Markov process amplitude EEG model for spontaneous background activity.

The recorded electroencephalography (EEG) signal is often contaminated with different kinds of artifacts and noise. Singular spectrum analysis (SSA) is a powerful tool for extracting the brain rhythm from a noisy EEG signal. By analyzing the frequency characteristics of the reconstructed component (RC) and the change rate in the trace of the Toeplitz matrix, it is demonstrated that the embedding dimension is related to the frequency bandwidth of each reconstructed component, in consistence with the component mixing in the singular value decomposition step. A method for selecting the embedding dimension is thereby proposed and verified by simulated EEG signal based on the Markov Process Amplitude (MPA) EEG Model. Real EEG signal is also collected from the experimental subjects under both eyes-open and eyes-closed conditions. The experimental results show that based on the embedding dimension selection method, the alpha rhythm can be extracted from the real EEG signal by the adaptive SSA, which can be effectively utilized to distinguish between the eyes-open and eyes-closed states.

Bernoulli and first-order Markov processes are used to approximate the output process of a class of slotted multiuser random-access communication networks. The parameters of the approximating processes are analytically calculated for a network operating under a specific random-access algorithm. The mean time that a packet spends in the central node of the star topology is calculated under the proposed approximations of the output processes of the interconnected networks. The results are compared with simulation results of the actual system. It turns out that the memoryless approximation gives satisfactory results up to a certain per-network-traffic load. Beyond that point, the first-order Markov processes performs better. >

We introduce LAMP: the Linear Additive Markov Process. Transitions in LAMP may be influenced by states visited in the distant history of the process, but unlike higher-order Markov processes, LAMP retains an efficient parameterization. LAMP also allows the specific dependence on history to be learned efficiently from data. We characterize some theoretical properties of LAMP, including its steady-state and mixing time. We then give an algorithm based on alternating minimization to learn LAMP models from data. Finally, we perform a series of real-world experiments to show that LAMP is more powerful than first-order Markov processes, and even holds its own against deep sequential models (LSTMs) with a negligible increase in parameter complexity.

An expanded form of the third-order Markov undulation model is developed which includes undulation of the geoid, vertical deflections, gravity anomaly, and the anomalous gravity gradients. First, the complete set of autocorrelation and cross-correlation functions, as specified by the autocorrelation of undulation, is obtained. Then, a time-domain approach is used to synthesize the corresponding linear system driven by white noise that represents the anomalous gravity field behavior along a straight horizontal track. The resulting nine-state Markov model provides a shaping filter for applying covariance analysis and optimal estimation techniques to inertial navigation and gravity gradiometry systems analysis. ONTINUED mechanical refinement has brought inertial navigation technology to the stage where unmodeled variations in the Earth's gravity field have become significant and sometimes dominant error sources.1 At the same time, inertial navigation system analysts have been facing the task of developing error models to evaluate the impact of gravity uncertainties on navigation system performance. Ad- ditionally, the development of gravity gradiometers has made it necessary to model gravity-gradient signals to specify sensor requirements and analyze gradiometer-aided inertial navigation or gradiometry survey performance. To apply the powerful tools of linear system theory and Kalman filtering, it has become common to consider gravity uncertainties random variables, and to model them as Markov processes. Following the first treatment of vertical deflections as a first-order Markov process,2 a succession of higher order Markov models was proposed culminating with the third- order Markov undulation model3'4 which is fully self- consistent; that is, the auto- and cross-correlation functions of undulation, vertical deflections, and gravity anomaly obey and are derived according to the mathematical relationships of physical geodesy. The motivation for using Markov models for gravity un- certainties is that they can be cast in the form of linear dif- ferential equations driven by white noise. This allows use of the model as a shaping filter in covariance analysis of linear dynamic systems, Kalman filters, and optimal smoothing algorithms. The expanded third-order Markov undulation model described in this paper is derived from the original version, but it has three differences. First, it was found that the original model could easily be extended to include all the anomalous gravity gradients by continued differentiation of auto- and cross-correlation functions. Second, the exact cross-correlation function between undulation and gravity anomaly contains modified Bessel functions.4 Modified Bessel functions are solutions to a class of differential equations whose coefficients are functions of the independent variable. To obtain a Markov shaping filter, it is necessary to substitute an approximate function which is the solution to a linear differential equation with constant coefficients. While the chosen exponential form did not approximate the exact Bessel function as well as at first hoped possible, it provides a suitable representation of the un- dulation-gravity anomaly cross-correlation.

Bayesian dynamic probit models for the analysis of longitudinal data

Awake background electroencephalogram (EEG) is interpreted by electroencephalographer (EEGer), and the results of EEG interpretation are described in EEG reports. Desired EEG reports should include enough information so that the time series of the raw EEG can be imagined from them. Then, it is important to know how much information about the characteristics of EEG is included in the report. In this study, a method for constructing an EEG model, which reflects the EEG report is proposed. First, EEG parameters for EEG interpretation items are determined based on EEGer’s report, then the model parameters are calculated from the determined EEG parameters. The proposed models were constructed from the EEG reports of 7 subjects. The time series of the constructed models were visually evaluated by the EEGer, and satisfactory results were obtained. The information included in the EEG report can be represented through the time series of the model constructed by the proposed method. The proposed method can be utilized for the training of EEG report making.

SummaryThis paper examines the long-run equilibrium wealth distribution in the context of a general equilibrium model in which heterogeneous agents are born into dynasties. When agents are born, they are randomly assigned to be either altruists or egoists. An altruistic agent cares about his progeny and so consumes part of his income (wages plus bequests) and bequeaths the rest to his heirs. These bequests determine the capital stock next period. An egoistic agent consumes all his income (wages plus bequests) leaving nothing to his heirs. Assuming that the probability that an altruist (egoist) is born to an altruist or an egoist follows a first-order Markov process, and given initial conditions on the distribution of wealth and bequests, the equilibrium dynamics of the economy can be characterised, and a stationary equilibrium (numerically) solved. This done, two fiscal policy tax/intragenerational transfer regimes are evaluated in terms of individual welfare and the distribution of wealth.

Recent empirical papers have analyzed collusion in the Joint Executive Committee in an attempt to determine which of several theories of cartel behavior is supported by the behavior of this 19th century railroad cartel. Non-parametric tests of whether high and low profit regimes followed a first-order Markov process when one controls for the number of firms support the theory of optimal collusion given by Abreu, Pearce, and Stachetti. Results on whether transition probabilities depend on the number of firms are inconclusive.

An analytical solution is presented for a discrete-time, steady-state Kalman filter with correlated measurement noise. The measurement model is a first-order Markov process, characterized by variance and correlation parameters. The analytical results are used to study the effect of a correlation on steady-state tracking accuracies. >

Recent work on the performance characterization of communication systems operating over correlated fading channels has largely concluded that modeling a mobile radio channel as a first-order Markov process is sufficient. In this paper, a new performance criterion that is directly related to the error probability of a communication system is introduced. This criterion suggests that employing a Markov model of higher order will greatly improve the accuracy of model-based performance characterizations. Next, two design techniques for higher-order Markov models are considered. Numerical results suggest that, with no increase in complexity, the use of a second-order Markov model significantly improves the accuracy of characterizing the performance of systems operating over fading channels.

This study proposes a simple estimator for dynamic choice models with continuous unobserved heterogeneity, state dependence induced by a first-order Markov process, and lagged choice coefficients that are not brand specific. As opposed to the estimator most frequently used in marketing studies, which drops the first choice of each panelist, this estimator keeps that choice in the estimation sample but ignores the impact of presample choices on first observed choice. The proposed method presents major advantages over dropping the first observation: (1) it yields low bias estimates for state dependence coefficients and, thus, it can be used to assess the presence and the magnitude of state dependence; (2) it is informative about the magnitude of bias in its estimates; and (3) it yields substantially and significantly smaller biases. The results of this study can be used to determine if the proposed method is suitable for specific applications on real data.

We investigate human error dynamics in sequential two-alternative choice tasks. When subjects repeatedly discriminate between two stimuli, their error rates and reaction times (RTs) systematically depend on prior sequences of stimuli. We analyze these sequential effects on RTs, separating error and correct responses, and identify a sequential RT tradeoff: a sequence of stimuli which yields a relatively fast RT on error trials will produce a relatively slow RT on correct trials and vice versa. We reanalyze previous data and acquire and analyze new data in a choice task with stimulus sequences generated by a first-order Markov process having unequal probabilities of repetitions and alternations. We then show that relationships among these stimulus sequences and the corresponding RTs for correct trials, error trials, and averaged over all trials are significantly influenced by the probability of alternations; these relationships have not been captured by previous models. Finally, we show that simple, sequential updates to the initial condition and thresholds of a pure drift diffusion model can account for the trends in RT for correct and error trials. Our results suggest that error-based parameter adjustments are critical to modeling sequential effects.

Emotional support is a core capability in human-AI interaction, with applications including psychological counseling, role play, and companionship. However, existing evaluations of large language models (LLMs) often rely on short, static dialogues and fail to capture the dynamic and long-term nature of emotional support. To overcome this limitation, we shift from snapshot-based evaluation to trajectory-based assessment, adopting a user-centered perspective that evaluates models based on their ability to improve and stabilize user emotional states over time. Our framework constructs a large-scale benchmark consisting of 328 emotional contexts and 1,152 disturbance events, simulating realistic emotional shifts under evolving dialogue scenarios. To encourage psychologically grounded responses, we constrain model outputs using validated emotion regulation strategies such as situation selection and cognitive reappraisal. User emotional trajectories are modeled as a first-order Markov process, and we apply causally-adjusted emotion estimation to obtain unbiased emotional state tracking. Based on this framework, we introduce three trajectory-level metrics: Baseline Emotional Level (BEL), Emotional Trajectory Volatility (ETV), and Emotional Centroid Position (ECP). These metrics collectively capture user emotional dynamics over time and support comprehensive evaluation of long-term emotional support performance of LLMs. Extensive evaluations across a diverse set of LLMs reveal significant disparities in emotional support capabilities and provide actionable insights for model development.

Several applications of deformable mirrors in adaptive optics and beam shaping rely on electrostatic actuation to provide the required deformation. In the case of membrane mirrors, the actuation force is frequently controlled via the potential difference across the gap between the metallized membrane and the electrode substrate. In our previous work we studied an alternative approach using a constant voltage and variable area, accomplished with appropriately centered clusters of switchable area segments. Here, we investigate controlling the force by driving the electrode substrate in a direction perpendicular to the actuator/ membrane surface. Using a single-mode non-linear model and the Lyapunov potential method, a closed-loop controller is designed for tracking a trajectory derived to meet prescribed performance criteria (such as steady deflection, bandwidth, and damping ratio). The velocity-observer input is derived from beam response measurements obtained using a quad cell beam position finder. The controller is found to be robust to a class of measurement errors affecting the quad cell output and a class of membrane velocity errors arising from platform vibrations, where both types of error are modeled as first-order Markov processes. The analytical results are confirmed using numerical simulations, showing the technique to be fairly successful at meeting the prescribed performance requirements for large deflections at moderate voltages and areas.

A setup involving zero-delay sequential transmission of a vector Markov source over a burst erasure channel is studied. A sequence of source vectors is compressed in a causal fashion at the encoder, and the resulting output is transmitted over a burst erasure channel. The destination is required to reconstruct each source vector with zero-delay, but those source sequences that are observed either during the burst erasure, or in the interval of length W following the burst erasure need not be reconstructed. The minimum achievable compression rate is called the rate-recovery function. We assume that each source vector is independent identically distributed (i.i.d.) across the spatial dimension and is sampled from a stationary, first-order Markov process across the temporal dimension. For discrete sources, the case of lossless recovery is considered, and upper and lower bounds on the rate-recovery function are established. Both these bounds can be expressed as the rate for predictive coding, plus a term that decreases at least inversely with the recovery window length W. For Gauss-Markov sources and a quadratic distortion measure, upper and lower bounds on the minimum rate are established when W = 0. These bounds are shown to coincide in the high resolution limit. Finally, another setup involving i.i.d. Gaussian sources is studied and the raterecovery function is completely characterized in this case.