In this study, we introduce a new type of surface curves called D-type curve. This curve is defined by the property that the unit Darboux vector W0 of a space curve r(s) and unit surface normal n along the curve r(s) satisfy the condition <n,W0>=constant. We point out that a D-type curve is a geodesic curve or an asymp…
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12 results for “D-type”
We prove the existence of Lagrangian fillings for -type Legendrian links.
problem Exact Lagrangian fillings of Legendrian links of -type.
method Legendrian weave calculus and construction of 1-cycles.
result Existence of a Lagrangian filling represented by a weave.
Certain momentum-dependent terms in the fermion sector of the Lorentz-violating Standard Model Extension (SME) yield solvable classical lagrangians of a type not mentioned in the literature. These cases yield new relatively simple examples of Finsler and pseudo-Finsler structures. One of the cases involves antisymmetri…
We give a complete description of finite braid group orbits in Aff(C)-character varieties of the punctured Riemann sphere. This is performed thanks to a coalescence procedure and to the theory of finite complex reflection groups. We then derive consequences in the theory of differential equations. These concern algebra…
The spherical manifold realization problem asks which spherical three-manifolds arise from surgeries on knots in . In recent years, the realization problem for C, T, O, and I-type spherical manifolds has been solved, leaving the D-type manifolds (also known as the prism manifolds) as the only remaining case. Every…
Crowdsourced labeling recovers task types with minimal queries.
problem Labeling tasks accurately with minimal queries.
method Worker clustering, skill estimation, weighted majority voting.
result Achieves any targeted recovery accuracy with minimum queries.
Paper constructs solutions to WDVV equations for Frobenius manifolds.
problem Solving open WDVV equations for Frobenius manifolds.
method Explicit construction of flat F-manifolds and principal hierarchies.
result Recovery of polynomial solutions for A- and D-type singularities.
We show that on a hyperbolic knot in , the distance between any two finite surgery slopes is at most two and consequently there are at most three nontrivial finite surgeries. Moreover in case that admits three nontrivial finite surgeries, must be the pretzel knot . In case that admits tw…
The paper classifies Hermitian manifolds with specific connection properties.
problem Classifying Hermitian manifolds with specific connection properties.
method Algebraic consideration of holonomy systems, structure theorems, and classification theorems.
result The universal cover of such Hermitian manifolds is the product of a complex Lie group and Hermitian symmetric spaces.
fSDE-Net generates time series with long-term memory using neural networks.
problem Generating time series with long-term memory from irregularly sampled data.
method fSDE-Net: neural fractional Stochastic Differential Equation Network using fractional Brownian motion.
result fSDE-Net can replicate distributional properties of real time-series data.
A Worker-Task Specialization Model for Crowdsourcing: Efficient Inference and Fundamental Limitscs.HC
New model optimizes worker-task specialization for crowdsourcing.
problem Inferring correct labels from noisy answers across varying worker and task skills.
method Introduced a -type specialization model to account for varying worker and task types, and proposed algorithms achieving optimal sample complexity.
result Optimal label inference algorithms for crowdsourcing with unknown worker and task types.
New criteria for ideal circle patterns on surfaces.
problem Determining when a surface supports ideal circle patterns.
method Introducing a character and using combinatorial Ricci flows.
result Simpler and more easily verifiable criteria for ideal circle patterns.