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Widely different time scales are common in systems of chemical reactions and can be exploited to obtain reduced models applicable to the time scales of interest. These reduced models enable more efficient computation and simplify analysis. A classic example is the irreversible enzymatic reaction, for which separation of time scales in a deterministic mass action kinetics model results in approximate rate laws for the slow dynamics, such as that of Michaelis–Menten. Recently, several methods have been developed for separation of slow and fast time scales in chemical master equation (CME) descriptions of stochastic chemical kinetics, yielding separate reduced CMEs for the slow variables and the fast variables. The paper begins by systematizing the preliminary step of identifying slow and fast variables in a chemical system from a specification of the slow and fast reactions in the system. The authors then present an enhanced time-scale-separation method that can extend the validity and improve the accuracy of existing methods by better accounting for slow reactions when equilibrating the fast subsystem. The resulting method is particularly accurate in systems such as enzymatic and protein interaction networks, where the rates of the slow reactions that modify the slow variables are not a function of the slow variables. The authors apply their methodology to the case of an irreversible enzymatic reaction and show that the resulting improvements in accuracy and validity are analogous to those obtained in the deterministic case by using the total quasi-steady-state approximation rather than the classical Michaelis–Menten. The other main contribution of this paper is to show how mass fluctuation kinetics models, which give approximate evolution equations for the means, variances, and covariances of the concentrations in a chemical system, can feed into time-scale-separation methods at a variety of stages. [ABSTRACT FROM AUTHOR]

The intrinsic stochastic effects in chemical reactions, and particularly in biochemical networks, may result in behaviors significantly different from those predicted by deterministic mass action kinetics (MAK). Analyzing stochastic effects, however, is often computationally taxing and complex. The authors describe here the derivation and application of what they term the mass fluctuation kinetics (MFK), a set of deterministic equations to track the means, variances, and covariances of the concentrations of the chemical species in the system. These equations are obtained by approximating the dynamics of the first and second moments of the chemical master equation. Apart from needing knowledge of the system volume, the MFK description requires only the same information used to specify the MAK model, and is not significantly harder to write down or apply. When the effects of fluctuations are negligible, the MFK description typically reduces to MAK. The MFK equations are capable of describing the average behavior of the network substantially better than MAK, because they incorporate the effects of fluctuations on the evolution of the means. They also account for the effects of the means on the evolution of the variances and covariances, to produce quite accurate uncertainty bands around the average behavior. The MFK computations, although approximate, are significantly faster than Monte Carlo methods for computing first and second moments in systems of chemical reactions. They may therefore be used, perhaps along with a few Monte Carlo simulations of sample state trajectories, to efficiently provide a detailed picture of the behavior of a chemical system. [ABSTRACT FROM AUTHOR]

Leveraging the relationship between Wiener filtering and the coherence function, a version of coherence is defined that captures the causal relationship between WSS processes. This causal coherence is interpreted in a modeling context and used to demonstrate what a frequency dependent measure for causality both can and cannot represent. To understand how well frequency dependent causal coherence spectra can be estimated with finite order approximations, the convergence of FIR causal Wiener filters to the full IIR causal Wiener filter is investigated as filter length goes to infinity. The main results prove L p convergence of the frequency responses for p = 1 , 2 , ∞ under certain Hölder continuity conditions on the power spectra, as well as give asymptotic upper bounds for the convergence error. As a corollary, under the same conditions, the uniform convergence of the power spectra of AR approximations is shown as model order goes to infinity. [ABSTRACT FROM AUTHOR]

We develop an approach to quantitative analysis of carbon dioxide concentration in exhaled breath, recorded as a function of time by capnography. The generated waveform—or capnogram—is currently used in clinical practice to establish the presence of respiration as well as determine respiratory rate and end-tidal CO 2 concentration. The capnogram shape also has diagnostic value, but is presently assessed qualitatively, by visual inspection. Prior approaches to quantitatively characterizing the capnogram shape have explored the correlation of various geometric parameters with pulmonary function tests. These studies attempted to characterize the capnogram in normal subjects and patients with cardiopulmonary disease, but no consistent progress was made, and no translation into clinical practice was achieved. We apply automated quantitative analysis to discriminate between chronic obstructive pulmonary disease (COPD) and congestive heart failure (CHF), and between COPD and normal. Capnograms were collected from 30 normal subjects, 56 COPD patients, and 53 CHF patients. We computationally extract four physiologically based capnogram features. Classification on a hold-out test set was performed by an ensemble of classifiers employing quadratic discriminant analysis, designed through cross validation on a labeled training set. Using 80 exhalations of each capnogram record in the test set, performance analysis with bootstrapping yields areas under the receiver operating characteristic (ROC) curve of 0.89 (95% CI: 0.72–0.96) for COPD/CHF classification, and 0.98 (95% CI: 0.82–1.0) for COPD/normal classification. This classification performance is obtained with a run time sufficiently fast for real-time monitoring. [ABSTRACT FROM PUBLISHER]

The joint dynamics of a collection or network of interacting discrete-time automata can often be described by a single Markov chain. In general, however, analyzing such a chain is computationally intractable for even moderately sized networks because of the explosion in the size of the state space. Asavathiratham introduced the influence model (IM) as a framework for overcoming such limitations. The IM imposes constraints on the update behavior of a network of automata, allowing efficient analysis while still permitting interesting global behavior. However, some of the constraints of the IM are unnecessarily restrictive. The generalized IM (GIM) presented here relaxes some restrictions of the IM, thereby permitting more complex behavior without losing many of the attractive properties of the IM and actually enabling simpler proofs of several results. The GIM is explained and illustrated in relation to the IM from a variety of different perspectives, including geometric. Several examples of GIMs are presented. [ABSTRACT FROM PUBLISHER]

Abstract: We outline a class of graph similarity measures that uses the structural similarity of local neighborhoods to derive pairwise similarity scores for the nodes of two different graphs, and present a related similarity measure that uses a linear update to generate both node and edge similarity scores. This measure is then applied to the task of graph matching. [Copyright &y& Elsevier]

A ubiquitous building block of signaling pathways is a cycle of covalent modification (e.g., phosphorylation and dephosphorylation in MAPK cascades). Our paper explores the kind of information processing and filtering that can be accomplished by this simple biochemical circuit. Signaling cycles are particularly known for exhibiting a highly sigmoidal (ultrasensitive) input-output characteristic in a certain steady-state regime. Here, we systematically study the cycle's steady-state behavior and its response to time-varying stimuli. We demonstrate that the cycle can actually operate in four different regimes, each with its specific input-output characteristics. These results are obtained using the total quasi-steady-state approximation, which is more generally valid than the typically used Michaelis-Menten approximation for enzymatic reactions. We invoke experimental data that suggest the possibility of signaling cycles operating in one of the new regimes. We then consider the cycle's dynamic behavior, which has so far been relatively neglected. We demonstrate that the intrinsic architecture of the cycles makes them act-in all four regimes-as tunable low-pass filters, filtering out high-frequency fluctuations or noise in signals and environmental cues. Moreover, the cutoff frequency can be adjusted by the cell. Numerical simulations show that our analytical results hold well even for noise of large amplitude. We suggest that noise filtering and tunability make signaling cycles versatile components of more elaborate cell-signaling pathways. [ABSTRACT FROM AUTHOR]

The article focuses on the solution to matching hats problem using mathematical probability. It is stated that the solution is a good practice with indicator random variables, which takes the value of one when an event has occurred. The said indicator random variables have a special property in which their expected value is simply the probability of the event that occurs. Moreover, the mathematical solution in finding the probability of the given cap that has been matched with its owner is further discussed.

This paper discusses fault tolerance in discrete-time dynamic systems, such as finite-state controllers or computer simulations, with focus on the use of coding techniques to efficiently provide fault tolerance to linear finite-state machines (LFSMs). Unlike traditional fault tolerance schemes, which rely heavily-particularly for dynamic systems operating over extended time horizons-on the assumption that the error-correcting mechanism is fault free, we are interested in the case when all components of the implementation are fault prone. The paper starts with a paradigmatic fault tolerance scheme that systematically adds redundancy into a discrete-time dynamic system in a way that achieves tolerance to transient faults in both the state transition and the error-correcting mechanisms. By combining this methodology with low-complexity error-correcting coding, we then obtain an efficient way of providing fault tolerance to k identical unreliable LFSMs that operate in parallel on distinct input sequences. The overall construction requires only a constant amount of redundant hardware per machine (but sufficiently large k) to achieve an arbitrarily small probability of overall failure for any prespecified (finite) lime interval, leading in this way to a lower bound on the computational capacity of unreliable LFSMs. [ABSTRACT FROM AUTHOR]

Presents information on a study which examined the problem of preserving the perturbation structure of inconsistent linear equations in signal processing when using total least squares solution. System identification example; Discussion on infeasible manifolds; Conclusion.

Examines the subset selection for non-linear least squares parameter estimation and applied the methodology to a test system that has been studied in the power system literature involving the on-line identification of a synchronous general model. Overview of least square estimation and subset selection; Overview of the test system; Results of various estimation experiments on the system.

Presents information on a study which examined some of the issues involved in applying frequency-selective averaging to modeling the dynamic behavior of pulsewidth-modulated (PWM) direct current (dc)-dc converters. Review of the results of frequency-selective averaging and their implications; Presentation of a multifrequency averaged model of the boost converter; Simulations of open-loop behavior.

Focuses on a simple but accurate continuous-time, large-signal dynamic models for a Thyristor-Controlled Series Capacitor. Time-varying fourier coefficients; Fundamental phasor dynamics model; Simplified model; Simulation results; Incorporating line dynamics; Concluding remarks.

Presents a general small-signal stability analysis of paralleled converter systems. How to obtain stable current sharing; Details on how paralleled converters can become unstable; Advantages of paralleling dc/dc converters; Examples of master-slave-current-sharing schemes.

Examines models for current-mode control through the investigation of time-varying effects and averaging issues. Analyzing of the effects of the current-sampling intrinsic to current-mode control.

Objective: We use a single-alveolar-compartment model to describe the partial pressure of carbon dioxide in exhaled breath, as recorded in time-based capnography. Respiratory parameters are estimated using this model, and then related to the clinical status of patients with obstructive lung disease. Methods: Given appropriate assumptions, we derive an analytical solution of the model, describing the exhalation segment of the capnogram. This solution is parametrized by alveolar CO2 concentration, dead-space fraction, and the time constant associated with exhalation. These quantities are estimated from individual capnogram data on a breath-by-breath basis. The model is applied to analyzing datasets from normal (n = 24) and chronic obstructive pulmonary disease (COPD) (n = 22) subjects, as well as from patients undergoing methacholine challenge testing for asthma (n = 22). Results: A classifier based on linear discriminant analysis in logarithmic coordinates, using estimated dead-space fraction and exhalation time constant as features, and trained on data from five normal and five COPD subjects, yielded an area under the receiver operating characteristic curve (AUC) of 0.99 in classifying the remaining 36 subjects as normal or COPD. Bootstrapping with 50 replicas yielded a 95% confidence interval of AUCs from 0.96 to 1.00. For patients undergoing methacholine challenge testing, qualitatively meaningful trends were observed in the parameter variations over the course of the test. Significance: A simple mechanistic model allows estimation of underlying respiratory parameters from the capnogram, and may be applied to diagnosis and monitoring of chronic and reversible obstructive lung disease. [ABSTRACT FROM PUBLISHER]

We develop a sufficient condition for the least-squares measurement (LSM), or the square-root measurement, to minimize the probability of a detection error when distinguishing between a collection of mired quantum states. Using this condition we derive the optimal measurement for state sets with a broad class of symmetries. We first consider geometrically uniform (GU) state sets with a possibly non-Abelian generating group, and show that if the generator satisfies a weighted norm constraint, then the LSM is optimal. In particular, for pure-state GU ensembles, the LSM is shown to be optimal. For arbitrary GU state sets we show that the optimal measurement operators are GU with generator that can be computed very efficiently in polynomial time, within any desired accuracy. We then consider compound GU (CGU) state sets which consist of subsets that are GU. When the generators satisfy a certain constraint, the LSM is again optimal. For arbitrary CGU state sets, the optimal measurement operators are shown to be CGU with generators that can be computed efficiently in polynomial time. [ABSTRACT FROM AUTHOR]

We consider the problem of designing an optimal quantum detector to minimize the probability of a detection error when distinguishing among a collection of quantum states, represented by a set of density operators. We show that the design of the optimal detector can be formulated as a semidefinite programming problem. Based on this formulation, we derive a set of necessary and sufficient conditions for an optimal quantum measurement. We then show that the optimal measurement can be found by solving a standard (convex) semidefinite program. By exploiting the many well-known algorithms for solving semidefinite programs, which are guaranteed to converge to the global optimum, the optimal measurement can be computed very efficiently in polynomial time within any desired accuracy. Using the semidefinite programming formulation, we also show that the rank of each optimal measurement operator is no larger than the rank of the corresponding density operator. In particular, if the quantum state ensemble is a pure-state ensemble consisting of (not necessarily independent) rank-one density operators, then we show that the optimal measurement is a pure-state measurement consisting of rank-one measurement operators. [ABSTRACT FROM AUTHOR]