New techniques are presented for the calculation of lower bounds to energies of atoms and ions. A combination of effective-field and intermediate-problem methods is used to seek intermediate operators which rapidly ap...
New techniques are presented for the calculation of lower bounds to energies of atoms and ions. A combination of effective-field and intermediate-problem methods is used to seek intermediate operators which rapidly approximate the lower spectrum of the full Hamiltonian. Effectiveness of the techniques is demonstrated by showing that very small-scale calculations suffice to free the ground state of Li from the continuum, and to approximate the Li+ ground state within 0.8%.
The motion of fluid particles due to the slow flow between two eccentric cylinders rotating alternately is examined experimentally and numerically. In 'return experiments' composed of alternate rotations of th...
The motion of fluid particles due to the slow flow between two eccentric cylinders rotating alternately is examined experimentally and numerically. In 'return experiments' composed of alternate rotations of the cylinders by N periods and their time reversal, the dye starting from one region almost returns to its initial position even for large N, whereas the deviation of the dye starting from the other region from its initial position is large and rapidly increases with N. These two regions correspond to the regular and chaotic regions in the numerically computed Poincare plot for the alternate rotations of the cylinders. These results suggest the significance of orbital instability in the chaotic region in the experiments with unavoidable imperfections. A part of the experimental results can be explained qualitatively using a local Lyapunov exponent (L.L.E.) for finite evolution time. The importance of the stagnation point of the flow due to the rotation of a cylinder in the orbital instability is also suggested using the L.L.E.
The dynamic behavior of RMSprop and Adam algorithms is studied through a combination of careful numerical experiments and theoretical explanations. Three types of qualitative features are observed in the training loss...
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In this paper, we introduce a new subclass of analytic functions defined on the symmetry domain . The subclass is characterized by a derivative operator associated with quantum calculus. We obtain estimations for the ...
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Given a parametrized family of finite frames, we consider the optimization problem of finding the member of this family whose coefficient space most closely contains a given data vector. This nonlinear least squares p...
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Cotangent sums play a significant role in the Nyman–Beurling criterion for the Riemann hypothesis. Here we investigate the maximum of the values of these cotangent sums over various sets of rational numbers in short ...
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We consider the problem of tracking the state of a hybrid system capable of performing a bounded number of mode transitions in the presence of spurious, or cluttered measurements. The system is assumed to follow, at e...
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ISBN:
(纸本)9781618399144
We consider the problem of tracking the state of a hybrid system capable of performing a bounded number of mode transitions in the presence of spurious, or cluttered measurements. The system is assumed to follow, at each time, one of a predefined dynamical models. Two types of uncertainties make the problem challenging. The first is the data uncertainty that follows from the fact that the true measurement of the state is indistinguishable from the clutter measurements that do not carry useful information. The second problem is the intrinsic model uncertainty. Both reasons prevent the computation of the optimal estimator. On the other hand, the mode transitions are not Markov thus ruling out the direct use of standard approaches for state estimation in cluttered environment. We derive an efficient estimation scheme for systems in cluttered environments capable of performing a bounded number of mode transitions. At the heart of this scheme is a transformation of the non-Markov model set to an equivalent Markovian one and a subsequent utilization of standard approaches matched to the new mode set. The algorithm's performance is evaluated via a simulation study, and shown to outperform the standard popular approaches in a typical example.
Power spectrum estimation is an important tool in many applications, such as the whitening of noise. The popular multitaper method enjoys significant success, but fails for short signals with few samples. We propose a...
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ISBN:
(纸本)9781538615669
Power spectrum estimation is an important tool in many applications, such as the whitening of noise. The popular multitaper method enjoys significant success, but fails for short signals with few samples. We propose a statistical model where a signal is given by a random linear combination of fixed, yet unknown, stochastic sources. Given multiple such signals, we estimate the subspace spanned by the power spectra of these fixed sources. Projecting individual power spectrum estimates onto this subspace increases estimation accuracy. We provide accuracy guarantees for this method and demonstrate it on simulated and experimental data from cryo-electron microscopy.
The main obstacle in sequential multiscale modeling is the pre-computation of the constitutive relationwhich often involvesmany independent *** constitutive relation of a polymeric fluid is a function of six variables...
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The main obstacle in sequential multiscale modeling is the pre-computation of the constitutive relationwhich often involvesmany independent *** constitutive relation of a polymeric fluid is a function of six variables,even after making the simplifying assumption that stress depends only on the rate of *** such a function is usually considered too *** the value of sequential multiscale modeling is often limited to“parameter passing”.Here we demonstrate that sparse representations can be used to drastically reduce the computational cost for precomputing functions of many *** strategy dramatically increases the efficiency of sequential multiscale modeling,making it very competitive in many situations.
Development of automatic shape design optimization algorithms requires the consideration of convergence issues. One issue is the approximation accuracy of the objective function and its gradient. This is of particular...
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