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Inference methods for the study of interacting biological oscillators in single-cells

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Stochastic differential equation

A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs have many applications throughout pure mathematics and are used to model various behaviours of stochastic models such as stock prices, random growth models or physical systems that are subjected to thermal fluctuations. SDEs have a random differential that is in the most basic case random white noise calculated as the derivative of a Brownian motion or more generally a semimartingale.

Finite element method

The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems).

Julia (programming language)

Julia is a high-level, general-purpose dynamic programming language. Its features are well suited for numerical analysis and computational science. Distinctive aspects of Julia's design include a type system with parametric polymorphism in a dynamic programming language; with multiple dispatch as its core programming paradigm. Julia supports concurrent, (composable) parallel and distributed computing (with or without using MPI or the built-in corresponding to "OpenMP-style" threads), and direct calling of C and Fortran libraries without glue code.

GTK

GTK (formerly GIMP ToolKit and GTK+) is a free and open-source cross-platform widget toolkit for creating graphical user interfaces (GUIs). It is licensed under the terms of the GNU Lesser General Public License, allowing both free and proprietary software to use it. It is one of the most popular toolkits for the Wayland and X11 windowing systems. The GTK team releases new versions on a regular basis. GTK 4 and GTK 3 are maintained, while GTK 2 is end-of-life. GTK1 is independently maintained by the CinePaint project.

SymPy

SymPy is an open-source Python library for symbolic computation. It provides computer algebra capabilities either as a standalone application, as a library to other applications, or live on the web as SymPy Live or SymPy Gamma. SymPy is simple to install and to inspect because it is written entirely in Python with few dependencies. This ease of access combined with a simple and extensible code base in a well known language make SymPy a computer algebra system with a relatively low barrier to entry.

Autonomous agency theory

Autonomous agency theory (AAT) is a viable system theory (VST) which models autonomous social complex adaptive systems. It can be used to model the relationship between an agency and its environment(s), and these may include other interactive agencies. The nature of that interaction is determined by both the agency's external and internal attributes and constraints. Internal attributes may include immanent dynamic "self" processes that drive agency change.

Source–sink dynamics

Source–sink dynamics is a theoretical model used by ecologists to describe how variation in habitat quality may affect the population growth or decline of organisms. Since quality is likely to vary among patches of habitat, it is important to consider how a low quality patch might affect a population. In this model, organisms occupy two patches of habitat. One patch, the source, is a high quality habitat that on average allows the population to increase.

PyQt

PyQt is a Python binding of the cross-platform GUI toolkit Qt, implemented as a Python plug-in. PyQt is free software developed by the British firm Riverbank Computing. It is available under similar terms to Qt versions older than 4.5; this means a variety of licenses including GNU General Public License (GPL) and commercial license, but not the GNU Lesser General Public License (LGPL). PyQt supports Microsoft Windows as well as various kinds of UNIX, including Linux and MacOS (or Darwin).

FLTK

Fast Light Toolkit (FLTK, pronounced fulltick) is a cross-platform widget (graphical control element) library for graphical user interfaces (GUIs), developed by Bill Spitzak and others. Made to accommodate 3D graphics programming, it has an interface to OpenGL, but it is also suitable for general GUI programming. Using its own widget, drawing and event systems abstracted from the underlying system-dependent code, it allows for writing programs which look the same on all supported operating systems.

Inference engine

In the field of artificial intelligence, an inference engine is a component of the system that applies logical rules to the knowledge base to deduce new information. The first inference engines were components of expert systems. The typical expert system consisted of a knowledge base and an inference engine. The knowledge base stored facts about the world. The inference engine applies logical rules to the knowledge base and deduced new knowledge. This process would iterate as each new fact in the knowledge base could trigger additional rules in the inference engine.