1,078,536 research outputs found
Bicriteria Network Design Problems
We study a general class of bicriteria network design problems. A generic
problem in this class is as follows: Given an undirected graph and two
minimization objectives (under different cost functions), with a budget
specified on the first, find a <subgraph \from a given subgraph-class that
minimizes the second objective subject to the budget on the first. We consider
three different criteria - the total edge cost, the diameter and the maximum
degree of the network. Here, we present the first polynomial-time approximation
algorithms for a large class of bicriteria network design problems for the
above mentioned criteria. The following general types of results are presented.
First, we develop a framework for bicriteria problems and their
approximations. Second, when the two criteria are the same %(note that the cost
functions continue to be different) we present a ``black box'' parametric
search technique. This black box takes in as input an (approximation) algorithm
for the unicriterion situation and generates an approximation algorithm for the
bicriteria case with only a constant factor loss in the performance guarantee.
Third, when the two criteria are the diameter and the total edge costs we use a
cluster-based approach to devise a approximation algorithms --- the solutions
output violate both the criteria by a logarithmic factor. Finally, for the
class of treewidth-bounded graphs, we provide pseudopolynomial-time algorithms
for a number of bicriteria problems using dynamic programming. We show how
these pseudopolynomial-time algorithms can be converted to fully
polynomial-time approximation schemes using a scaling technique.Comment: 24 pages 1 figur
Supersolid phases in the one dimensional extended soft core Bosonic Hubbard model
We present results of Quantum Monte Carlo simulations for the soft core
extended bosonic Hubbard model in one dimension exhibiting the presence of
supersolid phases similar to those recently found in two dimensions. We find
that in one and two dimensions, the insulator-supersolid transition has dynamic
critical exponent z=2 whereas the first order insulator-superfluid transition
in two dimensions is replaced by a continuous transition with z=1 in one
dimension. We present evidence that this transition is in the
Kosterlitz-Thouless universality class and discuss the mechanism behind this
difference. The simultaneous presence of two types of quasi long range order
results in two soliton-like dips in the excitation spectrum.Comment: 4 pages, 5 figure
R Melts Brains -- An IR for First-Class Environments and Lazy Effectful Arguments
The R programming language combines a number of features considered hard to
analyze and implement efficiently: dynamic typing, reflection, lazy evaluation,
vectorized primitive types, first-class closures, and extensive use of native
code. Additionally, variable scopes are reified at runtime as first-class
environments. The combination of these features renders most static program
analysis techniques impractical, and thus, compiler optimizations based on them
ineffective. We present our work on PIR, an intermediate representation with
explicit support for first-class environments and effectful lazy evaluation. We
describe two dataflow analyses on PIR: the first enables reasoning about
variables and their environments, and the second infers where arguments are
evaluated. Leveraging their results, we show how to elide environment creation
and inline functions
An Energetic Variational Approach for the Cahn--Hilliard Equation with Dynamic Boundary Condition: Model Derivation and Mathematical Analysis
The Cahn--Hilliard equation is a fundamental model that describes phase
separation processes of binary mixtures. In recent years, several types of
dynamic boundary conditions have been proposed in order to account for possible
short-range interactions of the material with the solid wall. Our first aim in
this paper is to propose a new class of dynamic boundary conditions for the
Cahn--Hilliard equation in a rather general setting. The derivation is based on
an energetic variational approach that combines the least action principle and
Onsager's principle of maximum energy dissipation. One feature of our model is
that it naturally fulfills three important physical constraints such as
conservation of mass, dissipation of energy and force balance relations. Next,
we provide a comprehensive analysis of the resulting system of partial
differential equations. Under suitable assumptions, we prove the existence and
uniqueness of global weak/strong solutions to the initial boundary value
problem with or without surface diffusion. Furthermore, we establish the
uniqueness of asymptotic limit as and characterize the stability
of local energy minimizers for the system.Comment: to appear in Arch. Rational Mech. Ana
Robust Adaptive Control via Neural Linearization and Compensation
We propose a new type of neural adaptive control via dynamic neural networks. For a class of unknown nonlinear systems, a neural identifier-based feedback linearization controller is first used. Dead-zone and projection techniques are applied to assure the stability of neural identification. Then four types of compensator are addressed. The stability of closed-loop system is also proven
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