25,081 research outputs found
Finding Optimal Strategies in a Multi-Period Multi-Leader-Follower Stackelberg Game Using an Evolutionary Algorithm
Stackelberg games are a classic example of bilevel optimization problems,
which are often encountered in game theory and economics. These are complex
problems with a hierarchical structure, where one optimization task is nested
within the other. Despite a number of studies on handling bilevel optimization
problems, these problems still remain a challenging territory, and existing
methodologies are able to handle only simple problems with few variables under
assumptions of continuity and differentiability. In this paper, we consider a
special case of a multi-period multi-leader-follower Stackelberg competition
model with non-linear cost and demand functions and discrete production
variables. The model has potential applications, for instance in aircraft
manufacturing industry, which is an oligopoly where a few giant firms enjoy a
tremendous commitment power over the other smaller players. We solve cases with
different number of leaders and followers, and show how the entrance or exit of
a player affects the profits of the other players. In the presence of various
model complexities, we use a computationally intensive nested evolutionary
strategy to find an optimal solution for the model. The strategy is evaluated
on a test-suite of bilevel problems, and it has been shown that the method is
successful in handling difficult bilevel problems.Comment: To be published in Computers and Operations Researc
Eigenvector Synchronization, Graph Rigidity and the Molecule Problem
The graph realization problem has received a great deal of attention in
recent years, due to its importance in applications such as wireless sensor
networks and structural biology. In this paper, we extend on previous work and
propose the 3D-ASAP algorithm, for the graph realization problem in
, given a sparse and noisy set of distance measurements. 3D-ASAP
is a divide and conquer, non-incremental and non-iterative algorithm, which
integrates local distance information into a global structure determination.
Our approach starts with identifying, for every node, a subgraph of its 1-hop
neighborhood graph, which can be accurately embedded in its own coordinate
system. In the noise-free case, the computed coordinates of the sensors in each
patch must agree with their global positioning up to some unknown rigid motion,
that is, up to translation, rotation and possibly reflection. In other words,
to every patch there corresponds an element of the Euclidean group Euc(3) of
rigid transformations in , and the goal is to estimate the group
elements that will properly align all the patches in a globally consistent way.
Furthermore, 3D-ASAP successfully incorporates information specific to the
molecule problem in structural biology, in particular information on known
substructures and their orientation. In addition, we also propose 3D-SP-ASAP, a
faster version of 3D-ASAP, which uses a spectral partitioning algorithm as a
preprocessing step for dividing the initial graph into smaller subgraphs. Our
extensive numerical simulations show that 3D-ASAP and 3D-SP-ASAP are very
robust to high levels of noise in the measured distances and to sparse
connectivity in the measurement graph, and compare favorably to similar
state-of-the art localization algorithms.Comment: 49 pages, 8 figure
Fuzzy Supernova Templates I: Classification
Modern supernova (SN) surveys are now uncovering stellar explosions at rates
that far surpass what the world's spectroscopic resources can handle. In order
to make full use of these SN datasets, it is necessary to use analysis methods
that depend only on the survey photometry. This paper presents two methods for
utilizing a set of SN light curve templates to classify SN objects. In the
first case we present an updated version of the Bayesian Adaptive Template
Matching program (BATM). To address some shortcomings of that strictly Bayesian
approach, we introduce a method for Supernova Ontology with Fuzzy Templates
(SOFT), which utilizes Fuzzy Set Theory for the definition and combination of
SN light curve models. For well-sampled light curves with a modest signal to
noise ratio (S/N>10), the SOFT method can correctly separate thermonuclear
(Type Ia) SNe from core collapse SNe with 98% accuracy. In addition, the SOFT
method has the potential to classify supernovae into sub-types, providing
photometric identification of very rare or peculiar explosions. The accuracy
and precision of the SOFT method is verified using Monte Carlo simulations as
well as real SN light curves from the Sloan Digital Sky Survey and the
SuperNova Legacy Survey. In a subsequent paper the SOFT method is extended to
address the problem of parameter estimation, providing estimates of redshift,
distance, and host galaxy extinction without any spectroscopy.Comment: 26 pages, 12 figures. Accepted to Ap
The effect of short ray trajectories on the scattering statistics of wave chaotic systems
In many situations, the statistical properties of wave systems with chaotic
classical limits are well-described by random matrix theory. However,
applications of random matrix theory to scattering problems require
introduction of system specific information into the statistical model, such as
the introduction of the average scattering matrix in the Poisson kernel. Here
it is shown that the average impedance matrix, which also characterizes the
system-specific properties, can be expressed in terms of classical trajectories
that travel between ports and thus can be calculated semiclassically.
Theoretical results are compared with numerical solutions for a model
wave-chaotic system
Randomized hybrid linear modeling by local best-fit flats
The hybrid linear modeling problem is to identify a set of d-dimensional
affine sets in a D-dimensional Euclidean space. It arises, for example, in
object tracking and structure from motion. The hybrid linear model can be
considered as the second simplest (behind linear) manifold model of data. In
this paper we will present a very simple geometric method for hybrid linear
modeling based on selecting a set of local best fit flats that minimize a
global l1 error measure. The size of the local neighborhoods is determined
automatically by the Jones' l2 beta numbers; it is proven under certain
geometric conditions that good local neighborhoods exist and are found by our
method. We also demonstrate how to use this algorithm for fast determination of
the number of affine subspaces. We give extensive experimental evidence
demonstrating the state of the art accuracy and speed of the algorithm on
synthetic and real hybrid linear data.Comment: To appear in the proceedings of CVPR 201
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