Stochastic Paradigm Research Articles

Sex differences in swallowing response to Gaussian stochastic surface electrical stimulation

One of the rehabilitation methods in practical use for dysphagia is electrical stimulation therapy, usually by stimulating the anterior neck muscles via surface electrodes. Electrostimulation therapy does not directly induce swallowing, but is used as resistance training or to alter drive to swallow muscles. Techniques to stimulate the sensory nervous system have been investigated as possible rehabilitation methods to activate the entire swallowing reflex circuit (such as direct magnetic stimulation of the primary somatosensory cortex). We hypothesized that electrical stimulation of the posterior thoracic region using surface electrodes on the back could work in a similar way to magnetic stimulation therapy to improve swallowing movements. We placed stimulating electrodes at three different locations on the back, neck, and subclavian region of adult Sprague Dawley rats ( n = 18). Using a stochastic paradigm, Gaussian probability electrical stimulation was applied to each site at a median frequency of 300 Hz. Natural swallow was evoked by oral water infusion, and swallow activity was recorded with electromyogram (EMG) wires placed in three swallow-related muscles: mylohyoid (laryngeal elevator), thyroarytenoid (laryngeal adductor), and thyropharyngeus (pharyngeal constrictor). A total of four 120 second electrical stimulus trials were applied with a median frequency of 300 Hz in a Gaussian distribution. EMG amplitudes during swallows after each stimulus were compared to those generated during control swallows. Results showed stimulator placement on the back facilitated all three muscles (mylohyoid, thyroarytenoid, and thyropharyngeus) in all male rats, and in some female rats. Stimulation placed on the lateral neck affected only the thyropharyngeus in male rats, and only the thyroarytenoid in female rats. EMG amplitudes were unchanged following subclavian stimulation. In conclusion, our finding that Gaussian electrical stimulation of the back activated a complement of swallowing muscles in male rats suggests that this may represent a novel swallowing treatment method. Additionally, male and female rats responded differently to simulation, indicating that potential sex differences need to be further elucidated. This work was supported by NIH grants HL 111215, HL 103415 and OT20D001983, the Craig H. Neilsen Foundation Pilot Research Grant 546714, Kentucky Spinal Cord and Head Injury Research Trust, and the Commonwealth of Kentucky Challenge for Excellence. This is the full abstract presented at the American Physiology Summit 2023 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

Artificial intelligence knacks-based stochastic paradigm to study lie group analysis with the impact of electric field on MHD Prandtl–Eyring fluid flow system

In this research paper, we observed the Prandtl–Eyring magneto hydrodynamic fluid model (PE-MHDFM) by applying the Bayesian regularization scheme as backpropagated artificial neural networks (BRS-BANNs). Effect of suction/injection at the wall is the source of convective steady flow. The nonlinear partial differential equations (PDEs) of PE-MHDFM are converted into ordinary differential equations (ODE) by applying some suitable similarity transformation. These ODEs are solved by utilizing Lobatto IIIA numerical procedure to acquire the reference dataset for different scenarios of BRS-BANN. The reference dataset is used to design the solver BRS-BANN. Further, the performance of BRS-BANN is clarified by MSE results, error analysis plots, regression and error histogram. Moreover, the solution of PE-MHDFM is observed through the validation, training and testing procedures. It is observed that the best correlation between the targeted values outcomes of the study is matched effectively, which definitely authenticates the validity and reliability of the designed solver. Furthermore, the impacts on the velocity profile and temperature profile are examined by the variation of different physical quantities along with their comparison with state-of-the-art Lobatto IIIA numerical approach.

From Epidemic to Pandemic Modelling

We present a methodology for systematically extending epidemic models to multilevel and multiscale spatio-temporal pandemic ones. Our approach builds on the use of coloured stochastic and continuous Petri nets facilitating the sound component-based extension of basic SIR models to include population stratification and also spatio-geographic information and travel connections, represented as graphs, resulting in robust stratified pandemic metapopulation models. The epidemic components and the spatial and stratification data are combined together in these coloured models and built in to the underlying expanded models. As a consequence this method is inherently easy to use, producing scalable and reusable models with a high degree of clarity and accessibility which can be read either in a deterministic or stochastic paradigm. Our method is supported by a publicly available platform PetriNuts; it enables the visual construction and editing of models; deterministic, stochastic and hybrid simulation as well as structural and behavioural analysis. All models are available as Supplementary Material, ensuring reproducibility. All uncoloured Petri nets can be animated within a web browser at https://www-dssz.informatik.tu-cottbus.de/DSSZ/Research/ModellingEpidemics, assisting the comprehension of those models. We aim to enable modellers and planners to construct clear and robust models by themselves.

Artificial intelligence knacks-based stochastic paradigm to study the dynamics of plant virus propagation model with impact of seasonality and delays.

The presented study deals with the exploitation of the artificial intelligence knacks-based stochastic paradigm for the numerical treatment of the nonlinear delay differential system for dynamics of plant virus propagation with the impact of seasonality and delays (PVP-SD) model by implementing neural networks backpropagation with Bayesian regularization scheme (NNs-BBRS). The PVP-SD model is represented with five classes-based ODEs systems for the interaction between insects and plants. The nonlinear PVP-SD model governs with five populations: S(t) susceptible plants, I(t) infected plants, X(t) susceptible insect vectors, Y(t) infected insect vectors and P(t) predators. Adams numerical procedure is adopted to generate the reference solutions of the nonlinear PVP-SD model based on the variety of cases by varying the plants bite rate due to vectors, vector bite rate due to plants, plant’s recovery rate, predator contact rate with healthy insects, predator contact rate with infected insects and death rate caused by insecticides. The approximate solutions of the nonlinear PVP-SD model are determined by executing the designed NNs-BBRS through different target and inputs arbitrary selected samples for the training and testing data. Validation of the consistent precision and convergence of the designed NNs-BBRS is efficaciously substantiated through exhaustive simulations and analyses on mean square error-based merit function, index of regression and error histogram illustrations.

EXPLORING BEHAVIORAL AND ATTITUDINAL BRAND LOYALTY USING TRIPARTITE MODEL OF ATTITUDE

Previously, scholars have studied behavioral and attitudinal brand loyalties separately by. Brand loyalty was first studied with behavior as one dimension in the brand loyalty structure, which predominantly measures brand loyalty by repeat purchase. However, the stochastic paradigm that views behavior as a single dimension cannot explain the motivation for consistent repeat purchase behavior. Subsequently, the stochastic paradigm was replaced with a deterministic paradigm that views attitude as a single dimension of brand loyalty. Since brand loyalty is a psychological abstraction in nature, scholars viewed that a combined approach of behavior and attitude is more appropriate to address the issue of brand loyalty. This paper proposes a Tripartite Model of Attitude to explain the dimensions and determinants of brand loyalty by combining behavioral loyalty and attitudinal loyalty in one framework.

FD-ZKF: A Zonotopic Kalman Filter optimizing fault detection rather than state estimation

Enhancing the sensitivity to faults with respect to disturbances, rather than optimizing the precision of the state estimation using Kalman Filters (KF) is the subject of this paper. The stochastic paradigm (KF) is based on minimizing the trace of the state estimation error covariance. In the context of the bounded-error paradigm using Zonotopic Kalman Filters (ZKF), this is analog to minimize the covariation trace. From this analogy and keeping a similar observer-based structure as in ZKF, a criterion jointly inspired by set-membership approaches and approximate decoupling techniques coming from parity-space residual generation is proposed. Its on-line maximization provides an optimal time-varying observer gain leading to the so-called FD-ZKF filter that allows enhancing the fault detection properties. The characterization of minimum detectable fault magnitude is done based on a sensitivity analysis. The effect of the uncertainty is addressed using a set-membership approach and a zonotopic representation reducing set operations to simple matrix calculations. A case study based on a quadruple-tank system is used both to illustrate and compare the effectiveness of the results obtained from the FD-ZKF approach compared to a pure ZKF approach.

Towards a Stochastic Paradigm: From Fuzzy Ensembles to Cellular Functions

The deterministic sequence → structure → function relationship is not applicable to describe how proteins dynamically adapt to different cellular conditions. A stochastic model is required to capture functional promiscuity, redundant sequence motifs, dynamic interactions, or conformational heterogeneity, which facilitate the decision-making in regulatory processes, ranging from enzymes to membraneless cellular compartments. The fuzzy set theory offers a quantitative framework to address these problems. The fuzzy formalism allows the simultaneous involvement of proteins in multiple activities, the degree of which is given by the corresponding memberships. Adaptation is described via a fuzzy inference system, which relates heterogeneous conformational ensembles to different biological activities. Sequence redundancies (e.g., tandem motifs) can also be treated by fuzzy sets to characterize structural transitions affecting the heterogeneous interaction patterns (e.g., pathological fibrillization of stress granules). The proposed framework can provide quantitative protein models, under stochastic cellular conditions.

Co-existence of stochastic and chaotic behaviour in the copper price time series

The possible scarcity of copper (and the likely resulting pressure on prices) is an issue of concern, especially in the light of its importance for the ever growing networking industry. Also for that reason, copper is the nonferrous metal most traded in the markets. Therefore, assessing the nature of its price fluctuations is an important task. Several papers have been devoted to analysing the characteristics of the time series of copper prices, especially for the purpose of predicting its future behaviour. The field of approaches can be divided roughly equally between those adopting a stochastic model and those opting for a deterministic nonlinear (chaotic) model. Nevertheless, while papers employing the stochastic paradigm have completely ignored the presence of chaotic features, at the same time papers recognizing the chaotic paradigm have neglected the presence of noise.The purpose of this paper is to investigate copper price behaviour in the CMX, considering a very long time series and adopting estimation methods that provide the coexistence of stochastic and chaotic features. We find that: a) the presence of noise is very significant (amounting to more than a quarter of the average signal value), as well as the presence of chaotic features; b) intermittency is present, which may be indicative of a bubble-related value that emerged without any fundamental cause.

Simulation of water-energy fluxes through small-scale reservoir systems under limited data availability

We present a stochastic approach accounting for input uncertainties within water-energy simulations. The stochastic paradigm, which allows for quantifying the inherent uncertainty of hydrometeorological processes, becomes even more crucial in case of missing or inadequate information. Our scheme uses simplified conceptual models which are subject to significant uncertainties, to generate the inputs of the overall simulation problem. The methodology is tested in a hypothetical hybrid renewable energy system across the small Aegean island of Astypalaia, comprising a pumped-storage reservoir serving multiple water uses, where both inflows and demands are regarded as random variables as result of stochastic inputs and parameters.

A generalized model for bacterial disinfection: Stochastic approach

This work proposes a novel, generalized model for bacterial disinfection formulated in light of a stochastic paradigm. The model⿿s formulation is based on an intensity of transition that is proportional to the product of general power functions of the bacteria⿿s number concentration and time; thus, the generalized stochastic model embodies the results obtained from our earlier models. The proposed model gives rise to linear and non-linear cases of the master equation whose solution can be obtained analytically as well as numerically via Monte Carlo simulation. Moreover, the generalized stochastic model has been validated with a specific instance of bacterial disinfection. The model⿿s analytical and numerical results are in excellent accord among themselves as well as with those obtained from our earlier models; in addition, the model⿿s results tend to describe the available experimental data reasonably well.

An Extended Zonotopic and Gaussian Kalman Filter (EZGKF) merging set-membership and stochastic paradigms: Toward non-linear filtering and fault detection

A framework merging the set-membership and the stochastic paradigms is formalized and used to design an Extended Zonotopic and Gaussian Kalman Filter (EZGKF) dealing with the robust state estimation and the fault detection of uncertain discrete-time nonlinear systems. The so-called Set-membership and Gaussian Mergers (SGM) are introduced and particularized to Zonotopes (ZGM). They provide a constructive and computationally efficient solution to propagate random uncertainties with incompletely specified probability distributions combining set-based support enclosures and upper covariance matrix bounds formalized as matrix inequalities. Based on a full time-varying LPV enclosure featuring structured state matrix uncertainties, and given some confidence level expressed in probabilistic terms (maximal false alarm rate), a detection test is developed and shown to merge the usually mutually exclusive benefits granted by set-membership techniques (robustness to the worst-case within specified bounds, domain computations) and stochastic approaches (taking noise distribution into account, probabilistic evaluation of tests). A numerical example illustrates the state estimation capabilities of EZGKF and the improved tradeoff between the sensitivity to faults and the robustness to disturbances/noises.

Energy Rationalization in Water Supply Networks via Stochastic Programming

This paper presents a two-stage stochastic programming model applied to energy rationalization in urban networks. The proposed model encompasses decisions regarding collection, transfer and storage of water, while minimizing the electricity costs associated to the pumping operations. To cope with the uncertainty nature of water-demands, we use the scenario-based approach within the two-stage stochastic paradigm. In order to mitigate both the variability of the recourse decisions and the infeasible solutions in the presence of multiple scenarios, we also analyze risk averse and robust policies. Numerical results show that it is possible to improve energy consumption by reducing water collection in critical periods, as well as by carrying out optimal levels of water in reservoirs before critical periods. Moreover, the analysis of EVPI and VSS evidence the importance of using the stochastic model over simpler expected approaches.

Zonotopes and Kalman observers: Gain optimality under distinct uncertainty paradigms and robust convergence

State bounding observation based on zonotopes is the subject of this paper. Dealing with zonotopes is motivated by set operations resulting in simple matrix calculations with regard to the often huge number of facets and vertices of the equivalent polytopes. Discrete-time LTV/LPV systems with state and measurement uncertainties are considered. Based on a new zonotope size criterion called FW-radius, and by merging optimal and robust observer gain designs, a Zonotopic Kalman Filter (ZKF) is proposed with a proof of robust convergence. The notion of covariation is introduced and results in an explicit bridge between the zonotopic set-membership and the stochastic paradigms for Kalman Filtering. No intersection is used and the influence of the reduction operator limiting to a tunable maximum the size of the matrices involved in the zonotopic set computations is fully taken into account in the LMI-based robust stability analysis. A numerical example illustrates the effectiveness of the proposed ZKF.

Computing the Flux Footprint

We address the flux footprint for measurement heights in the atmospheric surface layer, comparing eddy diffusion solutions with those furnished by the first-order Lagrangian stochastic (or “generalized Langevin”) paradigm. The footprint given by Langevin models differs distinctly from that given by the random displacement model (i.e. zeroth-order Lagrangian stochastic model) corresponding to its “diffusion limit,” which implies that a well-founded theory of the flux footprint must incorporate the turbulent velocity autocovariance. But irrespective of the choice of the eddy diffusion or Langevin class of model as basis for the footprint, tuning relative to observations is ultimately necessary. Some earlier treatments assume Monin–Obukhov profiles for the mean wind and eddy diffusivity and that the effective Schmidt number (ratio of eddy viscosity to the tracer eddy diffusivity) in the neutral limit \(S_c(0)=1\), while others calibrate the model to the Project Prairie Grass dispersion trials. Because there remains uncertainty as to the optimal specification of \(S_c\) (or a related parameter in alternative theories, e.g. the Kolmogorov coefficient \(C_0\) in Langevin models) it is recommended that footprint models should be explicit in this regard.

Stochastic Analysis of Hyperslab-Based Adaptive Projected Subgradient Method Under Bounded Noise

This letter establishes a novel analysis of the Adaptive Projected Subgradient Method (APSM) in the intersection of the stochastic and robust estimation paradigms. Utilizing classical worst-case bounds on the noise process, drawn from the robust estimation methodology, the present study demonstrates that the hyperslab-inspired version of the APSM generates a sequence of estimates which converges to a point located, with probability one, arbitrarily close to the estimand. Numerical tests and comparisons with classical time-adaptive algorithms corroborate the theoretical findings of the study.

Some Aspects on Filter Design for Target Tracking

Tracking filter design is discussed. It is argued that the basis of the present stochastic paradigm is questionable. White process noise is not adequate as a model for target manoeuvring, stochastic least-square optimality is not relevant or required in practice, the fact that requirements are necessary for design is ignored, and root mean square (RMS) errors are insufficient as performance measure. It is argued that there is no process noise and that the covariance of the assumed process noise contains the design parameters. Focus is on the basic tracking filter, the Kalman filter, which is convenient for clarity and simplicity, but the arguments and conclusions are relevant in general. For design the possibility of an observer transfer function approach is pointed out. The issues can also be considered as a consequence of the fact that there is a difference between estimation and design. The α-β filter is used for illustration.

Monte carlo simulation of bacterial disinfection: Nonlinear and time-explicit intensity of transition

Bacteria being disinfected in fluid media are discrete entities and mesoscopic in size; moreover, they are incessantly as well as irregularly in motion and in collision among themselves or with the surrounding solid surfaces. As such, it is highly likely that some of the attributes of the bacterial population, for example, their number concentration, will fluctuate randomly. This is especially the case at the tail-end of disinfection when the population of bacteria is sparse. It might be effectual, therefore, to explore the resultant random fluctuations via a stochastic paradigm. Proposed herein is a Markovian stochastic model for the rate of bacterial disinfection, whose intensity of transition takes into account the contact time of the bacteria with the disinfecting agent to eliminate any given percentage of the bacteria in terms of a nonlinear function of time. The model's master equation has been simulated by resorting to the Monte Carlo method to circumvent the undue complexities in solving it analytically or numerically via conventional numerical techniques. For illustration, the mean, the variance (standard deviation), and the coefficient of variation of the number concentration of bacteria during disinfection have been estimated through Monte Carlo simulation. The results of simulation compare favorably with the available experimental data as well as with those computed from the corresponding deterministic model.

Multi-year predictability in a coupled general circulation model

Multi-year to decadal variability in a 100-year integration of a BMRC coupled atmosphere-ocean general circulation model (CGCM) is examined. The fractional contribution made by the decadal component generally increases with depth and latitude away from surface waters in the equatorial Indo-Pacific Ocean. The relative importance of decadal variability is enhanced in off-equatorial “wings” in the subtropical eastern Pacific. The model and observations exhibit “ENSO-like” decadal patterns. Analytic results are derived, which show that the patterns can, in theory, occur in the absence of any predictability beyond ENSO time-scales. In practice, however, modification to this stochastic view is needed to account for robust differences between ENSO-like decadal patterns and their interannual counterparts. An analysis of variability in the CGCM, a wind-forced shallow water model, and a simple mixed layer model together with existing and new theoretical results are used to improve upon this stochastic paradigm and to provide a new theory for the origin of decadal ENSO-like patterns like the Interdecadal Pacific Oscillation and Pacific Decadal Oscillation. In this theory, ENSO-driven wind-stress variability forces internal equatorially-trapped Kelvin waves that propagate towards the eastern boundary. Kelvin waves can excite reflected internal westward propagating equatorially-trapped Rossby waves (RWs) and coastally-trapped waves (CTWs). CTWs have no impact on the off-equatorial sub-surface ocean outside the coastal wave guide, whereas the RWs do. If the frequency of the incident wave is too high, then only CTWs are excited. At lower frequencies, both CTWs and RWs can be excited. The lower the frequency, the greater the fraction of energy transmitted to RWs. This lowers the characteristic frequency (reddens the spectrum) of variability off the equator relative to its equatorial counterpart. At low frequencies, dissipation acts as an additional low pass filter that becomes more effective, as latitude increases. At the same time, ENSO-driven off-equatorial surface heating anomalies drive mixed layer temperature responses in both hemispheres. Both the eastern boundary interactions and the accumulation of surface heat fluxes by the surface mixed layer act to low pass filter the ENSO-forcing. The resulting off-equatorial variability is therefore more coherent with low pass filtered (decadal) ENSO indices [e.g. NINO3 sea-surface temperature (SST)] than with unfiltered ENSO indices. Consequently large correlations between variability and NINO3 extend further poleward on decadal time-scales than they do on interannual time-scales. This explains why decadal ENSO-like patterns have a broader meridional structure than their interannual counterparts. This difference in appearance can occur even if ENSO indices do not have any predictability beyond interannual time-scales. The wings around 15–20°S, and sub-surface variability at many other locations are predictable on interannual and multi-year time-scales. This includes westward propagating internal RWs within about 25° of the equator. The slowest of these take up to 4 years to reach the western boundary. This sub-surface predictability has significant oceanographic interest. However, it is linked to only low levels of SST variability. Consequently, extrapolation of delayed action oscillator theory to decadal time-scales might not be justified.

An algorithmic synthesis of the deterministic and stochastic paradigms via computer intensive methods

In this paper, an approach to synthesizing the deterministic and stochastic paradigms, via computer intensive methods, is presented within the framework of a stochastic model of a HIV/AIDS epidemic in a population of homosexuals. Because of dependence among members of a population, the problem of determining threshold conditions was approached by systematically embedding a system of differential equations in a stochastic process and determining if the Jacobian matrix of this system is stable or not stable, when evaluated at a disease free equilibrium. It has been shown in numerous Monte Carlo simulation experiments that if this matrix is not stable, then an epidemic will develop in a population with positive probability, following the introduction of infectives into a population of susceptibles. This technique was used to search for points in the parameter space such that an epidemic would develop in a population of susceptibles, following the entrance of one or more infectious recruits during any time interval with small probability. Such recurrent rare events are of interest in the studying the emergence of new diseases, involving the transmission of a virus from a species that has evolved resistance to it to another species that lacks resistance.

Instantaneous Phase and Amplitude Correlation in the Solar Cycle

In the present study we address the issue of discerning between deterministic and stochastic paradigms in order to understand the behavior of the solar cycle. To this end we show the degree of correlation between the instantaneous amplitude and frequency in the sunspot number time series by the use of the Gabor analytic signal. We compare this correlation with those arising from two theoretical models: (a) the Barnes model of widespread use in the literature and (b) a spatial truncation of the MHD equations. We show that comparisons between the correlation observed in the sunspot time series with those arising from theoretical models can be used to refute one of the models.