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The separation of an object from other objects or the background by selecting the optimal threshold values remains a challenge in the field of image segmentation. Threshold segmentation is one of the most popular image segmentation techniques. The traditional methods for finding the optimum threshold are computationally expensive, tedious, and may be inaccurate. Hence, this paper proposes an Improved Whale Optimization Algorithm (IWOA) based on Kapur’s entropy for solving multi-threshold segmentation of the gray level image. Also, IWOA supports its performance using linearly convergence increasing and local minima avoidance technique (LCMA), and ranking-based updating method (RUM). LCMA technique accelerates the convergence speed of the solutions toward the optimal solution and tries to avoid the local minima problem that may fall within the optimization process. To do that, it updates randomly the positions of the worst solutions to be near to the best solution and at the same time randomly within the search space according to a certain probability to avoid stuck into local minima. Because of the randomization process used in LCMA for updating the solutions toward the best solutions, a huge number of the solutions around the best are skipped. Therefore, the RUM is used to replace the unbeneficial solution with a novel updating scheme to cover this problem. We compare IWOA with another seven algorithms using a set of well-known test images. We use several performance measures, such as fitness values, Peak Signal to Noise Ratio, Structured Similarity Index Metric, Standard Deviation, and CPU time.

We consider the sparse optimization problem with nonlinear constraints and an objective function, which is given by the sum of a general smooth mapping and an additional term defined by the ℓ0-quasi-norm. This term is used to obtain sparse solutions, but difficult to handle due to its nonconvexity and nonsmoothness (the sparsity-improving term is even discontinuous). The aim of this paper is to present two reformulations of this program as a smooth nonlinear program with complementarity-type constraints. We show that these programs are equivalent in terms of local and global minima and introduce a problem-tailored stationarity concept, which turns out to coincide with the standard KKT conditions of the two reformulated problems. In addition, a suitable constraint qualification as well as second-order conditions for the sparse optimization problem are investigated. These are then used to show that three Lagrange–Newton-type methods are locally fast convergent. Numerical results on different classes of test problems indicate that these methods can be used to drastically improve sparse solutions obtained by some other (globally convergent) methods for sparse optimization problems.

We establish size limitations for assembling structures of controlled size and shape out of colloidal particles with short-ranged interactions. Through simulations we show that structures with highly variable shapes made out of dozens of particles can form with high yield, as long as each particle in the structure binds only to the particles in their local environment. To understand this, we identify the excited states that compete with the ground-state structure and demonstrate that these excited states have a completely topological characterization, valid when the interparticle interactions are short-ranged. This allows complete enumeration of the energy landscape and gives bounds on how large a colloidal structure can assemble with high yield. For large structures the yield can be significant, even with hundreds of particles. Significance Nature uses hierarchical assembly to make complex structures such as biomolecules, virus shells, and microtubules with high fidelity. Today a key challenge is to translate this process to artificial systems, which hinges on understanding the fundamental questions of efficiency and scalability of self-assembly. Although self-assembly has been studied for decades, the principles behind it and its fundamental and practical limits are still largely unknown. In this paper we establish size limitations for assembling structures of controlled size and shape out of colloidal particles with specific interactions. Inspired by simulations of structures with highly variable shapes and sizes, we develop an understanding of yield through a general theory of excited states that compete with the desired structure in assembly.

We present a global optimization routine for the variational quantum algorithms, which utilizes the dynamic tunneling flow. Originally designed to leverage information gathered by a gradient-based optimizer around local minima, we adapt the conventional dynamic tunneling flow to exploit the distance measure of quantum states, resolving issues of extrinsic degeneracy arising from the parametrization of quantum states. Our global optimization algorithm is applied to the variational quantum eigensolver for the transverse-field Ising model to demonstrate the performance of our routine while comparing it with the conventional dynamic tunneling method, which is based on the Euclidean distance measure on the parameter space.

The objective of this study was to apply the Sadegh, Ragno, and AghaKouchak (SRA) approach to the field of quantitative finance by analyzing, for the first time, the relationship between price and trading volume of the securities using four stock market indices: DJIA, FOOTSIE100, NIKKEI225, and IBEX35. This procedure is a completely new methodology in finance that consists of the application of a Bayesian framework and the development of a hybrid evolution algorithm of the Markov Chain Monte Carlo (MCMC) method to analyze a large number (26) of parametric copulas. With respect to the DJIA, the Joe’s copula is the one that most efficiently models its succinct dependence structures. One of the copulas included in the SRA approach, the Tawn’s copula, is jointly adjusted to the FOOTSIE100, NIKKEI225, and IBEX 35 indices to analyze the asymmetric relationship between price and trading volume. This adjustment can be considered almost perfect for the NIKKEI225, and a relatively different characterization for the IBEX35 seems to indicate the existence of endogenous patterns in the price and volume.

Deep learning networks have been trained using first-order-based methods. These methods often converge more quickly when combined with an adaptive step size, but they tend to settle at suboptimal points, especially when learning occurs in a large output space. When first-order-based methods are used with a constant step size, they oscillate near the zero-gradient region, which leads to slow convergence. However, these issues are exacerbated under nonconvexity, which can significantly diminish the performance of first-order methods. In this work, we propose a novel  B oltzmann Probability Weighted  S ine with a  C osine distance-based  A daptive  Grad ient ( BSCAGrad ) method. The step size in this method is carefully designed to mitigate the issue of slow convergence. Furthermore, it facilitates escape from suboptimal points, enabling the optimization process to progress more efficiently toward local minima. This is achieved by combining a Boltzmann probability-weighted sine function and cosine distance to calculate the step size. The Boltzmann probability-weighted sine function acts when the gradient vanishes and the cooling parameter remains moderate, a condition typically observed near suboptimal points. Moreover, using the sine function on the exponential moving average of the weight parameters leverages geometric information from the data. The cosine distance prevents zero in the step size. Together, these components accelerate convergence, improve stability, and guide the algorithm toward a better optimal solution. A theoretical analysis of the convergence rate under both convexity and nonconvexity is provided to substantiate the findings. The experimental results from language modeling, object detection, machine translation, and image classification tasks on a real-world benchmark dataset, including CIFAR 10, CIFAR 100, PennTreeBank , PASCALVOC and WMT 2014, demonstrate that the proposed step size outperforms traditional baseline methods. Graphical abstract

Some classic second-order sufficient optimality conditions in the calculus of variations are shown to be equivalent, while also introducing a new equivalent second-order condition which is extremely easy to apply: simply integrate a linear second-order initial value problem and check that the solution is positive over the problem domain.

In the study of autonomous obstacle avoidance of intelligent vehicles, the traditional artificial potential field method has the problem that the vehicle may fall into the local minima and lead to obstacle avoidance failure. Therefore, this paper improves the traditional potential field function. Based on the vehicle dynamics model, a strategy of jumping out of local minima based on smaller steering angles is proposed. By finding a smaller steering angle and setting a suitable jump out step length, the intelligent vehicle is enabled to jump out of the local minima. Simulation experiments by MATLAB show that the improved method can jump out of the local minima. By comparing the planned trajectories of the traditional method and the improved method in static and dynamic obstacles situations, the trajectory planned by the improved method is smooth and the curvature is smaller. The planned trajectory is tracked by the Carsim platform, and the test results show that the improved method reduces the front steering wheel angle while the intelligent vehicle satisfies the vehicle dynamics constraints during active obstacle avoidance, which verifies the stability and rationality of the improved method.

Abnormal event detection in video surveillance is critical for security, traffic management, and industrial monitoring applications. This paper introduces an innovative methodology for anomaly detection in video data, encompassing three primary stages: preprocessing, feature learning, and anomaly detection. We employ background subtraction and noise reduction during preprocessing to refine the data. The feature-learning stage involves training an LSTM autoencoder to capture the essential features of normal video sequences. For anomaly detection, we map video data to a lower-dimensional space (latent code) and compare it against the distribution of codes from normal sequences. We determine regularity scores and identify local minima points exceeding a specified threshold while scrutinizing shadows between adjacent maxima to confirm and pinpoint anomalies. When tested on the CUHK Avenue and UMN datasets, our methodology demonstrated performance with AUCs of 93.8% and 94.1%, respectively, outperforming several baseline models. Our results show the high precision of our method that can detect anomalies, highlighting its potential advantages that it can achieve for enhancing systems of surveillance. Article Highlights Novel method for detecting abnormal events in surveillance videos using LSTM autoencoder and local minima analysis. Achieves high accuracy on benchmark datasets, demonstrating its effectiveness in dynamic and complex environments. Reduces false positives, making it a reliable tool for enhancing security and traffic monitoring systems.