On compatibility between isogenies and polarisations of abelian varieties

We discuss the notion of polarised isogenies of abelian varieties, that is, isogenies which are compatible with given principal polarisations. This is motivated by problems of unlikely intersections in Shimura varieties. Our aim is to show that certain questions about polarised isogenies can be reduced to questions about unpolarised isogenies or vice versa. Our main theorem concerns abelian varieties B which are isogenous to a fixed abelian variety A. It establishes the existence of a polarised isogeny A to B whose degree is polynomially bounded in n, if there exist both an unpolarised isogeny A to B of degree n and a polarised isogeny A to B of unknown degree. As a further result, we prove that given any two principally polarised abelian varieties related by an unpolarised isogeny, there exists a polarised isogeny between their fourth powers. The proofs of both theorems involve calculations in the endomorphism algebras of the abelian varieties, using the Albert classification of these endomorphism algebras and the classification of Hermitian forms over division algebras

Study of Ultraviolet-Induces Chromatid and Chromosome Aberrations as a Function of Dose in G1 Phase Vertebrate Tissue Cultures

G1 phase A8 Xenopus laevis (toad) and V79B Cricetulus griseus (hamster) tissue cultures were used to observe the frequency of ultraviolet-induced chromosomal aberrations as a function of dose. When cultures are irradiated with ultraviolet light, visible aberrations are virtually absent until a threshold of approximately 80 ergs mm⁻¹ is reached. Aberrations then occur as a nonlinear function of dose. Chromatid aberrations are by far the most prevalent until doses in excess of 200 ergs mm⁻¹ are administered, at which point chromosome aberrations become common

The Implications of Future Wind-Driven Rain Exposure on the Hygrothermal Performance of Internally Insulated Solid Walls in London

With approximately 40% of the London building stock built before 1919, internal wall insulation (IWI) is one of the likely measures for deep retrofit to meet carbon emissions targets. However, IWI can lead to moisture accumulation and associated unintended consequences, especially in walls highly exposed to wind-driven rain (WDR). Climate change is predicted to exacerbate WDR exposure. This paper presents a comparative analysis between the hygrothermal performance of IWI under current and far future (2080) climates. Historic weather station data and UKCP18 climate projections were used to develop weather files for simulating current and future climate, respectively. Hygrothermal simulations were performed using DELPHIN. Assemblies include calcium silicate, phenolic foam, and wood fibre systems. Future climate predictions are associated with a rise of interstitial relative humidity, leading to patterns more favourable to mould growth

Climate Resilience of Internally-Insulated Historic Masonry Assemblies: Comparison of Moisture Risk under Current and Future Climate Scenarios

The conservation of cultural heritage built of historical brick masonry alongside meeting targets in energy reduction will most likely require widespread installation of internal wall insulation (IWI). In London, traditional buildings (pre-1919) make up 40% of the existing stock and insulating from the interior is a likely retrofit solution for solid brick walls. Adding insulation may introduce a higher risk to moisture accumulation and consequences such as mould growth and material decay. To investigate resilience to future moisture loads, three interior insulation assemblies (conforming to two U-value guidelines) were simulated in DELPHIN under reference, near-future (2040), and far-future climate (2080) scenarios. Calcium silicate, phenolic foam, and wood fibre assemblies were simulated. The reference year climate file was compiled from observed data and future files developed using the UK Climate Projections 2018 (UKCP18). Assemblies were evaluated for moisture accumulation, mould growth risk, and freeze-thaw (FT) risk. Results show low-to-medium risks in 2040 and high risks in 2080, assemblies of higher absorptivity and thinner insulation comparatively performing best. The calcium silicate assembly fared best for moisture performance; however, all assemblies will be subject to high moisture risk levels in the far future and responsible retrofits must take this and alternative design solutions into account

Real estate stock selection and attribute preferences

The majority of studies that explore property portfolio construction and management strategies utilise highly aggregated ex-post data, but stock selection is known to be a significant determinant of portfolio performance. Thus, here we look at stock selection, focusing on the choices faced by investors, necessitating the collection and analysis of primary data, carried out utilising conjoint analysis. This represents a new step in property research, with the data collection undertaken using a simulation exercise. This enables fund managers to make hypothetical purchase decisions, viewing properties comprising a realistic bundle of attributes and making complex contemporaneous trade-offs between attributes, subject to their stated market and economic forecasts and sector specialism. In total 51 fund managers were surveyed, producing 918 purchase decisions for analysis, with additional data collected regarding fund and personal characteristics. The results reveal that ‘fixed’ property characteristics (location and obsolescence) are dominant in the decision-making process, over and above ‘manageable’ tenant and lease characteristics which can be explicitly included within models of probabilities of income variation. This reveals investors are making ex-ante risk judgements and are considering post acquisition risk management strategies. The study also reveals that behavioural factors affect acquisition decisions

Developing a Climate Resilience Scorecard for Marin County, California

Marin County, located in the northern San Francisco Bay Area in California, faces significant threats due to climate change, including more frequent wildfires, flooding, and increased temperatures. Adaptation and mitigation efforts are necessary in order to promote resilience amidst these changing conditions. Scorecards and similar evaluation tools have previously been utilized by policymakers to address concerns within a community; these tools allow leaders to compare conditions across an array of focus areas and to identify priorities for action and investment. The purpose of this research is to understand the processes by which scorecards are developed as well as the challenges, benefits, and insights associated with these processes. These findings inform the development of a preliminary climate resilience scorecard template for Marin County, with the intent that local leaders may utilize this template to gauge their progress in regards to climate resilience and to inform policy changes

A parallel multistate framework for atomistic non-equilibrium reaction dynamics of solutes in strongly interacting organic solvents

We describe a parallel linear-scaling computational framework developed to implement arbitrarily large multi-state empirical valence bond (MS-EVB) calculations within CHARMM. Forces are obtained using the Hellman-Feynmann relationship, giving continuous gradients, and excellent energy conservation. Utilizing multi-dimensional Gaussian coupling elements fit to CCSD(T)-F12 electronic structure theory, we built a 64-state MS-EVB model designed to study the F + CD3CN -> DF + CD2CN reaction in CD3CN solvent. This approach allows us to build a reactive potential energy surface (PES) whose balanced accuracy and efficiency considerably surpass what we could achieve otherwise. We use our PES to run MD simulations, and examine a range of transient observables which follow in the wake of reaction, including transient spectra of the DF vibrational band, time dependent profiles of vibrationally excited DF in CD3CN solvent, and relaxation rates for energy flow from DF into the solvent, all of which agree well with experimental observations. Immediately following deuterium abstraction, the nascent DF is in a non-equilibrium regime in two different respects: (1) it is highly excited, with ~23 kcal mol-1 localized in the stretch; and (2) not yet Hydrogen bonded to the CD3CN solvent, its microsolvation environment is intermediate between the non-interacting gas-phase limit and the solution-phase equilibrium limit. Vibrational relaxation of the nascent DF results in a spectral blue shift, while relaxation of its microsolvation environment results in a red shift. These two competing effects result in a post-reaction relaxation profile distinct from that observed when DF vibration excitation occurs within an equilibrium microsolvation environment. The parallel software framework presented in this paper should be more broadly applicable to a range of complex reactive systems.Comment: 58 pages and 29 Figure