An n-in-a-row type game

We consider a Maker-Breaker type game on the plane, in which each player takes $t$ points on their $t^\textrm{th}$ turn. Maker wins if he obtains $n$ points on a line (in any direction) without any of Breaker's points between them. We show that, despite Maker's apparent advantage, Breaker can prevent Maker from winning until about his $n^\textrm{th}$ turn. We actually prove a stronger result: that Breaker only needs to play $\omega(\log t)$ points on his $t^\textrm{th}$ turn to prevent Maker from winning until this time. We also consider the situation when the number of points claimed by Maker grows at other speeds, in particular, when Maker claims $t^\alpha$ points on his $t^\textrm{th}$ turn.Comment: 17 page

Influence of Epoxidized Cardanol Functionality and Reactivity on Network Formation and Properties.

Cardanol is a renewable resource based on cashew nut shell liquid (CNSL), which consists of a phenol ring with a C15 long aliphatic side chain in the meta position with varying degrees of unsaturation. Cardanol glycidyl ether was chemically modified to form side-chain epoxidized cardanol glycidyl ether (SCECGE) with an average epoxy functionality of 2.45 per molecule and was cured with petroleum-based epoxy hardeners, 4-4\u27-methylenebis(cyclohexanamine) and diethylenetriamine, and a cardanol-based amine hardener. For comparison, cardanol-based diphenol diepoxy resin, NC514 (Cardolite), and a petroleum-based epoxy resin, diglycidyl ether of bisphenol-A (DGEBA) were also evaluated. Chemical and thermomechanical analyses showed that for SCECGE resins, incomplete cure of the secondary epoxides led to reduced cross-link density, reduced thermal stability, and reduced elongation at break when compared with difunctional resins containing only primary epoxides. However, because of functionality greater than two, amine-cured SCECGE produced

Epoxidation of Cardanol\u27s Terminal Double Bond.

In this investigation, the terminal double bonds of the side chain epoxidized cardanol glycidyl ether (SCECGE) molecule were further epoxidized in the presence of Oxone® (potassium peroxomonosulfate) and fluorinated acetone. Regular methods for the double bond epoxidation are not effective on the terminal double bonds because of their reduced electronegativity with respect to internal double bonds. The terminal double bond functionality of the SCECGE was epoxidized to nearly 70%, increasing the epoxy functionality of SCECGE from 2.45 to 2.65 epoxies/molecule as measured using proton magnetic nuclear resonance (1H-NMR). This modified material—side chain epoxidized cardanol glycidyl ether with terminal epoxies (TE-SCECGE)—was thermally cured with cycloaliphatic curing agent 4-4′-methylenebis(cyclohexanamine) (PACM) at stoichiometry, and the cured polymer properties, such as glass transition temperature (Tg) and tensile modulus, were compared with SCECGE resin cured with PACM. The Tg of the material was increased from 52 to 69 °C as obtained via a dynamic mechanical analysis (DMA) while the tensile modulus of the material increased from 0.88 to 1.24 GPa as a result of terminal double bond epoxidation. In addition to highlighting the effects of dangling side groups in an epoxy network, this modest increase in Tg and modulus could be sufficient to significantly expand the potential uses of amine-cured cardanol-based epoxies for fiber reinforced composite applications

Pyrophosphate-Dependent ATP Formation from Acetyl Coenzyme A in Syntrophus aciditrophicus, a New Twist on ATP Formation.

UnlabelledSyntrophus aciditrophicus is a model syntrophic bacterium that degrades key intermediates in anaerobic decomposition, such as benzoate, cyclohexane-1-carboxylate, and certain fatty acids, to acetate when grown with hydrogen-/formate-consuming microorganisms. ATP formation coupled to acetate production is the main source for energy conservation by S. aciditrophicus However, the absence of homologs for phosphate acetyltransferase and acetate kinase in the genome of S. aciditrophicus leaves it unclear as to how ATP is formed, as most fermentative bacteria rely on these two enzymes to synthesize ATP from acetyl coenzyme A (CoA) and phosphate. Here, we combine transcriptomic, proteomic, metabolite, and enzymatic approaches to show that S. aciditrophicus uses AMP-forming, acetyl-CoA synthetase (Acs1) for ATP synthesis from acetyl-CoA. acs1 mRNA and Acs1 were abundant in transcriptomes and proteomes, respectively, of S. aciditrophicus grown in pure culture and coculture. Cell extracts of S. aciditrophicus had low or undetectable acetate kinase and phosphate acetyltransferase activities but had high acetyl-CoA synthetase activity under all growth conditions tested. Both Acs1 purified from S. aciditrophicus and recombinantly produced Acs1 catalyzed ATP and acetate formation from acetyl-CoA, AMP, and pyrophosphate. High pyrophosphate levels and a high AMP-to-ATP ratio (5.9 ± 1.4) in S. aciditrophicus cells support the operation of Acs1 in the acetate-forming direction. Thus, S. aciditrophicus has a unique approach to conserve energy involving pyrophosphate, AMP, acetyl-CoA, and an AMP-forming, acetyl-CoA synthetase.ImportanceBacteria use two enzymes, phosphate acetyltransferase and acetate kinase, to make ATP from acetyl-CoA, while acetate-forming archaea use a single enzyme, an ADP-forming, acetyl-CoA synthetase, to synthesize ATP and acetate from acetyl-CoA. Syntrophus aciditrophicus apparently relies on a different approach to conserve energy during acetyl-CoA metabolism, as its genome does not have homologs to the genes for phosphate acetyltransferase and acetate kinase. Here, we show that S. aciditrophicus uses an alternative approach, an AMP-forming, acetyl-CoA synthetase, to make ATP from acetyl-CoA. AMP-forming, acetyl-CoA synthetases were previously thought to function only in the activation of acetate to acetyl-CoA

Appropriate disclosure of a diagnosis of dementia : identifying the key behaviours of 'best practice'

Background: Despite growing evidence that many people with dementia want to know their diagnosis, there is wide variation in attitudes of professionals towards disclosure. The disclosure of the diagnosis of dementia is increasingly recognised as being a process rather than a one-off behaviour. However, the different behaviours that contribute to this process have not been comprehensively defined. No intervention studies to improve diagnostic disclosure in dementia have been reported to date. As part of a larger study to develop an intervention to promote appropriate disclosure, we sought to identify important disclosure behaviours and explore whether supplementing a literature review with other methods would result in the identification of new behaviours. Methods: To identify a comprehensive list of behaviours in disclosure we conducted a literature review, interviewed people with dementia and informal carers, and used a consensus process involving health and social care professionals. Content analysis of the full list of behaviours was carried out. Results: Interviews were conducted with four people with dementia and six informal carers. Eight health and social care professionals took part in the consensus panel. From the interviews, consensus panel and literature review 220 behaviours were elicited, with 109 behaviours over-lapping. The interviews and consensus panel elicited 27 behaviours supplementary to the review. Those from the interviews appeared to be self-evident but highlighted deficiencies in current practice and from the panel focused largely on balancing the needs of people with dementia and family members. Behaviours were grouped into eight categories: preparing for disclosure; integrating family members; exploring the patient's perspective; disclosing the diagnosis; responding to patient reactions; focusing on quality of life and well-being; planning for the future; and communicating effectively. Conclusion: This exercise has highlighted the complexity of the process of disclosing a diagnosis of dementia in an appropriate manner. It confirms that many of the behaviours identified in the literature (often based on professional opinion rather than empirical evidence) also resonate with people with dementia and informal carers. The presence of contradictory behaviours emphasises the need to tailor the process of disclosure to individual patients and carers. Our combined methods may be relevant to other efforts to identify and define complex clinical practices for further study.This project is funded by UK Medical Research Council, Grant reference number G0300999

The Heroic and the Villainous: a qualitative study characterising the role models that shaped senior doctors’ professional identity

The successful development and sustaining of professional identity is critical to being a successful doctor. This study explores the enduring impact of significant early role models on the professional identity formation of senior doctors.Personal Interview Narratives were derived from the stories told by twelve senior doctors as they recalled accounts of people and events from the past that shaped their notions of being a doctor. Narrative inquiry methodology was used to explore and analyse video recording and transcript data from interviews.Role models were frequently characterised as heroic, or villainous depending on whether they were perceived as good or bad influences respectively. The degree of sophistication in participants' characterisations appeared to correspond with the stage of life of the participant at the time of the encounter. Heroes were characterised as attractive, altruistic, caring and clever, often in exaggerated terms. Conversely, villains were typically characterised as direct or covert bullies. Everyday events were surprisingly powerful, emotionally charged and persisted in participants' memories much longer than expected. In particular, unresolved emotions dating from encounters where bullying behaviour had been witnessed or experienced were still apparent decades after the event.The characterisation of role models is an important part of the professional identity and socialisation of senior doctors. The enduring impact of what role models say and do means that all doctors, need to consistently reflect on how their own behaviour impacts the development of appropriate professional behaviours in both students and training doctors. This is especially important where problematic behaviours occur as, if not dealt with, they have the potential for long-lasting undesirable effects. The importance of small acts of caring in building a nurturing and supportive learning atmosphere at all stages of medical education cannot be underestimated

Enlarging vertex-flames in countable digraphs

© 2021 The Author(s)A rooted digraph is a vertex-flame if for every vertex v there is a set of internally disjoint directed paths from the root to v whose set of terminal edges covers all ingoing edges of v. It was shown by Lovász that every finite rooted digraph admits a spanning subdigraph which is a vertex-flame and large, where the latter means that it preserves the local connectivity to each vertex from the root. Calvillo-Vives rediscovered and extended this theorem proving that every vertex-flame of a given finite rooted digraph can be extended to be large. The analogue of Lovász' result for countable digraphs was shown by the third author where the notion of largeness is interpreted in a structural way as in the infinite version of Menger's theorem. We give a common generalisation of this and Calvillo-Vives' result by showing that in every countable rooted digraph each vertex-flame can be extended to a large vertex-flame.11Nsciescopu