The Density Peak Clustering (DPC) algorithm is simple and efficient. But DPC and its variants identify clusters only by identifying the centers of single or multiple sparse clusters without considering the coherence of the clustering structure, which tends to result in clusters that cannot be accurately captured. In addition, relative distance and density are only used to identify the centers of clusters and do not provide a description of the relative positions of the remaining sample points. To address these issues, this paper proposes an adaptive density peak clustering algorithm based on centrifugal degree (CD-DPC). The centrifugal degree reflects the relative position of the sample points in the cluster. The CD-DPC categorizes sample points into support, structural, coherent and decoration points based on centrifugal degree. Based on this, the number of clusters is automatically obtained by using different association methods for sample points with different centrifugal degrees, which greatly reduces the influence of human factors. Finally, the clustering results are further improved by introducing shared nearest neighbors for the final association of decorated points. Extensive experiments on synthetic and UCI datasets show that this algorithm outperforms other comparative algorithms.

Global energy consumption is increasing substantially due to population growth and industrial transformation, with the industrial sector, characterized by high electricity usage, accounting for the largest share. Facing electricity supply constraints and time-varying demand, many governments implement time-of-use (ToU) tariffs to balance supply and mitigate peak loads. These tariffs introduce dynamic and period-dependent electricity costs, compelling industrial users to make trade-offs between operational efficiency and production costs. The flexible job shop scheduling problem (FJSP) is a widely adopted production model. To examine the impact of ToU tariffs on industrial operations, we investigate an FJSP variant with controllable processing speeds, sequence-dependent setups, and turn-on/off decisions under ToU settings (FJSPSS-ToU). A mathematical model is formulated to jointly optimize the production efficiency and total electricity costs, and its correctness is validated using CPLEX. To solve this problem, a twin-reinforced evolutionary algorithm (TREA) is introduced. TREA takes the evolutionary algorithm as its backbone and contains two reinforcement learning (RL) modules: an RL-guided parent-matching module that learns pairing utilities and an RL-assisted operator recommendation module that selects the most suitable operators. Moreover, a cost-saving strategy that combines a full-active decoding strategy with a right-shift operation is designed to reduce electricity cost. TREA is comprehensively evaluated against nine state-of-the-art algorithms, and the comparison results demonstrate its superior performance. Moreover, further experiments reveal that each learning module delivers measurable gains, and their organic integration makes the best contribution.

Density Peaks Clustering (DPC) is an effective density-based clustering method driven by its simplicity: a non-iterative process and minimal parameters. However, both the algorithm and its variants still face challenges in accurately identifying cluster centers, assigning points in overlapping boundary regions, and resolving chain reactions triggered by the domino effect. To overcome these shortcomings, an adaptive multi-stage density peaks clustering via core fusion and dual-tier constrained expansion (AMsDPC) is proposed. In the first stage, initial core points distributed across clusters are selected, and automatic core fusion is performed based on the linkage matrix and an adaptive threshold, which determines the number of clusters without requiring it as a priori input. Meanwhile, an improved connectivity based on reverse K-nearest neighbors is defined to better capture the local structure of the dataset. The second stage, starting from the initial core points in each cluster, executes a dual-tier constrained expansion mechanism to generate propagated core points via a consistency threshold test and a double-layer neighbor verification. In the third stage, representative points are dynamically selected from the existing core point sets to facilitate label propagation. By autonomously identifying cluster cores, AMsDPC can prevent error propagation and ensure precise boundary point assignment, thereby achieving superior accuracy and robustness. Finally, the algorithm's outstanding performance is demonstrated on both synthetic and real-world datasets.

With intensifying market competition and increasing customer demand for rapid fulfillment, the integrated scheduling between distributed production and logistics service has become increasingly important for improving supply chain operational efficiency. Meanwhile, manufacturing firms often operate multiple factories, making it necessary to determine which factories should be activated for order production according to delivery-time re quirements and customer locations. This paper considers an integrated problem involving factory activation, job scheduling, and logistics service decisions, referred to as the IFAJSLSP. The problem involves three distinct but tightly coupled subproblems: factory activation, distributed flexible job shop scheduling, and the multi-depot vehicle routing problem. The considered problem aims to minimize total cost, including factory operating costs, earliness and tardiness penalties, as well as energy consumption. A mathematical model is formulated to formal ize this challenging problem. Then, a dual-learning-powered evolutionary algorithm (DLEA) is proposed to solve it. In DLEA, a reinforcement learning-powered offspring breeding mechanism is developed, where Q-learning is used to identify promising partners for offspring generation. Meanwhile, a self-learning-driven local search strategy is introduced, with a self-learning mechanism employed to adaptively select local search operators. Extensive experiments are conducted to validate the performance of the DLEA. The results confirm the effective ness of the proposed learning modules and show that DLEA outperforms several well-established multi-objective evolutionary algorithms.

Turing patterns, typical examples of self-organization phenomena, are widely observed in the natural world. From Turing's pioneering work [Philos. Trans. R. Soc. Lond. B 237, 37 (1952)10.1098/rstb.1952.0012] to recent advances by Nakao et al. [Nat. Phys. 6, 544 (2010)10.1038/nphys1651], a fundamental framework has been established for analyzing pattern formation in network-organized reaction-diffusion systems. Notably, most existing studies assume identical diffusion coefficients for all network links to find the conditions for Turing patterns emergence. This naturally raises a question: is pattern formation possible if only a subset of network links has diffusion coefficients that fulfill the requirements? Links characterized by diffusion coefficients satisfying these conditions are termed as activated links. This paper investigates the emergence of Turing patterns through a partial link activation approach, encompassing both random and targeted activation schemes. The mean-field theory is employed to derive the conditions for pattern formation when network links are randomly activated. Numerical simulations are conducted to compare the efficiency of random and targeted activation schemes in triggering Turing patterns. The results demonstrate that the partial link activation approach can indeed generate Turing patterns, offering a more efficient mechanism. And the targeted activation scheme exhibits enhanced performance in promoting pattern formation relative to a random activation scheme. This study provides new perspectives on the role of local regulation in governing global network dynamics.

As the continuous deepening of low-carbon emission reduction policies, the manufacturing industries urgently need sensible energy-saving scheduling schemes to achieve the balance between improving production efficiency and reducing energy consumption. In energy-saving scheduling, reasonable machine states-switching is a key point to achieve expected goals, i.e., whether the machines need to switch speed between different operations, and whether the machines need to add extra setup time between different jobs. Regarding this matter, this work proposes a novel machine multi states-based energy saving flexible job scheduling problem (EFJSP-M), which simultaneously takes into account machine multi speeds and setup time. To address the proposed EFJSP-M, a kind of discrete differential evolution particle swarm optimization algorithm (D-DEPSO) is designed. In specific, D-DEPSO includes a hybrid initialization strategy to improve the initial population performance, an updating mechanism embedded with differential evolution operators to enhance population diversity, and a critical path variable neighborhood search strategy to expand the solution space. At last, based on datasets DPs and MKs, the experiment results compared with five state-of-the-art algorithms demonstrate the feasible of EFJSP-M and the superior of D-DEPSO.

Fractal is one of the most important branches in nonlinear science, and is well applicable to address various applications problems. Recently, a parameter estimation method for the classical Julia sets was proposed. However, high time-consumption and low estimation accuracy hinder its practical applications. Aiming for improving estimation efficiency, an objective space deviation (OSD) strategy is proposed. Simulation experiments are carried out on seven Julia set in different subspaces. Experimental results exhibit that the OSD strategy can effectively improve the accuracy and efficiency of Julia sets' parameter estimation.

With the continuous deepening of low-carbon emission reduction policies, the manufacturing industries urgently need reasonable energy-saving scheduling plans to achieve the balance between improving production efficiency and reducing energy consumption. In energy-saving scheduling, reasonable machine state switching is the key to achieving expected goals, that is, whether to switch speed between different operations, and whether to increase additional setup time between different Jobs. To address this issue, this study proposes an energy-saving flexible job scheduling problem based on machine multi state (EFJSP-M), which simultaneously considers the machine's multi-speeds and setup time. In order to solve the proposed EFJSP-M problem, a differential evolution particle swarm optimization algorithm (DEPSO) is designed. Based on the datasets MK, the experimental results are compared with three state-of-the-art algorithms, demonstrating the feasibility of EFJSP-M and the superiority of DEPSO.

Non-invasive imaging of brain function and energy supply is crucial for diagnosing and treating brain disorders. Conventional imaging struggles to capture altered relationships between energy supply and utilization caused by brain diseases. A novel method, which can be translated to human patients, is to calculate relative power (rPWR) and relative cost (rCST) to assess cerebral energy efficiency. However, whether rPWR/rCST can track individual changes and neural activity remains unproven. Our study compared these non-invasive measures with invasive two-photon microscopy in awake and anesthetized mice. We found that rPWR/rCST distributions were similar between awake mice and humans, but changed in anesthetized mice, indicating a shift in the brain's economic balance. Furthermore, changes in rPWR/rCST were linked to the reorganization of microscopic neural networks, observed with two-photon microscopy. Our work highlights the potential of rPWR/rCST for medical applications, and that neural network reorganization is linked to the brain's economic balance. ### Competing Interest Statement The authors have declared no competing interest.

This paper presents a complex-order quantum-behaved particle swarm optimization (CoQPSO) algorithm, aiming at improving the local exploitation and global exploration abilities of existing optimization methods. The core of the CoQPSO is the adoption of complex-order derivatives within the particles' position adaptation mechanisms. The complex-order derivatives are computed with historical state information of the particles, being naturally suitable for the iterative procedure of intelligent optimization algorithms. To prevent convergence to local optima, a double jump-out strategy is designed so that particles can escape from local attractors. The influence of the algorithm's control parameters on its performance is assessed by means of sensitivity analysis, which comprises a number of value- and rank-based tests on a set of classical benchmark functions and CEC 2022 single-objective global optimization competition test suite. The CoQPSO is compared with other PSO variants in terms of the mean, standard deviation and best value of the solutions. Additionally, the Wilcoxon-rank sum test assesses algorithms' performance differences. The experimental results illustrate the superiority of the CoQPSO in finding optimal solutions.

Driven by the "dual carbon"strategic goals, the coordinated optimization of energy consumption and production efficiency has become a core issue for manufacturing industries. As an important means to promote energy structure transformation, electric substitution has made significant progress in industrial manufacturing, transportation, household electrification, and other fields. Among them, industrial production accounts for over 60% of the total electric energy substitution, becoming the largest electricity consumer. Note that the electricity price is based on time-of-use pricing (TOU), meanwhile, electric consumption is related to the machine multistate (MM). Regarding these matters, this study focuses on determining sensible machine states and formulating reasonable production scheduling plan, to minimize both production time and power consumption. First, a novel energy-efficient flexible job shop scheduling problem is developed, which considers both the TOU strategy and the MM conditions (EFJSP-MM-TOU). Second, a self-learning classification-based multi-objective evolutionary algorithm (SCMOEA) is proposed to solve the EFJSP-MM-TOU. In specific, the SCMOEA enhances population diversity through a hybrid initialization strategy, adopts a dynamic selection of cross individuals based on the self-learning classification mechanism to improve the search efficiency, and designs four local search operators to increase the potential for approaching better positions. Third, by employing the MK standard dataset in EFJSP-MM-TOU, the proposed SCMOEA is compared with its three variants and five stateof-the-art algorithms to verify its optimization performance. The experimental results suggest that SCMOEA has advantages in terms of Pareto optimal solutions' diversity and convergence. Finally, by testing in an actual enterprise case, the results further support the effectiveness of the EFJSP-MM-TOU and the significance of SCMOEA.

Density peaks clustering (DPC) is a simple and efficient density-based clustering algorithm. However, the original DPC algorithm still has some shortcomings including manual selection of cluster centers, single cluster center representation of each cluster, and error cascade in the one-step assignment strategy of the remaining data points. To address these shortcomings, a novel density peaks clustering algorithm with multiple feature points adapting to the cluster structures (DPC-MFP) is developed. First, the DPC-MFP algorithm automatically selects multiple feature points for each cluster to eliminate the influence of manual cluster center selection. Second, multiple feature points belonging to the same cluster are identified by their similarity and are further used to represent the same cluster. DPC-MFP can adapt to the complex structures of different clusters and overcome the shortcoming of the inability of cluster centers used in DPC in representing complex clusters. Finally, in order to overcome the shortcoming of the one-step assignment strategy in DPC, dependent points are divided into ascertained and uncertain dependent points, and a hybrid strategy is adopted to assign the remaining points to clusters. Numerical experiments on a large number of real-word and synthetic datasets show that the DPC-MFP algorithm outperforms other existing algorithms, especially on some synthetic datasets with complex cluster structures.

The Sine-Cosine function, which is widely adopted in mathematics and physics, has attracted our attention due to its unique properties. By delving into the coupling effect of the Sine-Cosine function, we discover a previously unreported class of nonlinear systems, namely the Sine-Cosine Nonlinear System Family (SCNSF). This discovery is motivated by the need to expand the repertoire of nonlinear systems and understand the complex behaviors that can emerge from the combination of basic trigonometric functions. The SCNSF has both chaotic characteristics in the real number domain and fractal characteristics in the complex number domain. The classification and general mathematical description of SCNSF provide a solid theoretical foundation for further research. The proposal of three types of classic systems within SCNSF and the investigation of their chaotic properties and hardware implementation open up new avenues for practical applications. The large chaotic range exhibited by these systems implies their potential applications in various fields such as secure communication and chaotic circuit design. Moreover, the discovery of the chaos generation mechanism based on the coupling effect of the Sine-Cosine function deepens our understanding of the origin of chaos. In the complex number domain, the high parameter sensitivity and rich fractal patterns of SCNSF can be can be harnessed to develop more advanced encryption algorithms and more sensitive signal detection methods, thereby contributing to the advancement of information security and signal processing technologies. Overall, the chaotic and fractal properties of SCNSF make it a valuable asset in the pursuit of innovative solutions in multiple scientific and engineering disciplines.

Energy-aware scheduling has emerged as a well-defined research topic for achieving sustainable development. However, unexpected disruptions in workshop pose several challenges to the manufacturing process, causing the original schedules to become non-optimal or even infeasible, resulting in significant energy waste. Consequently, it is necessary to investigate the robust scheduling problem with energy-awareness. The energy-efficient robust flexible job shop scheduling problem (ERFJSP) aims to simultaneously optimize scheduling efficiency, total energy consumption, and robustness. A two-stage mixed-integer linear programming model considering machine breakdown and job insertion is formulated in this paper for the first time. To solve this problem, a double Q-learning (DQL)-assisted competitive evolutionary algorithm (DQCEA) is proposed. In DQCEA, a heuristic initialization strategy is first designed, which allows it to obtain high-quality and diverse solutions. Subsequently, a multi-objective competitive mechanism is proposed to classify search individuals into inferiors and superiors. Moreover, an inferior-pushing and superior-pulling-based crossover is designed for inferior members, facilitating knowledge transfer within the population and enhancing global diversification capability. Meanwhile, a hyper-mutation operator is devised for superior members, which incorporates eight search strategies to improve local intensification ability. Furthermore, DQL is employed to learn and recommend the most suitable strategy for each superior individual. Finally, extensive experiments are carried out to evaluate the correctness of the formulated MILP model and the performance of DQCEA. Experimental analysis confirms that DQCEA effectively provides promising schedules under different scenarios, demonstrating its reliability in addressing unexpected disruption challenges.

The cannabinoid receptor 1 (CB1) is famous as the target of Δ9-tetrahydrocannabinol (THC), which is the active ingredient of marijuana. Suppression of CB1 is frequently suggested as a drug target or gene therapy for many conditions (e.g., obesity, Parkinson's disease). However, brain networks affected by CB1 remain elusive, and unanticipated psychological effects in a clinical trial had dire consequences. To better understand the whole brain effects of CB1 suppression we performed in vivo imaging on mice under complete knockout of the gene for CB1 (cnr1-/-) and also under the CB1 inverse agonist rimonabant. We examined white matter structural changes and brain function (network activity and directional uniformity) in cnr1-/- mice. In cnr1-/- mice, white matter (in both sexes) and functional directional uniformity (in male mice) were altered across the brain but network activity was largely unaltered. Conversely, under rimonabant, functional directional uniformity was not altered but network activity was altered in cortical regions, primarily in networks known to be altered by THC (e.g., neocortex, hippocampal formation). However, rimonabant did not alter many brain regions found in both our cnr1-/- results and previous behavioral studies of cnr1-/- mice (e.g., thalamus, infralimbic area). This suggests that chronic loss of cnr1 is substantially different from short-term suppression, subtly rewiring the brain but largely maintaining the network activity. Our results help explain why pathological mutations in CB1 (e.g., chronic pain) do not always provide insight into the side effects of CB1 suppression (e.g., clinical depression), and thus urge more preclinical studies for any drugs that suppress CB1.

Abstract Background Quantitative mapping of the brain’s metabolism is a critical tool in studying and diagnosing many conditions, from obesity to neurodegenerative diseases. In particular, noninvasive approaches are urgently required. Recently, there have been promising drug development approaches for the treatment of disorders related to glucose metabolism in the brain and, therefore, against obesity-associated diseases. One of the most important drug targets to emerge has been the Glucagon-like peptide-1 (GLP-1) and its receptor (GLP-1R). GLP and GLP-1R play an important role in regulating blood sugar and maintaining energy homeostasis. However, the macroscopic effects on brain metabolism and function due to the presence of GLP-1R are unclear. Methods To explore the physiological role of GLP-1R in mouse brain glucose metabolism, and its relationship to brain function, we used three methods. We used deuterium magnetic resonance spectroscopy (DMRS) to provide quantitative information about metabolic flux, fluorodeoxyglucose positron emission tomography (FDG-PET) to measure brain glucose metabolism, and resting state-functional MRI (rs-fMRI) to measure brain functional connectivity. We used these methods in both mice with complete GLP-1R knockout (GLP-1R KO) and wild-type C57BL/6N (WT) mice. Results The metabolic rate of GLP-1R KO mice was significantly slower than that of WT mice (p = 0.0345, WT mice 0.02335 ± 0.057 mM/min, GLP-1R KO mice 0.01998 ± 0.07 mM/min). Quantification of the mean [18F]FDG signal in the whole brain also showed significantly reduced glucose uptake in GLP-1R KO mice versus control mice (p = 0.0314). Observing rs-fMRI, the functional brain connectivity in GLP-1R KO mice was significantly lower than that in the WT group (p = 0.0032 for gFCD, p = 0.0002 for whole-brain correlation, p < 0.0001 for ALFF). Conclusions GLP-1R KO mice exhibit impaired brain glucose metabolism to high doses of exogenous glucose, and they also have reduced functional connectivity. This suggests that the GLP-1R KO mouse model may serve as a model for correlated metabolic and functional connectivity loss.

Chronic migraine is closely related to the dysregulation of neurochemical substances in the brain, with metabolic imbalance being one of the proposed causes of chronic migraine. This study aims to evaluate the metabolic changes between energy metabolism and excitatory and inhibitory neurotransmitters in key brain regions of mice with chronic migraine-like state and to uncover the dysfunctional pathways of migraine. A chronic migraine-like state mouse model was established by repeated administration of nitroglycerin (NTG). We used von Frey filaments to assess the mechanical thresholds of the hind paw and periorbital in wild-type and familial hemiplegic migraine type 2 mice. After the experiments, tissue was collected from five brain regions: the somatosensory cortex (SSP), hippocampus, thalamus (TH), hypothalamus, and the spinal trigeminal nucleus caudalis (TNC). Proton magnetic resonance spectroscopy (1H-MRS) was employed to study the changes in brain metabolites associated with migraine, aiming to explore the mechanisms underlying metabolic imbalance in chronic migraine-like state. In NTG-induced chronic migraine-like state model, we observed a significant reduction in energy metabolism during central sensitization, an increase in excitatory neurotransmitters such as glutamate, and a tendency for inhibitory neurotransmitters like GABA to decrease. The TNC and thalamus were the most affected regions. Furthermore, the consistency of N-acetylaspartate levels highlighted the importance of the TNC-TH-SSP pathway in the ascending nociceptive transmission of migraine. Abnormal energy metabolism and neurotransmitter imbalance in the brain region of NTG-induced chronic migraine-like state model are crucial mechanisms contributing to the chronicity of migraine.

This paper investigates the dynamical behaviors of the classical dual-channel supply chain from the perspective of fractal theory. First, the definition of filled Julia set in supply chain price competition model is introduced. Second, according to the periodicities of the attractors, the filled Julia set is divided into several sub basins. On this basis, the importance of mixed coexisting attraction basins’ connectivity is further illustrated. Then, the inner characteristics of filled Julia sets under different online preferences are analyzed, which indicates that online preference increase has negative influence on filled Julia sets’ structures. Finally, for the unstable cases caused by high online preference, we adopt three control strategies and analyze their control effects by quantifying the connectivity restorations. The results suggest that the fractal viewpoint is beneficial for a global observation of the prices evolutions in different initial states, and could also evaluate the market status more comprehensively.

Introduction: In resting-state functional magnetic resonance imaging (rs-fMRI) studies, global signal regression (GSR) is a controversial preprocessing strategy. It effectively eliminates global noise driven by motion and respiration but also can introduce artifacts and remove functionally relevant metabolic information. Most preclinical rs-fMRI studies are performed in anesthetized animals, and anesthesia will alter both metabolic and neuronal activity.Methods: In this study, we explored the effect of GSR on rs-fMRI data collected under anesthetized and awake state in mice (n = 12). We measured global signal amplitude, and also functional connectivity (FC), functional connectivity density (FCD) maps, and brain modularity, all commonly used data-driven analysis methods to quantify connectivity patterns.Results: We found that global signal amplitude was similar between the awake and anesthetized states. However, GSR had a different impact on connectivity networks and brain modularity changes between states. We demonstrated that GSR had a more prominent impact on the anesthetized state, with a greater decrease in functional connectivity and increased brain modularity. We classified mice using the change in amplitude of brain modularity coefficient (Delta Q) before and after GSR processing. The results revealed that, when compared with the largest Delta Q group, the smallest Delta Q group had increased FCD in the cortex region in both the awake and anesthetized states. This suggests differences in individual mice may affect how GSR differentially affects awake versus anesthetized functional connectivity.Discussion: This study suggests that, for rs-fMRI studies which compare different physiological states, researchers should use GSR processing with caution. Impact statement Global signal regression (GSR) is a commonly used denoising technique, however, it can also introduce specific artifacts. In functional connectivity (FC) studies of functional magnetic resonance imaging, it is crucial to examine the impact of GSR on animals under various anesthesia conditions. Our results showed that GSR had distinct effects on FC and modularity of awake versus anesthetized mice. Therefore, caution should be taken when using GSR to remove noise, especially when comparing different neurometabolic states.

This paper preliminary examines a kind of Mandelbrot set generated by a fractional difference quadratic map involving Caputo-like fractional h-difference operators. A connectivity index is proposed based on numerical methods, which avoids difficulties in discussion at the topological level. The dynamics of those sets in two kinds of noise environments are considered involving connectivity, symmetry and dimension. Several typical cases are visualized to illustrate the main conclusions.