State Trajectories Research Articles

Hierarchical-based self-triggered control for linear systems with external disturbances

This paper introduces a hierarchical-based robust self-triggered control mechanism for linear systems with disturbances, with the goal of achieving anti-interference and computational resource saving. To address the potential external interference in the system, the H∞ performance index is introduced, and the self-triggered controller is developed based on this index to guarantee the system’s desired anti-interference capabilities. Furthermore, a hierarchical framework is employed to facilitate collaborative optimization of triggering mechanisms and control strategies. Within this framework, the triggering interval values and control input values are computed sequentially using a cyclic iteration approach. By upholding the H∞ performance standard and incorporating a hierarchical optimization framework, the system’s sampling frequency is notably diminished, anti-interference performance is safeguarded, and the convergence speed of the state trajectory is accelerated. The efficacy of the proposed method is validated through two illustrative examples.

Transportation characteristics analysis of the dense-phase gas-solid two-phase flow based on phase space reconstruction

The operational efficiency and safety of the dense phase pneumatic conveying system is deeply influenced by the transportation characteristics of the dense-phase gas-solid two-phase flow in conveying pipelines. This paper presents a framework for analyzing the transport characteristics of the gas-solid two-phase flow based on the phase space reconstruction. The framework explores the transport characteristics by reconstructing the state evolution trajectories of the two-phase flow system in state space. The main goal is to enhance the interpretability of feature analysis. By employing the phase space reconstruction method to process the output signals of an electrostatic sensor, the evolution trajectory of the dynamic state of the gas-solid two-phase flow system was reconstructed in phase space.This provides an effective entry point for extracting the essential dynamic characteristics of the gas-solid two-phase flow system. Furthermore, a series of feature values were proposed, including the average speed of the trajectory, Shannon entropy of the trajectory, and the average distance between state points in phase space, which were used to respectively evaluate important transportation characteristics such as flowability, stability, and particle aggregation degree of the gas-solid two-phase flow. Moreover, through comparative analysis with visualization images that represent actual conveying conditions, the effectiveness of these proposed feature values in evaluating these transportation characteristics was verified.

Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity

We report universal statistical properties displayed by ensembles of pure states that naturally emerge in quantum many-body systems. Specifically, two classes of state ensembles are considered: those formed by (i) the temporal trajectory of a quantum state under unitary evolution or (ii) the quantum states of small subsystems obtained by partial, local projective measurements performed on their complements. These cases, respectively, exemplify the phenomena of “Hilbert-space ergodicity” and “deep thermalization.” In both cases, the resultant ensembles are defined by a simple principle: The distributions of pure states have maximum entropy, subject to constraints such as energy conservation, and effective constraints imposed by thermalization. We present and numerically verify quantifiable signatures of this principle by deriving explicit formulas for all statistical moments of the ensembles, proving the necessary and sufficient conditions for such universality under widely accepted assumptions, and describing their measurable consequences in experiments. We further discuss information-theoretic implications of the universality: Our ensembles have maximal information content while being maximally difficult to interrogate, establishing that generic quantum state ensembles that occur in nature hide (scramble) information as strongly as possible. Our results generalize the notions of Hilbert-space ergodicity to time-independent Hamiltonian dynamics and deep thermalization from infinite to finite effective temperature. Our work presents new perspectives to characterize and understand universal behaviors of quantum dynamics using statistical and information-theoretic tools. Published by the American Physical Society 2024

Theoretical and experimental study on optical polarization states in overhead optical cables under complex weather conditions such as real lightning

Abstract By analyzing the changes in three Stokes vectors, the trajectory of polarization state on the Poincaré sphere, and the polarization change rate, both theoretical and practical aspects of polarization state variations in signal light within optical fiber composite overhead power ground wires (OPGWs) during real thunderstorm conditions, were examined. Our findings reveal that lightning and mechanical vibrations both impact the polarization state of the signal light in OPGW. Theoretical models demonstrate that lightning induces polarization changes through the Faraday magneto-optic effect and exhibits nonlinear electro-optic effects, leading to a maximum polarization change rate of Mrad s−1. In contrast, mechanical vibrations cause long-term, low-intensity polarization rate changes, with a maximum polarization rate of Krad s−1, highlighting a significant optical birefringence effect. Digital signal processing algorithms for coherent receivers with over 100G polarization multiplexing provide valuable guidance for recovering polarization states.

Multi-omics with dynamic network biomarker algorithm prefigures organ-specific metastasis of lung adenocarcinoma

Efficacious strategies for early detection of lung cancer metastasis are of significance for improving the survival of lung cancer patients. Here we show the marker genes and serum secretome foreshadowing the lung cancer site-specific metastasis through dynamic network biomarker (DNB) algorithm, utilizing two clinical cohorts of four major types of lung cancer distant metastases, with single-cell RNA sequencing (scRNA-seq) of primary lesions and liquid chromatography-mass spectrometry data of sera. Also, we locate the intermediate status of cancer cells, along with its gene signatures, in each metastatic state trajectory that cancer cells at this stage still have no specific organotropism. Furthermore, an integrated neural network model based on the filtered scRNA-seq data is successfully constructed and validated to predict the metastatic state trajectory of cancer cells. Overall, our study provides an insight to locate the pre-metastasis status of lung cancer and primarily examines its clinical application value, contributing to the early detection of lung cancer metastasis in a more feasible and efficacious way.

Reassessing Peace: The Implications of the Abraham Accords for Conflict Resolution in the Gulf Region

Established in 2020, the Abraham accords marked a remarkable step towards the normalisation of relations between Gulf Arab states and Israel. They have been hailed as a potential turning point for peace and regional cooperation. However, the recent Israeli military operations since the end of 2023 raise critical questions about the durability and impact of these accords. This paper proposes an in-depth examination of the implications of the Israel/Gaza war on the Abraham Accords and their dynamics in peace-building. It will explore how the war has potentially reshaped (or not) alliances, influenced public opinion, and altered the strategic calculations of Gulf states, particularly in their approaches to conflict resolution and engagement with external actors. This research aims to contribute to the understanding of the complex interplay between regional conflicts and their broader implications for peace and stability in the Gulf, offering insights into the future trajectory of Gulf states in the realm of conflict resolution and peace-building combined with self-interested dynamics. The comparative analysis will delve into two case studies: the United Arab Emirates, which signed the Abraham Accords, and Qatar, which did not, highlighting how similar conflicts have historically altered political alignments, economic dependencies, and social narratives within the Gulf.

Online Q-learning for stochastic linear systems with state and control dependent noise

For continuous-time (CT) systems that are characterized by stochastic differential equations (SDEs) with completely unknown dynamics parameters, a reinforcement learning (RL)-based optimal control framework is presented in this paper. To obtain the near-optimal control policy, an online Q-learning algorithm is proposed by learning the data sampled from the system state trajectory, while an integral reinforcement learning (IRL) approach is developed in stochastic situation so as to formulate the Q-learning iterative algorithm. In particular, an actor/critic neural network (NN) structure is applied in iteration, where a critic approximator is used for estimating the designed Q-function while an actor approximator is for estimating the optimal control policy online. To ensure the convergence of iteration, the tuning laws of two neural networks are designed, respectively, by a gradient descent scheme. Moreover, the mean-square stability of the closed-loop system is proved through rigorous analysis, and the convergence to optimal solution is guaranteed as well.

Real Estate Market Transformations Amidst Post-Pandemic Sino-U.S. Economic Trends

In the post-pandemic era, the global economic landscape has undergone profound changes. As the world’s largest economies, the economic policies and market performances of the United States and China have exerted far-reaching impacts on the global real estate market. This paper delves into the current state and future trajectory of the real estate market under Sino-U.S. economic trends, focusing on commercial real estate, residential investment, property taxes, financing, and laws and regulations. It also incorporates keywords such as easements, deed transfers, premium discount rates, home mortgages, police powers, liens, common law, fixtures, joint leases, marital property, private property, and trespassing to provide a comprehensive analysis.

Reachable Set Estimation for Singular Discrete‐Time Nonlinear Systems With Time‐Varying Delays

ABSTRACTIn this article, the reachable set estimation problems for a class of singular discrete‐time nonlinear systems (SDNS) with time‐varying delay (TVD) are presented. First, we employ a Lyapunov function scheme and utilize zero‐type free matrix equations. Based on this, a criterion is derived in the form of linear matrix inequalities (LMIs) to guarantee that the considered system to be regular, causal, and the state trajectory of the system is bounded. Second, by developing the singular systems decomposition technique into slow and fast subsystems and using the introduced auxiliary lemma, we establish that the state trajectory of the fast subsystem is also bounded, and the reachable set of singular nonlinear system is bounded within the ellipsoid. Finally, Numerical examples are presented to illustrate the effectiveness of the proposed method.

Asynchronous Sliding Mode Control of Networked Markov Jump Systems via an Asynchronous Observer Approach Based on a Dynamic Event Trigger

This paper explores the utilization of sliding mode control, which relies on an asynchronous observer, for Markov jump systems subject to external disturbances. Firstly, given that the system’s mode is not directly measurable and could potentially differ from the observer’s and controller’s mode, the paper constructs an asynchronous observer employing a hidden Markov model. Secondly, a sliding surface is designed to correspond with the asynchronous observer. Moreover, a multi-parameter event-triggered mechanism is incorporated into the observer design to alleviate bandwidth strain. Thirdly, by applying the integrated sliding mode control law, we ensure that the system state trajectories will reach the sliding surface within a finite time. Fourthly, the achievement of H∞ stability is realized by making use of the Lyapunov function. Lastly, a practical-oriented example is presented to illustrate the efficiency of the established method.

Reconstructing the Ocean State Using Argo Data and a Data-Driven Method

Abstract Over the past two decades, Argo profiles have provided unprecedented insight into the global patterns of space and time variability of ocean temperature and salinity, significantly reducing associated uncertainties. However, analyzing such assessments during the pre-Argo period remains challenging due to the scarcity of observations in many regions. From the Argo period, a set of dominant three-dimensional patterns can be estimated using Empirical Orthogonal Function (EOF) analysis, which helps to fill in observational gaps. From the associated principal components, temporal fluctuations can be observed, aiming to build a catalog of possible ocean state trajectories. To map pre-Argo observations, EOFs are used in a data assimilation framework that uses this catalog to feed an analog prediction and provide reanalysis. In this study, a new data-driven interpolation method called RedAnDA (Reduced-space Analog Data Assimilation) was tested in the tropical Pacific Ocean. RedAnDA was first validated through an Observing System Simulation Experiment (OSSE) approach, using synthetic observations extracted from a model simulation. It was subsequently applied to a real historical dataset and compared with other available reanalysis products. Overall, the reconstructed temperature field showed variability consistent with the OSSE true field and other reanalysis products in the real data application. Further improvements are needed to optimally estimate uncertainty, but RedAnDA already combines valuable information about state predictability, observational sampling, and unresolved scale issues.

Phenol Photostatic Spectra and Quantum‐Classical Photodynamic Deprotonation

ABSTRACTThe spectral‐luminescence properties and photochemical conversions of phenol were analyzed for an isolated molecule as well as in water solvents in a continuum implicit model and explicit atomistic surroundings. This involved employing cut‐edge hybrid quantum‐classical methodologies to generate static optical spectra and the excited dissipative crossing potential energy curves. A combination of electronic excitations, gradient calculations, and embedding electrostatic potential fitting charges on quantum‐classical molecular dynamic propagation trajectories provided statistically averaged absorption spectra. The mixed‐reference spin‐flip multiconfigurational linear response method based on reference triplet preprocessed in the time‐dependent density‐functional theory was utilized to determine conical intersections between the lowest excited and ground states, as well as two‐stage transitions from the second excitation to the ground state. Non‐adiabatic quantum‐classical molecular dynamics defined photodissipative trajectories of excited states, their lifetimes, and crossing points through trajectory surface hopping together with the mixed‐reference spin‐flip and embedding electrostatic potential fitting approaches. Dyson orbitals of the extended Koopmans' theorem were applied to reveal the nature of molecular states at conical intersections and key points on photodynamic trajectories. Potential hydroxyl group cleavage predicted with conical intersections searching turns to “swift” OH deprotonation through |π→⟩ transition along photodynamic propagations in contrast with “long” processes leading to benzene ring deformation with stable OH bond.

Hypoxia sensing in resident cardiac macrophages regulates monocyte fate specification following ischemic heart injury.

Myocardial infarction initiates cardiac remodeling and is central to heart failure pathogenesis. Following myocardial ischemia-reperfusion injury, monocytes enter the heart and differentiate into diverse subpopulations of macrophages. Here we show that deletion of Hif1α, a hypoxia response transcription factor, in resident cardiac macrophages led to increased remodeling and overrepresentation of macrophages expressing arginase 1 (Arg1). Arg1+ macrophages displayed an inflammatory gene signature and may represent an intermediate state of monocyte differentiation. Lineage tracing of Arg1+ macrophages revealed a monocyte differentiation trajectory consisting of multiple transcriptionally distinct states. We further showed that deletion of Hif1α in resident cardiac macrophages resulted in arrested progression through this trajectory and accumulation of an inflammatory intermediate state marked by persistent Arg1 expression. Depletion of the Arg1+ trajectory accelerated cardiac remodeling following ischemic injury. Our findings unveil distinct trajectories of monocyte differentiation and identify hypoxia sensing as an important determinant of monocyte differentiation following myocardial infarction.

Mapping the technological landscape of green smart buildings: A patent analytics of key topics, leading companies, and technology gaps

In this study, we investigate the technological landscape of green smart buildings, using patent data from the European Patent Office (EPO) from 2007 onwards. Latent Dirichlet Allocation identified five key technology topics, with the HVAC system (Topic 4) emerging as particularly promising. Technology life cycle analysis revealed a growth phase for leading companies' patents after the Kyoto Protocol's second commitment period, with a predicted shift towards maturity after the Paris Agreement. Self-Organizing Maps and Social Network Analysis further pinpointed eight vacant technology nodes and 39 high-centrality patents within them, predominantly held by Japanese companies. This research provides valuable insights into the current state and future trajectory of green smart building technologies, facilitating informed decision-making for industry stakeholders and contributing to a more sustainable built environment. The novelty lies in the combined application of topic modeling, technology life cycle analysis, and network analysis to comprehensively explore the green smart building patent landscape, offering a unique perspective on its evolution and potential future directions.

Anxiety and depression in papillary thyroid cancer patients: a longitudinal study.

Researches indicate that patients with papillary thyroid cancer (PTC) are prone to experiencing anxiety and depression. However, lacking of large-scale, prospective studies thoroughly examine the trajectory of these emotional states. Therefore, this study aims to investigate changes in anxiety and depression levels in PTC patients before and after operation and assess the impact of gender and menopausal states on emotional well-being. A prospective longitudinal study enrolled 320 PTC patients who completed the Self-Rating Anxiety Scale (SAS) and Self-Rating Depression Scale (SDS) at pre- and post-operation. Paired-sample T-tests and logistic regression analysis were used to evaluate emotional changes and identify influencing factors. Anxiety and depression levels significantly increased (p = 0.028, p = 0.005) postoperatively, with incidence of 13.8% for anxiety and 26.9% for depression. Multivariate regression analysis showed that gender was a factor affecting depression (p = 0.041), and menopausal state significantly influenced emotions including anxiety and depression (p = 0.004, p = 0.031). Subgroup analysis showed that female patients exhibited higher levels of adverse emotions postoperatively compared to preoperatively (p = 0.003, p < 0.001). Postoperatively, female patients were more susceptible to anxiety and depression (p = 0.011, p = 0.029), and postmenopausal women were particularly at risk for depression (p = 0.017). The study highlights the importance of postoperative psychological care, particularly for female and postmenopausal patients. Larger sample sizes and longer follow-up periods are needed for a comprehensive understanding of psychological changes in PTC survivors.

Optimal impulse control problems with time delays: An illustrative example

For impulse control systems described by a measure driven differential equation, depending linearly on the measure, it is customary to interpret the state trajectory corresponding to an impulse control, specified by a measure, as the limit of state trajectories associated with some sequence of conventional controls approximating the measure. It is known that, when the measure is vector valued, it is possible that different choices of approximating sequences for the measure give rise to different limiting state trajectories. If the measure is scalar valued, however, there is a unique limiting trajectory. Now consider impulse control systems, in which the right side of the measure driven differential equation depends on both the current and delayed states. In recent work by the authors it has been shown that, for such impulse control systems with time delay, the state trajectory corresponding to a given measure may be non-unique, even when the measure is scalar valued. It was also shown that each limiting state trajectory can be identified with the unique state trajectory associated with some measure together with a family of ‘attached controls’. (The attached controls capture the nature of the measure approximation.) The authors also derived a maximum principle governing minimizers for a general class of impulse optimal control problems with time delay, in which the domain of the optimization problem comprises measures coupled with a family of ‘attached controls’. The purpose of this paper is both to illustrate, by means of an example, this newly discovered non-uniqueness phenomenon and to provide the first application of the new maximum principle, to investigate minimizers for scalar input impulse optimal control problems with time delay, in circumstances when limiting state trajectories associated with a given measure control are not unique. The example is an optimal control problem, for which the underlying control system is a forced harmonic oscillator, with scalar impulse control, in which the control gain is a nonlinear function of the current and delayed states.

Loss of the Sturm–Liouville Property of Time-Varying Second-Order Differential Equations in the Presence of Delayed Dynamics

This paper considers a nominal undelayed and time-varying second-order Sturm–Liouville differential equation on a finite time interval which is a nominal version of another perturbed differential equation subject to a delay in its dynamics. The nominal delay-free differential equation is a Sturm–Liouville system in the sense that it is subject to prescribed two-point boundary conditions. However, the perturbed differential system is not a Sturm–Liouville system, in general, due to the presence of delayed dynamics. The main objective of the paper is to investigate the loss of the boundary values of the Sturm–Liouville nominal undelayed system in the presence of the delayed dynamics. Such a delayed dynamics is considered a perturbation of the nominal dynamics related to the Sturm–Liouville system with given two-point boundary values. In particular, this loss of the Sturm–Liouville exact tracking of the prescribed two-point boundary values might happen because the nominal boundary values may become lost by the state trajectory solution in the presence of delays, related to the undelayed case, due to the presence of the delayed dynamics. The worst-case error description of the deviation of the two-point boundary values of the current perturbed differential with respect to those of the nominal Sturm–Liouville system is characterized in terms of error norms related to the nominal system. Under sufficiently small deviations of the parameterization of the perturbed system with respect to the nominal one, such a worst-error characterization makes the current perturbed system an approximate Sturm–Liouville system of the nominal undelayed one.

The Present State and Prospective Trajectory of External Breast Prosthesis (EBP): A Global Overview.

This study intends to examine and describe the current and future status of the utilization of external breast prostheses (EBP) amongst global women diagnosed with breast cancer who have had a mastectomy. To avoid breast reconstruction, many women choose external breast prostheses (EBP) for varied reasons. This study included literature from ScienceDirect and PubMed to select relevant global articles from the year 2011 to the year 2023. The terms "external breast prosthesis breast cancer" were used as a search title for abstracts and keywords to source articles from both databases. Similar and related terms were used concurrently for searches conducted in ScienceDirect and PubMed. For this mixed-method review, qualitative data gave way to an in-depth exploration of the phenomenon, while the presentation of quantitative data demonstrated the tabulation of global publications on EBP. All studies focused on EBP use among post-operative women. A total of 22 journal articles were selected for this review. From the data six (6) themes were identified viz.; patient satisfaction, comfort, quality of life, knowledge about external breast prosthesis, cost, and material. Our findings showed that the literature had fifteen (68%) of the publications on patient satisfaction, sixteen (73 %) on comfort, twenty (91%) on quality of life, and fifteen (67%) on material. From the published literature, there was an observed dearth of information on knowledge and cost with only eleven (50%) and eight (36%) articles respectively, which indicates limited access to pertinent information for both healthcare providers and patients. The results suggest that more research is needed to provide the best quality information and approaches when looking at EBP for female breast cancer care and post-operative rehabilitation.

Improving extensions for the global uniform asymptotic stability of continuous-time nonlinear systems

This paper considers the classical problems of global asymptotic stability (GAS) of nonlinear autonomous (time-invariant) systems and global uniform asymptotic stability (GUAS) of nonlinear non-autonomous (time-varying) systems. By imposing new conditions on the Lyapunov function and its derivative, the state convergence to the origin from any initial condition with bounded norm in the classical setting is extended to the initial conditions with unbounded norms in the present work. The proposed new notions of stability are called extended global asymptotic stability (EGAS) and extended global uniform asymptotic stability (EGUAS) in this paper. The proposed Lyapunov-based criteria yield the global asymptotic stability of the origin and fixed-time/predefined-time attractiveness of any selected neighbourhood of the origin. The result is that the dynamical behaviour of the state trajectories from the convergence time point of view is improved considerably. The relationship between the smoothness and input-to-state stability (ISS) properties is also studied from a quantitative point of view. Under some new sufficient conditions, it is shown that dynamical systems with smaller Lipschitz constants represent smaller ultimate bounds, and as a result, are more robust. The desirable dynamical behaviour and robustness property of the proposed stability notion makes it comparable with the finite/fixed/predefined/prescribed (exact) stable systems that are naturally non-Lipschitz at the origin. Numerical results illustrate the effectiveness of the proposed theoretical results.

Building Digital Twins for Cardiovascular Health: From Principles to Clinical Impact.

The past several decades have seen rapid advances in diagnosis and treatment of cardiovascular diseases and stroke, enabled by technological breakthroughs in imaging, genomics, and physiological monitoring, coupled with therapeutic interventions. We now face the challenge of how to (1) rapidly process large, complex multimodal and multiscale medical measurements; (2) map all available data streams to the trajectories of disease states over the patient's lifetime; and (3) apply this information for optimal clinical interventions and outcomes. Here we review new advances that may address these challenges using digital twin technology to fulfill the promise of personalized cardiovascular medical practice. Rooted in engineering mechanics and manufacturing, the digital twin is a virtual representation engineered to model and simulate its physical counterpart. Recent breakthroughs in scientific computation, artificial intelligence, and sensor technology have enabled rapid bidirectional interactions between the virtual-physical counterparts with measurements of the physical twin that inform and improve its virtual twin, which in turn provide updated virtual projections of disease trajectories and anticipated clinical outcomes. Verification, validation, and uncertainty quantification builds confidence and trust by clinicians and patients in the digital twin and establishes boundaries for the use of simulations in cardiovascular medicine. Mechanistic physiological models form the fundamental building blocks of the personalized digital twin that continuously forecast optimal management of cardiovascular health using individualized data streams. We present exemplars from the existing body of literature pertaining to mechanistic model development for cardiovascular dynamics and summarize existing technical challenges and opportunities pertaining to the foundation of a digital twin.