3,093 research outputs found
Limitations of Passive Protection of Quantum Information
The ability to protect quantum information from the effect of noise is one of
the major goals of quantum information processing. In this article, we study
limitations on the asymptotic stability of quantum information stored in
passive N-qubit systems. We consider the effect of small imperfections in the
implementation of the protecting Hamiltonian in the form of perturbations or
weak coupling to a ground state environment. We prove that, regardless of the
protecting Hamiltonian, there exists a perturbed evolution that necessitates a
final error correcting step when the state of the memory is read. Such an error
correction step is shown to require a finite error threshold, the lack thereof
being exemplified by the 3D compass model. We go on to present explicit weak
Hamiltonian perturbations which destroy the logical information stored in the
2D toric code in a time O(log(N)).Comment: 17 pages and appendice
Variable Selection in General Multinomial Logit Models
The use of the multinomial logit model is typically restricted to applications with few predictors, because in
high-dimensional settings maximum likelihood estimates tend to deteriorate. In this paper we are proposing a sparsity-inducing penalty that accounts for the special structure of multinomial models. In contrast to existing methods, it penalizes the parameters that are linked to one variable
in a grouped way and thus yields variable selection instead of parameter selection. We develop a proximal gradient method that is able to efficiently compute stable estimates.
In addition, the penalization is extended to the important case of predictors that vary across response categories. We apply our estimator to the modeling of party choice of voters in Germany including voter-specific variables like age and gender but also party-specific features like stance on nuclear energy and immigration
Towards Optimal Distributed Node Scheduling in a Multihop Wireless Network through Local Voting
In a multihop wireless network, it is crucial but challenging to schedule
transmissions in an efficient and fair manner. In this paper, a novel
distributed node scheduling algorithm, called Local Voting, is proposed. This
algorithm tries to semi-equalize the load (defined as the ratio of the queue
length over the number of allocated slots) through slot reallocation based on
local information exchange. The algorithm stems from the finding that the
shortest delivery time or delay is obtained when the load is semi-equalized
throughout the network. In addition, we prove that, with Local Voting, the
network system converges asymptotically towards the optimal scheduling.
Moreover, through extensive simulations, the performance of Local Voting is
further investigated in comparison with several representative scheduling
algorithms from the literature. Simulation results show that the proposed
algorithm achieves better performance than the other distributed algorithms in
terms of average delay, maximum delay, and fairness. Despite being distributed,
the performance of Local Voting is also found to be very close to a centralized
algorithm that is deemed to have the optimal performance
Fuzzy ARTMAP: A Neural Network Architecture for Incremental Supervised Learning of Analog Multidimensional Maps
A new neural network architecture is introduced for incremental supervised learning of recognition categories and multidimensional maps in response to arbitrary sequences of analog or binary input vectors. The architecture, called Fuzzy ARTMAP, achieves a synthesis of fuzzy logic and Adaptive Resonance Theory (ART) neural networks by exploiting a close formal similarity between the computations of fuzzy subsethood and ART category choice, resonance, and learning. Fuzzy ARTMAP also realizes a new Minimax Learning Rule that conjointly minimizes predictive error and maximizes code compression, or generalization. This is achieved by a match tracking process that increases the ART vigilance parameter by the minimum amount needed to correct a predictive error. As a result, the system automatically learns a minimal number of recognition categories, or "hidden units", to met accuracy criteria. Category proliferation is prevented by normalizing input vectors at a preprocessing stage. A normalization procedure called complement coding leads to a symmetric theory in which the MIN operator (Λ) and the MAX operator (v) of fuzzy logic play complementary roles. Complement coding uses on-cells and off-cells to represent the input pattern, and preserves individual feature amplitudes while normalizing the total on-cell/off-cell vector. Learning is stable because all adaptive weights can only decrease in time. Decreasing weights correspond to increasing sizes of category "boxes". Smaller vigilance values lead to larger category boxes. Improved prediction is achieved by training the system several times using different orderings of the input set. This voting strategy can also be used to assign probability estimates to competing predictions given small, noisy, or incomplete training sets. Four classes of simulations illustrate Fuzzy ARTMAP performance as compared to benchmark back propagation and genetic algorithm systems. These simulations include (i) finding points inside vs. outside a circle; (ii) learning to tell two spirals apart; (iii) incremental approximation of a piecewise continuous function; and (iv) a letter recognition database. The Fuzzy ARTMAP system is also compared to Salzberg's NGE system and to Simpson's FMMC system.British Petroleum (89-A-1204); Defense Advanced Research Projects Agency (90-0083); National Science Foundation (IRI 90-00530); Office of Naval Research (N00014-91-J-4100); Air Force Office of Scientific Research (90-0175
Three Puzzles on Mathematics, Computation, and Games
In this lecture I will talk about three mathematical puzzles involving
mathematics and computation that have preoccupied me over the years. The first
puzzle is to understand the amazing success of the simplex algorithm for linear
programming. The second puzzle is about errors made when votes are counted
during elections. The third puzzle is: are quantum computers possible?Comment: ICM 2018 plenary lecture, Rio de Janeiro, 36 pages, 7 Figure
Local partial-likelihood estimation for lifetime data
This paper considers a proportional hazards model, which allows one to
examine the extent to which covariates interact nonlinearly with an exposure
variable, for analysis of lifetime data. A local partial-likelihood technique
is proposed to estimate nonlinear interactions. Asymptotic normality of the
proposed estimator is established. The baseline hazard function, the bias and
the variance of the local likelihood estimator are consistently estimated. In
addition, a one-step local partial-likelihood estimator is presented to
facilitate the computation of the proposed procedure and is demonstrated to be
as efficient as the fully iterated local partial-likelihood estimator.
Furthermore, a penalized local likelihood estimator is proposed to select
important risk variables in the model. Numerical examples are used to
illustrate the effectiveness of the proposed procedures.Comment: Published at http://dx.doi.org/10.1214/009053605000000796 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Exponential Decay of Correlations for Strongly Coupled Toom Probabilistic Cellular Automata
We investigate the low-noise regime of a large class of probabilistic
cellular automata, including the North-East-Center model of Toom. They are
defined as stochastic perturbations of cellular automata belonging to the
category of monotonic binary tessellations and possessing a property of
erosion. We prove, for a set of initial conditions, exponential convergence of
the induced processes toward an extremal invariant measure with a highly
predominant spin value. We also show that this invariant measure presents
exponential decay of correlations in space and in time and is therefore
strongly mixing.Comment: 21 pages, 0 figure, revised version including a generalization to a
larger class of models, structure of the arguments unchanged, minor changes
suggested by reviewers, added reference
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