Fixed Model Parameters Research Articles

Semianalytical Solution of the Nonlinear Dual-Porosity Flow Model with the Quadratic Pressure Gradient Term

The nonlinear dual-porosity flow model, specifically considering the quadratic pressure gradient term, wellbore storage coefficient, well skin factor, and interporosity flow of matrix to natural fractures, was established for well production in a naturally fractured formation and then solved using a semianalytical method, including Laplace transform and a transformation of the pressure function. Analytical solution of the model in Laplace space was converted to numerical solution in real space using Stehfest numerical inversion. Nonlinear flow process for well production in a naturally fractured formation with different external boundaries was simulated and analyzed using standard pressure curves. Influence of the quadratic pressure gradient coefficient on pressure curves was studied qualitatively and quantitatively in conditions of a group of fixed model parameters. The research results show that the semianalytical modelling method is applicable in simulating the nonlinear dual-porosity flow behavior.

Pulse Energy Optimization in Multipass-Cavity Mode-Locked Femtosecond Lasers

We describe a comprehensive model, which accounts for reflection and clipping losses of notched multipass-cavity (MPC) mode-locked lasers and determines the optimum q-preserving MPC configuration, which maximizes the output pulse energy for a given pump power. In order to make realistic predictions, an initial experimental MPC resonator with negligible clipping losses was built and its power performance was measured in order to determine the values of the fixed model parameters such as the round-trip loss of the short cavity and reflection coefficient of the MPC mirrors. Then, by using these parameters and by taking into account all possible reflection and clipping loss mechanisms, the output pulse energy for various q-preserving configurations was calculated. The simulation results indicated that, a mode-locked Ti 3+ :Sapphire laser based on the optimum MPC configuration should produce 30 nJ of pulse energy with a 3% output coupler at the pump power of 2 W. The experimental setup constructed at the optimum MPC configuration generated nearly transform-limited 74 fs pulses with 33 nJ of output pulse energy, in very good agreement with the model predictions. We believe that the model and the experimental procedure described in this paper should prove very useful in the practical design and optimization of energy-efficient MPC mode-locked lasers.

Estimated cost savings from reducing errors in the preparation of sterile doses of medications.

Preventing intravenous (IV) preparation errors will improve patient safety and reduce costs by an unknown amount. To estimate the financial benefit of robotic preparation of sterile medication doses compared to traditional manual preparation techniques. A probability pathway model based on published rates of errors in the preparation of sterile doses of medications was developed. Literature reports of adverse events were used to project the array of medical outcomes that might result from these errors. These parameters were used as inputs to a customized simulation model that generated a distribution of possible outcomes, their probability, and associated costs. By varying the important parameters across ranges found in published studies, the simulation model produced a range of outcomes for all likely possibilities. Thus it provided a reliable projection of the errors avoided and the cost savings of an automated sterile preparation technology. The average of 1,000 simulations resulted in the prevention of 5,420 medication errors and associated savings of $288,350 per year. The simulation results can be narrowed to specific scenarios by fixing model parameters that are known and allowing the unknown parameters to range across values found in previously published studies. The use of a robotic device can reduce health care costs by preventing errors that can cause adverse drug events.

Gradient Free Parameter Estimation for Hidden Markov Models with Intractable Likelihoods

In this article we focus on Maximum Likelihood estimation (MLE) for the static model parameters of hidden Markov models (HMMs). We will consider the case where one cannot or does not want to compute the conditional likelihood density of the observation given the hidden state because of increased computational complexity or analytical intractability. Instead we will assume that one may obtain samples from this conditional likelihood and hence use approximate Bayesian computation (ABC) approximations of the original HMM. Although these ABC approximations will induce a bias, this can be controlled to arbitrary precision via a positive parameter ϵ, so that the bias decreases with decreasing ϵ. We first establish that when using an ABC approximation of the HMM for a fixed batch of data, then the bias of the resulting log- marginal likelihood and its gradient is no worse than \(\mathcal{O}(n\epsilon)\), where n is the total number of data-points. Therefore, when using gradient methods to perform MLE for the ABC approximation of the HMM, one may expect parameter estimates of reasonable accuracy. To compute an estimate of the unknown and fixed model parameters, we propose a gradient approach based on simultaneous perturbation stochastic approximation (SPSA) and Sequential Monte Carlo (SMC) for the ABC approximation of the HMM. The performance of this method is illustrated using two numerical examples.

A hydrodynamical model for the Fermi-LAT γ-ray light curve of blazar PKS 1510−089

Abstract A physical description of the formation and propagation of working surfaces inside the relativistic jet of the blazar PKS 1510−089 are used to model its γ-ray variability light curve using Fermi-LAT data from 2008 to 2012. The physical model is based on conservation laws of mass and momentum at the working surface as explained by Mendoza et al. (2009). The hydrodynamical description of a working surface is parametrized by the initial velocity and mass injection rate at the base of the jet. We show that periodic variations on the injected velocity profiles are able to account for the observed luminosity, fixing model parameters such as mass ejection rates of the central engine injected at the base of the jet, oscillation frequencies of the flow and maximum Lorentz factors of the bulk flow during a particular burst.

Lee, Cadogan, and Chamberlain: an excellent point . . . But what about that iceberg?

It is an honor to be invited to comment on Nick, John andLaura’s paper. The “formative measurement” theme hasroiled methods literatures across the social sciences.Despite the number of publications on this topic, uncertaintyremains widespread, and Lee et al.’s(2013) paper shouldresolve some of this. I agree with their argument that aMIMIC model does not represent simultaneous “formativemeasurement” and “reflective measurement.” Factor-basedstructural equationmodeling is,indeed, afactor-based meth-od. If the MIMIC model is correct in the population, thenthe variance explained by the set of predictors, plus thevariance of an error term if present, will exactly equal thevariance of the factor which the MIMIC model engenders.Adding another predictor will not change this total variance—but using a different set of factor indicators may wellchange the total variance, demonstrating that the model isabout the factor.Still, I have significant differences with Lee, CadoganandChamberlain’sperspective andrecommendations.Inmyopinion, vague language lies at the root of the problem, somy own prescription would begin with scrapping the terms“construct,”“latent variable,”“reflective measurement,”and “formative measurement” at least as they are currentlyused. Their recommendation regarding fixing weights is afine idea, but our failure to fix model parameters moregenerally points to the failure of decades of published re-search to actually reveal much about the topics of study.Instead of the narrow issue and closely tailored solutionpresented by Lee, Cadogan and Chamberlain, researchersneed to confront the fundamental, unresolved problemswhich lie at the very root of psychological measurement.LanguageIn the course of their discussion, Lee, Cadogan andChamberlain note, “The situation is not helped by the pleth-ora of different terms used in the literature…” Rather thanbeing only an aggravating circumstance, however, vagary oflanguage is one of the most central problems not only in the“formative measurement” literature but across the field ofpsychological measurement. The terms “construct” (Maraunand Gabriel 2013; Rigdon 2012) and “latent variable” (asnoted by Lee et al. 2013; Maraun 1996) both carry multiplemeanings, with the result (and, one sometime suspects, theintent) that thinking is confused and distinctions areobscured.In typical research situations, researchers working withmultiple indicators operate at three levels of abstraction(Rigdon 2012). Researchers typically wish to make inferen-ces at the most abstract level, about the behavior of variableswhich are inherently unobservable but whose existence isimplied by theory. At the least abstract level, researchersmake their inferences on the basis of data, collected byobservation of one sort or another. At the intermediate level,in order to empirically evaluate their inferences, researchersform representations of the abstract variables using theobserved variables. Depending on statistical method, theserepresentations may be common factors, weighted compo-sites, or something else.“Construct” and “latent variable” are used to denote varia-bles at both the most abstract level and at the intermediatelevel. In places, Lee, Cadogan and Chamberlain seem to usethe term “latent variable” in precisely this way, referring toboth conceptual variables and intermediate level representa-tions.Thisblurringofdistinctionshasencouragedresearchersto believe that their empirical representations, at the interme-diatelevel,areequivalenttotheconceptualvariablesstandingatthe highest level of abstraction (Maraun and Gabriel 2013).

A hydrodynamical model for the Fermi-LATγ-ray light curve of blazar PKS 1510-089

A physical description of the formation and propagation of working surfaces inside the relativistic jet of the blazar PKS 1510-089 are used to model its γ -ray variability light curve using Fermi-LAT data from 2008 to 2012. The physical model is based on conservation laws of mass and momentum at the working surface as explained by Mendoza et al. (2009). The hydrodynamical description of a working surface is parametrized by the initial velocity and mass injection rate at the base of the jet. We show that periodic variations on the injected velocity profiles are able to account for the observed luminosity, fixing model parameters such as mass ejection rates of the central engine injected at the base of the jet, oscillation frequencies of the flow and maximum Lorentz factors of the bulk flow during a particular burst.

Dyadic Event Attribution in Social Networks with Mixtures of Hawkes Processes.

In many applications in social network analysis, it is important to model the interactions and infer the influence between pairs of actors, leading to the problem of dyadic event modeling which has attracted increasing interests recently. In this paper we focus on the problem of dyadic event attribution, an important missing data problem in dyadic event modeling where one needs to infer the missing actor-pairs of a subset of dyadic events based on their observed timestamps. Existing works either use fixed model parameters and heuristic rules for event attribution, or assume the dyadic events across actor-pairs are independent. To address those shortcomings we propose a probabilistic model based on mixtures of Hawkes processes that simultaneously tackles event attribution and network parameter inference, taking into consideration the dependency among dyadic events that share at least one actor. We also investigate using additive models to incorporate regularization to avoid overfitting. Our experiments on both synthetic and real-world data sets on international armed conflicts suggest that the proposed new method is capable of significantly improve accuracy when compared with the state-of-the-art for dyadic event attribution.

Solving Pavlov's puzzle: Attentional, associative, and flexible configural mechanisms in classical conditioning

This article introduces a new "real-time" model of classical conditioning that combines attentional, associative, and "flexible" configural mechanisms. In the model, attention to both conditioned (CS) and configural (CN) stimuli are modulated by the novelty detected in the environment. Novelty increases with the unpredicted presence or absence of any CS, unconditioned stimulus (US), or context. Attention regulates the magnitude of the associations CSs and CNs form with other CSs and the US. We incorporate a flexible configural mechanism in which attention to the CN stimuli increases only after the model has unsuccessfully attempted learn input-output combinations with CS-US associations. That is, CSs become associated with the US and other CSs on fewer trials than they do CNs. Because the CSs activate the CNs through unmodifiable connections, a CS can become directly and indirectly (through the CN) associated with the US or other CSs. In order to simulate timing processes, we simply assume that a CS is formed by a temporal spectrum of short-duration CSs that are activated by the nominal CS trace. The model accurately describes 94% of the basic properties of classical conditioning, using fixed model parameters and simulation values in all simulations.

Bifurcation analysis applied to a model of motion integration with a multistable stimulus

A computational study into the motion perception dynamics of a multistable psychophysics stimulus is presented. A diagonally drifting grating viewed through a square aperture is perceived as moving in the actual grating direction or in line with the aperture edges (horizontally or vertically). The different percepts are the product of interplay between ambiguous contour cues and specific terminator cues. We present a dynamical model of motion integration that performs direction selection for such a stimulus and link the different percepts to coexisting steady states of the underlying equations. We apply the powerful tools of bifurcation analysis and numerical continuation to study changes to the model’s solution structure under the variation of parameters. Indeed, we apply these tools in a systematic way, taking into account biological and mathematical constraints, in order to fix model parameters. A region of parameter space is identified for which the model reproduces the qualitative behaviour observed in experiments. The temporal dynamics of motion integration are studied within this region; specifically, the effect of varying the stimulus gain is studied, which allows for qualitative predictions to be made.

Chaotic dynamics as a possible mechanism of rapid change of hippocampal local field activity between theta rhythm and large irregular activity

Here we propose a possible role of chaotic dynamics in the generation of two distinctive rhythm patterns of local field potential of the hippocampus; namely the theta rhythm and large irregular activity (LIA). The basic idea is that the rapid alternation of the state between theta rhythm and LIA can be described as bifurcation of the attractor between limit cycle and chaos. It is well known that the hippocampus has two distinctive states described by the characteristic activity of the local field potential, the theta rhythm and LIA. The theta rhythm is a highly periodic activity thought to play an important role in learning and retrieving process, whereas LIA is a irregular field activity with sharp ripple complex, which is thought to play an important role in the consolidation process of old memories. However, the underlying mechanism of realizing these two distinctive field oscillations embedded in the same network remains unknown. On the other hand, Katori et al. reported that transitions between synchronous and asynchronous oscillatory state can be realized with gap junction-coupled simple conductance-based model neurons [1]. Further, Tsuda et al. reported that model network composed of simple class 1 model neurons connected with gap junctions show both asynchronous chaotic behavior and synchronous behavior with fixed model parameters [2]. Here we model the network of hippocampal interneurons with this model, taking into consideration that the hippocampal interneurons are thought to have gap junctions [3]. We compare the dynamics of the model with in vivo electrophysiological data and show that this model reproduces qualitative characteristics of the experimental data. Moreover, we show that oscillatory ascending activity mimicking the medial septal projection, which is known to project to the hippocampal interneurons and is widely assumed to be the theta rhythm pacemaker, can entrain the model network and change the network state rapidly to synchronized state (see Figure ​Figure1).1). We conduct bifurcation analysis and show how all-synchronized saddle periodic orbit is stabilized to stable periodic orbit by external input. Figure 1 Time evolution of the variables of the model representing the membrane potentials of the neurons (A) and the amplitude of the external current representing the septal inputs to the hippocampus (B).

A model for network server performance and power consumption

We investigate the power consumption of a network server based on a multiclass open queuing network with closed-form solution. The model consists of service stations that represent major subsystems within the server. We also propose a practical methodology for fixing model parameters through a set of simple tests. The resulting model can reasonably predict the power usage trends with respect to workload intensity that can be observed in real computing systems. Supporting experiments provide a cross validation of the model against performance and power measurements obtained on three types of commercial systems.

A mixed-timescale SGS model for thermal field at various Prandtl numbers

A new subgrid-scale (SGS) model for the thermal field is proposed. The model is an extended version of the mixed-timescale (MTS) SGS model for velocity field by Inagaki et al. (2005), which has been confirmed to be a refined SGS model for velocity field suited to engineering-relevant practical large eddy simulation (LES). In the proposed model for the thermal field, a hybrid timescale between the timescales of the velocity and thermal fields is introduced in a manner similar to velocity-field modeling. Thus, the present model dispenses with an ambiguous SGS turbulent Prandtl number, like the dynamic SGS model. In addition, the wall-limiting behavior of turbulence is satisfied, which is not in the original MTS model, by incorporating the wall-damping function for LES based on the Kolmogorov velocity scale proposed by Inagaki et al. (2010). The model performance is tested in plane channel flows at various Prandtl numbers, and the results show that this model gives the ratio of the timescales between the velocity and thermal fields similar to that obtained using the dynamic Smagorinsky model with locally calculated model parameters. It is also shown that the proposed model predicts better mean and fluctuating temperature profiles in cooperation with the revised MTS model for the velocity field, than the Smagorinsky model and the dynamic Smagorinsky model. The present model is constructed with fixed model parameters, so that it does not suffer from computational instability with the dynamic model. Thus, it is expected to be a refined and versatile SGS model suited for practical LES of the thermal field.

STUDY OF $N\bar{N}$ INTERACTION WITH CHANNEL-COUPLING IN CONSTITUENT QUARK MODELS

The nucleon–antinucleon interaction is studied by using resonating-group-method in the framework of two constituent quark models: the chiral quark model and the quark delocalization color screening model, which can give a good description of baryon properties and nucleon–nucleon interaction. The experimental data of proton–antiproton S-wave elastic scattering cross-section can be well reproduced by adjusting properly one-gluon annihilation coupling constant. With the fixed model parameters, a dynamical calculation of all possible S-wave nucleon–antinucleon states with channel-coupling is performed. The calculated results show that the effect of channel-coupling is not strong to form a bound state as indicated by a strong enhancement at threshold of [Formula: see text] in J/ψ radiative decay.

The validation of the dynamic food chain model BURN-POSEIDON on Cs-137 and Sr-90 data of the Dnieper-Bug estuary, Ukraine

The uptake of radioceasium and radiostrontium in biota in dose assessment models is mostly estimated on the basis of Concentration Factors (CF). For accidental releases, the dynamical foodweb model BURN has been implemented in the coastal model POSEIDON (part of the Decision Support System RODOS). BURN can be applied on water bodies with different salinity levels, since in the model the uptake of radioceasium and radiostrontium in phytoplankton is governed by potassium and calcium in the water, which are calculated via the easier-to-obtain parameter salinity. Recently a dataset on radiocaesium and radiostrontium has been collected for various aquatic organisms in the Dnieper-Bug Estuary (DBE) in Ukraine, which enabled model validation with BURN. Considering the limitation of compartment models and the fact BURN is a predictive model, with fixed model parameters, the model results are within a reasonable range with the measurement data. Besides comparison with measurement data, the model calculations were also used to derive values for CF and compared with literature, which gave reasonable results for Cs-137 in fish and molluscs. For Sr-90 however, the calculated values exceeded the levels given in literature, since equilibrium between radionuclides in biota and water is not reached. Longer time periods for the radionuclide flux into the DBE, both from the Dnieper and the Black Sea are required to obtain high quality model results for the years after 1989.

Online EM Algorithm for Hidden Markov Models

Online (also called “recursive” or “adaptive”) estimation of fixed model parameters in hidden Markov models is a topic of much interest in times series modeling. In this work, we propose an online parameter estimation algorithm that combines two key ideas. The first one, which is deeply rooted in the Expectation-Maximization (EM) methodology, consists in reparameterizing the problem using complete-data sufficient statistics. The second ingredient consists in exploiting a purely recursive form of smoothing in HMMs based on an auxiliary recursion. Although the proposed online EM algorithm resembles a classical stochastic approximation (or Robbins–Monro) algorithm, it is sufficiently different to resist conventional analysis of convergence. We thus provide limited results which identify the potential limiting points of the recursion as well as the large-sample behavior of the quantities involved in the algorithm. The performance of the proposed algorithm is numerically evaluated through simulations in the case of a noisily observed Markov chain. In this case, the algorithm reaches estimation results that are comparable to those of the maximum likelihood estimator for large sample sizes. The supplemental material for this article available online includes an appendix with the proofs of Theorem 1 and Corollary 1 stated in Section 4 as well as the MATLAB/OCTAVE code used to implement the algorithm in the case of a noisily observed Markov chain considered in Section 5.

A delay differential model of ENSO variability – Part 2: Phase locking, multiple solutions and dynamics of extrema

Abstract. We consider a highly idealized model for El Niño/Southern Oscillation (ENSO) variability, as introduced in an earlier paper. The model is governed by a delay differential equation for sea-surface temperature T in the Tropical Pacific, and it combines two key mechanisms that participate in ENSO dynamics: delayed negative feedback and seasonal forcing. We perform a theoretical and numerical study of the model in the three-dimensional space of its physically relevant parameters: propagation period τ of oceanic waves across the Tropical Pacific, atmosphere-ocean coupling κ, and strength of seasonal forcing b. Phase locking of model solutions to the periodic forcing is prevalent: the local maxima and minima of the solutions tend to occur at the same position within the seasonal cycle. Such phase locking is a key feature of the observed El Niño (warm) and La Niña (cold) events. The phasing of the extrema within the seasonal cycle depends sensitively on model parameters when forcing is weak. We also study co-existence of multiple solutions for fixed model parameters and describe the basins of attraction of the stable solutions in a one-dimensional space of constant initial model histories.

Adaptive Mixture Modeling Metropolis Methods for Bayesian Analysis of Nonlinear State-Space Models

We describe a strategy for Markov chain Monte Carlo analysis of nonlinear, non-Gaussian state-space models involving batch analysis for inference on dynamic, latent state variables and fixed model parameters. The key innovation is a Metropolis–Hastings method for the time series of state variables based on sequential approximation of filtering and smoothing densities using normal mixtures. These mixtures are propagated through the nonlinearities using an accurate, local mixture approximation method, and we use a regenerating procedure to deal with potential degeneracy of mixture components. This provides accurate, direct approximations to sequential filtering and retrospective smoothing distributions, and hence a useful construction of global Metropolis proposal distributions for simulation of posteriors for the set of states. This analysis is embedded within a Gibbs sampler to include uncertain fixed parameters. We give an example motivated by an application in systems biology. Supplemental materials provide an example based on a stochastic volatility model as well as MATLAB code.

Evaluation of a terrestrial carbon cycle submodel in an Earth system model using networks of eddy covariance observations

Improvement of terrestrial submodels in Earth system models (ESMs) is important to reduce uncertainties in future projections of global carbon cycle and climate. Since these submodels lack detailed validation, evaluation of terrestrial submodels using networks of field observations is necessary. The purpose of this study is to improve an ESM by refining a terrestrial submodel using eddy covariance observations.We evaluated the terrestrial submodel (MOSES2/TRIFFID) included in the UVic Earth System Climate Model (UVic-ESCM) and tested the effects of terrestrial submodel improvements on future projection of carbon cycle and climate. First, we evaluated the terrestrial submodel as an off-line mode at point scales using 48 eddy covariance observation data, and improved it through fixing model parameters and structures. The terrestrial submodel was improved with the reduction of the root mean square error and the closer simulation of the seasonal carbon fluxes. Second, using the UVic-ESCM with the improved terrestrial submodel, we confirmed model improvement at most observation sites. The terrestrial submodel refinement also affected future projections; the UVic-ESCM with the improved terrestrial submodel simulated 100 ppmv lower atmospheric CO2 concentration in 2100 compared with the default UVic-ESCM. Our study underscores the importance of refinement of terrestrial submodels in ESM simulations.

Synchronization of multi-agent systems without connectivity assumptions

Multi-agent systems arise from diverse fields in natural and artificial systems, such as schooling of fish, flocking of birds, coordination of autonomous agents. In multi-agent systems, a typical and basic situation is the case where each agent has the tendency to behave as other agents do in its neighborhood. Through computer simulations, Vicsek et al. (1995) showed that such a simple local interaction rule can lead to a certain kind of cooperative phenomenon (synchronization) of the overall system, if the initial states are randomly distributed and the size of the system population is large. Since this model is of fundamental importance in understanding the multi-agent systems, it has attracted much research attention in recent years. In this paper, we will present a comprehensive theoretical analysis for this class of multi-agent systems under a random framework with large population, but without imposing any connectivity assumptions as did in almost all of the previous investigations. To be precise, we will show that for any given and fixed model parameters concerning with the interaction radius r and the agents’ moving speed v , the overall system will synchronize as long as the population size n is large enough. Furthermore, to keep the synchronization property as the population size n increases, both r and v can actually be allowed to decrease according to certain scaling rates.