Similar to the role of Markov decision processes in reinforcement learning, Stochastic Games (SGs) lay the foundation for the study of multi-agent reinforcement learning (MARL) and sequential agent interactions. In this paper, we derive that computin
g an approximate Markov Perfect Equilibrium (MPE) in a finite-state discounted Stochastic Game within the exponential precision is textbf{PPAD}-complete. We adopt a function with a polynomially bounded description in the strategy space to convert the MPE computation to a fixed-point problem, even though the stochastic game may demand an exponential number of pure strategies, in the number of states, for each agent. The completeness result follows the reduction of the fixed-point problem to {sc End of the Line}. Our results indicate that finding an MPE in SGs is highly unlikely to be textbf{NP}-hard unless textbf{NP}=textbf{co-NP}. Our work offers confidence for MARL research to study MPE computation on general-sum SGs and to develop fruitful algorithms as currently on zero-sum SGs.
Image matting is an ill-posed problem that aims to estimate the opacity of foreground pixels in an image. However, most existing deep learning-based methods still suffer from the coarse-grained details. In general, these algorithms are incapable of f
elicitously distinguishing the degree of exploration between deterministic domains (certain FG and BG pixels) and undetermined domains (uncertain in-between pixels), or inevitably lose information in the continuous sampling process, leading to a sub-optimal result. In this paper, we propose a novel network named Prior-Induced Information Alignment Matting Network (PIIAMatting), which can efficiently model the distinction of pixel-wise response maps and the correlation of layer-wise feature maps. It mainly consists of a Dynamic Gaussian Modulation mechanism (DGM) and an Information Alignment strategy (IA). Specifically, the DGM can dynamically acquire a pixel-wise domain response map learned from the prior distribution. The response map can present the relationship between the opacity variation and the convergence process during training. On the other hand, the IA comprises an Information Match Module (IMM) and an Information Aggregation Module (IAM), jointly scheduled to match and aggregate the adjacent layer-wise features adaptively. Besides, we also develop a Multi-Scale Refinement (MSR) module to integrate multi-scale receptive field information at the refinement stage to recover the fluctuating appearance details. Extensive quantitative and qualitative evaluations demonstrate that the proposed PIIAMatting performs favourably against state-of-the-art image matting methods on the Alphamatting.com, Composition-1K and Distinctions-646 dataset.
Moire superlattices of two-dimensional (2D) materials with a small twist angle are thought to exhibit appreciable flexoelectric effect, though unambiguous confirmation of their flexoelectricity is challenging due to artifacts associated with commonly
used piezoresponse force microscopy (PFM). For example, unexpectedly small phase contrast ($sim$$8^{circ}$) between opposite flexoelectric polarizations was reported in twisted bilayer graphene (tBG), though theoretically predicted value is $180^{circ}$. Here we developed a methodology to extract intrinsic moire flexoelectricity using twisted double bilayer graphene (tDBG) as a model system, probed by lateral PFM. For small twist angle samples, we found that a vectorial decomposition is essential to recover the small intrinsic flexoelectric response at domain walls from a large background signal. The obtained three-fold symmetry of commensurate domains with significant flexoelectric response at domain walls is fully consistent with our theoretical calculations. Incommensurate domains in tDBG with relatively large twist angles can also be observed by this technique. Our work provides a general strategy for unraveling intrinsic flexoelectricity in van der Waals moire superlattices while providing insights into engineered symmetry breaking in centrosymmetric materials.
Moire superlattices in van der Waals heterostructures are gaining increasing attention because they offer new opportunities to tailor and explore unique electronic phenomena when stacking 2D materials with small twist angles. Here, we reveal local su
rface potentials associated with stacking domains in twisted double bilayer graphene (TDBG) moire superlattices. Using a combination of both lateral Piezoresponse Force Microscopy (LPFM) and Scanning Kelvin Probe Microscopy (SKPM), we distinguish between Bernal (ABAB) and rhombohedral (ABCA) stacked graphene and directly correlate these stacking configurations with local surface potential. We find that the surface potential of the ABCA domains is ~15 mV higher (smaller work function) than that of the ABAB domains. First-principles calculations based on density functional theory further show that the different work functions between ABCA and ABAB domains arise from the stacking dependent electronic structure. We show that, while the moire superlattice visualized by LPFM can change with time, imaging the surface potential distribution via SKPM appears more stable, enabling the mapping of ABAB and ABCA domains without tip-sample contact-induced effects. Our results provide a new means to visualize and probe local domain stacking in moire superlattices along with its impact on electronic properties.
Flat band moire superlattices have recently emerged as unique platforms for investigating the interplay between strong electronic correlations, nontrivial band topology, and multiple isospin flavor symmetries. Twisted monolayer-bilayer graphene (tMBG
) is an especially rich system owing to its low crystal symmetry and the tunability of its bandwidth and topology with an external electric field. Here, we find that orbital magnetism is abundant within the correlated phase diagram of tMBG, giving rise to the anomalous Hall effect (AHE) in correlated metallic states nearby most odd integer fillings of the flat conduction band, as well as correlated Chern insulator states stabilized in an external magnetic field. The behavior of the states at zero field appears to be inconsistent with simple spin and valley polarization for the specific range of twist angles we investigate, and instead may plausibly result from an intervalley coherent (IVC) state with an order parameter that breaks time reversal symmetry. The application of a magnetic field further tunes the competition between correlated states, in some cases driving first-order topological phase transitions. Our results underscore the rich interplay between closely competing correlated ground states in tMBG, with possible implications for probing exotic IVC ordering.
A variety of correlated phases have recently emerged in select twisted van der Waals (vdW) heterostructures owing to their flat electronic dispersions. In particular, heterostructures of twisted double bilayer graphene (tDBG) manifest electric field-
tunable correlated insulating (CI) states at all quarter fillings of the conduction band, accompanied by nearby states featuring signatures suggestive of superconductivity. Here, we report electrical transport measurements of tDBG in which we elucidate the fundamental role of spontaneous symmetry breaking within its correlated phase diagram. We observe abrupt resistivity drops upon lowering the temperature in the correlated metallic phases neighboring the CI states, along with associated nonlinear $I$-$V$ characteristics. Despite qualitative similarities to superconductivity, concomitant reversals in the sign of the Hall coefficient instead point to spontaneous symmetry breaking as the origin of the abrupt resistivity drops, while Joule heating appears to underlie the nonlinear transport. Our results suggest that similar mechanisms are likely relevant across a broader class of semiconducting flat band vdW heterostructures.
