State Space Research Articles

The structure and symmetry of modular state space for complex quantum systems.

Understanding the state space structure of complex quantum systems can help to effectively characterize the system properties and explore underlying mechanisms. The structure of the state space could be quite complicated for quantum many-body systems, and the systematic decomposition of the state space is normally involved. Recently, a modular tensor diagram approach was proposed to reorganize the state space hierarchically based on a modular basis. Here, we review the construction of spin eigenfunctions for multiple exciton systems and further develop modular tensor diagrams to exemplify the hierarchical symmetry of the state space. The newly constructed spin eigenfunctions for quadruple excitons, along with the results for triple excitons, are used to demonstrate the effective decomposition of the state space into hierarchical tensorial structures. A universal recursive relation is derived to determine the coefficients of spin eigenfunctions exhibiting transformation symmetry between different classes of elementary modules for an arbitrary number of exciton units. Interestingly, different coupling schemes mapped to quantum many-body interactions lead to different spin adapted basis states, which may correspond to different realistic systems upon the breakdown of spin degeneracy. This work highlights the hierarchical symmetry of the tensorial structure of quantum many-body systems, which may facilitate a better understanding of the structure property relationship toward the object-oriented materials design.

Diffusion Model-Based Path Follower for a Salamander-Like Robot.

Salamander-like robots, renowned for their versatile locomotion, present unique challenges in the development of effective path-following controllers due to their distinctive movement patterns and complex body structures. Conventional path-following controllers, while effective for various bionic robots, struggle with the intricate modeling for salamander-like robots and often require laborious manual tuning. Conversely, learning-based methods offer promising alternatives but face issues such as reliance on environmental interactions, short-sighted prediction, and irrational design of state space and reward function. To overcome these limitations, this article proposes a diffusion model-based hierarchical control framework that treats path tracking as a sequence generation problem. The diffusion model's capability to model joint distributions of state, action, and reward sequences enables it to outperform other learning-based approaches in efficient data utilization, stable training, and long-horizon dependency modeling. Our framework integrates a high-level policy driven by guided diffusion with a low-level controller for parsing commands into executable movements via inverse kinematics, reducing the action space and improving learning efficiency. In addition, we design a more reasonable state space and reward function tailored to the path-following task, addressing shortcomings in prior learning-based controllers. Furthermore, we optimize the diffusion model (DM) by developing lightweight network architectures and incorporating advanced attention mechanisms, to ensure its practical deployment on physical robots with limited computational resources, without compromising performance. Extensive simulations and real-world experiments demonstrate the framework's effectiveness, efficiency, and robustness in diverse path-following tasks for salamander-like robots, marking a significant advancement in the control of biomimetic robots.

A State Space Model for Multiobject Full 3-D Information Estimation From RGB-D Images.

Visual understanding of 3-D objects is essential for robotic manipulation, autonomous navigation, and augmented reality. However, existing methods struggle to perform this task efficiently and accurately in an end-to-end manner. We propose a single-shot method based on the state space model (SSM) to predict the full 3-D information (pose, size, shape) of multiple 3-D objects from a single RGB-D image in an end-to-end manner. Our method first encodes long-range semantic information from RGB and depth images separately and then combines them into an integrated latent representation that is processed by a modified SSM to infer the full 3-D information in two separate task heads within a unified model. A heatmap/detection head predicts object centers, and a 3-D information head predicts a matrix detailing the pose, size and latent code of shape for each detected object. We also propose a shape autoencoder based on the SSM, which learns canonical shape codes derived from a large database of 3-D point cloud shapes. The end-to-end framework, modified SSM block and SSM-based shape autoencoder form major contributions of this work. Our design includes different scan strategies tailored to different input data representations, such as RGB-D images and point clouds. Extensive evaluations on the REAL275, CAMERA25, and Wild6D datasets show that our method achieves state-of-the-art performance. On the large-scale Wild6D dataset, our model significantly outperforms the nearest competitor, achieving 2.6% and 5.1% improvements on the IOU-50 and 5∘10 cm metrics, respectively.

Discrete-Time Dynamical Systems on Structured State Spaces: State-Transition Laws in Finite-Dimensional Lie Algebras

Discrete-Time Dynamical Systems on Structured State Spaces: State-Transition Laws in Finite-Dimensional Lie Algebras

An enhanced visual state space model for myocardial pathology segmentation in multi-sequence cardiac MRI.

Myocardial pathology (scar and edema) segmentation plays a crucial role in the diagnosis, treatment, and prognosis of myocardial infarction (MI). However, the current mainstream models for myocardial pathology segmentation have the following limitations when faced with cardiac magnetic resonance(CMR) images with multiple objects and large changes in object scale: the remote modeling ability of convolutional neural networks is insufficient, and the computational complexity of transformers is high, which makes myocardial pathology segmentationchallenging. This study aims to develop a novel model to address the image characteristics and algorithmic challenges faced in the myocardial pathology segmentation task and improve the accuracy and efficiency of myocardial pathologysegmentation. We developed a novel visual state space (VSS)-based deep neural network, MPS-Mamba. In order to accurately and adequately extract CMR image features, the encoder employs a dual-branch structure to extract global and local features of the image. Among them, the VSS branch overcomes the limitations of the current mainstream models for myocardial pathology segmentation by modeling remote relationships through linear computability, while the convolutional-based branch provides complementary local information. Given the unique properties of the dual branches, we design a modular dual-branch fusion module for fusing dual branches to enhance the feature representation of the dual encoder. To improve the ability to model objects of different scales in cardiac magnetic resonance (CMR) images, a multi-scale feature fusion (MSF) module is designed to achieve effective integration and fine expression of multi-scale information. To further incorporate anatomical knowledge to optimize segmentation results, a decoder with three decoding branches is designed to output segmentation results of scar, edema, and myocardium, respectively. In addition, multiple sets of constraint functions are used to not only improve the segmentation accuracy of myocardial pathology but also effectively model the spatial position relationship between myocardium, scar, andedema. The proposed method was comprehensively evaluated on the MyoPS 2020 dataset, and the results showed that MPS-Mamba achieved an average Dice score of 0.717 0.169 in myocardial scar segmentation, which is superior to the current mainstream methods. In addition, MPS-Mamba also performed well in the edema segmentation task, with an average Dice score of 0.735 0.073. The experimental results further demonstrate the effectiveness of MPS-Mamba in segmenting myocardial pathologies in multi-sequence CMR images, verifying its advantages in myocardial pathology segmentationtasks. Given the effectiveness and superiority of MPS-Mamba, this method is expected to become a potential myocardial pathology segmentation tool that can effectively assist clinical diagnosis.

High-accuracy tracking control for uncertain robot manipulators: a sparse online Gaussian process approach

Purpose This paper aims to develop a novel model-free controller for uncertain robot manipulators that achieves high-accuracy tracking performance with adaptive feedback gains. Design/methodology/approach This study uses sparse online Gaussian processes (SOGP) to model unknown robot dynamics and design the motion tracking controller. SOGP facilitates online updates using a sensor data stream. The authors integrate SOGP into a robust sliding mode controller for trajectory tracking and design adaptive feedback gains proportional to the predicted variance from SOGP, balancing response speed and robustness. Findings Simulation results for a 2-degree of freedom robot manipulator indicate that the proposed SOGP-based controller outperforms GP, radial basis function neural network and PD controllers, particularly in unexplored regions of the state space. Furthermore, the proposed method maintains tracking accuracy under external perturbations, such as payload changes and disturbances. Originality/value SOGP facilitates online adaptation and enhances tracking in unexplored regions compared to offline-trained GP models. Adaptive feedback gains, based on SOGP confidence, balance response speed and robustness. The method demonstrates effectiveness through practical simulations involving payload changes and disturbances.

Intelligent Robot in Unknown Environments: Walk Path Using Q-Learning and Deep Q-Learning

Autonomous navigation is essential for mobile robots to efficiently operate in complex environments. This study investigates Q-learning and Deep Q-learning to improve navigation performance. The research examines their effectiveness in complex maze configurations, focusing on how the epsilon-greedy strategy influences the agent’s ability to reach its goal in minimal time using Q-learning. A distinctive aspect of this work is the adaptive tuning of hyperparameters, where alpha and gamma values are dynamically adjusted throughout training. This eliminates the need for manually fixed parameters and enables the learning algorithm to automatically determine optimal values, ensuring adaptability to diverse environments rather than being constrained to specific cases. By integrating neural networks, Deep Q-learning enhances decision-making in complex navigation tasks. Simulations carried out in MATLAB environments validate the proposed approach, illustrating its effectiveness in resource-constrained systems while preserving robust and efficient decision-making. Experimental results demonstrate that adaptive hyperparameter tuning significantly improves learning efficiency, leading to faster convergence and reduced navigation time. Additionally, Deep Q-learning exhibits superior performance in complex environments, showcasing enhanced decision-making capabilities in high-dimensional state spaces. These findings highlight the advantages of reinforcement learning-based navigation and emphasize how adaptive exploration strategies and dynamic parameter adjustments enhance performance across diverse scenarios.

Finite-Time Stabilizers for Large-Scale Stochastic Boolean Networks.

This article presents a distributed pinning control strategy aimed at achieving global stabilization of Markovian jump Boolean control networks. The strategy relies on network matrix information to choose controlled nodes and adopts the algebraic state space representation approach for designing pinning controllers. Initially, a sufficient criterion is established to verify the global stability of a given Markovian jump Boolean network (MJBN) with probability one at a specific state within finite time. To stabilize an unstable MJBN at a predetermined state, the selection of pinned nodes involves removing the minimal number of entries, ensuring that the network matrix transforms into a strictly lower (or upper) triangular form. For each pinned node, two types of state feedback controllers are developed: 1) mode-dependent and 2) mode-independent, with a focus on designing a minimally updating controller. The choice of controller type is determined by the feasibility condition of the mode-dependent pinning controller, which is articulated through the solvability of matrix equations. Finally, the theoretical results are illustrated by studying the T cell large granular lymphocyte survival signaling network consisting of 54 genes and 6 stimuli.

VSS-SpatioNet: a multi-scale feature fusion network for multimodal image integrations

Infrared and visible image fusion (vis-ir) enhances diagnostic accuracy in medical imaging and biological analysis. Existing CNN-based and Transformer-based methods face computational inefficiencies in modeling global dependencies. The author proposes VSS-SpatioNet, a lightweight architecture that replaces self-attention in Transformers with a Visual State Space (VSS) module for efficient dependency modeling. The framework employs an asymmetric encoder-decoder with a multi-scale autoencoder and a novel VSS-Spatial (VS) fusion block for local-global feature integration. Evaluations on TNO, Harvard Medical, and RoadScene datasets demonstrate superior performance. On TNO, VSS-SpatioNet achieves state-of-the-art Entropy (En = 7.0058) and Mutual Information (MI = 14.0116), outperforming 12 benchmark methods. For RoadScene, it attains gradient-based fusion performance (=0.5712), Piella’s metric (=0.7926), and average gradient (AG = 5.2994), surpassing prior works. On Harvard Medical, the VS strategy improves Mean Gradient by 18.7% (0.0224 vs. 0.0198) against FusionGAN, validating enhanced feature preservation. Results confirm the framework’s efficacy in medical applications, particularly precise tissue characterization.

Evolutionary Dynamics of Signals with Type-specific Payoff Increments

Abstract This paper studies the replicator dynamics and the best-response dynamics of a signaling game with type-specific preferences over signals—a generalization of the beer-quiche game (Cho and Kreps in Q J Econ 102(2):179–221, 1987). When the prior probability of the high type is below the critical value at which player 2 is indifferent between accepting and not accepting, there is a unique, partially revealing equilibrium with partial pooling in the signal that the high type prefers. Under the replicator dynamics, this equilibrium is (Lyapunov) stable but not asymptotically stable. It is surrounded by periodic orbits each of which attracting a three-dimensional stable manifold from the interior of the state space. When the prior probability of the high type is above the critical value (the case usually considered), there are two equilibrium outcomes, each with pooling in one of the two signals. Under the replicator dynamics, the equilibrium outcome with pooling in the signal that the high type prefers is stable but not asymptotically stable. The equilibrium outcome with pooling in the signal that the low type prefers is unstable. Still, both components have basins of attraction with nonempty interior. The proofs use center manifold theory and chain recurrence. Throughout, results of the dynamic analysis are compared to equilibrium selection based on the intuitive criterion and index theory.

Koopman-Based Model Predictive Control of Functional Electrical Stimulation for Ankle Dorsiflexion and Plantarflexion Assistance.

Functional Electrical Stimulation (FES) can be an effective tool to augment paretic muscle function and restore normal ankle function. Our approach incorporates a real-time, data-driven Model Predictive Control (MPC) scheme built upon a Koopman operator theory (KOT) framework. This framework adeptly captures the complex nonlinear dynamics of ankle motion in a linearized form, enabling the application of linear control approaches for highly nonlinear FES-actuated dynamics. Our method accurately predicts the FES-induced ankle movements, accounting for nonlinear muscle actuation dynamics, including the muscle activation for both plantarflexors and dorsiflexors (Tibialis Anterior (TA)). The linear prediction model derived through KOT allowed the formulation of the MPC problem with linear state space dynamics, enhancing the FES-driven controls real-time feasibility, precision, and adaptability. We demonstrate the effectiveness and applicability of our approach through comprehensive simulations and experimental trials, including three participants with no disability and a participant with Multiple Sclerosis. Our findings highlight the potential of a KOT-based MPC approach for FES-based gait assistance that offers effective and personalized assistance for individuals with gait impairment conditions.

Boundary-enhanced local-global collaborative network for medical image segmentation

Medical imaging plays a vital role as an auxiliary tool in clinical diagnosis and treatment, with segmentation serving as a crucial foundational process in medical image analysis. Nonetheless, challenges such as class imbalance and indistinct boundaries of regions of interest (ROIs) often complicate medical image segmentation. Constructing a network capable of precisely locating small ROIs and achieving precise segmentation is a significant task. In this paper, we propose a boundary information-enhanced local-global collaborative network. This network leverages the local feature extraction capabilities of CNNs, the global feature recognition prowess of state space models exemplified by Mamba, and boundary feature enhancement to learn a more comprehensive representation. Specifically, we propose a local-global collaborative encoder via attention fusion. This encoder adeptly integrates local and global features through a deep attention fusion module to address the challenge of segmenting small ROIs in class-imbalanced scenarios. Subsequently, we develop a boundary information-enhanced decoder. Through the incremental implementation of boundary attention modules, this decoder emphasizes boundary features during image restoration, steering the network to achieve more complete segmentation. Extensive experiments on various public class-imbalanced medical image segmentation datasets demonstrate that the proposed BELGNet outperforms state-of-the-art methods.

Verifier's Dilemma in Proof-of-Work Public Blockchains: A Quantitative Analysis

A blockchain is an immutable ledger driven by a distributed consensus protocol. In public blockchains, such as Bitcoin and Ethereum Classic, consensus is established through a computational effort called Proof-of-Work (PoW). Special users called miners contribute to the PoW in exchange for a fee and also verify the data stored in blocks mined by the other miners. Here is where the Verifier’s Dilemma emerges. Verification of blocks does not receive a reward, and to maximise their profits, miners may be incentivised to forego verifying blocks and to only invest their resources in PoW. In this paper, we study the Verifier’s Dilemma and a possible countermeasure consisting in the injection of invalid blocks using a quantitative model based on a Markovian process algebra. To avoid the state space explosion problem, we study the underlying Markov chain by using a lumping that allows us to derive closed-form solutions for interesting performance indices. The analysis demonstrates the circumstances under which non-verifying miners gain fees higher than those of verifying miners. The model also allows us to derive the optimal rate at which invalid blocks must be injected, so that skipping the verifying phase becomes economically disadvantageous while the throughput of the blockchain is only minimally reduced. The impact on miners’ rewards and overall performance is also assessed.

Quasi-Stationary Distributions of Non-Absorbing Markov Chains

We consider reversible ergodic Markov chains with finite state space, and we introduce a new notion of quasi-stationary distribution that does not require the presence of any absorbing state. In our setting, the hitting time of the absorbing set is replaced by an optimal strong stationary time, representing the “hitting time of the stationary distribution”. On the one hand, we show that our notion of quasi-stationary distribution corresponds to the natural generalization of the Yaglom limit. On the other hand, similarly to the classical quasi-stationary distribution, we show that it can be written in terms of the eigenvectors of the underlying Markov kernel, and it is therefore amenable of a geometric interpretation. Moreover, we recover the usual exponential behavior that characterizes quasi-stationary distributions and metastable systems. We also provide some toy examples, which show that the phenomenology is richer compared to the absorbing case. Finally, we present some counterexamples, showing that the assumption on the reversibility cannot be weakened in general.

Developing a seasonal-adjusted machine-learning-based hybrid time‑series model to forecast heatwave warning

Heatwaves pose a significant threat to environmental sustainability and public health, particularly in vulnerable regions and rapidly growing cities. They cause water shortages, stress on plants, and an overall drying out of landscapes, reducing plant growth—the basis of energy production and the food chain. Accurate heatwave forecasting is crucial for early warning systems, public health interventions, and disaster preparedness strategies, reducing heat-related mortality risk through modeling and evaluation of warnings. However, anticipating heatwave warnings requires handling the daily time series data, which is a large-scale and high-frequency time series data. High-frequency time series data forecasting presents unique challenges due to its inherent complexity and characteristics. Therefore, the study proposes two algorithms to develop Machine-Learning (ML)-based hybrid models as well as seasonal adjusted ML-based hybrid models, which can handle large datasets and reveal complex seasonal patterns. The performance of these developed ML-based hybrid models and seasonal adjusted ML-based hybrid models were compared with other traditional time series, Autoregressive Integrated Moving Average (ARIMA), Exponential Smoothing State Space (ETS), and Trigonometric Box-Cox ARMA Trend Seasonal (TBATS) and ML models, Artificial Neural Network (ANN), Support Vector Regression (SVR), Prophet, Random Forest Regression (RFR), and Long Short-Term Memory (LSTM), to forecast heatwave warnings in Rajshahi, one of Bangladesh’s warmest districts, based on 42-year historical daily instances. Our findings indicate that the seasonal adjusted ML-based hybrid model, by integrating the Seasonal-Trend decomposition procedure based on LOESS (STL) approach with different time series and ML models, STL-ARIMA-LSTM, outperformed all other models with MAE (0.8974), MAPE (2.9232), RMSE (1.1794), MASE (0.3814) and ACF1 (0.0026). Hence, our suggested seasonal adjusted ML-based hybrid model, ensures a more accurate forecast and helps to determine the number and days of heatwaves, enabling people to plan ahead and take necessary safety measures before they occur.

NaMA-Mamba: Foundation model for generalizable nasal disease detection using masked autoencoder with Mamba on endoscopic images.

NaMA-Mamba: Foundation model for generalizable nasal disease detection using masked autoencoder with Mamba on endoscopic images.

Linear Model for Concentration Measurement of Mixed Gases.

Electronic noses have been widely used in industrial production, food preservation, agricultural product storage, environmental monitoring, and other fields. However, due to the cross-sensitivity of gas-sensing responses, accurately measuring the concentration of mixed gases remains challenging. To address this issue, this study attempts to determine the number of state variables that produce the cross-influence based on the experimental data, establish the state space model from the equivalent circuit model, and obtain model parameters through parameter correlation iterative algorithms and a Kalman filter. The sensor response model and the concentration measurement model of mixed gases are established accordingly. The simulation and experimental results show that these two models have high accuracy in predicting the sensor response and measuring the concentrations of mixed gases under the influence of mixed gases on the sensors.

Active Learning Attraction Basins of Dynamical System

Abstract Dynamical systems often exhibit multiple attractors representing significantly different functioning conditions. A global map of attraction basins can offer valuable guidance for stabilizing or transitioning system states. Such a map can be constructed without prior system knowledge by identifying attractors across a sufficient number of points in the state space. However, determining the attractor for each initial state can be a laborious task. Here, we tackle the challenge of reconstructing attraction basins using as few initial points as possible. In each iteration of our approach, informative points are selected through random seeding and are driven along the current classification boundary, promoting the eventual selection of points that are both diverse and enlightening. The results across various experimental dynamical systems demonstrate that our approach requires fewer points than baseline methods while achieving comparable mapping accuracy. Additionally, the reconstructed map allows us to accurately estimate the minimum escape distance required to transition the system state to a target basin.

Reduction of a Markov decision process with non-linear discounting to a stochastic game with standard total undiscounted criterion

Abstract We consider a Markov decision process (MDP), whose total discounted utility is aggregated recursively with a concave discount function that is not necessarily linear. The state and action spaces are Borel spaces, and the utility function is nonnegative. We show that it can be reduced to a turn-based stochastic game model with the total undiscounted utility. This reduction result is then applied to the MDP problem with recursively aggregated utility to be maximized or cost to be minimized.

Advanced Trajectory Analysis of NASA’s Juno Mission Using Unsupervised Machine Learning: Insights into Jupiter’s Orbital Dynamics

NASA’s Juno mission, involving a pioneering spacecraft the size of a basketball court, has been instrumental in observing Jupiter’s atmosphere and surface from orbit since it reached the intended orbit. Over its first decade of operation, Juno has provided unprecedented insights into the solar system’s origins through advanced remote sensing and technological innovations. This study focuses on change detection in terms of Juno’s trajectory, leveraging cutting-edge data computing techniques to analyze its orbital dynamics. Utilizing 3D position and velocity time series data from NASA, spanning 11 years and 5 months (August 2011 to January 2023), with 5.5 million samples at 1 min accuracy, we examine the spacecraft’s trajectory modifications. The instantaneous average acceleration, jerk, and snap are computed as approximations of the first, second, and third derivatives of velocity, respectively. The Hilbert transform is employed to visualize the spectral properties of Juno’s non-stationary 3D movement, enabling the detection of extreme events caused by varying forces. Two unsupervised machine learning algorithms, DBSCAN and OPTICS, are applied to cluster the sampling events in two 3D state spaces: (velocity, acceleration, jerk) and (acceleration, jerk, snap). Our results demonstrate that the OPTICS algorithm outperformed DBSCAN in terms of the outlier detection accuracy across all three operational phases (OP1, OP2, and OP3), achieving accuracies of 99.3%, 99.1%, and 98.9%, respectively. In contrast, DBSCAN yielded accuracies of 98.8%, 98.2%, and 97.4%. These findings highlight OPTICS as a more effective method for identifying outliers in elliptical orbit data, albeit with higher computational resource requirements and longer processing times. This study underscores the significance of advanced machine learning techniques in enhancing our understanding of complex orbital dynamics and their implications for planetary exploration.