Instantaneous Probability Research Articles

Model reduction for stochastic CaMKII reaction kinetics in synapses by graph-constrained correlation dynamics

A stochastic reaction network model of Ca2+ dynamics in synapses (Pepke et al PLoS Comput. Biol. 6 e1000675) is expressed and simulated using rule-based reaction modeling notation in dynamical grammars and in MCell. The model tracks the response of calmodulin and CaMKII to calcium influx in synapses. Data from numerically intensive simulations is used to train a reduced model that, out of sample, correctly predicts the evolution of interaction parameters characterizing the instantaneous probability distribution over molecular states in the much larger fine-scale models. The novel model reduction method, ‘graph-constrained correlation dynamics’, requires a graph of plausible state variables and interactions as input. It parametrically optimizes a set of constant coefficients appearing in differential equations governing the time-varying interaction parameters that determine all correlations between variables in the reduced model at any time slice.

Nanoscopic Characterization of DNA within Hydrophobic Pores: Thermodynamics and Kinetics

The energetic and transport properties of a double-stranded DNA dodecamer encapsulated in hydrophobic carbon nanotubes are probed employing two limiting nanotube diameters, D=4nm and D=3nm, corresponding to (51,0) and (40,0) zig–zag topologies, respectively. It is observed that the thermodynamically spontaneous encapsulation in the 4nm nanopore (ΔG≈–40kJ/mol) is annihilated when the solid diameter narrows down to 3nm, and that the confined DNA termini directly contact the hydrophobic walls with no solvent slab in-between. During the initial moments after confinement (t≤2–3ns), the biomolecule translocates along the nanopore’s inner volume according to Fick’s law (∼t) with a self-diffusion coefficient D=1.713×10−9m2/s, after which molecular diffusion assumes a single-file type mechanism (∼t1/2). As expected, diffusion is anisotropic, with the pore main axis as the preferred direction, but an in-depth analysis shows that the instantaneous velocity probabilities are essentially identical along the x, y and z directions. The 3D velocity histogram shows a maximum probability located at <v>=30.8m/s, twice the observed velocity for a single-stranded three nucleotide DNA encapsulated in comparable armchair geometries (<v>=16.7m/s, D=1.36–1.89nm). Because precise physiological conditions (310K and [NaCl]=134mM) are employed throughout, the present study establishes a landmark for the development of next generation in vivo drug delivery technologies based on carbon nanotubes as encapsulation agents.

Modelling of metal-coating delamination incorporating variable environmental parameters

A mathematical model for metal-coating delamination of degrading metal was developed incorporating multiple variable environmental and physical parameters. Metal-coating delamination not only depends on the electrochemical reactions at metal-coating interface but also on the factors like the type of propagating metal ions and their varying concentration with annual weather changes (summer and winter), time of exposure of the coated objects, type of coated objects, i.e. stationary or mobile vehicles and frequency with which certain vehicles are operating in various environments, e.g. controlled or uncontrolled in terms of environmental conditions. A cutting edge model has been developed to calculate the varying environmental conditions using iteration algorithm, time dependent uncertain position of objects like vehicle in various environments (controlled and uncontrolled) using stochastic approach, effect of seasonal changes (summer and winter) on ionic compounds concentration using algebraic method and instantaneous failure probability due to varying conditions. Based on the developed model, a detailed simulation study was conducted to investigate the metal-coating delamination process and the ways to regress the under coating metal corrosion.

Tracking the sleep onset process: an empirical model of behavioral and physiological dynamics.

The sleep onset process (SOP) is a dynamic process correlated with a multitude of behavioral and physiological markers. A principled analysis of the SOP can serve as a foundation for answering questions of fundamental importance in basic neuroscience and sleep medicine. Unfortunately, current methods for analyzing the SOP fail to account for the overwhelming evidence that the wake/sleep transition is governed by continuous, dynamic physiological processes. Instead, current practices coarsely discretize sleep both in terms of state, where it is viewed as a binary (wake or sleep) process, and in time, where it is viewed as a single time point derived from subjectively scored stages in 30-second epochs, effectively eliminating SOP dynamics from the analysis. These methods also fail to integrate information from both behavioral and physiological data. It is thus imperative to resolve the mismatch between the physiological evidence and analysis methodologies. In this paper, we develop a statistically and physiologically principled dynamic framework and empirical SOP model, combining simultaneously-recorded physiological measurements with behavioral data from a novel breathing task requiring no arousing external sensory stimuli. We fit the model using data from healthy subjects, and estimate the instantaneous probability that a subject is awake during the SOP. The model successfully tracked physiological and behavioral dynamics for individual nights, and significantly outperformed the instantaneous transition models implicit in clinical definitions of sleep onset. Our framework also provides a principled means for cross-subject data alignment as a function of wake probability, allowing us to characterize and compare SOP dynamics across different populations. This analysis enabled us to quantitatively compare the EEG of subjects showing reduced alpha power with the remaining subjects at identical response probabilities. Thus, by incorporating both physiological and behavioral dynamics into our model framework, the dynamics of our analyses can finally match those observed during the SOP.

Research on Aircraft Target Detection Probability for OTHR

In this paper, a simulation method of detection probability of aircraft target for Over-The-Horizon Radar (OTHR) by computer is proposed. The effects of different ionosphere states on detection range for OTHR is concluded, which become constraint on simulation of detection probability. Taking variety of target RCS with attitude during flight through given track into consideration, simulation model of target dynamic RCS is established. Models of instantaneous detection probability and comprehensive detection probability are also presented. Then, detection probability of aircraft can be obtained through utilizing all models above based on given calculation steps. Simulations show that ionosphere state and target RCS have a great influence on detection probability.

Thermostatistics of small nonlinear systems: Gaussian thermal bath.

We discuss the statistical properties of small mechanothermodynamic systems (one- and two-particle cases) subject to nonlinear coupling and in contact with standard Gaussian reservoirs. We use a method that applies averages in the Laplace-Fourier space, which relates to a generalization of the final-value theorem. The key advantage of this method lies in the possibility of eschewing the explicit computation of the propagator, traditionally required in alternative methods like path integral calculations, which is hardly obtainable in the majority of the cases. For one-particle equilibrium systems we are able to compute the instantaneous (equilibrium) probability density functions of injected and dissipated power as well as the respective large deviation functions. Our thorough calculations explicitly show that for such models nonlinearities are irrelevant in the long-term statistics, which preserve the exact same values as computed for linear cases. Actually, we verify that the thermostatistical effect of the nonlinearities is constricted to the transient towards equilibrium, since it affects the average total energy of the system. For the two-particle system we consider each element in contact with a heat reservoir, at different temperatures, and focus on the problem of heat flux between them. Contrarily to the one-particle case, in this steady state nonequilibrium model we prove that the heat flux probability density function reflects the existence of nonlinearities in the system. An important consequence of that it is the temperature dependence of the conductance, which is unobserved in linear(harmonic) models. Our results are complemented by fluctuation relations for the injected power (equilibrium case) and heat flux (nonequilibrium case).

Timing in reward and decision processes

Sensitivity to time, including the time of reward, guides the behaviour of all organisms. Recent research suggests that all major reward structures of the brain process the time of reward occurrence, including midbrain dopamine neurons, striatum, frontal cortex and amygdala. Neuronal reward responses in dopamine neurons, striatum and frontal cortex show temporal discounting of reward value. The prediction error signal of dopamine neurons includes the predicted time of rewards. Neurons in the striatum, frontal cortex and amygdala show responses to reward delivery and activities anticipating rewards that are sensitive to the predicted time of reward and the instantaneous reward probability. Together these data suggest that internal timing processes have several well characterized effects on neuronal reward processing.

Encoding frequency contrast in primate auditory cortex

Changes in amplitude and frequency jointly determine much of the communicative significance of complex acoustic signals, including human speech. We have previously described responses of neurons in the core auditory cortex of awake rhesus macaques to sinusoidal amplitude modulation (SAM) signals. Here we report a complementary study of sinusoidal frequency modulation (SFM) in the same neurons. Responses to SFM were analogous to SAM responses in that changes in multiple parameters defining SFM stimuli (e.g., modulation frequency, modulation depth, carrier frequency) were robustly encoded in the temporal dynamics of the spike trains. For example, changes in the carrier frequency produced highly reproducible changes in shapes of the modulation period histogram, consistent with the notion that the instantaneous probability of discharge mirrors the moment-by-moment spectrum at low modulation rates. The upper limit for phase locking was similar across SAM and SFM within neurons, suggesting shared biophysical constraints on temporal processing. Using spike train classification methods, we found that neural thresholds for modulation depth discrimination are typically far lower than would be predicted from frequency tuning to static tones. This "dynamic hyperacuity" suggests a substantial central enhancement of the neural representation of frequency changes relative to the auditory periphery. Spike timing information was superior to average rate information when discriminating among SFM signals, and even when discriminating among static tones varying in frequency. This finding held even when differences in total spike count across stimuli were normalized, indicating both the primacy and generality of temporal response dynamics in cortical auditory processing.

Reliability analysis of structures with complex limit state functions using probability density evolution method

In reliability-based structural analysis and design optimization, there exist some limit state functions exhibiting disjoint failure domains, multiple design points and discontinuous responses. This study addresses this type of challenging problem of reliability assessment of structures with complex limit state functions based on the probability density evolution method (PDEM). Probability density function (PDF) of stochastic structures under static and dynamic loads can be acquired, which is independent of the specific form of limit state functions. Numerical results of several typical examples illustrate that, the time-invariant and instantaneous PDF curves and failure probabilities of stochastic structures with disjoint failure domains, multiple design points and discontinuous responses are calculated effectively and accurately. Moreover, the PDEM is validated to be more efficient than the Monte Carlo simulation and the subset simulation, and is a feasible and general approach to tackle the reliability analysis of complicated problems. In addition, the influence of random design parameters of structures on uncertainty propagation is also scrutinized.

Dynamic clustering scheme for distributed spectrum sensing in cognitive radio networks

The detection performance of cooperative spectrum sensing in cognitive radio networks is compromised by shadowing, multi-path fading and receiver uncertainty problems when the sensing results are forwarded to the fusion centre. In this paper, we propose a dynamic clustering scheme for a two-level hierarchical cognitive radio network to improve the sensing efficiency. By dynamic optimal clustering of all the cognitive radio users and selection of the user with highest instantaneous channel gain and highest detection probability for making cluster decision, our proposed model exploits spatial diversity and improves local sensing accuracy. Further, our scheme also exploits user selection diversity by forwarding results to the fusion centre using channel with highest instantaneous SNR. Moreover, by dynamic switching in the fusion centre along with forwarding of the censored results, our scheme achieves increased energy efficiency and reduced control channel bandwidth. Furthermore, consideration of fading channels within clusters, makes our scheme more generic than existing works. Performance evaluations evaluate and validate the improved spectrum sensing accuracy and energy efficiency of our proposed scheme compared to the conventional spectrum sensing methods.

A Brain-Machine Interface for Control of Medically-Induced Coma

Medically-induced coma is a drug-induced state of profound brain inactivation and unconsciousness used to treat refractory intracranial hypertension and to manage treatment-resistant epilepsy. The state of coma is achieved by continually monitoring the patient's brain activity with an electroencephalogram (EEG) and manually titrating the anesthetic infusion rate to maintain a specified level of burst suppression, an EEG marker of profound brain inactivation in which bursts of electrical activity alternate with periods of quiescence or suppression. The medical coma is often required for several days. A more rational approach would be to implement a brain-machine interface (BMI) that monitors the EEG and adjusts the anesthetic infusion rate in real time to maintain the specified target level of burst suppression. We used a stochastic control framework to develop a BMI to control medically-induced coma in a rodent model. The BMI controlled an EEG-guided closed-loop infusion of the anesthetic propofol to maintain precisely specified dynamic target levels of burst suppression. We used as the control signal the burst suppression probability (BSP), the brain's instantaneous probability of being in the suppressed state. We characterized the EEG response to propofol using a two-dimensional linear compartment model and estimated the model parameters specific to each animal prior to initiating control. We derived a recursive Bayesian binary filter algorithm to compute the BSP from the EEG and controllers using a linear-quadratic-regulator and a model-predictive control strategy. Both controllers used the estimated BSP as feedback. The BMI accurately controlled burst suppression in individual rodents across dynamic target trajectories, and enabled prompt transitions between target levels while avoiding both undershoot and overshoot. The median performance error for the BMI was 3.6%, the median bias was -1.4% and the overall posterior probability of reliable control was 1 (95% Bayesian credibility interval of [0.87, 1.0]). A BMI can maintain reliable and accurate real-time control of medically-induced coma in a rodent model suggesting this strategy could be applied in patient care.

Design and Research on Video-on-Demand System Mathematical Model Based on Operations

Operations research theory of stochastic service at fast food restaurants, banks, video-on-demand, and web access should be extensive. This paper is a study of the design of its video-on-demand system model. We design and built a specific mathematical model, and analysis of algorithms and test results. We propose video stream control method based on popularity, and the popularity of the program is divided into two types of popular and unpopular, analysis of the system instantaneous transition probability, and designs the popularity of video streaming bandwidth prediction formula. The results show that this method can effectively save server resources, and improve the level of service of video. This queuing analysis method can also be applied in other similar random service system.

A closed-loop anesthetic delivery system for real-time control of burst suppression

Objective. There is growing interest in using closed-loop anesthetic delivery (CLAD) systems to automate control of brain states (sedation, unconsciousness and antinociception) in patients receiving anesthesia care. The accuracy and reliability of these systems can be improved by using as control signals electroencephalogram (EEG) markers for which the neurophysiological links to the anesthetic-induced brain states are well established. Burst suppression, in which bursts of electrical activity alternate with periods of quiescence or suppression, is a well-known, readily discernible EEG marker of profound brain inactivation and unconsciousness. This pattern is commonly maintained when anesthetics are administered to produce a medically-induced coma for cerebral protection in patients suffering from brain injuries or to arrest brain activity in patients having uncontrollable seizures. Although the coma may be required for several hours or days, drug infusion rates are managed inefficiently by manual adjustment. Our objective is to design a CLAD system for burst suppression control to automate management of medically-induced coma. Approach. We establish a CLAD system to control burst suppression consisting of: a two-dimensional linear system model relating the anesthetic brain level to the EEG dynamics; a new control signal, the burst suppression probability (BSP) defining the instantaneous probability of suppression; the BSP filter, a state-space algorithm to estimate the BSP from EEG recordings; a proportional–integral controller; and a system identification procedure to estimate the model and controller parameters. Main results. We demonstrate reliable performance of our system in simulation studies of burst suppression control using both propofol and etomidate in rodent experiments based on Vijn and Sneyd, and in human experiments based on the Schnider pharmacokinetic model for propofol. Using propofol, we further demonstrate that our control system reliably tracks changing target levels of burst suppression in simulated human subjects across different epidemiological profiles. Significance. Our results give new insights into CLAD system design and suggest a control-theory framework to automate second-to-second control of burst suppression for management of medically-induced coma.

Average channel capacity of composite κ-μ/gamma fading channels

A new analytical expression is presented for the instantaneous power Probability Density Function (PDF) of receiver signals over composite κ-μ/gamma fading channels. Moreover, the exact expression of channel capacity is derived in the form of an infinite series, while an accurate approximation expression is obtained in closed form. To reveal the implications of the model parameters on capacity, we provide an expression for the case of a high-SNR environment. The relationship of the presented results with previously reported results on generalised-K and K fading channels is also discussed. Finally, numerical and simulation results are presented to prove the correctness of our derived expressions.

Tobacco smoking among students in an urban area in Northern Italy.

Tobacco smoking, which usually begins in teenage, is one of the most important lifestyle risk factors for chronic diseases and a major public health problem worldwide. The aims of the study were to determine the prevalence of tobacco smoking and the mean age of initiation among adolescents in Genoa (Italy) and to identify some socio-demographic predictors that could be associated with the onset of smoking. 2,301 randomly selected students (14-19 years old) in Genoa completed an ad hoc questionnaire. The Kaplan-Meier method was used to evaluate the instantaneous risk of experimenting with smoking. A multivariate logistic regression model was used to determine whether current or previous smoking status was associated with socio-demographic characteristics. 59.5% of respondents had tried smoking, while 35.6% defined themselves as current smokers. No difference in current smoking prevalence emerged between males and females (35.2% and 35.9%, respectively, p = 0.83). The mean age on initiation was 13.5 years for males and 13.9 years for females. The instantaneous probability of trying smoking changed with age, reaching a maximum at 14 years. Subjects who tried smoking before this age were more inclined to continue smoking. The probability of being a current smoker was significantly higher among students from unmarried-parent families and those attending vocational and technical secondary schools. There is a great need for the activation of new health promotion interventions and enforcement of those already existing, in order to raise awareness of the damage caused by smoking among adolescents, especially those belonging to high-risk groups.

Feedback Power Control with Bit Error Outage Probability QoS Measure on the Rayleigh Fading Channel

We propose to use the probability of instantaneous bit error outage (IBEO) as a new performance measure in the design of an actual feedback power control system. It is defined as the probability that the instantaneous bit error probability (IBEP) exceeds an IBEP threshold. We propose the IBEO-based power control law where the transmitted power is adjusted according to the variations of the channel such that the IBEO probability is kept within some quality of service (QoS)-specified threshold. It ensures that in the long term, no more than a certain fraction of received bits would have IBEP exceeding some IBEP threshold. Therefore, the instantaneous QoS is guaranteed. Based on a practical system model with channel estimation and prediction, we develop the traditional average bit error probability (ABEP)-based power control law and the new IBEO-based power control law. For both laws, we derive explicit ABEP and IBEO probability results. The IBEO-based law shows a remarkable gain over the ABEP-based law in terms of IBEO probability, and sacrifices only a little in the ABEP performance.

LLR-aware smart link-adaptive strategy for decode-and-forward cooperative communication

Error propagation seriously degenerate the diversity order of Decode-and-Forward (DF) cooperative communication. To address this problem, a novel Log Likelihood Ratio (LLR)-based Link Adaptive Relaying (LAR) is proposed to promote adaption accuracy at relay. The instantaneous Bit Error Probability (BEP) is calculated according to the LLR of the received signals firstly, then based on it, the equivalent Signal-to-Noise Ratio (SNR) is employed to operate dynamic power scaling by relay. It is theoretically proved that the full diversity order can be attained by the scheme. Besides, the power sensitivity is also analyzed. Simulation results show that the proposed scheme outperform the conventional LAR and can achieve full diversity order. Moreover, its strong adaptation to SNR fluctuation is validated.

The Impact of Bispectral Index Versus End-Tidal Anesthetic Concentration-Guided Anesthesia on Time to Tracheal Extubation in Fast-Track Cardiac Surgery

Bispectral Index (BIS)-guided anesthesia administration has been reported to reduce the time to tracheal extubation. However, no trials have compared the ability of BIS guidance to promote earlier tracheal extubation relative to guidance by end-tidal anesthetic concentration (ETAC). We hypothesized that BIS-guided anesthesia would result in earlier tracheal extubation compared with ETAC-guided anesthesia in fast-track cardiac surgery patients. This study consisted of patients at a single institution who were enrolled in the larger, multicenter BIS or Anesthesia Gas to Reduce Explicit Recall (BAG-RECALL) clinical trial that compared rates of postoperative awareness for patient whose anesthetic was guided by BIS versus ETAC. Patients undergoing cardiac surgery were randomized to BIS (n = 361) or ETAC (n = 362) guided anesthesia. Volatile anesthetic was titrated either to maintain a BIS value of 40 to 60 (BIS group), or an age-adjusted minimum alveolar concentration of 0.7 to 1.3 (ETAC group). In the ETAC group, anesthesiologists were blinded to the BIS values. In this substudy, time to tracheal extubation was compared between groups. Cox regression identified predictors affecting the instantaneous probability of tracheal extubation. Time to tracheal extubation was not significantly different between groups (odds ratio 1.04, 95% confidence interval, 0.88-1.23, P = 0.643). In addition, group assignment did not influence the instantaneous probability of tracheal extubation (P = 0.433). Predictors decreasing the instantaneous probability of tracheal extubation included higher body mass index (P = 0.001), higher logistic EuroSCORE (P = 0.015), complex surgery type (P = 0.034), and surgery completion in the evening (P = 0.03). Compared with management based on ETAC, anesthetic management based on BIS guidance does not strongly increase the probability of earlier tracheal extubation in patients undergoing fast-track cardiac surgery. The decision to extubate the trachea is more influenced by patient characteristics and perioperative course than the assignment to BIS or ETAC monitoring.

Real-Time Measurement and Closed Loop Control of Burst Suppression for Management of Medical Coma

This talk will provide an overview of recent results on the design of a closed-loop anesthesia delivery (CLAD) system for controlling burst suppression for management of medical coma. I. EXTENDED ABSTRACT Medical coma is a state of profound unconsciousness and brain inactivation induced to treat status epilepticus – unrelenting seizures – and to facilitate recovery following traumatic brain injuries [1], [2]. Typically, an anesthetic drug such as propofol is titrated to achieve a specific clinical target that indicates a coma-like state of large-scale brain inactivation. The standard approach is to monitor the patient’s brain activity with the electroencephalogram (EEG) and use a specified level of burst suppression as an electrophysiological target. Burst suppression is an EEG pattern indicating a state of highly reduced electrical and metabolic activity in the brain defined by periods of high-voltage bursts that alternate with flatline periods termed suppressions [3]. Burst suppression can be controlled systematically, once the state is achieved, as the level of suppression can be increased or decreased by adjusting the infusion rate of the anesthetic. In general, there are no established guidelines for specifying the level of burst suppression. A target level is agreed upon by the intensive care unit staff and control of the level is undertaken by continually monitoring the EEG and manually adjusting the drug infusion rate. A common goal of medical coma is to maintain a stable state of reduced brain activity and metabolism for 12 to 48 hours, a period significantly longer than any human operator can be expected to maintain tight control by visually monitoring the EEG and manually changing the infusion rate of the anesthetic. Defining a precise, quantitative target for the level of burst suppression and designing an automated system for maintaining that level would be a more prudent approach. Automation could be achieved by implementing a closed loop anesthesia delivery system. *This work has been supported by NIH DP1-OD003646 (to ENB), DP2OD006454 (to PLP) and K08-GM094394 (to KS). S.C. holds a Career Award at the Scientific Interface from the Burroughs-Wellcome Fund Department of Anesthesia, Critical Care and Pain Medicine, Massachusetts General Hospital & Harvard Medical School, Boston, MA Department of Brain and Cognitive Science, Massachusetts Institute of Technology, Cambridge, MA Harvard-Massachusetts Institute of Technology Division of Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, MA Institute for Medical Engineering and Sciences, Massachusetts Institute of Technology, Cambridge, MA The essential elements of a CLAD system are: a specific control or target criterion; a means of measuring or estimating the value of the criterion in real time from EEG recordings; and a controller that adjusts the instantaneous dosing of the anesthetic based on the difference between the current value of the criterion and its target value. We present a CLAD system to automatically and precisely control the EEG state of burst suppression and efficiently maintain a medically-induced coma. Specifically, we constructed a CLAD system to control burst suppression reliably and accurately in real-time in both simulation [4] and in a rodent model using EEG and a computer-controlled infusion of propofol [5]. The CLAD system uses a two-compartment pharmacokinetics model to characterize the effect of propofol on the EEG. We introduce the burst suppression probability (BSP) algorithm [6], [7] to compute from the EEG in real time the instantaneous probability of the brain being in a state of suppression. We estimate the parameters of a pharmacokinetics model online and use them to define a proportional-integral (PI) controller. To assess performance of our CLAD system, we establish new statistical criteria to assess reliability and accuracy at individual target levels of burst suppression and a Bayesian statistical approach to assess reliability and accuracy across target levels and animals. We illustrate the application of our CLAD system by demonstrating precise control of burst suppression in individual rats. Finally, we discuss outstanding problems and forthcoming work related to translating the CLAD system for use in human patients.

Safety design of steel beams with time-dependent stability

The expediency of using probability-based approaches in the analysis of rolled and welded steel beams subjected to lateral torsional buckling is discussed. Buckling resisting moments and their mechanical uncertainties for rolled and equivalent welded flanged steel sections as particular members are analyzed. Time-dependent statistics of resisting and bending moments of steel beams is considered and their essential features are determined. Instantaneous and time-dependent survival probabilities of deteriorating and non-deteriorating steel beams in consecutive and cascade levels are also considered. Probabilistic design of steel beams with time-dependent stability is based on the generalized reliability index concept. Differences in design computation results of rolled and welded steel beams under lateral torsional buckling obtained by using the consecutive and cascade approaches are illustrated by a numerical example.