Perturbation, extraction and refinement of invariant pairs for matrix polynomials

Generalizing the notion of an eigenvector, invariant subspaces are frequently used in the context of linear eigenvalue problems, leading to conceptually elegant and numerically stable formulations in applications that require the computation of several eigenvalues and/or eigenvectors. Similar benefits can be expected for polynomial eigenvalue problems, for which the concept of an invariant subspace needs to be replaced by the concept of an invariant pair. Little has been known so far about numerical aspects of such invariant pairs. The aim of this paper is to fill this gap. The behavior of invariant pairs under perturbations of the matrix polynomial is studied and a first-order perturbation expansion is given. From a computational point of view, we investigate how to best extract invariant pairs from a linearization of the matrix polynomial. Moreover, we describe efficient refinement procedures directly based on the polynomial formulation. Numerical experiments with matrix polynomials from a number of applications demonstrate the effectiveness of our extraction and refinement procedures.

The management of positive inter-store externalities in shopping centres: some empirical evidence

In enclosed shopping centres, stores benefit from the positive externalities of other stores in the centre. Some stores provide greater benefits to their neighbours than others – for example anchor tenants and brand leading stores. In managing shopping centres, these positive externalities might be captured through rental variations. This paper explores the determinants of rent – including externalities – for UK regional shopping centres. Two linked databases were utilised in the research. One contains characteristics of 148 shopping centres; the other has some 1,930 individual tenant records including rent level. These data were analysed to provide information on the characteristics of centres and retailers that help determine rent. Factors influencing tenant rents include market potential factors derived from urban and regional economic theory and shopping centre characteristics identified in prior retail research. The model also includes variables that proxy for the interaction between tenants and the impact of positive in-centre externalities. We find that store size is significantly and negatively related to tenant with both anchor and other larger tenants, perhaps as a result of the positive effects generated by their presence, paying relatively lower rents while smaller stores, benefiting from the generation of demand, pay relatively higher rents. Brand leader tenants pay lower rents than other tenants within individual retail categories.

Social networks and positive and negative affect

We followed 100 university students in the UK for one week, instructing them to record all face-to-face, phone and digital contacts during the day as well as their positive and negative affect. We wanted to see how positive and negative affect spread around a social network while taking into account participants’ socio-demographic data, personality, general health and gratitude scores. We focused on the participants’ connections with those in their class; excluding friends and family outside this group. The data was analysed using actor-based models implemented in SIENA. Results show differences between positive and negative affect dynamics in this environment and an influence of personality traits on the average number and rate of communication.

Evaluation of the environmental specificity of fluorescence in situ hybridization (FISH) using fluorescence-activated cell sorting (FACS) of probe (PSE1284)-positive cells extracted from rhizosphere soil

We explicitly tested for the first time the ‘environmental specificity’ of traditional 16S rRNAtargeted fluorescence in situ hybridization (FISH) through comparison of the bacterial diversity actually targeted in the environment with the diversity that should be exactly targeted (i.e. without mismatches) according to in silico analysis. To do this, we exploited advances in modern Flow Cytometry that enabled improved detection and therefore sorting of sub-micron-sized particles and used probe PSE1284 (designed to target Pseudomonads) applied to Lolium perenne rhizosphere soil as our test system. The 6-carboxyfluorescein (6-FAM)-PSE1284-hybridised population, defined as displaying enhanced green fluorescence in Flow Cytometry, represented 3.51±1.28% of the total detected population when corrected using a nonsense (NON-EUB338) probe control. Analysis of 16S rRNA gene libraries constructed from Fluorescence Activated Cell Sorted (FACS) -recovered fluorescent populations (n=3), revealed that 98.5% (Pseudomonas spp. comprised 68.7% and Burkholderia spp. 29.8%) of the total sorted population was specifically targeted as evidenced by the homology of the 16S rRNA sequences to the probe sequence. In silico evaluation of probe PSE1284 with the use of RDP-10 probeMatch justified the existence of Burkholderia spp. among the sorted cells. The lack of novelty in Pseudomonas spp. sequences uncovered was notable, probably reflecting the well-studied nature of this functionally important genus. To judge the diversity recorded within the FACS-sorted population, rarefaction and DGGE analysis were used to evaluate, respectively, the proportion of Pseudomonas diversity uncovered by the sequencing effort and the representativeness of the Nycodenz® method for the extraction of bacterial cells from soil.

Easing transition and promoting a positive student experience within an international partnership scheme for British and Chinese teachers

This article investigates the needs and challenges of a group of Chinese secondary school teachers in their transition to postgraduate studies in the UK in the context of a British-Chinese partnership. The strategies and efforts of the host institution, local community and the Chinese students themselves to help ease the transition and promote a positive student experience are discussed. The article highlights the sociological processes of international postgraduate student transition and contributes to our understanding of issues of student support pertinent to international partnership arrangements.

Robust eigenstructure assignment in quadratic matrix polynomials: nonsingular case

Feedback design for a second-order control system leads to an eigenstructure assignment problem for a quadratic matrix polynomial. It is desirable that the feedback controller not only assigns specified eigenvalues to the second-order closed loop system but also that the system is robust, or insensitive to perturbations. We derive here new sensitivity measures, or condition numbers, for the eigenvalues of the quadratic matrix polynomial and define a measure of the robustness of the corresponding system. We then show that the robustness of the quadratic inverse eigenvalue problem can be achieved by solving a generalized linear eigenvalue assignment problem subject to structured perturbations. Numerically reliable methods for solving the structured generalized linear problem are developed that take advantage of the special properties of the system in order to minimize the computational work required. In this part of the work we treat the case where the leading coefficient matrix in the quadratic polynomial is nonsingular, which ensures that the polynomial is regular. In a second part, we will examine the case where the open loop matrix polynomial is not necessarily regular.

Can Rachman’s indirect pathways be used to un-learn fear? A prospective paradigm to test whether children’s fears can be reduced using positive information and modelling a non-anxious response

This study investigated whether children’s fears could be un-learned using Rachman’s indirect pathways for learning fear. We hypothesised that positive information and modelling a non-anxious response are effective methods of un-learning fears acquired through verbal information. One hundred and seven children aged 6–8 years received negative information about one animal and no information about another. Fear beliefs and behavioural avoidance were measured. Children were randomised to receive positive verbal information, modelling, or a control task. Fear beliefs and behavioural avoidance were measured again. Positive information and modelling led to lower fear beliefs and behavioural avoidance than the control condition. Positive information was more effective than modelling in reducing fear beliefs and both methods significantly reduced behavioural avoidance. The results support Rachman’s indirect pathways as viable fear un-learning pathways and supports associative learning theories.

Relationships between changes in sustained fronto-striatal connectivity and positive affect with antidepressant treatment in major depression

Objective: Deficits in positive affect and their neural bases have been associated with major depression. However, whether reductions in positive affect result solely from an overall reduction in nucleus accumbens activity and fronto-striatal connectivity or the additional inability to sustain engagement of this network over time is unknown. The authors sought to determine whether treatment-induced changes in the ability to sustain nucleus accumbens activity and fronto-striatal connectivity during the regulation of positive affect are associated with gains in positive affect. Method: Using fMRI, the authors assessed the ability to sustain activity in reward-related networks when attempting to increase positive emotion during per- formance of an emotion regulation para- digm in 21 depressed patients before and after 2 months of antidepressant treat- ment. Over the same interval, 14 healthy comparison subjects underwent scanning as well. Results: After 2 months of treatment, self-reported positive affect increased. The patients who demonstrated the largest increases in sustained nucleus accumbens activity over the 2 months were those who demonstrated the largest increases in positive affect. In addition, the patients who demonstrated the largest increases in sustained fronto-striatal connectivity were also those who demonstrated the largest increases in positive affect when control- ling for negative affect. None of these associations were observed in healthy comparison subjects. Conclusions: Treatment-induced change in the sustained engagement of fronto- striatal circuitry tracks the experience of positive emotion in daily life. Studies examining reduced positive affect in a va- riety of psychiatric disorders might benefit from examining the temporal dynamics of brain activity when attempting to under- stand changes in daily positive affect.

Whole-brain functional connectivity during emotional word classification in medication-free Major Depressive Disorder: abnormal salience circuitry and relations to positive emotionality

Major Depressive Disorder (MDD) has been associated with biased processing and abnormal regulation of negative and positive information, which may result from compromised coordinated activity of prefrontal and subcortical brain regions involved in evaluating emotional information. We tested whether patients with MDD show distributed changes in functional connectivity with a set of independently derived brain networks that have shown high correspondence with different task demands, including stimulus salience and emotional processing. We further explored if connectivity during emotional word processing related to the tendency to engage in positive or negative emotional states. In this study, 25 medication-free MDD patients without current or past comorbidity and matched controls (n=25) performed an emotional word-evaluation task during functional MRI. Using a dual regression approach, individual spatial connectivity maps representing each subject’s connectivity with each standard network were used to evaluate between-group differences and effects of positive and negative emotionality (extraversion and neuroticism, respectively, as measured with the NEO-FFI). Results showed decreased functional connectivity of the medial prefrontal cortex, ventrolateral prefrontal cortex, and ventral striatum with the fronto-opercular salience network in MDD patients compared to controls. In patients, abnormal connectivity was related to extraversion, but not neuroticism. These results confirm the hypothesis of a relative (para)limbic-cortical decoupling that may explain dysregulated affect in MDD. As connectivity of these regions with the salience network was related to extraversion, but not to general depression severity or negative emotionality, dysfunction of this network may be responsible for the failure to sustain engagement in rewarding behavior.