共查询到20条相似文献,搜索用时 78 毫秒
1.
《Journal of computational physics》2008,227(2):1500-1509
Global optimization is one of the key challenges in computational physics as several problems, e.g. protein structure prediction, the low-energy landscape of atomic clusters, detection of community structures in networks, or model-parameter fitting can be formulated as global optimization problems. Extremal optimization (EO) has become in recent years one particular, successful approach to the global optimization problem. As with almost all other global optimization approaches, EO is driven by an internal dynamics that depends crucially on one or more parameters. Recently, the existence of an optimal scheme for this internal parameter of EO was proven, so as to maximize the performance of the algorithm. However, this proof was not constructive, that is, one cannot use it to deduce the optimal parameter itself a priori. In this study we analyze the dynamics of EO for a test problem (spin glasses). Based on the results we propose an online measure of the performance of EO and a way to use this insight to reformulate the EO algorithm in order to construct optimal values of the internal parameter online without any input by the user. This approach will ultimately allow us to make EO parameter free and thus its application in general global optimization problems much more efficient. 相似文献
2.
Global optimization is one of the key challenges in computational physics as several problems, e.g. protein structure prediction, the low-energy landscape of atomic clusters, detection of community structures in networks, or model-parameter fitting can be formulated as global optimization problems. Extremal optimization (EO) has become in recent years one particular, successful approach to the global optimization problem. As with almost all other global optimization approaches, EO is driven by an internal dynamics that depends crucially on one or more parameters. Recently, the existence of an optimal scheme for this internal parameter of EO was proven, so as to maximize the performance of the algorithm. However, this proof was not constructive, that is, one cannot use it to deduce the optimal parameter itself a priori. In this study we analyze the dynamics of EO for a test problem (spin glasses). Based on the results we propose an online measure of the performance of EO and a way to use this insight to reformulate the EO algorithm in order to construct optimal values of the internal parameter online without any input by the user. This approach will ultimately allow us to make EO parameter free and thus its application in general global optimization problems much more efficient. 相似文献
3.
In this paper we study constrained variational problems in one independent variable defined on the space of integral curves of a Frenet system in a homogeneous space G/H. We prove that if the Lagrangian is G-invariant and coisotropic then the extremal curves can be found by quadratures. Our proof is constructive and relies on the reduction theory for coisotropic optimal control problems. This gives a unified explanation of the integrability of several classical variational problems such as the total squared curvature functional, the projective, conformal and pseudo-conformal arc-length functionals, the Delaunay and the Poincaré variational problems. 相似文献
4.
Wendoloski JC 《The Journal of the Acoustical Society of America》2000,107(1):51-69
This paper applies Green's function modal expansion techniques to inverse source problems within an acoustically rigid rectangular cavity. In particular, solutions are developed for the reconstruction of a random spatially incoherent distributed source and a deterministic point source by using pressure-field measurements on adjacent walls. Such problems have seemingly not been addressed previously. Several example problems are studied in this paper. As is characteristic of inverse problems in general, numerical instabilities are encountered in the example problems addressed in this paper. These are linked to the notion of compactness in the forward operator, and dealt with using magnitude regularization and projections onto convex sets. The behavior of the example problems studied in this paper greatly deteriorates at frequencies near cavity resonances, particularly low frequency resonances (i.e., with ka < or = 2pi, where a is the smallest cavity dimension). Other results concerning the example problems are also given. A proof of compactness of an infinite rank version of the type of operator used in this paper is given in the Appendix. This proof implies that the convergence of the Green's function modal expansion in the kernel of the forward problem is related to the instability of the inverse problem. This implies that, if it suffices to know an integral of the source profile rather than the actual profile, the problem becomes more stable. 相似文献
5.
We get a rigorous bound for the diffusion constant of the hamiltonian dynamical system generated by a sawtooth map on a cylinder. The momentum variable properly renormalized then behaves almost like a brownian motion in the limit of infinite coupling constants. The strategy of the proof is a rigorous reformulation of the Random Phase Approximation.Supported by Contract CEE n0 SC1*0281 相似文献
6.
7.
Recently, based on the semigroup approach a new proof was presented of the existence of a unique solution of the non-stationary Boltzmann equation for the electron component of a collision dominated plasma. The proof underlies some restrictions which should be overcome to extend the validity range to other problems of physical interest. One of the restrictions is the boundary condition applied. The choice of the boundary condition is essential for the proof because it determines the range of definition of the infinitesimal generator and thus the operator semigroup itself. The paper proves the existence of a unique solution for generalized boundary conditions, this solution takes non-negative values, which is necessary for a distribution function from the physical point of view. 相似文献
8.
Small random perturbations of dynamical systems: Exponential loss of memory of the initial condition
We consider Markov processes arising from small random perturbations of non-chaotic dynamical systems. Under rather general conditions we prove that, with large probability, the distance between two arbitrary paths starting close to a same attractor of the unperturbed system decreases exponentially fast in time. The case of paths starting in different basins of attraction is also considered as well as some applications to the analysis of the invariant measure and to elliptic problems with small parameter in front to the second derivatives. The proof is based on a multiscale analysis of the typical trajectories of the Markov process; this analysis is done using techniques involved in the proof of Anderson localization for disordered quantum systems. 相似文献
9.
The axially symmetric steady-state motion of a viscous incompressible fluid in a region of the type of a spherical layer is considered. The boundary problem for the Navier-Stokes equations is formulated in terms of the stream function and vorticity. The solvability of this problem was previously established provided that the fluid flow rate through each layer boundary is sufficiently small. The main result of this study is in proving the solvability of the axially symmetric flow-through problem without limitations on the magnitude of the flow rate. The proof is based on the a priori Dirichlet estimate of the flow velocity field. The asymptotic properties of the solution near the symmetry axis are established conditionally. The proof procedure admits the generalization to the case of axially symmetric problems in multiply-connected domains. 相似文献
10.
W. F. Shadwick 《Letters in Mathematical Physics》1982,6(4):271-276
It is demonstrated that, for a certain class of Lagrangians, which includes those for the Korteweg-de Vries (KdV) hierarchy, the Hamiltonian structure provided by the Hamilton-Cartan formalism is precisely the one discovered by Gardner for the KdV equation. A simple geometric relation between the Cartan 2-forms for this class of Lagrangians and the Cartan 1-forms for the associated stationary problems is given. This relation provides a new proof of the theorem of Bogoyavlenski-Novikov and Gel'fand-Dikii on the integrability of the stationary Korteweg-de Vries equations.Research supported by the Natural Sciences and Engineering Research Council of Canada. 相似文献
11.
We study the problem of existence of response solutions for a real-analytic one-dimensional system, consisting of a rotator subject to a small quasi-periodic forcing with Bryuno frequency vector. We prove that at least one response solution always exists, without any assumption on the forcing besides smallness and analyticity. This strengthens the results available in the literature, where generic non-degeneracy conditions are assumed. The proof is based on a diagrammatic formalism and relies on renormalisation group techniques, which exploit the formal analogy with problems of quantum field theory; a crucial role is played by remarkable identities between classes of diagrams. 相似文献
12.
The effectiveness of the Metropolis algorithm (MA) (constant-temperature simulated annealing) in optimization by the method of search-space smoothing (SSS) (potential smoothing) is studied on two types of random traveling salesman problems. The optimization mechanism of this hybrid approach (MASSS) is investigated by analyzing the exploration dynamics observed in the rugged landscape of the cost function (energy surface). The results show that the MA can be successfully utilized as a local search algorithm in the SSS approach. It is also clarified that the optimization characteristics of these two constituent methods are improved in a mutually beneficial manner in the MASSS run. Specifically, the relaxation dynamics generated by employing the MA work effectively even in a smoothed landscape and more advantage is taken of the guiding function proposed in the idea of SSS; this mechanism operates in an adaptive manner in the de-smoothing process and therefore the MASSS method maintains its optimization function over a wider temperature range than the MA. 相似文献
13.
Mirko Navara 《International Journal of Theoretical Physics》2004,43(7-8):1587-1594
The famous Gleason's Theorem gives a characterization of measures on lattices of subspaces of Hilbert spaces. The attempts to simplify its proof lead to geometrical lemmas that possess also easy proofs of some consequences of Gleason's Theorem. We contribute to these results by solving two open problems formulated by Chevalier, Dvure?enskij and Svozil. Besides, our use of orthoideals provides a unified approach to finite and infinite measures. 相似文献
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15.
This is a conceptual overview on a polemical subject: the problem of time asymmetry. It is proved that time asymmetry can
be considered as a global generalized symmetry breaking, produced by a choice of a physically admissible state space, in a
global Gel'fand triplet. The well-known physics of irreversible process can be studied using this mathematical structure and
all the arrows of time can be explained and coordinated. But the deeper problems of time definition and time arrow in quantum
gravity remain outside of this landscape. 相似文献
16.
Bremner MJ Dawson CM Dodd JL Gilchrist A Harrow AW Mortimer D Nielsen MA Osborne TJ 《Physical review letters》2002,89(24):247902
Which gates are universal for quantum computation? Although it is well known that certain gates on two-level quantum systems (qubits), such as the controlled-not, are universal when assisted by arbitrary one-qubit gates, it has only recently become clear precisely what class of two-qubit gates is universal in this sense. We present an elementary proof that any entangling two-qubit gate is universal for quantum computation, when assisted by one-qubit gates. A proof of this result for systems of arbitrary finite dimension has been provided by Brylinski and Brylinski; however, their proof relies on a long argument using advanced mathematics. In contrast, our proof provides a simple constructive procedure which is close to optimal and experimentally practical. 相似文献
17.
Carlo Lancellotti 《Journal of statistical physics》2009,136(4):643-665
Whereas the Vlasov (a.k.a. “mean-field”) limit for N-particle systems with sufficiently smooth potentials has been the subject of many studies, the literature on the dynamics
of the fluctuations around the limit is sparse and somewhat incomplete. The present work fulfills two goals: 1) to provide
a complete, simple proof of a general theorem describing the evolution of a given initial fluctuation field for the particle
density in phase space, and 2) to characterize the most general class of initial symmetric probability measures that lead
(in the infinite-particle limit) to the same Gaussian random field that arises when the initial phase space coordinates of
the particles are assumed to be i.i.d. random variables (so that the standard central limit theorem applies). The strategy
of the proof of the fluctuation evolution result is to show first that the deviations from mean-field converge for each individual
system, in a purely deterministic context. Then, one obtains the corresponding probabilistic result by a modification of the
continuous mapping theorem. The characterization of the initial probability measures is in terms of a higher-order chaoticity
condition (a.k.a. “Boltzmann property”). 相似文献
18.
Efficient and robust routing on scale-free networks 总被引:1,自引:0,他引:1
Information routing is one of the most important problems in large communication networks. In this paper we propose a novel routing strategy in which the optimal paths between all pairs of nodes are chosen according to a cost function that incorporates degrees of nodes in paths. Results on large scale-free networks demonstrate that our routing strategy is more efficient than the shortest path algorithm and the efficient routing strategy proposed by Yan et al. [Phys. Rev. E 73, 046108 (2006)]. Furthermore our routing strategy has strong robustness against cascading failure attacks on networks. 相似文献
19.
A number theoretic approach to string compactification is developed for Calabi–Yau hypersurfaces in arbitrary dimensions. The motivic strategy involved is illustrated by showing that the Hecke eigenforms derived from Galois group orbits of the holomorphic two-form of a particular type of K3 surface can be expressed in terms of modular forms constructed from the worldsheet theory. The process of deriving string physics from spacetime geometry can be reversed, allowing the construction of K3 surface geometry from the string characters of the partition function. A general argument for K3 modularity is given by combining mirror symmetry with the proof of the Shimura–Taniyama conjecture. 相似文献
20.
Ovidiu Costin Roland Donninger Irfan Glogić Min Huang 《Communications in Mathematical Physics》2016,343(1):299-310
We consider an explicit self-similar solution to an energy-supercritical Yang-Mills equation and prove its mode stability. Based on earlier work by one of the authors, we obtain a fully rigorous proof of the nonlinear stability of the self-similar blowup profile. This is a large-data result for a supercritical wave equation. Our method is broadly applicable and provides a general approach to stability problems related to self-similar solutions of nonlinear wave equations. 相似文献