Asymptotic homogenisation is considered for problems with integral constraints imposed on a slowly varying microstructure; an insulator with an array of perfectly dielectric inclusions of slowly varying size serves as a paradigm. Although it is well-known how to handle each of these effects (integral constraints, slowly varying microstructure) independently within multiple scales analysis, additional care is needed when they are combined. Using the flux transport theorem, the multiple scales form of an integral constraint on a slowly varying domain is identified. The proposed form is applied to obtain a homogenised model for the electric potential in a dielectric composite, where the microstructure slowly varies and the integral constraint arises due to a statement of charge conservation. A comparison with multiple scales analysis of the problem with established approaches provides validation that the proposed form results in the correct homogenised model.

Objectives/Goals: One in 14 individuals have a substance use disorder (SUD). We suggest that a trait of poor impulse control, or high impulsivity, may predict relapse risk. We explore how changes in brain structure linked to decision-making and reward might drive high impulsivity, helping create a “biosignature” to identify those most at risk and guide treatment choices. Methods/Study Population: Male rats were phenotyped as high impulsive (HI) or low impulsive (LI) based on premature responses on the one-choice serial reaction time (1-CSRT) task. Rats then received an intracranial infusion of a retrograde virus (AAVr2) in the nucleus accumbens (NAc) to trace corticoaccumbens neurons back to the medial prefrontal cortex (mPFC). After impulsivity phenotyping (ITI8), another cohort of animals performed cocaine self-administration followed by 30 days of abstinence. Cue reactivity, a measure of relapse-like behaviors, was performed on abstinence day 30. Analyses of microtubule-associated protein 2 (MAP2), a cytoskeletal marker of dendrites, spines, and somas was performed with western blotting and fluorescent images of brain slices after phenotyping and cocaine abstinence. Results/Anticipated Results: HI rats made greater premature responses, a marker of impulsive action vs. LI rats at baseline (p Discussion/Significance of Impact: Poor inherent impulse control and drug cues heighten relapse risk. We found high impulsivity linked to brain structure differences and lower protein markers of synaptic (units supporting signaling) strengthening. Future investigations into brain-behavior links with impulsivity may further identify a SUD relapse vulnerability biosignature.

We study density and partition properties of polynomial equations in prime variables. We consider equations of the form $a_1h(x_1) + \cdots + a_sh(x_s)=b$, where the ai and b are fixed coefficients and h is an arbitrary integer polynomial of degree d. We establish that the natural necessary conditions for this equation to have a monochromatic non-constant solution with respect to any finite colouring of the prime numbers are also sufficient when the equation has at least $(1+o(1))d^2$ variables. We similarly characterize when such equations admit solutions over any set of primes with positive relative upper density. In both cases, we obtain lower bounds for the number of monochromatic or dense solutions in primes that are of the correct order of magnitude. Our main new ingredient is a uniform lower bound on the cardinality of a prime polynomial Bohr set.

Singularly perturbed ordinary differential equations often exhibit Stokes’ phenomenon, which describes the appearance and disappearance of oscillating exponentially small terms across curves in the complex plane known as Stokes lines. These curves originate at singular points in the leading-order solution to the differential equation. In many important problems, it is impossible to obtain a closed-form expression for these leading-order solutions, and it is therefore challenging to locate these singular points. We present evidence that the analytic leading-order solution of a linear differential equation can be replaced with a numerical rational approximation using the adaptive Antoulas–Anderson (AAA) method. Despite such an approximation having completely different singularity types and locations, we show that the subsequent exponential asymptotic analysis accurately predicts the exponentially small behaviour present in the solution. For sufficiently small values of the asymptotic parameter, this approach breaks down; however, the range of validity may be extended by increasing the number of poles in the rational approximation. We present a related nonlinear problem and discuss the challenges that arise due to nonlinear effects. Overall, our approach allows for the study of exponentially small asymptotic effects without requiring an exact analytic form for the leading-order solution; this permits exponential asymptotic methods to be used in a much wider range of applications.

From the safety inside vehicles, Knowsley Safari offers visitors a close-up encounter with captive olive baboons. As exiting vehicles may be contaminated with baboon stool, a comprehensive coprological inspection was conducted to address public health concerns. Baboon stools were obtained from vehicles, and sleeping areas, inclusive of video analysis of baboon–vehicle interactions. A purposely selected 4-day sampling period enabled comparative inspections of 2662 vehicles, with a total of 669 baboon stools examined (371 from vehicles and 298 from sleeping areas). As informed by our pilot study, front-line diagnostic methods were: QUIK-CHEK rapid diagnostic test (RDT) (Giardia and Cryptosporidium), Kato–Katz coproscopy (Trichuris) and charcoal culture (Strongyloides). Some 13.9% of vehicles were contaminated with baboon stool. Prevalence of giardiasis was 37.4% while cryptosporidiosis was <0.01%, however, an absence of faecal cysts by quality control coproscopy, alongside lower than the expected levels of Giardia-specific DNA, judged RDT results as misleading, grossly overestimating prevalence. Prevalence of trichuriasis was 48.0% and strongyloidiasis was 13.7%, a first report of Strongyloides fuelleborni in UK. We advise regular blanket administration(s) of anthelminthics to the colony, exploring pour-on formulations, thereafter, smaller-scale indicator surveys would be adequate.

OBJECTIVES/GOALS: The primary goals of this study are 1) expand our understanding of the neural circuitry influenced by the neuropeptide Neuromedin U (NMU) via its receptor Neuromedin U Receptor 2 (NMUR2), and 2) provide alternative top-down mechanisms for how NMU regulates high fat food intake and cocaine taking. METHODS/STUDY POPULATION: Immunohistochemistry (IHC) for NMUR2 and cell markers was performed on rat brain tissue containing the medial prefrontal cortex (mPFC). To identify the source of the presynaptic NMUR2, anterograde tracing from the paraventricular nucleus or dorsal raphe nucleus to the mPFC utilizing an AAV2- dsRed-synaptobrevin fusion protein were performed (n=3) and will be followed by IHC. Using in vivo calcium imaging technology (InScopix nVista), neuronal activity (calcium transients) was recorded from the mPFC of two awake, freely behaving rats. Each animal underwent a single session of 30 minutes baseline activity, intraperitoneal NMU administration, and 30 minutes of post-treatment activity. Activity was then processed and recorded as distinct events using the InScopix data acquisition software. RESULTS/ANTICIPATED RESULTS: Medial prefrontal cortex staining for NMUR2 revealed a characteristic “beads on a string” motif, consistent with presynaptic receptor expression. Furthermore, we expect the anterograde tracing experiment will show colocalization of the dsRed-synaptobrevin fusion protein with NMUR2 on synaptic inputs into the medial prefrontal cortex. Following quantification of pre- and post- treatment events using the InScopix data acquisition software, total events during the pre- and post-treatment time periods were calculated. In these studies, both animals demonstrated a clear increase in calcium transient activity between pre- and post- treatment evaluations, suggesting that NMU administration increases the neuronal activity of neurons in the prefrontal cortex. DISCUSSION/SIGNIFICANCE: This research provides a new site of action for the known therapeutic effects of NMU. We demonstrate the presence of presynaptic NMUR2 in the mPFC and show that systemic administration of NMU increases mPFC neuronal activity. This illustrates NMU may act as a top-down mediator for substance use disorders and binge eating behaviors.

The study of free-surface flows over vegetative structures presents a challenging setting for theoretical, computational and experimental analysis. In this work, we develop a multiple-scales asymptotic framework for the evolution of free-surface waves over rigid vegetation and a slowly varying substrate. The analysis quantifies the balance between the competing effects of vegetation and shoaling, and provides a prediction of the amplitude as the wave approaches a coastline. Our analysis unifies and extends existing theories that study these effects individually. The asymptotic predictions are shown to provide good agreement with full numerical simulations (varying depth) and published experimental results (constant depth).

This paper investigates whether high borrowing costs deterred investment in sanitation infrastructure in late nineteenth-century Britain. Town Councils had to borrow to fund investment, with considerable variation in interest rates across towns and over time. Panel regressions, using annual data from more than 800 town councils, indicate that higher interest rates were associated with lower levels of infrastructure investment between 1887 and 1903. Instrumental variable regressions show that falling interest rates after 1887 stimulated investment and led to lower infant mortality. These findings suggest that Parliament could have expedited mortality decline by subsidizing loans or facilitating private borrowing.

Performance-based managed entry agreements (PB-MEAs) might allow patient access to new medicines, but practical hurdles make competent authorities for pricing and reimbursement (CAPR) reluctant to implement PB-MEAs. We explored if the feasibility of PB-MEAs might improve by better aligning regulatory postauthorization requirements with the data generation of PB-MEAs and by active collaboration and data sharing. Reviewers from seven CAPRs provided structured assessments of the information available at the European Medicines Agency (EMA) Web site on regulatory postauthorization requirements for fifteen recently authorized products. The reviewers judged to what extent regulatory postauthorization studies could help implement PB-MEAs by addressing uncertainty gaps. Study domains assessed were: patient population, intervention, comparators, outcomes, time horizon, anticipated data quality, and anticipated robustness of analysis. Reviewers shared general comments about PB-MEAs for each product and on cooperation with other CAPRs. Reviewers rated regulatory postauthorization requirements at least partly helpful for most products and across domains except the comparator domain. One quarter of responses indicated that public information provided by the EMA was insufficient to support the implementation of PB-MEAs. Few PB-MEAs were in place for these products, but the potential for implementation of PB-MEAs or collaboration across CAPRs was seen as more favorable. Responses helped delineate a set of conditions where PB-MEAs may help reduce uncertainty. In conclusion, PB-MEAs are not a preferred option for CAPRs, but we identified conditions where PB-MEAs might be worth considering. The complexities of implementing PB-MEAs remain a hurdle, but collaboration across silos and more transparency on postauthorization studies could help overcome some barriers.

We consider the instabilities of flows through a submerged canopy and show how the full governing equations of the fluid–structure interactions can be reduced to a compact framework that captures many key features of vegetative flow. First, by modelling the canopy as a collection of homogeneous elastic beams, we predict the steady configuration of the plants in response to a unidirectional flow. This treatment couples the beam equations in the canopy to the fluid momentum equations. Subsequently, a linear stability analysis suggests new insights into the development of instabilities at the surface of the vegetative region. In particular, we show that shear at the top of the canopy is a dominant factor in determining the onset of instabilities known as monami. Based on numerical and asymptotic analysis of the quadratic eigenvalue problem, the system is shown to be stable if the canopy is sufficiently sparse.

We present a detailed overview of the cosmological surveys that we aim to carry out with Phase 1 of the Square Kilometre Array (SKA1) and the science that they will enable. We highlight three main surveys: a medium-deep continuum weak lensing and low-redshift spectroscopic HI galaxy survey over 5 000 deg2; a wide and deep continuum galaxy and HI intensity mapping (IM) survey over 20 000 deg2 from $z = 0.35$ to 3; and a deep, high-redshift HI IM survey over 100 deg2 from $z = 3$ to 6. Taken together, these surveys will achieve an array of important scientific goals: measuring the equation of state of dark energy out to $z \sim 3$ with percent-level precision measurements of the cosmic expansion rate; constraining possible deviations from General Relativity on cosmological scales by measuring the growth rate of structure through multiple independent methods; mapping the structure of the Universe on the largest accessible scales, thus constraining fundamental properties such as isotropy, homogeneity, and non-Gaussianity; and measuring the HI density and bias out to $z = 6$. These surveys will also provide highly complementary clustering and weak lensing measurements that have independent systematic uncertainties to those of optical and near-infrared (NIR) surveys like Euclid, LSST, and WFIRST leading to a multitude of synergies that can improve constraints significantly beyond what optical or radio surveys can achieve on their own. This document, the 2018 Red Book, provides reference technical specifications, cosmological parameter forecasts, and an overview of relevant systematic effects for the three key surveys and will be regularly updated by the Cosmology Science Working Group in the run up to start of operations and the Key Science Programme of SKA1.