State Matrices Research Articles

Modeling Nuclear-Centric Scenarios for Ukraine’s Low-Carbon Energy Transition Using Diffusion and Regression Techniques

This study presents a mathematical model for forecasting the development of Ukraine’s Integrated Power System (IPS) until 2040, with a specific focus on the expansion of nuclear energy as a cornerstone of the nation’s low-carbon transition. The model is an extension of Frank Bass’s mixed influence diffusion model, incorporating both economic and technological factors. These factors are treated as stochastic variables essential for accurately predicting the evolution of an integrated energy system, particularly in the context of rapid renewable energy sources (RES) growth. The model employs regression techniques using generalized logistic curves, improving forecasting efficiency by aligning modeling parameters with experimental data. The study’s results indicate the potential for optimizing IPS components, including nuclear and thermal power generation, through the model’s application. The model is distinguished by its inclusion of economic and technological impacts, such as state matrices, control actions, and external influence matrices, which enhance the accuracy of simulations and predictions. The validation of the model, based on scenarios of electricity consumption and generation, shows significant alignment with observed trends, confirming the model’s reliability. The findings suggest that this model is an effective tool for developing and refining energy system scenarios, with nuclear energy playing a pivotal role in Ukraine’s sustainable energy future.

Deep reinforcement learning for solving car resequencing with selectivity banks in automotive assembly shops

In the automobile manufacturing process, the complexity of the production environment and the different objectives of the upstream and downstream shops necessitate the resequencing of the car sequences using buffers. This paper addresses a car resequencing problem in automotive assembly shops by utilising selectivity banks to reshuffle the given upstream sequences to minimise the number of violations of sequencing rules in the downstream sequence. A new resequencing approach combining heuristics and deep reinforcement learning is proposed to solve the problem. Heuristics solve the automobile storage problem, while a deep reinforcement learning method based on proximal policy optimisation addresses the automobile release problem. Three state matrices, agent actions, and the reward function are designed based on the characteristics of the objective and selectivity banks. Additionally, a novel network structure combining convolutional neural networks and long short-term memory networks is proposed to train the agent. The results demonstrate that the proposed method outperforms two efficient deep reinforcement learning algorithms and two heuristics and obtains better solutions in handling dynamic events.

A second-order structure-preserving discretization for the Cahn-Hilliard/Allen-Cahn system with cross-kinetic coupling

We study the numerical solution of a Cahn-Hilliard/Allen-Cahn system with strong coupling through state and gradient dependent non-diagonal mobility matrices. A fully discrete approximation scheme in space and time is proposed which preserves the underlying gradient flow structure and leads to dissipation of the free-energy on the discrete level. Existence and uniqueness of the discrete solution is established and relative energy estimates are used to prove optimal convergence rates in space and time under minimal smoothness assumptions. Numerical tests are presented for illustration of the theoretical results and to demonstrate the viability of the proposed methods.

Quantum state reconstruction in a noisy environment via deep learning

Quantum noise is currently limiting efficient quantum information processing and computation, impacting on the fidelity and reliability of quantum states. In this work, we consider the tasks of reconstructing and classifying quantum states corrupted by the action of an unknown noisy channel using classical feed-forward neural networks. By framing reconstruction as a regression problem, we show how such an approach can be used to recover with fidelities exceeding 99% the noiseless density matrices of quantum states of up to three qubits undergoing noisy evolution, and we test its performance with both single-qubit (bit-flip, phase-flip, depolarizing, and amplitude damping) and two-qubit quantum channels (correlated amplitude damping). Furthermore, a critical aspect of our investigation involves also a comprehensive comparison between mean squared error and infidelity as loss functions. Our findings reveal that these two metrics yield comparable results in the context of state reconstruction. Moreover, we also consider the task of distinguishing between different quantum noisy channels, and show how a neural network-based classifier is able to solve such a classification problem with perfect accuracy.

Excitonic Configuration Interaction: Going Beyond the Frenkel Exciton Model.

We present the excitonic configuration interaction (ECI) method─a fragment-based analogue of the CI method for electronic structure calculations of multichromophoric systems. It can also be viewed as a generalization of the exciton approach, with the following properties: (i) It constructs the effective Hamiltonian exclusively from monomer calculations. (ii) It employs the strong orthogonality assumption and is exact within McWeeny's group function theory, thus requiring only one-electron density matrices of the monomer states. (iii) It is agnostic of the monomer electronic structure method, allowing us to use/combine different methods. (iv) It includes an embedding point charge scheme (called excitonic Hartree-Fock, EHF) to improve the accuracy of the monomer states, but such that the effective full-system Hamiltonian is not explicitly dependent on the embedding. (v) It is systematically improvable, by expanding the set of monomer states and by including configurations where two or more monomers are excited (defining the ECIS, ECISD, etc., methods). The performance of ECI is assessed by computing the absorption spectrum of two exemplary multichromophoric systems, using CIS as the monomer electronic structure method. The accuracy of ECI significantly depends on the chosen embedding charges and the ECI expansion. The most accurate assessed combinations─ECIS or ECISD with EHF embedding─yield spectra that agree qualitatively and quantitatively with full-system direct calculations, with deviations of the excitation energies below 0.1 eV. We also show that ECISD based on CIS monomer calculations can predict states where two monomers are excited simultaneously (e.g., triplet-triplet double-local excitations) that are inaccessible in a full-system CIS calculation.

Uncertainty disturbance estimator control for delayed linear systems with input constraint

This paper proposes a novel Uncertainty and Disturbance Estimator (UDE) based controller for Multi-Input Multi-Output (MIMO) systems. The controller handles input constraints, time-varying matched uncertainties in state and input matrices, unknown input–output delays, and partial state measurement. The UDE error dynamics are augmented with a time-varying variable to handle input constraints effectively. The proposed controller employs a Proportional Integral Observer (PIO) and a state predictor to accurately estimate the future state of the system with only partial state measurement. We develop sufficient conditions for system stability in tracking a reference model while only an estimation of the total delay is available. Numerical simulations and experiments on a multi-rotor platform validate the proposed controller’s effectiveness, demonstrating improved tracking performance and stability compared to existing methods. The proposed UDE-based controller, with a PIO and state predictor, is capable of handling various matched uncertainties and disturbances in MIMO systems with input constraints and partial state measurement. It offers improved tracking performance and stability compared to existing studies.

Private and utility enhanced intrusion detection based on attack behavior analysis with local differential privacy on IoV

In recent years, with the escalating security demands of the Internet of Vehicles (IoV), concerns over safety have intensified. To prevent security incidents and privacy breaches, IoV must address various threats promptly and effectively. The use of deep learning methods for intrusion detection in IoV has garnered widespread attention. Compared to traditional security defenses, deep learning can learn from heterogeneous data sources, enhancing the accuracy of detecting various security threats. However, current research based on deep learning primarily focuses on constructing intrusion detection models and overlooks the analysis and processing of extensive behavioral data. Moreover, model training requires access to and transmission of sensitive data, which may lead to high communication costs and potential privacy leaks. To ensure the network security of IoV, we propose FDL-IDM, an innovative behavior-analysis-based intrusion detection model leveraging differential privacy within federated learning. It extracts driving behavior spatiotemporally and employs noise perturbation pre-aggregation, reducing communication costs and ensuring privacy without compromising accuracy. Specifically, we process data from both temporal and spatial dimensions. Data are grouped based on sender identity and then sliced according to the time sequence to create state matrices that vary over time, enhancing the performance and robustness of the detection model. Next, we incorporate an attention mechanism to merge outputs from each time step and hidden layer, strengthening the time series model and reducing information loss. Lastly, in federated learning, we add noise perturbation to the uploaded parameters, reducing the risk of privacy breaches. Additionally, we employ a random scheduling strategy during training to select clients and assign an adjusted learning rate that decreases with iterations, enhancing the stability of model training. Therefore, FDL-IDM helps prevent security attacks and protect IoV privacy. Through experiments and privacy analysis, as well as tests on vehicle-level devices, FDL-IDM achieved F1-scores of 0.9751, 0.9851, and 0.9789 on three public datasets, demonstrating not only high accuracy but also robust privacy protection capabilities.

Aerodynamic modeling and performance analysis of model predictive controller for fixed wing vertical takeoff and landing unmanned aerial vehicle

This research focuses mainly on the aerodynamic modelling and performance analysis of a model predictive controller for a hybrid fixed-wing vertical takeoff and landing of unmanned aerial vehicle. The aerodynamics, which comprises several aerodynamic characteristics including the lift, drag, and thrust coefficients, is modelled using Newton’s second law of motion. The force and moment equations were obtained, and they were then converted into matrix and state equation form, together with the transformation matrices. The essential equations with six degrees of freedom (6 DoF) and 12 state matrices including the control input and manipulating variables were obtained. The proposed model predictive controller (MPC) was designed using the optimal model predictive controller design parameters, such as a sampling time of 0.1, a prediction horizon of 15, a control horizon of 3 and additional controller settings. With a settling period of 3 s, an overshoot of 0.5865, and a steady state inaccuracy of 0.00785, the MATLAB simulation demonstrates that the system variables, including roll, pitch, and yaw, are stabilized. This MPC control is more effective in anticipating and optimizing the UAV than other control strategies. Eventually, the controller’s simulation on MATLAB Simulink demonstrates the controller’s ability to stabilize and control the system in a real-time application. Autonomous vertical takeoff and landing operations depend heavily on the mathematical model and architecture of the flight controller. Among the uses are inspection, monitoring, and rescue.

Quantum knot mosaics and bounds of the growth constant

The discovery of the Jones polynomial made an important connection between quantum physics and knot theory. Kauffman and Lomonaco introduced the knot mosaic system to define the quantum knot system for the purpose of representing an actual physical quantum system. This paper is inspired by an open question about the knot mosaic enumeration suggested by them. A knot [Formula: see text]-mosaic is an [Formula: see text] array of 11 mosaic tiles representing a knot diagram by adjoining properly. The total number [Formula: see text] of knot [Formula: see text]-mosaics, which indicates the dimension of the Hilbert space of the quantum knot system, is known to grow in a quadratic exponential rate. Recently, Oh et al. developed the state matrix recursion method producing the exact enumeration of knot mosaics, which uses a recursion formula of state matrices. Furthermore, they showed the existence of the knot mosaic constant [Formula: see text] and found its upper and lower bounds in a series of papers. The latest upper bound was obtained through two new concepts: quasimosaics and cling mosaics. As a sequel to this research program, we adjust the state matrix recursion method to handle cling mosaics inside a quasimosaic, which is called the progressive state matrix recursion method. This method provides recursive matrix-relations producing a sharper bound of the knot mosaic constant: [Formula: see text]

Learning quantum many-body systems from a few copies

Estimating physical properties of quantum states from measurements is one of the most fundamental tasks in quantum science. In this work, we identify conditions on states under which it is possible to infer the expectation values of all quasi-local observables of a state from a number of copies that scales polylogarithmically with the system's size and polynomially on the locality of the target observables. We show that this constitutes a provable exponential improvement in the number of copies over state-of-the-art tomography protocols. We achieve our results by combining the maximum entropy method with tools from the emerging fields of classical shadows and quantum optimal transport. The latter allows us to fine-tune the error made in estimating the expectation value of an observable in terms of how local it is and how well we approximate the expectation value of a fixed set of few-body observables. We conjecture that our condition holds for all states exhibiting some form of decay of correlations and establish it for several subsets thereof. These include widely studied classes of states such as one-dimensional thermal and high-temperature Gibbs states of local commuting Hamiltonians on arbitrary hypergraphs or outputs of shallow circuits. Moreover, we show improvements of the maximum entropy method beyond the sample complexity that are of independent interest. These include identifying regimes in which it is possible to perform the postprocessing efficiently as well as novel bounds on the condition number of covariance matrices of many-body states.

Emergent behaviours of a non-abelian quantum synchronisation model over the unitary group

Abstract We introduce a new non-abelian quantum synchronisation model over the unitary group, represented as a gradient flow, where state matrices asymptotically converge to a common one up to phase translation. We provide a sufficient framework leading to quantum synchronisation based on Riccati-type differential inequalities. In addition, uniform time-delayed interaction is considered for modelling realistic communication, and we demonstrate that quantum synchronisation is persistent when a small time delay is allowed. Finally, numerical simulation is performed to visualise qualitative behaviours and support theoretical results.

An automata theoretic approach to observer design for switched linear systems

We present an approach for designing asymptotic observers for discrete-time switched linear systems. We first give an automata theoretic characterization of switching signals containing an infinite number of reconstructible sequences, i.e. sequences allowing to estimate the state of the system. We show that such switching signals can be generated by a deterministic Büchi automaton whose construction is given in the paper. Then, we present a methodology to design switched observers. These observers have an internal discrete state variable whose dynamics is given by the transition map of the Büchi automaton. We then present two approaches to design observer gains such that the observer is convergent for all switching signals whose occurrence rate of reconstructible sequences is higher than a tunable threshold. The first approach gives an explicit construction of the observer gains while the second one is based on linear matrix inequalities. For switched systems with invertible state matrices, we show that the proposed observer structure is universal in the sense that it is always possible to design an observer of the proposed form. We use a simple example to illustrate our methodology and then consider a case study in which we design an observer for a multicellular converter.

Finite-Time Time-Varying Formation Tracking for Heterogeneous Nonlinear Multiagent Systems Using Adaptive Output Regulation.

The finite-time output time-varying formation tracking (TVFT) problem for heterogeneous nonlinear multiagent system (MAS) is investigated in this article, where the dynamics of the agents can be nonidentical, and leader's input is unknown. The target of this article is that the outputs of followers need to track leader's output and realize the desired formation in finite time. First, for removing the assumption that all agents are required to know the information of leader's system matrices and the upper boundary of its unknown control input in previous studies, a kind of finite-time observer is constructed by exploiting the neighboring information, which can estimate not only the leader's state and system matrices but also can compensate for the effects of unknown input. On the basis of the developed finite-time observers and adaptive output regulation method, a novel finite-time distributed output TVFT controller is proposed with the help of the technique of coordinate transformation by introducing an extra variable, which removes the assumption that the generalized inverse matrix of follows' input matrix needs to be found in the existing results. By means of the Lyapunov and finite-time stability theory, it is proven that the expected finite-time output TVFT can be realized by the considered heterogeneous nonlinear MASs within a finite time. Finally, simulation results demonstrate the efficacy of the proposed approach.

Robustly exponentially almost sure stabilization of uncertain discrete‐time composite switched systems

AbstractThis paper is concerned with the robustly exponentially almost sure (EAS) stabilization of uncertain discrete‐time composite switched systems (CSSs), in which the dominant signal subjects to a semi‐Markov chain, while the subordinate signals follow a family of different Markov chains. Norm‐bounded uncertainties impacting the state and input matrices of the system are taken into account. Utilizing numerical computation methods, bounds on the transient statistical properties of Markov chain are provided. Based on this, sufficient conditions for robustly EAS stabilization are established by combining an estimate of the sojourn time for modes in a semi‐Markov chain. Our result is the discrete counterpart of prior work concerning continuous‐time dual‐switching systems. Two examples are provided to validate the effectiveness of developed results.

Exploring Brain Dynamics via EEG and Steady-State Activation Map Networks in Music Composition.

In recent years, the integration of brain-computer interface technology and neural networks in the field of music generation has garnered widespread attention. These studies aimed to extract individual-specific emotional and state information from electroencephalogram (EEG) signals to generate unique musical compositions. While existing research has focused primarily on brain regions associated with emotions, this study extends this research to brain regions related to musical composition. To this end, a novel neural network model incorporating attention mechanisms and steady-state activation mapping (SSAM) was proposed. In this model, the self-attention module enhances task-related information in the current state matrix, while the extended attention module captures the importance of state matrices over different time frames. Additionally, a convolutional neural network layer is used to capture spatial information. Finally, the ECA module integrates the frequency information learned by the model in each of the four frequency bands, mapping these by learning their complementary frequency information into the final attention representation. Evaluations conducted on a dataset specifically constructed for this study revealed that the model surpassed representative models in the emotion recognition field, with recognition rate improvements of 1.47% and 3.83% for two different music states. Analysis of the attention matrix indicates that the left frontal lobe and occipital lobe are the most critical brain regions in distinguishing between 'recall and creation' states, while FP1, FPZ, O1, OZ, and O2 are the electrodes most related to this state. In our study of the correlations and significances between these areas and other electrodes, we found that individuals with musical training exhibit more extensive functional connectivity across multiple brain regions. This discovery not only deepens our understanding of how musical training can enhance the brain's ability to work in coordination but also provides crucial guidance for the advancement of brain-computer music generation technologies, particularly in the selection of key brain areas and electrode configurations. We hope our research can guide the work of EEG-based music generation to create better and more personalized music.

Impact of fast charging station for electric vehicles with grid integration: Forensic‐based investigation and Archimedes optimization algorithm approach

AbstractThis manuscript proposes a novel technique for the precise model of electric vehicles (EVs) in the reliability and adequacy model of smart grids (SG). The proposed method combines forensic‐based investigation (FBI) and Archimedes optimization algorithm (AOA), named the FBIAOA technique. The objective of the proposed method is to rise the profit of fast charging stations and lessen the rising energy demand on the grid that is made up of storage systems and renewable energy generation (wind and PV). The demand for EVs and renewable generation is calculated using the FBI algorithm method. The growth of the proposed method is to examine the reliability of SG depending on the aggregation of the state matrices of EV stochastic parameters. The proposed method can help accelerate the reliability calculations by determining the desired count of EV states. The proposed strategy is run in MATLAB and is evaluated in its performance with existing methods. The proposed method gives a lower cost than the existing genetic algorithm, cuttlefish algorithm, and tunicate swarm algorithm methods.

Optimal remote restoring of quantum states in communication lines via local magnetic field

Optimal state transport across spin chains, which are proposed as quantum wires for information transfer in solid state quantum architectures, is an important topic for quantum technologies. In this work, we study the remote restoring of a quantum state transferred along a spin chain. The structural state-restoring technique provides proportionality between the appropriate elements of the density matrices of the initial sender state and receiver state at some time instant. We develop a remote state-restoring protocol which uses an inhomogeneous magnetic field with step-wise time-dependent Larmor frequencies as the state-control tool. For simulating the multiparametric Hamiltonian we use two approximating models. First model is based on the Trotter-Suzuki method, while the second model is based on using short pulses of high intensity. In both cases we estimate the accuracy of the approximation and find the optimal restoring parameters (Larmor frequencies) of the protocol which maximize the coefficients in the proportionality for spin chains of various lengths.

Zero-Norm Distance to Controllability of Linear Dynamic Networks.

In this article, we consider the "nearest distance" from a given uncontrollable dynamical network to the set of controllable ones. We consider networks whose behaviors are represented via linear dynamical systems. The problem of interest is then finding the smallest number of entries/parameters in the system matrices, corresponding to the smallest number of edges of the networks, that need to be perturbed to achieve controllability. Such a value is called the zero-norm distance to controllability (ZNDC). We show genericity exists in this problem, so that other matrix norms (such as the 2 -norm or the Frobenius norm) adopted in this notion are nonsense. For ZNDC, we show it is NP-hard to compute, even when only the state matrices can be perturbed. We then provide some nontrivial lower and upper bounds for it. For its computation, we provide two heuristic algorithms. The first one is by transforming the ZNDC into a problem of structural controllability of linearly parameterized systems, and then greedily selecting the candidate links according to a suitable objective function. The second one is based on the weighted l1 -norm relaxation and the convex-concave procedure, which is tailored for ZNDC when additional structural constraints are involved in the perturbed parameters. Finally, we examine the performance of our proposed algorithms on several typical uncontrollable networks arising in multiagent systems.

On existence, uniqueness and stability of solutions to Cahn–Hilliard/Allen–Cahn systems with cross-kinetic coupling

A system of phase-field equations with strong-coupling through state and gradient dependent non-diagonal mobility matrices is studied. Existence of weak solutions is established by the Galerkin approximation and a-priori estimates in strong norms. Relative energy estimates are used to derive a general nonlinear stability estimate. As a consequence, a weak–strong uniqueness principle is obtained and stability with respect to model parameters is investigated.

Pisot-Number-Based Discrete-Time Controllers With Integer State Matrices to Ensure Monotonic Closed-Loop Step Responses

Pisot-Number-Based Discrete-Time Controllers With Integer State Matrices to Ensure Monotonic Closed-Loop Step Responses