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THE ASSOCIATIVE OPERAD AND THE WEAK ORDER ON THE SYMMETRIC GROUPS
Hopf algebr factorizable inverse monoid uniform block permutation
2015/8/14
We introduce the Hopf algebra of uniform block permutations and show that
it is self-dual, free, and cofree. These results are closely related to the fact that uniform
block permutations form a fact...
Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras
noncommuting variables related Hopf algebras
2015/8/14
We identify two seemingly disparate structures: supercharacters, a useful way of doing
Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite
field, and th...
THE APOLLONIAN STRUCTURE OF INTEGER SUPERHARMONIC MATRICES
APOLLONIAN STRUCTURE INTEGER SUPERHARMONIC MATRICES
2015/8/14
We prove that the set of quadratic growths attainable by integervalued superharmonic functions on the lattice Z2 has the structure of an Apollonian circle packing. This completely characterizes the PD...
Optimal design of a CMOS op-amp via geometric programming
Component values the transistor variable function geometric programming
2015/8/11
We describe a new method for determining component values and transistor dimensions for CMOS operational amplifiers (op-amps). We observe that a wide variety of design objectives and constraints have ...
Convex optimization of output link scheduling and active queue management in QoS constrained packet switches
Algorithm switches generalized geometric programming convex optimization
2015/8/11
We present two novel algorithms at the ingress and egress of packet switches with QoS provisioning and fairness constraints. We first provide a suite of generalized weighted fair queuing formulations ...
Mixing times for random walks on geometric random graphs
Random geometric random graph nodes wireless network model and threshold properties random walk figure d dimension
2015/8/11
A geometric random graph, G^d(n,r), is formed as follows: place n nodes uniformly at random onto the surface of the d-dimensional unit torus and connect nodes which are within a distance r of each oth...
Optimal doping profiles via geometric programming
Doping profile bipolar junction transistor geometrical plan convex optimization breakdown voltage and semiconductors
2015/8/10
We first consider the problem of determining the doping profile that minimizes base transit time in a (homojunction) bipolar junction transistor. We show that this problem can be formulated as a geome...
Digital circuit optimization via geometric programming
Digital circuit geometrical plan mathematical optimization scalability generalized geometric programming
2015/8/10
This tutorial paper concerns a method for digital circuit sizing based on formulating the problem as a geometric program (GP), a special type of mathematical optimization problem that can be very effi...
Geometric programming for circuit optimization
Circuit sizing geometric programming generalized geometric programming convex optimization
2015/8/10
This tutorial concerns a method for solving a variety of circuit sizing and optimization problems, which is based on formulating the problem as a geometric program (GP), or a generalized geometric pro...
Commonly-used subdivision schemes require manifold control meshes and produce manifold surfaces. However, it is often necessary to model nonmanifold surfaces, such as several surface patches meeting a...
A Simple Manifold-Based Construction of Surfaces of Arbitrary Smoothness
Geometric modeling manifolds
2015/7/14
We present a smooth surface construction based on the manifold approach of Grimm and Hughes. We demonstrate how this approach can relatively easily produce a number of desirable properties which are h...
We develop bounds for the second largest eigenvalue and spectral gap
of a reversible Markov chain. The bounds depend on geometric quantities
such as the maximum degree, diameter and covering numbe...
COMPARISON THEOREMS FOR REVERSIBLE MARKOV CHAINS
Geometry inequality reversible markov chain the characteristic value
2015/7/14
We introduce geometric comparison inequalities that give bounds on
the eigenvalues of a reversible Markov chain in terms of the eigenvalues
of a second chain. The bounds are applied to get sharp r...
Geometric positivity in the cohomology of homogeneous spaces and generalized Schubert calculus
homogeneous spaces generalized Schubert calculus
2015/7/14
We describe recent work on positive descriptions of the structure constants of the cohomology of homogeneous spaces such as the Grassmannian, by degenerations and related methods. We
give various ext...
Hypoelliptic estimates in radiative transfer.