chaste codegen: automatic CellML to C++ code generation with fixes for singularities and automatically generated Jacobians

Hundreds of different mathematical models have been proposed for describing electrophysiology of various cell types. These models are quite complex (nonlinear systems of typically tens of ODEs and sometimes hundreds of parameters) and software packages such as the Cancer, Heart and Soft Tissue Environment (Chaste) C++ library have been designed to run simulations with these models in isolation or coupled to form a tissue simulation. The complexity of many of these models makes sharing and translating them to new simulation environments difficult. CellML is an XML format that offers a solution to this problem and has been widely-adopted. This paper specifically describes the capabilities of chaste_codegen, a Python-based CellML to C++ converter based on the new cellmlmanip Python library for reading and manipulating CellML models. While chaste_codegen is a Python 3 redevelopment of a previous Python 2 tool (called PyCML) it has some additional new features that this paper describes. Most notably, chaste_codegen has the ability to generate analytic Jacobians without the use of proprietary software, and also to find singularities occurring in equations and automatically generate and apply linear approximations to prevent numerical problems at these points.

Download Full-text

Searching for Analytical Solutions of the (2+1)-Dimensional KP Equation by Two Different Systematic Methods

Complexity ◽

10.1155/2019/9314693 ◽

2019 ◽

Vol 2019 ◽

pp. 1-11 ◽

Cited By ~ 3

Author(s):

Yongyi Gu ◽

Fanning Meng

Keyword(s):

Nonlinear Systems ◽

Exact Solutions ◽

Rational Function ◽

Analytical Solutions ◽

Direct Methods ◽

Expansion Method ◽

Complex Method ◽

Kp Equation ◽

Extended Complex ◽

Complex Nonlinear Systems

In this paper, we derive analytical solutions of the (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation by two different systematic methods. Using the exp⁡(-ψ(z))-expansion method, exact solutions of the mentioned equation including hyperbolic, exponential, trigonometric, and rational function solutions have been obtained. Based on the work of Yuan et al., we proposed the extended complex method to seek exact solutions of the (2+1)-dimensional KP equation. The results demonstrate that the applied methods are efficient and direct methods to solve the complex nonlinear systems.

Download Full-text

Online Health Management for Complex Nonlinear Systems Based on Hidden Semi-Markov Model Using Sequential Monte Carlo Methods

Mathematical Problems in Engineering ◽

10.1155/2012/951584 ◽

2012 ◽

Vol 2012 ◽

pp. 1-22

Author(s):

Qinming Liu ◽

Ming Dong

Keyword(s):

Monte Carlo ◽

Nonlinear System ◽

Nonlinear Systems ◽

Markov Model ◽

Sequential Monte Carlo ◽

Health Management ◽

Health State ◽

Health States ◽

Complex Nonlinear System ◽

Complex Nonlinear Systems

Health management for a complex nonlinear system is becoming more important for condition-based maintenance and minimizing the related risks and costs over its entire life. However, a complex nonlinear system often operates under dynamically operational and environmental conditions, and it subjects to high levels of uncertainty and unpredictability so that effective methods for online health management are still few now. This paper combines hidden semi-Markov model (HSMM) with sequential Monte Carlo (SMC) methods. HSMM is used to obtain the transition probabilities among health states and health state durations of a complex nonlinear system, while the SMC method is adopted to decrease the computational and space complexity, and describe the probability relationships between multiple health states and monitored observations of a complex nonlinear system. This paper proposes a novel method of multisteps ahead health recognition based on joint probability distribution for health management of a complex nonlinear system. Moreover, a new online health prognostic method is developed. A real case study is used to demonstrate the implementation and potential applications of the proposed methods for online health management of complex nonlinear systems.

Download Full-text

Soft tissue myoepithelial carcinoma

Vojnosanitetski pregled ◽

10.2298/vsp0606611s ◽

2006 ◽

Vol 63 (6) ◽

pp. 611-614 ◽

Cited By ~ 6

Author(s):

Zorica Stojsic ◽

Dimitrije Brasanac ◽

Dragoljub Bacetic ◽

Radmila Jankovic ◽

Neda Drndarevic

Keyword(s):

Soft Tissue ◽

Cell Types ◽

Giant Cells ◽

Myoepithelial Cells ◽

High Grade ◽

Myoepithelial Carcinoma ◽

Cytologic Atypia ◽

S 100 ◽

Myxoid Matrix ◽

Subcutaneous Adipose

Background. Myoepitheliomas are tumors composed predominantly or exclusively of myoepithelial cells, usually arising in salivary glands. Cutaneous/soft tissue localization is very rare, especially for the malignant myoepitheliomas. Case report. We presented a case of myoepithelial carcinoma involving subcutaneous adipose tissue of the left forearm in a woman aged 62 years. The tumor was composed of epithelioid and hyaline cell types, arranged in diffuse sheets, nests and loose clusters within hyalinized and myxoid matrix. The neoplasm displayed high-grade cytologic atypia with some cells having pleomorphic, hyperchromatic nuclei, and others showing vesicular nuclei, large nucleoli with scattered bizarre giant cells. High mean mitotic count of 7 mitoses/10 high power fields and extensive necrosis favored the diagnosis of malignancy. Immunohistochemical staining was positive for cytokeratin (AE1/AE3), epithelial membrane antigen, S-100 protein, glial fibrillary acidic protein, and vimentin. Conclusion. Considering the subcutaneous localization, myoepithelial immunophenotype and high-grade cytologic atypia the neoplasm was classified as a soft-tissue myoepithelial carcinoma.

Download Full-text

Application of hybrid asymptotic methods and modern software for mathematical models developing for nonlinear dynamics of structures with variables in time parameters

Innovative Materials and Technologies in Metallurgy and Mechanical Engineering ◽

10.15588/1607-6885-2020-2-9 ◽

2021 ◽

pp. 66-70

Author(s):

S. Homeniuk ◽

S. Grebenyuk ◽

D. Gristchak

Keyword(s):

Nonlinear Dynamics ◽

Numerical Methods ◽

Nonlinear Systems ◽

Analytical Solution ◽

Mathematical Models ◽

Nonlinear Dynamic ◽

Numerical Solutions ◽

Hybrid Approach ◽

Time Dependent ◽

Forced Oscillations

The relevance. The aerospace domain requires studies of mathematical models of nonlinear dynamic structures with time-varying parameters. The aim of the work. To obtain an approximate analytical solution of nonlinear forced oscillations of the designed models with time-dependent parameters. The research methods. A hybrid approach based on perturbation methods, phase integrals, Galorkin orthogonalization criterion is used to obtain solutions. Results. Nonlocal investigation of nonlinear systems behavior is done using results of analytical and numerical methods and developed software. Despite the existence of sufficiently powerful numerical software systems, qualitative analysis of nonlinear systems with variable parameters requires improved mathematical models based on effective analytical, including approximate, solutions, which using numerical methods allow to provide a reliable analysis of the studied structures at the stage designing. An approximate solution in analytical form is obtained with constant coefficients that depend on the initial conditions. Conclusions. The approximate analytical results and direct numerical solutions of the basic equation were compared which showed a sufficient correlation of the obtained analytical solution. The proposed algorithm and program for visualization of a nonlinear dynamic process could be implemented in nonlinear dynamics problems of systems with time-dependent parameters.

Download Full-text

An Optimization Procedure of Model’s Base Construction in Multimodel Representation of Complex Nonlinear Systems

10.5772/intechopen.96458 ◽

2021 ◽

Author(s):

Bennasr Hichem ◽

M’Sahli Faouzi

Keyword(s):

Nonlinear Systems ◽

Learning Algorithm ◽

Batch Reactor ◽

Optimization Procedure ◽

Base Number ◽

Deterministic Approach ◽

Modeling Analysis ◽

Complex Nonlinear Systems ◽

Definition Of ◽

And Control

The multimodel approach is a research subject developed for modeling, analysis and control of complex systems. This approach supposes the definition of a set of simple models forming a model’s library. The number of models and the contribution of their validities is the main issues to consider in the multimodel approach. In this chapter, a new theoretical technique has been developed for this purpose based on a combination of probabilistic approaches with different objective function. First, the number of model is constructed using neural network and fuzzy logic. Indeed, the number of models is determined using frequency-sensitive competitive learning algorithm (FSCL) and the operating clusters are identified using Fuzzy K- means algorithm. Second, the Models’ base number is reduced. Focusing on the use of both two type of validity calculation for each model and a stochastic SVD technique is used to evaluate their contribution and permits the reduction of the Models’ base number. The combination of FSCL algorithms, K-means and the SVD technique for the proposed concept is considered as a deterministic approach discussed in this chapter has the potential to be applied to complex nonlinear systems with dynamic rapid. The recommended approach is implemented, reviewed and compared to academic benchmark and semi-batch reactor, the results in Models’ base reduction is very important witch gives a good performance in modeling.

Download Full-text