The problem of incomplete data - i.e., data with missing or unknown values - in multi-way arrays is ubiquitous in biomedical signal processing, network traffic analysis, bibliometrics, social network analysis, chemometrics, computer vision, communication networks, etc. We consider the problem of how to factorize data sets with missing values with the goal of capturing the underlying latent structure of the data and possibly reconstructing missing values (i.e., tensor completion). We focus on one of the most well-known tensor factorizations that captures multi-linear structure, CANDECOMP/PARAFAC (CP). In the presence of missing data, CP can be formulated as a weighted least squares problem that models only the known entries. We develop an algorithm called CP-WOPT (CP Weighted OPTimization) that uses a first-order optimization approach to solve the weighted least squares problem. Based on extensive numerical experiments, our algorithm is shown to successfully factorize tensors with noise and up to 99% missing data. A unique aspect of our approach is that it scales to sparse large-scale data, e.g., 1000 x 1000 x 1000 with five million known entries (0.5% dense). We further demonstrate the usefulness of CP-WOPT on two real-world applications: a novel EEG (electroencephalogram) application where missing data is frequently encountered due to disconnections of electrodes and the problem of modeling computer network traffic where data may be absent due to the expense of the data collection process.
Recent work on eigenvalues and eigenvectors for tensors of order m >= 3 has been motivated by applications in blind source separation, magnetic resonance imaging, molecular conformation, and more. In this paper, we consider methods for computing real symmetric-tensor eigenpairs of the form Ax{sup m-1} = lambda x subject to ||x||=1, which is closely related to optimal rank-1 approximation of a symmetric tensor. Our contribution is a shifted symmetric higher-order power method (SS-HOPM), which we show is guaranteed to converge to a tensor eigenpair. SS-HOPM can be viewed as a generalization of the power iteration method for matrices or of the symmetric higher-order power method. Additionally, using fixed point analysis, we can characterize exactly which eigenpairs can and cannot be found by the method. Numerical examples are presented, including examples from an extension of the method to finding complex eigenpairs.
The precipitation of Ag{sub 2}Te in a PbTe matrix is investigated using electron microscopy and atom probe tomography. We observe the formation of oriented nanoscale Ag{sub 2}Te precipitates in PbTe. These precipitates initially form as coherent spherical nanoparticles and evolve into flattened semi-coherent disks during coarsening. This change in morphology is consistent with equilibrium shape theory for coherently strained precipitates. Upon annealing at elevated temperatures these precipitates eventually revert to an equiaxed morphology. We suggest this shape change occurs once the precipitates grow beyond a critical size, making it favorable to relieve the elastic coherency strains by forming interfacial misfit dislocations. These investigations of the shape and coherency of Ag{sub 2}Te precipitates in PbTe should prove useful in the design of nanostructured thermoelectric materials.
Co-design has been identified as a key strategy for achieving Exascale computing in this decade. This paper describes the need for co-design in High Performance Computing related research in embedded computing the development of hardware/software co-simulation methods.
Cyber security analysis tools are necessary to evaluate the security, reliability, and resilience of networked information systems against cyber attack. It is common practice in modern cyber security analysis to separately utilize real systems of computers, routers, switches, firewalls, computer emulations (e.g., virtual machines) and simulation models to analyze the interplay between cyber threats and safeguards. In contrast, Sandia National Laboratories has developed novel methods to combine these evaluation platforms into a hybrid testbed that combines real, emulated, and simulated components. The combination of real, emulated, and simulated components enables the analysis of security features and components of a networked information system. When performing cyber security analysis on a system of interest, it is critical to realistically represent the subject security components in high fidelity. In some experiments, the security component may be the actual hardware and software with all the surrounding components represented in simulation or with surrogate devices. Sandia National Laboratories has developed a cyber testbed that combines modeling and simulation capabilities with virtual machines and real devices to represent, in varying fidelity, secure networked information system architectures and devices. Using this capability, secure networked information system architectures can be represented in our testbed on a single, unified computing platform. This provides an 'experiment-in-a-box' capability. The result is rapidly-produced, large-scale, relatively low-cost, multi-fidelity representations of networked information systems. These representations enable analysts to quickly investigate cyber threats and test protection approaches and configurations.
This 1/2 day workshop will survey various applications of XRD analysis, including in-situ analyses and neutron diffraction. The analyses will include phase ID, crystallite size and microstrain, preferred orientation and texture, lattice parameters and solid solutions, and residual stress. Brief overviews of high-temperature in-situ analysis, neutron diffraction and synchrotron studies will be included.
The analysis of networked activities is dramatically more challenging than many traditional kinds of analysis. A network is defined by a set of entities (people, organizations, banks, computers, etc.) linked by various types of relationships. These entities and relationships are often uninteresting alone, and only become significant in aggregate. The analysis and visualization of these networks is one of the driving factors behind the creation of the Titan Toolkit. Given the broad set of problem domains and the wide ranging databases in use by the information analysis community, the Titan Toolkit's flexible, component based pipeline provides an excellent platform for constructing specific combinations of network algorithms and visualizations.