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We study zero-sum differential games with state constraints and one-sided information, where the informed player (Player 1) has a categorical payoff type unknown to the uninformed player (Player 2). The goal of Player 1 is to minimize his payoff without violating the constraints, while that of Player 2 is to either violate the state constraints, or otherwise, to maximize the payoff. One example of the game is a man-to-man matchup in football. Without state constraints, Cardaliaguet (2007) showed that the value of such a game exists and is convex to the common belief of players. Our theoretical contribution is an extension of this result to differential games with state constraints and the derivation of the primal and dual subdynamic principles necessary for computing the behavioral strategies. Compared with existing works on imperfect-information dynamic games that focus on scalability and generalization, our focus is instead on revealing the mechanism of belief manipulation behaviors resulted from information asymmetry and state constraints. We use a simplified football game to demonstrate the utility of this work, where we reveal player positions and belief states in which the attacker should (or should not) play specific random fake moves to take advantage of information asymmetry, and compute how the defender should respond. 

The values of two-player general-sum differential games are viscosity solutions to Hamilton-Jacobi-Isaacs (HJI) equations. Value and policy approximations for such games suffer from the curse of dimensionality (CoD). Alleviating CoD through physics-informed neural networks (PINN) encounters convergence issues when value discontinuity is present due to state constraints. On top of these challenges, it is often necessary to learn generalizable values and policies across a parametric space of games, eg, for game parameter inference when information is incomplete. To address these challenges, we propose in this paper a Pontryagin-mode neural operator that outperforms existing state-of-the-art (SOTA) on safety performance across games with parametric state constraints. Our key contribution is the introduction of a costate loss defined on the discrepancy between forward and backward costate rollouts, which are computationally cheap. We show that the discontinuity of costate dynamics (in the presence of state constraints) effectively enables the learning of discontinuous values, without requiring manually supervised data as suggested by the current SOTA. More importantly, we show that the close relationship between costates and policies makes the former critical in learning feedback control policies with generalizable safety performance. 

Abstract We present near-infraredJHKphotometry for the resolved stellar populations in 13 nearby galaxies: NGC 6822, IC 1613, NGC 3109, Sextans B, Sextans A, NGC 300, NGC 55, NGC 7793, NGC 247, NGC 5253, Cen A, NGC 1313, and M83, acquired from the 6.5 m Baade–Magellan telescope. We measure distances to each galaxy using the J-region asymptotic giant branch (JAGB) method, a new standard candle that leverages the constant luminosities of color-selected, carbon-rich AGB stars. While only single-epoch, random-phase photometry is necessary to derive JAGB distances, our photometry is time-averaged over multiple epochs, thereby decreasing the contribution of the JAGB stars’ intrinsic variability to the measured dispersions in their observed luminosity functions. To cross-validate these distances, we also measure near-infrared tip of the red giant branch (TRGB) distances to these galaxies. The residuals obtained from subtracting the distance moduli from the two methods yield an rms scatter ofσ_JAGB−TRGB= ±0.07 mag. Therefore, all systematics in the JAGB method and TRGB method (e.g., crowding, differential reddening, star formation histories) must be contained within these ±0.07 mag bounds for this sample of galaxies because the JAGB and TRGB distance indicators are drawn from entirely distinct stellar populations and are thus affected by these systematics independently. Finally, the composite JAGB star luminosity function formed from this diverse sample of galaxies is well described by a Gaussian function with a modal value ofM_J= –6.20 ± 0.003 mag (stat), indicating that the underlying JAGB star luminosity function of a well-sampled full star formation history is highly symmetric and Gaussian based on over 6700 JAGB stars in the composite sample. 

Generative models have enabled the creation of contents that are indistinguishable from those taken from nature. Open-source development of such models raised concerns about the risks of their misuse for malicious purposes. One potential risk mitigation strategy is to attribute generative models via fingerprinting. Current fingerprinting methods exhibit a significant tradeoff between robust attribution accuracy and generation quality while lacking design principles to improve this tradeoff. This paper investigates the use of latent semantic dimensions as fingerprints, from where we can analyze the effects of design variables, including the choice of fingerprinting dimensions, strength, and capacity, on the accuracy-quality tradeoff. Compared with previous SOTA, our method requires minimum computation and is more applicable to large-scale models. We use StyleGAN2 and the latent diffusion model to demonstrate the efficacy of our method. 

Finding Nash equilibrial policies for two-player differential games requires solving Hamilton-Jacobi-Isaacs (HJI) PDEs. Self-supervised learning has been used to approximate solutions of such PDEs while circumventing the curse of dimensionality. However, this method fails to learn discontinuous PDE solutions due to its sampling nature, leading to poor safety performance of the resulting controllers in robotics applications when player rewards are discontinuous. This paper investigates two potential solutions to this problem: a hybrid method that leverages both supervised Nash equilibria and the HJI PDE, and a value-hardening method where a sequence of HJIs are solved with a gradually hardening reward. We compare these solutions using the resulting generalization and safety performance in two vehicle interaction simulation studies with 5D and 9D state spaces, respectively. Results show that with informative supervision (e.g., collision and near-collision demonstrations) and the low cost of self-supervised learning, the hybrid method achieves better safety performance than the supervised, self-supervised, and value hardening approaches on equal computational budget. Value hardening fails to generalize in the higher-dimensional case without informative supervision. Lastly, we show that the neural activation function needs to be continuously differentiable for learning PDEs and its choice can be case dependent. 

Vapor phase infiltration (VPI) is a post-polymerization modification technique that infuses inorganics into polymers to create organic–inorganic hybrid materials with new properties. Much is yet to be understood about the chemical kinetics underlying the VPI process. The aim of this study is to create a greater understanding of the process kinetics that govern the infiltration of trimethyl aluminum (TMA) and TiCl 4 into PMMA to form inorganic-PMMA hybrid materials. To gain insight, this paper initially examines the predicted results for the spatiotemporal concentrations of inorganics computed from a recently posited reaction–diffusion model for VPI. This model provides insight on how the Damköhler number (reaction versus diffusion rates) and non-Fickian diffusional processes (hindering) that result from the material transforming from a polymer to a hybrid can affect the evolution of inorganic concentration depth profiles with time. Subsequently, experimental XPS depth profiles are collected for TMA and TiCl 4 infiltrated PMMA films at 90 °C and 135 °C. The functional behavior of these depth profiles at varying infiltration times are qualitatively compared to various computed predictions and conclusions are drawn about the mechanisms of each of these processes. TMA infiltration into PMMA appears to transition from a diffusion-limited process at low temperatures (90 °C) to a reaction-limited process at high temperatures (135 °C) for the film thicknesses investigated here (200 nm). While TMA appears to fully infiltrate these 200 nm PMMA films within a few hours, TiCl 4 infiltration into PMMA is considerably slower, with full saturation not occurring even after 2 days of precursor exposure. Infiltration at 90 °C is so slow that no clear conclusions about mechanism can be drawn; however, at 135 °C, the TiCl 4 infiltration into PMMA is clearly a reaction-limited process, with TiCl 4 permeating the entire thickness (at low concentrations) within only a few minutes, but inorganic loading continuously increasing in a uniform manner over a course of 2 days. Near-surface deviations from the uniform-loading expected for a reaction-limited process also suggest that diffusional hindering is high for TiCl 4 infiltration into PMMA. These results demonstrate a new, ex situ analysis approach for investigating the rate-limiting process mechanisms for vapor phase infiltration. 

Macrophages can be characterized as a very multifunctional cell type with a spectrum of phenotypes and functions being observed spatially and temporally in various disease states. Ample studies have now demonstrated a possible causal link between macrophage activation and the development of autoimmune disorders. How these cells may be contributing to the adaptive immune response and potentially perpetuating the progression of neurodegenerative diseases and neural injuries is not fully understood. Within this review, we hope to illustrate the role that macrophages and microglia play as initiators of adaptive immune response in various CNS diseases by offering evidence of: (1) the types of immune responses and the processes of antigen presentation in each disease, (2) receptors involved in macrophage/microglial phagocytosis of disease-related cell debris or molecules, and, finally, (3) the implications of macrophages/microglia on the pathogenesis of the diseases.