A physics-based computer model has been developed to support the development of volatile extraction from regolith of the Moon and asteroids. The model is based upon empirical data sets for extraterrestrial soils and simulants, including thermal conductivity of regolith and mixed composition ice, heat capacity of soil and mixed composition ice, hydrated mineral volatile release patterns, and sublimation of ice. A new thermal conductivity relationship is derived that generalizes cases of regolith with varying temperature, soil porosity, and pore vapor pressure. Ice composition is based upon measurements of icy ejecta from the Lunar CRater Observation and Sensing Satellite (LCROSS) impact and it is shown that thermal conductivity and heat capacity equations for water ice provide adequate accuracy at the present level of development. The heat diffusion equations are integrated with gas diffusion equations using multiple adaptive timesteps. The entire model is placed into a Crank-Nicholson framework where the finite difference formalism was extended to two dimensions in axisymmetry. The one-dimensional version of the model successfully predicts heat transfer that matches lunar and asteroid data sets. The axisymmetric model has been used to study heat dissipation around lunar drills and water extraction in asteroid coring devices.

This paper presents a rich knowledge representation language aimed at formalizing causal knowledge. This language is used for accurately and directly formalizing common benchmark examples from the literature of actual causality. A definition of cause is presented and used to analyze the actual causes of changes with respect to sequences of actions representing those examples.

Large language models (LLMs) encode a vast amount of world knowledge acquired from massive text datasets. Recent studies have demonstrated that LLMs can assist an algorithm agent in solving complex sequential decision making tasks in embodied environments by providing high-level instructions. However, interacting with LLMs can be time-consuming, as in many practical scenarios, they require a significant amount of storage space that can only be deployed on remote cloud server nodes. Additionally, using commercial LLMs can be costly since they may charge based on usage frequency. In this paper, we explore how to enable efficient and cost-effective interactions between the agent and an LLM. We propose a reinforcement learning based mediator model that determines when it is necessary to consult LLMs for high-level instructions to accomplish a target task. Experiments on 4 MiniGrid environments that entail planning sub-goals demonstrate that our method can learn to solve target tasks with only a few necessary interactions with an LLM, significantly reducing interaction costs in testing environments, compared with baseline methods. Experimental results also suggest that by learning a mediator model to interact with the LLM, the agent's performance becomes more robust against both exploratory and stochastic environments.

Interactive machine learning (IML) is a beneficial learning paradigm in cases of limited data availability, as human feedback is incrementally integrated into the training process. In this paper, we present an IML pipeline for image captioning which allows us to incrementally adapt a pre-trained image captioning model to a new data distribution based on user input. In order to incorporate user input into the model, we explore the use of a combination of simple data augmentation methods to obtain larger data batches for each newly annotated data instance and implement continual learning methods to prevent catastrophic forgetting from repeated updates. For our experiments, we split a domain-specific image captioning dataset, namely VizWiz, into non-overlapping parts to simulate an incremental input flow for continually adapting the model to new data. We find that, while data augmentation worsens results, even when relatively small amounts of data are available, episodic memory is an effective strategy to retain knowledge from previously seen clusters.

We study first-order Sobolev spaces on reflexive Banach spaces via relaxation, test plans, and divergence. We show the equivalence of the different approaches to the Sobolev spaces and to the related tangent bundles.

We propose a Randomized Progressive Training algorithm (RPT) -- a stochastic proxy for the well-known Progressive Training method (PT) (Karras et al., 2017). Originally designed to train GANs (Goodfellow et al., 2014), PT was proposed as a heuristic, with no convergence analysis even for the simplest objective functions. On the contrary, to the best of our knowledge, RPT is the first PT-type algorithm with rigorous and sound theoretical guarantees for general smooth objective functions. We cast our method into the established framework of Randomized Coordinate Descent (RCD) (Nesterov, 2012; Richt\'arik & Tak\'a\v{c}, 2014), for which (as a by-product of our investigations) we also propose a novel, simple and general convergence analysis encapsulating strongly-convex, convex and nonconvex objectives. We then use this framework to establish a convergence theory for RPT. Finally, we validate the effectiveness of our method through extensive computational experiments.

Time-reversal symmetry (TRS) is pivotal for materials optical, magnetic, topological, and transport properties. Chiral phonons, characterized by atoms rotating unidirectionally around their equilibrium positions, generate dynamic lattice structures that break TRS. Here we report that coherent chiral phonons, driven by circularly polarized terahertz light pulses, can polarize the paramagnetic spins in CeF3 like a quasi-static magnetic field on the order of 1 Tesla. Through time-resolved Faraday rotation and Kerr ellipticity, we found the transient magnetization is only excited by pulses resonant with phonons, proportional to the angular momentum of the phonons, and growing with magnetic susceptibility at cryogenic temperatures, as expected from the spin-phonon coupling model. The time-dependent effective magnetic field quantitatively agrees with that calculated from phonon dynamics. Our results may open a new route to directly investigate mode-specific spin-phonon interaction in ultrafast magnetism, energy-efficient spintronics, and non-equilibrium phases of matter with broken TRS.

Let $A=(a_1, a_2, ..., a_n)$ be relative prime positive integers with $a_i\geq 2$. The Frobenius number $F(A)$ is the largest integer not belonging to the numerical semigroup $\langle A\rangle$ generated by $A$. The genus $g(A)$ is the number of positive integer elements that are not in $\langle A\rangle$. The Frobenius problem is to find $F(A)$ and $g(A)$ for a given sequence $A$. In this paper, we study the Frobenius problem of $A=(a,2a+d,2^2a+3d,...,2^ka+(2^k-1)d)$ and obtain formulas for $F(A)$ and $g(A)$ when $a+d\geq k$. Our formulas simplifies further for some special cases, such as Mersenne and Thabit numerical semigroups. We obtain explicit formulas for generalized Mersenne and Thabit numerical semigroups and some more general numerical semigroups.

Employing the inverse problem of the calculus of variation, the homogeneous phantom Lagrangian can be expressed in the multiplicative form, while the equation of motion of the canonical phantom field is still intact. According to the nonuniqueness principle, the standard and the multiplicative Lagrangian can be linearly combined. This linear combination of Lagrangian can be used as a guideline to add the higher dimension operators and, consequently, the energy scale discrepancy between the particle physics and the cosmology could possibly be resolved.

We argue that the mixing phenomenon of a neutral meson formed by a fictitious massive quark will disappear, if the electroweak symmetry of the Standard Model (SM) is restored at a high energy scale. This disappearance is taken as the high-energy input for the dispersion relation, which must be obeyed by the width difference between two meson mass eigenstates. The solution to the dispersion relation at low energy, i.e., in the symmetry broken phase, then connects the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements to the quark masses involved in the box diagrams responsible for meson mixing. It is demonstrated via the analysis of the $D$ meson mixing that the typical $d$, $s$ and $b$ quark masses demand the CKM matrix elements in agreement with measured values. In particular, the known numerical relation $V_{us}\approx \sqrt{m_s/m_b}$ with the $s$ ($b$) quark mass $m_s$ ($m_b$) can be derived analytically from our solution. Next we apply the same formalism to the mixing of the $\mu^- e^+$ and $\mu^+ e^-$ states through similar box diagrams with intermediate neutrino channels. It is shown that the neutrino masses in the normal hierarchy (NH), instead of in the inverted hierarchy or quasi-degenerate spectrum, match the observed Pontecorvo-Maki-Nakagawa-Sakata matrix elements. The lepton mixing angles larger than the quark ones are explained by means of the inequality $m_2^2/m_3^2\gg m_s^2/m_b^2$, $m_{2,3}$ being the neutrino masses in the NH. At last, the solution for the $\tau^-e^+$-$\tau^+e^-$ mixing specifies the mixing angle $\theta_{23}\approx 45^\circ$ with slight preference for the first octant. Our work suggests that the fermion masses and mixing parameters are constrained dynamically, and the neutrino mass orderings can be discriminated by the internal consistency of the SM.