In this paper the notion of a quadratic automaton transformation is defined and studied. The automata considered transform infinite input sequences of elements from a finite commutative ring with identity to infinite output sequences. Results extending the linear automaton transformation theory of 4. Nerode are derived and two distinct approaches to machine realization arise depending upon whet...

We show that if f : M →M is a pseudo-Anosov homeomorphism on an orientable surface with oriented unstable manifolds and a quadratic expanding factor, then there is a hyperbolic toral automorphism on T2 and a map h : M → T2 such that h is a semi-conjugacy and (M, h) is a branched covering space of T2. We also give another characterization of pseudo-Anosov homeomorphisms with quadratic expansion ...

A crease pattern is an embedded planar graph on a piece of paper. An m×n map is a rectangular piece of paper with a crease pattern that partitions the paper into an m×n regular grid of unit squares. If a map has a configuration such that all the faces of the map are stacked on a unit square and the paper does not self-intersect, then it is flat foldable, and the linear ordering of the faces is ...

Near a nonresonant, elliptic fixed point, a symplectic map can be transformed into Birkhoff normal form. In these coordinates, the dynamics is represented entirely by the Lagrangian ‘‘frequency map’’ that gives the rotation number as a function of the action. The twist matrix, given by the Jacobian of the rotation number, describes the anharmonicity in the system. When the twist is singular the...

Given compactly supported 0 ≤ f, g ∈ L1(R), the problem of transporting a fraction m ≤ min{‖f‖L1 , ‖g‖L1} of the mass of f onto g as cheaply as possible is considered, where cost per unit mass transported is given by a cost function c, typically quadratic c(x,y) = |x − y|/2. This question is shown to be equivalent to a double obstacle problem for the Monge-Ampère equation, for which sufficient ...

The support function of a free-form–surface is closely related to the implicit equation of the dual surface, and the process of computing both the dual surface and its support function can be seen as dual implicitization. The support function can be used to parameterize a surface by its inverse Gauss map. This map makes it relatively simple to study offset surfaces and isophotes (which are simp...

Finding maximum a posterior (MAP) estimation is common problem in computer vision, such as the inference in Markov random fields. However, it is in general intractable, and one has to resort to approximate solutions, e.g. quadratic programming. In this paper, we propose a robust Frank-Wolfe method [6] to do the MAP inference. Our algorithm optimizes the quadratic programming problem by alternat...

The support function of a free-form–surface is closely related to the implicit equation of the dual surface, and the process of computing both the dual surface and the support function can be seen as dual implicitization. The support function can be used to parameterize a surface by its inverse Gauss map. This map makes it relatively simple to study isophotes (which are simply images of spheric...

Bayesian MAP (maximum a posteriori) methods for SPECT reconstruction can both stabilize reconstructions and lead to better bias and variance relative to ML methods. In previous work [1], a nonquadratic prior (the weak plate) that imposed piecewise smoothness on the first derivative of the solution led to much improved bias/variance behavior relative to results obtained using a more conventional...

For a large class of relay feedback systems (RFS) there will be limit cycle oscillations. Conditions to check existence and local stability of limit cycles for these systems are well known. Global stability conditions, however, are practically non-existent. This paper presents conditions in the form of linear matrix inequalities (LMIs) that guarantee global asymptotic stability of a limit cycle...