O-minimality and certain atypical intersections

We show that the strategy of point counting in o-minimal structures can be applied to various problems on unlikely intersections that go beyond the conjectures of Manin-Mumford and Andr\'e-Oort. We verify the so-called Zilber-Pink Conjecture in a product of modular curves on assuming a lower bound for Galois orbits and a sufficiently strong modular Ax-Schanuel Conjecture. In the context of abelian varieties we obtain the Zilber-Pink Conjecture for curves unconditionally when everything is defined over a number field. For higher dimensional subvarieties of abelian varieties we obtain some weaker results and some conditional results

Healthy Relationships, Employment, and Reentry

This brief will provide an overview of the evidence supporting the interrelatedness of employment, healthy relationships, family well-being, and recidivism. It will also give the perspectives of expert program practitioners who are successfully integrating programming related to employment, prison reentry, healthy relationships, and responsible fatherhood. Finally, this brief will offer program and policy recommendations for leveraging the positive impacts of healthy relationships on employment and reentry and vice versa

A Probabilistic State Space Model for Joint Inference from Differential Equations and Data

Mechanistic models with differential equations are a key component of scientific applications of machine learning. Inference in such models is usually computationally demanding, because it involves repeatedly solving the differential equation. The main problem here is that the numerical solver is hard to combine with standard inference techniques. Recent work in probabilistic numerics has developed a new class of solvers for ordinary differential equations (ODEs) that phrase the solution process directly in terms of Bayesian filtering. We here show that this allows such methods to be combined very directly, with conceptual and numerical ease, with latent force models in the ODE itself. It then becomes possible to perform approximate Bayesian inference on the latent force as well as the ODE solution in a single, linear complexity pass of an extended Kalman filter / smoother - that is, at the cost of computing a single ODE solution. We demonstrate the expressiveness and performance of the algorithm by training, among others, a non-parametric SIRD model on data from the COVID-19 outbreak.Comment: 12 pages (+ 5 pages appendix), 7 figures. In: Advances in Neural Information Processing Systems (NeurIPS 2021

Updates from the Global Dataverse Community Consortium (GDCC)

Academic presentation at Dataverse Community Meeting 2022, 14.06.22 - 16.06.22

A new buoyancy instability in galaxy clusters due to streaming cosmic rays

Active Galactic Nuclei (AGN) are believed to provide the energy that prevents runaway cooling of gas in the cores of galaxy clusters. However, how this energy is transported and thermalized throughout the Intracluster Medium (ICM) remains unclear. In recent work we showed that streaming cosmic rays (CRs) destabilise sound waves in dilute ICM plasmas. Here we show that CR streaming in the presence of gravity also destabilises a pressure-balanced wave. We term this new instability the CR buoyancy instability (CRBI). In stark contrast to standard results without CRs, the pressure-balanced mode is highly compressible at short wavelengths due to CR streaming. Maximal growth rates are of order $(p_c / p_g) \beta^{1/2} \omega_{\rm ff}$, where $p_c/p_g$ is the ratio of CR pressure to thermal gas pressure, $\beta$ is the ratio of thermal to magnetic pressure and $\omega_{\rm ff}$ is the free-fall frequency. The CRBI operates alongside buoyancy instabilities driven by background heat fluxes, i.e. the heat-flux-driven buoyancy instability (HBI) and the magneto-thermal instability (MTI). When the thermal mean free path $l_{\rm mfp}$ is $\ll$ the gas scale height $H$, the HBI/MTI set the growth rate on large scales, while the CRBI sets the growth rate on small scales. Conversely, when $l_{\rm mfp} \sim H$ and $(p_c/p_g) \beta^{1/2} \gtrsim 1$, CRBI growth rates exceed HBI/MTI growth rates even on large scales. Our results suggest that CR-driven instabilities may be partially responsible for the sound waves/weak shocks and turbulence observed in galaxy clusters. CR-driven instabilities generated near radio bubbles may also play an important role redistributing AGN energy throughout clusters.Comment: Submitted to MNRA

Reliability assessment and criticality analysis for Wave Energy Converters

This paper applies existing reliability methods, namely Reliability Block diagrams, to a notional wave energy converter configuration. It shows possible source of information and difficulties associated with an omnipresent lack of failure rate data.The reliability of wave energy converters (WECs) is a key issue that has to be addressed in order to make them a viable energy option. At this stage of early industrial development the reliability assessment of WECs is a challenging task. In this paper existing reliability methods, namely Reliability Block diagrams, have been applied to a notional configuration. It was found that omnipresent lack of failure rate data makes rather crude adjustments of often generic data necessary which generally lead to rather unfavourable and highly uncertain results. Reliability data is either not available due to sparse field experience or is kept confidential, within different project developments to secure competitive advantages and intellectual property. In order to foster the progress of the marine energy industry, the reliability of devices must be demonstrated and improved. This requires a joint effort between industry stakeholders to collect, share and disseminate existing failure knowledge and future operational experience.Engineering and Physical Sciences Research Council (EPSRC) under the SUPERGEN Marine Doctoral Programm