for CCA on Riemannian manifolds with fast convergence.
problem Efficiently computing canonical correlation components on Riemannian manifolds.
method Reparametrization of projection matrices for stochastic optimization on Riemannian manifolds.
result Achieves $O( rac{1}{t})$ convergence rate for top components with runtime complexity.
The study characterizes and analyzes spacelike surfaces with a canonical normal null direction in Minkowski 4-space.
problem Characterizing and analyzing spacelike surfaces with a specific null direction in Minkowski space.
method Using geometric properties, Gauss map, and a nonlinear partial differential equation, the study characterizes and analyzes these surfaces.
result Characterizations and properties of spacelike surfaces with a canonical normal null direction are obtained.
Klt varieties with trivial canonical class -- Holonomy, differential forms, and fundamental groupsmath.AG
Study on Klt varieties with trivial canonical class, focusing on holonomy and stability.
problem Holonomy group of singular Kähler-Einstein metrics on klt varieties with numerically trivial canonical divisor.
method Investigation of holonomy group properties, finiteness of connected components, Bochner principle for holomorphic tensors, and connections between irreducibility of holonomy representations and stability of the tangent sheaf.
result Refinement of known decompositions for tangent sheaves of varieties with trivial canonical divisor, showing that up to finite quasi-étale covers, varieties with strongly stable tangent sheaves are either Calabi-Yau or irreducible holomorphic symplectic.
A two-component link produces a torus as the product of the component knots in a two-point configuration space of a three-sphere. This space can be identified with a cotangent bundle and also with an indefinite Grassmannian. We show that the integration of the absolute value of the canonical symplectic form is equal to…
D-GCCA improves multi-view data analysis by separating common and distinctive components.
problem Analyzing multi-view high-dimensional data with latent factors.
method Decomposes each view's data matrix into common and distinctive sources with orthogonality constraints.
result Consistent estimators with good performance and efficient computation.
Recently, there has been a trend to combine independent component analysis and canonical polyadic decomposition (ICA-CPD) for an enhanced robustness for the computation of CPD, and ICA-CPD could be further converted into CPD of a 5th-order partially symmetric tensor, by calculating the eigenmatrices of the 4th-order cu…
A new projective structure on Riemann surfaces differs from the uniformization theorem's structure.
problem Comparing two projective structures on compact Riemann surfaces.
method Using Hodge theory and the Torelli map to compare the -component of the differential of sections of moduli spaces.
result The two projective structures differ in general, with the -component of the differential of the section corresponding to being a nonzero constant multiple of the Siegel form.
We compute the A-polynomial 2-tuple of twisted Whitehead links. As applications, we determine canonical components of twisted Whitehead links and give a formula for the volume of twisted Whitehead link cone-manifolds.
Let S be a compact connected oriented surface with one boundary component. We extend each of Johnson's and Morita's homomorphisms to the Ptolemy groupoid of S. Our extensions are canonical and take values into finitely generated free abelian groups. The constructions are based on the 3-dimensional interpretation of the…
Lisa Traynor has described an example of a two-component Legendrian `circular helix link' in the 1-jet space of the circle (with its canonical contact structure) that is topologically but not Legendrian isotopic to that same link with the order of the two components reversed. We give a complete classification of the Le…
Detecting essential surfaces in 3-manifolds and orbifolds using character varieties.
problem Detecting essential surfaces in 3-manifolds and orbifolds.
method Extending Culler and Shalen's construction to 3-orbifolds using character variety.
result Any slope detected on a canonical component of the character variety of a one-cusped hyperbolic 3-manifold with symmetries must be the slope of a symmetric surface.
FRAPPE estimates tensor canonical rank without CPD computation.
problem Estimating the canonical rank of tensors efficiently.
method Generates synthetic data matching input tensor's size and sparsity, trains a regression model to estimate rank.
result 24 times faster than best baseline, 10% improvement in MAPE on synthetic dataset.
Bayesian correlated component analysis identifies brain process similarities across multiple stimulus views.
problem Investigating brain process similarity in responses to multiple views of a stimulus.
method Hierarchical probabilistic model that evaluates universality of spatial networks across multi-view data.
result Bayesian correlated component analysis evaluates favorably against other algorithms and identifies variability in spatial representations.
Computes canonical heights for arithmetic log surfaces using Hurwitz zeta function.
problem Computing canonical heights for arithmetic log surfaces.
method Introduces a canonical height and uses limits of periods to compute it.
result Explicit formulas for canonical heights of arithmetic log surfaces, including (P_1,D).
In this paper we consider left-invariant pseudo-Kähler structures on six-dimensional nilpotent Lie algebras. The explicit expressions of the canonical complex structures are calculated, and the curvature properties of the associated pseudo-Kähler metrics are investigated. It is proved that the associated pseudo-Kähler …
A very important class of homogeneous Riemannian manifolds are the so-called normal homogeneous spaces, which have associated a canonical connection. In this work we obtain geometrically the (connected component of the) group of affine transformations with respect to the canonical connection for a normal homogeneous sp…
Simplified method for multi-set correlated component analysis.
problem Performing multi-set correlated component analysis efficiently.
method Single-step solution using eigenvectors of ${f D}^{-1} {f R}$, where ${f R}$ is concatenated data covariance and ${f D}$ is block-diagonal.
result The solution maximizes inter-set correlation without additional constraints.
Residual Component Analysisstat.ML
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an eigenvalue problem on the sample covariance matrix. In this paper we consider the situa…
DICCA maps multi-view data into a shared latent space with interpretable components.
problem Learning from multiple related but distinct data views.
method DICCA extends CCA to deep generative networks and uses sparsity-inducing priors for interpretability.
result DICCA effectively disentangles shared and view-specific variations in multi-view data.
Generators of skein algebra of surfaces are algebraic curves.
problem Describe generators of the skein algebra of surfaces.
method Prove algebraic generators are simple closed curves associated to mapping class group generators.
result Conjecture a presentation for the skein algebra of surfaces.
In this paper we prove that the zeroth Milnor-Thurston homology group coincides with singular homology for Peano Continua. More- over, we show that the canonical homomorphism between these ho- mology theories may not be injective. However, it is proved that it is injective when a space has Borel path-components.
CorrCA identifies reliable dimensions in multivariate data across repetitions.
problem Finding consistent dimensions in multivariate data across trials, subjects, or raters.
method Maximizes the ratio of between-repetition to within-repetition covariance.
result CorrCA leads to repeat-reliability maximization and is equivalent to Linear Discriminant Analysis for zero-mean signals.
Generalized canonical correlation analysis (GCCA) aims at finding latent low-dimensional common structure from multiple views (feature vectors in different domains) of the same entities. Unlike principal component analysis (PCA) that handles a single view, (G)CCA is able to integrate information from different feature …
Introduces a new triple coproduct for knots on surfaces, preserving local crossing patterns.
problem Tackles the lack of fine-grained detection in classical cobrackets for local crossing patterns.
method Defines an integer-valued invariant using a coproduct and intersection theory, extending Turaev's cobracket theory.
result Reveals an intrinsic simplicity in the algebraic framework, uniquely determining relations in the word space.
Independent component analysis (ICA) is a method for recovering statistically independent signals from observations of unknown linear combinations of the sources. Some of the most accurate ICA decomposition methods require searching for the inverse transformation which minimizes different approximations of the Mutual I…
We classify the effective and transitive actions of a Lie group on an n-dimensional non-degenerate hyperboloid (also called real pseudo-hyperbolic space), under the assumption that is a closed, connected Lie subgroup of , the connected component of the indefinite special orthogonal group. Assumin…
The paper bounds eigenvalues of specific operators on certain manifolds.
problem Bounding eigenvalues of Paneitz and third-order boundary operators on locally conformally flat manifolds.
method Proof based on conformal equivalence to canonical models, showing injectivity of developing maps, and explicit computations on canonical models.
result Eigenvalue bounds for the Paneitz operator and its associated third-order boundary operator on locally conformally flat manifolds.