Exceptional sets for Diophantine inequalities

We apply Freeman's variant of the Davenport-Heilbronn method to investigate the exceptional set of real numbers not close to some value of a given real diagonal form at an integral argument. Under appropriate conditions, we show that the exceptional set in the interval [-N,N] has measure O(N^{1-c}), for a positive number c

Near-optimal mean value estimates for multidimensional Weyl sums

We obtain sharp estimates for multidimensional generalisations of Vinogradov's mean value theorem for arbitrary translation-dilation invariant systems, achieving constraints on the number of variables approaching those conjectured to be the best possible. Several applications of our bounds are discussed

On generating functions in additive number theory, II: lower-order terms and applications to PDEs

We obtain asymptotics for sums of the formSigma(p)(n=1) e(alpha(k) n(k) + alpha(1)n),involving lower order main terms. As an application, we show that for almost all alpha(2) is an element of [0, 1) one hassup(alpha 1 is an element of[0,1)) | Sigma(1 \u3c= n \u3c= P) e(alpha(1)(n(3) + n) + alpha(2)n(3))| \u3c\u3c P3/4+epsilon,and that in a suitable sense this is best possible. This allows us to improve bounds for the fractal dimension of solutions to the Schrodinger and Airy equations

On generating functions in additive number theory, II: Lower-order terms and applications to PDEs

We obtain asymptotics for sums of the form $$\sum_{n=1}^P e(\alpha_kn^k + \alpha_1n),$$ involving lower order main terms. As an application, we show that for almost all $\alpha_2 \in [0,1)$ one has $$\sup_{\alpha_1 \in [0,1)} \Big| \sum_{1 \le n \le P} e(\alpha_1(n^3+n) + \alpha_2 n^3) \Big| \ll P^{3/4 + \varepsilon},$$ and that in a suitable sense this is best possible. This allows us to improve bounds for the fractal dimension of solutions to the Schr\"odinger and Airy equations

On Pairs of Diagonal Quintic Forms

We demonstrate that a pair of additive quintic equations in at least 34 variables has a nontrivial integral solution, subject only to an 11-adic solubility hypothesis. This is achieved by an application of the Hardy–Littlewood method, for which we require a sharp estimate for a 33.998th moment of quintic exponential sums. We are able to employ p -adic iteration in a form that allows the estimation of such a mean value over a complete unit square, thereby providing an approach that is technically simpler than those of previous workers and flexible enough to be applied to related problems.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42604/1/10599_2004_Article_334960.pd

Nonlinear Protein Degradation and the Function of Genetic Circuits

The functions of most genetic circuits require sufficient degrees of cooperativity in the circuit components. While mechanisms of cooperativity have been studied most extensively in the context of transcriptional initiation control, cooperativity from other processes involved in the operation of the circuits can also play important roles. In this study, we examine a simple kinetic source of cooperativity stemming from the nonlinear degradation of multimeric proteins. Ample experimental evidence suggests that protein subunits can degrade less rapidly when associated in multimeric complexes, an effect we refer to as cooperative stability. For dimeric transcription factors, this effect leads to a concentration-dependence in the degradation rate because monomers, which are predominant at low concentrations, will be more rapidly degraded. Thus cooperative stability can effectively widen the accessible range of protein levels in vivo. Through theoretical analysis of two exemplary genetic circuits in bacteria, we show that such an increased range is important for the robust operation of genetic circuits as well as their evolvability. Our calculations demonstrate that a few-fold difference between the degradation rate of monomers and dimers can already enhance the function of these circuits substantially. These results suggest that cooperative stability needs to be considered explicitly and characterized quantitatively in any systematic experimental or theoretical study of gene circuits.Comment: 42 pages, 10 figure

Are female students in general and nursing students more ready for teamwork and interprofessional collaboration in healthcare?

<p>Abstract</p> <p>Background</p> <p>Interprofessional Education (IPE) is now spreading worldwide and many universities are now including IPE in their curricula. The aim of this study was to investigate whether or not such student characteristics as gender, previous working experience in healthcare, educational progress and features of the learning environment, such as educational programmes and curriculum design, have an impact on their open-mindedness about co-operation with other professions.</p> <p>Methods</p> <p>Medical and nursing students at two Swedish universities were invited to fill in the Readiness for Interprofessional Learning Scale (RIPLS). Totally, 955 students were invited and 70.2% (n = 670) participated in the study. A factor analysis of the RIPLS revealed four item groupings (factors) for our empirical data, but only one had sufficient internal consistency. This factor was labelled "Team Player".</p> <p>Results</p> <p>Regardless of the educational programme, female students were more positive to teamwork than male students. Nursing students in general displayed more positive beliefs about teamwork and collaboration than medical students. Exposure to different interprofessional curricula and previous exposure to interprofessional education were only to a minor extent associated with a positive attitude towards teamwork. Educational progress did not seem to influence these beliefs.</p> <p>Conclusions</p> <p>The establishment of interprofessional teamwork is a major challenge for modern healthcare. This study indicates some directions for more successful interprofessional education. Efforts should be directed at informing particularly male medical students about the need for teamwork in modern healthcare systems. The results also imply that study of other factors, such as the student's personality, is needed for fully understanding readiness for teamwork and interprofessional collaboration in healthcare. We also believe that the RIPL Scale still can be further adjusted.</p

Inefficient Quality Control of Thermosensitive Proteins on the Plasma Membrane

BACKGROUND: Misfolded proteins are generally recognised by cellular quality control machinery, which typically results in their ubiquitination and degradation. For soluble cytoplasmic proteins, degradation is mediated by the proteasome. Membrane proteins that fail to fold correctly are subject to ER associated degradation (ERAD), which involves their extraction from the membrane and subsequent proteasome-dependent destruction. Proteins with abnormal transmembrane domains can also be recognised in the Golgi or endosomal system and targeted for destruction in the vacuole/lysosome. It is much less clear what happens to membrane proteins that reach their destination, such as the cell surface, and then suffer damage. METHODOLOGY/PRINCIPAL FINDINGS: We have tested the ability of yeast cells to degrade membrane proteins to which temperature-sensitive cytoplasmic alleles of the Ura3 protein or of phage lambda repressor have been fused. In soluble form, these proteins are rapidly degraded upon temperature shift, in part due to the action of the Doa10 and San1 ubiquitin ligases and the proteasome. When tethered to the ER protein Use1, they are also degraded. However, when tethered to a plasma membrane protein such as Sso1 they escape degradation, either in the vacuole or by the proteasome. CONCLUSIONS/SIGNIFICANCE: Membrane proteins with a misfolded cytoplasmic domain appear not to be efficiently recognised and degraded once they have escaped the ER, even though their defective domains are exposed to the cytoplasm and potentially to cytoplasmic quality controls. Membrane tethering may provide a way to reduce degradation of unstable proteins

Never Let a Crisis Go to Waste: Opportunities to Reduce Social Disadvantage from COVID-19

This paper identifies and examines a range of policy reform opportunities in Australia arising from COVID-19. The authors demonstrate how COVID-19 presents unique opportunities for rethinking and redesigning long-standing rules and regulations covering how people live and work in Australia, with some opportunities arising coincidentally and others requiring purposeful policy and institutional redesign. They present a broad range of ideas to address entrenched disadvantage in health, labour markets, the tax and transfer system, gender equality, education, housing and criminal justice in Australia, in order to leverage the COVID-19 crisis to build a better society