Improved image set classification via joint sparse approximated nearest subspaces

Existing multi-model approaches for image set classification extract local models by clustering each image set individually only once, with fixed clusters used for matching with other image sets. However, this may result in the two closest clusters to represent different characteristics of an object, due to different undesirable environmental conditions (such as variations in illumination and pose). To address this problem, we propose to constrain the clustering of each query image set by forcing the clusters to have resemblance to the clusters in the gallery image sets. We first define a Frobenius norm distance between subspaces over Grassmann manifolds based on reconstruction error. We then extract local linear subspaces from a gallery image set via sparse representation. For each local linear subspace, we adaptively construct the corresponding closest subspace from the samples of a probe image set by joint sparse representation. We show that by minimising the sparse representation reconstruction error, we approach the nearest point on a Grassmann manifold. Experiments on Honda, ETH-80 and Cambridge-Gesture datasets show that the proposed method consistently outperforms several other recent techniques, such as Affine Hull based Image Set Distance (AHISD), Sparse Approximated Nearest Points (SANP) and Manifold Discriminant Analysis (MDA).

The 3rd Knowledge Cities World Summit Proceedings

FROM KCWS 2010 Ch airs and Summit Proceeding Ed ito rs ‘Knowledge’ is a resource, which relies on the past for a better future. In the 21st century, more than ever before, cities around the world depend on the knowledge of their citizens, their institutions and their firms and enterprises. The knowledge image, the human competence and the reputation of their public and private institutions and corporations profiles a city. It attracts investment, qualified labour and professionals, as well as students and researchers. And it creates local life spaces and professional milieus, which offer the quality of life to the citizens that are seeking to cope with the challenges of modern life in a competitive world. Integrating knowledge-based development in urban strategies and policies, beyond the provision of schools and locations for higher education, has become a new ambitious arena of city politics. Coming from theory to practice, and bringing together the manifold knowledge stakeholders in a city and preparing joint visions for the knowledge city is a new challenge for city managers, urban planners and leaders of the civic society . It requires visionary power, creativity, holistic thinking, the willingness to cooperate with all groups of the local civil society, and the capability to moderate communication processes to overcome conflicts and to develop joint action for a sustainable future. This timely Melbourne 2010 – The Third Knowledge City World Summit makes an important reminder that ‘knowledge’ is the key notion in the 21st Century development. Considering this notion, the summit aims to shed light on the multi-faceted dimensions and various scales of building the ‘knowledge city’ and on ‘knowledge-based development’ paradigms. At this summit, the theoretical and practical maturing of knowledge-based development paradigms will be advanced through the interplay between the world’s leading academic’s theories and the practical models and strategies of practitioners’ and policy makers’ drawn from around the world. As chairs of The Melbourne 2010 Summit, we have compiled this summit proceeding in order to disseminate the knowledge generated and shared in Melbourne with the wider research, governance, and practice communities. The papers in the proceedings reflect the broad range of contributions to the summit. They report on recent developments in planning and managing knowledge cities and ICT infrastructure, they assess the role of knowledge institutions in regional innovation systems and of the intellectual capital of cities and regions; they describe the evolution of knowledge-based approaches to urban development in differing cultural environments; they finally bridge the discourse on the knowledge city to other urban development paradigms such as the creative city, the ubiquitous city or the compact city. The diversity of papers presented shows how different scholars from planning cultures around the world interpret the knowledge dimension in urban and regional development. All papers of this proceeding have gone through a double-blind peer review process and been reviewed by our summit editorial review and advisory board members. We cordially thank the members of the Summit Proceeding Editorial Review and Advisory Board for their diligent work in the review of the papers. We hope the papers in this proceeding will inspire and make a significant contribution to the research, governance, and practice circles.

On the effect of topology on cellular automata rule spaces

This thesis presents an empirical study of the effects of topology on cellular automata rule spaces. The classical definition of a cellular automaton is restricted to that of a regular lattice, often with periodic boundary conditions. This definition is extended to allow for arbitrary topologies. The dynamics of cellular automata within the triangular tessellation were analysed when transformed to 2-manifolds of topological genus 0, genus 1 and genus 2. Cellular automata dynamics were analysed from a statistical mechanics perspective. The sample sizes required to obtain accurate entropy calculations were determined by an entropy error analysis which observed the error in the computed entropy against increasing sample sizes. Each cellular automata rule space was sampled repeatedly and the selected cellular automata were simulated over many thousands of trials for each topology. This resulted in an entropy distribution for each rule space. The computed entropy distributions are indicative of the cellular automata dynamical class distribution. Through the comparison of these dynamical class distributions using the E-statistic, it was identified that such topological changes cause these distributions to alter. This is a significant result which implies that both global structure and local dynamics play a important role in defining long term behaviour of cellular automata.

Wearable neuroimaging and emotion : investigating emotional responses to architectural environments with functional near-infrared spectroscopy (fNIRS)

Supported by contemporary theories of architectural aesthetics and neuro-aesthetics this paper presents a case for the use of portable fNIRS imaging in the assessment of emotional responses to spatial environments experienced by both blind and sighted. The aim of the paper is to outline the implications of fNIRS for spatial research and practice within the field of architecture, thereby suggesting a potential taxonomy of particular formations of space and affect. Empirical neurological study of affect and spatial experience from an architectural design perspective remains in many instances unchartered. Clinical research using the portable non-invasive neuro-imaging device, functional near infrared spectroscopy (fNIRS) is proving convincing in its ability to detect emotional responses to visual, spatio-auditory and task based stimuli, providing a firm basis to potentially track cortical activity in the appraisal of architectural environments. Additionally, recent neurological studies have sought to explore the manifold sensory abilities of the visually impaired to better understand spatial perception in general. Key studies reveal that early blind participants perform as well as sighted due to higher auditory and somato-sensory spatial acuity. For instance, face vision enables the visually impaired to detect environments through skin pressure, enabling at times an instantaneous impression of the layout of an unfamiliar environment. Studies also report pleasant and unpleasant emotional responses such as ‘weightedness’ or ‘claustrophobia’ within certain interior environments, revealing a deeper perceptual sensitivity then would be expected. We conclude with justification that comparative fNIRS studies between the sighted and blind concerning spatial experience have the potential to provide greater understanding of emotional responses to architectural environments.

Emotion and architectural environments : a case for Functional Near Infrared Spectroscopy (fNIRS) in assessing emotional responses to spatial environments

Collaboration between neuroscience and architecture is emerging as a key field of research as demonstrated in recent times by development of the Academy of Neuroscience for Architecture (ANFA) and other societies. Neurological enquiry of affect and spatial experience from a design perspective remains in many instances unchartered. Research using portable near infrared spectroscopy (fNIRs) - an emerging non-invasive neuro-imaging device, is proving convincing in its ability to detect emotional responses to visual, spatio-auditory and task based stimuli. This innovation provides a firm basis to potentially track cortical activity in the appraisal of architectural environments. Additionally, recent neurological studies have sought to explore the manifold sensory abilities of the visually impaired to better understand spatial perception in general. Key studies reveal that early blind participants perform as well as sighted due to higher auditory and somato-sensory spatial acuity. Studies also report pleasant and unpleasant emotional responses within certain interior environments revealing a deeper perceptual sensitivity than would be expected. Comparative fNIRS studies between the sighted and blind concerning spatial experience has the potential to provide greater understanding of emotional responses to architectural environments. Supported by contemporary theories of architectural aesthetics, this paper presents a case for the use of portable fNIRS imaging in the assessment of emotional responses to spatial environments experienced by both blind and sighted. The aim of the paper is to outline the implications of fNIRS upon spatial research and practice within the field of architecture and points to a potential taxonomy of particular formations of space and affect.

Novel solutions for a model of wound healing angiogenesis

We prove the existence of novel, shock-fronted travelling wave solutions to a model of wound healing angiogenesis studied in Pettet et al (2000 IMA J. Math. App. Med. 17 395–413) assuming two conjectures hold. In the previous work, the authors showed that for certain parameter values, a heteroclinic orbit in the phase plane representing a smooth travelling wave solution exists. However, upon varying one of the parameters, the heteroclinic orbit was destroyed, or rather cut-off, by a wall of singularities in the phase plane. As a result, they concluded that under this parameter regime no travelling wave solutions existed. Using techniques from geometric singular perturbation theory and canard theory, we show that a travelling wave solution actually still exists for this parameter regime. We construct a heteroclinic orbit passing through the wall of singularities via a folded saddle canard point onto a repelling slow manifold. The orbit leaves this manifold via the fast dynamics and lands on the attracting slow manifold, finally connecting to its end state. This new travelling wave is no longer smooth but exhibits a sharp front or shock. Finally, we identify regions in parameter space where we expect that similar solutions exist. Moreover, we discuss the possibility of more exotic solutions.

Butterfly catastrophe for fronts in a three-component reaction–diffusion system

We study the dynamics of front solutions in a three-component reaction–diffusion system via a combination of geometric singular perturbation theory, Evans function analysis, and center manifold reduction. The reduced system exhibits a surprisingly complicated bifurcation structure including a butterfly catastrophe. Our results shed light on numerically observed accelerations and oscillations and pave the way for the analysis of front interactions in a parameter regime where the essential spectrum of a single front approaches the imaginary axis asymptotically.

Book Review: "Gender and Global Justice edited by Alison M. Jaggar, Cambridge: Polity Press, 2014"

Hidden aspects of assumed gender-neutral global policies and transnational institutions that have “systematically disparate and often burdensome consequences for specific groups of women in both the global North and the global South” (10) are the focus of Gender and Global Justice edited by Alison M Jagger. In response to the frequent neglect of gender in considerations of moral philosophy in global issues, the chapters assembled in this edited collection highlight the manifold ways in which our attention to a broad range of questions of justice at a global level is enhanced by close attention to the gendered dimensions of injustice and inequality.

Comparison of fractional and geodesic anisotropy in diffusion tensor images of 90 monozygotic and dizygotic twins

We used diffusion tensor magnetic resonance imaging (DTI) to reveal the extent of genetic effects on brain fiber microstructure, based on tensor-derived measures, in 22 pairs of monozygotic (MZ) twins and 23 pairs of dizygotic (DZ) twins (90 scans). After Log-Euclidean denoising to remove rank-deficient tensors, DTI volumes were fluidly registered by high-dimensional mapping of co-registered MP-RAGE scans to a geometrically-centered mean neuroanatomical template. After tensor reorientation using the strain of the 3D fluid transformation, we computed two widely used scalar measures of fiber integrity: fractional anisotropy (FA), and geodesic anisotropy (GA), which measures the geodesic distance between tensors in the symmetric positive-definite tensor manifold. Spatial maps of intraclass correlations (r) between MZ and DZ twins were compared to compute maps of Falconer's heritability statistics, i.e. the proportion of population variance explainable by genetic differences among individuals. Cumulative distribution plots (CDF) of effect sizes showed that the manifold measure, GA, comparably the Euclidean measure, FA, in detecting genetic correlations. While maps were relatively noisy, the CDFs showed promise for detecting genetic influences on brain fiber integrity as the current sample expands.

The multivariate A/C/E model and the genetics of fiber architecture

We present a new algorithm to compute the voxel-wise genetic contribution to brain fiber microstructure using diffusion tensor imaging (DTI) in a dataset of 25 monozygotic (MZ) twins and 25 dizygotic (DZ) twin pairs (100 subjects total). First, the structural and DT scans were linearly co-registered. Structural MR scans were nonlinearly mapped via a 3D fluid transformation to a geometrically centered mean template, and the deformation fields were applied to the DTI volumes. After tensor re-orientation to realign them to the anatomy, we computed several scalar and multivariate DT-derived measures including the geodesic anisotropy (GA), the tensor eigenvalues and the full diffusion tensors. A covariance-weighted distance was measured between twins in the Log-Euclidean framework [2], and used as input to a maximum-likelihood based algorithm to compute the contributions from genetics (A), common environmental factors (C) and unique environmental ones (E) to fiber architecture. Quanititative genetic studies can take advantage of the full information in the diffusion tensor, using covariance weighted distances and statistics on the tensor manifold.

Visualization tools for high angular resolution diffusion imaging

There is a major effort in medical imaging to develop algorithms to extract information from DTI and HARDI, which provide detailed information on brain integrity and connectivity. As the images have recently advanced to provide extraordinarily high angular resolution and spatial detail, including an entire manifold of information at each point in the 3D images, there has been no readily available means to view the results. This impedes developments in HARDI research, which need some method to check the plausibility and validity of image processing operations on HARDI data or to appreciate data features or invariants that might serve as a basis for new directions in image segmentation, registration, and statistics. We present a set of tools to provide interactive display of HARDI data, including both a local rendering application and an off-screen renderer that works with a web-based viewer. Visualizations are presented after registration and averaging of HARDI data from 90 human subjects, revealing important details for which there would be no direct way to appreciate using conventional display of scalar images.

Analyzing multi-fiber reconstruction in high angular resolution diffusion imaging using the tensor distribution function

High-angular resolution diffusion imaging (HARDI) can reconstruct fiber pathways in the brain with extraordinary detail, identifying anatomical features and connections not seen with conventional MRI. HARDI overcomes several limitations of standard diffusion tensor imaging, which fails to model diffusion correctly in regions where fibers cross or mix. As HARDI can accurately resolve sharp signal peaks in angular space where fibers cross, we studied how many gradients are required in practice to compute accurate orientation density functions, to better understand the tradeoff between longer scanning times and more angular precision. We computed orientation density functions analytically from tensor distribution functions (TDFs) which model the HARDI signal at each point as a unit-mass probability density on the 6D manifold of symmetric positive definite tensors. In simulated two-fiber systems with varying Rician noise, we assessed how many diffusionsensitized gradients were sufficient to (1) accurately resolve the diffusion profile, and (2) measure the exponential isotropy (EI), a TDF-derived measure of fiber integrity that exploits the full multidirectional HARDI signal. At lower SNR, the reconstruction accuracy, measured using the Kullback-Leibler divergence, rapidly increased with additional gradients, and EI estimation accuracy plateaued at around 70 gradients.

Infinite Dimensional Slow Modulations In A Delayed Model For Orthogonal Cutting Vibrations

We apply the method of multiple scales (MMS) to a well known model of regenerative cutting vibrations in the large delay regime. By ``large'' we mean the delay is much larger than the time scale of typical cutting tool oscillations. The MMS upto second order for such systems has been developed recently, and is applied here to study tool dynamics in the large delay regime. The second order analysis is found to be much more accurate than first order analysis. Numerical integration of the MMS slow flow is much faster than for the original equation, yet shows excellent accuracy. The main advantage of the present analysis is that infinite dimensional dynamics is retained in the slow flow, while the more usual center manifold reduction gives a planar phase space. Lower-dimensional dynamical features, such as Hopf bifurcations and families of periodic solutions, are also captured by the MMS. Finally, the strong sensitivity of the dynamics to small changes in parameter values is seen clearly.

Efficient Output-Sensitive Construction of Reeb Graphs

The Reeb graph tracks topology changes in level sets of a scalar function and finds applications in scientific visualization and geometric modeling. This paper describes a near-optimal two-step algorithm that constructs the Reeb graph of a Morse function defined over manifolds in any dimension. The algorithm first identifies the critical points of the input manifold, and then connects these critical points in the second step to obtain the Reeb graph. A simplification mechanism based on topological persistence aids in the removal of noise and unimportant features. A radial layout scheme results in a feature-directed drawing of the Reeb graph. Experimental results demonstrate the efficiency of the Reeb graph construction in practice and its applications.

NMR-Studies of Octahedral Dicyano-(2,2' Bipyridine) and Tetracyano-(2,2'-Bipyridine) Iron(ii) Complexes

Coordination compounds of the polypyridines, 2,2 ' -bipyridine (bipy) and 1,10-penanthroline (phen) have offered renewed interest on account of their manifold applications and from the point of view of understanding their structure-reactivity relationships.1 Iron(II) reacts with them to form tris-complexes possessing spin-paired ground states. Cyanide ion greatly enhances the rate of displacement of bipy or phen to form the Schilt class of compounds. Fe(bipy)2(CN)2 and Fe(phen)2(CN)2. They display varying colours in solution depending upon the nature of the solvent and react reversibly with acids to form diprotonated species.2 Magnetic circular dichroism studies have been reported to describe their lowest electronic excitation.