scholarly journals Complete visual metrology using relative affine structure

2013 ◽  
Author(s):  
Adersh Miglani ◽  
Sumantra Dutta Roy ◽  
Santanu Chaudhury ◽  
J B Srivastava
Keyword(s):  
Affine Structure

scholarly journals Quantum Orlicz Spaces in Information Geometry

2004 ◽  
Vol 11 (04) ◽  
pp. 359-375 ◽  
Author(s):  
R. F. Streater
Keyword(s):  
Quantum Information ◽  
Tangent Space ◽  
Selfadjoint Operator ◽  
Affine Connection ◽  
Orlicz Spaces ◽  
Trace Class ◽  
Information Geometry ◽  
Young Function ◽  
Affine Structure ◽  
Cotangent Space

Let H0 be a selfadjoint operator such that Tr e−βH0 is of trace class for some β < 1, and let χɛ denote the set of ɛ-bounded forms, i.e., ∥(H0+C)−1/2−ɛX(H0+C)−1/2+ɛ∥ < C for some C > 0. Let χ := Span ∪ɛ∈(0,1/2]χɛ. Let [Formula: see text] denote the underlying set of the quantum information manifold of states of the form ρx = e−H0−X−ψx, X ∈ χ. We show that if Tr e−H0 = 1. 1. the map Φ, [Formula: see text] is a quantum Young function defined on χ 2. The Orlicz space defined by Φ is the tangent space of [Formula: see text] at ρ0; its affine structure is defined by the (+1)-connection of Amari 3. The subset of a ‘hood of ρ0, consisting of p-nearby states (those [Formula: see text] obeying C−1ρ1+p ≤ σ ≤ Cρ1 − p for some C > 1) admits a flat affine connection known as the (−1) connection, and the span of this set is part of the cotangent space of [Formula: see text] 4. These dual structures extend to the completions in the Luxemburg norms.

scholarly journals The non-archimedean SYZ fibration

2019 ◽  
Vol 155 (5) ◽  
pp. 953-972 ◽  
Author(s):  
Johannes Nicaise ◽  
Chenyang Xu ◽  
Tony Yue Yu
Keyword(s):  
Explicit Description ◽  
Affine Structure ◽  
Technical Tool ◽  
One Dimensional ◽  
Codimension Two ◽  
Main Technical Tool

We construct non-archimedean SYZ (Strominger–Yau–Zaslow) fibrations for maximally degenerate Calabi–Yau varieties, and we show that they are affinoid torus fibrations away from a codimension-two subset of the base. This confirms a prediction by Kontsevich and Soibelman. We also give an explicit description of the induced integral affine structure on the base of the SYZ fibration. Our main technical tool is a study of the structure of minimal dlt (divisorially log terminal) models along one-dimensional strata.

scholarly journals A CHANGE OF MEASURE PRESERVING THE AFFINE STRUCTURE IN THE BARNDORFF-NIELSEN AND SHEPHARD MODEL FOR COMMODITY MARKETS

2015 ◽  
Vol 18 (06) ◽  
pp. 1550038 ◽  
Author(s):  
FRED ESPEN BENTH ◽  
SALVADOR ORTIZ-LATORRE
Keyword(s):  
Risk Premium ◽  
Asymptotic Properties ◽  
Commodity Markets ◽  
Spot Price ◽  
Change Of Measure ◽  
Affine Structure ◽  
Volatility Risk ◽  
Affine Model ◽  
The Mean ◽  
Pricing Measure

For a commodity spot price dynamics given by an Ornstein–Uhlenbeck (OU) process with Barndorff-Nielsen and Shephard stochastic volatility, we price forwards using a class of pricing measures that simultaneously allow for change of level and speed in the mean reversion of both the price and the volatility. The risk premium is derived in the case of arithmetic and geometric spot price processes, and it is demonstrated that we can provide flexible shapes that are typically observed in energy markets. In particular, our pricing measure preserves the affine model structure and decomposes into a price and volatility risk premium. In the geometric spot price model, we need to resort to a detailed analysis of a system of Riccati equations, for which we show existence and uniqueness of solution and asymptotic properties that explain the possible risk premium profiles. Among the typical shapes, the risk premium allows for a stochastic change of sign, and can attain positive values in the short end of the forward market and negative in the long end.

scholarly journals Finding Point Correspondences in Motion Sequences Preserving Affine Structure

1997 ◽  
Vol 68 (2) ◽  
pp. 237-246 ◽  
Author(s):  
G. Sudhir ◽  
Subhashis Banerjee ◽  
Andrew Zisserman
Keyword(s):  
Affine Structure ◽  
Finding Point

scholarly journals THE UNIVERSAL COVER OF AN AFFINE THREE-MANIFOLD WITH HOLONOMY OF SHRINKABLE DIMENSION ≤ TWO

2000 ◽  
Vol 11 (03) ◽  
pp. 305-365 ◽  
Author(s):  
SUHYOUNG CHOI
Keyword(s):  
Affine Connection ◽  
Holonomy Group ◽  
Singular Locus ◽  
Universal Cover ◽  
Affine Structure ◽  
Affine Manifold ◽  
Cone Type ◽  
Parallel Volume ◽  
A Cell ◽  
Simply Connected

An affine manifold is a manifold with an affine structure, i.e. a torsion-free flat affine connection. We show that the universal cover of a closed affine 3-manifold M with holonomy group of shrinkable dimension (or discompacité in French) less than or equal to two is diffeomorphic to R3. Hence, M is irreducible. This follows from two results: (i) a simply connected affine 3-manifold which is 2-convex is diffeomorphic to R3, whose proof using the Morse theory takes most of this paper; and (ii) a closed affine manifold of holonomy of shrinkable dimension less or equal to d is d-convex. To prove (i), we show that 2-convexity is a geometric form of topological incompressibility of level sets. As a consequence, we show that the universal cover of a closed affine three-manifold with parallel volume form is diffeomorphic to R3, a part of the weak Markus conjecture. As applications, we show that the universal cover of a hyperbolic 3-manifold with cone-type singularity of arbitrarily assigned cone-angles along a link removed with the singular locus is diffeomorphic to R3. A fake cell has an affine structure as shown by Gromov. Such a cell must have a concave point at the boundary.

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