Mathematical modeling

thumb|Adriaen van Ostade, "Analysis" (1666)

description of a system using mathematical concepts and language

growth of quantities at rate proportional to the current amount

system composed of many interacting components

type of mathematical model

first-order nonlinear differential equations, frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey

abstract mathematical model describing the way colors can be represented as tuples of numbers

Simulink is a MATLAB-based graphical programming environment for modeling, simulating and analyzing multidomain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block libraries. It offers tight integration with the rest of the MATLAB environment and can either drive MATLAB or be scripted from it. Simulink is widely used in automatic control and digital signal processing for multidomain simulation and model-based design.

thumb|300px|Figure 1.  The green line represents an overfitted model and the black line represents a regularized model. While the green line best follows the training data, it is too dependent on that data and is likely to have a higher error rate on new unseen data, illustrated by black-outlined dots, compared to the black line. thumb|300x300px|Figure 2.  Noisy (roughly linear) data is fitted to a linear function and a polynomial function. Although the polynomial function is a perfect fit, the linear function can be expected to generalize better: If the two functions were used to ex

study of uncertainty in the output of a mathematical model or system

mathematical term

mathematical model of a system based on the use of a linear operator

exponential growth based on a constant rate

statistics

AMPL (A Mathematical Programming Language) is an algebraic modeling language to describe and solve high-complexity problems for large-scale mathematical computing (e.g. large-scale optimization and scheduling-type problems).

type of mathematical model

Backtesting is a term used in modeling to refer to testing a predictive model on historical data. Backtesting is a type of retrodiction, and a special type of cross-validation applied to previous time period(s). In quantitative finance, backtesting is an important step before deploying algorithmic strategies in live markets.

VisSim is a visual block diagram program for the simulation of dynamical systems and model-based design of embedded systems, with its own visual language. It is developed by Visual Solutions of Westford, Massachusetts. Visual Solutions was acquired by Altair in August 2014 and its products have been rebranded as Altair Embed as a part of Altair's Model Based Development Suite. With Embed, virtual prototypes of dynamic systems can be developed. Models are built by sliding blocks into the work area and wiring them together with the mouse. Embed automatically converts the control diagrams into C-

mathematical model of a complex system, e.g. weather

classical information retrieval model

mathematical field

term

method of making decisions based on insufficient or fuzzy information

how patterns in nature, such as stripes and spots, can arise naturally and autonomously from a homogeneous, uniform state

Darwinian evolution of self-replicating entities within framework of physical chemistry

engineering method used when an outcome of interest cannot be easily directly measured, so a model of the outcome is used instead

type of growth curve model for a time series

Mathematical model

AIMMS (acronym for Advanced Interactive Multidimensional Modeling System) is a prescriptive analytics software company with offices in the Netherlands, United States, and Singapore.

model combining a partly theoretical model with data to complete the model

1952 article by Alan Turing

Autowaves are self-supporting non-linear waves in active media (i.e. those that provide distributed energy sources). The term is generally used in processes where the waves carry relatively low energy, which is necessary for synchronization or switching the active medium.

monitoring volatile organic compounds present in the exhaled breath

In plasma physics, the particle-in-cell (PIC) method refers to a technique used to solve a certain class of partial differential equations. In this method, individual particles (or fluid elements) in a Lagrangian frame are tracked in continuous phase space, whereas moments of the distribution such as densities and currents are computed simultaneously on Eulerian (stationary) mesh points.