286 research outputs found
Implementation of Quantum Gates via Optimal Control
Starting with the basic control system model often employed in NMR pulse
design, we derive more realistic control system models taking into account
effects such as off-resonant excitation for systems with fixed inter-qubit
coupling controlled by globally applied electromagnetic fields, as well as for
systems controlled by a combination of a global fields and local control
electrodes. For both models optimal control is used to find controls that
implement a set of two- and three-qubit gates with fidelity greater than
99.99%. While in some cases the optimal pulses obtained appear to be
surprisingly simple and experimentally realistic, the results also show that
the "optimal" pulses obtained in other cases are experimentally infeasible, and
more sophisticated parametrization of the control fields and numerical
algorithms are needed.Comment: 10 pages, 4 figure
Regularity of solutions to higher-order integrals of the calculus of variations
We obtain new regularity conditions for problems of calculus of variations
with higher-order derivatives. As a corollary, we get non-occurrence of the
Lavrentiev phenomenon. Our main regularity result asserts that autonomous
integral functionals with a Lagrangian having coercive partial derivatives with
respect to the higher-order derivatives admit only minimizers with essentially
bounded derivatives
Pursuit-Evasion Games and Zero-sum Two-person Differential Games
International audienceDifferential games arose from the investigation, by Rufus Isaacs in the 50's, of pursuit-evasion problems. In these problems, closed-loop strategies are of the essence, although defining what is exactly meant by this phrase, and what is the Value of a differential game, is difficult. For closed-loop strategies, there is no such thing as a " two-sided Maximum Principle " , and one must resort to the analysis of Isaacs' equation, a Hamilton Jacobi equation. The concept of viscosity solutions of Hamilton-Jacobi equations has helped solve several of these issues
Signal processing with Levy information
Levy processes, which have stationary independent increments, are ideal for
modelling the various types of noise that can arise in communication channels.
If a Levy process admits exponential moments, then there exists a parametric
family of measure changes called Esscher transformations. If the parameter is
replaced with an independent random variable, the true value of which
represents a "message", then under the transformed measure the original Levy
process takes on the character of an "information process". In this paper we
develop a theory of such Levy information processes. The underlying Levy
process, which we call the fiducial process, represents the "noise type". Each
such noise type is capable of carrying a message of a certain specification. A
number of examples are worked out in detail, including information processes of
the Brownian, Poisson, gamma, variance gamma, negative binomial, inverse
Gaussian, and normal inverse Gaussian type. Although in general there is no
additive decomposition of information into signal and noise, one is led
nevertheless for each noise type to a well-defined scheme for signal detection
and enhancement relevant to a variety of practical situations.Comment: 27 pages. Version to appear in: Proc. R. Soc. London
Join forces or cheat: evolutionary analysis of a consumer-resource system
International audienceIn this contribution we consider a seasonal consumer-resource system and focus on the evolution of consumer behavior. It is assumed that consumer and resource individuals live and interact during seasons of fixed lengths separated by winter periods. All individuals die at the end of the season and the size of the next generation is determined by the the consumer-resource interaction which took place during the season. Resource individuals are assumed to reproduce at a constant rate, while consumers have to trade-off between foraging for resources, which increases their reproductive abilities, or reproducing. Firstly, we assume that consumers cooperate in such a way that they maximize each consumer's individual fitness. Secondly, we consider the case where such a population is challenged by selfish mutants who do not cooperate. Finally we study the system dynamics over many seasons and show that mutants eventually replace the original cooperating population, but are finally as vulnerable as the initial cooperating consumers
Groups of diffeomorphisms and geometric loops of manifolds over ultra-normed fields
The article is devoted to the investigation of groups of diffeomorphisms and
loops of manifolds over ultra-metric fields of zero and positive
characteristics. Different types of topologies are considered on groups of
loops and diffeomorphisms relative to which they are generalized Lie groups or
topological groups. Among such topologies pairwise incomparable are found as
well. Topological perfectness of the diffeomorphism group relative to certain
topologies is studied. There are proved theorems about projective limit
decompositions of these groups and their compactifications for compact
manifolds. Moreover, an existence of one-parameter local subgroups of
diffeomorphism groups is investigated.Comment: Some corrections excluding misprints in the article were mad
Fixed duration pursuit-evasion differential game with integral constraints
We investigate a pursuit-evasion differential game of countably many pursuers and one evader. Integral constraints are imposed on control functions of the players. Duration of the game is fixed and the payoff of the game is infimum of the distances between the evader and pursuers when the game is completed. Purpose of the pursuers is to minimize the payoff and that of the evader is to maximize it. Optimal strategies of the players are constructed, and the value of the game is found. It should be noted that energy resource of any pursuer may be less than that of the evader
Artificial Neural Network Design for Tours of Multiple Asteroids
Designing multiple near-Earth asteroid (NEA) rendezvous missions is a complex global optimization problem, which involves the solution of a large combinatorial part to select the sequences of asteroids to visit. Given that more than 22,000 NEAs are known to date, trillions of permutations between asteroids need to be considered. This work develops a method based on Artificial Neural Networks (ANNs) to quickly estimate the cost and duration of low-thrust transfers between asteroids. The capability of the network to map the relationship between the characteristics of the departure and arrival orbits and the transfer cost and duration is studied. To this end, the optimal network architecture and hyper-parameters are identified for this application. An analysis of the type of orbit parametrization used as network inputs for best performance is performed. The ANN is employed within a sequence-search algorithm based on a tree-search method, which identifies multiple rendezvous sequences and selects those with lowest time of flight and propellant mass needed. To compute the full trajectory and control history, the sequences are subsequently optimized using an optimal control solver based on a pseudospectral method. The performance of the proposed methodology is assessed by investigating NEA sequences of interest. Results show that ANN can estimate the cost or duration of optimal low-thrust transfers with high accuracy, resulting into a mean relative error of less than 4%
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