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Extracting latent nonlinear dynamics from observed time-series data is important for understanding a dynamic system against the background of the observed data. A state space model is a probabilistic graphical model for time-series data, which describes the probabilistic dependence between latent variables at subsequent times and between latent variables and observations. Since, in many situations, the values of the parameters in the state space model are unknown, estimating the parameters from observations is an important task. The particle marginal Metropolis–Hastings (PMMH) method is a method for estimating the marginal posterior distribution of parameters obtained by marginalization over the distribution of latent variables in the state space model. Although, in principle, we can estimate the marginal posterior distribution of parameters by iterating this method infinitely, the estimated result depends on the initial values for a finite number of times in practice. In this paper, we propose a replica exchange particle marginal Metropolis–Hastings (REPMMH) method as a method to improve this problem by combining the PMMH method with the replica exchange method. By using the proposed method, we simultaneously realize a global search at a high temperature and a local fine search at a low temperature. We evaluate the proposed method using simulated data obtained from the Izhikevich neuron model and Lévy-driven stochastic volatility model, and we show that the proposed REPMMH method improves the problem of the initial value dependence in the PMMH method, and realizes efficient sampling of parameters in the state space models compared with existing methods.

Our fascination with parietal art (also known as cave art), as with most prehistoric artifacts, often lies in the mystery of its origins, and the fact, astonishingly, of its enduring presence; it appears to us in images that speak through time. This auratic allure is obscured, however, by the uncanny conditions in which we now encounter these images: as most of the original sites are closed to the public in order to preserve them, we find exceptionally crafted replicas constructed in their place. Here, Veber examines whether images still carry through time.

Objectives This study compared the silicone replica method with swept-source optical coherence tomography (SS-OCT) to analyze marginal adaptation and investigated the effect of the light incidence angle of SS-OCT on measurement precision. Materials and methods A typodont-prepared mandibular right first molar was scanned using an intraoral scanner (Trios 3). Fourteen crowns were fabricated from CAD/CAM resin blocks (Katana Avencia P) using a 5-axis milling machine (DWX-50). Marginal adaptation at the buccal, lingual, mesial, and distal points was assessed using the silicone replica method and SS-OCT at light incidence angles of 60°, 75°, and 90°. Statistical comparisons were performed using two-way analysis of variance (ANOVA) and t-tests with Bonferroni correction, and t-tests at a significance level of 0.05. Results At 60°, SS-OCT showed significantly larger marginal discrepancies than the silicone replica method at the buccal, lingual, and mesial points ( p  < 0.05). At 75°, only the lingual point showed a significantly larger value than the silicone replica method ( p  < 0.05). At 90°, no significant differences were observed between the SS-OCT and silicone replica methods ( p  > 0.05). Marginal discrepancy values increased as the angle changed from 90° to 75° to 60°, with significant differences between 60° and 75° and between 60° and 90° at the buccal and lingual points ( p  < 0.05). Conclusions SS-OCT is a viable alternative to the silicone replica method for assessing marginal adaptation at an incidence angle of 90 °. Clinical relevance SS-OCT, a non-invasive method, has the potential to be applied clinically for evaluating marginal fit in indirect restorations in vivo.

Groundwater inrush is a hazard that always occurs during underground mining. Grouting is one of the most effective processes to seal underground water inflow for hazard prevention. In this study, grouting experiments are conducted by using a visualized transparent single‐fracture replica with plane roughness. Image processing and analysis are performed to investigate the thermo–hydro–mechanical coupling effect on the grouting diffusion under coal mine flowing water conditions. The results show that higher ambient temperature leads to shorter initial gel time of chemical grout and leads to a better relative sealing efficiency in the case of a lower flow rate. However, with a higher water flow rate, the relative sealing efficiency is gradually reduced under higher temperature conditions. The grouting pressure, the seepage pressure, and the temperature are measured. The results reveal that the seepage pressure shows a positive correlation with the grouting pressure, while the temperature change shows a negative correlation with the seepage pressure and the grouting pressure. The “equivalent grouting point offset” effect of grouting shows an eccentric elliptical diffusion with larger grouting distance and width under lower temperature conditions. Higher temperature leads to a better relative sealing efficiency with a slow flow rate. Temperature change shows a negative correlation with the seepage pressure and the grouting pressure. The “equivalent grouting point offset” effect of grouting shows an eccentric elliptical propagation. Highlights Higher temperature leads to a better relative sealing efficiency with a slow flow rate. Seepage pressure shows a positive correlation with grouting pressure. Temperature change shows a negative correlation with seepage pressure and grouting pressure. Small breakthrough holes are formed and the diffusion interface is shifted from the center, resulting in the “equivalent grouting point offset” effect.

Glass transition, in which viscosity of liquids increases dramatically upon decrease of temperature without any major change in structural properties, remains one of the most challenging problems in condensed matter physics despite tremendous research efforts in past decades. On the other hand, disordered freezing of spins in magnetic materials with decreasing temperature, the so-called “spin glass transition,” is understood relatively better. A previously found similarity between some spin glass models and the structural glasses inspired development of theories of structural glasses based on the scenario of spin glass transition. This scenario, although it looks very appealing, is still far from being well established. One of the main differences between standard spin systems and molecular systems is the absence of quenched disorder and the presence of translational invariance: it often is assumed that this difference is not relevant, but this conjecture still needs to be established. The quantities, which are well-defined and characterized for spin models, are not easily calculable for molecular glasses because of the lack of quenched disorder that breaks the translational invariance in the system. Thus the characterization of the similarity between spin and the structural glass transition remains an elusive subject. In this study, we introduced a model structural glass with built-in quenched disorder that alleviates this main difference between the spin and molecular glasses, thereby helping us compare these two systems: the possibility of producing a good thermalization at rather low temperatures is one of the advantages of this model.

We study the fundamental limits of detecting the presence of an additive rank-one perturbation, or spike, to a Wigner matrix. When the spike comes from a prior that is i.i.d. across coordinates, we prove that the log-likelihood ratio of the spiked model against the nonspiked one is asymptotically normal below a certain reconstruction threshold which is not necessarily of a “spectral” nature, and that it is degenerate above. This establishes the maximal region of contiguity between the planted and null models. It is known that this threshold also marks a phase transition for estimating the spike: the latter task is possible above the threshold and impossible below. Therefore, both estimation and detection undergo the same transition in this random matrix model. Further information on the performance of the optimal test is also provided. Our proofs are based on Gaussian interpolation methods and a rigorous incarnation of the cavity method, as devised by Guerra and Talagrand in their study of the Sherrington–Kirkpatrick spin-glass model.

The proposed work aims to develop a sensitive surface-enhanced Raman spectroscopy (SERS) nano-biosensor. The inverted nano pyramid array on silicon substrate fabricated using electron beam lithography (EBL) was utilised as a master template and the mold was later replicated via nanoimprinting process to prepare gold-coated polymer nanopyramid three-dimensional (3D) SERS substrate. The fast and versatile replication process using nanoimprinting lithography (NIL) can produce polymer nanopyramids in a low-cost and reproducible fashion. Also, the proposed fabrication protocol can be easily upscale for large scale fabrication. The intense electric field confinement at nanotips and four edges of gold-coated polymer nanopyramid enhanced the Raman signal of probe molecules, i.e., Rhodamine 6G with a limit of detection down to 3.277 × 10 −9 M was achieved. This work also underlines the efficiency of gold-coated polymer nanopyramid arrays in the spectral detection of hemoglobin proteins at low concentrations. The Raman signal enhancement mechanism was further studied through the electromagnetic simulation using COMSOL Multiphysics. In addition, bending test experiments were performed to understand the effect of flexibility on SERS signal response. The fabricated gold-coated polymer nanopyramids arrays could pave the way for the development of low-cost SERS platforms for the detection of hazardous biological and chemical compounds at ultra-low concentrations in practical applications.

Although various higher-order protein structure prediction methods have been developed, almost all of them were developed based on the three-dimensional (3D) structure information of known proteins. Here we predicted the short protein structures by molecular dynamics (MD) simulations in which only Newton’s equations of motion were used and 3D structural information of known proteins was not required. To evaluate the ability of MD simulationto predict protein structures, we calculated seven short test protein (10–46 residues) in the denatured state and compared their predicted and experimental structures. The predicted structure for Trp-cage (20 residues) was close to the experimental structure by 200-ns MD simulation. For proteins shorter or longer than Trp-cage, root-mean square deviation values were larger than those for Trp-cage. However, secondary structures could be reproduced by MD simulations for proteins with 10–34 residues. Simulations by replica exchange MD were performed, but the results were similar to those from normal MD simulations. These results suggest that normal MD simulations can roughly predict short protein structures and 200-ns simulations are frequently sufficient for estimating the secondary structures of protein (approximately 20 residues). Structural prediction method using only fundamental physical laws are useful for investigating non-natural proteins, such as primitive proteins and artificial proteins for peptide-based drug delivery systems.

Background The success of a restoration largely depends on the quality of its fit. This study aimed to investigate the fit quality of monolithic zirconia veneers (MZVs) produced through traditional and digital workflows. Methods A typodont maxillary right central incisor was prepared. The maxillary arch with the prepared tooth was scanned with Trios 3 Pod intra-oral scanner (IOS), which served as a pattern to create thirty 3D resin models through printing. Additionally, thirty conventional impressions of the maxillary with the prepared tooth were taken using polyvinyl siloxane (PVS) impression material. These impressions were cast using dental gypsum products to create thirty stone dies, which were then scanned externally. Sixty MZVs were milled from multi-layered zirconia disks. The marginal and internal gaps of restorations were assessed using the silicone replica technique. Results The highest marginal accuracy for both the conventional and digital impression groups was observed in the cervical area, with values of 74.6 μm and 61.9 μm, respectively. The smallest internal gaps for both groups were also recorded in the cervical area, at 109.9 μm for the conventional group and 109.7 μm for the digital group. The digital group exhibited better marginal fit, particularly in the incisal and mesial areas (79.3 μm and 75.7 μm, respectively), compared to the conventional group (88.1 μm and 90.8 μm). No statistically significant differences in internal fit were observed. Conclusion MZVs fabricated using the digital workflow exhibited superior marginal fit compared to those fabricated using the conventional workflow, though both techniques yielded clinically acceptable results.

Ceramic components require very high energy consumption due to synthesis, shaping, and thermal treatment. However, this study suggests that combining the sol–gel process, replica technology, and stereolithography has the potential to produce highly complex geometries with energy savings in each process step. We fabricated light-frame honeycombs of Al2O3, Ba0.85Ca0.15Zr0.1Ti0.9O3 (BCZT), and BaTiO3 (BT) using 3D-printed templates with varying structural angles between −30° and 30° and investigated their mechanical and piezoelectric properties. The Al2O3 honeycombs showed a maximum strength of approximately 6 MPa, while the BCZT and BaTiO3 honeycombs achieved a d33 above 180 pC/N. Additionally, the BCZT powder was prepared via a sol–gel process, and the impact of the calcination temperature on phase purity was analyzed. The results suggest that there is a large energy-saving potential for the synthesis of BCZT powder. Overall, this study provides valuable insights into the fabrication of complex ceramic structures with improved energy efficiency and enhancement of performance.