Study of Dirac operators on S3 and S2 spheres.
problem Analyzing Dirac operators on specific spheres.
method Using Kähler's formalism, spectral resolution of eigenspinors.
result Complete spectral resolution of Dirac operators on S3 and S2.
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169,341 papers · 148 categories
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48 results for “S2 sphere”
S2 is a graph-based active learning algorithm for binary label prediction with theoretical guarantees.
problem Binary label prediction on graphs with theoretical guarantees.
method S2 selects vertices to label based on shortest shortest paths between oppositely labeled vertices.
result S2 achieves near minimax optimal excess risk for nonparametric classification problems.
Researchers create finite-time blow-up solutions for harmonic map flow into S2.
problem Constructing finite-time blow-up solutions for harmonic map flow into S2.
method Constructing finite time blow-up solutions with specific conditions and proving the blow-up behavior.
result First example of blow-up solution with a space-codimension 2 singular set.
Physics-Informed Teleconnection-Aware Transformer for Global Subseasonal-to-Seasonal Forecastingstat.ML
TelePiT improves S2S forecasting by integrating physics and teleconnections.
problem Challenges in subseasonal-to-seasonal climate forecasting due to chaotic dynamics and complex interactions.
method Integrates physics and teleconnections into a transformer architecture with spherical embedding and multi-scale physics-informed neural ODE.
result Significantly outperforms state-of-the-art methods across all forecast horizons.
We study stable compact constant mean curvature surfaces in the product spaces S2 X R and H2 X R and in some other Riemannian 3-manifolds.
On a natural circle bundle T(M) over a 4-dimensional manifold M equipped with a split signature metric g, whose fibers are real totally null selfdual 2-planes, we consider a tautological rank 2 distribution D obtained by lifting each totally null plane horizontally to its point in the fiber. Over the open set where g i…
The paper shows how certain circle families in relate to sphere families in and induces nontrivial barbell diffeomorphisms.
problem Understanding the relationship between circle and sphere families in specific 3-manifolds.
method Analyzing the fundamental groups and ambient extensions of circle and sphere families.
result Induces nontrivial barbell diffeomorphisms of .
Capillarity functionals are parameter invariant functionals defined on classes of two-dimensionals parametric surfaces in R3 as the sum of the area integral with an anisotropic term of suitable form. In the class of parametric surfaces with the topological type of S2 and with fixed volume, extremals of capillarity func…
We induce a Poisson algebra on the configuration space of twisted polygons in from the swapping algebra \cite{L12}, which is found coincide with Faddeev-Takhtajan-Volkov algebra for . There is another Poisson algebra $\{\cdot,\cdot\}…
Complete, conformally flat metrics of constant positive scalar curvature on the complement of points in the -sphere, , , were constructed by R\. Schoen [S2]. We consider the problem of determining the moduli space of all such metrics. All such metrics are asymptotically periodic, and we develop…
Sharp systolic inequalities for invariant tight contact forms on principal S1-bundles over S2math.SG
Sharp systolic inequality for invariant tight contact forms on S1-bundles over S2.
problem Finding the shortest period of closed Reeb orbits on invariant tight contact forms.
method Proving a sharp systolic inequality based on the Euler class of the bundle.
result A behavior of the systolic inequality depends on the Euler class of the bundle.
New biharmonic functions found on Thurston geometries.
problem Finding biharmonic functions on Thurston geometries.
method Constructing explicit proper biharmonic functions.
result Explicit biharmonic functions constructed on various Thurston geometries.
Researchers use conformal infinity to study spacetimes near AdS2×S2.
problem Studying the rigidity of asymptotically AdS2×S2 spacetimes.
method Developed a new approach based on conformal infinity.
result Obtained new results including similar to [4] but for higher dimensions and more than two ends.
Study describes bifurcations and solutions of a specific equation on a particular manifold.
problem Analyzing bifurcations and solutions of the vacuum Lichnerowicz equation.
method Exhaustive description of bifurcations and solutions on with invariant seed data.
result Description of CMC slicings of Schwarzschild-de Sitter and Nariai solutions.
ANN model predicts zinc leaching filter cake moisture accurately.
problem Modeling cake moisture in zinc leaching pressure filtration.
method Developed ANN model using 7 parameters.
result High accuracy in predicting cake moisture (R2 > 0.8, MSE < 1e-6).
RNGI model bridges two probability densities on Riemannian manifolds efficiently.
problem Limited applicability of Euclidean stochastic interpolants to Riemannian manifolds.
method Introduces RNGI model interpolating between Riemannian manifold probability densities along geodesics.
result Proves temporal marginal density solves transport equation on Riemannian manifold.
Construct structures on bundles over complex manifolds.
problem Creating globally-defined structures on bundles.
method Construction on smooth compact toric varieties and extensions to Kähler-Einstein manifolds.
result Extends structures to non-toric Kähler-Einstein manifolds.
This is a survey on the global theory of constant mean curvature surfaces in Riemannian homogeneous 3-manifolds. These ambient 3-manifolds include the eight canonical Thurston 3-dimensional geometries, i.e. R3, H3, S3, H2 \times R, S2 \times R, the Heisenberg space Nil3, the universal cover of PSL2(R) and the Lie group…
Many-to-Many VTN improves voice conversion across multiple speakers.
problem Voice conversion across multiple speakers.
method Sequence-to-sequence learning framework with many-to-many VTN architecture.
result Improved sound quality and speaker similarity compared to baseline methods.
Study proves existence of special surface shapes in capillarity problems.
problem Existence of volume-constrained minimal surfaces in capillarity problems.
method Variational techniques to find saddle-type critical points.
result Existence of extremals characterized as saddle-type critical points.
Study links with specific surgeries in 4-manifolds.
problem Understanding which links have surgeries yielding specific 4-manifolds.
method Examining trisections and link surgeries in 4-manifolds.
result Found families of links with the specified surgeries, but not all.
New non-holomorphic Lefschetz fibrations with -sections found.
problem Existence of non-holomorphic Lefschetz fibrations.
method Constructing fibrations over with -sections using positive relators.
result Found two types of non-holomorphic Lefschetz fibrations with -sections.
In our previous work [PSSW], we showed that the Ricci flow on S^2 whose initial metric has conical singularities \sum_{j=1}^k β_j[p_j] converges to a constant curvature metric with conic singularities (in the stable and semi-stable cases) or to a gradient shrinking soliton with conical singularities (in the unstable ca…
Paper proposes a deep learning method for person re-identification using set to set distance.
problem Matching images of the same person across different camera views with large appearance variations.
method Uses deep learning to model set to set (S2S) distance, focusing on intra-class compactness and inter-class separation.
result The method effectively finds matched targets in video galleries, outperforming state-of-the-art approaches.
A categorification of the stable SU(2) Witten-Reshetikhin-Turaev invariant of links in S2 x S1math.GT
The WRT invariant of a link L in S2xS1 at sufficiently high values of the level r can be expresses as an evaluation of a special polynomial invariant of L at 2r-th root of unity. We categorify this polynomial invariant by associating to L a bigraded homology whose graded Euler characteristic is equal to this polynomial…
We define a manifold where objects are curves, which we parameterize as (, is the circle). Given a curve , we define the tangent space of at including in it all deformations of . In this paper we study geometries on the manifold of curves, pr…
Study Mabuchi rays on toric Kähler manifolds to understand quantization.
problem Understanding quantization in toric Kähler manifolds.
method Analyzing Mabuchi rays associated with test configurations and moment polytopes.
result Quantization in limit polarizations corresponds to restrictions of monomial sections.
Reflection principles for harmonic and holomorphic maps from Hermitian symmetric spaces.
problem Establishing reflection principles for harmonic and holomorphic maps between Riemannian manifolds.
method Introducing recursive real forms and proving reflection principles for harmonic and holomorphic maps from Hermitian symmetric spaces.
result Reflection principles for harmonic and holomorphic maps from a class of Hermitian symmetric spaces.
Model financial dynamics using 2-manifold geometries, revealing the torus as best for cyclical data.
problem Financial forecasting using complex market data.
method Embedding market data onto 2-manifolds (S2, R2, H2, T) guided by uniformization theorem, inferring latent curvature.
result The torus geometry best predicts cyclical financial data, aligning with IS-LM theory.
A flat complex vector bundle (E,D) on a compact Riemannian manifold (X,g) is stable (resp. polystable) in the sense of Corlette [C] if it has no D-invariant subbundle (resp. if it is the D-invariant direct sum of stable subbundles). It has been shown in [C] that the polystability of (E,D) in this sense is equivalent to…
A new causal deepset framework improves off-policy evaluation under complex interference.
problem Handling spatio-temporal interference in off-policy evaluation.
method Permutation invariance assumption and novel algorithms incorporating it.
result Significantly more precise estimations than existing methods.
Paper improves text-to-SQL models with schema-aware denoising.
problem Text-to-SQL models struggle with schema linking and grammar correctness.
method Adapts transformer-based seq-to-seq model with SeaD denoising objectives and clause-sensitive decoding.
result Improves seq-to-seq model performance on WikiSQL benchmark.
New method maps land cover using radar and optical satellite images.
problem Efficiently exploiting multiple sources of information for land cover mapping.
method Deep learning framework with attention mechanism and pretraining strategy.
result Attention mechanism and extended RNN model outperform competitors.
Machine Learning Accelerated Likelihood-Free Event Reconstruction in Dark Matter Direct Detectionastro-ph.IM
New algorithm improves Dark Matter detection accuracy.
problem Reconstructing Dark Matter interactions with high precision.
method Likelihood-free framework with Bayesian Optimization for Likelihood-Free Inference (BOLFI).
result BOLFI improved reconstruction accuracy by up to 15%.
The paper computes the Kauffman bracket skein module of via braids.
problem Computing the Kauffman bracket skein module of .
method Two methods: extending a universal invariant to via braid band moves and a diagrammatic approach.
result The Kauffman bracket skein module of is not torsion-free and its free part is generated by the unknot.
Study examines how body segments respond to random vibrations.
problem Understanding human body responses to random vibrations.
method 35 participants were tested with random noise signals. Multiple linear regression models were created to determine influential predictors of peak translational gains.
result Multiple predictors, including motion direction and body segment, significantly influence peak translational gains.
Solving Large-scale Systems of Random Quadratic Equations via Stochastic Truncated Amplitude Flowcs.IT
STAF solves large-scale phase retrieval problems from magnitude-only measurements.
problem Phase retrieval from magnitude-only quadratic equations.
method STAF is a novel iterative approach combining stochastic variance reduced gradient and stochastic truncated gradient iterations.
result STAF can recover any signal exactly from about 2.3n magnitude-only measurements, outperforming existing methods.
New research finds 145 infinite families of CS spheres are standard.
problem Determining which Cappell-Shaneson spheres are diffeomorphic to the standard 4-sphere.
method Using Kirby calculus and new families of CS spheres.
result Proves 145 new infinite families of CS spheres are standard.
Smooth homotopy 4-spheremath.GT
Every smooth 4-sphere is the same as the standard one.
problem Identifying smooth 4-spheres.
method Proved diffeomorphism to the standard 4-sphere.
result Smooth homotopy 4-spheres are diffeomorphic to the 4-sphere.
Paper shows maps from m-sphere to n-sphere are trivial cobordant.
problem Understanding cobordism classes of maps and covers for spheres.
method Analyzes cobordism classes of maps from m-sphere to n-sphere.
result For m>n, cobordism classes of maps from m-sphere to n-sphere are trivial.
The study classifies branched Willmore spheres in 3- and 4-spheres.
problem Classifying branched Willmore spheres in 3- and 4-spheres.
method Analyzing variational branched Willmore spheres and their projections onto and .
result Improved regularity of unit normals and integer multiples of width in sphere eversion.
Ribbonness of Kervaire's sphere-link in homotopy 4-sphere and its consequences to 2-complexesmath.GT
Kervaire's sphere-link is equivalent to a ribbon sphere-link, simplifying complex 2-complexes.
problem Understanding the structure of 2-complexes and their asphericity.
method Using Kervaire's sphere-link and ribbon sphere-link equivalence, analyzing the compact complement of ribbon disk-links.
result Every connected subcomplex of a contractible finite 2-complex is aspherical.
New theory proves infinite homology 3-spheres in homology 4-spheres.
problem Existence of homology 3-spheres in homology 4-spheres.
method Diagrammatics of surface cross sections, Taubes' work.
result Infinite number of homology 3-spheres in homology 4-spheres.
Proves a theorem connecting graph theory spheres, reformulating Morse conditions.
problem Defines and connects spheres in graph theory.
method Proves a theorem bridging two graph theory sphere definitions.
result Reformulates Morse conditions using center manifolds and level surface graphs.
The 3-sphere has either 2 minimal 2-spheres or an optimal foliation by 2-spheres.
problem Proving existence of minimal 2-spheres or optimal foliations in arbitrary Riemannian 3-spheres.
method Analyzing the properties of arbitrary Riemannian metrics on 3-spheres.
result The existence of at least two minimal 2-spheres or an optimal foliation in 3-spheres with arbitrary metrics.
ConvS2S-VC converts voice characteristics and pitch contour using a fully convolutional seq2seq model.
problem Voice conversion with preservation of pitch contour and duration.
method Fully convolutional seq2seq architecture with conditional batch normalization.
result ConvS2S-VC outperforms baseline methods in sound quality and speaker similarity.
New homotopy spheres help solve complex manifold problems.
problem Constructing and characterizing exotic manifolds.
method Introducing Farrell-Jones spheres and studying their properties.
result Farrell-Jones spheres provide examples of exotic manifolds.
Infinitely many splitting spheres found for unlinked 2-spheres in 4-space.
problem Existence of pairwise non-isotopic splitting spheres for unlinked 2-spheres in 4-space.
method Analytical proof showing non-isotopic spheres.
result Infinitely many non-isotopic splitting spheres found.