Résultats de recherche pour « Hybrid Model »

Symmetries are ubiquitous in a wide range of nonlinear systems. Particularly in systems whose dynamics are determined by a Lagrangian or Hamiltonian function. For hybrid systems which possess a continuous-time dynamics determined by a Lagrangian function, with a cyclic variable, the degrees of freedom for the corresponding hybrid Lagrangian system can be reduced by means of a method known as \textit{hybrid Routhian reduction}. In this paper we study sufficient conditions for the existence of periodic orbits in hybrid Routhian systems which also exhibit time-reversal symmetry. Likewise, we explore some stability aspects of such orbits through the characterization of the eigenvalues for the corresponding linearized Poincaré map. Finally, we apply the results to find periodic solutions in underactuated hybrid Routhian control systems.

Abstract Cancer is a complex, multiscale process in which genetic mutations occurring at a subcellular level manifest themselves as functional changes at the cellular and tissue scale. The multiscale nature of cancer requires mathematical modeling approaches that can handle multiple intracellular and extracellular factors acting on different time and space scales. Hybrid models provide a way to integrate both discrete and continuous variables that are used to represent individual cells and concentration or density fields, respectively. Each discrete cell can also be equipped with submodels that drive cell behavior in response to microenvironmental cues. Moreover, the individual cells can interact with one another to form and act as an integrated tissue. Hybrid models form part of a larger class of individual‐based models that can naturally connect with tumor cell biology and allow for the integration of multiple interacting variables both intrinsically and extrinsically and are therefore perfectly suited to a systems biology approach to tumor growth. WIREs Syst Biol Med 2011 3 115–125 DOI: 10.1002/wsbm.102 This article is categorized under: Analytical and Computational Methods > Dynamical Methods Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models

Dynamics of the hybrid systems of aerial cable-ways is investigated. The eigenvalue problems are considered for such hybrid systems with different assumptions. An overview of different methods for eigenvalue problems is given. In the research, the method of the normal fundamental systems is applied, which turns out to be very effective for the considered problems. Changes of dynamical characteristics of the systems depending on the controlled parameter are studied.

We provide explicit closed form expressions for strict Lyapunov functions for time-varying discrete time systems. Our Lyapunov functions are expressed in terms of known nonstrict Lyapunov functions for the dynamics and finite sums of persistency of excitation parameters. This provides a discrete time analog of our previous continuous time Lyapunov function constructions. We also construct explicit strict Lyapunov functions for systems satisfying nonstrict discrete time analogs of the conditions from Matrosov's Theorem. We use our methods to build strict Lyapunov functions for time-varying hybrid systems that contain mixtures of continuous and discrete time evolutions.

PURPOSE: Even though holistic care has been widely discussed in the health care and professional nursing literature, there is no comprehensive definition of it. Therefore, the aim of this article is to present a concept analysis of holistic care which was developed using the hybrid model. METHODS: The hybrid model comprises three phases. In the theoretical phase, characteristics of holistic care were identified through a review of the literature from CINAHL, MEDLINE, PubMed, OVID, and Google Scholar databases. During the fieldwork phase, in-depth interviews were conducted with eight nurses who were purposely selected. Finally, following an analysis of the literature and the qualitative interviews, a theoretical description of the concept of holistic care was extracted. RESULTS: Two main themes were extracted of analytical phase: "Holistic care for offering a comprehensive model for caring" and "holistic care for improving patients' and nurses' conditions." CONCLUSION: By undertaking a conceptual analysis of holistic care, its meaning can be clarified which will encourage nursing educators to include holistic care in nursing syllabi, and consequently facilitate its provision in practice.

The waveform for Blazhko stars can be substantially different during the ascending and descending parts of the Blazhko cycle. A hybrid model, consisting of two component oscillators of the same frequency, is proposed as a means to fit the data over the entire cycle. One component exhibits a sawtooth-like velocity waveform while the other is nearly sinusoidal. One method of generating such a hybrid is presented: a nonlinear model is developed for the first overtone mode, which, if excited to large amplitude, is found to drop strongly in frequency and become highly non-sinusoidal. If the frequency drops sufficiently to become equal to the fundamental frequency, the two can become phase locked and form the desired hybrid. A relationship is assumed between the hybrid mode velocity and the observed light curve, which is approximated as a power series. An accurate fit of the hybrid model is made to actual Kepler data for RR Lyr. The sinusoidal component may tend to stabilize the period of the hybrid which is found in real Blazhko data to be extremely stable. It is proposed that the variations in amplitude and phase might result from a nonlinear interaction with a third mode, possibly a nonradial mode at 3/2 the fundamental frequency. The hybrid model also applies to non-Blazhko RRab stars and provides an explanation for the light curve bump. A method to estimate the surface gravity is also proposed.

Modelling and simulation (M&S) techniques are frequently used in Operations Research (OR) to aid decision-making. With growing complexity of systems to be modelled, an increasing number of studies now apply multiple M&S techniques or hybrid simulation (HS) to represent the underlying system of interest. A parallel but related theme of research is extending the HS approach to include the development of hybrid models (HM). HM extends the M&S discipline by combining theories, methods and tools from across disciplines and applying multidisciplinary, interdisciplinary and transdisciplinary solutions to practice. In the broader OR literature, there are numerous examples of cross-disciplinary approaches in model development. However, within M&S, there is limited evidence of the application of conjoined methods for building HM. Where a stream of such research does exist, the integration of approaches is mostly at a technical level. In this paper, we argue that HM requires cross-disciplinary research engagement and a conceptual framework. The framework will enable the synthesis of discipline-specific methods and techniques, further cross-disciplinary research within the M&S community, and will serve as a transcending framework for the transdisciplinary alignment of M&S research with domain knowledge, hypotheses and theories from diverse disciplines. The framework will support the development of new composable HM methods, tools and applications. Although our framework is built around M&S literature, it is generally applicable to other disciplines, especially those with a computational element. The objective is to motivate a transdisciplinarity-enabling framework that supports the collaboration of research efforts from multiple disciplines, allowing them to grow into transdisciplinary research.

A complex contagion is an infectious process in which individuals may require multiple transmissions before changing state. These are used to model behaviors if an individual only adopts a particular behavior after perceiving a consensus among others. We may think of individuals as beginning inactive and becoming active after contact with a sufficient number of active partners. These have been studied in a number of cases, but analytic models for the dynamic spread of complex contagions are typically complex. Here we study the dynamics of the Watts Threshold Model (WTM) assuming transmission occurs in continuous time as a Poisson process, or in discrete time where individuals transmit to all partners in the time step following their activation. We adapt techniques developed for infectious disease modeling to develop and analyze analytic models for the dynamics of the WTM in Configuration Model networks and a class of random clustered (triangle-based) networks. The resulting model is relatively simple and compact. We use it to gain insights into the contagion dynamics. In the infinite population limit, we derive conditions under which cascades happen with an arbitrarily small initial proportion active, confirming a hypothesis of Watts for this case. We also observe hybrid phase transitions when cascades are not possible for small initial conditions, but occur for large enough initial conditions. We derive sufficient conditions for this hybrid phase transition to occur. We show that in many cases, if the hybrid phase transition occurs, all individuals eventually become active. Finally, we discuss the role clustering plays in facilitating or impeding the spread and find that the hypothesis of Watts that was confirmed in Configuration Model networks does not hold in general. This approach allows us to unify many existing disparate observations and derive new results.

We propose a neural hybrid model consisting of a linear model defined on a set of features computed by a deep, invertible transformation (i.e. a normalizing flow). An attractive property of our model is that both p(features), the density of the features, and p(targets | features), the predictive distribution, can be computed exactly in a single feed-forward pass. We show that our hybrid model, despite the invertibility constraints, achieves similar accuracy to purely predictive models. Moreover the generative component remains a good model of the input features despite the hybrid optimization objective. This offers additional capabilities such as detection of out-of-distribution inputs and enabling semi-supervised learning. The availability of the exact joint density p(targets, features) also allows us to compute many quantities readily, making our hybrid model a useful building block for downstream applications of probabilistic deep learning.