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We explore a comprehensive class of distributionally robust optimization models that maximize the probability of exceedance defined as a ratio of stochastic functions. We develop a general reformulation framework that encompasses two forms of ambiguity (moment and Wasserstein), two types of distributional support (uncertain probabilities and continuum of realizations), and multiple functional forms for the probability of exceedance which we successively express as a ratio of linear-to-linear, linear-to-quadratic, quadratic-to-linear, quadratic-to-quadratic, and linear-to-quadratic norm functions. For each case, we first construct the hypographical formulation taking the form of a semi-infinite optimization problem with a distributionally robust chance constraint in which the probability level is a random variable, and derive then a finite-dimensional and computationally tractable reformulation. For the continuum of realizations support, the reformulations are biconvex problems for which we design a customized algorithm that converges finitely and is general enough to handle all (integer and continuous) biconvex reformulations. The numerical experiments demonstrate the computational efficiency of the proposed reformulations and solution method, and the benefits of adopting a distributionally robust approach for the probability of exceedance. The models with moment-based ambiguity sets outperform those with Wasserstein ambiguity in terms of out-of-sample Sharpe ratio and cumulative return when the asset universes’ size is small. In contrast, Wasserstein-based models exhibit superior performance and scale better as the size of the asset universe increases. 

Entropy stabilized oxide of MgNiCoCuZnO5, also known as J14, is a material of active research interest due to a high degree of lattice distortion and tunability. Lattice distortion in J14 plays a crucial role in understanding the elastic constants and lattice thermal conductivity within the single-phase crystal. In this work, a neuroevolution machine learning potential (NEP) is developed for J14, and its accuracy has been compared to density functional theory calculations. The training errors for energy, force, and virial are 5.60 meV/atom, 97.90 meV/Å, and 45.67 meV/atom, respectively. Employing NEP potential, lattice distortion, and elastic constants is studied up to 900 K. In agreement with experimental findings, this study shows that the average lattice distortion of oxygen atoms is relatively higher than that of all transition metals in entropy-stabilized oxide. The observed distortion saturation in the J14 arises from the competing effects of minimum site distortion, which increases with increasing temperature due to enhanced thermal vibrations, and maximum site distortion, which decreases with increasing temperature. Furthermore, a series of molecular dynamics simulations up to 900 K are performed to study the stress–strain behavior. The elastic constants, bulk modulus, and ultimate tensile strength obtained from these simulations indicate a linear decrease in these properties with temperature, as J14 becomes softer owing to thermal effects. Finally, to gain some insight into thermal transport in these materials, with the so-developed NEP potential, and using non-equilibrium molecular dynamics simulations, we study the lattice thermal conductivity (κ) of the ternary compound MgNiO2 as a function of temperature. It is found that κ decreases from 4.25 W m−1 K−1 at room temperature to 3.5 W m−1 K−1 at 900 K. This suppression is attributed to the stronger scattering of low-frequency modes at higher temperatures. 

Locomoting organisms often carry loads such as captured prey or young. Load-carrying effects on high-Reynolds-number flight have been studied, but the fluid dynamics of load carrying by low-Reynolds-number microorganisms has not. We studied low-Reynolds-number load carrying using unicellular choanoflagellates, which wave a flagellum to swim and create a water current transporting bacterial prey to a food-capturing collar of microvilli. A regularized Stokeslet framework was used to model the hydrodynamics of a swimming choanoflagellate with bacterial prey on its collar. Both the model and microvideography of choanoflagellates showed that swimming speed decreases as number of prey being carried increases. Flux of water into the capture zone is reduced by bacteria on the collar, which redirect the water flow and occlude parts of the collar. Feeding efficiency (prey captured per work to produce the feeding current) is decreased more by large prey, prey in the plane of flagellar beating and prey near microvillar tips than by prey in other locations. Some choanoflagellates can attach themselves to surfaces. We found that the reduction in flux due to bacterial prey on the collars of these attached thecate cells was similar to the reduction in flux for swimmers.