Coxeter-Petrie complexes naturally arise as thin diagram geometries whose rankthree residues contain all of the dual forms of a regular algebraic mapM. Corresponding to an algebraic map is its classical dual, which is obtained simply by interchanging the vertices and faces, as well as its Petrie dual, which comes about by replacing the faces by the so-called Petrie polygons. G. A. Jones and J. ...

This is the second part of a series of papers on a revisit to the bidirectional Bahl-Cocke-JelinekRaviv (BCJR) soft-in-soft-out (SISO) maximum a posteriori probability (MAP) decoding algorithm. Part I revisited the BCJR MAP decoding algorithm for rate-1 binary convolutional codes and proposed a linear complexity decoder using shift registers in the complex number field. Part II proposes a low c...

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, we generalize dual decomposition to a generic power sum inference task, whic...

A cellular embedding of a connected graph (also known as a map) on an orientable surface has trinity symmetry if it is isomorphic to both its dual and its Petrie dual. A map is regular if for any two incident vertex-edge pairs there is an automorphism of the map sending the first pair onto the second. Given a map M with all vertices of the same degree d, for any e relatively prime to d the powe...

We study planar gluon scattering amplitudes and Wilson loops in non-commutative gauge theory. Our main results are: 1. We find the map between observables in non-commutative gauge theory and their holographic dual. In that map, the region near the boundary of the gravitational dual describes the physics in terms of T-dual variables. 2. We show that in the presence of a large magnetic background...

p42mapk [mitogen activated protein (MAP) kinase; extracellular signal-regulated protein kinase (ERK)] is a serine/threonine-specific protein kinase that is activated by dual tyrosine and threonine phosphorylation in response to diverse agonists. Both the tyrosine and threonine phosphorylations are necessary for full enzymic activity. A MAP kinase activator recently purified and cloned has been ...

In this paper we consider Artinian modules over power series rings endowed with a Frobenius map. We describe a method for finding the set of all prime annihilators of submodules which are preserved by the given Frobenius map and on which the Frobenius map is not nilpotent. This extends the algorithm by Karl Schwede and the first author, which solved this problem for submodules of the injective ...

In free-boundary problems, the accuracy of a goal quantity of interest depends on both the accuracy of the approximate solution and the accuracy of the domain approximation. We develop duality-based a posteriori error estimates for functional outputs of solutions of free-boundary problems that include both sources of error. The derivation of an appropriate dual problem (linearized adjoint) is, ...

We construct the dual Cantor set for a degree two expanding map f acting as cover of the circle T onto itself. Then we use the criterion for a continuous function on this Cantor set to be the scaling function of a uniformly asymptotically affine UAA expanding map to show that the scaling function for f descends to a continuous function on a dual circle T∗. We use this representation to view the...

The pseudodeterminant pdet(M) of a square matrix is the last nonzero coefficient in its characteristic polynomial; for a nonsingular matrix, this is just the determinant. If ∂ is a symmetric or skewsymmetric matrix then pdet(∂∂t) = pdet(∂)2. Whenever ∂ is the kth boundary map of a self-dual CWcomplex X, this linear-algebraic identity implies that the torsion-weighted generating function for cel...