arXiv research

Study on generalized ξ-parallel maps in Riemannian geometry.

Parallel transport map over reductive spaces is an affine submersion.

Examines how meridians and parallels help in map drawing.

Study nearly parallel G2-structures with torus symmetry using multi-moment maps.

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.

New construction method for special geometric structures.

Discrete Flow Maps bypass sequential prediction limits for parallel text generation.

Study proves 3-manifolds with parallel vector fields have odd Betti numbers.

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.

The paper parallelizes HMM inference for efficient long-term computations.

Study monodromy relations in Seifert fibered spaces for 3-manifold fillings.

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 $\parallel μ\parallel^2$ is constant. This result works also in the almost-Kähler setting. Then we…

We explore an ensembled $Σ$-net for fast parallel MR imaging, including parallel coil networks, which perform implicit coil weighting, and sensitivity networks, involving explicit sensitivity maps. The networks in $Σ$-net are trained in a supervised way, including content and GAN losses, and with various ways of data c…

The paper proves properties of Finsler submanifolds and analytic maps.

Invariant covariant derivatives on homogeneous spaces are characterized.

We provide some properties and characterizations of homologically $UV^n$-maps and $lc^n_G$-spaces. We show that there is a parallel between recently introduced by Cauty algebraic $ANR$'s and homologically $lc^n_G$-metric spaces, and this parallel is similar to the parallel between ordinary $ANR$'s and $LC^n$-metric spa…

Study of normal and tangent maps to frontals.

LA-VDM accelerates VDM using landmarks to improve data analysis.

New algorithms improve causal direction inference accuracy using parallel ensemble methods.

Unified view of integrable systems linking CMC, isothermic, and Willmore surfaces.

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.

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.

In this paper, we study the Gauss map of the surfaces in the de Sitter space-time $\mathbb S^4_1(1)$. 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.

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.

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.

New method normalizes Milnor fibrations for real analytic maps.

New solver MPLP++ outperforms existing solvers for dense graph models.

New proof shows affine manifolds with parallel volume are Riemannian-flat.

Study extends reflective submanifold theory to compact homogeneous spaces.

PMP improves sampling and learning in complex energy models.

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.

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.

Mathematical theory of super fiber bundles and connections developed.

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.