What is a 4-connected matroid?

The breadth of a tangle $\mathcal{T}$ in a matroid is the size of the largest spanning uniform submatroid of the tangle matroid of $\mathcal{T}$. The matroid $M$ is weakly 4-connected if it is 3-connected and whenever $(X,Y)$ is a partition of $E(M)$ with $|X|,|Y|>4$, then $\lambda(X)\geq 3$. We prove that if $\mathcal{T}$ is a tangle of order $k\geq 4$ and breadth $l$ in a matroid $M$, then $M$ has a weakly 4-connected minor $N$ with a tangle $\mathcal{T}_N$ of order $k$, breadth $l$ and has the property that $\mathcal{T}$ is the tangle in $M$ induced by $\mathcal{T}_N$. A set $Z$ of elements of a matroid $M$ is 4-connected if $\lambda(A)\geq\min\{|A\cap Z|,|Z-A|,3\}$ for all $A\subseteq E(M)$. As a corollary of our theorems on tangles we prove that if $M$ contains an $n$-element 4-connected set where $n\geq 7$, then $M$ has a weakly $4$-connected minor that contains an $n$-element $4$-connected set.Comment: 34 page

Protocol for Past BP: a randomised controlled trial of different blood pressure targets for people with a history of stroke of transient ischaemic attack (TIA) in primary care.

BACKGROUND: Blood pressure (BP) lowering in people who have had a stroke or transient ischaemic attack (TIA) leads to reduced risk of further stroke. However, it is not clear what the target BP should be, since intensification of therapy may lead to additional adverse effects. PAST BP will determine whether more intensive BP targets can be achieved in a primary care setting, and whether more intensive therapy is associated with adverse effects on quality of life. METHODS/DESIGN: This is a randomised controlled trial (RCT) in patients with a past history of stroke or TIA. Patients will be randomised to two groups and will either have their blood pressure (BP) lowered intensively to a target of 130 mmHg systolic, (or by 10 mmHg if the baseline systolic pressure is between 125 and 140 mmHg) compared to a standard group where the BP will be reduced to a target of 140 mmHg systolic. Patients will be managed by their practice at 1-3 month intervals depending on level of BP and followed-up by the research team at six monthly intervals for 12 months.610 patients will be recruited from approximately 50 general practices. The following exclusion criteria will be applied: systolic BP <125 mmHg at baseline, 3 or more anti-hypertensive agents, orthostatic hypotension, diabetes mellitus with microalbuminuria or other condition requiring a lower treatment target or terminal illness.The primary outcome will be change in systolic BP over twelve months. Secondary outcomes include quality of life, adverse events and cardiovascular events.In-depth interviews with 30 patients and 20 health care practitioners will be undertaken to investigate patient and healthcare professionals understanding and views of BP management. DISCUSSION: The results of this trial will inform whether intensive blood pressure targets can be achieved in people who have had a stroke or TIA in primary care, and help determine whether or not further research is required before recommending such targets for this population. TRIAL REGISTRATION: ISRCTN29062286.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

The Beaker phenomenon and the genomic transformation of northwest Europe

From around 2750 to 2500 bc, Bell Beaker pottery became widespread across western and central Europe, before it disappeared between 2200 and 1800 bc. The forces that propelled its expansion are a matter of long-standing debate, and there is support for both cultural diffusion and migration having a role in this process. Here we present genome-wide data from 400 Neolithic, Copper Age and Bronze Age Europeans, including 226 individuals associated with Beaker-complex artefacts. We detected limited genetic affinity between Beaker-complex-associated individuals from Iberia and central Europe, and thus exclude migration as an important mechanism of spread between these two regions. However, migration had a key role in the further dissemination of the Beaker complex. We document this phenomenon most clearly in Britain, where the spread of the Beaker complex introduced high levels of steppe-related ancestry and was associated with the replacement of approximately 90% of Britain’s gene pool within a few hundred years, continuing the east-to-west expansion that had brought steppe-related ancestry into central and northern Europe over the previous centuries

Linking perfectionism with moral behaviours in sport: The mediating role of burnout and moral disengagement

Purpose: Research has identified a range of intrapersonal variables associated with moral behaviours in sport. However, research investigating how perfectionism and burnout are associated with prosocial and antisocial behaviour toward teammates and opponents in sport has received scant attention. In the present study, we addressed this issue by examining whether perfectionism was associated with prosocial and antisocial behaviour in sport directly and indirectly via burnout and moral disengagement. Method: A total of 312 team sport players completed validated measures for each variable. Results: Path analyses revealed that perfectionistic concerns had a negative relationship with prosocial behaviour toward teammates, and an indirect positive association with antisocial behaviour toward both teammates and opponents via being positively associated with burnout, which in turn, was positively associated with moral disengagement. In contrast, perfectionistic strivings had a positive association with prosocial behaviour toward teammates, and an indirect positive association with antisocial behaviour toward teammates and opponents via moral disengagement. Conclusion: Our findings offer new insights about how perfectionism and burnout are associated with prosocial and antisocial behaviour in sport as well as highlight the need to consider perfectionistic tendencies and approaches to help reduce burnout and moral disengagement in the regulation of antisocial behaviour in sport

Modeling the Formation of Transverse Weld during Billet-on-Billet Extrusion

A comprehensive mathematical model of the hot extrusion process for aluminum alloys has been developed and validated. The plasticity module was developed using a commercial finite element package, DEFORM-2D, a transient Lagrangian model which couples the thermal and deformation phenomena. Validation of the model against industrial data indicated that it gave excellent predictions of the pressure during extrusion. The finite element predictions of the velocity fields were post-processed to calculate the thickness of the surface cladding as one billet is fed in after another through the die (i.e., the transverse weld). The mathematical model was then used to assess the effect a change in feeder dimensions would have on the shape, thickness and extent of the transverse weld during extrusion. Experimental measurements for different combinations of billet materials show that the model is able to accurately predict the transverse weld shape as well as the clad surface layer to thicknesses of 50 µm. The transverse weld is significantly affected by the feeder geometry shape, but the effects of ram speed, billet material and temperature on the transverse weld dimensions are negligible.Applied Science, Faculty ofNon UBCMaterials Engineering, Department ofReviewedFacult

Effect of feeder pocket geometry on the streaking tendency of 6xxx extrusions

NRC publication: Ye

ILC1 drive intestinal epithelial and matrix remodelling

Organoids can shed light on the dynamic interplay between complex tissues and rare cell types within a controlled microenvironment. Here, we develop gut organoid cocultures with type-1 innate lymphoid cells (ILC1) to dissect the impact of their accumulation in inflamed intestines. We demonstrate that murine and human ILC1 secrete transforming growth factor β1, driving expansion of CD44v6+ epithelial crypts. ILC1 additionally express MMP9 and drive gene signatures indicative of extracellular matrix remodelling. We therefore encapsulated human epithelial–mesenchymal intestinal organoids in MMP-sensitive, synthetic hydrogels designed to form efficient networks at low polymer concentrations. Harnessing this defined system, we demonstrate that ILC1 drive matrix softening and stiffening, which we suggest occurs through balanced matrix degradation and deposition. Our platform enabled us to elucidate previously undescribed interactions between ILC1 and their microenvironment, which suggest that they may exacerbate fibrosis and tumour growth when enriched in inflamed patient tissues