State Space Of Model Research Articles

Computational Analysis of the Hypothalamic Control of Food Intake.

Food-intake control is mediated by a heterogeneous network of different neural subtypes, distributed over various hypothalamic nuclei and other brain structures, in which each subtype can release more than one neurotransmitter or neurohormone. The complexity of the interactions of these subtypes poses a challenge to understanding their specific contributions to food-intake control, and apparent consistencies in the dataset can be contradicted by new findings. For example, the growing consensus that arcuate nucleus neurons expressing Agouti-related peptide (AgRP neurons) promote feeding, while those expressing pro-opiomelanocortin (POMC neurons) suppress feeding, is contradicted by findings that low AgRP neuron activity and high POMC neuron activity can be associated with high levels of food intake. Similarly, the growing consensus that GABAergic neurons in the lateral hypothalamus suppress feeding is contradicted by findings suggesting the opposite. Yet the complexity of the food-intake control network admits many different network behaviors. It is possible that anomalous associations between the responses of certain neural subtypes and feeding are actually consistent with known interactions, but their effect on feeding depends on the responses of the other neural subtypes in the network. We explored this possibility through computational analysis. We made a computer model of the interactions between the hypothalamic and other neural subtypes known to be involved in food-intake control, and optimized its parameters so that model behavior matched observed behavior over an extensive test battery. We then used specialized computational techniques to search the entire model state space, where each state represents a different configuration of the responses of the units (model neural subtypes) in the network. We found that the anomalous associations between the responses of certain hypothalamic neural subtypes and feeding are actually consistent with the known structure of the food-intake control network, and we could specify the ways in which the anomalous configurations differed from the expected ones. By analyzing the temporal relationships between different states we identified the conditions under which the anomalous associations can occur, and these stand as model predictions.

Scalable posterior approximations for large-scale Bayesian inverse problems via likelihood-informed parameter and state reduction

Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or noisy data, the state variation and parameter dependence of the forward model, and correlations in the prior collectively provide useful structure that can be exploited for dimension reduction in this setting--both in the parameter space of the inverse problem and in the state space of the forward model. To this end, we show how to jointly construct low-dimensional subspaces of the parameter space and the state space in order to accelerate the Bayesian solution of the inverse problem. As a byproduct of state dimension reduction, we also show how to identify low-dimensional subspaces of the data in problems with high-dimensional observations. These subspaces enable approximation of the posterior as a product of two factors: (i) a projection of the posterior onto a low-dimensional parameter subspace, wherein the original likelihood is replaced by an approximation involving a reduced model; and (ii) the marginal prior distribution on the high-dimensional complement of the parameter subspace. We present and compare several strategies for constructing these subspaces using only a limited number of forward and adjoint model simulations. The resulting posterior approximations can rapidly be characterized using standard sampling techniques, e.g., Markov chain Monte Carlo. Two numerical examples demonstrate the accuracy and efficiency of our approach: inversion of an integral equation in atmospheric remote sensing, where the data dimension is very high; and the inference of a heterogeneous transmissivity field in a groundwater system, which involves a partial differential equation forward model with high dimensional state and parameters.

Proof Tree Preserving Tree Interpolation

Craig interpolation has a wide range of applications in model checking, verification, and state space abstraction. Recent advances use a more general version of interpolation called tree interpolation. In this paper, we present a method to extract tree interpolants from a proof tree generated by an SMT solver without modifying the proof tree. The framework is general with respect to the theories involved. We instantiate the framework to the combination of the theories of uninterpreted functions and linear arithmetic.

Improving the scalability of formal human–automation interaction verification analyses that use task-analytic models

The enhanced operator function model with communications (EOFMCs) is a task-analytic modeling formalism used for including human behavior in formal models of larger systems. This allows the contribution of human behavior to the safety of the system to be evaluated with model checking. The previous method for translating the EOFMCs into model checker input language was conceptually straightforward, but extremely statespace inefficient. This limited the applications that could be formally verified using EOFMC. In this paper, we present an alternative approach for formally representing EOFMCs that substantially decreases the model's statespace size and verification time. This paper motivates this effort, describes how the improvement was achieved, presents benchmarks demonstrating the improvements in statespace size and verification time, discusses the implications of these results, and outlines directions for future improvement.

Model-Based Diagnosis of Multi-Track Level Crossing Plants

As is witnessed by railway statistics, level crossing (LC) safety has always been one of the major concerns for railway stakeholders. LC safety is an issue at the crossroads between technical aspects, operational procedures, and human factors, making the search for effective solutions a challenging task. This paper deals with technical aspects related to LC safety. In particular, we carry out an analysis pertaining to the diagnosability of two main failure classes that can affect the protection system at automatic LCs. In this paper, a labeled Petri net behavioral model depicting the global system function, including both the normal operation and the faulty behavior, is first established. Petri net has been used as the modeling formalism mainly for its mathematical foundations and expressiveness capabilities. Using such a mathematical notation is highly recommended to deal with dependability issues in safety-critical systems, particularly in railways. Based on the established model, different model-based approaches for the diagnosis of discrete event systems (DESs) will be brought into play to investigate the diagnosability of two considered failure classes, whereas the obtained results will be compared. In particular, a technique that we have established, which is based on on-the-fly and incremental analysis of the model state space, shows interesting efficiency, making it possible to tackle the combinatorial explosion problem, which arises particularly when considering multi-track LCs. The originality of this technique w.r.t. existing DES model-based diagnosis approaches is that, in general, a partial building/investigation of the state space suffices to decide diagnosability and build an online diagnoser. Findings pertaining to LC safety are drawn based on a thorough discussion of the obtained results. In particular, we show how the diagnosability analysis outputs can be taken into account in the global LC risk assessment process.

Robust frequency-domain identification of parametric radiation force models for a floating wind turbine

This paper mainly concerns the hydrodynamic responses prediction of a floating wind turbine. A new frequency-domain identification approach is first proposed to fit a parametric model (state space model) to approximate the convolution term in the Cummins equation of the floating wind turbine. This frequency-domain identification approach consists of finding the vector of parameters that give the best least squares fitting to the frequency responses, and a damped Gauss–Newton algorithm is first proposed to solve this non-linear least squares problem. The damped Gauss–Newton algorithm consists of calculating an increment vector based on the information of residuals and Jacobian values, finding a “fraction” factor by using a line search algorithm, then updating the values of the vector of parameters until the norm of the gradient vector is less than a specific tolerance value. Various kinds of hydrodynamic radiation forces (moments) and motion responses of this floating wind turbine have been calculated. For comparison purpose, the calculation results based on a time-domain identification approach for fitting the state space model are also included in this paper. This time-domain identification approach is based on finding a parametric transfer function of an auto-regressive moving-average (ARMA) filter based on prescribed time domain responses by using Prony׳s method. The accuracy and efficiency of our proposed frequency-domain identification approach have been convincingly substantiated through the comparisons of the calculation results in this article.

Server consolidation for heterogeneous computer clusters using Colored Petri Nets and CPN Tools

In this paper, we present a new approach to server consolidation in heterogeneous computer clusters using Colored Petri Nets (CPNs). Server consolidation aims to reduce energy costs and improve resource utilization by reducing the number of servers necessary to run the existing virtual machines in the cluster. It exploits the emerging technology of live migration which allows migrating virtual machines between servers without stopping their provided services. Server consolidation approaches attempt to find migration plans that aim to minimize the necessary size of the cluster. Our approach finds plans which not only minimize the overall number of used servers, but also minimize the total data migration overhead. The latter objective is not taken into consideration by other approaches and heuristics. We explore the use of CPN Tools in analyzing the state spaces of the CPNs. Since the state space of the CPN model can grow exponentially with the size of the cluster, we examine different techniques to generate and analyze the state space in order to find good plans to server consolidation within acceptable time and computing power.

Modeling and Projecting Mortality. A New Model of Heterogeneity and Selection in Survivorship

The demographic and epidemiological literature offers abundant examples of a range of shortcomings of statistical modeling to describe mortality by sex, age, time/cohort, and cause-of-death. Statistical modeling of mortality operating with implicitly homogenous sub-groupings exposed to mortality risk fails to consider latent biological heterogeneity at the level of individuals, and thereby important biological and social selection of survivorship. Defined on the state space of the simple life model, this study presents a proportional hazard model that makes up for such drawbacks as far as latent biological heterogeneity is concerned. The model describes heterogeneity and selection in individual survivorship by iterative stochastic micro simulation using cohort-based population mortality as an empirical benchmark. The model offers efficient linkage between past assorted mortality, on one hand, and informed anticipation of future heterogeneous survivorship, on the other hand. The combination of stochastic micro-simulation and log-linear modeling of the period effect or trend uncovered under the model makes the new Heterogeneity and Selection Model a powerful analytic and predictive tool of survivorship. Postulating a trend independent of age makes the popular Lee-Carter model (1992) unfit for professional demographic and actuarial use. Moreover, by sweeping latent biological heterogeneity under the rug, mortality analysis and projection based on central rates such as the Lee-Carter model (1992) underrates mortality in the mature and elderly ages. This is demonstrated by comparing current official mortality projections of Sweden, Denmark, and England & Wales to a set of alternative mortality projections under the Heterogeneity and Selection Model.

Discovery of Drug Synergies in Gastric Cancer Cells Predicted by Logical Modeling.

Discovery of efficient anti-cancer drug combinations is a major challenge, since experimental testing of all possible combinations is clearly impossible. Recent efforts to computationally predict drug combination responses retain this experimental search space, as model definitions typically rely on extensive drug perturbation data. We developed a dynamical model representing a cell fate decision network in the AGS gastric cancer cell line, relying on background knowledge extracted from literature and databases. We defined a set of logical equations recapitulating AGS data observed in cells in their baseline proliferative state. Using the modeling software GINsim, model reduction and simulation compression techniques were applied to cope with the vast state space of large logical models and enable simulations of pairwise applications of specific signaling inhibitory chemical substances. Our simulations predicted synergistic growth inhibitory action of five combinations from a total of 21 possible pairs. Four of the predicted synergies were confirmed in AGS cell growth real-time assays, including known effects of combined MEK-AKT or MEK-PI3K inhibitions, along with novel synergistic effects of combined TAK1-AKT or TAK1-PI3K inhibitions. Our strategy reduces the dependence on a priori drug perturbation experimentation for well-characterized signaling networks, by demonstrating that a model predictive of combinatorial drug effects can be inferred from background knowledge on unperturbed and proliferating cancer cells. Our modeling approach can thus contribute to preclinical discovery of efficient anticancer drug combinations, and thereby to development of strategies to tailor treatment to individual cancer patients.

Removing the Computational Burden of Adding Cyclic Variable to Structural Dynamic Models

In this paper, I develop Cyclic Value Function Iteration (CVFI), which is an adjustment to the value function iteration. When using this algorithm, the inclusion of cyclic variables of any size into the state space of an infinite horizon dynamic structural model does not increase the computational complexity of solving for the value function. This result is proven theoretically, and shown to closely hold in practice using Monte Carlo simulations.

Improved Region-Based TCTL Model Checking of Time Petri Nets

The most important challenge in the region-based abstraction method as an approach to compute the state space of time Petri Nets (TPNs) for model checking is that the method results in a huge number of regions, causing a state explosion problem. Thus, region-based abstraction methods are not appropriate for use in developing practical tools. To address this limitation, this paper applies a modification to the basic region abstraction method to be used specially for computing the state space of TPN models, so that the number of regions becomes smaller than that of the situations in which the current methods are applied. The proposed approach is based on the special features of TPN that helps us to construct suitable and small region graphs that preserve the time properties of TPN. To achieve this, we use TPN-TCTL as a timed extension of CTL for specifying a subset of properties in TPN models. Then, for model checking TPN-TCTL properties on TPN models, CTL model checking is used on TPN models by translating TPN-TCTL to the equivalent CTL. Finally, we compare our proposed method with the current region-based abstraction methods proposed for TPN models in terms of the size of the resulting region graph.

Performability Evaluation of Grid Environments Using Stochastic Reward Nets

In this paper, performance of grid computing environment is studied in the presence of failure-repair of the resources. To achieve this, in the first step, each of the grid resource is individually modeled using Stochastic Reward Nets (SRNs), and mean response time of the resource for grid tasks is computed as a performance measure. In individual models, three different scheduling schemes called random selection, non-preemptive priority, and preemptive priority are considered to simultaneously schedule local and grid tasks to the processors of a single resource. In the next step, single resource models are combined to shape an entire grid environment. Since the number of the resources in a large-scale grid environment is more than can be handled using such a monolithic SRN, two approximate SRN models using folding and fixed-point techniques are proposed to evaluate the performance of the whole grid environment. Brouwer’s fixed-point theorem is used to theoretically prove the existence of a solution to the fixed-point approximate model. Numerical results indicate an improvement of several orders of magnitude in the model state space reduction without a significant loss of accuracy.

Comparing different approaches for modeling the vertical motion of the EC 135

Helicopters like the EC 135 with its bearingless main rotor design feature large equivalent hinge offsets of about 10 %, significantly higher than conventional rotor designs and leading to improved maneuverability and agility. For such a helicopter, the fuselage and rotor responses become fully coupled and the quasi-steady assumption using a 6-DoF rigid-body model state space description and approximating the neglected rotor degrees of freedom by equivalent time delays is not suitable. Depending on the intended use of the model, the accurate mathematical description of the vertical motion for these configurations requires an extended model structure that includes inflow and coning dynamics. The paper first presents different modeling approaches and their relationship. Next, identification results for the DLR EC 135 are presented for a model that only describes the vertical motion excluding coupling to the other axes. Here, the differences between the modeling approaches and the respective deficits are explained. Next, the modeling approach most widely used in the rotorcraft identification literature is extended to account for hinge offset. In addition, some model parameters are estimated instead of fixing them at their theoretical predictions which leads to a very good match with EC 135 flight test data. Results for a complete model of the EC 135 including flapping, coning/inflow, and regressive lead–lag are shown as a final result.

A Unified Authentication Scheme Based on Analytic Mechanism

To resolve security issues and management issues of different Certificate Authorities (CAs), this paper proposed a unified authentication scheme, which will make different Certificate Authorities (CAs) be uniformly authenticated. In addition, it showed the whole structure of the scheme, added an extensional registration number to certificates and designed unified authentication process for the scheme. The unified authentication process was modelled and simulated by Coloured Petri Net (CPN) Tools and verified by analyzing the state space of CPN model. In conclusion, this paper provides a unified authentication service and confirms that the proposed scheme is totally controllable, realizable and feasible. The suggested scheme can enhance the efficiency and security of authentication systems and achieve good results in practical applications.

Parametric multisingular hybrid Petri nets: Formal definitions and analysis techniques

Multisingular hybrid Petri net (MSHPN) is an extension of hybrid Petri nets enriched with the capabilities of hybrid automata to achieve the practical expressive power of multisingular hybrid automata. In this paper, we define parametric multisingular hybrid Petri nets (P-MSHPNs), as a parametric extension of MSHPNs. We present the parametric reachability analysis techniques and algorithms and prove that the parametric reachability analysis of P-MSHPNs amounts to the analysis of standard MSHPNs. Once the parametric state space of a P-MSHPNs model is computed, it can either be used for parametric model checking analysis using the existing techniques or be instantiated to obtain non-parametric state spaces. P-MSHPNs models can be analysed to obtain the set of feasible configurations for the system parameters. We also give a method for deriving the set of constraints on the parameters that ensure the correctness of an invariant property and a method for finding the optimum parameter configuration.

Transition-Tempered Metadynamics: Robust, Convergent Metadynamics via On-the-Fly Transition Barrier Estimation.

Well-tempered metadynamics has proven to be a practical and efficient adaptive enhanced sampling method for the computational study of biomolecular and materials systems. However, choosing its tunable parameter can be challenging and requires balancing a trade-off between fast escape from local metastable states and fast convergence of an overall free energy estimate. In this article, we present a new smoothly convergent variant of metadynamics, transition-tempered metadynamics, that removes that trade-off and is more robust to changes in its own single tunable parameter, resulting in substantial speed and accuracy improvements. The new method is specifically designed to study state-to-state transitions in which the states of greatest interest are known ahead of time, but transition mechanisms are not. The design is guided by a picture of adaptive enhanced sampling as a means to increase dynamical connectivity of a model's state space until percolation between all points of interest is reached, and it uses the degree of dynamical percolation to automatically tune the convergence rate. We apply the new method to Brownian dynamics on 48 random 1D surfaces, blocked alanine dipeptide in vacuo, and aqueous myoglobin, finding that transition-tempered metadynamics substantially and reproducibly improves upon well-tempered metadynamics in terms of first barrier crossing rate, convergence rate, and robustness to the choice of tuning parameter. Moreover, the trade-off between first barrier crossing rate and convergence rate is eliminated: the new method drives escape from an initial metastable state as fast as metadynamics without tempering, regardless of tuning.

Topos models for physics and topos theory

What is the role of topos theory in the topos models for quantum theory as used by Isham, Butterfield, Döring, Heunen, Landsman, Spitters, and others? In other words, what is the interplay between physical motivation for the models and the mathematical framework used in these models? Concretely, we show that the presheaf topos model of Butterfield, Isham, and Döring resembles classical physics when viewed from the internal language of the presheaf topos, similar to the copresheaf topos model of Heunen, Landsman, and Spitters. Both the presheaf and copresheaf models provide a “quantum logic” in the form of a complete Heyting algebra. Although these algebras are natural from a topos theoretic stance, we seek a physical interpretation for the logical operations. Finally, we investigate dynamics. In particular, we describe how an automorphism on the operator algebra induces a homeomorphism (or isomorphism of locales) on the associated state spaces of the topos models, and how elementary propositions and truth values transform under the action of this homeomorphism. Also with dynamics the focus is on the internal perspective of the topos.

Reinforcement Learning in an Environment Synthetically Augmented with Digital Pheromones

Reinforcement learning requires information about states, actions, and outcomes as the basis for learning. For many applications, it can be difficult to construct a representative model of the environment, either due to lack of required information or because of that the model's state space may become too large to allow a solution in a reasonable amount of time, using the experience of prior actions. An environment consisting solely of the occurrence or nonoccurrence of specific events attributable to a human actor may appear to lack the necessary structure for the positioning of responding agents in time and space using reinforcement learning. Digital pheromones can be used to synthetically augment such an environment with event sequence information to create a more persistent and measurable imprint on the environment that supports reinforcement learning. We implemented this method and combined it with the ability of agents to learn from actions not taken, a concept known as fictive learning. This approach was tested against the historical sequence of Somali maritime pirate attacks from 2005 to mid-2012, enabling a set of autonomous agents representing naval vessels to successfully respond to an average of 333 of the 899 pirate attacks, outperforming the historical record of 139 successes.

Structure-preserving model reduction of nonlinear building thermal models

This paper proposes an aggregation-based model reduction method for nonlinear models of multi-zone building thermal dynamics. The full-order model, which is already a lumped-parameter approximation, quickly grows in state space dimension as the number of zones increases. An advantage of the proposed method, apart from being applicable to the nonlinear thermal models, is that the reduced model obtained has the same structure and physical intuition as the original model. The key to the methodology is an analogy between a continuous-time Markov chain and the linear part of the thermal dynamics. A recently developed aggregation-based method of Markov chains is employed to aggregate the large state space of the full-order model into a smaller one. Simulations are provided to illustrate tradeoffs between modeling error and computation time.

A practical scheme of the sigma‐point Kalman filter for high‐dimensional systems

AbstractWhile applying a sigma‐point Kalman filter (SPKF) to a high‐dimensional system such as the oceanic general circulation model (OGCM), a major challenge is to reduce its heavy burden of storage memory and costly computation. In this study, we propose a new scheme for SPKF to address these issues. First, a reduced rank SPKF was introduced on the high‐dimensional model state space using the truncated single value decomposition (TSVD) method (T‐SPKF). Second, the relationship of SVDs between the model state space and a low‐dimensional ensemble space is used to construct sigma points on the ensemble space (ET‐SPKF). As such, this new scheme greatly reduces the demand of memory storage and computational cost and makes the SPKF method applicable to high‐dimensional systems. Two numerical models are used to test and validate the ET‐SPKF algorithm. The first model is the 40‐variable Lorenz model, which has been a test bed of new assimilation algorithms. The second model is a realistic OGCM for the assimilation of actual observations, including Argo and in situ observations over the Pacific Ocean. The experiments show that ET‐SPKF is computationally feasible for high‐dimensional systems and capable of precise analyses. In particular, for realistic oceanic assimilations, the ET‐SPKF algorithm can significantly improve oceanic analysis and improve ENSO prediction. A comparison between the ET‐SPKF algorithm and EnKF (ensemble Kalman filter) is also tribally conducted using the OGCM and actual observations.