HIGHEST WEIGHT VECTORS AND TRANSMUTATION

Let G = GLn be the general linear group over an algebraically closed field k, let g=gln be its Lie algebra and let U be the subgroup of G which consists of the upper uni-triangular matrices. Let k[g] be the algebra of polynomial functions on g and let k[g]G be the algebra of invariants under the conjugation action of G. We consider the problem of giving finite homogeneous spanning sets for the k[g]G -modules of highest weight vectors for the conjugation action on k[g] . We prove a general result in arbitrary characteristic which reduces the problem to giving spanning sets for the vector spaces of highest weight vectors for the action of GLr × GLs on tuples of r × s matrices. This requires the technique called “transmutation” by R. Brylinsky which is based on an instance of Howe duality. In characteristic zero, we give for all dominant weights χ ∈ ℤn finite homogeneous spanning sets for the k[g]G -modules k[g]Uχ of highest weight vectors. This result was already stated by J. F. Donin, but he only gave proofs for his related results on skew representations for the symmetric group. We do the same for tuples of n × n-matrices under the diagonal conjugation action

Embeddings of spherical homogeneous spaces in characteristic p

Let G be a reductive group over an algebraically closed field of characteristic p>0. We study properties of embeddings of spherical homogeneous G-spaces. We look at Frobenius splittings, canonical or by a (p−1)-th power, compatible with certain subvarieties. We show the existence of rational G-equivariant resolutions by toroidal embeddings, and give results about cohomology vanishing and surjectivity of restriction maps of global sections of line bundles. We show that the class of homogeneous spaces for which our results hold contains the symmetric homogeneous spaces in characteristic ≠2 and is closed under parabolic induction

Molecular ferroelectric contributions to anomalous hysteresis in hybrid perovskite solar cells

We report a model describing the molecular orientation disorder in CH3NH3PbI3, solving a classical Hamiltonian parametrised with electronic structure calculations, with the nature of the motions informed by ab-initio molecular dynamics. We investigate the temperature and static electric field dependence of the equilibrium ferroelectric (molecular) domain structure and resulting polarisability. A rich domain structure of twinned molecular dipoles is observed, strongly varying as a function of temperature and applied electric field. We propose that the internal electrical fields associated with microscopic polarisation domains contribute to hysteretic anomalies in the current--voltage response of hybrid organic-inorganic perovskite solar cells due to variations in electron-hole recombination in the bulk.Comment: 10 pages; 4 figures, 2 SI figure

On the first restricted cohomology of a reductive Lie algebra and its Borel subalgebras

Let k be an algebraically closed field of characteristic p>0 and let G be a connected reductive group over k. Let B be a Borel subgroup of G and let g and b be the Lie algebras of G and B. Denote the first Frobenius kernels of G and B by G1 and B1. Furthermore, denote the algebras of regular functions on G and g by k[G] and k[g], and similarly for B and b. The group G acts on k[G] via the conjugation action and on k[g] via the adjoint action. Similarly, B acts on k[B] via the conjugation action and on k[b] via the adjoint action. We show that, under certain mild assumptions, the cohomology groups H1(G1,k[g]), H1(B1,k[b]), H1(G1,k[G]) and H1(B1,k[B]) are zero. We also extend all our results to the cohomology for the higher Frobenius kernels

Bases for Spaces of Highest Weight Vectors in Arbitrary Characteristic

Let k be an algebraically closed field of arbitrary characteristic. First we give explicit bases for the highest weight vectors for the action of GLr ×GLs on the coordinate ring k[Mat m rs ] of m-tuples of r × s-matrices. It turns out that this is done most conveniently by giving an explicit good GLr ×GLs-filtration on k[Mat m rs ]. Then we deduce from this result explicit spanning sets of the k[Mat n ] GL n -modules of highest weight vectors in the coordinate ring k[Matn] under the conjugation action of GLn

Usability testing of a monitoring and feedback tool to stimulate physical activity

Introduction: A monitoring and feedback tool to stimulate physical activity, consisting of an activity sensor, smartphone application (app), and website for patients and their practice nurses, has been developed: the 'It's LiFe!' tool. In this study the usability of the tool was evaluated by technology experts and end users (people with chronic obstructive pulmonary disease or type 2 diabetes, with ages from 40-70 years), to improve the user interfaces and content of the tool. Patients and methods: The study had four phases: 1) a heuristic evaluation with six technology experts; 2) a usability test in a laboratory by five patients; 3) a pilot in real life wherein 20 patients used the tool for 3 months; and 4) a final lab test by five patients. In both lab tests (phases 2 and 4) qualitative data were collected through a thinking-aloud procedure and video recordings, and quantitative data through questions about task complexity, text comprehensiveness, and readability. In addition, the post-study system usability questionnaire (PSSUQ) was completed for the app and the website. In the pilot test (phase 3), all patients were interviewed three times and the Software Usability Measurement Inventory (SUMI) was completed. Results: After each phase, improvements were made, mainly to the layout and text. The main improvement was a refresh button for active data synchronization between activity sensor, app, and server, implemented after connectivity problems in the pilot test. The mean score on the PSSUQ for the website improved from 5.6 (standard deviation [SD] 1.3) to 6.5 (SD 0.5), and for the app from 5.4 (SD 1.5) to 6.2 (SD 1.1). Satisfaction in the pilot was not very high according to the SUMI. Discussion: The use of laboratory versus real-life tests and expert-based versus user-based tests revealed a wide range of usability issues. The usability of the It's LiFe! tool improved considerably during the study

ClaimChain: Improving the Security and Privacy of In-band Key Distribution for Messaging

The social demand for email end-to-end encryption is barely supported by mainstream service providers. Autocrypt is a new community-driven open specification for e-mail encryption that attempts to respond to this demand. In Autocrypt the encryption keys are attached directly to messages, and thus the encryption can be implemented by email clients without any collaboration of the providers. The decentralized nature of this in-band key distribution, however, makes it prone to man-in-the-middle attacks and can leak the social graph of users. To address this problem we introduce ClaimChain, a cryptographic construction for privacy-preserving authentication of public keys. Users store claims about their identities and keys, as well as their beliefs about others, in ClaimChains. These chains form authenticated decentralized repositories that enable users to prove the authenticity of both their keys and the keys of their contacts. ClaimChains are encrypted, and therefore protect the stored information, such as keys and contact identities, from prying eyes. At the same time, ClaimChain implements mechanisms to provide strong non-equivocation properties, discouraging malicious actors from distributing conflicting or inauthentic claims. We implemented ClaimChain and we show that it offers reasonable performance, low overhead, and authenticity guarantees.Comment: Appears in 2018 Workshop on Privacy in the Electronic Society (WPES'18

A monitoring and feedback tool embedded in a counselling protocol to increase physical activity of patients with COPD or type 2 diabetes in primary care: study protocol of a three-arm cluster randomised controlled trial

BACKGROUND: Physical activity is important for a healthy lifestyle. Although physical activity can delay complications and decrease the burden of the disease, the level of activity of patients with chronic obstructive pulmonary disease (COPD) or type 2 Diabetes Mellitus (DM2) is often far from optimal. To stimulate physical activity, a monitoring and feedback tool, consisting of an accelerometer linked to a smart phone and webserver (It’s LiFe! tool), and a counselling protocol for practice nurses in primary care was developed (the Self-management Support Program). The main objective of this study is to measure the longitudinal effects of this counselling protocol and the added value of using the tool. METHODS/DESIGN: This three-armed cluster randomised controlled trial with 120 participants with COPD and 120 participants with DM2 (aged 40–70), compares the counselling protocol with and without the use of the tool (group 1 and 2) with usual care (group 3). Recruitment takes place at GP practices in the southern regions of the Netherlands. Randomisation takes place at the practice level. The intended sample (three arms of 8 practices) powers the study to detect a 10-minute difference of moderate and intense physical activity per day between groups 1 and 3. Participants in the intervention groups have to visit the practice nurse 3–4 times for physical activity counselling, in a 4-6-month period. Specific activity goals tailored to the individual patient's preferences and needs will be set. In addition, participants in group 1 will be instructed to use the tool in daily life. The primary outcome, physical activity, will be measured in all groups with a physical activity monitor (PAM). Secondary outcomes are quality of life, general - and exercise - self-efficacy, and health status. Follow-up will take place after 6 and 9 months. Separately, a process evaluation will be conducted to explore reasons for trial non-participation, and the intervention’s acceptability for participating patients and nurses. DISCUSSION: Results of this study will give insight into the effects of the It’s LiFe! monitoring and feedback tool combined with care from a practice nurse for people with COPD or DM2 on physical activity. TRIAL REGISTRATION: ClinicalTrials.gov: NCT0186797

A monitoring and feedback tool embedded in a counselling protocol to increase physical activity of patients with COPD or type 2 diabetes in primary care: study protocol of a three-arm cluster randomised controlled trial

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