A sequential refinement approach for parameter optimization in continuous dynamic models

In this article, a mathematical model of controlling the system in conditions of fuzzy processes is presented. Such a system can also be a power supply system. Analytical approaches that can be used to describe the mutual impact of output and stocks (additional capacities) on hierarchically distributed occurrence/usage/variation or demand already exist. We add dynamics to the system with the use of continuous and discrete dynamic processes, which are of a random (stochastic) form. The dynamic discrete model of control for this system is built with a system of difference equations, and the dynamic continuous model is built with a system of differential equations. These systems of equations can be solved with a one-part z-transform in discrete situations in with Laplace transform in the continuous systems. Fuzzy system control follows a continuous and discrete stochastic mathematical closed-loop model of control of stocks (additional capacities) in production systems. The fuzzy model is demonstrated with a numerical example.

Chapter 47 is a brief outline of a paper presented at a meeting at Nuffield College, Oxford in 1962. It refers to chapter 48 for details of proposed methods of estimating the parameters of continuous time dynamic models from observations of the variables at equispaced points of time. Chapter 48 is a sequel to chapter 42, an important and influential essay which Phillips had published in Biometrika in 1959.

Introduction The previous four chapters emphasized the advantages of using discrete mass mathematicaxsl models wherein both the structural mass and the nonstructural mass is “lumped” at selected (usually a relatively few) finite element nodes or at short distances from those finite element nodes. The alternative in mass modeling is the seemingly more realistic mathematical model where the mass is distributed throughout each structural element. Such distributed or continuous mass models are not nearly as useful as discrete mass models. However, continuous mass models do have enough instructional value and occasional engineering value that they cannot be wholly ignored. Their instructional value resides in (i) seeing the results of dealing with what is essentially an infinite DOF system; (ii) the reinforcement, and perhaps deeper understanding, obtained through repetition of the same analysis procedures used with discrete mass systems in a different context; and (iii) discovering the very few types of structures which can be usefully described by this much more concise type of modeling. Therefore the purpose of this chapter is to discuss some of those situations where the use of continuous mass models is of some, albeit small, value in the study of structural dynamics. Again, continuous mass models are practical only in quite restricted circumstances. All cases examined here are limited to structures that are modeled as a single structural element (e.g., one beam or one plate).

In the theoretical part of this article, we provide a brief introduction to differenttypes of repeated measure designs and methods to analyze repeatedly measured data, with aparticular focus on continuous time modelling of intensive longitudinal data (ILD) withN≥1 analysis. We built on the distinction betweenwithin-person versus between-person effects, and how this is addressed in static versusdynamic models. Further, we elaborate on the distinction between discrete time dynamicmodels versus continuous time dynamic models. In particular, we deal with continuous timestructural equation models (CTSEM), and we provide a brief introduction into theunderlying math. Since smart devices have become useful tools in monitoring health, we usethe applied part of this article for explaining how to retrieveN=1 bivariate ILD from popular smart watches and how toprepare them for CTSEM (including N>1 multivariateextensions). We show how to specify a cross-lagged panel CTSEM using the R package ctsem,how to fit the specified model to the retrieved data, and how to interpret the results.Limitations of CTSEM are discussed, too. Monitoring and forecasting industrial healthrepresent important issues for organizations.

In this paper, we discuss the models of continuous dynamics on the 2-simplex that arise when different qualitative restrictions are imposed on the (continuous) functions that generate the dynamics on the 2-simplex. We consider three types of qualitative restrictions: inequality (or set-theoretical) conditions, monotonicity/curvature (or differential-geometrical) conditions, and topological conditions (referring to (transversal) non-(self-)intersection of trajectories). We discuss the implications of these restrictions for transitional and limit dynamics on the 2-simplex and the wide range of potential and existing applications of the resulting system-theoretical models in economics and, in particular, in economic growth and development theory.

Stacked self-attention models receive widespread attention, due to its ability of capturing global dependency among words. However, the stacking of many layers and components generates huge parameters, leading to low parameter efficiency. In response to this issue, we propose a lightweight architecture named Continuous Self-Attention models with neural ODE networks (CSAODE). In CSAODE, continuous dynamical models (i.e., neural ODEs) are coupled with our proposed self-attention block to form a self-attention ODE solver. This solver continuously calculates and optimizes the hidden states via only one layer of parameters to improve the parameter efficiency. In addition, we design a novel accelerated continuous dynamical model to reduce computing costs, and integrate it in CSAODE. Moreover, since the original self-attention ignores local information, CSAODE makes use of N-gram convolution to encode local representations, and a fusion layer with only two trainable scalars are designed for generating sentence vectors. We perform a series of experiments on text classification, neural language inference (NLI) and text matching tasks. With fewer parameters, CSAODE outperforms state-of-the-art models on text classification tasks (e.g., 1.3% accuracy improved on SUBJ task), and has competitive performances for NLI and text matching tasks as well.

Pluralistic ignorance, a well-documented socio-psychological conformity phenomenon, involves discrepancies between private attitude and public opinion in certain social contexts. However, continuous opinion dynamics models based on a bounded confidence assumption fail to accurately model pluralistic ignorance because they do not address scenarios in which non-conformists do not need to worry about holding and expressing conflicting opinions. Such scenarios reduce the power of continuous opinion dynamics models to explain why certain groups doubt or change their opinions in response to minority views. To simulate the effects of (a) private acceptance of informational social influence and (b) public compliance with normative social influence on pluralistic ignorance and minority influences, we have created an agent-based simulation model in which attitude and opinion respectively represent an agent's private and expressed thoughts. Results from a series of simulation experiments indicate model validity equal to or exceeding those of existing opinion dynamics models that are also based on the bounded confidence assumption, but with different dynamics and outcomes in terms of collective opinion and attitude. The results also support the use of our proposed model for computational social psychology applications.

Electrode kinetics of porous Ni-3YSZ cermet operated in fuel cell and electrolysis modes for solid oxide cell application

Optimal aggregated control of in- and outflows for a congested area

We introduce an automated, formal, counterexample-based approach to synthesise Barrier Certificates (BC) for the safety verification of continuous and hybrid dynamical models. The approach is underpinned by an inductive framework: this is structured as a sequential loop between a learner, which manipulates a candidate BC structured as a neural network, and a sound verifier, which either certifies the candidate's validity or generates counter-examples to further guide the learner. We compare the approach against state-of-the-art techniques, over polynomial and non-polynomial dynamical models: the outcomes show that we can synthesise sound BCs up to two orders of magnitude faster, with in particular a stark speedup on the verification engine (up to five orders less), whilst needing a far smaller data set (up to three orders less) for the learning part. Beyond improvements over the state of the art, we further challenge the new approach on a hybrid dynamical model and on larger-dimensional models, and showcase the numerical robustness of our algorithms and codebase.

ObjectiveWe demonstrate a new model framework as an innovative approach to more accurately estimate and project prevalence and survival outcomes in oncology.MethodsWe developed an oncology simulation model (OSM) framework that offers a customizable, dynamic simulation model to generate population-level, country-specific estimates of prevalence, incidence of patients progressing from earlier stages (progression-based incidence), and survival in oncology. The framework, a continuous dynamic Markov cohort model, was implemented in Microsoft Excel. The simulation runs continuously through a prespecified calendar time range. Time-varying incidence, treatment patterns, treatment rates, and treatment pathways are specified by year to account for guideline-directed changes in standard of care and real-world trends, as well as newly approved clinical treatments. Patient cohorts transition between defined health states, with transitions informed by progression-free survival and overall survival as reported in published literature.ResultsModel outputs include point prevalence and period prevalence, with options for highly granular prevalence predictions by disease stage, treatment pathway, or time of diagnosis. As a use case, we leveraged the OSM framework to estimate the prevalence of bladder cancer in the United States.ConclusionThe OSM is a robust model that builds upon existing modeling practices to offer an innovative, transparent approach in estimating prevalence, progression-based incidence, and survival for oncologic conditions. The OSM combines and extends the capabilities of other common health-economic modeling approaches to provide a detailed and comprehensive modeling framework to estimate prevalence in oncology using simulation modeling and to assess the impacts of new treatments on prevalence over time.

Convergence in a continuous dynamic queueing model for traffic networks

Nonlinear vibration analysis of piezoelectric bending actuators: Theoretical and experimental studies

Automated guided vehicles (AGVs) in the U-shaped automated container terminal travel longer and more complex paths. The conflicts among AGVs are trickier. The scheduling strategy of the traditional automated container terminal is difficult to be applied to the U-shaped automated container terminal. In order to minimize the handling time of all tasks and avoid AGV conflicts simultaneously in the U-shaped automated container terminal, this paper establishes a hybrid programming model for conflict-free integrated scheduling of quay cranes, AGVs, and double-cantilever rail cranes in the unloading process. It consists of a discrete event dynamic model and a continuous time dynamic model. An improved genetic seagull optimization algorithm (GSOA) is designed. A series of numerical experiments are conducted to verify the effectiveness and the efficiency of the model and the algorithm. The results show that the proposed method can simultaneously realize the AGVs collision avoidance and multi-equipment integrated scheduling optimization in the U-shaped automated container terminal.

Aerosol particles are ubiquitous in Earth's atmosphere, influencing the quality of life through their climatic and health effects and by affecting visibility. In recent years, the formation and growth of nanometer-scale particles have been observed in situ in many different atmospheric environments, including urban plumes, clean Arctic air, the continental boundary layer, and coastal environments. However, as [Kulmala][1] explains in his Perspective, the mechanisms of atmospheric nucleation have not yet been resolved. An interdisciplinary approach involving laboratory experiments, continuous field observations, new theories, and dynamic models will be required to determine which mechanisms dominate in different environments. [1]: http://www.sciencemag.org/cgi/content/full/302/5647/1000