5,383 research outputs found
Design of Predictive Controllers by Dynamic Programming and Neural Networks
This paper proposes a method for the design of predictive controllers for nonlinear systems. The method consists of two phases, a solution phase and a learning phase. In the solution phase, dynamic programming is applied to obtain a closed-loop control law. In the learning phase, neural networks are used to simulate the control law. This phase overcomes the curse of dimensionality problem that has often hindered the implementation of control laws generated by dynamic programming. Experimental results demonstrate the effectiveness of the metho
Correlated Phases of Population Imbalanced Fermi-Fermi Mixtures on an Optical Lattice
We study a two species fermion mixture with different populations on a square
lattice modeled by a Hubbard Hamiltonian with on-site inter-species repulsive
interaction. Such a model can be realized in a cold atom system with fermionic
atoms in two different hyperfine states loaded on an optical lattice and with
tunable inter-species interaction strength via external fields. For a
two-dimensional square lattice, when at least one of the fermion species is
close to half-filling, the system is highly affected by lattice effects. With
the majority species near half-filling and varying densities for the minority
species, we find that several correlated phases emerge as the ground state,
including a spin density wave state, a charge density wave state with stripe
structure, and various p-wave BCS pairing states for both species. We study
this system using a functional renormalization group method, determine its
phase diagram at weak coupling, discuss the origin and characteristics of each
phase, and provide estimates for the critical temperatures.Comment: 5 pages, 4 figures, figures update
Unconventional superconducting phases on a two-dimensional extended Hubbard model
We study the phase diagram of the extended Hubbard model on a two-dimensional
square lattice, including on-site (U) and nearest-neighbor (V) interactions, at
weak couplings. We show that the charge-density-wave phase that is known to
occur at half-filling when 4V > U gives way to a d_{xy} -wave superconducting
instability away from half-filling, when the Fermi surface is not perfectly
nested, and for sufficiently large repulsive and a range of on-site repulsive
interaction. In addition, when nesting is further suppressed and in presence of
a nearest-neighbor attraction, a triplet time-reversal breaking (p_x +
ip_y)-wave pairing instability emerges, competing with the d_{x2+y2} pairing
state that is known to dominate at fillings just slightly away from half. At
even smaller fillings, where the Fermi surface no longer presents any nesting,
the (p_x +ip_y)-wave superconducting phase dominates in the whole regime of
on-site repulsions and nearest-neighbor attractions, while d_{xy}-pairing
occurs in the presence of on-site attraction. Our results suggest that
zero-energy Majorana fermions can be realized on a square lattice in the
presence of a magnetic field. For a system of cold fermionic atoms on a
two-dimensional square optical lattice, both an on-site repulsion and a
nearest-neighbor attraction would be required, in addition to rotation of the
system to create vortices. We discuss possible ways of experimentally
engineering the required interaction terms in a cold atom system
d_{xy}-Density wave in fermion-fermion cold atom mixtures
We study density wave instabilities in a doubly-degenerate Fermi-Fermi
mixture with symmetry on a square lattice. For sufficiently
large on-site inter-species repulsion, when the two species of fermions are
both at half-filling, two conventional (-wave) number density waves are
formed with a -phase difference between them to minimize the inter-species
repulsion. Upon moving one species away from half-filling, an unconventional
density wave with -wave symmetry emerges. When both species are away
from the vicinity of half-filling, superconducting instabilities dominate. We
present results of a functional renormalization-group calculation that maps out
the phase diagram at weak couplings. Also, we provide a simple explanation for
the emergence of the -density wave phase based on a four-patch model.
We find a robust and general mechanism for -density-wave formation that
is related to the shape and size of the Fermi surfaces. The density imbalance
between the two species of fermions in the vicinity of half-filling leads to
phase-space discrepancy for different inter-species Umklapp couplings. Using a
phase space argument for leading corrections in the one-loop renormalization
group approach to fermions, we show that the phase-space discrepancy in our
system causes opposite flows for the two leading intra-species Umklapp
couplings and that this triggers the -density-wave instability.Comment: revised long version; 8 pages, 7 figure
A False Acceptance Error Controlling Method for Hyperspherical Classifiers
Controlling false acceptance errors is of critical importance in many pattern recognition applications, including signature and speaker verification problems. Toward this goal, this paper presents two post-processing methods to improve the performance of hyperspherical classifiers in rejecting patterns from unknown classes. The first method uses a self-organizational approach to design minimum radius hyperspheres, reducing the redundancy of the class region defined by the hyperspherical classifiers. The second method removes additional redundant class regions from the hyperspheres by using a clustering technique to generate a number of smaller hyperspheres. Simulation and experimental results demonstrate that by removing redundant regions these two post-processing methods can reduce the false acceptance error without significantly increasing the false rejection error
A Training Sample Sequence Planning Method for Pattern Recognition Problems
In solving pattern recognition problems, many classification methods, such as the nearest-neighbor (NN) rule, need to determine prototypes from a training set. To improve the performance of these classifiers in finding an efficient set of prototypes, this paper introduces a training sample sequence planning method. In particular, by estimating the relative nearness of the training samples to the decision boundary, the approach proposed here incrementally increases the number of prototypes until the desired classification accuracy has been reached. This approach has been tested with a NN classification method and a neural network training approach. Studies based on both artificial and real data demonstrate that higher classification accuracy can be achieved with fewer prototypes
One-Class-at-a-Time Removal Sequence Planning Method for Multiclass Classification Problems
Using dynamic programming, this work develops a one-class-at-a-time removal sequence planning method to decompose a multiclass classification problem into a series of two-class problems. Compared with previous decomposition methods, the approach has the following distinct features. First, under the one-class-at-a-time framework, the approach guarantees the optimality of the decomposition. Second, for a K-class problem, the number of binary classifiers required by the method is only K-1. Third, to achieve higher classification accuracy, the approach can easily be adapted to form a committee machine. A drawback of the approach is that its computational burden increases rapidly with the number of classes. To resolve this difficulty, a partial decomposition technique is introduced that reduces the computational cost by generating a suboptimal solution. Experimental results demonstrate that the proposed approach consistently outperforms two conventional decomposition methods
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