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The integration of multiterminal hybrid HVDC grids connecting LCC- and VSC-based networks faces several technical challenges such as DC fault isolation, ensuring multi-vendor interoperability, managing high DC voltage levels, and facilitating high-speed power reversal without interruptions. The two-stage DC-DC converter emerges as a key solution to address these challenges. By implementing the modular multilevel converter (MMC) structure, the converter's basic topology includes half-bridge sub-modules on the VSC side and full-bridge sub-modules on the LCC side. However, while this topology has been discussed in the literature, its connection to an LCC-based network with controlled current magnitude lacks detailed analysis regarding operational challenges, control strategies under various scenarios, and design considerations. This paper fills this gap by providing comprehensive mathematical analysis, design insights, and control strategies for the modular DC-DC converter to regulate DC voltage on the LCC-HVDC side. Additionally, the proposed control scheme minimizes the interfacing inductor between the two bridges, ensuring uninterrupted power flow during reversal and effective handling of DC faults. Validation through Control-Hardware-in-the-Loop testing across diverse operational and fault scenarios, along with a comparative analysis of different converters, further strengthens the findings. © 2017 Elsevier Inc. All rights reserved. [ABSTRACT FROM AUTHOR]

The paper proposes an ameliorated methodology to minimize the effect of charge injection over a wide input common-mode range. Instead of a conventional single dummy switch compensation [1] , the multi-dummy switches are proposed and employed to eradicate the injected charge on to the sampling capacitor. A detailed methodology is presented to compensate the charge injection in a MOS switch. The closed-form equations are derived mathematically to substantiate the proposed technique. For the proof-of-concept, a track-and-hold (T/H) stage has been simulated in 0. 18 μ m CMOS technology with the proposed technique for a 10-bit resolution. The proposed technique based T/H stage exhibits the spurious free dynamic range (SFDR) of 62.6 dB, effective number of bits (ENOB) of 9.36, peak input-referred third-order intercept point (IIP3) of 13.02 dBm and an input-referred 1 dB compression point (P 1dB) of 3.8 dBm at 1.074 MHz input frequency, sampled at 100 MSa/s. The performance of the proposed method is compared with the existing single dummy switch compensation method where our technique shows 88.8% compensation in minimizing the charge injection error and 272% improvement in dynamic linearity. Moreover, the presented technique quantifies 9 × improvement in mean percentage error (MPE) when simulated across the various process corners and rail-to-rail input common-mode voltage. • The paper presents a multi-dummy switch technique to minimize the charge injection error in a MOS switch. • Mathematical analysis has been carried out to validate the concept. • A design methodology is proposed to limit the charge injection error within ±0.5 LSB for 10-bit track-and-hold circuit. • The presented method is compared with existing single dummy switch compensation technique and the results depict 272% improvement in dynamic linearity. • The proposed method provides 9X improvement in the mean percentage error over the existing method. • The design is simulated in CMOS 180 nm technology and the post-layout simulation results are reported in the paper. [ABSTRACT FROM AUTHOR]

The rapid growth in HVDC grids is becoming inevitable for long-distance power transmission. Therefore, the idea of interconnection between the point-to-point links becomes essential. However, these point-to-point connections face several challenges such as the requirement of DC fault blocking capability, interfacing of different grounding schemes, offering multi-vendor interoperability, and difficulty to achieve high DC voltage stepping. DC-DC converters are considered the optimum solution to tackle these challenges in DC grids interconnection. In this paper, a new hybrid modular DC-DC converter is proposed that achieves a low number of semiconductors, low losses, and cost in comparison to other DC-DC converters due to the utilization of thyristors. The new DC-DC converter consists of two hybrid MMC bridges connected through an isolating transformer. Each MMC bridge is comprised of half bridge submodules and bidirectional thyristors. Detailed mathematical analysis, design, and control are illustrated. A comparison is carried out between different topologies in terms of semiconductor count, power loss, and cost. Also, both simulation model and experimental test rig are built to validate the proposed hybrid modular DC-DC converter under different scenarios. Finally, another variant of the hybrid-thyristor based converter (version two) is proposed for multiport DC-Hub application to achieve DC fault blocking without turning off all connected bridges. [ABSTRACT FROM AUTHOR]

Investigating the effects of periodic magnetic field and triple diffusion on bioconvection flow through a rotating cone populated by oxytactic bacteria and an Eyring-Powell fluid is innovative and significant. The magneto-bioconvection flow of an Eyring-Powell multi-diffusive fluid across a spinning cone is investigated in this paper, considering the effect of oxytactic microorganisms. The non-similar technique is used in the mathematical analysis of the flow over a spinning cone. The flow under consideration contains two diffusive species: liquid hydrogen and liquid oxygen. In light of the periodic magnetic field, the surface gradients, notably skin friction, exhibit wavy effects in the boundary layer domain. The governing equations for the fluid flow in the current flow problem, accompanied by heat diffusion, species diffusion, rotation, bioconvection, and periodic magnetic, are highly coupled nonlinear PDEs dependent on the proper initial and boundary conditions. Mangler's transformations convert them into non-dimensional forms, and numerical non-similar solutions are produced using implicit finite difference approximation and quasi-linearisation. The enriching values of bioconvective Rayleigh number Rb decline the velocity F, as a result, lessen the friction between the surrounding fluid and the cone's surface. The improving Peclet number Pe and microbial density difference σ reduced the microorganism density profile and heightened the microorganism density number R e - 1 / 2 N n. [ABSTRACT FROM AUTHOR]

In this manuscript, we are going to study a novel model of the dynamics of alcohol consumption under induced complications. The mentioned model is considered under the concept of conformable fractional order derivative (CFOD). Currently, most of real-world problems are considered under fractional order derivatives because of their stable and global behavior. First, we will investigate the model for qualitative theory including existence and uniqueness of solution and Ulam-Hyers stability. For qualitative theory, we will use fixed point theory. In addition, we use a numerical method to find the approximate solution of the proposed model. In the final part of the paper, we give a detailed discussion of its numerical results and its graphical presentation. [ABSTRACT FROM AUTHOR]

[Display omitted] • This article proposes a new robust nonlinear controller that stabilizes a chaotic finance system in a finite-time without cancellation of the spacecraft's nonlinear terms, it improves the efficiency of the closed-loop. • It accomplishes an oscillation-free faster convergence of the perturbed state variables to the desired steady-state. • The proposed controller is insensitive to the parameter uncertainties of the nonlinear terms and exogenous disturbances. • The paper performs a comparative study to verify the performance and efficiency of the proposed controller. Robust, stable financial systems significantly improve the growth of an economic system. The stabilization of financial systems poses the following challenges. The state variables' trajectories (i) lie outside the basin of attraction, (ii) have high oscillations, and (iii) converge to the equilibrium state slowly. This paper aims to design a controller that develops a robust, stable financial closed-loop system to address the challenges above by (i) attracting all state variables to the origin, (ii) reducing the oscillations, and (iii) increasing the gradient of the convergence. This paper proposes a detailed mathematical analysis of the steady-state stability, dissipative characteristics, the Lyapunov exponents, bifurcation phenomena, and Poincare maps of chaotic financial dynamic systems. The proposed controller does not cancel the nonlinear terms appearing in the closed-loop. This structure is robust to the smoothly varying system parameters and improves closed-loop efficiency. Further, the controller eradicates the effects of inevitable exogenous disturbances and accomplishes a faster, oscillation-free convergence of the perturbed state variables to the desired steady-state within a finite time. The Lyapunov stability analysis proves the closed-loop global stability. The paper also discusses finite-time stability analysis and describes the controller parameters' effects on the convergence rates. Computer-based simulations endorse the theoretical findings, and the comparative study highlights the benefits. Theoretical analysis proofs and computer simulation results verify that the proposed controller compels the state trajectories, including trajectories outside the basin of attraction, to the origin within finite time without oscillations while being faster than the other controllers discussed in the comparative study section. This article proposes a novel robust, nonlinear finite-time controller for the robust stabilization of the chaotic finance model. It provides an in-depth analysis based on the Lyapunov stability theory and computer simulation results to verify the robust convergence of the state variables to the origin. [ABSTRACT FROM AUTHOR]

• According to the comparative small-signal analysis of GCC adopting PLL and RPS, it is demonstrated that the current information introduced by the RPS is equivalent to adding a positive real part to its open-loop transfer function, which improves the stability of the GCC system. • Based on the admittance model developed in this paper, it is revealed that RPS can effectively reduce the negative resistance area and reduce the frequency coupling effect. Then the stability of GCC in a weak grid is improved. However, the specific mechanistic analysis cannot be easily carried out on the unified admittance model. • Finally, a SISO model is derived to intuitively visualize the mechanism of instability for GCC adopting PLL in a weak grid, which can be attributed to the gain spike and phase jump. RPS with a lower-order structure can effectively avoid the above two shortcomings, which achieves the same dynamic performance as PLL. For grid-connected converters (GCC), the synchronization unit (SU) is indispensable for the vector current control (VCC). Usually, the phase-locked loop (PLL) is employed as SU. However, PLL could introduce negative resistance contributing to potential instability issues. Thus, the second-order generalized integrator PLL (SOGI-PLL) and the reactive power-based synchronization method (RPS) are proposed to enhance the stability. Nevertheless, the intrinsic reason why RPS enhances stability is not clear. Therefore, a detailed comparative analysis among PLL, SOGI-PLL, and RPS is presented in this paper to reveal the mechanism of this stability enhancement. Firstly, an admittance model is derived to analyze the differences between these three synchronization methods. However, it is not intuitive enough to explain the detailed mechanism. Then, a SISO model containing the current controller, physical circuit, and synchronization unit is developed, which is established on the relationship between power and angle. According to this SISO model, it is revealed that the presence of the gain spike introduced by PLL and SOGI-PLL leads to instability. RPS avoids these issues due to its introducing current information for phase margin enhancement and its lower-order structure. Finally, the validity of the mathematical analysis and derived models are verified by experimental results. [ABSTRACT FROM AUTHOR]

In this paper, the consensus tracking problem for the linear and nonlinear partial difference multi-agent systems with switching communication topology and control delay is investigated. Based on relative local measurements of neighboring followers, while considering spatio-temporal discretization and initial state deviation, a discrete distributed consensus protocol with initial value learning is designed for each agent via D-type iterative learning approach. Through rigorous mathematical theoretical analysis, the necessary and sufficient conditions are obtained. Under the switching of the communication topology, these conditions ensure that the consensus tracking control of the MASs can be solved. After applying the designed protocol, in the sense of the L 2 norm and along the positive direction of the iteration axis, the consensus tracking error between any two agents can converge to zero. Finally, some simulation examples are used to demonstrate the validity of the protocol and theoretical results. • A novel partial difference MASs dynamic model is established to describe the discrete spatio-temporal evolution behavior. • A new distributed iterative learning approach with initial value learning for partial difference MASs is given. • The proposed control approach can solve the problem of switching topology and control delay simultaneously. [ABSTRACT FROM AUTHOR]

In this paper, we present a calcium dynamics model that firmly orchestrates exchanges of calcium flux through intracellular/extracellular sources of calcium to investigate cellular activities and calcium homeostasis. The generalized two-dimensional space-time reaction-diffusion model is formulated and analyzed for a wide range of calcium flux. The analytical technique is applied to solve the model by use of the fractional integral transform and some special functions. The existence and uniqueness of the proposed model are discussed. Finally, the obtained results are presented graphically to show the significance of calcium flux by amalgamating the memory of cells and prove the efficiency of the method. • We developed a calcium dynamics model to investigate the interplay of calcium flux based on a reaction-diffusion equation. • We present the computational technique to derive the model's solution using integral transform and special functions. • The existence and uniqueness of the calcium dynamics model are discussed. • We estimated the concentration profile in the presence/absence of VGCC, ER leak, SERCA pump, NCX, and mitochondrial flux. • The modulation of calcium flux provides a noteworthy effect due to the intermediate memory of cells. [ABSTRACT FROM AUTHOR]

• The functional relationship between the heat transport coefficients is explored. • The well-posedness of the Guyer–Krumhansl equation is proved. • The uniform stabilization property is proved. • The results are supported by a numerical demonstration. The Guyer–Krumhansl heat equation has numerous important practical applications in heat conduction problems. In recent years, it turned out that the Guyer–Krumhansl model can effectively describe the thermal behavior of macroscale heterogeneous materials. Thus, the Guyer–Krumhansl equation is a promising candidate to be the next standard model in engineering. However, to support the Guyer–Krumhansl equation's introduction into the engineering practice, its mathematical properties must be thoroughly investigated and understood. In the present paper, we show the basic structure of this particular heat equation, focusing on the differences in comparison to the Fourier heat equation obtained when (τ q , μ 2) → (0 , 0). Additionally, we prove the well-posedness of a particular, practically significant initial and boundary value problem. The stability of the solution is also investigated in the discrete space using a finite difference approach. [ABSTRACT FROM AUTHOR]

This paper aims to explore the accurate control of hole shape for AWJ hole-making of C f / SiC based on experimental and mathematical analysis methods, and the influence mechanism involved is emphatically analyzed. The results reveal that D difference is most influenced by the standoff distance, followed by the traverse speed, while it is less influenced by the pressure and the abrasive flow rate. The traverse speed, pressure and abrasive flow rate affect the D difference by changing the total energy of the jet; while the standoff distance mainly affects the D difference by changing the effective impact area, which is fundamentally different from other process parameters. In terms of interaction effects, decreasing the traverse speed and increasing the waterjet pressure can amplify the effect of interaction with the involvement of the standoff distance on the D difference. Based on the established D difference model and D offset model, a control method that can gain acquired hole shape is finally obtained for selecting the process parameters of AWJ machining. [ABSTRACT FROM AUTHOR]

• A coupling mechanism model of an FSDB unit is developed and verified. • Mathematical analysis is explored to reveal the coupling mechanism of an FSDB system. • Rigid and elastic motions of disk and cyclic blades induce diagonal and cross-coupling terms. • The motion patterns of cyclic blades are classified and clarified. • Effects of motion patterns of cyclic blades on NFs and CSs are applied to interpret and validate the dynamic coupling. This paper focuses on the influence mechanism of cyclic blades on the dynamic coupling of a flexible shaft-disk-blade (FSDB) system through mathematical analysis and numerical simulation. Firstly, a coupling mechanism model of an FSDB unit is developed through a Lagrange method and the assumed mode method (AMM), after considering the coupling behavior among shaft bending, shaft torsion, disk vibration, and blade bending. The modal comparison results between the proposed model and FEM affirm the validity of the model. Then the analytical interpretation is explored by decomposing and discussing the diagonal coupling and cross-coupling matrices of the FSDB system. The mechanism discussion reveals that the coupling matrices originate from the rigid and elastic motions of flexible disk and cyclic blades, indicating that the motions of cyclic blades play an important role in dynamic coupling. Therefore, the motions of cyclic blades are classified and analyzed, and their effects on natural frequencies (NFs) and critical speeds (CSs) are applied to further interpret and validate the dynamic coupling through numerical simulation. The numerical results indicate that motions of cyclic blades can increase, decrease, and eliminate the magnitude of dynamic coupling significantly. [ABSTRACT FROM AUTHOR]

The highly reliable nanosatellite platforms have broad application prospects in the construction of satellite Internet. Obtaining accurate attitude information is crucial to enhance the reliability of nanosatellite platforms. However, the traditional attitude sensors are not suitable for nanosatellite and attitude sensor faults are the main ones in space field. Therefore, sensor fault detection and fault-tolerant processing are essential to improve the reliability of platforms. In this paper, the distributed fusion fault-tolerant attitude estimation (FTAE) problems for nanosatellite with commercial off-the-shelf (COTS) sensors are investigated. Considering the low development cost of nanosatellite platforms, a FTAE scheme using COTS sensors is developed, which can acquire high-precision attitude information and improve the fault tolerance of nanosatellite platforms. Moreover, a novel fault detection method is designed and strict mathematical analysis is applied to fault threshold in FTAE scheme, which can significantly reduce complicated debugging work in engineering application and improve the design efficiency of FTAE scheme. Some case studies are given to illustrate the efficacy of the designed distributed fusion FTAE scheme. [ABSTRACT FROM AUTHOR]

In this paper, a fractional-order Hantavirus infection model incorporating harvesting is formulated and investigated. The populations are divided into susceptible mice, infected mice and alien species. Mathematical analysis and numerical simulations are performed to clarify the characteristics of the proposed fractional-order Hantavirus infection model. The existence, uniqueness, non-negativity and boundedness of the solutions are examined. The local stability of the equilibrium points of the fractional-order model is studied. The mathematical proof of the existence of transcritical bifurcation is given by using Sotomayor's theorem. The theoretical findings are illustrated by numerical simulations. The impact of fractional-order, competitive effect of alien species on mice, competitive effect of mice on alien species, carrying capacity and harvesting efforts on the stability of the Hantavirus infection model are studied. The basin of attraction regions is also illustrated. [ABSTRACT FROM AUTHOR]

With an increase in the number of internet users and the need to secure internet traffic, the IPv4 protocol has been replaced by a more secure protocol, namely IPv6. The IPv6 protocol does not allow intermediate routers to fragment the on-going packets. Moreover, due to IP tunneling, some extra headers are added to the IPv6 packet, exceeding the packet size, resulting in increased packet drops due to lower path mtu. One probable solution is to use Path MTU Discovery (PMTUD) to know the path mtu using ICMP packets. Due to dependency on ICMP error messages, this method faces security and failure issues. In this paper, we propose a Dynamic MTU (DMTU) scheme, which tries to handle the packet drops in IPv6 network, by dynamically adjusting the MTU of each link depending upon the incoming packet size, thereby reducing the number of packet drops by a significant amount. Unlike PMTUD, the algorithm works on intermediate node level which is further optimised by assigning specific phases for validation and then, for processing. The method has ability to work in standalone and in parallel with PMTUD. Using mathematical and graphical analysis, our scheme proves to be much more efficient than the state-of-the-art PMTUD scheme. [ABSTRACT FROM AUTHOR]

This paper studies the underwater glider trajectory tracking in currents field. The objective is to ensure that trajectories fit to the straight target track. The underwater glider model is introduced to demonstrate the vehicle dynamic properties. Considering currents disturbance as well as the uncertain status of the glider controlled by complicated roll policies, the trajectory tracking task can be classified into the model-free optimization. Such problem is difficult to solve with mathematical analysis. This work transfers the underwater glider trajectory tracking into a Markov Decision Process by specifying the actions and observations as well as rewards. On this basis, a neural network controls framework called experience breeding actor-critic is proposed to handle the trajectory tracking. The EBAC enhances the explorations to the potentially high reward area. And it steers glider heading meticulously so as to counteract the currents influence. Through simulation results, the EBAC shows a desired performance in controlling the gliders to accurately fit the target track • The underwater glider simulator is established to develop algorithms and evaluate the effectiveness. • The novel experience breeding actor-critic algorithm is applied for underwater gliders trajectory tracking. • The optimizing framework of glider trajectory tracking from the Markov decision process perspective is proposed. • The proposed method enhance the tracking accuracy compared with PID and SMC with the LOS guidance. [ABSTRACT FROM AUTHOR]

• A new DC-hub is proposed for interconnection of VSC-based HVDC ports based on thyristor device. • Zero-reactive power control across the common AC link is proposed to achieve reduced RMS current. • Comprehensive mathematical analysis is illustrated for circuit design parameters for the DC-Hub under study. • Transformation from Sinusoidal to Quasi-Trapezoidal to accommodate the utilization of thyristor based DC-Hub. • Small scale hardware setup is built to test the proposed DC-Hub under different healthy and unhealthy scenarios of power flow. The promising features of HVDC technology have led to the possibility of numerous renewable resources integration and enormous DC grids interconnection. In spite of the obstacles, these interconnections encounter such as the necessity to block DC faults, achieving isolation between different schemes, the ability to maintain power flow throughout different power flow profiles, and the interfacing with various infrastructures, the DC-Hub arises to overcome these interconnection obstacles being the excellent approach to enhance the DC grid capabilities. This paper proposes a new monolithic modular thyristor-based multilevel converter, which serves as the fundamental building block of the DC-Hub, offering advantages such as lower switch count, bidirectional power flow, and DC fault blocking capability. Moreover, a control algorithm, for zero reactive power circulation in the DC-Hub, is introduced. The proposed algorithm successfully mitigates the circulation of reactive power throughout the entire range of power flow. A comprehensive mathematical analysis, optimum design of converter parameters, and the proposed control technique, which suppress the circulating reactive power at full range of power flow, are illustrated. Finally, simulation modelling and hardware test rig are established to validate the claims of the DC-Hub at different normal and faulty scenarios. [ABSTRACT FROM AUTHOR]

Multiphysics processes are common in nature and can occur in conjuction with intense strains. When strain softening is also present, the original uniform strain distribution is lost and strain localization occurs. In a classical continuum strain localization happens on a mathematical plane (i.e shear band of zero thickness). This leads to mesh dependent numerical analyses, in which strain localizes on the smallest mesh length. In this paper we investigate under which conditions multiphysics processes regularize the problem of strain localization. We study, for the first time, the influence of all the different coupling terms present in the original coupled multiphysics balance equations on the strain localization profile. We also consider the influence of viscosity and inertia effects. We show that the multiphysics processes do not always lead to mesh independent results. Furthermore, our rigorous mathematical analysis provides bounds for the different coupling parameters, for which multiphysics processes lead to strain regularization and mesh independent numerical results. Finally, we corroborate our mathematical findings, applying them to a numerical example of a coupled hydro-mechanical system of a fault under shear. [Display omitted] • The hypothesis that multiphysics couplings alleviate mesh dependence is tested. • All mechanisms of the multiphysics coupling are considered. • The influence of viscosity and inertia is investigated. • Bounds are given for the different coupling parameters for strain regularization. • A numerical example of the hydro-mechanical system of a fault under shear is shown. [ABSTRACT FROM AUTHOR]

Compared with the two-valued memristor, the three-valued memristor has higher data density, richer dynamic characteristics, and more potential in digital logic and chaotic circuit. The present model of the three-valued memristor has several limitations. It doesn't perform well enough in three-valued applications since its hysteresis loops are linear and asymmetric. The mathematical model of the three-valued memristor with nonlinear and symmetric hysteresis loops is proposed in this research. To further investigate the electrical characteristics of the three-valued memristor, a circuit emulator of the memristor has been constructed with fundamental components. Multisim simulations and hardware experiments demonstrate the emulator's effectiveness. The three-valued memristor application in chaotic circuits shows fascinating dynamic characteristics and lays the foundation for future research. • The mathematical model of the three-valued memristor with nonlinear and symmetric hysteresis loops is proposed in this paper. • A circuit emulator of the three-valued memristor is proposed and verified using hardware and software. • The three-valued memristor application in chaotic circuits shows fascinating dynamic characteristics. [ABSTRACT FROM AUTHOR]

[Display omitted] • The counties with high abandonment rates are close to 30%, while those with low rates are between 0 and 2%. • The abandoned farmland in Chongqing expanded from the northeast to the whole area. • Wild boar invasion has become the leading factor of farmland abandonment. • Ecological restoration and land abandonment are a vicious cycle of mutual causality. • A vicious cycle of farmland abandonment, mainly by wild boars, has emerged. Farmland abandonment reflects the decline of rural areas, resulting in a series of vicious chain reactions, hindering the promotion of the comprehensive rural revitalization strategy. From the perspective of ecological restoration, this paper integrated multi-source data such as Landsat, GF-1, and Google Earth images and household survey data, aiming to reveal the spatiotemporal pattern, attribution, and mechanism of farmland abandonment in typical mountainous areas over the past 20 years by employing spatial analysis and mathematical models and to promote comprehensive management of abandoned farmland. The results are as follows. (1) The scope of abandoned farmland in Chongqing has been expanding, with the abandoned area growing from 142,385.8 hm2 to 345,778.4 hm2 from 2000 to 2020, with the initially abandoned farmland mostly concentrated in the northeastern areas, such as Chengkou, with an abandonment rate of 21.8%, and thereafter, spreading in all directions; In the end, abandoned farmland was concentrated in northeastern and southeastern Chongqing, such as Wuxi and Youyang, with abandonment rates of approximately 25.1% and 20%, respectively. (2) The attribution of farmland abandonment mainly includes wild boar damage, labour shortage, and natural conditions, among which wild boar proliferation has become an important factor under the background of ecological restoration. (3) Ecological restoration has produced a counter-servicing effect of the ecosystem on human beings, forming a vicious circle in the mountainous countryside where ecological restoration continues to aggravate farmland abandonment. The contribution of this study is to investigate the pattern of farmland abandonment from both macroscopic and microscopic perspectives. At the same time, this paper explores the intrinsic mechanism between ecological restoration and farmland abandonment and proposes scientific countermeasures to break the vicious cycle of ecological restoration that continues to exacerbate farmland abandonment in mountainous areas. [ABSTRACT FROM AUTHOR]

The aim of this study is to develop new and efficient theories for handling complex and unreliable data in real-world scenarios. The proposed approach integrates two distinct theories: the Bipolar Complex Fuzzy Set (BCFS) and the Soft Set (SS), resulting in a novel and superior method compared to existing solutions. Furthermore, the value of big data analytics cannot be overstated as it provides businesses with the opportunity to use their data to find areas for development and progress. To gain insights from raw data, it must first be collected and organized. Data modeling represents these large, complex data sets in a visual format, such as a chart or diagram. However, the visualization process often results in uncertainties and inaccuracies, highlighting the need for a more robust approach to data analysis. To address this issue, this paper introduces the concept of Bipolar Complex Fuzzy Soft Relations (BCFSRs), a fuzzy decision-making method within a complex bipolar fuzzy environment that can have the advantages of both a Bipolar Complex fuzzy relation and a soft relation at the same time. In BCFSRs, an element can have degrees of membership in both the positive and negative directions, reflecting a more nuanced and versatile representation of uncertainty or ambiguity. These mathematical ideas are explained through the Cartesian product of two Bipolar Complex Fuzzy Soft Sets (BCFSSs) and serve to simplify the decision-making process by presenting the BCFSSs in a clear and concise manner. The inventive notion of the BCFSRs elucidates the combined positive and negative effects of anything with parameterization. To support organizations in making data-driven choices and obtain insights for strategic planning and inventiveness, the analysis of big data is essential in several industries, including financial services, marketing, and medical treatment, among others. To choose the optimal big data analytics for efficient operation, this research presents modeling methodologies based on BCFSRs, including the formulation and analysis of scoring functions. The validity of the proposed work is demonstrated through a comparison study with existing methods, providing valuable insights for effective data analysis. • Bipolar Complex fuzzy and soft sets are presented. • Introduced novel, and effective ideas to manage complex, unreliable data. • Presents modeling methodologies based on Bipolar Complex fuzzy soft information. • Conducted a comparative study of existing techniques. [ABSTRACT FROM AUTHOR]

The holes are very easy to appear delamination and burr during CFRP drilling. The tool geometry has a great impact on the hole making. In this paper, according to the principle of bionics and structural features, a novel bionic drill bit was designed. The mathematical model of the lower incisor teeth occlusal movement was established. The cutting mechanism of the bamboo rat lower incisor on PW-CFRP material was studied. It was found that the curvature of the contour curves of the front cutter faces were constantly changing, which was conducive to the removal of chips. The curvature change of the contour curve of the rear cutter surface is small and the curve is relatively smooth, which is conducive to reducing friction. The mathematical modeling analysis was carried out on the feeding process of bamboo rats, and the mathematical relationship between the bite radius R and the cutting angle θ was obtained. The optimal cutting angle θ = 10° and the corresponding biting radius R = 40 mm were obtained by finite element simulation. The surface cutting quality of bamboo rat's lower incisors is better than that of ordinary cutting tools. The novel bionic tool can effectively reduce the burr and delamination of the exit layer. [ABSTRACT FROM AUTHOR]

This paper investigates the connection between non-prehensile manipulation, specifically juggling, and legged locomotion, focusing on biped robots. In this direction, the hybrid nature of juggler robot dynamics and biped robots, the zero moment point stability, and the non-prehensile dynamic grasping conditions are provided and analysed. The similarities between juggling actions and bipedal robot locomotion are discussed. The descriptive and mathematical analysis demonstrates many similitudes between juggler systems with cubic objects and flat-feet biped robots in throwing, catching, and stabilization phases, and between juggler actions with impact and point-feet legged robots in their switching (hybrid) dynamic behaviours. Finally, a common control framework based on the zero dynamic concept and integral sliding mode approach is proposed, and it applies to both classes of non-prehensile juggler systems and biped robots. To test the performance of the devised control system, a three-degrees-of-freedom juggler robot and a two-link walker are selected as case studies, whose simulation results demonstrate the effectiveness and feasibility of the proposed unified control framework for both systems. [ABSTRACT FROM AUTHOR]

In this paper, it is addressed by mathematical analysis how network-oriented modeling relates to the dynamical systems perspective on mental processes. It has been mathematically proven that any dynamical system can be modeled as a temporal-causal network model and that any adaptive dynamical system (of any order) can be modeled by a self-modeling network (of the same order). [ABSTRACT FROM AUTHOR]

With the recent focus marked on energy efficiency and solar energy development, much research is being dedicated to the development of enhanced maximum power point tracking (MPPT) algorithms for photovoltaic applications. However, the main criteria with regard to tracking performances and circuit implementation are still considered as a major challenge under rapid varying weather conditions. In this paper, a T-S Fuzzy–integral backstepping-based hybrid MPPT technique is proposed for rapid, accurate and efficient tracking. The proposed technique enables reliable and stable operation under fast dynamic environmental changes. Besides, it is simple as it does not require extra atmospheric sensors. The theoretical analysis addressed in this study is verified through simulations via Matlab/Simulink and experimental outdoor tests. A comparison with different other MPPT techniques is provided to highlight the performances of the developed MPPT method. • An MPPT controller based on TS Fuzzy and integral backstepping control is proposed. • A detailed mathematical analysis has been presented. • The suggested MPPT technique has been compared to P&O, MIC, PSO and P&O-FOPI. • The proposed controller is validated through simulations and experimental tests. [ABSTRACT FROM AUTHOR]

• Based on the derivation method, a new derived grey multi-parameter prediction model (DMGM (1, n)) is proposed. • The mathematical analysis is used to discuss the main reason why DMGM (1, n) is superior to GMC (1, n). • DMGM (1, n) outperforms the other grey multivariable models by comparing the results of these models in three cases. In this study, in order to reduce the morbidity and improve the structural stability of the existing grey multivariable convolution forecasting model, a new derived multivariable grey model based on the derivation method, abbreviated as DMGM (1, n), is presented. Firstly, the time response formula of DMGM (1, n) is deduced by derivation method, which can avoid solving the inverse matrix so as to reduce the morbidity of the model. Secondly, the parameter identification of the model is given based on the least-squares method. Then, it is proved theoretically that DMGM (1, n) is superior to GMC (1, n) because the solution of the former overcomes the shortcoming of the latter that the original model does not take full advantage of all the information from the raw data for modeling. Finally, three real cases with different variables were performed. The fitting and prediction results indicate that DMGM (1, n) is better than GMC (1, n) and the other multivariate grey prediction models in these cases, which also demonstrates that this novel model outperforms the other grey models in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we propose a simple approach to the construction of a general class of L -stable explicit second-order one-step methods for solving stiff problems. These methods are nonlinear and derive from a novel approximation for the right-hand side functions of differential equations inspired by the nonstandard finite difference methodology introduced by Mickens. Through rigorous mathematical analysis, it is proved that the proposed numerical methods are not only explicit and L -stable, but also convergent of order two. Therefore, they are suitable and efficient to solve stiff problems. The proposed numerical methods generalize and improve a nonstandard explicit integration scheme for initial value problems formulated by Ramos (2007). Moreover, the present approach can be extended to construct A -stable and L -stable high-order explicit one-step methods for differential equations. Finally, the theoretical findings and advantages of the developed numerical methods are supported and illustrated by a series of numerical experiments in which stiff problems are considered. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a novel model that simulates the spread of the monkeypox virus. The new model takes into account the effect of the interaction between the human and rodent population along with some realistic factors that have not been introduced before such as imperfect vaccination and nonlinear incidence rates. Moreover, the human population is further divided into low-risk and high-risk groups to better reflect recent observations. To understand the dynamics of the new model, the existence, uniqueness, and continuous dependence on initial conditions, as well as its positivity and boundedness of the model are investigated in detail. The obtained solution is proved to be positive and has bounded behavior. Furthermore, the reproduction number R 0 for the proposed system is computed and detailed bifurcation analysis is performed to reveal major qualitative changes in the model's dynamics. In addition, we investigate the influence of key parameters on the basic reproduction number. We also explore and analyze the stability of equilibrium points in the space of parameters. The new findings reveal that the virus is more frequently witnessed among the high-risk group, which may provide some restrictions to stop the spread through social limitations. To validate our theoretical results, we conduct numerical simulations, which provide insights into the behavior of the model under different conditions. The new findings aim in developing preventive control measures to suppress the spread of the virus and to develop effective strategies for controlling and preventing outbreaks, ultimately protecting public health and minimizing the impact of the disease. [ABSTRACT FROM AUTHOR]

• A correct formulation of average Nusselt number for the case of linearly heated wall is derived. • Thermal balance analysis provides the verification of the correct formulation. • Comparison of the existing and the correct formulation is included. The comment below addresses an inaccurate formulation in the calculation of the Nusselt number for linear heating as presented in the paper titled "Steady natural convection flows in a square cavity with linearly heated side wall(s)" by M. Sathiyamoorthy, T. Basak, S. Roy, and I. Pop, Int. J. Heat Mass Transfer 50 (2007) 766–775. Consequently, this analysis provides a mathematical reformulation for the local and mean Nusselt numbers of a linearly heated side wall. It regenerates a few quantitative results for a specific case solely intended for comparative purposes. [ABSTRACT FROM AUTHOR]

• An active mitigating control approach is proposed to reduce torsional and edgewise vibrations in the PMSG-based WTs on the basis of a high fidelity dynamic model for the drivetrain and blade structures. • In the proposed approach, an auxiliary damping term, based on the difference between the blade and hub speeds, is added into the original electromagnetic torque, when the mechanical-structural modes are excited. • The needed variables for implementing the damping control term are estimated by a novel robust method based on the sliding-mode observer. • The efficiency of the proposed mitigating approach is evaluated by mathematical analyses and simulation results under several case studies. Fatigue loads associated with torsional and blade-edgewise vibrations are recognized as major reasons of large scale wind turbine failures. This paper presents an active mitigating control approach to reduce torsional and edgewise vibrations in the PMSG-based wind turbine. Due to the interactions of both vibrations, the active control is designed based on the expanded dynamic model of the mechanical-structural flexibilities. In this way, the blades are modeled as flexible cantilever beams, and thus, in the drive-train model the dynamics of the blades are considered. The control input to suppress the vibrations is achieved by the power electronic converters through adding an axillary term proportional to the speed difference between the blade and hub into the power control loop. This term manipulates the generator torque to counteract the unwanted vibrations. The needed drive-train and mechanical variables for making the auxiliary term are estimated by a novel robust method based on the sliding-mode observer. Using mathematical analyses and simulation results, it is shown that the proposed active mitigating approach well alleviates the fatigue loads of the torsional and edgewise modes even under severe changes in the drive-train stiffness coefficients. Thus, the proposed sensorless control approach is an appropriate remedy action for alleviation of WT fatigue loads even under parameters uncertainties. [ABSTRACT FROM AUTHOR]

[Display omitted] • Mathematical tools are made good use of realizing the screening and optimization of chemical experiment conditions in terms of Microorganism Inspired Porous Hydrogel. • Box-Behnken design-based response surface methodology and artificial neural network coupled genetic algorithm were herein employed to optimize and predict the optimal preparation conditions. • It can accurately predict the best experimental results without performing hundreds of experiments. • Mathematical methods solve the related problems of linear and nonlinear data processing. To optimize the synthetic process of microorganism inspired multistage porous hydrogel, the mathematical analysis strategies was applied to select the optimal experimental parameters. One-factor-at-a-time (OFAT) design was used to optimize the preparation process of yeast fermentation multistage porous hydrogels. The analysis of variance (ANOVA) was applied to determine the significant influencing factors, and the results revealed that the mass ratio of yeast to glucose (R yeast/glucose), gelation temperature of yeast fermentation (T gelation) and reaction time (t reaction) had a significant influence on responses. Box-Behnken design (BBD) based response surface methodology (RSM) was used to design experiments and build the relationship between the input parameters and output responses. Ideal point method was used to transform a multi-objective optimization problem into a single-objective optimization problem. Artificial neural network (ANN) coupled genetic algorithm (GA) were employed to further optimize and predict the optimal preparation conditions of yeast fermentation multistage porous hydrogels. The results showed ANN coupled GA was a more effective tool in the modelling and optimization of the preparation of yeast fermentation multistage porous hydrogels. The optimized preparation conditions are R yeast/glucose 1.84, T gelation 25.00 °C, t reaction 239.97 min. These values are expected to give us the minimum density, the maximum swelling degree and compressive strength. The research content of this paper provides theoretical support and factual basis for process optimization with complex influencing factors. [ABSTRACT FROM AUTHOR]

The presence of the golden mussel in Brazil is a matter of great concern and causes harm to the country, particularly affecting the power generation sector. Infestation control represents a challenge, and there is a need to mathematically describe the dynamics of the problem. This work proposes to analyze a mathematical model based on differential equations that relate the populations of larvae, mussels, and algae. For this model, the critical points and stationary states are determined, seeking steady-state conditions stability, through the basic reproduction rate. In addition, it presents the sensitivity analysis of the parameters involved. The paper results are relevant as they allow mathematical interpretation of the golden mussel infestation potential through the basic reproduction rate. Furthermore, the sensitivity analysis suggests how important the parameters are for this potential. For that matter, this work can provide baseline information to guide future control strategies as it provides quantification of the species involved over time as well as a condition for infestation. • Mussel-algae interaction model. • Stability analysis of stationary solutions of the model. • Basal reproduction rate for the golden mussel model. [ABSTRACT FROM AUTHOR]

Non-standard fuzzy sets play a significant role in uncertainty modeling. In addition to membership and non-membership degree, how to handle the hesitant degree is the key issue in the uncertain information process. In this paper, we model the Pythagorean fuzzy set (PFS) under the belief structure and measure its uncertainty based on fractal-based belief (FB) entropy. A novel fuzzy entropy for PFS called belief structure-based Pythagorean fuzzy (BSPF) entropy is proposed, whose effectiveness and advantages are proven based on mathematical analysis and numerical examples. A comparative analysis between BSPF entropy and other methods shows that BSPF entropy can obtain more reasonable results. Besides, a BSPF entropy-based multi-criteria decision-making (MCDM) method and a classification method are designed to solve practical problems. The experimental results demonstrate the effectiveness of these two proposed methods in solving real-world problems of decision-making and classification. • A novel entropy measure for PFSs was defined and proposed. • Comparisons made with other state-of-art approaches. • The TOPSIS method with the presented entropy measure was applied to fault diagnosis. • Medical diagnoses were more reasonable by reassigning the hesitation degree. • Performance of the classification improved with the presented entropy measure. [ABSTRACT FROM AUTHOR]

In this paper, considering the emergency braking problem for double pendulum crane systems, we propose a swing suppression guaranteed braking method with safety limits consideration, whose performance is also theoretically proved. Since the workspace for double pendulum cranes may be complex, while the transported payload may be large, it is of great significance to design proper emergency braking methods to make the entire double pendulum crane brake quickly and avoid possible accidents. By carefully analyzing the crane dynamics and taking into account the important swing suppression objective, coupling enhanced terms are designed based on the coupling behavior between the trolley motion and the swing angles. Then the coupling enhanced terms are combined with crane mechanical energy function, which further introduces swing angle-related feedback terms and achieves better swing suppression performance. Furthermore, safety limits are also taken into consideration by designing a special barrier function-like term, which can restrict the payload and hook horizontal positions in permitted domains. Based on all these terms, the swing suppression guaranteed braking method is designed with rigorous mathematical analysis proposed to shown its proper performance. To the best of our knowledge, it is the first emergency braking method for double pendulum cranes. Experimental tests are also implemented by using a hardware crane testbed, which further verify the effectiveness of the proposed method. • Both swing angles are effectively suppressed to improve the safety performance. • Safety limits are carefully tackled to avoid possible accidents like collisions. • The performance is ensured with theoretical analysis and hardware experiments. [ABSTRACT FROM AUTHOR]

A critical review of the paper "Transportation of hybrid nanoparticles in forced convective Darcy-Forchheimer flow by a rotating disk", M. Ijaz Khan, International Communications in Heat and Mass Transfer, 122 (2021) 105177, is presented in this paper, and the comments are given. The author (Khan, 2021) has made an attempt to present similarity solutions for the flow problem considered therein. The comments on (Khan, 2021) are that, firstly, the proposed similarity transformations are incorrect and, thus, the subsequent mathematical analysis is erroneous. Hence, the findings presented in (Khan, 2021) lead to invalid conclusions. [ABSTRACT FROM AUTHOR]

Zeroing neural network (ZNN) is a powerful tool in designing suitable control schemes since it is a systematic approach. It has been used in fields like robot manipulator control and tracking control, but few researchers have investigated the possible application of the ZNN in multi-agent systems. Based on the elegant zeroing neural network (ZNN) scheme, in this paper, two novel noise-tolerant ZNN (NTZNN) models are proposed to achieve consensus, which is a crucial problem in the field of cooperative control of the multi-agent systems. Besides, the novel noise-tolerant sign-bi-power (NTSBP) and noise-tolerant sign-exp-power (NTSEP) activation functions are used in this study. The NTZNN models activated by NTSBP and NTSEP are more robust than traditional ZNN models activated by the traditional sign-bi-power (SBP) and sign-exp-power (SEP) activation functions, respectively. The detailed mathematical analysis is presented to prove the robustness and predefined-time stability of the NTZNN models, and the upper bounds of the settling-time function are also estimated by a novel method based on improper integral. Combining the traditional Polyakov method and the proposed method based on improper integral, we can estimate the upper bounds of the settling-time function in a more precise way. Then, the robustness of the NTZNN models under both dynamic bounded vanishing noise and dynamic bounded non-vanishing noise is further evaluated by numerical experiments, and results show that the models are effective at both situations. We also present several practical examples of formation control, and parallel experiments are provided to further demonstrate that our results are general. All the theoretical and numerical verification results show that the NTZNN models are more robust than the traditional ZNN models activated by SBP or SEP activation functions, and it is also predefined-time stable. • This study provides an insight into the application of ZNN in networked control systems. • Two NTZNN models are proposed to solve the consensus problem under various noise. • Settling-time functions are estimated through a novel improper integral based method. • The proposed protocal are verified in MAS with fixed and switching communication topology. • We also verify our protocol in practical formation control experiments. [ABSTRACT FROM AUTHOR]

The fractional complex Ginzburg–Landau model is widely used in the description of wave propagation through optical transmission lines. It has many useful applications in the fields of telecommunications and nonlinear optics. This paper investigates the fractional effects of the complex Ginzburg–Landau model with quadratic–cubic, anti–cubic and generalized anti–cubic laws of nonlinearity by using generalized projective Riccati equation method. The variation in the traveling wave behavior of the governing model is examined for beta, conformable and M-truncated derivatives. Some constraint conditions are carried out during mathematical analysis, which are further used for evaluating the traveling wave solutions. The analytic solutions of the considered model are determined in terms of hyperbolic and trigonometric function solutions. Consequently, dark, bright, kink, bell-shaped and singular solitons are extracted. The reported solutions are presented using 2D and 3D graphs. These graphs are showing the fractional effects for different values of fractional parameter. The evolution of the wave profiles shows that the retrieved solitons become similar for all three definitions of fractional derivatives as the fractional parameter approaches unity. [ABSTRACT FROM AUTHOR]

Generative Adversarial Networks (GANs) are the models that generate data samples from the statistical distribution of the data. It is one of the most well-known branches of machine learning and deep learning. Different techniques are involved in the processing and production of visual data, which sometimes gives rise to misperception uncertainties. Bearing this issue in mind, we define some solid mathematical concepts to model and resolve the stated problem named complex picture fuzzy soft relations (CPFSRs) which is defined by the Cartesian product (CP) of two complex picture fuzzy soft sets (CPFSSs). The major objective of this study is to develop some innovative and useful notions that may be used to handle difficult and inconsistent information in practical situations. The proposed notion is foremost and superior to the prevailing ideas, where the presented idea is the improved technique of two different theories, named picture fuzzy set (PFS) and soft set (SS). Additionally, it presents the picture fuzzy soft set (PFSS) in professional decision-making by reducing complexions. The evaluated CPFSRs are the improved versions of soft relations, fuzzy relations, complex soft relations, and complex fuzzy relations. Therefore, this paper provides modeling methodologies based on CPFSRs which are used for the analysis of electing the best GAN for effective working. In the process, the score functions are also formulated and analyzed. Finally, a comparative study of existing techniques has been done to show the validity of the proposed work. • Introduced some solid mathematical concepts to model and resolve the stated problem named Complex picture fuzzy soft relations. • Types of Complex picture fuzzy soft relations are elucidated and some authentic results also have been discussed. • Some authentic results also have been discussed. • The analysis of electing the best GAN for effective working provides modeling methodologies based on Complex picture fuzzy soft relations. • For showing the validity of the proposed work, a comparative study of existing techniques has been done. [ABSTRACT FROM AUTHOR]

In this paper, we study a stochastic SIQR epidemic model with imperfect quarantine. We perform a detailed mathematical analysis of the dynamics of the stochastic model. The basic reproduction number R 0 s turns out to be a sharp threshold, that is, if R 0 s < 1 , then the disease-free equilibrium of the stochastic model is globally stable almost surely, whereas if R 0 s > 1 , the Markov process is positive recurrence which indicates that the disease will prevail. We also adopt the data of weekly infected cases for northern China from the first week of 2014 to the 26th week of 2014, to fit the model and estimate the parameters. [ABSTRACT FROM AUTHOR]

Beyond the well-documented conventional phase equilibrium calculations at pressure and temperature (PT) specifications, other specifications, such as volume, temperature and moles (VTN) and internal energy, volume and moles (UVN) have received an increasingly interest in the last years. Whatever the selected set of independent variables, phase stability at UVN conditions can be asserted by solving simpler VTN or PT stability problems (a non-linear equation is solved only once at UVN specifications for temperature). In VTN stability, modified Newton iterations were previously used to achieve convergence, since successive substitution iterations (SSI) may exhibit problematic convergence. A mathematical analysis of convergence properties of the successive substitution (SSI) method for VTN stability reveals its potential instability, unlike for PT stability, in which SSI is very robust. This problem can be theoretically overcome by using a damping factor, but severe damping may lead to unacceptable slow convergence rates. It is shown that the SSI method should never be used alone, combined undamped SSI-standard Newton method is neither robust nor efficient as claimed previously and must be avoided; moreover, damped SSI can be used with caution only in early iteration stages. The convergence behavior of several methods for VTN stability is analyzed for a variety of mixtures and the numbers of iterations are compared with those reported in the literature. Several domains in the molar density-temperature plane were identified, where SSI is either systematically not detecting a phase split (converging to the trivial solution from all initial guesses) or systematically diverges. Our calculation procedures are highly robust and systematically faster than previous methods (for some test points up to one or even two orders of magnitude) and are able to find the global minimum of the TPD function in all test cases, unlike previously proposed SSI/Newton methods, which either are strongly attracted by local minima or they diverge. This paper gives for the first time a detailed mathematical and numerical analysis of the convergence behavior of SSI and combined SSI-Newton methods in VTN stability testing. [ABSTRACT FROM AUTHOR]

In this paper, we created a general mathematical equation for the cushion curves of polymeric foams, using the measurement results of drop weight impact tests on commercially available, closed-cell ethylene-vinyl acetate and cross-linked polyethylene foams of different densities. We found exponential relationship between the results of the drop tests and the static load, and investigated the effect of the input parameters on the fitted constants using analysis of covariance and multiple linear regression. In the second part of the study, we used a novel approach to theoretically determine the cushion curves of different thicknesses. We predicted material behavior using the Burgess method on the fitted exponential equations and assessed the limitations and accuracy of this extrapolation approach by comparing the measured and simulated data. We validated the results by quantifying the permanently damaged volume of the foams with the use of a 3D optical measuring system. • A new approach was implemented to determining the cushion curves of polymer foams. • Several drop tests were performed on XPE and EVA foams with varying impact energy. • The results were analyzed using covariance analysis and multiple linear regression. • The damage of the structures was investigated with a 3D optical measuring system. • The limitations and the accuracy of the Burgess method were determined. [ABSTRACT FROM AUTHOR]

Dynamics of predator–prey systems is of great importance in ecosystems. In this paper, we present and analyse a stochastic eco-epidemiological predator–prey model where the influence of anti-predator behaviour is investigated due to the fear induced from the predators. Through mathematical analysis, it has been observed that the model has a unique and global positive solution. Sufficient criteria are established for the existence and ergodicity of a unique stationary distribution. Moreover, stochastic extinction for the whole eco-epidemiological system or only the infectious disease have been analysed. [ABSTRACT FROM AUTHOR]

Link-based similarity search aims to find similar nodes for a given query node in a graph, which arises in numerous applications, including web spam detection, social network analysis and web search. Among existing methods, SimRank is a well-known similarity model, which provides an effective and trustful function for similarity search. A large amount of techniques on SimRank similarity search are devoted recently, which compute the similarity scores by traversing the paths between query and candidate nodes. However, the number of paths increases exponentially as path length increases, which makes the computation expensive and cannot support fast similarity search over large graphs. In this paper, we propose an efficient index-free SimRank similarity search approach, namely DisSim, which reduces the computational cost by discounting path length. We observe that SimRank could rapidly converge at a stable state and the results change little after a few of iterations. Based on the fast convergence, the similarity between nodes is defined as the SimRank score at the second iteration. For the computation of DisSim, we divide the similarity into one-step and two-step first-meeting probabilities. The one-step first-meeting probabilities are computed by path traverses from query to candidate nodes, which reduces computational cost by skipping unnecessary nodes. And the two-step first-meeting probabilities are computed by integrating the repeated parts of the paths. For further speeding up query processing, we develop a pruning algorithm, which prunes unpromising path traverses by setting a threshold, and the accuracy loss under threshold is given through mathematical analysis. Extensive experiments on real graphs demonstrate the performance of DisSim through comparing with the state-of-the-art algorithms. • The proposed approach supports fast query processing without preprocessing. • A pruning algorithm is developed for further speeding up fast query processing. • The computation time of query processing is further reduced by setting a threshold. • Experiments on real datasets demonstrate the performance of the proposed approach. [ABSTRACT FROM AUTHOR]

As a common mathematical operation, the time-varying matrix inversion (TVMI) is frequently arisen in many complex problems. It has been proved in a large number of studies that the zeroing neural network (ZNN) is a reliable tool to solve TVMI problems. However, the previous reported conventional zeroing neural network (CZNN) models only achieve undesirable exponential convergence or finite-time convergence, and they are difficult to be popularized in practical applications. Therefore, by introducing a novel activation function (NAF), a fixed-time convergence and noise-tolerant zeroing neural network (FTCNTZNN) model for solving TVMI problems is proposed in this paper. Different from existing CZNN models, the proposed FTCNTZNN model possesses both fixed-time convergence and anti-noise properties for TVMI solving. To comprehensively show the superiority of the proposed FTCNTZNN model for solving TVMI, a lot of theoretical demonstrations and comparative simulation experiments have been provided in this work. Firstly, the fixed-time convergence and robustness of the proposed FTCNTZNN model are verified by detailed theoretical analysis in noiseless and noisy environment, respectively. Then, the proposed FTCNTZNN model is applied to solve two different TVMI problems in a variety of situations. In addition, a successful manipulator trajectory tracking application using the proposed FTCNTZNN model in noisy environment further validates its practicability. Both of theoretical analysis and experimental results convincingly verify that the proposed FTCNTZNN model can effectively solve TVMI problems in noiseless and noisy environment. • A novel activation function (NAF) with simple structure is presented. • Based on the NAF, a new FTCNTZNN model is constructed. • Fixed-time convergence and robustness of the FTCNTZNN are validated by theoretical analysis and mathematical verification. [ABSTRACT FROM AUTHOR]

Optimizing the heat source distribution is an effective strategy to enhance the heat dissipation in electronic devices. In this paper, a topology optimization (TO) scheme with a penalty factor between 0 and 1 is developed to solve the volume-to-point heat source distribution. The topology-optimized heat source always lies around the heat sink with continuous design, and the isotherms show semicircular arcs with the semicircle center located at the heat sink. Compared with other optimization methods, the current TO method obtains better designs approximate to the theoretical optimal solution with higher cooling performance and lower computational cost. Moreover, an equivalent distance function reflecting the distance between the heat source and the heat sink is introduced to evaluate the performance of different heat source distributions. Topology-optimized designs and mathematical analyses show that reducing the equivalent distance between the heat source and the heat sink is an effective way to enhance heat transport. This work extends the application of the TO method and deepens the understanding of the optimization of heat source distribution. • Topology optimization with penalty factor <1 is developed for heat source. • Theoretically optimal solutions are obtained for volume-to-point heat conduction. • Performance and efficiency are improved compared with other optimization methods. • The concept of equivalent distance function is introduced for theoretical analyses. [ABSTRACT FROM AUTHOR]