Picard–Fuchs Uniformization and Modularity¶of the Mirror Map

2000 ◽  
Vol 212 (3) ◽  
pp. 625-647 ◽  
Author(s):  
Charles F. Doran
Keyword(s):  
Mirror Map

scholarly journals Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces

1995 ◽  
Vol 433 (3) ◽  
pp. 501-552 ◽  
Author(s):  
S. Hosono ◽  
A. Klemm ◽  
S. Theisen ◽  
S.-T. Yau
Keyword(s):  
Complete Intersection ◽  
Mirror Symmetry ◽  
Mirror Map

The 𝑛th root of the mirror map

2003 ◽  
pp. 195-199 ◽  
Author(s):  
Bong Lian ◽  
Shing-Tung Yau
Keyword(s):  
Mirror Map

AN ${\rm SL}(2, {\mathbb C})$ ACTION ON CHIRAL RINGS AND THE MIRROR MAP

1992 ◽  
Vol 07 (35) ◽  
pp. 3277-3289 ◽  
Author(s):  
TRISTAN HÜBSCH ◽  
SHING-TUNG YAU
Keyword(s):  
Complex Structure ◽  
Inner Product ◽  
General Definition ◽  
Canonical Class ◽  
Hodge Operator ◽  
Volume Limit ◽  
Chiral Rings ◽  
Lefschetz Type ◽  
Definition Of ◽  
Mirror Map

Each transversal degree-d hypersurface ℳ in a weighted projective space defines a Landau-Ginzburg orbifold, the superpotential of which equals the defining polynomial of ℳ. For a generic such ℳ with trivial canonical class, the degree-0 (mod d) subring of the Jacobian ring (that is, the (c, c)-ring of the Landau-Ginzburg orbifold) is shown to admit an [Formula: see text] action and the corresponding Lefschetz-type decomposition. This leads to a general definition of a “large complex structure” limit, the mirror of the “large volume” limit, and the mirror images on ⊕qH3−q,q of the Hodge *-operator, duality and inner product on ⊕qHq,q.

scholarly journals The mirror map for invertible LG models

1994 ◽  
Vol 328 (3-4) ◽  
pp. 312-318 ◽  
Author(s):  
Maximilian Kreuzer
Keyword(s):  
Mirror Map

scholarly journals A (0,2) mirror map

2011 ◽  
Vol 2011 (2) ◽  
pp. 1-15 ◽  
Author(s):  
Ilarion V. Melnikov ◽  
M. Ronen Plesser
Keyword(s):  
Mirror Map

Analysis of Online Composite Mirror Descent Algorithm

2017 ◽  
Vol 29 (3) ◽  
pp. 825-860 ◽  
Author(s):  
Yunwen Lei ◽  
Ding-Xuan Zhou
Keyword(s):  
Error Analysis ◽  
Objective Function ◽  
Convergence Rates ◽  
Hölder Continuous ◽  
Descent Algorithm ◽  
Strongly Convex ◽  
Mirror Descent ◽  
One Step ◽  
Error Decomposition ◽  
Mirror Map

We study the convergence of the online composite mirror descent algorithm, which involves a mirror map to reflect the geometry of the data and a convex objective function consisting of a loss and a regularizer possibly inducing sparsity. Our error analysis provides convergence rates in terms of properties of the strongly convex differentiable mirror map and the objective function. For a class of objective functions with Hölder continuous gradients, the convergence rates of the excess (regularized) risk under polynomially decaying step sizes have the order [Formula: see text] after [Formula: see text] iterates. Our results improve the existing error analysis for the online composite mirror descent algorithm by avoiding averaging and removing boundedness assumptions, and they sharpen the existing convergence rates of the last iterate for online gradient descent without any boundedness assumptions. Our methodology mainly depends on a novel error decomposition in terms of an excess Bregman distance, refined analysis of self-bounding properties of the objective function, and the resulting one-step progress bounds.

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