Discrete States Research Articles

Spatial Markov matrices for measuring the spatial dependencies of an epidemiological spread : case Covid’19 Madagascar

BackgroundThis article applies a variant of the Markov chain that explicitly incorporates spatial effects. It is an extension of the Markov class allowing a more complete analysis of the spatial dimensions of transition dynamics. The aim is to provide a methodology for applying the explicit model to spatial dependency analysis.MethodsHere, the question is to study and quantify whether neighborhood context affects transitional dynamics. Rather than estimating a homogeneous law, the model requires the estimation of k transition laws each dependent on spatial neighbor state. This article used published data on confirmed cases of Covid’19 in the 22 regions of Madagascar. These data were discretized to obtain a discrete state of propagation intensity.ResultsThe analysis gave us the transition probabilities between Covid’19 intensity states knowing the context of neighboring regions, and the propagation time laws knowing the spatial contexts. The results showed that neighboring regions had an effect on the propagation of Covid’19 in Madagascar.ConclusionAfter analysis, we can say that there is spatial dependency according to these spatial transition matrices.

Polygon relations and subadditivity of entropic measures for discrete and continuous multipartite entanglement

In a recent work by us Ge et al [Phys. Rev. A 110, L010402 (2024)], we have derived a series of polygon relations of bipartite entanglement measures that is useful to reveal entanglement properties of discrete, continuous, and even hybrid multipartite quantum systems. In this work, with the information-theoretical measures of Rényi and Tsallis entropies, we study the relationship between the polygon relation and the subadditivity of entropy. In particular, the entropy-polygon relations are derived for pure multi-qubit states and then generalized to multi-mode Gaussian states, by utilizing the known results from the quantum marginal problem. Then the equivalence between the polygon relation and subadditivity is established, in the sense that for all discrete or continuous multipartite states, the polygon relation holds if and only if the underlying entropy is subadditive. As a byproduct, the subadditivity of Rényi and Tsallis entropies is proven for all bipartite Gaussian states. Finally, the difference between polygon relations and monogamy relations is clarified, and generalizations of our results are discussed. Our work provides a better understanding of the rich structure of multipartite states, and hence is expected to be helpful for the study of multipartite entanglement.

Autonomous stabilization with programmable stabilized state

Reservoir engineering is a powerful technique to autonomously stabilize a quantum state. Traditional schemes involving multi-body states typically function for discrete entangled states. In this work, we enhance the stabilization capability to a continuous manifold of states with programmable stabilized state selection using multiple continuous tuning parameters. We experimentally achieve 84.6% and 82.5% stabilization fidelity for the odd and even-parity Bell states as two special points in the manifold. We also perform fast dissipative switching between these opposite parity states within 1.8 μs and 0.9 μs by sequentially applying different stabilization drives. Our result is a precursor for new reservoir engineering-based error correction schemes.

Inferring Kinetics and Entropy Production from Observable Transitions in Partially Accessible, Periodically Driven Markov Networks

For a network of discrete states with a periodically driven Markovian dynamics, we develop an inference scheme for an external observer who has access to some transitions. Based on waiting-time distributions between these transitions, the periodic probabilities of states connected by these observed transitions and their time-dependent transition rates can be inferred. Moreover, the smallest number of hidden transitions between accessible ones and some of their transition rates can be extracted. We prove and conjecture lower bounds on the total entropy production for such periodic stationary states. Even though our techniques are based on generalizations of known methods for steady states, we obtain original results for those as well.

Abnormal dynamics of functional connectivity density and effective connectivity in overactive bladder.

The study aims to analyze alterations in dynamic functional connectivity density (dFCD) and effective connectivity (dEC) patterns using functional magnetic resonance imaging (fMRI), hypothesizing that overactive bladder (OAB) patients will exhibit distinct dFCD and dEC patterns, reflecting altered neural communication underlying the OAB. Forty-three female OAB patients and 40 female healthy controls (HC) underwent resting-state fMRI. Sliding window correlation was used to calculate the variability of the dFCD. The changes in dFCD-based dEC between the two groups were examined using Granger causal analysis. To describe the time-varying Granger causality, a sliding-window approach was utilized to divide time courses into a group of windows. We adopted a k-means clustering method to cluster all matrices into discrete connectivity states. Compared with HC, OAB females consistently had a dFCD (decreased) in the left anterior cingulate cortex (ACC) and left medial prefrontal cortex (mPFC) (p < 0.05, GRF corrected). In state 1, OAB patients had excitatory effective connections from bilateral ACC to left mPFC in comparison to HC. In state 2, there was an increase in dEC from the SMA to the mPFC. Participants with OAB showed significantly more inhibitory dorsolateral prefrontal cortex (dlPFC) connections between the left ACC and the right ACC in state 4, as well as an excitatory dEC connection between the right dlPFC and the left ACC in state 2 (p < 0.05, GRF corrected). OAB patients demonstrate significant alterations in dFCD and dEC patterns, which may be indicative of the neural mechanisms involved in OAB pathophysiology.

Prefrontal Cortex subregions provide distinct visual and behavioral feedback modulation to the Primary Visual Cortex.

The mammalian Prefrontal Cortex (PFC) has been suggested to modulate sensory information processing across multiple cortical regions via long-range axonal projections. These axonal projections arise from PFC subregions with unique brain-wide connectivity and functional repertoires, which may provide the architecture for modular feedback intended to shape sensory processing. Here, we used axonal tracing, axonal and somatic 2-photon calcium imaging, and chemogenetic manipulations in mice to delineate how projections from the Anterior Cingulate Cortex (ACA) and ventrolateral Orbitofrontal Cortex (ORB) of the PFC modulate sensory processing in the primary Visual Cortex (VISp) across behavioral states. Structurally, we found that ACA and ORB have distinct patterning of projections across both cortical regions and layers. ACA axons in VISp had a stronger representation of visual stimulus information than ORB axons, but both projections showed non-visual, behavior-dependent activity. ACA input to VISp enhanced the encoding of visual stimuli by VISp neurons, and modulation of visual responses scaled with arousal. On the other hand, ORB input shaped movement and arousal related modulation of VISp visual responses, but specifically reduced the encoding of high-contrast visual stimuli. Thus, ACA and ORB feedback have separable projection patterns and encode distinct visual and behavioral information, putatively providing the substrate for their unique effects on visual representations and behavioral modulation in VISp. Our results offer a refined model of cortical hierarchy and its impact on sensory information processing, whereby distinct as opposed to generalized properties of PFC projections contribute to VISp activity during discrete behavioral states.

A sticky Poisson Hidden Markov Model for spike data.

Fitting a hidden Markov Model (HMM) to neural data is a powerful method to segment a spatiotemporal stream of neural activity into sequences of discrete hidden states. Application of HMM has allowed to uncover hidden states and signatures of neural dynamics that seem relevant for sensory and cognitive processes. This has been accomplished especially in datasets comprising ensembles of simultaneously recorded cortical spike trains. However, the HMM analysis of spike data is involved and requires a careful handling of model selection. Two main issues are: (i) the cross-validated likelihood function typically increases with the number of hidden states; (ii) decoding the data with an HMM can lead to very rapid state switching due to fast oscillations in state probabilities. The first problem is related to the phenomenon of over-segmentation and leads to overfitting. The second problem is at odds with the empirical fact that hidden states in cortex tend to last from hundred of milliseconds to seconds. Here, we show that we can alleviate both problems by regularizing a Poisson-HMM during training so as to enforce large self-transition probabilities. We call this algorithm the 'sticky Poisson-HMM' (sPHMM). When used to-gether with the Bayesian Information Criterion for model selection, the sPHMM successfully eliminates rapid state switching, outperforming an alternative strategy based on an HMM with a large prior on the self-transition probabilities. The sPHMM also captures the ground truth in surrogate datasets built to resemble the statistical properties of the experimental data.

Multistable Soft Robots Assembled from Bistable Auxetic Building Blocks

Soft robotics have significantly influenced both scientific and industrial domains over the past decades. However, their inherent limitations of material or structural softness pose a persistent challenge in terms of shape retention and load capacity for various applications. To address this challenge, bistable and multistable structures with two or more mechanically stable states and snap‐through switchability emerge as a promising solution. Herein, a multistable soft robot design assembled from bistable auxetic building blocks with negative Poisson's ratio and a large volumetric change is presented. The bistable mechanical behavior and optimal structural parameters have been investigated by mechanical modeling, finite element analysis, and experimental testing. To demonstrate the shape retention ability and enhanced load capacity of our robotic design, a multistable manipulator with a low‐complexity closed‐loop control system is presented, capable of maintaining 216 discrete stable states even when the pneumatic pressure supply is removed. To validate the multifunctionality of design, a multistable tube crawler with a notable load capacity of approximately five times its own body weight is developed.

Comprehensive evaluation of solder joint integrity in power semiconductors: Exploring multiple failure mechanisms and cumulative impact

Investigating the impact of solder joint degradation in power semiconductors is crucial given their widespread use. Solder joints, being the weakest link, are prone to multiple failure mechanisms, exacerbating degradation under normal operation. This paper presents a novel approach for assessing solder joint degradation, particularly in electric vehicles, where severe thermal and vibration stresses are prevalent. Our method categorizes solder joint conditions into discrete states, from fully perfect to fully damaged, integrating both thermal and vibration-induced failures. By considering cumulative effects, our approach yields more precise reliability estimates. Moreover, it offers a versatile framework applicable across various failure scenarios and readily deployable in the design phase.

Tuning nonequilibrium colloidal structure in external fields by density-dependent state switching.

Biological cells have the ability to switch internal states depending on the density of other cells in their local environment, referred to as "quorum sensing." The latter can be utilized to control collective structuring, such as in biofilm formation. In this work, we study a simple quorum sensing model of ideal (noninteracting) colloids with a switchable internal degree of freedom in the presence of external potentials. The colloids have two possible discrete states, in which they are affected differently by the external field, and switch with rates dependent on the local density in their environment. We study this model with reactive Brownian dynamics simulations, as well as with an appropriate reaction-diffusion theory. We find remarkable structuring in the system controlled by the density-mediated interactions between the ideal colloids. We report results of different functional forms for the rate dependence and quantify the influence of their parameters, in particular, discuss the role of the spatiotemporal sensing range, i.e., how the resulting structures depend on how the environmental information is "measured" by the colloids. Especially in the case of a rate function with sigmoidal dependence on local density, i.e., requiring a threshold density for switching, we observe significant correlation effects in the density profiles which are tuneable by the sensing ranges but also sensitive to noise and fluctuations. Hence, our model gives some basic insights into the nonequilibrium structuring mediated by simple quorum sensing protocols.

Complex behavior from intrinsic motivation to occupy future action-state path space

Most theories of behavior posit that agents tend to maximize some form of reward or utility. However, animals very often move with curiosity and seem to be motivated in a reward-free manner. Here we abandon the idea of reward maximization and propose that the goal of behavior is maximizing occupancy of future paths of actions and states. According to this maximum occupancy principle, rewards are the means to occupy path space, not the goal per se; goal-directedness simply emerges as rational ways of searching for resources so that movement, understood amply, never ends. We find that action-state path entropy is the only measure consistent with additivity and other intuitive properties of expected future action-state path occupancy. We provide analytical expressions that relate the optimal policy and state-value function and prove convergence of our value iteration algorithm. Using discrete and continuous state tasks, including a high-dimensional controller, we show that complex behaviors such as “dancing”, hide-and-seek, and a basic form of altruistic behavior naturally result from the intrinsic motivation to occupy path space. All in all, we present a theory of behavior that generates both variability and goal-directedness in the absence of reward maximization.

Photocatalysis-promoted tumor ferroptosis enabled by MOF-derived black TiO2

Ferroptosis has emerged as a novel approach to suppress tumor growth through the iron-dependent accumulation of lipid peroxides, providing new opportunities for cancer therapy. However, the effectiveness of ferroptosis is impeded by the substantial neutralization of reactive oxygen species (ROS), generated through the Fenton reaction, by the high level of glutathione in cancer cells. Here we report a titanium metal–organic frameworks (MOFs)-derived method to create black TiO2 nanoparticles with excellent photocatalytic performance. The nanoparticle has a narrow bandgap of 1.02 eV, multiple discrete gap states, and a high density of oxygen vacancies (46.2 %), facilitating ROS generation under 1064-nm light irradiation. When coated with a tannic acid/Fe3+ layer, the resulting nanocomposite possesses the ability to deplete glutathione concentration, preventing the newly generated ROS from being neutralized and promoting ferroptotic cancer cell death. Complemented by photothermal and chemodynamic effects, in vivo experiments demonstrate a high tumor inhibition rate of 89.8 %. The utilization of MOF-derived nanomaterials represents a universal strategy, offering a solution for ferroptosis-based therapy in solid tumors and contributing to the development of smart, optically active materials with diverse applications in biological contexts.

Generation of neutron spectra and emission yields from proton-induced reactions on natC and natLi targets using CR-39 detectors

Fast neutron spectrometry and dosimetry at a specified location in a compact radiation environment is difficult due to large size of the conventional neutron spectrometers. In such situations, a small-size bare CR-39 detector can be used as a neutron detector to quantify the fast neutron fraction. In the present study, CR-39 detectors were placed very close to natural lithium and carbon targets during the proton irradiations to acquire the emission neutron spectra. The neutron spectra and the ambient dose equivalents in the forward and lateral directions with respect to the incident proton beam were estimated for both targets at incident proton energies between 8 and 20 MeV. The measured neutron spectra using CR-39 detectors could identify the quasi mono-energetic neutron features from the Li(p,n) and 13C(p,n) reactions effectively. An important observation of the present study is the identification of the fast neutron signature from the 13C(p,n) system from the discrete state de-excitations of excited 14N composite nuclei. The theoretical evaluation of the neutron spectral features and relative neutron energy distributions were performed using the FLUKA: FLUktuierende KAskade, a Monte Carlo simulation package, and the estimates agreed with the experimental results for both systems. The neutron ambient dose equivalents were also estimated from the measured spectra. These neutron fluence and dose estimates at close vicinity to the target can serve as an essential basis for shielding calculations and planning the pertinent radiation protection strategies.

Shedding light on evolution of Raman line shape with probing laser power: Light-induced perturbation in electron-phonon coupling.

The laser power mediated changes in the Raman line shape have been considered in terms of interference between discrete phonon states ρ and the electronic continuum states ϰ contributed by Urbach tail states. The laser-induced effects are treated in terms of the increase in the surface temperature and thereby the scaling of electronic disorder, i.e., Urbach energy, which can further contribute to the electron-phonon interactions. Therefore, the visualization of this effect is attempted analytically as a perturbation term in the Hamiltonian, which clearly accounts for the observed changes with laser power. This has been investigated based on the experimental results of laser power dependent Raman spectra of bulk EuFeO3 and silicon nanowires, which are found to provide convincing interpretations.

DEVELOPMENT OF A HYBRID NETWORK CONGESTION MONITORING SYSTEM

Constantly growing requirements for the information systems service quality require monitoring of network congestion. The experimental results proved that when using hybrid networks, it is difficult to estimate the network load based on the average time of information delivery due to the presence of a significant scatter of time data. A mathematical model of information transmission in wireless computer networks in the form of a queuing system has been developed. The system identifies the main elements: a data transmission channel, a data frame and a device that transmits data. Analysis of transmission standards allows us to identify the following main transmission modes for modeling: one frame successful transmission; transmitting a frame with an error and repeating the transmission (possibly several times); frame transmission using performance-enhancing technology (Bursting technology is used as an example). Events associated with the transmission of information over the wireless network of one device are considered as monitoring system states under consideration. Packet exchange process was considered to be a homogeneous Markov process with discrete states, continuous time and constant intensities. A mathematical model has been developed based on the state graph of the device-frame-transmission channel system, which allows one to determine the timing characteristics for the previously identified modes. The methods for assessing network congestion based on statistical information during data transmission is proposed. Delivery times are broken down into ranges derived from the simulation. The proportion of packets whose delivery time lies within the selected test range is estimated. To evaluate the results, experimental studies were carried out on a fragment of the hybrid network. Delivery time results for each experiment were divided into four ranges: corresponding to accelerated delivery of fragments, successful delivery on the first, second and third attempts, respectively. Results analysis showed that it is preferable to use the fourth range to assess network congestion. Approximation reliability in this case is 0.85, the correlation coefficient is 0.92. The proposed methodology allows us to estimate network congestion based on testing data with a fairly high degree of reliability.

Constraints of local stiffness adaption for reduced-order models of large-scale steel bridges

Large and complex structures, such as bridges, are subjected to a variety of environmental factors and loads over time, leading to evolving structural states. To assess their current condition and plan predictive maintenance, Digital Twins enriched with Structural Health Monitoring (SHM) data are essential. However, for large-scale structures, the creation of physics-based Digital Twins necessitates reduced-order modeling to ensure efficient adaptation to SHM data. Many of these methods for structural damage assessment rely on localized stiffness reduction to characterize discrete damage states. The Static Condensation Reduced Basis Element (SCRBE) method is a promising approach for model order reduction by decomposing the structure into parametric components. However, SCRBE's effectiveness and the accuracy of the Digital Twin depend on an appropriate partitioning of the structure into to components with reduced stiffness. This paper systematically investigates the process and the constraints of component selection for steel bridges with discrete damages, considering factors like numerics, sensor placement and complex geometries. A comprehensive analysis is conducted using a real bridge case study augmented with synthetic measurement data representing damage scenarios. The results reveal both challenges and the potential of the SCRBE method for Digital Twins. A systematic approach for component selection within the SCRBE framework is proposed, specifically tailored for real-world application scenarios. This structured methodology facilitates the efficient and adaptive development of Digital Twins for large, intricate structures, such as steel bridges.

Noise intensity of a Markov chain.

Stochastic transitions between discrete microscopic states play an important role in many physical and biological systems. Often these transitions lead to fluctuations on a macroscopic scale. A classic example from neuroscience is the stochastic opening and closing of ion channels and the resulting fluctuations in membrane current. When the microscopic transitions are fast, the macroscopic fluctuations are nearly uncorrelated and can be fully characterized by their mean and noise intensity. We show how, for an arbitrary Markov chain, the noise intensity can be determined from an algebraic equation, based on the transition rate matrix; these results are in agreement with earlier results from the theory of zero-frequency noise in quantum mechanical and classical systems. We demonstrate the validity of the theory using an analytically tractable two-state Markovian dichotomous noise, an eight-state model for a calcium channel subunit (De Young-Keizer model), and Markov models of the voltage-gated sodium and potassium channels as they appear in a stochastic version of the Hodgkin-Huxley model.

Coordinated configuration of hybrid energy storage for electricity-hydrogen integrated energy system

This paper proposes an optimal coordinated configuration method of hybrid electricity and hydrogen storage for the electricity‑hydrogen integrated energy system (EH-ES) to promote the renewable energy source (RES) utilization and reduce the deployment cost. To simulate the practical operation of EH-ES, an energy hub framework with a discrete state space system matrix is designed to characterize the internal interconnection topology and quantify the steady-state production, storage, conversion and utilization processes of electricity and hydrogen energy carriers within EH-ES. A chronological operation simulation based electricity and hydrogen storage configuration model over a year-round time horizon is formulated to collaboratively optimize the capacity of the electrolyzer, fuel cell, battery energy storage (BES) and hydrogen storage tank. In this model, the power and capacity complementarity of BES and generalized hydrogen storage is fully exploited to compensate for power and energy imbalances, and additional capacity configuration of BES is considered to mitigate the drastic electrolytic power fluctuation. Besides, a typical source-load scenario reduction method based on K-means and ordered clustering is developed to avoid a large number of operation variables due to year-round hourly simulation. Comparative studies demonstrate that the proposed methodology can achieve the RES consumption rate of 98.873 % while the equipment investment cost can be reduced by 10.034 %.

Discontinuous polynomial approximation in electrical impedance tomography with total variational regularization

In this paper, we present an alternative discrete total variation type functional for image reconstruction in electrical impedance tomography. The modified functional deals with unknown inclusions and values of conductivity. The convergence of the proposed finite element method with uniform refinement is also established: the sequence of discrete solutions contains a subsequence that converges to a solution of the continuous functional. Additionally, we propose an adaptive reconstruction algorithm in which the estimators are based on the discrete state variable, the discrete adjoint variable and the gradient of the discrete functional. A series of numerical examples are provided to illustrate the convergence behavior in diverse scenarios.

Implementation of unknown parameter estimation procedure for hybrid and discrete non‐linear systems

AbstractThe application of the hybrid extended Kalman filter (HEKF), hybrid unscented Kalman filter (HUKF), hybrid particle filter (HPF), and hybrid extended Kalman particle filter (HEKPF) is discussed for hybrid non‐linear filter problems, when prediction equations are continuous‐time and the update equations are discrete‐time, and also the discrete extended Kalman filter (DEKF), discrete unscented Kalman filter (DUKF), discrete particle filter (DPF), and discrete extended Kalman particle filter (DEKPF) for discrete‐time non‐linear filter problems, when prediction equations and update equations are discrete‐time. In order to assess the performance of the filters, the authors consider the non‐linear dynamics for a re‐entry vehicle. The filters are used in two hybrid and discrete states to estimate the position, velocity, and drag parameter associated with the re‐entry vehicle. Theoretical topics concerning estimating the drag parameter of a vehicle in re‐entry phase have been dealt with. Drag parameter estimation is carried out using a combination of hybrid filters and discrete filters as an effective estimator and fixed value, forgetting factor, and Robbins‐Monro stochastic approximation methods as the noise covariance matrix adjuster of the parameter.