On the spectra and pseudospectra of a class of non-self-adjoint random matrices and operators

In this paper we develop and apply methods for the spectral analysis of non-selfadjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous deterministic matrices which are pseudo-ergodic in the sense of E. B. Davies (Commun. Math. Phys. 216 (2001), 687–704). As a major application to illustrate our methods we focus on the “hopping sign model” introduced by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433–6443), in which the main objects of study are random tridiagonal matrices which have zeros on the main diagonal and random ±1’s as the other entries. We explore the relationship between spectral sets in the finite and infinite matrix cases, and between the semi-infinite and bi-infinite matrix cases, for example showing that the numerical range and p-norm ε - pseudospectra (ε > 0, p ∈ [1,∞] ) of the random finite matrices converge almost surely to their infinite matrix counterparts, and that the finite matrix spectra are contained in the infinite matrix spectrum Σ. We also propose a sequence of inclusion sets for Σ which we show is convergent to Σ, with the nth element of the sequence computable by calculating smallest singular values of (large numbers of) n×n matrices. We propose similar convergent approximations for the 2-norm ε -pseudospectra of the infinite random matrices, these approximations sandwiching the infinite matrix pseudospectra from above and below.

Supporting visual assessment of food and nutrient intake in a clinical care setting

Monitoring nutritional intake is an important aspect of the care of older people, particularly for those at risk of malnutrition. Current practice for monitoring food intake relies on hand written food charts that have several inadequacies. We describe the design and validation of a tool for computer-assisted visual assessment of patient food and nutrient intake. To estimate food consumption, the application compares the pixels the user rubbed out against predefined graphical masks. Weight of food consumed is calculated as a percentage of pixels rubbed out against pixels in the mask. Results suggest that the application may be a useful tool for the conservative assessment of nutritional intake in hospitals.

Introducing matrix management within a children's services setting - personal reflections

This article reflects on the introduction of ‘matrix management’ arrangements for an Educational Psychology Service (EPS) within a Children’s Service Directorate of a Local Authority (LA). It seeks to demonstrate critical self-awareness, consider relevant literature with a view to bringing insights to processes and outcomes, and offers recommendations regarding the use of matrix management. The report arises from an East Midland’s LA initiative: ALICSE − Advanced Leadership in an Integrated Children’s Service Environment. Through a literature review and personal reflection, the authors consider the following: possible tensions within the development of matrix management arrangements; whether matrix management is a prerequisite within complex organizational systems; and whether competing professional cultures may contribute barriers to creating complementary and collegiate working. The authors briefly consider some research paradigms, notably ethnographic approaches, soft systems methodology, activity theory and appreciative inquiry. These provide an analytic framework for the project and inform this iterative process of collaborative inquiry. Whilst these models help illuminate otherwise hidden processes, none have been implemented following full research methodologies, reflecting the messy reality of local authority working within dynamic organizational structures and shrinking budgets. Nevertheless, this article offers an honest reflection of organizational change within a children’s services environment.

Sex/gender differences and autism: setting the scene for future research

Objective The relationship between sex/gender differences and autism has attracted a variety of research ranging from clinical, neurobiological to etiological, stimulated by the male bias in autism prevalence. Findings are complex and do not always relate to each other in a straightforward manner. Distinct but interlinked questions on the relationship between sex/gender differences and autism remain under addressed. To better understand the implications from existing research and to help design future studies, we propose a four-level conceptual framework to clarify the embedded themes. Method We searched PubMed for publications before September 2014 using search terms “‘sex OR gender OR females’ AND autism.” 1,906 citations were screened for relevance, along with publications identified via additional literature reviews, resulting in 329 reports that were reviewed. Results Level 1 “Nosological and diagnostic challenges” concerns the question “How should autism be defined and diagnosed in males and females?” Level 2 “Sex/gender-independent and sex/gender-dependent characteristics” addresses the question “What are the similarities and differences between males and females with autism?” Level 3 “General models of etiology: liability and threshold” asks the question “How is the liability for developing autism linked to sex/gender?” Level 4 “Specific etiological-developmental mechanisms” focuses on the question “What etiological-developmental mechanisms of autism are implicated by sex/gender and/or sexual/gender differentiation?” Conclusions Using this conceptual framework, findings can be more clearly summarized, and the implications of the links between findings from different levels can become clearer. Based on this four-level framework, we suggest future research directions, methodology, and specific topics in sex/gender differences and autism.

Sample preparation: a crucial factor for the analytical performance of rationally designed MALDI matrices

Evidence is presented that the performance of the rationally designed MALDI matrix 4-chloro-α-cyanocinnamic acid (ClCCA) in comparison to its well-established predecessor α-cyano-4-hydroxycinnamic acid (CHCA) is significantly dependent on the sample preparation, such as the choice of the target plate. In this context, it becomes clear that any rational designs of MALDI matrices and their successful employment have to consider a larger set of physicochemical parameters, including sample crystallization and morphology/topology, in addition to parameters of basic (solution and/or gas-phase) chemistry.

Commercial thickeners used by patients with dysphagia: rheological and structural behaviour in different food matrices

In order to achieve a safe swallowing in patients with dysphagia, liquids must be thickened. In this work, two commercial starch based thickeners dissolved in water, whole milk, apple juice and tomato juice were studied. The thickeners were Resource®, composed of modified maize starch and Nutilis®, composed of modified maize starch and gums. They were formulated at two different concentrations corresponding to nectar- and pudding-like consistencies. Influence of composition, concentration and food matrix on rheological properties and structure of the resulting pastes were analysed. Viscoelastic measurements and microscopic observations of the thickeners dissolved in water revealed structural differences due to the presence of gums. When the thickeners were dissolved in the other food matrices significant statistical interactions were found between the matrix and the thickener-type in both the viscoelastic and flow parameters. The most relevant differences were observed for the nectar-like consistency with Nutilis® thickener in milk and apple juice. These samples had lower zero viscosity values and higher loss tangent values, that corresponded to weaker structured systems. Light microscopy images showed that the matrix formed by swollen starch granules was interrupted by the presence of gums. The structure of the matrices in pudding-like formulations became more continuous irrespectively of the matrix employed, and also differences in viscoelasticity among samples diminished. Although differences were observed in zero shear viscosity values among samples, the viscosity of the beverages at 50 s−1 – commonly used as a reference for swallowing – was similar for all samples regardless of the matrix used.

The uniqueness of signature problem in the non-Markov setting

We establish a general framework for a class of multidimensional stochastic processes over [0,1] under which with probability one, the signature (the collection of iterated path integrals in the sense of rough paths) is well-defined and determines the sample paths of the process up to reparametrization. In particular, by using the Malliavin calculus we show that our method applies to a class of Gaussian processes including fractional Brownian motion with Hurst parameter H>1/4, the Ornstein–Uhlenbeck process and the Brownian bridge.

Understanding complexities in international accounting standard setting: agenda entry and the case of IFRS for SMEs

Earlier accounting works have shown that an understanding of agenda entry is critical to better understanding the accounting standards setting process. Consider Walker and Robinson (1993; 1994) and Ryan (1998); and more generally agenda entrance as theorized in Kingdon (2011). In 2003, the IASB placed on its agenda a project to promulgate a standard for small and medium-sized entities (SMEs). This provides our focus. It seemed to be a departure from the IASB’s constitutional focus on capital market participants. Kingdon’s three-streams model of agenda entry helps to identify some of the complexities related to politics and decision making messiness that resulted in a standard setting project for simplified IFRS, misleadingly titled IFRS for SMEs. Complexities relate to the broader international regulatory context, including the boundaries of the IASB’s standard-setting jurisdiction, the role of board members in changing those boundaries, and such sensitivities over the language that the IASB could not agree on a suitably descriptive title. The paper shows similarities with earlier agenda entrance studies by Walker and Robinson (1994) and Ryan (1998). By drawing on interviewees’ recollections and other material it especially reinforces the part played by the nuanced complexities that influence what emerges as an international accounting standard.

The environmental setting of Epipalaeolithic aggregation site Kharaneh IV

The archaeological site of Kharaneh IV in Jordan's Azraq Basin, and its relatively near neighbour Jilat 6 show evidence of sustained occupation of substantial size through the Early to Middle Epipalaeolithic (c. 24,000 - 15,000 cal BP). Here we review the geomorphological evidence for the environmental setting in which Kharaneh IV was established. The on-site stratigraphy is clearly differentiated from surrounding sediments, marked visually as well as by higher magnetic susceptibility values. Dating and analysis of off-site sediments show that a significant wetland existed at the site prior to and during early site occupation (~ 23,000 - 19,000 BP). This may explain why such a substantial site existed at this location. This wetland dating to the Last Glacial Maximum also provides important information on the palaeoenvironments and potential palaeoclimatic scenarios for today's eastern Jordanian desert, from where such evidence is scarce.

Low rank representation on Riemannian manifold of symmetric positive definite matrices

Sparse coding aims to find a more compact representation based on a set of dictionary atoms. A well-known technique looking at 2D sparsity is the low rank representation (LRR). However, in many computer vision applications, data often originate from a manifold, which is equipped with some Riemannian geometry. In this case, the existing LRR becomes inappropriate for modeling and incorporating the intrinsic geometry of the manifold that is potentially important and critical to applications. In this paper, we generalize the LRR over the Euclidean space to the LRR model over a specific Rimannian manifold—the manifold of symmetric positive matrices (SPD). Experiments on several computer vision datasets showcase its noise robustness and superior performance on classification and segmentation compared with state-of-the-art approaches.

Endogenous managerial compensation contracts in experimental quantity-setting duopolies

Given the ongoing debate on managerial compensation schemes, our paper offers empirical insights on the strategic choice of firms' owners over the terms of a managerial compensation contract, as a commitment device aiming at gaining competitive advantage in the product market. In a quantity setting duopoly we experimentally test whether firms' owners compensate their managers through contracts combining own profits either with revenues or with relative performance, and the resulting managerial behaviour in the product market. Prominent among our results is that firms' owners choose relative performance over profit revenue contracts more frequently. Further, firms' owners successfully induce a more aggressive behaviour by their managers in the market, by setting incentives which deviate from strict profit maximization.