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The one-loop effective action of QED obtained by Heisenberg and Euler and by Schwinger has been expressed by an asymptotic perturbative series which is divergent. In this Letter we present a nonperturbative but convergent series of the effective action. With the convergent series we establish the existence of the manifest electric-magnetic duality in the one-loop effective action of QED.
High-convergence implosion experiments have been performed on the Omega laser facility [T.R. Boehly, Opt. Commun. 133, 495 (1997)]] using cylindrical gold hohlraums with 40 drive beams arranged into multiple cones. These experiments make use of improved hohlraum radiation symmetry conditions [T.J. Murphy, Phys. Rev. Lett. 81, 108 (1998)]] to demonstrate near predicted primary (2.45 MeV) neutron production from single-shell implosions with measured deuterium fuel convergence ratios exceeding 20 at an ignition-relevant hohlraum case-to-capsule ratio approximately 3.
The dynamical attractors are thought to underlie many biological functions of recurrent neural networks. Here we show that stable periodic spike sequences with precise timings are the attractors of the spiking dynamics of recurrent neural networks with global inhibition. Almost all spike sequences converge within a finite number of transient spikes to these attractors. The convergence is fast, especially when the global inhibition is strong. These results support the possibility that precise spatiotemporal sequences of spikes are useful for information encoding and processing in biological neural networks.
The linear delta expansion (LDE) is applied to the critical O(N) phi4 three-dimensional field theory which has been widely used to study the temperature of condensation of dilute weakly interacting homogeneous Bose gases. We study the higher order convergence of the LDE as it is usually applied to this problem. We show how to improve both the large N and finite N=2 LDE results with an efficient resummation technique which accelerates convergence. In the large N limit, it reproduces the known exact result within numerical integration accuracy. In the finite N=2 case, our improved results support the recent numerical Monte Carlo estimates for the transition temperature.
The linear delta expansion is applied to the three-dimensional O(N) scalar field theory at its critical point in a way that is compatible with the large-N limit. For a range of the arbitrary mass parameter, the linear delta expansion for (2)> converges, with errors decreasing as a power of the order n in delta. If the principal of minimal sensitivity is used to optimize the convergence rate, the errors seem to decrease exponentially with n.
We present the first wavelet-based all-electron density-functional calculations to include gradient corrections and the first in a solid. Direct comparison shows this approach to be unique in providing systematic "transparent" convergence, convergence with a priori prediction of errors, to beyond chemical (millihartree) accuracy. The method is ideal both for exploration of materials under novel conditions where there is little experience with how traditional methods perform and for the development and use of chemically accurate density functionals, which demand access to such precision.
Strongly shocked cylindrically convergent implosions were conducted on the OMEGA laser. The directly driven targets consist of a low-density foam core and an embedded aluminum shell covered by an epoxy ablator. The outer surface of the aluminum shell has imposed single-mode perturbations with wave numbers k=0.08, 0.25, and 0.7 (rad/microm) and initial amplitudes eta(0)/lambda=0.013, 0.04 and 0.11. The perturbation growth rate is found to scale with k and, in our convergent geometry, no evidence of saturation for eta/lambda as large as 5 is observed.
A data-collection method for macromolecular crystals using convergent sources is described here. Because of the unique characteristics of the diffraction patterns, a software package CBMPRO has been developed specifically for processing data images collected with the convergent beam method (CBM). The resulting data sets from crystals with two different sets of unit-cell parameters are presented and compared. There is good agreement between data sets from the same type of crystals under slightly different experimental conditions and data sets collected and processed with CBM also agree well with those from conventional oscillation methods, marking an important step to establishing CBM as a viable alternate data-collection method for macromolecular crystals.
A different contour search algorithm is presented in this paper that provides a faster convergence to the object contours than both the greedy snake algorithm (GSA) and the fast greedy snake (FGSA) algorithm. This new algorithm performs the search in an alternate skipping way between the even and odd nodes (snaxels) of a snake with different step sizes such that the snake moves to a likely local minimum in a twisting way. The alternative step sizes are adjusted so that the snake is less likely to be trapped at a pseudo-local minimum. The iteration process is based on a coarse-to-fine approach to improve the convergence. The proposed algorithm is compared with the FGSA algorithm that employs two alternating search patterns without altering the search step size. The algorithm is also applied in conjunction with the subband decomposition to extract face profiles in a hierarchical way.
In electrical impedance tomography, currents are applied to the body through electrodes that are attached to the surface and the corresponding surface voltages are measured. Based on these boundary measurements, the internal admittivity distribution of the body can be reconstructed. In order to improve the image quality it is necessary and useful to apply physiologically meaningful prior information into the image reconstruction. Such prior information usually can be obtained from other sources. For example, information on the object's boundary shape and internal structure can be obtained from computed tomography and magnetic resonance imaging scan. However, this type of prior information may change from time to time and from person to person. As these changes are limited anatomically and physiologically, the prior information including the possible changes can be presented in a number of variational forms. The aim of this paper is to find which form of prior information is more compatible for a specific imaged object at the time of imaging. This paper proposes a new method for selecting the most appropriate form of prior information, through the procedure of iterative image reconstruction by using the information obtained from boundary measurements. The method is based on the principle that incompatible prior information causes errors which are able to affect the image reconstruction's convergence behavior. In this method, according to the various forms of prior information available, several image reconstruction configurations are designed. Then, through monitoring the convergence behavior in an iterative image reconstruction, the configuration with compatible prior information can be found among those different configurations. As an example, the prior information regarding the imaged object's boundary shape and internal structure was studied by computer simulation. Results were shown and discussed.
Real-time recurrent learning (RTRL), commonly employed for training a fully connected recurrent neural network (RNN), has a drawback of slow convergence rate. In the light of this deficiency, a decision feedback recurrent neural equalizer (DFRNE) using the RTRL requires long training sequences to achieve good performance. In this paper, extended Kalman filter (EKF) algorithms based on the RTRL for the DFRNE are presented in state-space formulation of the system, in particular for complex-valued signal processing. The main features of global EKF and decoupled EKF algorithms are fast convergence and good tracking performance. Through nonlinear channel equalization, performance of the DFRNE with the EKF algorithms is evaluated and compared with that of the DFRNE with the RTRL.
When the independent sources are known to be nonnegative and well-grounded, which means that they have a nonzero pdf in the region of zero, Oja and Plumbley have proposed a "Nonnegative principal component analysis (PCA)" algorithm to separate these positive sources. Generally, it is very difficult to prove the convergence of a discrete-time independent component analysis (ICA) learning algorithm. However, by using the skew-symmetry property of this discrete-time "Nonnegative PCA" algorithm, if the learning rate satisfies suitable condition, the global convergence of this discrete-time algorithm can be proven. Simulation results are employed to further illustrate the advantages of this theory.
A new continuum model complementary to traditional cellular neural networks is introduced in this note. We consider a cellular neural field formed by infinitely many cellular neurons and modelled by an integrodifferential equation. Then, using LaSalle's invariance principle on Banach space, we show that the field quantity will asymptotically converge to an equilibrium state under the condition that all equilibria of the system are isolated. From the practical sense, the convergence indicates the essential capability of retrieving message from original raw data.
We address the problem of autocalibration of a moving camera with unknown constant intrinsic parameters. Existing autocalibration techniques use numerical optimization algorithms whose convergence to the correct result cannot be guaranteed, in general. To address this problem, we have developed a method where an interval branch-and-bound method is employed for numerical minimization. Thanks to the properties of Interval Analysis this method converges to the global solution with mathematical certainty and arbitrary accuracy and the only input information it requires from the user are a set of point correspondences and a search interval. The cost function is based on the Huang-Faugeras constraint of the essential matrix. A recently proposed interval extension based on Bernstein polynomial forms has been investigated to speed up the search for the solution. Finally, experimental results are presented.
In this paper, an Instant Goal approach is proposed for collision-free boundary following of obstacles of arbitrary shape and globally convergent path planning in unknown environments. Firstly, for effective knowledge representation and manipulation, a vector representation is presented, which not only saves much space but also conforms to the physical properties of range sensors. Secondly, the concept of Instant Goals is introduced enabling the robot to perform boundary following in a "natural" human-like manner, with additional measures taken to ensure that the robot is moving "forward" along the boundary, even if the obstacle is of arbitrary shape and disturbing obstacles are present. Collision checking is performed simultaneously and, when needed, collision avoidance is efficiently incorporated in. Based on the approach of boundary following, a realistic sensor-based path planner with global convergence property is designed for the robot capable of acquiring discrete and noisy range data. Realistic simulation experiments validate the effectiveness of the proposed approaches.
Elongated tails are exaggerated ornaments observed in various bird species, and their functional and evolutionary dynamics have attracted considerable attention. Empirical studies consistently show that sexual selection is a major drive of tail elongation. However, the genetic basis of this trait remains poorly understood. To address this gap, we performed comparative genomic analyses of 23 bird species, including 7 with extremely long tails and 16 with relative short tails. Genes related to feather development exhibited amino acid convergence replacement (e.g., APC) or displayed faster evolutionary rates (e.g., LEF1, WISP3) in the long-tailed species. Importantly, we identified convergence replacements of amino acids and rapid evolution in genes related to reproductive functions (e.g., PAQR7) and immunity (e.g., ADA), suggesting that elongated tails may serve as honest signals of genetic quality. In conclusion, this study provides genomic evidence supporting the role of sexual selection in the evolution of elongated tails, revealing an intricate interplay between sexually selected traits, fitness, and immune competence.
Convergent-beam electron diffraction on cross-sectional transmission electron microscopy specimens can map strains in the silicon substrate of microelectronics devices with high spatial resolution. However, at shallow depths below the interface, most of the diffraction lines within a convergent-beam electron diffraction pattern are split, rendering pattern interpretation impossible in the classic way. The splitting effect was systematically analysed for a variety of materials, and the same qualitative behaviour that can be explained by stress relaxation at the surfaces of the thin transmission electron microscopy specimen was observed. The effects of surface relaxation are modelled by finite elements simulations. The results predict well the experimental magnitude of the splitting for a variety of diffraction lines at different positions below the interface, but fail to simulate the intensity of the secondary lines. Possible reasons for such discrepancies are discussed and assessed.
The bucco-lingual and mesio-distal convergence angles in vital and rootfilled teeth prepared for complete crowns were measured microscopically on 190 stone dies. In vital teeth the mean convergence angles varied between approximately 19 and 27 degrees. In rootfilled teeth the mean angles varied between 12 and 37.