We settle the existence of certain anti-magic cubes using combinatorial block designs and graph decompositions to align a handful of small examples.
Given a stochastic dynamical system modelled via stochastic differential equations (SDEs), we evaluate the safety of the system through characterisations of its exit time moments. We lift the (possibly nonlinear) dynamics into the space of the occupa
tion and exit measures to obtain a set of linear evolution equations which depend on the infinitesimal generator of the SDE. Coupled with appropriate semidefinite positive matrix constraints, this yields a moment-based approach for the computation of exit time moments of SDEs with polynomial drift and diffusion dynamics. To extend the capability of the moment approach, we propose a state augmentation method which allows us to generate the evolution equations for a broader class of nonlinear stochastic systems and apply the moment method to previously unsupported dynamics. In particular, we show a general augmentation strategy for sinusoidal dynamics which can be found in most physical systems. We employ the methodology on an Ornstein-Uhlenbeck process and stochastic spring-mass-damper model to characterise their safety via their expected exit times and show the additional exit distribution insights that are afforded through higher order moments.
The behavior of self driving cars may differ from people expectations, (e.g. an autopilot may unexpectedly relinquish control). This expectation mismatch can cause potential and existing users to distrust self driving technology and can increase the
likelihood of accidents. We propose a simple but effective framework, AutoPreview, to enable consumers to preview a target autopilot potential actions in the real world driving context before deployment. For a given target autopilot, we design a delegate policy that replicates the target autopilot behavior with explainable action representations, which can then be queried online for comparison and to build an accurate mental model. To demonstrate its practicality, we present a prototype of AutoPreview integrated with the CARLA simulator along with two potential use cases of the framework. We conduct a pilot study to investigate whether or not AutoPreview provides deeper understanding about autopilot behavior when experiencing a new autopilot policy for the first time. Our results suggest that the AutoPreview method helps users understand autopilot behavior in terms of driving style comprehension, deployment preference, and exact action timing prediction.
We apply the 1+1+2 covariant approach to describe a general static and spherically symmetric relativistic stellar object which contains two interacting fluids. We then use the 1+1+2 equations to derive the corresponding Tolman-Oppenheimer-Volkoff (TO
V) equations in covariant form in the isotropic, non-interacting case. These equations are used to obtain new exact solutions by means of direct resolution and reconstruction techniques. Finally, we show that the generating theorem known for the single fluid case can also be used to obtain two-fluid solutions from single fluid ones.
We assess the value of machine learning as an accelerator for the parameterisation schemes of operational weather forecasting systems, specifically the parameterisation of non-orographic gravity wave drag. Emulators of this scheme can be trained to p
roduce stable and accurate results up to seasonal forecasting timescales. Generally, more complex networks produce more accurate emulators. By training on an increased complexity version of the existing parameterisation scheme we build emulators that produce more accurate forecasts. {For medium range forecasting we find evidence our emulators are more accurate} than the version of the parametrisation scheme that is used for operational predictions. Using the current operational CPU hardware our emulators have a similar computational cost to the existing scheme, but are heavily limited by data movement. On GPU hardware our emulators perform ten times faster than the existing scheme on a CPU.
Geological evidence suggests liquid water near the Earths surface as early as 4.4 gigayears ago when the faint young Sun only radiated about 70 % of its modern power output. At this point, the Earth should have been a global snowball. An extreme atmo
spheric greenhouse effect, an initially more massive Sun, release of heat acquired during the accretion process of protoplanetary material, and radioactivity of the early Earth material have been proposed as alternative reservoirs or traps for heat. For now, the faint-young-sun paradox persists as one of the most important unsolved problems in our understanding of the origin of life on Earth. Here we use astrophysical models to explore the possibility that the new-born Moon, which formed about 69 million years (Myr) after the ignition of the Sun, generated extreme tidal friction - and therefore heat - in the Hadean and possibly the Archean Earth. We show that the Earth-Moon system has lost about 3e31 J, (99 % of its initial mechanical energy budget) as tidal heat. Tidal heating of roughly 10 W/m^2 through the surface on a time scale of 100 Myr could have accounted for a temperature increase of up to 5 degrees Celsius on the early Earth. This heating effect alone does not solve the faint-young-sun paradox but it could have played a key role in combination with other effects. Future studies of the interplay of tidal heating, the evolution of the solar power output, and the atmospheric (greenhouse) effects on the early Earth could help in solving the faint-young-sun paradox.
As autonomous systems begin to operate amongst humans, methods for safe interaction must be investigated. We consider an example of a small autonomous vehicle in a pedestrian zone that must safely maneuver around people in a free-form fashion. We inv
estigate two key questions: How can we effectively integrate pedestrian intent estimation into our autonomous stack. Can we develop an online monitoring framework to give formal guarantees on the safety of such human-robot interactions. We present a pedestrian intent estimation framework that can accurately predict future pedestrian trajectories given multiple possible goal locations. We integrate this into a reachability-based online monitoring scheme that formally assesses the safety of these interactions with nearly real-time performance (approximately 0.3 seconds). These techniques are integrated on a test vehicle with a complete in-house autonomous stack, demonstrating effective and safe interaction in real-world experiments.
This work presents a new toolkit for describing the acoustic properties of the ocean environment before, during and after a sound event caused by an underwater seismic air-gun. The toolkit uses existing sound measures, but uniquely applies these to c
apture the early time period (actual pulse) and late time period (reverberation and multiple arrivals). In total, 183 features are produced for each air-gun sound. This toolkit was utilized on data retrieved from a field deployment encompassing five marine autonomous recording units during a 46-day seismic air-gun survey in Baffin Bay, Greenland. Using this toolkit, a total of 147 million data points were identified from the Greenland deployment recordings. The feasibility of extracting a large number of features was then evaluated using two separate methods: a serial computer and a high performance system. Results indicate that data extraction performance took an estimated 216 hours for the serial system, and 18 hours for the high performance computer. This paper provides an analytical description of the new toolkit along with details for using it to identify relevant data.
We study the dynamical complexity of an open quantum driven double-well oscillator, mapping its dependence on effective Plancks constant $hbar_{eff}equivbeta$ and coupling to the environment, $Gamma$. We study this using stochastic Schrodinger equati
ons, semiclassical equations, and the classical limit equation. We show that (i) the dynamical complexity initially increases with effective Hilbert space size (as $beta$ decreases) such that the most quantum systems are the least dynamically complex. (ii) If the classical limit is chaotic, that is the most dynamically complex (iii) if the classical limit is regular, there is always a quantum system more dynamically complex than the classical system. There are several parameter regimes where the quantum system is chaotic even though the classical limit is not. While some of the quantum chaotic attractors are of the same family as the classical limiting attractors, we also find a quantum attractor with no classical counterpart. These phenomena occur in experimentally accessible regimes.
Agent-based models are versatile tools for studying how societal opinion change, including political polarization and cultural diffusion, emerges from individual behavior. This study expands agents psychological realism using empirically-motivated ru
les governing interpersonal influence, commitment to previous beliefs, and conformity in social contexts. Computational experiments establish that these extensions produce three novel results: (a) sustained strong diversity of opinions within the population, (b) opinion subcultures, and (c) pluralistic ignorance. These phenomena arise from a combination of agents intolerance, susceptibility and conformity, with extremist agents and social networks playing important roles. The distribution and dynamics of simulated opinions reproduce two empirical datasets on Americans political opinions.
