FIRST PASSAGE APPROXIMATION FOR NORMAL STATIONARY RANDOM PROCESSES.

A new approximate solution for the first passage probability of a stationary Gaussian random process is presented which is based on the estimation of the mean clump size. A simple expression for the mean clump size is derived in terms of the cumulative normal distribution function, which avoids the lengthy numerical integrations which are required by similar existing techniques. The method is applied to a linear oscillator and an ideal bandpass process and good agreement with published results is obtained. By making a slight modification to an existing analysis it is shown that a widely used empirical result for the asymptotic form of the first passage probability can be deduced theoretically.

Electrically switchable random to photonic band-edge laser emission in chiral nematic liquid crystals

Using a chiral nematic liquid crystal with a negative dielectric anisotropy, it is possible to switch between band-edge laser emission and random laser emission with an electric field. At low frequencies (1 kHz), random laser emission is observed as a result of scattering due to electro-hydrodynamic instabilities. However, band-edge laser emission is found to occur at higher frequencies (5 kHz), where the helix is stabilized due to dielectric coupling. These results demonstrate a method by which the linewidth of the laser source can be readily controlled externally (from 4 nm to 0.5 nm) using electric fields. © 2012 American Institute of Physics.

Lowering the excitation threshold of a random laser using the dynamic scattering states of an organosiloxane smectic A liquid crystal

Smectic A liquid crystals, based upon molecular structures that consist of combined siloxane and mesogenic moieties, exhibit strong multiple scattering of light with and without the presence of an electric field. This paper demonstrates that when one adds a laser dye to these compounds it is possible to observe random laser emission under optical excitation, and that the output can be varied depending upon the scattering state that is induced by the electric field. Results are presented to show that the excitation threshold of a dynamic scattering state, consisting of chaotic motion due to electro-hydrodynamic instabilities, exhibits lower lasing excitation thresholds than the scattering states that exist in the absence of an applied electric field. However, the lowest threshold is observed for a dynamic scattering state that does not have the largest scattering strength but which occurs when there is optimization of the combined light absorption and scattering properties. © 2012 American Institute of Physics.

A coordination-based approach to elasticity of floppy and stiff random networks

We study the role of connectivity on the linear and nonlinear elastic behavior of amorphous systems using a two-dimensional random network of harmonic springs as a model system. A natural characterization of these systems arises in terms of the network coordination relative to that of an isostatic network $\delta z$; a floppy network has $\delta z<0$, while a stiff network has $\delta z>0$. Under the influence of an externally applied load we observe that the response of both floppy and rigid network are controlled by the same critical point, corresponding to the onset of rigidity. We use numerical simulations to compute the exponents which characterize the shear modulus, the amplitude of non-affine displacements, and the network stiffening as a function of $\delta z$, derive these theoretically and make predictions for the mechanical response of glasses and fibrous networks.

Boundary effects on the vibration statistics of a random plate

This paper considers the estimation of statistics of displacement of a vibrating rectangular plate with random wave scatterers. The influence of uncertainty is investigated using point impedance theory. Coherent boundary effects are seen, which decrease when the number of scatterers increases. The boundary effect is investigated using images and the first side and corner reflections are found to be a minimum requirement to estimate the spatial correlation. Statistics for point driven response are investigated under the assumption that the statistics of the natural frequencies follow those of the Gaussian Orthogonal Ensemble (GOE). The estimates are compared with Monte Carlo simulation results, and they show good agreement. © 2012 Elsevier Ltd. All rights reserved.

Random function priors for exchangeable arrays with applications to graphs and relational data

A fundamental problem in the analysis of structured relational data like graphs, networks, databases, and matrices is to extract a summary of the common structure underlying relations between individual entities. Relational data are typically encoded in the form of arrays; invariance to the ordering of rows and columns corresponds to exchangeable arrays. Results in probability theory due to Aldous, Hoover and Kallenberg show that exchangeable arrays can be represented in terms of a random measurable function which constitutes the natural model parameter in a Bayesian model. We obtain a flexible yet simple Bayesian nonparametric model by placing a Gaussian process prior on the parameter function. Efficient inference utilises elliptical slice sampling combined with a random sparse approximation to the Gaussian process. We demonstrate applications of the model to network data and clarify its relation to models in the literature, several of which emerge as special cases.

Band alignment between Ta2O5 and metals for resistive random access memory electrodes engineering

Band alignment of resistive random access memory (RRAM) switching material Ta2O5 and different metal electrode materials was examined using high-resolution X-ray photoelectron spectroscopy. Schottky and hole barrier heights at the interface between electrode and Ta2O 5 were obtained, where the electrodes consist of materials with low to high work function (Φ m, v a c from 4.06 to 5.93 eV). Effective metal work functions were extracted to study the Fermi level pinning effect and to discuss the dominant conduction mechanism. An accurate band alignment between electrodes and Ta2O5 is obtained and can be used for RRAM electrode engineering and conduction mechanism study. © 2013 American Institute of Physics.

On the applicability of the lognormal distribution in random dynamical systems

This paper is concerned with the probability density function of the energy of a random dynamical system subjected to harmonic excitation. It is shown that if the natural frequencies and mode shapes of the system conform to the Gaussian Orthogonal Ensemble, then under common types of loading the distribution of the energy of the response is approximately lognormal, providing the modal overlap factor is high (typically greater than two). In contrast, it is shown that the response of a system with Poisson natural frequencies is not approximately lognormal. Numerical simulations are conducted on a plate system to validate the theoretical findings and good agreement is obtained. Simulations are also conducted on a system made from two plates connected with rotational springs to demonstrate that the theoretical findings can be extended to a built-up system. The work provides a theoretical justification of the commonly used empirical practice of assuming that the energy response of a random system is lognormal.

Shock dynamics of random structures.

Predicting the response of a structure following an impact is of interest in situations where parts of a complex assembly may come into contact. Standard approaches are based on the knowledge of the impulse response function, requiring the knowledge of the modes and the natural frequencies of the structure. In real engineering structures the statistics of higher natural frequencies follows those of the Gaussian Orthogonal Ensemble, this allows the application of random point process theory to get a mean impulse response function by the knowledge of the modal density of the structure. An ensemble averaged time history for both the response and the impact force can be predicted. Once the impact characteristics are known in the time domain, a simple Fourier Transform allows the frequency range of the impact excitation to be calculated. Experimental and numerical results for beams, plates, and cylinders are presented to confirm the validity of the method.

Using sub-word-level information for confidence estimation with conditional random field models

The task of word-level confidence estimation (CE) for automatic speech recognition (ASR) systems stands to benefit from the combination of suitably defined input features from multiple information sources. However, the information sources of interest may not necessarily operate at the same level of granularity as the underlying ASR system. The research described here builds on previous work on confidence estimation for ASR systems using features extracted from word-level recognition lattices, by incorporating information at the sub-word level. Furthermore, the use of Conditional Random Fields (CRFs) with hidden states is investigated as a technique to combine information for word-level CE. Performance improvements are shown using the sub-word-level information in linear-chain CRFs with appropriately engineered feature functions, as well as when applying the hidden-state CRF model at the word level.

Efficient numerical models for investigating the statistics of random dynamic systems

The study of random dynamic systems usually requires the definition of an ensemble of structures and the solution of the eigenproblem for each member of the ensemble. If the process is carried out using a conventional numerical approach, the computational cost becomes prohibitive for complex systems. In this work, an alternative numerical method is proposed. The results for the response statistics are compared with values obtained from a detailed stochastic FE analysis of plates. The proposed method seems to capture the statistical behaviour of the response with a reduced computational cost.

The Random Forest Kernel and other kernels for big data from random partitions

We present Random Partition Kernels, a new class of kernels derived by demonstrating a natural connection between random partitions of objects and kernels between those objects. We show how the construction can be used to create kernels from methods that would not normally be viewed as random partitions, such as Random Forest. To demonstrate the potential of this method, we propose two new kernels, the Random Forest Kernel and the Fast Cluster Kernel, and show that these kernels consistently outperform standard kernels on problems involving real-world datasets. Finally, we show how the form of these kernels lend themselves to a natural approximation that is appropriate for certain big data problems, allowing $O(N)$ inference in methods such as Gaussian Processes, Support Vector Machines and Kernel PCA.