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Abstract The multiple-try Metropolis method is an interesting extension of the classical Metropolis–Hastings algorithm. However, theoretical understanding about its usefulness and convergence behavior is still lacking. We here derive the exact convergence rate for the multiple-try Metropolis Independent sampler (MTM-IS) via an explicit eigen analysis. As a by-product, we prove that an naive application of the MTM-IS is less efficient than using the simpler approach of “thinned” independent Metropolis–Hastings method at the same computational cost. We further explore more variants and find it possible to design more efficient algorithms by applying MTM to part of the target distribution or creating correlated multiple trials. 

Optical phase-change materials exhibit tunable permittivity and switching properties during phase transition, which offers the possibility of dynamic control of optical devices. Here, a wavelength-tunable infrared chiral metasurface integrated with phase-change material GST-225 is demonstrated with the designed unit cell of parallelogram-shaped resonator. By varying the baking time at a temperature above the phase transition temperature of GST-225, the resonance wavelength of the chiral metasurface is tuned in the wavelength range of 2.33 µm to 2.58 µm, while the circular dichroism in absorption is maintained around 0.44. The chiroptical response of the designed metasurface is revealed by analyzing the electromagnetic field and displacement current distributions under left- and right-handed circularly polarized (LCP and RCP) light illumination. Moreover, the photothermal effect is simulated to investigate the large temperature difference in the chiral metasurface under LCP and RCP illumination, which allows for the possibility of circular polarization-controlled phase transition. The presented chiral metasurfaces with phase-change materials offer the potential to facilitate promising applications in the infrared regime, such as chiral thermal switching, infrared imaging, and tunable chiral photonics.

 

The paper extends the recent star reachability method to verify the robustness of recurrent neural networks (RNNs) for use in safety-critical applications. RNNs are a popular machine learning method for various applications, but they are vulnerable to adversarial attacks, where slightly perturbing the input sequence can lead to an unexpected result. Recent notable techniques for verifying RNNs include unrolling, and invariant inference approaches. The first method has scaling issues since unrolling an RNN creates a large feedforward neural network. The second method, using invariant sets, has better scalability but can produce unknown results due to the accumulation of overapproximation errors over time. This paper introduces a complementary verification method for RNNs that is both sound and complete. A relaxation parameter can be used to convert the method into a fast overapproximation method that still provides soundness guarantees. The method is designed to be used with NNV, a tool for verifying deep neural networks and learning-enabled cyber-physical systems. Compared to state-of-the-art methods, the extended exact reachability method is 10 × faster, and the overapproximation method is 100 × to 5000 × faster. 

Abstract The design and formation of van der Waals (vdW) heterostructures with different two-dimensional (2D) materials provide an opportunity to create materials with extraordinary physical properties tailored toward specific applications. Mechanical exfoliation of natural vdW materials has been recognized as an effective way for producing high-quality ultrathin vdW heterostructures. Abramovite is one of such naturally occurring vdW materials, where the superlattice is composed of alternating Pb 2 BiS 3 and SnInS 4 2D material lattices. The forced commensuration between the two incommensurate constituent 2D material lattices induces in-plane structural anisotropy in the formed vdW heterostructure of abramovite, even though the individual 2D material lattices are isotropic in nature. Here, we show that ultrathin layers of vdW heterostructures of abramovite can be achieved by mechanical exfoliation of the natural mineral. Furthermore, the structural anisotropy induced highly anisotropic vibrational and optical responses of abramovite thin flakes are demonstrated by angle-resolved polarized Raman scattering, linear dichroism, and polarization-dependent third-harmonic generation. Our results not only establish abramovite as a promising natural vdW material with tailored linear and nonlinear optical properties for building future anisotropic integrated photonic devices, but also provide a deeper understanding of the origin of structural, vibrational and optical anisotropy in vdW heterostructures. 

Cannizzarite is a naturally occurring mineral formed by van der Waals (vdW) stacking of alternating layers of PbS-like and Bi₂S₃-like two-dimensional (2D) materials. Although the PbS-type and Bi₂S₃-type 2D material layers are structurally isotropic individually, the forced commensuration between these two types of layers while forming the heterostructure of cannizzarite induces strong structural anisotropy. Here we demonstrate the mechanical exfoliation of natural cannizzarite mineral to obtain thin vdW heterostructures of PbS-type and Bi₂S₃-type atomic layers. The structural anisotropy induced anisotropic optical properties of thin cannizzarite flakes are explored through angle-resolved polarized Raman scattering, linear dichroism, and polarization-dependent anisotropic third-harmonic generation. Our study establishes cannizzarite as a new natural vdW heterostructure-based 2D material with highly anisotropic optical properties for realizing polarization-sensitive linear and nonlinear photonic devices for future on-chip optical computing and optical information processing.

 

Multi-element layered materials have gained substantial attention in the context of achieving the customized light-matter interactions at subwavelength scale via stoichiometric engineering, which is crucial for the realization of miniaturized polarization-sensitive optoelectronic and nanophotonic devices. Herein, naturally occurring hydrated sodium sulfosalt gerstleyite is introduced as one new multi-element van der Waals (vdW) layered material. The mechanically exfoliated thin gerstleyite flakes are demonstrated to exhibit polarization-sensitive anisotropic linear and nonlinear optical responses including angle-resolved Raman scattering, anomalous wavelength-dependent linear dichroism transition, birefringence effect, and polarization-dependent third-harmonic generation (THG). Furthermore, the third-order nonlinear susceptibility of gerstleyite crystal is estimated by the probed flake thickness-dependent THG response. We envisage that our findings in the context of polarization-sensitive light-matter interactions in the exfoliated hydrated sulfosalt layers will be a valuable addition to the vdW layered material family and will have many implications in compact waveplates, on-chip photodetectors, optical sensors and switches, integrated photonic circuits, and nonlinear signal processing applications.

 

Naturally occurring layered mineral livingstonite is identified as a new type of van der Waals (vdW) heterostructure based 2D material, consisting of two commensurately modulated alternating layers of HgSb 2 S 4 and Sb 2 S 4 . The heterostructures of livingstonite crystal are prepared as thin flakes via mechanical exfoliation method. The prepared livingstonite crystals are further investigated in the context of vibrational, linear, and nonlinear optical properties, including anisotropic Raman scattering, wavelength-dependent linear dichroism (LD) transition effect, birefringence, and anisotropic third-harmonic generation (THG). Owing to the monoclinic crystal structure, livingstonite crystals exhibit strong anisotropic vibrational and optical responses. In contrast to conventional vdW heterostructures, the anomalous LD transition effect and the evolution of butterfly-shaped THG emission pattern in livingstonite crystals are demonstrated. Furthermore, the third-order nonlinear susceptibility is estimated for livingstonite crystal using the thickness-dependent THG emission response. Overall, the discussed outcomes establish livingstonite as a new type of naturally grown vdW heterostructure based 2D material and offer insights in tailoring linear and nonlinear light-matter interactions in such vdW heterostructures, which may find further relevance in polarized optical applications and on-chip integrated photonic circuits.