Probabilistic learning on manifolds (PLoM) with partition

The probabilistic learning on manifolds (PLoM) introduced in 2016 has solved difficult supervised problems for the “small data” limit where the number N of points in the training set is small. Many extensions have since been proposed, making it possible to deal with increasingly complex cases. However, the performance limit has been observed and explained for applications for which N is very small and for which the dimension of the diffusion-map basis is close to N. For these cases, we propose a novel extension based on the introduction of a partition in independent random vectors. We take advantage of this development to present improvements of the PLoM such as a simplified algorithm for constructing the diffusion-map basis and a new mathematical result for quantifying the concentration of the probability measure in terms of a probability upper bound. The analysis of the efficiency of this extension is presented through two applications.     

Some Grubbs-Type Statistics for the Detection of Several Outliers

Several widely used tests for outlying observations are reviewed. Problems of repeated application and “masking” are described. Suggested as appropriate to over-come these problems are two new statistics: L_k which is based on the k largest (observed) values and E_k which is based on the k largest (in absolute value) residuals. Tables of approximate critical values for these statistics are given for 0.01, .025,0.05, and 0.10 levels of significance and for sample size n = 3 (1) 20 (5) 50.     

Inductive transfer for learning Bayesian networks

In several domains it is common to have data from different, but closely related problems. For instance, in manufacturing, many products follow the same industrial process but with different conditions; or in industrial diagnosis, where there is equipment with similar specifications. In these cases it is common to have plenty of data for some scenarios but very little for others. In order to learn accurate models for rare cases, it is desirable to use data and knowledge from similar cases; a technique known as transfer learning. In this paper we propose an inductive transfer learning method for Bayesian networks, that considers both structure and parameter learning. For structure learning we use conditional independence tests, by combining measures from the target task with those obtained from one or more auxiliary tasks, using a novel weighted sum of the conditional independence measures. For parameter learning, we propose two variants of the linear pool for probability aggregation, combining the probability estimates from the target task with those from the auxiliary tasks. To validate our approach, we used three Bayesian networks models that are commonly used for evaluating learning techniques, and generated variants of each model by changing the structure as well as the parameters. We then learned one of the variants with a small dataset and combined it with information from the other variants. The experimental results show a significant improvement in terms of structure and parameters when we transfer knowledge from similar tasks. We also evaluated the method with real-world data from a manufacturing process considering several products, obtaining an improvement in terms of log-likelihood between the data and the model when we do transfer learning from related products.     

Performance comparison of the CRAY X-MP/24 with SDD and the CRAY-2

The CRAY-2 is considered to be one of the most powerful supercomputers. Its state-of-the-art technology features a faster clock and more memory than any other supercomputer available today. In this report the single processor performance of the CRAY-2 is compared with the older, more mature CRAY X-MP. Benchmark results are included for both the slow and the fast memory DRAM MOS CRAY-2. Our comparison is based on a kernel benchmark set aimed at evaluating the performance of these two machines on some standard tasks in scientific computing. Particular emphasis is placed on evaluating the impact of the availability of large real memory on the CRAY-2 versus fast secondary memory on the CRAY X-MP with SSD. Our benchmark includes large linear equation solvers and FFT routines, which test the capabilities of the different approaches to providing large memory. We find that in spite of its higher processor speed the CRAY-2 does not perform as well as the CRAY X-MP on the Fortran kernel benchmark. We also find that for large-scale applications, which have regular and predictable memory access patterns, a high-speed secondary memory device such as the SSD can provide performance equal to the large real memory of the CRAY-2.The author is an employee of SCA Division of Boeing Computer Services.     

Towards van der Waals Epitaxial Growth of GaAs on Si using a Graphene Buffer Layer

Van der Waals growth of GaAs on silicon using a two‐dimensional layered material, graphene, as a lattice mismatch/thermal expansion coefficient mismatch relieving buffer layer is presented. Two‐dimensional growth of GaAs thin films on graphene is a potential route towards heteroepitaxial integration of GaAs on silicon in the developing field of silicon photonics. Hetero‐layered GaAs is deposited by molecular beam epitaxy on graphene/silicon at growth temperatures ranging from 350 °C to 600 °C under a constant arsenic flux. Samples are characterized by plan‐view scanning electron microscopy, atomic force microscopy, Raman microscopy, and X‐ray diffraction. The low energy of the graphene surface and the GaAs/graphene interface is overcome through an optimized growth technique to obtain an atomically smooth low­ temperature GaAs nucleation layer. However, the low adsorption and migration energies of gallium and arsenic atoms on graphene result in cluster‐growth mode during crystallization of GaAs films at an elevated temperature. In this paper, we present the first example of an ultrasmooth morphology for GaAs films with a strong (111) oriented fiber‐texture on graphene/silicon using quasi van der Waals epitaxy, making it a remarkable step towards an eventual demonstration of the epitaxial growth of GaAs by this approach for heterogeneous integration.     

An invariant subspace‐based approach to the random eigenvalue problem of systems with clustered spectrum

The repeated or closely spaced eigenvalues and corresponding eigenvectors of a matrix are usually very sensitive to a perturbation of the matrix, which makes capturing the behavior of these eigenpairs very difficult. Similar difficulty is encountered in solving the random eigenvalue problem when a matrix with random elements has a set of clustered eigenvalues in its mean. In addition, the methods to solve the random eigenvalue problem often differ in characterizing the problem, which leads to different interpretations of the solution. Thus, the solutions obtained from different methods become mathematically incomparable. These two issues, the difficulty of solving and the non‐unique characterization, are addressed here. A different approach is used where instead of tracking a few individual eigenpairs, the corresponding invariant subspace is tracked. The spectral stochastic finite element method is used for analysis, where the polynomial chaos expansion is used to represent the random eigenvalues and eigenvectors. However, the main concept of tracking the invariant subspace remains mostly independent of any such representation. The approach is successfully implemented in response prediction of a system with repeated natural frequencies. It is found that tracking only an invariant subspace could be sufficient to build a modal‐based reduced‐order model of the system. Copyright © 2012 John Wiley & Sons, Ltd.     

Ultrananocrystalline Diamond-Coated Microporous Silicon Nitride Membranes for Medical Implant Applications

Ultrananocrystalline diamond (UNCD) exhibits excellent biological and mechanical properties, which make it an appropriate choice for promoting epidermal cell migration on the surfaces of percutaneous implants. We deposited a ~150 nm thick UNCD film on a microporous silicon nitride membrane using microwave plasma chemical vapor deposition. Scanning electron microscopy and Raman spectroscopy were used to examine the pore structure and chemical bonding of this material, respectively. Growth of human epidermal keratinocytes on UNCD-coated microporous silicon nitride membranes and uncoated microporous silicon nitride membranes was compared using the 3-(4,5-dimethylthiazol-2-yl)2,5-diphenyltetrazolium bromide (MTT) assay. The results show that the UNCD coating did not significantly alter the viability of human epidermal keratinocytes, indicating potential use of this material for improving skin sealing around percutaneous implants.     

Particle breakdown dynamics of heterogeneous foods during mastication: Peanuts embedded inside different food matrices

Heterogeneous foods are widely consumed but little is known about the dynamics of their breakdown during mastication. To investigate these dynamics the particle size and bolus mass at regular stages of the chewing sequence were investigated using a single subject, who was carefully selected according to strict mastication and dental criteria. A standardized volume of both a gelatine gel and chocolate matrix containing roasted peanuts was chewed and expectorated after a specified number of chews or at the point of swallowing. The mass of various components of the bolus was determined along with peanut particle parameters (d₅₀, broadness (b), and specific surface area) at each interval.Results showed that for this subject the type of matrix influenced the pathway that the peanut particles (embedded inside each matrix) were broken down. The d₅₀ of peanut particles within the bolus of the gelatine gel were greater than within the bolus of the chocolate throughout the chewing sequence until the point of swallowing. At the point of swallowing, the d₅₀ of peanut particles inside the bolus of the gelatine gel and chocolate were the same. The broadness value (b) and specific surface area of the peanut particles in the bolus of the chocolate were greater than those in the bolus of the gelatine gel throughout the chewing sequence. The matrices also induced different dynamic trends in the mass of bolus components during the chewing sequence.     

Determination of dyers’ perceived components of colour difference (depth,brightness and hue) between two similar colours from their spectral reflectance values

The partitioning of colour differences into ΔL^*, ΔC^* and ΔH^* is not directly equivalent to the dyer’s method of partitioning. The dyer’s method involves separation into the components of depth (ΔD), brightness (ΔB) and hue (ΔH), of which only hue difference has a qualitative (and quantitative) equivalent in the CIELAB system. Depth and brightness are important terms to dyers. Depth is related to the amount of dye taken up by a textile material and brightness to that component of colour difference that is neither depth nor hue. Brightness is best defined as the opposite of dullness, dullness being related to the amount of neutral grey present in the colour. An algorithm, called the Wardman–Smith–Farooq algorithm, has been developed to compute the dyers’ variables of ΔD,ΔB and ΔH from spectral reflectance values, enabling dyers to take full advantage of colorimetry. The algorithm is based on extensive experimental work to map surfaces of constant visual depth through the colour space and this paper describes the methodology of the calculation. The correlations of the values of ΔD,ΔB and ΔH, determined using the Wardman–Smith–Farooq algorithm with other empirical models for 117 sample pairs, are given.     

Tracking and characterizing the head motion of unanaesthetized rats in positron emission tomography

Positron emission tomography (PET) is an important in vivo molecular imaging technique for translational research. Imaging unanaesthetized rats using motion-compensated PET avoids the confounding impact of anaesthetic drugs and enables animals to be imaged during normal or evoked behaviour. However, there is little published data on the nature of rat head motion to inform the design of suitable marker-based motion-tracking set-ups for brain imaging—specifically, set-ups that afford close to uninterrupted tracking. We performed a systematic study of rat head motion parameters for unanaesthetized tube-bound and freely moving rats with a view to designing suitable motion-tracking set-ups in each case. For tube-bound rats, using a single appropriately placed binocular tracker, uninterrupted tracking was possible greater than 95 per cent of the time. For freely moving rats, simulations and measurements of a live subject indicated that two opposed binocular trackers are sufficient (less than 10% interruption to tracking) for a wide variety of behaviour types. We conclude that reliable tracking of head pose can be achieved with marker-based optical-motion-tracking systems for both tube-bound and freely moving rats undergoing PET studies without sedation.