Study on generalized ξ-parallel maps in Riemannian geometry.
problem Characterizing and understanding generalized ξ-parallel maps.
method Defined energy functional, derived first variation formula, and Euler-Lagrange equation.
result Established fundamental properties and relationships with harmonic and biharmonic maps.
Parallel transport map over reductive spaces is an affine submersion.
problem Understanding parallel transport in reductive homogeneous spaces with torsion.
method Generalizing previous results on affine symmetric spaces, proving compactness of shape operators, and proposing definitions for regularized mean curvatures.
result Each fiber of the parallel transport map over a reductive homogeneous space is minimal in both senses.
Examines how meridians and parallels help in map drawing.
problem Understanding map drawing and foliations of the sphere.
method Analyzes Euler's work on cartography and meridians/parallels.
result Meridians and parallels are crucial for map drawing.
Study nearly parallel G2-structures with torus symmetry using multi-moment maps.
problem Characterize and construct nearly parallel G2-structures with torus symmetry.
method Use multi-moment map techniques and analyze the geometry of the base spaces.
result Locally, the construction may produce examples with four-torus symmetry.
We consider the problem of maximum a posteriori (MAP) inference in discrete graphical models. We present a parallel MAP inference algorithm called Bethe-ADMM based on two ideas: tree-decomposition of the graph and the alternating direction method of multipliers (ADMM). However, unlike the standard ADMM, we use an inexa…
We propose a parallel-data-free voice-conversion (VC) method that can learn a mapping from source to target speech without relying on parallel data. The proposed method is general purpose, high quality, and parallel-data free and works without any extra data, modules, or alignment procedure. It also avoids over-smoothi…
Study SKT and CYT manifolds with parallel Bismut torsion.
problem Characterize and construct compact complex manifolds with specific geometric properties.
method Characterization via universal cover, construction using mapping torus, investigation of generalized Kaehler structures.
result Existence of non-Bismut flat examples and characterization of universal covers.
New construction method for special geometric structures.
problem Creating strong HKT and generalized hyperkähler structures.
method Mapping tori construction of skew-symmetric torsion.
result Non-product structures with parallel skew-symmetric torsion.
Discrete Flow Maps bypass sequential prediction limits for parallel text generation.
problem Sequential autoregressive prediction limits large language model speed.
method Flow Maps compress generative trajectories into single-step mappings.
result Discrete Flow Maps surpass previous state-of-the-art results in discrete flow modeling.
Study proves 3-manifolds with parallel vector fields have odd Betti numbers.
problem Determining when 3-manifolds can have parallel vector fields.
method Analyzing Kähler mapping tori and Lorentzian manifolds.
result Betti numbers of 3-manifolds with parallel vector fields are always odd.
A concise discussion of the axiomatic approach to the concept of parallel transport is presented. Attention is drawn to a bijective map between the sets of connections and (axiomatically defined) parallel transports. The transports along paths are pointed as a generalization of the (axiomatically defined) parallel tran…
Maps on Sasakian manifolds limit to sub-Riemannian distance bounds.
problem Understanding sub-Riemannian distances on Sasakian manifolds.
method Parallel and mirror maps along geodesics of a taming Riemannian metric.
result Limits of transport maps outside sub-Riemannian cut-locus provide bounds on sub-Riemannian distance.
The paper parallelizes HMM inference for efficient long-term computations.
problem Efficiently computing inference in long-term hidden Markov models.
method Parallelization using associative elements and operators for sum-product and max-product algorithms.
result The proposed parallel algorithms are computationally efficient for long time horizons.
Study monodromy relations in Seifert fibered spaces for 3-manifold fillings.
problem Understanding symplectic fillings of Seifert fibered 3-manifolds.
method Analyzes monodromy factorizations and their impact on fillings.
result Computes and bounds Euler characteristics of different fillings.
Ensembled neural networks improve MRI image quality.
problem Accelerated parallel MR imaging with high SSIM scores.
method Ensembled Σ-net combining parallel coil and sensitivity networks, trained with supervised and semi-supervised methods. result Ensembling models achieves visually sharp and textured images with robust SSIM scores.
The CR analogue of B.-Y. Chen's conjecture on pseudo biharmonic maps will be shown. Pseudo biharmonic, but not pseudo harmonic, isometric immersions with parallel pseudo mean curvature vector fields, will be characterized. Several examples of pseudo biharmonic maps will be given.
We consider a connected symplectic manifold M acted on by a connected Lie group G in a Hamiltonian fashion. If G is compact, we prove give an Equivalence Theorem for the symplectic manifolds whose squared moment map ∥μ∥2 is constant. This result works also in the almost-Kähler setting. Then we…
The paper proves properties of Finsler submanifolds and analytic maps.
problem Analyzing properties of Finsler submanifolds and their analytic maps.
method Proving properties of regular fibers of analytic maps and Finsler submersions.
result Regular fibers of an analytic map are equifocal under certain conditions.
Invariant covariant derivatives on homogeneous spaces are characterized.
problem Understanding invariant covariant derivatives on homogeneous spaces.
method Expressing covariant derivatives in terms of horizontally lifted vector fields and bilinear maps.
result Existence and characterization of invariant covariant derivatives.
We provide some properties and characterizations of homologically UVn-maps and lcGn-spaces. We show that there is a parallel between recently introduced by Cauty algebraic ANR's and homologically lcGn-metric spaces, and this parallel is similar to the parallel between ordinary ANR's and LCn-metric spa…
Study of normal and tangent maps to frontals.
problem Understanding geometric and dynamical properties of frontals.
method Geometrical and dynamical analysis of normal and tangent maps.
result Parallels of the tangent map to a frontal curve are right equivalent to the tangent map of a frontal curve under certain conditions.
LA-VDM accelerates VDM using landmarks to improve data analysis.
problem Efficiently analyzing complex datasets with nonuniform sampling densities.
method Landmark-constrained two-stage normalization to accelerate VDM.
result LA-VDM accurately recovers parallel transport and converges to the connection Laplacian.
New algorithms improve causal direction inference accuracy using parallel ensemble methods.
problem Stability of causal direction inference results from observational data.
method Parallel ensemble frameworks to map and improve inference accuracy.
result Significant improvement in accuracy of causal direction inference.
Unified view of integrable systems linking CMC, isothermic, and Willmore surfaces.
problem Understanding the relationships between different types of surfaces and their integrable systems.
method Unified view through families of flat connections and parallel sections.
result Complete description of links between different surface types and their dressing transformations.
Recombinant binomial trees are binary trees where each non-leaf node has two child nodes, but adjacent parents share a common child node. Such trees arise in finance when pricing an option. For example, valuation of a European option can be carried out by evaluating the expected value of asset payoffs with respect to r…
The article approximates solutions to the Beltrami equation using similarity surfaces.
problem Approximating solutions to the Beltrami equation.
method Constructing similarity surfaces from polygons and analyzing their conformal uniformization.
result Holomorphic dependence of Christoffel symbols on polygons and convergence to a specific affine connection.
Using Hilbert's criterion, we consider the stress-energy tensor associated to the bienergy functional. We show that it derives from a variational problem on metrics and exhibit the peculiarity of dimension four. First, we use this tensor to construct new examples of biharmonic maps, then classify maps with vanishing or…
A simple method makes Euclidean patterns look like Escher's art.
problem Transforming Euclidean patterns into Circle Limit-style art.
method A simple, parallelizable algorithm using conformal maps.
result A simple method is highly efficient and can be parallelized.
In this paper, we study the Gauss map of the surfaces in the de Sitter space-time S14(1). First, we prove that a space-like surface lying in the de Sitter space-time has pointwise 1-type Gauss map if and only if it has parallel mean curvature vector. Then, we obtain the complete classification of the quasi-…
A marginally trapped surface in the four-dimensional Minkowski space is a spacelike surface whose mean curvature vector is lightlike at each point. In the present paper we find all marginally trapped surfaces with pointwise 1-type Gauss map. We prove that a marginally trapped surface is of pointwise 1-type Gauss map if…
Smooth maps preserve distances on specific revolution surfaces.
problem Existence of smooth maps on revolution surfaces.
method Proving existence of maps preserving distances on meridians and parallels.
result Smooth maps exist from revolution surfaces to Euclidean plane.
Can one parallelize complex exploration exploitation tradeoffs? As an example, consider the problem of optimal high-throughput experimental design, where we wish to sequentially design batches of experiments in order to simultaneously learn a surrogate function mapping stimulus to response and identify the maximum of t…
As a result of the growing size of Deep Neural Networks (DNNs), the gap to hardware capabilities in terms of memory and compute increases. To effectively compress DNNs, quantization and connection pruning are usually considered. However, unconstrained pruning usually leads to unstructured parallelism, which maps poorly…
Program connects quantum computing and topological field theories.
problem Connecting quantum computing and topological field theories.
method Formalizes the connection using cobordisms and parallel transport.
result Realizes quantum circuits as cobordisms in a double category.
This paper proposes a method that allows non-parallel many-to-many voice conversion (VC) by using a variant of a generative adversarial network (GAN) called StarGAN. Our method, which we call StarGAN-VC, is noteworthy in that it (1) requires no parallel utterances, transcriptions, or time alignment procedures for speec…
The paper introduces surface signatures for irregular surfaces and rough surfaces.
problem Characterizing and integrating highly irregular paths and surfaces.
method Introducing surface signatures and proving extension theorems.
result Surface signatures are universal for surface holonomy and rough surfaces.
New method normalizes Milnor fibrations for real analytic maps.
problem Existence of normalized Milnor fibrations for real analytic maps.
method Introducing a homeomorphism to transform a non-normalized Milnor fibration into a normalized one.
result Normalized map (h−1f)/∣∣h−1f∣∣ defines a smooth locally trivial fibration on the sphere. New solver MPLP++ outperforms existing solvers for dense graph models.
problem Efficiently solving dense, discrete Graphical Models with pairwise potentials.
method Dual Block-Coordinate Ascent with MPLP++ modification.
result MPLP++ significantly outperforms existing solvers, including TRWS.
New proof shows affine manifolds with parallel volume are Riemannian-flat.
problem Characterize compact affine manifolds with parallel volume.
method Construct a representative metric with Levi-Civita connection, using Hessian of volume-normalized distance functions.
result Affine manifolds with parallel volume are Riemannian-flat.
PMP improves sampling and learning in complex energy models.
problem Intractability of MAP computation in EBMs.
method Perturb-and-max-product (PMP) for parallel and scalable sampling and learning.
result PMP outperforms existing methods in various models, including Ising and RBMs.
Study extends reflective submanifold theory to compact homogeneous spaces.
problem Characterize reflective submanifolds in compact isotropy irreducible spaces.
method Extend previous results to infinite-dimensional Hilbert spaces.
result Inverse image of reflective submanifolds is also reflective.
Non-parallel multi-domain voice conversion (VC) is a technique for learning mappings among multiple domains without relying on parallel data. This is important but challenging owing to the requirement of learning multiple mappings and the non-availability of explicit supervision. Recently, StarGAN-VC has garnered atten…
We develop a convex relaxation method for analyzing neural network generalization.
problem Analyzing the generalization of parallel positively homogeneous networks.
method Linking non-convex ERM to a convex optimization problem over prediction functions.
result Achieved generalization bounds with almost linear sample complexity in network width.
Marginal MAP inference involves making MAP predictions in systems defined with latent variables or missing information. It is significantly more difficult than pure marginalization and MAP tasks, for which a large class of efficient and convergent variational algorithms, such as dual decomposition, exist. In this work,…
Geometric cohomology model uses co-oriented maps to define a product structure.
problem Constructing a geometric model for cohomology of smooth manifolds.
method Develops a cochain complex model based on co-oriented smooth maps, focusing on their pull-back product structure.
result Geometric cochains with a partially defined product structure induce the cup product in cohomology.
Mathematical theory of super fiber bundles and connections developed.
problem Modeling anticommuting fermionic fields in mathematical physics.
method Detailed introduction to super fiber bundles, relative supermanifolds, and connections; construction of parallel transport map.
result Construction and comparison of parallel transport map with other methods in the literature.
In this paper, we determine the type numbers of the pseudo-hyperbolic Gauss maps of all oriented Lorentzian surfaces of constant mean and Gaussian curvatures and non-diagonalizable shape operator in the 3-dimensional anti-de Sitter space. Also, we investigate the behavior of type numbers of the pseudo-hyperbolic Gaus…
Study closed manifolds with rank one ray structures, proving completeness or covering properties.
problem Characterize closed manifolds with specific affine structures.
method Analyze the developing map and automorphism group properties.
result Closed manifolds with rank one ray structures are either complete or cover the complement of an affine subspace.