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We present comprehensive numerical results from a study of model H, which describes phase separation kinetics in binary fluid mixtures. We study the pattern dynamics of both density and velocity fields in d = 2, 3. The density length scales show three distinct regimes, in accordance with analytical arguments. The velocity length scale shows a diffusive behavior. We also study the scaling behavior of the morphologies for density and velocity fields and observe dynamical scaling in the relevant correlation functions and structure factors. Finally, we study the effect of quenched random field disorder on spinodal decomposition in model H. [ABSTRACT FROM AUTHOR]

Product service system (PSS) is an effective approach to achieve win–win situation between service providers and consumers, and the design of PSS is the first step of its application. However, on the one hand, PSS is relatively an abstract concept, and what exactly should be considered when designing a PSS still require further exploration; on the other hand, the fast development of information and web technologies bring both opportunities and challenges for PSS design. For example, how to efficiently design the smart & connected products that support remote monitoring and control of service operation, how to build the dynamic service activity flow model that can be intuitively and visually read by human engineers and also can be conveniently deployed on computers, and how to realise edge–cloud collaboration between service providers and consumers. In this regard, a service requirement-oriented four-step generic PSS design method is established, including service mode selection and structured service order generation → smart & connected service product configuration → dynamic event-state knowledge graph-based service activity flow and service resource network configuration → industrial internet-based edge–cloud collaborative service delivering. Finally, a real design case of carbon block grinding and polishing PSS is used for verification. ABBREVIATIONS: AS: assembly service; C: controlling targets or objectives; I: input; M: enabling methods or mechanisms; MRO: maintenance, repair, and operation; MS: maintenance service; O: output; OEE: overall equipment effectiveness; PSS: product service system; PV: processing volume; RxEy-Sz: the relation from Event y to the State z of Service activity x; RxSz-Ey: the relation from the State z of Service activity x to Event y; StateAiCurrent: the current state of Service activity i; StateAiFuturek: the kth possible future state of Service activity i; StateAiHistoryj: the jth historical state of service activity i; StateEy: the state of Event y; Tq: the qth time point in the time line. [ABSTRACT FROM AUTHOR]

The time-dependent relaxation of a dynamical system may exhibit a power-law behavior that is superimposed by log-periodic oscillations. D. Sornette [Phys. Rep. 297, 239 (1998)] showed that this behavior can be explained by a discrete scale invariance of the system, which is associated with discrete and equidistant timescales on a logarithmic scale. Examples include such diverse fields as financial crashes, random diffusion, and quantum topological materials. Recent time-resolved experiments and molecular dynamics simulations suggest that discrete scale invariance may also apply to hierarchical dynamics in proteins, where several fast local conformational changes are a prerequisite for a slow global transition to occur. Employing entropy-based timescale analysis and Markov state modeling to a simple one-dimensional hierarchical model and biomolecular simulation data, it is found that hierarchical systems quite generally give rise to logarithmically spaced discrete timescales. By introducing a one-dimensional reaction coordinate that collectively accounts for the hierarchically coupled degrees of freedom, the free energy landscape exhibits a characteristic staircase shape with two metastable end states, which causes the log-periodic time evolution of the system. The period of the log-oscillations reflects the effective roughness of the energy landscape and can, in simple cases, be interpreted in terms of the barriers of the staircase landscape. [ABSTRACT FROM AUTHOR]

This paper proposes a maintenance policy for a k-out-of-n: F system operating to fulfil several jobs without interruptions. The system is replaced when the Nth job completes or at the kth failure, whichever occurs first. So, there are some non-failed components when a replacement is done. These components can be sold as second-hand products to continue working in other systems for a while. The price of them is also considered in the proposed maintenance policy. An optimal maintenance policy is studied to minimise long-run average cost under the constraint of relative mean operating time. Comprehensive numerical studies are done to assess the effect of the model parameters on the optimal solutions. Also, to demonstrate the applicability of the proposed plan, a data set related to wind turbine generator failures is considered as a case study. [ABSTRACT FROM AUTHOR]

Memory effects are ubiquitous in a wide variety of complex physical phenomena, ranging from glassy dynamics and metamaterials to climate models. The Generalized Langevin Equation (GLE) provides a rigorous way to describe memory effects via the so-called memory kernel in an integro-differential equation. However, the memory kernel is often unknown, and accurately predicting or measuring it via, e.g., a numerical inverse Laplace transform remains a herculean task. Here, we describe a novel method using deep neural networks (DNNs) to measure memory kernels from dynamical data. As a proof-of-principle, we focus on the notoriously long-lived memory effects of glass-forming systems, which have proved a major challenge to existing methods. In particular, we learn the operator mapping dynamics to memory kernels from a training set generated with the Mode-Coupling Theory (MCT) of hard spheres. Our DNNs are remarkably robust against noise, in contrast to conventional techniques. Furthermore, we demonstrate that a network trained on data generated from analytic theory (hard-sphere MCT) generalizes well to data from simulations of a different system (Brownian Weeks–Chandler–Andersen particles). Finally, we train a network on a set of phenomenological kernels and demonstrate its effectiveness in generalizing to both unseen phenomenological examples and supercooled hard-sphere MCT data. We provide a general pipeline, KernelLearner, for training networks to extract memory kernels from any non-Markovian system described by a GLE. The success of our DNN method applied to noisy glassy systems suggests that deep learning can play an important role in the study of dynamical systems with memory. [ABSTRACT FROM AUTHOR]

When dielectric-elastomer (DE) resonators are operated under large alternating voltage excitations, strong geometric and material nonlinearities can significantly affect the dynamic performance. Based on the virtual work principle, a dynamic model of a circular DE resonator is established in this work. Static analysis is conducted to study the impacts of the control voltage on the strain and natural frequency of the DE resonator at equilibrium. A modified Incremental Harmonic Balance and arc-length methods are used to obtain dynamic responses of the system excited by alternating voltages, and stability analysis is conducted using the Floquet theory. The effects of the mechanical parameters are studied, and period-doubling bifurcations are observed, which are produced by the parametric excitation of the voltage. The bifurcation phenomenon is comprehensively investigated through analysis of the voltage, stress, and damping coefficient, which provides design guidance for DE resonators. [ABSTRACT FROM AUTHOR]

A cloud manufacturing (CMfg) system is presented as a novel service- and customer-oriented manufacturing paradigm that integrates the distributed manufacturing enterprises to share their manufacturing capabilities or resources and collaborate as an interconnected system in a dynamic environment. Since the high performance of this system depends on the formation of a suitable group of manufacturing service providers, this paper develops an integrated c onfiguration design and capacity planning problem for the CMfg system by considering the dynamic environment of this system. In this regard, dynamic service providers and dynamic demand are considered as two aspects of the dynamic nature of this system. A multi-period multi-objective mathematical model is proposed by maximising the utilities of all three stakeholders of the system. Moreover, three extensions of a discrete multi-objective grey wolf optimiser (DMOGWO) algorithm are devised to solve the medium- and large-scale instances. A comprehensive computational experiment is conducted to assess the performance of the developed meta-heuristic algorithms. Furthermore, by carrying out a sensitivity analysis, some managerial insight is suggested for the managers. [ABSTRACT FROM AUTHOR]

In Born–Oppenheimer molecular dynamics (BOMD) simulations based on the density functional theory (DFT), the potential energy and the interatomic forces are calculated from an electronic ground state density that is determined by an iterative self-consistent field optimization procedure, which, in practice, never is fully converged. The calculated energies and forces are, therefore, only approximate, which may lead to an unphysical energy drift and instabilities. Here, we discuss an alternative shadow BOMD approach that is based on backward error analysis. Instead of calculating approximate solutions for an underlying exact regular Born–Oppenheimer potential, we do the opposite. Instead, we calculate the exact electron density, energies, and forces, but for an underlying approximate shadow Born–Oppenheimer potential energy surface. In this way, the calculated forces are conservative with respect to the approximate shadow potential and generate accurate molecular trajectories with long-term energy stabilities. We show how such shadow Born–Oppenheimer potentials can be constructed at different levels of accuracy as a function of the integration time step, δt, from the constrained minimization of a sequence of systematically improvable, but approximate, shadow energy density functionals. For each energy functional, there is a corresponding ground state Born–Oppenheimer potential. These pairs of shadow energy functionals and potentials are higher-level generalizations of the original "zeroth-level" shadow energy functionals and potentials used in extended Lagrangian BOMD [Niklasson, Eur. Phys. J. B 94, 164 (2021)]. The proposed shadow energy functionals and potentials are useful only within this extended dynamical framework, where also the electronic degrees of freedom are propagated as dynamical field variables together with the atomic positions and velocities. The theory is quite general and can be applied to MD simulations using approximate DFT, Hartree–Fock, or semi-empirical methods, as well as to coarse-grained flexible charge models. [ABSTRACT FROM AUTHOR]

In both manual and automated warehouses, a combination of efficient zoning and picker routing plays an important role in improving travel time, congestion, and system throughput. This paper considers the order picker routing problem in a dynamic and synchronised zoning environment, where the items corresponding to each customer order are picked simultaneously in multiple zones, and zones may change between different orders. The objective is to minimise the maximum time of completing the picking activities in any zone. Using a min–max type of objective not only minimises the makespan of an order picking wave, but it also helps balance the workload of the order pickers more effectively. We present a mathematical model for the optimal solution of this problem, as well as a dynamic programming approach to find the optimal solution for the case where a zone is a set of adjacent aisles. Computational experiments on randomly generated instances show that the dynamic programming approach is able to find optimal solutions in negligible computational times. [ABSTRACT FROM AUTHOR]

A hybrid system interacts with the discrete and continuous dynamics of a physical dynamical system. The notion of a hybrid system gives embedded control systems a great advantage. The Langevin differential equation can accurately depict many physical phenomena and help researchers effectively represent anomalous diffusion. This paper considers a fractional hybrid Langevin differential equation, including the ψ-Caputo fractional operator. Furthermore, some novel boundaries selected are considered to be a problem. We used the Schauder and Banach fixed-point theorems to prove the existence and uniqueness of solutions to the considered problem. Additionally, the Ulam-Hyer stability is evaluated. Finally, we present a representative example to verify the theoretical outcomes of our findings. [ABSTRACT FROM AUTHOR]

As people age, their ability to maintain homeostasis in response to stressors diminishes. Physical frailty, a syndrome characterized by loss of resilience to stressors, is thought to emerge due to dysregulation of and breakdowns in communication among key physiological systems. Dynamical systems modeling of these physiological systems aims to model the underlying processes that govern response to stressors. We hypothesize that dynamical systems model summaries are predictive of age-related declines in health and function. In this study, we analyze data obtained during 75-gram oral-glucose tolerance tests (OGTT) on 1,120 adults older than 50 years of age from the Baltimore Longitudinal Study on Aging. We adopt a two-stage modeling approach. First, we fit OGTT curves with the Ackerman model—a nonlinear, parametric model of the glucose-insulin system—and with functional principal components analysis. We then fit linear and Cox proportional hazards models to evaluate whether usual gait speed and survival are associated with the stage-one model summaries. We also develop recommendations for identifying inadequately-fitting nonlinear model fits in a cohort setting with numerous heterogeneous response curves. These recommendations include: (1) defining a constrained parameter space that ensures biologically plausible model fits, (2) evaluating the relative discrepancy between predicted and observed responses of biological interest, and (3) identifying model fits that have notably poor model fit summary measures, such as Rpseudo2 , relative to other fits in the cohort. The Ackerman model was unable to adequately fit 36% of the OGTT curves. The stage-two regression analyses found no associations between Ackerman model summaries and usual gait speed, nor with survival. The second functional principal component score was associated with faster gait speed (p<0.01) and improved survival (p<0.01). [ABSTRACT FROM AUTHOR]

We consider the hyperbolic relaxation of the viscous Cahn-Hilliard equation with a symport term. This equation is characterized by the presence of the additional inertial term τDΦtt that accounts for the relaxation of the diffusion flux. We suppose that τD is dominated by the viscosity coefficient δ. Endowing the equation with Dirichlet boundary conditions, we show that it generates a dissipative dynamical system acting on a certain phase-space, depending on τD. This system is shown to possess a global attractor that is upper semicontinuous at τD = δ = 0. Then, we construct a family of exponential attractors ℑτD,δ which is a robust perturbation of an exponential attractor of the Cahn-Hilliard equation; namely, the symmetric Hausdorff distance between ℑτD,δ and ℑ0,0 tends to 0 as (τD,δ) tends to (0,0) in an explicitly controlled way. Finally, we present numerical simulations of the time evolution of weak solutions as a function of parameters. [ABSTRACT FROM AUTHOR]

The axiomatic theory of ordinary differential equations, owing to its simplicity, can provide a useful framework to describe various generalizations of dynamical systems. In this study, we consider how dynamical properties can be generalized to this setting. First, we study the generalizations of dynamical properties, such as invariance and limit sets and show that compact weakly invariant sets can be characterized in terms of the corresponding shift-invariant sets in the function space. This result enables us to consider weakly invariant sets in terms of shift-invariant sets. Next, we compare the axiomatic theory of ODE with other formalisms of generalized dynamical systems, namely generalized semiflow and multivalued semigroup. Finally, we introduce the notion of invariant measures and show that we can generalize classical results, such as Poincaré recurrence theorem. [ABSTRACT FROM AUTHOR]

This paper presents and investigates a novel methodology for validating high-resolution ocean models using satellite imagery. High-resolution ocean models provide detailed information in coastal areas where other available data products are too coarse. Models are usually fitted by comparing them with observations; However, accessing in situ data in all small coastal areas is not feasible, as in situ observations are scarce and obtained through dedicated ships or instruments in limited and selected regions. Our work aims to use alternative remote sensing information to overcome this challenge. The approach involves establishing connections between the satellite observations and the outcomes of various computational experiments carried out using the Regional Ocean Modeling System, which allows the selection of different parameters to run the ocean model. These choices are not fully determined a priori and each one produces distinct outputs, which are then linked to the images through dynamical systems objects. By defining a performance index, we are able to quantify which experiment provides a better representation of the local ocean state. [ABSTRACT FROM AUTHOR]

In light of fractional theory, this paper presents several new effective solitonic formulations for the Langmuir and ion sound wave equations. Prior to this study, no previous research has presented the comparision and obtained the generalized fractional soliton solutions of this kind with power law kernel and Mittag-Leffler kernel. The ion sound and Langmuir wave equations are essential in plasma physics, offering insights into the collective behavior of charged particles in plasmas and enabling diagnostics and control of these complex, ionized gas systems. The two distinct fractional order differential operators are substituted for the traditional order derivative to reshape the examined model. The Atangana-Baleanu non-singular and non-local operator and conformable fractional operator are the fractional-order operators that are used to create the fractional complex system equations for Langmuir waves and ion sound. A constructive approach new auxiliary equation method utilizes to obtain the exact analytical soliton solutions for ion sound and Langmuir wave equation. A wide range of soliton solutions is obtained, including mixed complex solitary shock solutions, singular solutions, mixed shock singular solutions, mixed trigonometric solutions, mixed singular solutions, exact solutions, mixed periodic solutions, and mixed hyperbolic solutions, dark soliton, bright soliton, trigonometric solutions, periodic results, and hyperbolic results. The solitons solution of the ion sound and Langmuir wave equations lies in their ability to maintain wave stability, their role in modeling wave propagation and nonlinear effects, their potential use as diagnostic tools, and their relevance in wave-particle interactions in plasma physics. The solitons provide a valuable framework for understanding the behavior of waves in plasmas and offer insights into the complex dynamics of these charged particle systems. A graphical comparison analysis of a few solutions is also shown here, taking into account appropriate parametric values through the use of the software package. Moreover, the results of this study have important implications for Hamilton's equations and generalized momentum, where solitons are employed in long-range interactions. [ABSTRACT FROM AUTHOR]

For the first time, a control strategy based on Fuzzy Sliding Mode Control is implemented in the control of a large amplitude limit cycle of a composite cantilever beam in a multi-dimensional nonlinear form. In the dynamic model establishment of the investigated structure, the higher-order shearing effect is applied, as well as the second-order discretization. Numerical simulation demonstrates that a multi-dimensional nonlinear dynamic system of the investigated structure is demanded for accurate estimation of large amplitude limit cycle responses. Therefore, a control strategy is employed to effectively suppress such responses of the beam in multi-dimensional nonlinear form. [ABSTRACT FROM AUTHOR]

Dynamical systems on hypergraphs can display a rich set of behaviors not observable for systems with pairwise interactions. Given a distributed dynamical system with a putative hypergraph structure, an interesting question is thus how much of this hypergraph structure is actually necessary to faithfully replicate the observed dynamical behavior. To answer this question, we propose a method to determine the minimum order of a hypergraph necessary to approximate the corresponding dynamics accurately. Specifically, we develop a mathematical framework that allows us to determine this order when the type of dynamics is known. We use these ideas in conjunction with a hypergraph neural network to directly learn the dynamics itself and the resulting order of the hypergraph from both synthetic and real datasets consisting of observed system trajectories. [ABSTRACT FROM AUTHOR]

Rapid processing of tactile information is essential to human haptic exploration and dexterous object manipulation. Conventional electronic skins generate frames of tactile signals upon interaction with objects. Unfortunately, they are generally ill-suited for efficient coding of temporal information and rapid feature extraction. In this work, we report a neuromorphic tactile system that uses spike timing, especially the first-spike timing, to code dynamic tactile information about touch and grasp. This strategy enables the system to seamlessly code highly dynamic information with millisecond temporal resolution on par with the biological nervous system, yielding dynamic extraction of tactile features. Upon interaction with objects, the system rapidly classifies them in the initial phase of touch and grasp, thus paving the way to fast tactile feedback desired for neuro-robotics and neuro-prosthetics. [ABSTRACT FROM AUTHOR]

Summary: The reduced‐order observer‐based finite‐time control problem for one‐sided Lipschitz nonlinear switched singular systems is addressed in this paper. First, the design method of the reduced‐order observer is given via state transformation. Then, based on the average dwell time (ADT) approach, some new sufficient conditions for regularity, impulse‐freeness, have a unique solution and finite‐time boundedness (FTB) of the dynamic augmented systems are obtained by exploring the reduced‐order observer‐based controller. Further, the lower finite‐time bound can be obtained by using singular value decomposition method. And the state feedback gain and the observer gain are computed by solving linear matrix inequalities (LMIs). Finally, the validity of the obtained method is illustrated by means of a numerical example and a DC motor system. [ABSTRACT FROM AUTHOR]

Monitoring changes of signaling molecules and metabolites with high temporal resolution is key to understanding dynamic biological systems. Here, we use directed evolution to develop a genetically encoded ratiometric biosensor for c-di-GMP, a ubiquitous bacterial second messenger regulating important biological processes like motility, surface attachment, virulence and persistence. The resulting biosensor, cdGreen2, faithfully tracks c-di-GMP in single cells and with high temporal resolution over extended imaging times, making it possible to resolve regulatory networks driving bimodal developmental programs in different bacterial model organisms. We further adopt cdGreen2 as a simple tool for in vitro studies, facilitating high-throughput screens for compounds interfering with c-di-GMP signaling and biofilm formation. The sensitivity and versatility of cdGreen2 could help reveal c-di-GMP dynamics in a broad range of microorganisms with high temporal resolution. Its design principles could also serve as a blueprint for the development of similar, orthogonal biosensors for other signaling molecules, metabolites and antibiotics. The ubiquitous second messenger c-di-GMP regulates many biological processes in bacteria, including cell cycle, motility, virulence and biofilm formation. Here, Kaczmarczyk et al. develop a c-di-GMP biosensor that enables dynamic real-time tracking of c-di-GMP levels in individual living cells. [ABSTRACT FROM AUTHOR]

The measurement of sense of coherence (SOC) has received attention for more than three decades. Despite the extensive use of SOC-13, there is still a long debate regarding its dimensionality structure. Recently, there has been an increasing use of network modeling as a valid alternative to latent-variable modeling. This study proposes an exploratory approach to the structure of SOC-13 by adopting a network perspective. The network structure was estimated with a Gaussian Graphical Model, and Exploratory Graph Analysis (EGA) was used to inspect network dimensionality. We fit and compared the unidimensional, first- and second-order confirmatory factor analysis (CFA), bifactor-CFA, and structure derived from EGA. Our results showed unacceptable fit values for the CFA models, suggesting that SOC-13 is not unidimensional. Inspection of the estimated network suggested that the SOC-13 items emerged as a dynamic system of mutually interacting nodes that formed three distinct clusters of items (communities) that are not those defined in the literature. EGA identified three communities of items: the first community was characterized by comprehensibility and manageability items, the second community was characterized by comprehensibility and manageability items, and the third dimension was characterized by all meaningfulness items and one comprehensibility item. Our study presented a novel perspective in investigating the structure of SOC-13 that strengthens the assumption that SOC should be conceptualized as a complex system of cognitive (comprehensibility), behavioral (manageability), and motivational dimensions (meaningfulness) that are deeply linked and not necessarily distinct. [ABSTRACT FROM AUTHOR]

Interoperability is a central problem in digitization and System of Systems (SoS) engineering, which concerns the capacity of systems to exchange information and cooperate. The task to dynamically establish interoperability between heterogeneous cyber-physical systems (CPSs) at run-time is a challenging problem. Different aspects of the interoperability problem have been studied in fields such as SoS, neural translation, and agent-based systems, but there are no unifying solutions beyond domain-specific standardization efforts. The problem is complicated by the uncertain and variable relations between physical processes and human-centric symbols, which result from, e.g., latent physical degrees of freedom, maintenance, re-configurations, and software updates. Therefore, we surveyed the literature for concepts and methods needed to automatically establish SoSs with purposeful CPS communication, focusing on machine learning and connecting approaches that are not integrated in the present literature. Here, we summarize recent developments relevant to the dynamic interoperability problem, such as representation learning for ontology alignment and inference on heterogeneous linked data; neural networks for transcoding of text and code; concept learning-based reasoning; and emergent communication. We find that there has been a recent interest in deep learning approaches to establishing communication under different assumptions about the environment, language, and nature of the communicating entities. Furthermore, we present examples of architectures and discuss open problems associated with artificial intelligence (AI)-enabled solutions in relation to SoS interoperability requirements. Although these developments open new avenues for research, there are still no examples that bridge the concepts necessary to establish dynamic interoperability in complex SoSs, and realistic testbeds are needed. [ABSTRACT FROM AUTHOR]

This contribution focuses on the detection of tracer particles within non-homogeneous bulk media, aiming to enhance insights into particulate systems. Polarimetric radar measurements are employed, utilizing cross-polarizing channels in order to mitigate interference from bulk media reflections. To distinguish the tracer particle in the measurements, a resonant cross-polarizing structure is constructed, facilitating the isolation of frequency signatures from the surrounding bulk clutter. In addition to characterizing the bulk and tracer components, this study provides a detailed presentation and discussion of the measurement setup, along with the employed signal processing methods. The effectiveness of the proposed methods is demonstrated through comprehensive measurements, where a tracer particle is systematically positioned at various locations. The results affirm the feasibility and efficacy of the approach, highlighting its applicability for enhanced dynamic monitoring in particulate systems within industrial processes. [ABSTRACT FROM AUTHOR]

To perform the accurate and efficient dynamic load identification (DLI) on time-varying (TV) structural systems, this paper proposes a novel time-domain dynamic load identification method, which we call the inverse Wentzel–Kramers–Brillouin (WKB) real function recursive solution. The proposed method can identify the dynamic loads of TV structural systems with different masses, damping, and stiffness online. Based on the WKB real function recursive solution, we first derive the acceleration recursive solution for linear time-varying (LTV) dynamic systems. Then, by reversing the acceleration recursive solution, we obtain the recursive formula for the dynamic load as a function of time. At each time step, this method performs recursion using the load and response of the previous time step to derive the current load. Finally, we demonstrate through numerical simulations that this algorithm has higher identification accuracy and computational efficiency than the inverse Wilson-θ method, and reduces the computation time significantly. [ABSTRACT FROM AUTHOR]

We derive efficient algorithms to compute weakly Pareto optimal solutions for smooth, convex and unconstrained multiobjective optimization problems in general Hilbert spaces. To this end, we define a novel inertial gradient-like dynamical system in the multiobjective setting, which trajectories converge weakly to Pareto optimal solutions. Discretization of this system yields an inertial multiobjective algorithm which generates sequences that converge weakly to Pareto optimal solutions. We employ Nesterov acceleration to define an algorithm with an improved convergence rate compared to the plain multiobjective steepest descent method (Algorithm 1). A further improvement in terms of efficiency is achieved by avoiding the solution of a quadratic subproblem to compute a common step direction for all objective functions, which is usually required in first-order methods. Using a different discretization of our inertial gradient-like dynamical system, we obtain an accelerated multiobjective gradient method that does not require the solution of a subproblem in each step (Algorithm 2). While this algorithm does not converge in general, it yields good results on test problems while being faster than standard steepest descent. [ABSTRACT FROM AUTHOR]

By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expansions with respect to multiplicatively independent bases. In this work, we introduce and study — in the discrete context of the integers — analogs of some of the notions and results surrounding Furstenberg's work. In particular, we define a new class of fractal sets of integers that parallels the notion of ×r$\times r$‐invariant sets on the 1‐torus and investigate the additive and geometric independence between two such fractal sets when they are structured with respect to multiplicatively independent bases. Our main results in this direction parallel the works of Furstenberg, Hochman–Shmerkin, Shmerkin, Wu, and Lindenstrauss–Meiri–Peres and include: a classification of all subsets of the positive integers that are simultaneously ×r$\times r$‐ and ×s$\times s$‐invariant;integer analogs of two of Furstenberg's transversality conjectures pertaining to the dimensions of the intersection A∩B$A\cap B$ and the sumset A+B$A+B$ of ×r$\times r$‐ and ×s$\times s$‐invariant sets A$A$ and B$B$ when r$r$ and s$s$ are multiplicatively independent; anda description of the dimension of iterated sumsets A+A+⋯+A$A+A+\cdots +A$ for any ×r$\times r$‐invariant set A$A$.We achieve these results by combining ideas from fractal geometry and ergodic theory to build a bridge between the continuous and discrete regimes. For the transversality results, we rely heavily on quantitative bounds on the Lq$L^q$‐dimensions of projections of restricted digit Cantor measures obtained recently by Shmerkin. We end by outlining a number of open questions and directions regarding fractal subsets of the integers. [ABSTRACT FROM AUTHOR]

Summary: In this article, the cluster consensus problems of two classes of nonlinear multi‐agent systems (NMASs) are studied under the dynamic event‐triggered control (ETC) strategy, where cooperative‐competitive interactions among agents and high‐order dynamics are considered. First, two dynamic ETC protocols are developed to realize the cluster synchronization of NMASs. Different from the static ETC, a dynamic parameter regulated by an adaptive law is used in place of a constant which can improve the trigger time intervals and reduce the energy consumption. Subsequently, an adaptive control mechanism based on the proposed ETC strategy is designed to adjust the controller parameter for agents. Some sufficient conditions for achieving the cluster consensus of NMASs are derived by using the Lyapunov stability theory and algebraic graph theory. Moreover, it is proved in theory that Zeno phenomenon can be excluded with these control schemes. Finally, two simulation examples validate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In the current computing environment, the significance of distributed heterogeneous systems has gained prominence. The research on scheduling problems in distributed systems that consider energy consumption has garnered substantial attention due to its potential to enhance system stability, achieve energy savings, and contribute to environmental preservation. However, efficient scheduling in such systems necessitates not only the consideration of energy consumption but also the ability to adapt to the dynamic nature of the system. To tackle these challenges, we propose an online energy-aware scheduling algorithm for deadline-constrained applications in distributed heterogeneous systems, leveraging dynamic voltage and frequency scaling (DVFS) techniques. First, the algorithm models the continuously arriving applications and heterogeneous processors and proposes a novel task-sorting method to prioritize tasks, ensuring that more applications are completed within their respective deadlines. Second, the algorithm controls the selection range of processors based on the task's subdeadline and assigns the task to the processor with the minimum energy consumption. Through experiments conducted with randomly generated applications, our approach consistently exhibits superior performance when compared to similar scheduling algorithms. [ABSTRACT FROM AUTHOR]

Non-linear dynamical systems describe numerous real-world phenomena, ranging from the weather, to financial markets and disease progression. Individual systems may share substantial common information, for example patients' anatomy. Lately, deep-learning has emerged as a leading method for data-driven modeling of non-linear dynamical systems. Yet, despite recent breakthroughs, prior works largely ignored the existence of shared information between different systems. However, such cases are quite common, for example, in medicine: we may wish to have a patient-specific model for some disease, but the data collected from a single patient is usually too small to train a deep-learning model. Hence, we must properly utilize data gathered from other patients. Here, we explicitly consider such cases by jointly modeling multiple systems. We show that the current single-system models consistently fail when trying to learn simultaneously from multiple systems. We suggest a framework for jointly approximating the Koopman operators of multiple systems, while intrinsically exploiting common information. We demonstrate how we can adapt to a new system using order-of-magnitude less new data and show the superiority of our model over competing methods, in terms of both forecasting ability and statistical fidelity, across chaotic, cardiac, and climate systems. From the cardiac system of various human patients, to changes in sea surface temperature across different oceans, dynamical systems often exhibit many common characteristics. Here we develop a framework for jointly learning the dynamics of multiple interrelated systems while leveraging their shared traits. [ABSTRACT FROM AUTHOR]

In this article, a partial differential equation (PDE) model for atherosclerosis disease is presented that analyzes the anti-oxidative activity of high-density lipoprotein (HDL) during the reverse cholesterol transport (RCT) process. The model thoroughly investigates the complex interplay between oxidized low-density lipoprotein (ox-LDL) and high-density lipoprotein in the context of atherosclerosis, emphasizing their combined impact on plaque formation, disease progression, and regression. In addition to this, we considered that monocytes are also attracted by the presence of ox-LDL within the intima. Detailed discussions on stability analyses of the reaction dynamical system at non-inflammatory and chronic equilibrium are provided, followed by a bifurcation analysis for the proposed system. Furthermore, stability analysis for the PDE model in the presence of diffusion is conducted. Our study reveals that the oxidation rate of LDL by monocytes (δ) and the influx rate of HDL (ϕ) due to drugs/diet are primarily responsible for the existence of bi-stability of equilibrium points. In the numerical results, we observe that non-inflammatory or chronic equilibrium points exist for either a short or a long time, and these findings are validated with existing results. The biological elucidation shows the novelty in terms of enhancing our ability to assess intervention efficacy to generate therapeutic strategies resulting in the reduction of the atherosclerotic burden and associated cardiovascular risks. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the (2+1)-dimensional Kadomtsev-Petviashvili-Benjamin-Bona Mahony equation using two effective methods: the unified scheme and the advanced auxiliary equation scheme, aiming to derive precise wave solutions. These solutions are expressed as combinations of trigonometric, rational, hyperbolic, and exponential functions. Visual representations, including three-dimensional (3D) and two-dimensional (2D) combined charts, are provided for some of these solutions. The influence of the nonlinear parameter p on the wave type is thoroughly examined through diverse figures, illustrating the profound impact of nonlinearity. Additionally, we briefly investigate the Hamiltonian function and the stability of the model using a planar dynamical system approach. This involves examining trajectories, isoclines, and nullclines to illustrate stable solution paths for the wave variables. Numerical results demonstrate that these methods are reliable, straightforward, and potent tools for analyzing various nonlinear evolution equations found in physics, applied mathematics, and engineering. [ABSTRACT FROM AUTHOR]