Search Results (129)

The dynamic reconfiguration of active distribution networks (ADNDR) essentially belongs to a complex high-dimensional mixed-integer nonlinear stochastic optimization problem. Traditional mathematical optimization algorithms tend to encounter issues like slow computational speed and difficulties in solving large-scale models, while heuristic algorithms are prone to fall into local optima. Furthermore, few scholars in the existing research on distribution network (DN) reconfiguration have considered the graph structure information, resulting in the loss of critical topological information and limiting the effect of optimization. Therefore, this paper proposes an ADNDR approach based on the graph convolutional network deep deterministic policy gradient (GCNDDPG). Firstly, a nonlinear stochastic optimization mathematical model for the ADNDR is constructed, taking into account the uncertainty of sources and loads. Secondly, a loop-based encoding method is employed to reduce the action space and complexity of the ADNDR. Then, based on graph theory, the DN structure is transformed into a dynamic network graph model, and a GCNDDPG-based ADNDR approach is proposed for the solution. In this method, graph convolutional networks are used to extract features from the graph structure information, and the state of the DN, and the deep deterministic policy gradient is utilized to optimize the ADNDR decision-making process to achieve the safe, stable, and economic operation of the DN. Finally, the effectiveness of the proposed approach is verified on an improved IEEE 33-bus power system. The simulation results demonstrate that the method can effectively enhance the economy and stability of the DN, thus validating the effectiveness of the proposed approach. Full article

We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. This complexity is a generalization of entanglement entropy. It is inspired by the statistical or forecasting complexity of predictive state analysis of stochastic and complex systems theory but is intrinsically quantum. Predictive states of a subsystem are formed by equivalence classes of state vectors in the exterior Hilbert space that effectively predict the same future behavior of that subsystem for some time. As an illustrative example, we present calculations in the dynamics of an isotropic Heisenberg model spin chain and show that, in comparison to the entanglement entropy, the predictive complexity better signifies dynamically important events, such as magnon collisions. It can also serve as a local order parameter that can distinguish long and short range entanglement. Full article

In this work, we consider the problem of jointly minimizing the average cost of sampling and transmitting status updates by users over a wireless channel subject to average Age of Information (AoI) constraints. Errors in the transmission may occur and a policy has to decide if the users sample a new packet or attempt to retransmission the packet sampled previously. The cost consists of both sampling and transmission costs. The sampling of a new packet after a failure imposes an additional cost on the system. We formulate a stochastic optimization problem with the average cost in the objective under average AoI constraints. To solve this problem, we propose three scheduling policies: (a) a dynamic policy, which is centralized and requires full knowledge of the state of the system and (b) two stationary randomized policies that require no knowledge of the state of the system. We utilize tools from Lyapunov optimization theory and Discrete-Time Markov Chain (DTMC) to provide the dynamic policy and the randomized ones, respectively. Simulation results show the importance of providing the option to transmit an old packet in order to minimize the total average cost. Full article

Despite the huge number of studies of the three-body problem in physics and mathematics, the study of this problem remains relevant due to both its wide practical application and taking into account its fundamental importance for the theory of dynamical systems. In addition, one often has to answer the cognitive question: is irreversibility fundamental for the description of the classical world? To answer this question, we considered a reference classical dynamical system, the general three-body problem, formulating it in conformal Euclidean space and rigorously proving its equivalence to the Newtonian three-body problem. It has been proven that a curved configuration space with a local coordinate system reveals new hidden symmetries of the internal motion of a dynamical system, which makes it possible to reduce the problem to a sixth-order system instead of the eighth order. An important consequence of the developed representation is that the chronologizing parameter of the motion of a system of bodies, which we call internal time, differs significantly from ordinary time in its properties. In particular, it more accurately describes the irreversible nature of multichannel scattering in a three-body system and other chaotic properties of a dynamical system. The paper derives an equation describing the evolution of the flow of geodesic trajectories, with the help of which the entropy of the system is constructed. New criteria for assessing the complexity of a low-dimensional dynamical system and the dimension of stochastic fractal structures arising in three-dimensional space are obtained. An effective mathematical algorithm is developed for the numerical simulation of the general three-body problem, which is traditionally a difficult-to-solve system of stiff ordinary differential equations. Full article

The integration of AI and robotics in healthcare raises concerns, and additional issues regarding autonomous systems are anticipated. Effective communication is crucial for robots to be seen as “caring”, necessitating advanced mechatronic design and natural language processing (NLP). This paper examines the potential of humanoid robots to autonomously replicate compassionate care. The study employs computational simulations using mathematical and agent-based modeling to analyze human–robot interactions (HRIs) surpassing Tetsuya Tanioka’s TRETON. It incorporates stochastic elements (through neuromorphic computing) and quantum-inspired concepts (through the lens of Martha Rogers’ theory), running simulations over 100 iterations to analyze complex behaviors. Multisensory simulations (visual and audio) demonstrate the significance of “dynamic communication”, (relational) “entanglement”, and (healthcare system and robot’s function) “superpositioning” in HRIs. Quantum and neuromorphic computing may enable humanoid robots to empathetically respond to human emotions, based on Jean Watson’s ten caritas processes for creating transpersonal states. Autonomous AI humanoid robots will redefine the norms of “caring”. Establishing “pluralistic agreements” through open discussions among stakeholders worldwide is necessary to align innovations with the values of compassionate care within a “posthumanist” framework, where the compassionate care provided by Level 4 robots meets human expectations. Achieving compassionate care with autonomous AI humanoid robots involves translating nursing, communication, computer science, and engineering concepts into robotic care representations while considering ethical discourses through collaborative efforts. Nurses should lead the design and implementation of AI and robots guided by “technological knowing” in Rozzano Locsin’s TCCN theory. Full article

Symmetry is a fundamental property of many natural systems, which is observable through signals. In most out-of-equilibrium complex dynamic systems, the observed signals are asymmetric. However, for certain operating modes, some systems have demonstrated a resurgence of symmetry in their signals. Research has naturally focused on examining time invariance to quantify this symmetry. Measures based on the statistical and harmonic properties of signals have been proposed, but most of them focused on harmonic distortion without explicitly measuring symmetry. This paper introduces a new mathematical framework based on group theory for analyzing signal symmetry beyond time invariance. It presents new indicators to evaluate different types of symmetry in non-stochastic symmetric signals. Both periodic and non-periodic symmetric signals are analyzed to formalize the problem. The study raises critical questions about the completeness of symmetry in signals and proposes a new classification for periodic and non-periodic signals that goes beyond the traditional classification based on Fourier coefficients. Furthermore, new measures such as “symmetrometry” and “distorsymmetry” are introduced to quantify symmetry. These measures outperform traditional indicators like Total Harmonic Distortion (THD) and provide a more accurate measurement of symmetry in complex signals from applications where duty cycle plays a major role. Full article

This paper studies the dynamic behavior of a stochastic SEIRM model of COVID-19 with a standard incidence rate. The existence of global solutions for dynamic system models is proven by integrating stochastic process theory and the concept of stopping times, together with the contradiction method. Moreover, we construct appropriate Lyapunov functions to analyze system stability and apply Dynkin’s formula and Fatou’s lemma to handle stopping times and expectations of stochastic processes. Notably, the extinction study provides mathematical proof that under the given system dynamics, the total population does not grow indefinitely but tends to stabilize over time. The properties of the diffusion matrix are harnessed to guarantee the system’s stationary distribution. Conclusively, numerical simulations confirm the model’s extinction outcomes. Full article

The population dynamics of early replicators has revealed numerous puzzles, highlighting the difficulty of transitioning from simple template-directed replicating molecules to complex biological systems. The resolution of these puzzles has set the research agenda on prebiotic evolution since the seminal works of Manfred Eigen in the 1970s. Here, we study the effects of demographic noise on the population dynamics of template-directed (non-enzymatic) and protein-mediated (enzymatic) replicators. We borrow stochastic algorithms from evolutionary game theory to simulate finite populations of two types of replicators. These algorithms recover the replicator equation framework in the infinite population limit. For large but finite populations, we use finite-size scaling to determine the probability of fixation and the mean time to fixation near a threshold that delimits the regions of dominance of each replicator type. Since enzyme-producing replicators cannot evolve in a well-mixed population containing replicators that benefit from the enzyme but do not encode it, we study the evolution of enzyme-producing replicators in a finite population structured in temporarily formed random groups of fixed size n. We argue that this problem is identical to the weak-altruism version of the n-player prisoner’s dilemma, and show that the threshold is given by the condition that the reward for altruistic behavior is equal to its cost. Full article

The issue of black-odorous water (BOW) represents a formidable challenge to the current aquatic ecosystems, and its governance exhibits characteristics of low efficiency, susceptibility to relapse, and fragmented management under the Central Environmental Protection Inspection, thereby emerging as a dynamically complex issue in the ecological governance of urban and rural settings. This study introduces Gaussian white noise to simulate environmental uncertainty and design a stochastic evolutionary game model encompassing the central government, local governments, and societal forces based on evolutionary game theory and classical governance theories and concepts. Numerical simulations are conducted to explore trajectories of the strategic evolution of various subjects influenced by numerous factors. Results indicate that under the environment of random disturbances, the strategies of the game subjects show significant fluctuations, but actively cultivating the subject’s initial willingness facilitates collaboration governance in inspection. Moreover, joint construction of a “belief system” by multi-subjects, the intensity of inspection interventions, the integration of heterogeneous resources, and effective punitive measures all influence the governance of BOW, but the efficiency of resource allocation should be considered throughout the governance process. Recommendations are made finally for collaborative governance of urban and rural BOW, promoting the sustainable development of the ecological environment. Full article

Nucleation is a fundamental and general process at the initial stage of first-order phase transition. Although various models based on the classical nucleation theory (CNT) have been proposed to explain the energetics and kinetics of nucleation, detailed understanding at nanoscale is still required. Here, in view of the homogeneous bubble nucleation, we focus on cavity formation, in which evaluation of the size dependence of free energy change is the key issue. We propose the application of a formula in stochastic thermodynamics, the Jarzynski equality, for data analysis of molecular dynamics (MD) simulation to evaluate the free energy of cavity formation. As a test case, we performed a series of MD simulations with a Lennard-Jones (LJ) fluid system. By applying an external spherical force field to equilibrated LJ liquid, we evaluated the free energy change during cavity growth as the Jarzynski’s ensemble average of required works. A fairly smooth free energy curve was obtained as a function of bubble radius in metastable liquid of mildly negative pressure conditions. Full article

This paper is concerned with the mathematical modeling of complex living systems whose element microscopic state contains variables which can attain discrete values. Specifically, the main mathematical frameworks of the discrete thermostatted kinetic theory for active particles are reviewed and generalized. In the generalized thermostatted frameworks, which are based on nonlinear ordinary or partial differential equations, the elements of the system are viewed as active particles that are able to perform certain strategies modeled by introducing a functional-state variable called activity. Interactions, which are responsible of the evolution of the system, are modeled using the fundamentals of stochastic game theory and may be influenced by the action of an external force field coupled to a Gaussian-type thermostat. In particular, the interaction domain is modeled by introducing a weighted function and different non-homogeneous discrete frameworks are proposed and coupled with a specific thermostat. Two recent models derived within this approach are reviewed and refer to vehicular and pedestrian dynamics. Future research perspectives are discussed in the whole paper from theoretical and modeling viewpoints. Full article

Mobile Edge Computing (MEC) integrated with Wireless Power Transfer (WPT) is emerging as a promising solution to reduce task delays and extend the battery life of Mobile Devices (MDs). However, maximizing the long-term energy efficiency (EE) of a user-cooperative WPT-MEC system presents significant challenges due to uncertain load dynamics at the edge MD and the time-varying state of the wireless channel. In this paper, we propose an online control algorithm to maximize the long-term EE of a WPT-MEC system by making decisions on time allocations and transmission powers of mobile devices (MDs) for a three-node network. We formulate a stochastic programming problem considering the stability of network queues and time-coupled battery levels. By leveraging Dinkelbach’s method, we transform the fractional optimal problem into a more manageable form and then use the Lyapunov optimization technique to decouple the problem into a deterministic optimization problem for each time slot. For the sub-problem in each time slot, we use the variable substitution technique and convex optimization theory to convert the non-convex problem into a convex problem, which can be solved efficiently. Extensive simulation results demonstrate that our proposed algorithm outperforms baseline algorithms, achieving a 20% improvement in energy efficiency. Moreover, our algorithm achieves an $\left[O\right(1/V),O(V\left)\right]$ trade-off between EE and network queue stability. Full article

The detection of gravitational waves in 2015 ushered in a new era of gravitational wave (GW) astronomy capable of probing the strong field dynamics of black holes and neutron stars. It has opened up an exciting new window for laboratory and space tests of Einstein’s theory of classical general relativity (GR). In recent years, two interesting proposals have aimed to reveal the quantum nature of perturbative gravity: (1) theoretical predictions on how graviton noise from the early universe, after the vacuum of the gravitational field was strongly squeezed by inflationary expansion; (2) experimental proposals using the quantum entanglement between two masses, each in a superposition (gravitational cat, or gravcat) state. The first proposal focuses on the stochastic properties of quantum fields (QFs), and the second invokes a key concept of quantum information (QI). An equally basic and interesting idea is to ask whether (and how) gravity might be responsible for a quantum system becoming classical in appearance, known as gravitational decoherence. Decoherence due to gravity is of special interest because gravity is universal, meaning, gravitational interaction is present for all massive objects. This is an important issue in macroscopic quantum phenomena (MQP), underlining many proposals in alternative quantum theories (AQTs). To fully appreciate or conduct research in these exciting developments requires a working knowledge of classical GR, QF theory, and QI, plus some familiarity with stochastic processes (SPs), namely, noise in quantum fields and decohering environments. Traditionally a new researcher may be conversant in one or two of these four subjects: GR, QFT, QI, and SP, depending on his/her background. This tutorial attempts to provide the necessary connective tissues between them, helping an engaged reader from any one of these four subjects to leapfrog to the frontier of these interdisciplinary research topics. In the present version, we shall address the three topics listed in the title, excluding gravitational entanglement, because, despite the high attention some recent experimental proposals have received, its nature and implications in relation to quantum gravity still contain many controversial elements. Full article

After coarse-graining a complex system, the dynamics of its macro-state may exhibit more pronounced causal effects than those of its micro-state. This phenomenon, known as causal emergence, is quantified by the indicator of effective information. However, two challenges confront this theory: the absence of well-developed frameworks in continuous stochastic dynamical systems and the reliance on coarse-graining methodologies. In this study, we introduce an exact theoretic framework for causal emergence within linear stochastic iteration systems featuring continuous state spaces and Gaussian noise. Building upon this foundation, we derive an analytical expression for effective information across general dynamics and identify optimal linear coarse-graining strategies that maximize the degree of causal emergence when the dimension averaged uncertainty eliminated by coarse-graining has an upper bound. Our investigation reveals that the maximal causal emergence and the optimal coarse-graining methods are primarily determined by the principal eigenvalues and eigenvectors of the dynamic system’s parameter matrix, with the latter not being unique. To validate our propositions, we apply our analytical models to three simplified physical systems, comparing the outcomes with numerical simulations, and consistently achieve congruent results. Full article

In this paper, we present a new class of extended oscillators in light of chaos theory. It is based on dynamical complex systems built on the concept of self-describing with a stopping criterion process. We offer an effective studying approach with a specific focus on learning, provoking students’ thinking through the triad of enigmatics–creativity–acmeology. Dynamic processes are the basis of mathematical modeling; thus, we can reach the goal of the above-mentioned triad by the proposed differential systems. The results we derive strongly confirm the presence of symmetry in the outcomes of the proposed models. We suggest a stochastic approach to structuring the proposed dynamical systems by modeling the coefficients that drive them by some discrete probability distribution that exhibits symmetry or asymmetry. We propose specific tools for researching the behavior of these systems. Full article