Integers represented as a sum of primes and powers of two

It is shown that every sufficiently large even integer is a sum of two primes and exactly 13 powers of 2. Under the Generalized Rieman Hypothesis one can replace 13 by 7. Unlike previous work on this problem, the proof avoids numerical calculations with explicit zero-free regions of Dirichlet L-functions. The argument uses a new technique to bound the measure of the set on which the exponential sum formed from powers of 2 is large.Comment: 32 Pages; typos correcte

The irrationality of a number theoretical series

Denote by $\sigma_k(n)$ the sum of the $k$-th powers of the divisors of $n$, and let $S_k=\sum_{n\geq 1}\frac{\sigma_k(n)}{n!}$. We prove that Schinzel's conjecture H implies that $S_k$ is irrational, and give an unconditional proof for the case $k=3$

A homologue of the breast cancer associated gene BARD1 is involved in DNA repair in plants

hBRCA1 and hBARD1 are tumor suppressor proteins that are involved as heterodimer via ubiquitinylation in many cellular processes, such as DNA repair. Loss of BRCA1 or BARD1 results in early embryonic lethality and chromosomal instability. The Arabidopsis genome carries a BRCA1 homologue, and we were able to identify a BARD1 homologue. AtBRCA1 and the putative AtBARD1 protein are able to interact with each other as indicated by in vitro and in planta experiments. We have identified T-DNA insertion mutants for both genes, which show no visible phenotype under standard growth conditions and are fully fertile. Thus, in contrast to animals, both genes have no indispensable role during development and meiosis in plants. The two single as well as the double mutant are to a similar extent sensitive to mitomycin C, indicating an epistatic interaction in DNA crosslink repair. We could further demonstrate that in Arabidopsis BARD1 plays a prominent role in the regulation of homologous DNA repair in somatic cells

Engaging Without Exposing: Use of a Fictional Character to Facilitate Mental Health Talk in Focus Groups With Men Who Have Been Subject to the Criminal Justice System.

In an effort to encourage men with experience of being subject to the criminal justice system to contribute to focus group discussions on the sensitive topic of mental health, while also doing our utmost to protect them from discomfort or risk of exploitation, we used a novel technique involving the creation of a fictional character, supplemented by an audio-recorded vignette. We studied the role played by this technique in achieving our stated aims of "engaging without exposing." In this article, we report on the use of this technique in three focus groups, showing how in very different ways it shaped the interaction between participants and generated crucial insights into the lives and service needs of each group. We conclude that the technique may lend itself to being used in focus groups with other marginalized or seldom-heard populations

One vertex spin-foams with the Dipole Cosmology boundary

We find all the spin-foams contributing in the first order of the vertex expansion to the transition amplitude of the Bianchi-Rovelli-Vidotto Dipole Cosmology model. Our algorithm is general and provides spin-foams of arbitrarily given, fixed: boundary and, respectively, a number of internal vertices. We use the recently introduced Operator Spin-Network Diagrams framework.Comment: 23 pages, 30 figure

Feynman diagrammatic approach to spin foams

"The Spin Foams for People Without the 3d/4d Imagination" could be an alternative title of our work. We derive spin foams from operator spin network diagrams} we introduce. Our diagrams are the spin network analogy of the Feynman diagrams. Their framework is compatible with the framework of Loop Quantum Gravity. For every operator spin network diagram we construct a corresponding operator spin foam. Admitting all the spin networks of LQG and all possible diagrams leads to a clearly defined large class of operator spin foams. In this way our framework provides a proposal for a class of 2-cell complexes that should be used in the spin foam theories of LQG. Within this class, our diagrams are just equivalent to the spin foams. The advantage, however, in the diagram framework is, that it is self contained, all the amplitudes can be calculated directly from the diagrams without explicit visualization of the corresponding spin foams. The spin network diagram operators and amplitudes are consistently defined on their own. Each diagram encodes all the combinatorial information. We illustrate applications of our diagrams: we introduce a diagram definition of Rovelli's surface amplitudes as well as of the canonical transition amplitudes. Importantly, our operator spin network diagrams are defined in a sufficiently general way to accommodate all the versions of the EPRL or the FK model, as well as other possible models. The diagrams are also compatible with the structure of the LQG Hamiltonian operators, what is an additional advantage. Finally, a scheme for a complete definition of a spin foam theory by declaring a set of interaction vertices emerges from the examples presented at the end of the paper.Comment: 36 pages, 23 figure

Regulation and Role of Arabidopsis CUL4-DDB1A-DDB2 in Maintaining Genome Integrity upon UV Stress

Plants use the energy in sunlight for photosynthesis, but as a consequence are exposed to the toxic effect of UV radiation especially on DNA. The UV-induced lesions on DNA affect both transcription and replication and can also have mutagenic consequences. Here we investigated the regulation and the function of the recently described CUL4-DDB1-DDB2 E3 ligase in the maintenance of genome integrity upon UV-stress using the model plant Arabidopsis. Physiological, biochemical, and genetic evidences indicate that this protein complex is involved in global genome repair (GGR) of UV-induced DNA lesions. Moreover, we provide evidences for crosstalks between GGR, the plant-specific photo reactivation pathway and the RAD1-RAD10 endonucleases upon UV exposure. Finally, we report that DDB2 degradation upon UV stress depends not only on CUL4, but also on the checkpoint protein kinase Ataxia telangiectasia and Rad3-related (ATR). Interestingly, we found that DDB1A shuttles from the cytoplasm to the nucleus in an ATR-dependent manner, highlighting an upstream level of control and a novel mechanism of regulation of this E3 ligase

Developing an online learning community for mental health professionals and service users: a discursive analysis

<p>Abstract</p> <p>Background</p> <p>There is increasing interest in online collaborative learning tools in health education, to reduce costs, and to offer alternative communication opportunities. Patients and students often have extensive experience of using the Internet for health information and support, and many health organisations are increasingly trying out online tools, while many healthcare professionals are unused to, and have reservations about, online interaction.</p> <p>Methods</p> <p>We ran three week-long collaborative learning courses, in which 19 mental health professionals (MHPs) and 12 mental health service users (MHSUs) participated. Data were analysed using a discursive approach to consider the ways in which participants interacted, and how this contributed to the goal of online learning about using Internet technologies for mental health practice.</p> <p>Results</p> <p>MHSUs and MHPs were able to discuss issues together, listening to the views of the other stakeholders. Discussions on synchronous format encouraged participation by service users while the MHPs showed a preference for an asynchronous format with longer, reasoned postings. Although participants regularly drew on their MHP or MHSU status in discussions, and participants typically drew on either a medical expert discourse or a "lived experience" discourse, there was a blurred boundary as participants shifted between these positions.</p> <p>Conclusions</p> <p>The anonymous format was successful in that it produced a "co-constructed asymmetry" which permitted the MHPs and MHSUs to discuss issues online, listening to the views of other stakeholders. Although anonymity was essential for this course to 'work' at all, the recourse to expert or lay discourses demonstrates that it did not eliminate the hierarchies between teacher and learner, or MHP and MHSU. The mix of synchronous and asynchronous formats helped MHSUs to contribute. Moderators might best facilitate service user experience by responding within an experiential discourse rather than an academic one.</p