Rank-preserving geometric means of positive semi-definite matrices

The generalization of the geometric mean of positive scalars to positive definite matrices has attracted considerable attention since the seminal work of Ando. The paper generalizes this framework of matrix means by proposing the definition of a rank-preserving mean for two or an arbitrary number of positive semi-definite matrices of fixed rank. The proposed mean is shown to be geometric in that it satisfies all the expected properties of a rank-preserving geometric mean. The work is motivated by operations on low-rank approximations of positive definite matrices in high-dimensional spaces.© 2012 Elsevier Inc. All rights reserved.

Mapping experience in organizations: A learning process for strategic technology planning

Today's fast-paced, dynamic environments mean that for organizations to keep "ahead of the game", engineering managers need to maximize current opportunities and avoid repeating past mistakes. This article describes the development study of a collaborative strategic management tool - the Experience Scan to capture past experience and apply learning from this to present and future situations. Experience Scan workshops were held in a number of different technology organizations, developing and refining the tool until its format stabilized. From participants' feedback, the workshop-based tool was judged to be a useful and efficient mechanism for communication and knowledge management, contributing to organizational learning.

Determinantal Clustering Processes - A Nonparametric Bayesian Approach to Kernel Based Semi-Supervised Clustering

Semi-supervised clustering is the task of clustering data points into clusters where only a fraction of the points are labelled. The true number of clusters in the data is often unknown and most models require this parameter as an input. Dirichlet process mixture models are appealing as they can infer the number of clusters from the data. However, these models do not deal with high dimensional data well and can encounter difficulties in inference. We present a novel nonparameteric Bayesian kernel based method to cluster data points without the need to prespecify the number of clusters or to model complicated densities from which data points are assumed to be generated from. The key insight is to use determinants of submatrices of a kernel matrix as a measure of how close together a set of points are. We explore some theoretical properties of the model and derive a natural Gibbs based algorithm with MCMC hyperparameter learning. The model is implemented on a variety of synthetic and real world data sets.

A value mapping tool for sustainable business modelling

Purpose: Although business models that deliver sustainability are increasingly popular in the literature, few tools that assist in sustainable business modelling have been identified. This paper investigates how businesses might create balanced social, environmental and economic value through integrating sustainability more fully into the core of their business. A value mapping tool is developed to help firms create value propositions better suited for sustainability. Design/methodology/approach: In addition to a literature review, six sustainable companies were interviewed to understand their approaches to business modelling, using a case study approach. Building on the literature and practice, a tool was developed which was pilot tested through use in a workshop. The resulting improved tool and process was subsequently refined through use in 13 workshops. Findings: A novel value mapping tool was developed to support sustainable business modelling, which introduces three forms of value (value captured, missed/destroyed or wasted, and opportunity) and four major stakeholder groups (environment, society, customer, and network actors). Practical implications: This tool intends to support business modelling for sustainability by assisting firms in better understanding their overall value proposition, both positive and negative, for all relevant stakeholders in the value network. Originality/value: The tool adopts a multiple stakeholder view of value, a network rather than firm centric perspective, and introduces a novel way of conceptualising value that specifically introduces value destroyed or wasted/ missed, in addition to the current value proposition and new opportunities for value creation. © Emerald Group Publishing Limited.

Direct temperature mapping of nanoscale plasmonic devices.

Side by side with the great advantages of plasmonics in nanoscale light confinement, the inevitable ohmic loss results in significant joule heating in plasmonic devices. Therefore, understanding optical-induced heat generation and heat transport in integrated on-chip plasmonic devices is of major importance. Specifically, there is a need for in situ visualization of electromagnetic induced thermal energy distribution with high spatial resolution. This paper studies the heat distribution in silicon plasmonic nanotips. Light is coupled to the plasmonic nanotips from a silicon nanowaveguide that is integrated with the tip on chip. Heat is generated by light absorption in the metal surrounding the silicon nanotip. The steady-state thermal distribution is studied numerically and measured experimentally using the approach of scanning thermal microscopy. It is shown that following the nanoscale heat generation by a 10 mW light source within a silicon photonic waveguide the temperature in the region of the nanotip is increased by ∼ 15 °C compared with the ambient temperature. Furthermore, we also perform a numerical study of the dynamics of the heat transport. Given the nanoscale dimensions of the structure, significant heating is expected to occur within the time frame of picoseconds. The capability of measuring temperature distribution of plasmonic structures at the nanoscale is shown to be a powerful tool and may be used in future applications related to thermal plasmonic applications such as control heating of liquids, thermal photovoltaic, nanochemistry, medicine, heat-assisted magnetic memories, and nanolithography.

Near field phase mapping exploiting intrinsic oscillations of aperture NSOM probe.

An innovative, simple, compact and low cost approach for phase mapping based on the intrinsic modulation of an aperture Near Field Scanning Optical Microscope probe is analyzed and experimentally demonstrated. Several nanoscale silicon waveguides are phase-mapped using this approach, and the different modes of propagation are obtained via Fourier analysis. The obtained measured results are in good agreement with the effective indexes of the modes calculated by electromagnetic simulations. Owing to its simplicity and effectiveness, the demonstrated system is a potential candidate for integration with current near field systems for the characterization of nanophotonic components and devices.

Nanoscale temperature mapping of photonic and plasmonic devices

We experimentally demonstrate nanoscale thermal mapping of light induced heat in photonic and plasmonic devices using a thermocouple AFM tip. Numerical simulations results and nanoscale temperature measurements are presented and discussed. © OSA 2013.

Near field phase mapping exploiting intrinsic oscillations of aperture NSOM probe

An innovative, simple, compact and low cost approach for phase mapping based on the intrinsic modulation of an aperture Near Field Scanning Optical Microscope probe is analyzed and experimentally demonstrated. Several nanoscale silicon waveguides are phase-mapped using this approach, and the different modes of propagation are obtained via Fourier analysis. The obtained measured results are in good agreement with the effective indexes of the modes calculated by electromagnetic simulations. Owing to its simplicity and effectiveness, the demonstrated system is a potential candidate for integration with current near field systems for the characterization of nanophotonic components and devices. © 2011 Optical Society of America.

Near field phase mapping exploiting intrinsic oscillations of NSOM probe

An innovative, simple compact and low cost approach for phase mapping based on the intrinsic modulation of a Near Field Scanning Optical Microscope probe is analyzed and experimentally demonstrated. © OSA/ CLEO 2011.