349 research outputs found
Unitarily invariant norm inequalities for operators
We present several operator and norm inequalities for Hilbert space
operators. In particular, we prove that if , then
for all unitarily invariant norms. We also show that if
are projections in , then
&&|||(\sum_{i=1}^{4}(-1)^{i+1}A_{i})\oplus0\oplus0\oplus0|||&\leq&|||(A_{1}+|A_{3}A_{1}|)\oplus
(A_{2}+|A_{4}A_{2}|)\oplus(A_{3}+|A_{1}A_{3}|)\oplus(A_{4}+|A_{2}A_{4}|)||| for
any unitarily invariant norm.Comment: 10 pages, Accepted pape
Cooperative co-evolution with differential grouping for large scale optimization
Cooperative co-evolution has been introduced into evolutionary algorithms with the aim of solving increasingly complex optimization problems through a divide-and-conquer paradigm. In theory, the idea of co-adapted subcomponents is desirable for solving large-scale optimization problems. However, in practice, without prior knowledge about the problem, it is not clear how the problem should be decomposed. In this paper, we propose an automatic decomposition strategy called differential grouping that can uncover the underlying interaction structure of the decision variables and form subcomponents such that the interdependence between them is kept to a minimum. We show mathematically how such a decomposition strategy can be derived from a definition of partial separability. The empirical studies show that such near-optimal decomposition can greatly improve the solution quality on large-scale global optimization problems. Finally, we show how such an automated decomposition allows for a better approximation of the contribution of various subcomponents, leading to a more efficient assignment of the computational budget to various subcomponents
Radiance cache optimization for global illumination
Radiance caching methods have proven efficient for global illumination. Their goal is to compute precisely illumination values (incident radiance or irradiance) at a reasonable number of points lying on the scene surfaces. These points, called records, are stored in a cache used for estimating illumination of other points in the scene. Unfortunately, with records lying on glossy surfaces, the irradiance value alone is not sufficient to evaluate the reflected radiance; each record should also store the incident radiance for all incident directions. Memory storage can be reduced with projection techniques using spherical harmonics or other basis functions. These techniques provide good results with low shininess BRDFs. However, they get impractical for shininess of even moderate value since the number of projection coefficients increase drastically. In this paper, we propose a new radiance caching method, that handles highly glossy surfaces, while requiring a low memory storage. Each cache record stores a coarse representation of the incident illumination thanks to a new data structure called Equivalent Area light Sources (EAS), capable of handling fuzzy mirror surfaces. In addition, our method proposes a new simplification of the interpolation process since it avoids the need for expressing and evaluating complex gradients
Facies analysis and paleoenvironmental reconstruction of Upper Cretaceous sequences in the eastern Para-Tethys Basin, NW Iran
Upper Cretaceous mixed carbonate-siliciclastic sequences are among the most important targets for hydrocarbon exploration in the Moghan area, located in the eastern Para-Tethys Basin. Despite of their significance, little is known about their facies characteristics and depositional environments. Detailed facies analysis and paleoenvironmental reconstruction of these sequences have been carried out in eight surface sections. Accordingly, four siliciclastic facies, eight carbonate facies and one volcanic facies have been recognized. Detailed facies descriptions and interpretations, together with the results of facies frequency analysis, standard facies models and Upper Cretaceous depositional models of Para-Tethys Basin, have been integrated and a non-rimmed carbonate platform is presented. This platform was affected by siliciclastic influx, in the form of coastal fan delta and submarine fans in the shallow- to deep-marine parts, respectively. This model is interpreted to be shallower in the central and northeastern parts of the Moghan area. Toward the southeast and southwest, this shallow platform turns into deep marine settings along steep slopes without remarkable marginal barriers
Solving Ratio-Dependent Predator-Prey System with Constant Effort Harvesting using Variational Iteration Method
Due to wide range of interest in use of bio-economic models
to gain insight into the scientific management of renewable resources like
fisheries and forestry,variational iteration method (VIM) is employed to
approximate the solution of the ratio-dependent predator-prey system with
constant effort prey harvesting.The results are compared with the results
obtained by Adomian decomposition method and reveal that VIM is very
effective and convenient for solving nonlinear differential equations
Hydrogen Balmer line formation in solar flares affected by return currents
Aims. We investigate the effect of the electric return currents in solar
flares on the profiles of hydrogen Balmer lines. We consider the monoenergetic
approximation for the primary beam and runaway model of the neutralizing return
current. Methods. Propagation of the 10 keV electron beam from a coronal
reconnection site is considered for the semiempirical chromosphere model F1. We
estimate the local number density of return current using two approximations
for beam energy fluxes between and . Inelastic collisions of beam and return-current electrons
with hydrogen are included according to their energy distributions, and the
hydrogen Balmer line intensities are computed using an NLTE radiative transfer
approach. Results. In comparison to traditional NLTE models of solar flares
that neglect the return-current effects, we found a significant increase
emission in the Balmer line cores due to nonthermal excitation by return
current. Contrary to the model without return current, the line shapes are
sensitive to a beam flux. It is the result of variation in the return-current
energy that is close to the hydrogen excitation thresholds and the density of
return-current electrons.Comment: 4 pages, 3 figures, 1 table, accepted for publication in Astronomy
and Astrophysics Letter
Efficient Resource Allocation in Cooperative Co-Evolution for Large-Scale Global Optimization
Cooperative co-evolution (CC) is an explicit means of problem decomposition in multipopulation evolutionary algorithms for solving large-scale optimization problems. For CC, subpopulations representing subcomponents of a large-scale optimization problem co-evolve, and are likely to have different contributions to the improvement of the best overall solution to the problem. Hence, it makes sense that more computational resources should be allocated to the subpopulations with greater contributions. In this paper, we study how to allocate computational resources in this context and subsequently propose a new CC framework named CCFR to efficiently allocate computational resources among the subpopulations according to their dynamic contributions to the improvement of the objective value of the best overall solution. Our experimental results suggest that CCFR can make efficient use of computational resources and is a highly competitive CCFR for solving large-scale optimization problems
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