Design Adaptive Nearest Neighbor Regression Estimation

This paper deals with nonparametric regression estimation under arbitrary sampling with an unknown distribution. The effect of the distribution of the design, which is a nuisance parameter, can be eliminated by conditioning. An upper bound for the conditional mean squared error of k−NN estimates leads us to consider an optimal number of neighbors, which is a random function of the sampling. The corresponding estimate can be used for nonasymptotic inference and is also consistent under a minimal recurrence condition. Some deterministic equivalents are found for the random rate of convergence of this optimal estimate, for deterministic and random designs with vanishing or diverging densities. The proposed estimate is rate optimal for standard designs.     

Controlled Markov processes on the infinite planning horizon: Weighted and overtaking cost criteria

Stochastic control problems for controlled Markov processes models with an infinite planning horizon are considered, under some non-standard cost criteria. The classical discounted and average cost criteria can be viewed as complementary, in the sense that the former captures the short-time and the latter the long-time performance of the system. Thus, we study a cost criterion obtained as weighted combinations of these criteria, extending to a general state and control space framework several recent results by Feinberg and Shwartz, and by Krass et al. In addition, a functional characterization is given for overtaking optimal policies, for problems with countable state spaces and compact control spaces; our approach is based on qualitative properties of the optimality equation for problems with an average cost criterion.Research partially supported by the Engineering Foundation under grant RI-A-93-10, in part by the National Science Foundation under grant NSF-INT 9201430, and in part by a grant from the AT&T Foundation.Research partially supported by the Air Force Office of Scientific Research under Grant F49620-92-J-0045, and in part by the National Science Foundation under Grant CDR-8803012.     

Investigating nonlinear dynamics from time series: The influence of symmetries and the choice of observables

When a dynamical system is investigated from a time series, one of the most challenging problems is to obtain a model that reproduces the underlying dynamics. Many papers have been devoted to this problem but very few have considered the influence of symmetries in the original system and the choice of the observable. Indeed, it is well known that there are usually some variables that provide a better representation of the underlying dynamics and, consequently, a global model can be obtained with less difficulties starting from such variables. This is connected to the problem of observing the dynamical system from a single time series. The roots of the nonequivalence between the dynamical variables will be investigated in a more systematic way using previously defined observability indices. It turns out that there are two important ingredients which are the complexity of the coupling between the dynamical variables and the symmetry properties of the original system. As will be mentioned, symmetries and the choice of observables also has important consequences in other problems such as synchronization of nonlinear oscillators. (c) 2002 American Institute of Physics.     

Noise-induced outer synchronization between two different complex dynamical networks

In this paper, based on the theory of stochastic differential equations, we study the outer synchronization between two different complex dynamical networks with noise coupling. The theoretical result shows that two different complex networks can achieve generalized outer synchronization only with white-noise-based coupling. Numerical examples further verify the effectiveness and feasibility of the theoretical results. Numerical evidence shows that the synchronization rate is proportional to the noise intensity.     

Displacement discontinuity method for modeling axisymmetric cracks in an elastic half-space

This paper describes a displacement discontinuity method for modeling axisymmetric cracks in an elastic half-space or full space. The formulation is based on hypersingular integral equations that relate displacement jumps and tractions along the crack. The integral kernels, which represent stress influence functions for ring dislocation dipoles, are derived from available axisymmetric dislocation solutions. The crack is discretized into constant-strength displacement discontinuity elements, where each element represents a slice of a cone. The influence integrals are evaluated using a combination of numerical integration and a recursive procedure that allows for explicit integration of hyper- and Cauchy singularities. The accuracy of the solution at the crack tip is ensured by adding corrective stresses across the tip element. The method is validated by a comparison with analytical and numerical reference solutions.     

Reactivity of B‐Xanthyl N‐Heterocyclic Carbene‐Boranes

The synthesis and reactivity of mono‐ and bis‐S‐xanthyl NHC‐boranes is reported. The new NHC‐boranes are prepared through nucleophilic exchange at boron from either mono‐ or bis‐triflyl NHC‐boranes, themselves obtained by protolysis of the NHC‐BH₃ starting compounds. The B?H bond of the S‐xanthyl NHC‐boranes can be cleaved both homolytically and heterolytically, albeit the latter is more synthetically useful. The S‐xanthyl NHC‐boranes can reduce both aldehydes and imines. The B?S bond can also be cleaved homolytically. Under UV irradiation, the S‐xanthyl NHC‐boranes generate NHC‐boryl radicals that can initiate radical polymerizations of acrylates.     

One-Pot Synthesis of Metastable 2,5-Dihydrooxepines through Retro-Claisen Rearrangements: Method and Applications

A one-pot methodology to synthesize metastable bicyclic 2,5-dihydrooxepines from cyclic 1,3-diketones and 1,4-dibromo-2-butenes through the retro-Claisen rearrangement of syn-2-vinylcyclopropyl diketone intermediates is reported. DFT calculations were performed to understand the reaction selectivity and mechanisms towards [1,3]- or [3,3]-sigmatropic rearrangements, highlighting the crucial influence of the temperature. The reaction was successfully applied to a short protecting group-free total synthesis of radulanin A, a natural 2,5-dihydrobenzoxepine. Moreover, the strong herbicidal potential of this natural product is demonstrated for the first time.     

An analysis of over-relaxation in a kinetic approximation of systems of conservation laws

The over-relaxation approach is an alternative to the Jin–Xin relaxation method in order to apply the equilibrium source term in a more precise way. This is also a key ingredient of the lattice Boltzmann method for achieving second-order accuracy. In this work, we provide an analysis of the over-relaxation kinetic scheme. We compute its equivalent equation, which is particularly useful for devising stable boundary conditions for the hidden kinetic variables.     

A brittle material with tunable elasticity: Crêpe paper

We study the mechanical response, and tearing features of crêpe paper, a two-dimensional, very anisotropic material, with one direction much less stiff than the other one. Depending on how the soft direction has been pre-stretched or not, the apparent Young modulus of the material can be varied over a broad range, while its fracture energy remains unaltered. The classical tearing concertina problem shows that a macroscopic measurement (the shape of the teared region) provides a direct access to the fracture properties of the material (effective Young's modulus, and fracture energy). The overall discussion is conducted in the frame of Griffith's theory of fracture.     

Intrinsic magnetic properties of In2O3 and transition metal-doped-In2O3

This paper reports on the influence of the sintering temperature and atmosphere and transition-metal doping on the magnetic properties of nanocrystalline and bulk In₂O₃. Undoped nanocrystalline In₂O₃ is diamagnetic whatever the sintering temperature and atmosphere. All single-phase transition-metal-doped In₂O₃ samples are paramagnetic, with a paramagnetic effective moment originating from weakly interacting transition metal ions. No trace of ferromagnetism has been detected even with samples sintered under argon, except extrinsic ferromagnetism for samples with magnetic dopant concentrations exceeding the solubility limit.