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41.
For Principal Component Analysis in Reproducing Kernel Hilbert Spaces (KPCA), optimization over sets containing only linear
combinations of all n-tuples of kernel functions is investigated, where n is a positive integer smaller than the number of data. Upper bounds on the accuracy in approximating the optimal solution,
achievable without restrictions on the number of kernel functions, are derived. The rates of decrease of the upper bounds
for increasing number n of kernel functions are given by the summation of two terms, one proportional to n
−1/2 and the other to n
−1, and depend on the maximum eigenvalue of the Gram matrix of the kernel with respect to the data. Primal and dual formulations
of KPCA are considered. The estimates provide insights into the effectiveness of sparse KPCA techniques, aimed at reducing
the computational costs of expansions in terms of kernel units. 相似文献
42.
Constitutive branching analysis of cylindrical bodies under in-plane equibiaxial dead-load tractions
Finite homogeneous deformations of hyperelastic cylindrical bodies subjected to in-plane equibiaxial dead-load tractions are analyzed. Four basic equilibrium problems are formulated considering incompressible and compressible isotropic bodies under plane stress and plane deformation condition. Depending on the form of the stored energy function, these plane problems, in addition to the obvious symmetric solutions, may admit asymmetric solutions. In other words, the body may assume an equilibrium configuration characterized by two unequal in-plane principal stretches corresponding to equal external forces. In this paper, a mathematical condition, in terms of the principal invariants, governing the global development of the asymmetric deformation branches is obtained and examined in detail with regard to different choices of the stored energy function. Moreover, explicit expressions for evaluating critical loads and bifurcation points are derived. With reference to neo-Hookean, Mooney-Rivlin and Ogden-Ball materials, a broad numerical analysis is performed and the qualitatively more interesting asymmetric equilibrium branches are shown. Finally, using the energy criterion, a number of considerations are put forward about the stability of the computed solutions. 相似文献
43.
Silvia Sternativo Francesca Del Verme Antonella Calandriello Lorenzo Testaferri Marcello Tiecco 《Tetrahedron》2010,66(34):6851-9385
Variously substituted aziridines were conveniently prepared by an aza-Michael Initiated Ring Closure (aza-MIRC) reaction starting from vinyl selenones and primary amines, aminoalcohols or diamines. The reactions proceed in very high yields at room temperature in toluene or water. A significant rate acceleration was observed under aqueous conditions. 相似文献
44.
Three new N2S2 donor ligands 1,1′-((2-(2-(phenylthio)phenylthio)phenyl)methylene)bis(3,5-R-1H-pyrazole), R = H (LH), R = Me (LMe), R = i-Pr (Li-Pr) have been prepared and characterized. These bifunctional ligands incorporate two distinct chelate donor systems, by virtue of the presence of bispyrazole and bisthioether functions. The preferred conformation of these ligands is such that the N2 and S2 donor moieties may be oriented in opposite directions, thus favoring the formation of molecular chains when treated with AgBF4. The X-ray structures of Ag(I) complexes show that, depending on the steric hindrance present on the pyrazole rings, these ligands behave as κ4-SSNN-μ bridging tetradentate (when R = H), or κ3-SNN-μ bridging tridentate (when R = Me, i-Pr). Interestingly, [Ag(LH)]BF4 crystallizes in the chiral space group P41, with the molecular chain that is folded around the 41 screw axis. 相似文献
45.
We give short and self-contained proofs of Γ-convergence results for Ginzburg–Landau energy functionals in two dimensions, in the logarithmic energetic regime. In particular, we derive the renormalized energy by Γ-convergence. 相似文献
46.
Mauro Gaggero Giorgio Gnecco Marcello Sanguineti 《Computational Optimization and Applications》2014,58(1):31-85
Stochastic optimization problems with an objective function that is additive over a finite number of stages are addressed. Although Dynamic Programming allows one to formally solve such problems, closed-form solutions can be derived only in particular cases. The search for suboptimal solutions via two approaches is addressed: approximation of the value functions and approximation of the optimal decision policies. The approximations take on the form of linear combinations of basis functions containing adjustable parameters to be optimized together with the coefficients of the combinations. Two kinds of basis functions are considered: Gaussians with varying centers and widths and sigmoids with varying weights and biases. The accuracies of such suboptimal solutions are investigated via estimates of the error propagation through the stages. Upper bounds are derived on the differences between the optimal value of the objective functional and its suboptimal values corresponding to the use at each stage of approximate value functions and approximate policies. Conditions under which the number of basis functions required for a desired approximation accuracy does not grow “too fast” with respect to the dimensions of the state and random vectors are provided. As an example of application, a multidimensional problem of optimal consumption under uncertainty is investigated, where consumers aim at maximizing a social utility function. Numerical simulations are provided, emphasizing computational pros and cons of the two approaches (i.e., value-function approximation and optimal-policy approximation) using the above-mentioned two kinds of basis functions. To investigate the dependencies of the performances on dimensionality, the numerical analysis is performed for various numbers of consumers. In the simulations, discretization techniques exploiting low-discrepancy sequences are used. Both theoretical and numerical results give insights into the possibility of coping with the curse of dimensionality in stochastic optimization problems whose decision strategies depend on large numbers of variables. 相似文献
47.
Phenylseleno-acetoxylation, hydroxylation, etherification and lactonization products are obtained in good yields from the reaction of alkenes with diphenyl diselenide and iodosobenzene diacetate, in acetonitrile. 相似文献
48.
The stability of a cantilever elastic beam with rectangular cross-section under the action of a follower tangential force and a bending conservative couple at the free end is analyzed. The beam is herein modeled as a non-linear Cosserat rod model. Non-linear, partial integro-differential equations of motion are derived expanded up to cubic terms in the transversal displacement and torsional angle of the beam. The linear stability of the trivial equilibrium is studied, revealing the existence of buckling, flutter and double-zero critical points. Interaction between conservative and non-conservative loads with respect to the stability problem is discussed. The critical spectral properties are derived and the corresponding critical eigenspace is evaluated. 相似文献
49.
Roberto?Alicandro Lucia?De?Luca Adriana?Garroni Marcello?PonsiglioneEmail author 《Calculus of Variations and Partial Differential Equations》2017,56(5):148
In Alicandro et al. (J Mech Phys Solids 92:87–104, 2016) a simple discrete scheme for the motion of screw dislocations toward low energy configurations has been proposed. There, a formal limit of such a scheme, as the lattice spacing and the time step tend to zero, has been described. The limiting dynamics agrees with the maximal dissipation criterion introduced in Cermelli and Gurtin (Arch Ration Mech Anal 148, 1999) and predicts motion along the glide directions of the crystal. In this paper, we provide rigorous proofs of the results in [3], and in particular of the passage from the discrete to the continuous dynamics. The proofs are based on \(\Gamma \)-convergence techniques. 相似文献
50.
This paper proposes an approximate explicit probability density function for the analysis of external and parametric oscillation of a simply supported beam driven by random pulses. The impulsive loading model adopted is Poisson white noise, which is a process having Dirac delta occurrences with random intensity distributed in time according to Poisson's law. The response probability density function can be obtained by solving the related Kolmogorov–Feller integro-differential equation. An approximate solution is derived by transforming this equation to a first-order partial differential equation. The method of characteristics is then applied to obtain an explicit solution. The theory has been validated through numerical simulations. 相似文献