Discretisation for odd quadratic twists

The discretisation problem for even quadratic twists is almost understood, with the main question now being how the arithmetic Delaunay heuristic interacts with the analytic random matrix theory prediction. The situation for odd quadratic twists is much more mysterious, as the height of a point enters the picture, which does not necessarily take integral values (as does the order of the Shafarevich-Tate group). We discuss a couple of models and present data on this question.Comment: To appear in the Proceedings of the INI Workshop on Random Matrix Theory and Elliptic Curve

Random Matrix Theory and the Fourier Coefficients of Half-Integral Weight Forms

Conjectured links between the distribution of values taken by the characteristic polynomials of random orthogonal matrices and that for certain families of L-functions at the centre of the critical strip are used to motivate a series of conjectures concerning the value-distribution of the Fourier coefficients of half-integral weight modular forms related to these L-functions. Our conjectures may be viewed as being analogous to the Sato-Tate conjecture for integral weight modular forms. Numerical evidence is presented in support of them.Comment: 28 pages, 8 figure

Incorporating Writing Into An Introductory Business And Economics Statistics Course: A Practical Approach

Writing across the curriculum (WAC) has become a guiding principle at many institutions of higher education.  Unfortunately for many students of economics and business the standard vehicles of WAC do not adequately prepare them for the type of writing appropriate for the audience they are expected to address upon graduation.  We describe a method of implementing writing into the introductory statistics courses that are required by many programs in economics and business.  This method addresses the shortcomings of the standard vehicles of WAC while at the same time providing instructors with a feasible solution to do so in light of the multiple constraints faced by many instructors of this type of course.  (JEL A22

Lower order terms in the full moment conjecture for the Riemann zeta function

We describe an algorithm for obtaining explicit expressions for lower terms for the conjectured full asymptotics of the moments of the Riemann zeta function, and give two distinct methods for obtaining numerical values of these coefficients. We also provide some numerical evidence in favour of the conjecture.Comment: 37 pages, 4 figure

Split & mix assembly of DNA libraries for ultrahigh throughput on-bead screening of functional proteins.

Site-saturation libraries reduce protein screening effort in directed evolution campaigns by focusing on a limited number of rationally chosen residues. However, uneven library synthesis efficiency leads to amino acid bias, remedied at high cost by expensive custom synthesis of oligonucleotides, or through use of proprietary library synthesis platforms. To address these shortcomings, we have devised a method where DNA libraries are constructed on the surface of microbeads by ligating dsDNA fragments onto growing, surface-immobilised DNA, in iterative split-and-mix cycles. This method-termed SpliMLiB for Split-and-Mix Library on Beads-was applied towards the directed evolution of an anti-IgE Affibody (ZIgE), generating a 160,000-membered, 4-site, saturation library on the surface of 8 million monoclonal beads. Deep sequencing confirmed excellent library balance (5.1% ± 0.77 per amino acid) and coverage (99.3%). As SpliMLiB beads are monoclonal, they were amenable to direct functional screening in water-in-oil emulsion droplets with cell-free expression. A FACS-based sorting of the library beads allowed recovery of hits improved in Kd over wild-type ZIgE by up to 3.5-fold, while a consensus mutant of the best hits provided a 10-fold improvement. With SpliMLiB, directed evolution workflows are accelerated by integrating high-quality DNA library generation with an ultra-high throughput protein screening platform.ERC, EU H202

Multidrug resistance plasmids commonly reprogram the expression of metabolic genes in <i>Escherichia coli</i>

Multidrug-resistant Escherichia coli is a leading cause of global mortality. Transfer of plasmids carrying genes encoding beta-lactamases, carbapenamases, and colistin resistance between lineages is driving the rising rates of hard-to-treat nosocomial and community infections. Multidrug resistance (MDR) plasmid acquisition commonly causes transcriptional disruption, and while a number of studies have shown strain-specific fitness and transcriptional effects of an MDR plasmid across diverse bacterial lineages, fewer studies have compared the impacts of different MDR plasmids in a common bacterial host. As such, our ability to predict which MDR plasmids are the most likely to be maintained and spread in bacterial populations is limited. Here, we introduced eight diverse MDR plasmids encoding resistances against a range of clinically important antibiotics into E. coli K-12 MG1655 and measured their fitness costs and transcriptional impacts. The scale of the transcriptional responses varied substantially between plasmids, ranging from &gt;650 to &lt;20 chromosomal genes being differentially expressed. However, the scale of regulatory disruption did not correlate significantly with the magnitude of the plasmid fitness cost, which also varied between plasmids. The identities of differentially expressed genes differed between transconjugants, although the expression of certain metabolic genes and functions were convergently affected by multiple plasmids, including the downregulation of genes involved in L-methionine transport and metabolism. Our data show the complexity of the interaction between host genetic background and plasmid genetic background in determining the impact of MDR plasmid acquisition on E. coli.IMPORTANCE: The increase in infections that are resistant to multiple classes of antibiotics, including those isolates that carry carbapenamases, beta-lactamases, and colistin resistance genes, is of global concern. Many of these resistances are spread by conjugative plasmids. Understanding more about how an isolate responds to an incoming plasmid that encodes antibiotic resistance will provide information that could be used to predict the emergence of MDR lineages. Here, the identification of metabolic networks as being particularly sensitive to incoming plasmids suggests the possible targets for reducing plasmid transfer. </p

Using remote substituents to control solution structure and anion binding in lanthanide complexes.

A study of the anion-binding properties of three structurally related lanthanide complexes, which all contain chemically identical anion-binding motifs, has revealed dramatic differences in their anion affinity. These arise as a consequence of changes in the substitution pattern on the periphery of the molecule, at a substantial distance from the binding pocket. Herein, we explore these remote substituent effects and explain the observed behaviour through discussion of the way in which remote substituents can influence and control the global structure of a molecule through their demands upon conformational space. Peripheral modifications to a binuclear lanthanide motif derived from α,α′-bis(DO3 Ayl)-m-xylene are shown to result in dramatic changes to the binding constant for isophthalate. In this system, the parent compound displays considerable conformational flexibility, yet can be assumed to bind to isophthalate through a well-defined conformer. Addition of steric bulk remote from the binding site restricts conformational mobility, giving rise to an increase in binding constant on entropic grounds as long as the ideal binding conformation is not excluded from the available range of conformers

Retrospective evaluation support study on State aid rules for environmental protection and energy

This report provides input for the evaluation of the State aid rules related to environmental protection and energy, with a particular focus on the EU Guidelines on State aid for environmental protection and energy (EEAG) applicable in 2014-2020 and on the provisions applicable to aid for environmental protection and energy (Section 7) of Commission Regulation (EU) 651/2014 (GBER). The overall objective of the report is to provide background information for the review of these provisions. The topics covered in the report are related to the effectiveness, efficiency and relevance of the State aid rules

Mixed moments of characteristic polynomials of random unitary matrices

Following the work of Conrey, Rubinstein and Snaith and Forrester and Witte we examine a mixed moment of the characteristic polynomial and its derivative for matrices from the unitary group U(N) (also known as the CUE) and relate the moment to the solution of a Painleve differential equation. We also calculate a simple form for the asymptotic behaviour of moments of logarithmic derivatives of these characteristic polynomials evaluated near the unit circle