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In this paper we present a first non-iterative imaging method for nonlinear materials, based on Monotonicity Principle. Specifically, we deal with the inverse obstacle problem, where the aim is to retrieve a nonlinear anomaly embedded in linear known background. The Monotonicity Principle (MP) is a general property for various class of PDEs, that has recently generalized to nonlinear elliptic PDEs. Basically, it states a monotone relation between the point-wise value of the unknown material property and the boundary measurements. It is at the foundation of a class of non-iterative imaging methods, characterized by a very low execution time that makes them ideal candidates for real-time applications. In this work, we develop an inversion method that overcomes some of the peculiar difficulties in practical application of MP to imaging of nonlinear materials, preserving the feasibility for real-time applications. For the sake of clarity, we focus on a specific application, i.e. the Magnetostatic Permeability Tomography where the goal is retrieving the unknown (nonlinear) permeability by boundary measurements in DC operations. This choice is motivated by applications in the inspection of boxes and containers for security. Reconstructions from simulated data prove the effectiveness of the presented method.

Safety assessment of crash and conflict avoidance systems is important for both the automotive industry and other stakeholders. One type of system that needs such an assessment is a driver monitoring system (DMS) with some intervention (e.g., warning or nudging) when the driver looks off-road for too long. Although using computer simulation to assess safety systems is becoming increasingly common, it is not yet commonly used for systems that affect driver behavior, such as DMSs. Models that generate virtual crashes, taking crash-causation mechanisms into account, are needed to assess these systems. However, few such models exist, and those that do have not been thoroughly validated on real-world data. This study aims to address this research gap by validating a rear-end crash-causation model which is based on four crash-causation mechanisms related to driver behavior: a) off-road glances, b) too-short headway, c) not braking with the maximum deceleration possible, and d) sleepiness (not reacting before the crash). The pre-crash kinematics were obtained from the German GIDAS in-depth crash database. Challenges with the validation process were identified and addressed. Most notably, a process was developed to transform the generated crashes to mimic the crash severity distribution in GIDAS. This step was necessary because GIDAS does not include property-damage-only (PDO) crashes, while the generated crashes cover the full range of severities (including low-severity crashes, of which many are PDOs). Our results indicate that the proposed model is a reasonably good crash generator. We further demonstrated that the model is a valid method for assessing DMSs in virtual simulations; it shows the safety impact of shorter "longest" off-road glances. As expected, cutting away long off-road glances substantially reduces the number of crashes that occur and reduces the average delta-v.

In this paper, we develop a novel fast iterative moment method for the steady-state simulation of near-continuum flows, which are modeled by the high-order moment system derived from the Boltzmann-BGK equation. The fast convergence of the present method is mainly achieved by alternately solving the moment system and the hydrodynamic equations with compatible constitutive relations and boundary conditions. To be specific, the compatible hydrodynamic equations are solved in each iteration to get improved predictions of macroscopic quantities, which are subsequently utilized to expedite the evolution of the moment system. Additionally, a semi-implicit scheme treating the collision term implicitly is introduced for the moment system. With cell-by-cell sweeping strategy, the resulting alternating iteration can be further accelerated for steady-state computation. It is also worth mentioning that such an alternating iteration works well with the nonlinear multigrid method. Numerical experiments for planar Couette flow, shock structure, and lid-driven cavity flow are carried out to investigate the performance of the proposed fast iterative moment method, and all results show wonderful efficiency and robustness.

In this paper, we investigate hypothesis testing for the linear combination of mean vectors across multiple populations through the method of random integration. We have established the asymptotic distributions of the test statistics under both null and alternative hypotheses. Additionally, we provide a theoretical explanation for the special use of our test statistics in situations when the nonzero signal in the linear combination of the true mean vectors is weakly dense. Moreover, Monte-Carlo simulations are presented to evaluate the suggested test against existing high-dimensional tests. The findings from these simulations reveal that our test not only aligns with the performance of other tests in terms of size but also exhibits superior power.

In this paper, without requiring any constraint qualifications, we establish tight error bounds for the log-determinant cone, which is the closure of the hypograph of the perspective function of the log-determinant function. This error bound is obtained using the recently developed framework based on one-step facial residual functions.

In this paper, we discuss the development and deployment of a robust autonomous system capable of performing various tasks in the maritime domain under unknown dynamic conditions. We investigate a data-driven approach based on modular design for ease of transfer of autonomy across different maritime surface vessel platforms. The data-driven approach alleviates issues related to a priori identification of system models that may become deficient under evolving system behaviors or shifting, unanticipated, environmental influences. Our proposed learning-based platform comprises a deep Koopman system model and a change point detector that provides guidance on domain shifts prompting relearning under severe exogenous and endogenous perturbations. Motion control of the autonomous system is achieved via an optimal controller design. The Koopman linearized model naturally lends itself to a linear-quadratic regulator (LQR) control design. We propose the C3D control architecture Cascade Control with Change Point Detection and Deep Koopman Learning. The framework is verified in station keeping task on an ASV in both simulation and real experiments. The approach achieved at least 13.9 percent improvement in mean distance error in all test cases compared to the methods that do not consider system changes.

In this paper, we introduce quadratic and cubic polynomial enrichments of the classical Crouzeix--Raviart finite element, with the aim of constructing accurate approximations in such enriched elements. To achieve this goal, we respectively add three and seven weighted line integrals as enriched degrees of freedom. For each case, we present a necessary and sufficient condition under which these augmented elements are well-defined. For illustration purposes, we then use a general approach to define two-parameter families of admissible degrees of freedom. Additionally, we provide explicit expressions for the associated basis functions and subsequently introduce new quadratic and cubic approximation operators based on the proposed admissible elements. The efficiency of the enriched methods is compared to the triangular Crouzeix--Raviart element. As expected, the numerical results exhibit a significant improvement, confirming the effectiveness of the developed enrichment strategy.

In this paper, we propose a new modified likelihood ratio test (LRT) for simultaneously testing mean vectors and covariance matrices of two-sample populations in high-dimensional settings. By employing tools from Random Matrix Theory (RMT), we derive the limiting null distribution of the modified LRT for generally distributed populations. Furthermore, we compare the proposed test with existing tests using simulation results, demonstrating that the modified LRT exhibits favorable properties in terms of both size and power.

In this manuscript, we combine non-intrusive reduced order models (ROMs) with space-dependent aggregation techniques to build a mixed-ROM. The prediction of the mixed formulation is given by a convex linear combination of the predictions of some previously-trained ROMs, where we assign to each model a space-dependent weight. The ROMs taken into account to build the mixed model exploit different reduction techniques, such as Proper Orthogonal Decomposition (POD) and AutoEncoders (AE), and/or different approximation techniques, namely a Radial Basis Function Interpolation (RBF), a Gaussian Process Regression (GPR) or a feed-forward Artificial Neural Network (ANN). The contribution of each model is retained with higher weights in the regions where the model performs best, and, vice versa, with smaller weights where the model has a lower accuracy with respect to the other models. Finally, a regression technique, namely a Random Forest, is exploited to evaluate the weights for unseen conditions. The performance of the aggregated model is evaluated on two different test cases: the 2D flow past a NACA 4412 airfoil, with an angle of attack of 5 degrees, having as parameter the Reynolds number varying between 1e5 and 1e6 and a transonic flow over a NACA 0012 airfoil, considering as parameter the angle of attack. In both cases, the mixed-ROM has provided improved accuracy with respect to each individual ROM technique.

In this paper, we address the critical challenges of double-spending and selfish mining attacks in blockchain-based digital currencies. Double-spending is a problem where the same tender is spent multiple times during a digital currency transaction, while selfish mining is an intentional alteration of a blockchain to increase rewards to one miner or a group of miners. We introduce a new attack that combines both these attacks and propose a machine learning-based solution to mitigate the risks associated with them. Specifically, we use the learning automaton, a powerful online learning method, to develop two models, namely the SDTLA and WVBM, which can effectively defend against selfish mining attacks. Our experimental results show that the SDTLA method increases the profitability threshold of selfish mining up to 47$\%$, while the WVBM method performs even better and is very close to the ideal situation where each miner's revenue is proportional to their shared hash processing power. Additionally, we demonstrate that both methods can effectively reduce the risks of double-spending by tuning the $Z$ Parameter. Our findings highlight the potential of SDTLA and WVBM as promising solutions for enhancing the security and efficiency of blockchain networks.