Exploiting symmetries in SDP-relaxations for polynomial optimization

In this paper we study various approaches for exploiting symmetries in polynomial optimization problems within the framework of semi definite programming relaxations. Our special focus is on constrained problems especially when the symmetric group is acting on the variables. In particular, we investigate the concept of block decomposition within the framework of constrained polynomial optimization problems, show how the degree principle for the symmetric group can be computationally exploited and also propose some methods to efficiently compute in the geometric quotient.Comment: (v3) Minor revision. To appear in Math. of Operations Researc

On the Potts model partition function in an external field

We study the partition function of Potts model in an external (magnetic) field, and its connections with the zero-field Potts model partition function. Using a deletion-contraction formulation for the partition function Z for this model, we show that it can be expanded in terms of the zero-field partition function. We also show that Z can be written as a sum over the spanning trees, and the spanning forests, of a graph G. Our results extend to Z the well-known spanning tree expansion for the zero-field partition function that arises though its connections with the Tutte polynomial

Revisiting the Local Scaling Hypothesis in Stably Stratified Atmospheric Boundary Layer Turbulence: an Integration of Field and Laboratory Measurements with Large-eddy Simulations

The `local scaling' hypothesis, first introduced by Nieuwstadt two decades ago, describes the turbulence structure of stable boundary layers in a very succinct way and is an integral part of numerous local closure-based numerical weather prediction models. However, the validity of this hypothesis under very stable conditions is a subject of on-going debate. In this work, we attempt to address this controversial issue by performing extensive analyses of turbulence data from several field campaigns, wind-tunnel experiments and large-eddy simulations. Wide range of stabilities, diverse field conditions and a comprehensive set of turbulence statistics make this study distinct

Religious transformations in the Middle Ages: towards a new archaeological agenda

The study of religious change in Europe between the collapse of the Roman Empire and the Reformation forms one of the cornerstones of medieval archaeology but has been riven by period, denominational and geographical divisions. This paper lays the groundwork for a fundamental rethink of archaeological approaches to medieval religions, by adopting a holistic framework that places Christian, pagan, Islamic and Jewish case studies of religious transformation in a long-term, comparative perspective. Focused around the analytical themes of ‘hybridity and resilience’ and ‘tempo and trajectories’, our approach shifts attention away from the singularities of national narratives of religious conversion towards a deeper understanding of how religious beliefs, practices and identity were renegotiated by medieval people in their daily lives

Visions of a more precise soil biology

Includes bibliographical references (pages 389-390).Soils have often been viewed as a black box. Soil biology is difficult to study with the precision we would wish, due to the presence of considerable soil heterogeneity, a huge diversity of organisms, and a plethora of interacting processes taking place in a complex physical-chemical environment. We have isolated a tiny fraction of the known organisms, and the possible interactions of soil parent materials, landscape, land use, depth and time with the biota mean that we are to some extent still fumbling in the dark. There have been great advances, but we argue that the pace of advance could be faster. To progress, science needs new theory and concepts but also acceptable methodologies. Coherent and generally accepted theoretical knowledge exists in many areas, but there is a shortage of valid and exact methods to test new and sometimes even old hypotheses. New methods add knowledge, but they also can add to the confusion if they are not tied to the existing knowledge base. We speculate on how to improve soil biology through improving the way we perform and interpret research. Can we deal with soil variability? Can we measure the critical variables with adequate precision to test our hypotheses? Can we avoid reinventing the wheel? Can we find a balance between the freedom to test new and maybe even controversial ideas and the control and direction of research required by society?

Temperature sensitivity of decomposition in relation to soil organic matter pools: Critique and outlook

Knorr et al. (2005) concluded that soil organic carbon pools with longer turnover times are more sensitive to temperature. We show that this conclusion is equivocal, largely dependent on their specific selection of data and does not persist when the data set of Kätterer et al. (1998) is analysed in a more appropriate way. Further, we analyse how statistical properties of the model parameters may interfere with correlative analyses that relate the Q 10 of soil respiration with the basal rate, where the latter is taken as a proxy for soil organic matter quality. We demonstrate that negative parameter correlations between Qio-values and base respiration rates are statistically expected and not necessarily provide evidence for a higher temperature sensitivity of low quality soil organic matter. Consequently, we propose it is premature to conclude that stable soil carbon is more sensitive to temperature than labile carbon

Temperature sensitivity of decomposition in relation to soil organic matter pools: Critique and outlook

Knorr et al. (2005) concluded that soil organic carbon pools with longer turnover times are more sensitive to temperature. We show that this conclusion is equivocal, largely dependent on their specific selection of data and does not persist when the data set of Kätterer et al. (1998) is analysed in a more appropriate way. Further, we analyse how statistical properties of the model parameters may interfere with correlative analyses that relate the Q 10 of soil respiration with the basal rate, where the latter is taken as a proxy for soil organic matter quality. We demonstrate that negative parameter correlations between Qio-values and base respiration rates are statistically expected and not necessarily provide evidence for a higher temperature sensitivity of low quality soil organic matter. Consequently, we propose it is premature to conclude that stable soil carbon is more sensitive to temperature than labile carbon

Fidelity of delivery and contextual factors influencing children’s level of engagement: Process evaluation of the Online Remote Behavioural Intervention for Tics (ORBIT) Trial (Preprint)

BACKGROUND: The Online Remote Behavioural Intervention for Tics (ORBIT) study was a multicentre randomized controlled trial of a complex intervention that consisted of an online behavioural intervention for children and young people (CYP) with tic disorders. In this first part of a two-stage process evaluation, we conducted a mixed-methods study exploring reach, dose, and fidelity of the intervention and contextual factors influencing engagement with the intervention. OBJECTIVE: This study aims to explore the fidelity of delivery and the contextual factors underpinning the ORBIT intervention. METHODS: Baseline study data and intervention usage metrics from participants in the intervention arm were used as quantitative implementation data (n=112). The experiences of being in the intervention were explored by semi-structured interviews with children (n=20) and parent (n=20) participants, therapists (n=4), and referring clinicians (n=6). A principal components analysis was used to create a comprehensive, composite measure of CYP’s engagement with the intervention. Engagement factor scores reflected relative uptake as assessed by a range of usage indices including chapters accessed, number of pages visited and number of logins. RESULTS: The intervention was implemented with high fidelity, and participants deemed the intervention acceptable and satisfactory. Engagement and adherence were high with child participants completing an average of 7.5/10 chapters and 100/112 (89.3%) participants completed a minimum of 4 chapters: the pre-defined threshold for effective dose. Compared to the total population of children with tic disorders, the sample tended to have more educated parents and live in more economically advantaged areas but socioeconomic factors were not related to engagement factor scores. Factors associated with higher engagement factor scores included participants enrolled at the London site vs. the Nottingham site (P=.011), self-referred vs. clinic-referred (P=.041), higher parental engagement as evidenced by number of parental chapters completed (ρ=0.73, n=111, P<.001) and more therapist time for parent (ρ=0.46, n=111, P<.001). A multiple linear regression indicated that parents’ chapter completion (β=.69, t110=10.18, P<.001) and therapist time for parent (β=.19, t110=2.95, P=.004) were the only significant independent predictors of engagement factor scores. CONCLUSIONS: Overall, the intervention had high fidelity of delivery and was evaluated positively by participants, although reach may have been constrained by the nature of the randomized controlled trial. Parental engagement and therapist time for parent were strong predictors of intervention implementation which has important implications for the design and implementation of digital therapeutic interventions into Child and Adolescent Mental Health Services. Clinical Trial: International Standard Randomized Controlled Trial Number (ISRCTN) 70758207; https://doi.org/10.1186/ISRCTN70758207 and ClinicalTrials.gov NCT03483493; https://clinicaltrials.gov/ct2/show/NCT0348349

Factors influencing the efficacy of an online behavioural intervention for children and young people with tics: Process evaluation of a randomised controlled trial

The Online Remote Behavioural Intervention for Tics (ORBIT) trial found that an internet-delivered, therapist-supported, and parent-assisted Exposure and Response Prevention (ERP) intervention reduced tic severity and improved clinical outcomes. This process evaluation aimed to explore mechanisms of impact and factors influencing efficacy. Participants were 112 children with a tic disorder and their parents randomised to the active intervention arm of the ORBIT trial. Child engagement was assessed by usage metrics and parent engagement by chapter completion. Experiences of the digital intervention were explored by semi-structured interviews. Outcomes (3-months post randomisation) were change in tic severity and overall clinical improvement. Tic severity reduced from baseline to 3-month follow-up and 36% were rated as much improved clinically. Greater tic severity at baseline predicted reduction in tic severity. Parental engagement was the only independent predictor of clinical improvement. There were no statistically significant mediators or moderators of the relationship between level of child engagement and outcome. From the qualitative findings, child participants appreciated working together with parents on the intervention and participants found the intervention engaging. ORBIT may be an effective and acceptable intervention for children and young people with tic disorders, with parental engagement being a key factor in successful outcomes