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.

Rejection thresholds (RjT) of sweet likers and dislikers

Sweetness is generally a desirable taste, however consumers can be grouped into sweet likers and dislikers according to optimally preferred sucrose concentrations. Understanding the levels of sweetness in products that are acceptable and unacceptable to both consumer groups is important to product development and for influencing dietary habits. The concentrations at which sucrose decreases liking (the rejection threshold; RjT) in liquid and semi-solid matrices were investigated in this study. Thirty six consumers rated their liking of 5 sucrose aqueous solutions; this identified 36% sweet likers (SL) whose liking ratings increased with increasing sucrose and 64% sweet dislikers (SD) whose liking ratings decreased above 6% (w/v) sucrose. We hypothesized that SL and SD would have different RjT for sucrose in products. This was tested by preparing 8 levels of sucrose in orange juice and orange jelly and presenting each against the lowest level in forced choice preference tests. In orange juice, as sucrose increased from 33g/L to 75g/L the proportion of people preferring the sweeter sample increased in both groups. However, at higher sucrose levels, the proportion of consumers preferring the sweet sample decreased. For SD, a RjT was reached at 380 g/L, whereas a significant RjT for SL was not reached. RjT in jelly were not reached as the sweetness in orange jelly was significantly lower than for orange juice (p<0.001). Despite statistically significant differences in rated sweetness between SL and SD (p=0.019), the extent of difference between the two groups was minor. The results implied that sweet liker status was not substantially related to differences in sweetness perception. Self-reported dietary intake of carbohydrate, sugars and sucrose were not significantly affected by sweet liker status. However the failure to find an effect may be due to the small sample size and future studies within a larger, more representative population sample are justifiable from the results of this study.

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.

Interactive effect of floral abundance and semi-natural habitats on pollinators in field beans (Vicia faba)

Pollination services are economically important component of agricultural biodiversity which enhance the yield and quality of many crops. An understanding of the suitability of extant habitats for pollinating species is crucial for planning management actions to protect and manage these service providers. In a highly modified agricultural ecosystem, we tested the effect of different pollination treatments (open, autonomous self- and wind-pollination) on pod set, seed set, and seed weight in field beans (Vicia faba). We also investigated the effect of semi-natural habitats and flower abundance on pollinators of field beans. Pollinator sampling was undertaken in ten field bean fields along a gradient of habitat complexity; CORINE land cover classification was used to analyse the land use patterns between 500–3000 m around the sites. Total yield from open-pollination increased by 185% compared to autonomous self-pollination. There was positive interactive effect of local flower abundance and cover of semi-natural habitats on overall abundance of pollinators at 1500 and 2000 m, and abundance of bumblebees (Bombus spp.) at 1000–2000 m. In contrast, species richness of pollinators was only correlated with flower abundance and not with semi-natural habitats. We did not find a link between pod set from open-pollination and pollinator abundance, possibly due to variations in the growing conditions and pollinator communities between sites. We conclude that insect pollination is essential for optimal bean yields and therefore the maintenance of semi-natural habitats in agriculture-dominated landscapes should ensure stable and more efficient pollination services in field beans.

A model analysis of climate and CO2 controls on tree growth in a semi-arid woodland

We used a light-use efficiency model of photosynthesis coupled with a dynamic carbon allocation and tree-growth model to simulate annual growth of the gymnosperm Callitris columellaris in the semi-arid Great Western Woodlands, Western Australia, over the past 100 years. Parameter values were derived from independent observations except for sapwood specific respiration rate, fine-root turnover time, fine-root specific respiration rate and the ratio of fine-root mass to foliage area, which were estimated by Bayesian optimization. The model reproduced the general pattern of interannual variability in radial growth (tree-ring width), including the response to the shift in precipitation regimes that occurred in the 1960s. Simulated and observed responses to climate were consistent. Both showed a significant positive response of tree-ring width to total photosynthetically active radiation received and to the ratio of modeled actual to equilibrium evapotranspiration, and a significant negative response to vapour pressure deficit. However, the simulations showed an enhancement of radial growth in response to increasing atmospheric CO2 concentration (ppm) ([CO2]) during recent decades that is not present in the observations. The discrepancy disappeared when the model was recalibrated on successive 30-year windows. Then the ratio of fine-root mass to foliage area increases by 14% (from 0.127 to 0.144 kg C m-2) as [CO2] increased while the other three estimated parameters remained constant. The absence of a signal of increasing [CO2] has been noted in many tree-ring records, despite the enhancement of photosynthetic rates and water-use efficiency resulting from increasing [CO2]. Our simulations suggest that this behaviour could be explained as a consequence of a shift towards below-ground carbon allocation.

A randomised controlled trial of positive memory training for the treatment of depression within schizophrenia

Abstract Background: Depression is highly prevalent within individuals diagnosed with schizophrenia, and is associated with an increased risk of suicide. There are no current evidence based treatments for low mood within this group. The specific targeting of co-morbid conditions within complex mental health problems lends itself to the development of short-term structured interventions which are relatively easy to disseminate within health services. A brief cognitive intervention based on a competitive memory theory of depression, is being evaluated in terms of its effectiveness in reducing depression within this group. Methods/Design: This is a single blind, intention-to-treat, multi-site, randomized controlled trial comparing Positive Memory Training plus Treatment as Usual with Treatment as Usual alone. Participants will be recruited from two NHS Trusts in Southern England. In order to be eligible, participants must have a DSM-V diagnosis of schizophrenia or schizo-affective disorder and exhibit at least a mild level of depression. Following baseline assessment eligible participants will be randomly allocated to either the Positive Memory Training plus Treatment as Usual group or the Treatment as Usual group. Outcome will be assessed at the end of treatment (3-months) and at 6-month and 9-month post randomization by assessors blind to group allocation. The primary outcome will be levels of depression and secondary outcomes will be severity of psychotic symptoms and cost-effectiveness. Semi-structured interviews will be conducted with all participants who are allocated to the treatment group so as to explore the acceptability of the intervention. Discussion: Cognitive behaviour therapy is recommended for individuals diagnosed with schizophrenia. However, the number of sessions and length of training required to deliver this intervention has caused a limit in availability. The current trial will evaluate a short-term structured protocol which targets a co-morbid condition often considered of primary importance by service users. If successful the intervention will be an important addition to current initiatives aimed at increasing access to psychological therapies for people diagnosed with severe mental health problems. Trial registration: Current Controlled Trials. ISRCTN99485756. Registered 13 March 2014.