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Difference Equations and Recurrece Relations

Visual modeling. Visual modeling is the graphic representation of objects and systems of interest using graphical languages.

Visual modeling

Visual modeling languages may be General-Purpose Modeling (GPM) languages (e.g., UML, Southbeach Notation, IDEF) or Domain-Specific Modeling (DSM) languages (e.g., SysML). They include industry open standards (e.g., UML, SysML), as well as proprietary standards, such as the visual languages associated with VisSim, MATLAB and Simulink, OPNET, and NI Multisim. VisSim is unique in that it provides a royalty-free, downloadable Viewer that lets anyone open and interactively simulate VisSim models. Visual modeling languages are an area of active research that continues to evolve, as evidenced by increasing interest in DSM languages, visual requirements, and visual OWL (Web Ontology Language).[1] See also[edit] References[edit] External links[edit]

Rgraphviz. Bioconductor version: Release (2.14) Interfaces R with the AT and T graphviz library for plotting R graph objects from the graph package.


Author: Jeff Gentry, Li Long, Robert Gentleman, Seth Falcon, Florian Hahne, Deepayan Sarkar, Kasper Daniel Hansen Maintainer: Kasper Daniel Hansen <khansen at> To install this package, start R and enter: source(" biocLite("Rgraphviz") Graphviz. Teacher package: Mathematical Modelling. September 2007 This is the second installment of a new feature in Plus: the teacher package.

Teacher package: Mathematical Modelling

Every issue contains a package bringing together all Plus articles about a particular subject from the UK National Curriculum. Whether you're a student studying the subject, or a teacher teaching it, all relevant Plus articles are available to you at a glance. What do you think? This is the second package in a new series for Plus, and we'd be very pleased to hear what our readers think. Thank you! Plus articles go far beyond the explicit maths taught at school, while still being accessible to someone doing A level maths. Mathematical modelling Mathematics is often called "the language of the universe".

The Plus articles listed below all deal with mathematical modelling. Explicit maths. Models in Science. 1.

Models in Science

Semantics: Models and Representation Models can perform two fundamentally different representational functions. On the one hand, a model can be a representation of a selected part of the world (the ‘target system’). Depending on the nature of the target, such models are either models of phenomena or models of data. On the other hand, a model can represent a theory in the sense that it interprets the laws and axioms of that theory. Mathematical model. Control Systems/Signal Flow Diagrams - Wikibooks, collection of open-content textbooks. Signal Flow Diagrams[edit] Signal Flow Diagrams are another method for visually representing a system.

Control Systems/Signal Flow Diagrams - Wikibooks, collection of open-content textbooks

Signal Flow Diagrams are especially useful, because they allow for particular methods of analysis, such as Mason's Gain Formula. Control theory. The concept of the feedback loop to control the dynamic behavior of the system: this is negative feedback, because the sensed value is subtracted from the desired value to create the error signal, which is amplified by the controller.

Control theory

Extensive use is usually made of a diagrammatic style known as the block diagram. The transfer function, also known as the system function or network function, is a mathematical representation of the relation between the input and output based on the differential equations describing the system. Although a major application of control theory is in control systems engineering, which deals with the design of process control systems for industry, other applications range far beyond this. Graphical Models. By Kevin Murphy, 1998.

Graphical Models

"Graphical models are a marriage between probability theory and graph theory. They provide a natural tool for dealing with two problems that occur throughout applied mathematics and engineering -- uncertainty and complexity -- and in particular they are playing an increasingly important role in the design and analysis of machine learning algorithms.

Fundamental to the idea of a graphical model is the notion of modularity -- a complex system is built by combining simpler parts. Probability theory provides the glue whereby the parts are combined, ensuring that the system as a whole is consistent, and providing ways to interface models to data. The graph theoretic side of graphical models provides both an intuitively appealing interface by which humans can model highly-interacting sets of variables as well as a data structure that lends itself naturally to the design of efficient general-purpose algorithms. This tutorial. gRaphical models in R. Graph algebra (social sciences) Graph algebra is systems-centric modeling tool for the social sciences.

Graph algebra (social sciences)

It was first developed by Sprague, Pzeworski, and Cortes[1] as a hybridized version of engineering plots to describe social phenomena. Jump up ^ Cortés, Fernando, Adam Przeworski, and John Sprague. 1974. Signal-flow graph. A signal-flow graph (SFG) is a special type of block diagram[1]—and directed graph—consisting of nodes and branches.

Signal-flow graph

Its nodes are the variables of a set of linear algebraic relations. An SFG can only represent multiplications and additions. Multiplications are represented by the weights of the branches; additions are represented by multiple branches going into one node. Courtney Brown, Ph.D. Selected Bibliography for Modeling Social Phenomena Abraham, Ralph H. and Christopher D.

Courtney Brown, Ph.D.

Shaw. 1992. Dynamics: The Geometry of Behavior, Second Edition. Redwood City, California: Addison-Wesley. Graph Algebra and Social Theory : SAGE Research Methods Online. Little Green Book Nearly everything that occurs in the universe can be considered a part of some system, and that certainly includes human behavior and, potentially, human attitudes as well. But this does not mean that systems theory, and thus graph algebra, is appropriate for use in all situations. There are many competing approaches to the study of social and political phenomena, and systems theory using graph algebra is only one such approach.

Graph Algebra: Mathematical Modeling with a Systems Approach. From the publisher's description of the book: Graph Algebra: Mathematical Modeling with a Systems Approach introduces a new modeling tool to students and researchers in the social sciences. Derived from engineering literature that uses similar techniques to map electronic circuits and physical systems, graph algebra utilizes a systems approach to modeling that offers social scientists a variety of tools that are both sophisticated and easily applied. Key Features: Designed for readers in the social sciences with minimal mathematical training: In this volume, the author assists readers in developing their own difference and differential equation model specifications. 15595_Chapter_1.pdf (objeto application/pdf)

Systems Analysis for Social Scientists (Comparative studies in behavioral science) (9780471175094): Fernando Cortes, Adam Przeworski, John Sprague. Dynamic Modeling 1: Linear Difference Equations. Dynamic Modeling 2: Our First Substantive Model. (This is the second of a series of ongoing posts on using Graph Algebra in the Social Sciences.) First-order linear difference equations are powerful, yet simple modeling tools. They can provide access to useful substantive insights to real-world phenomena. They can have powerful predictive ability when used appropriately. Additionally, they may be classified in any number of ways in accordance with the parameters by which they are defined. And though they are not immune to any of a host of issues, a thoughtful approach to their application can always yield meaningful information, if not for discussion then for further refinement of the model.

Dynamic Modeling 3: When the first-order difference model doesn’t cut it. Data must be selected carefully. The predictive usefulness of the model is grossly diminished if outliers taint the available data. Figure 1, for instance, shows the Defense spending (as a fraction of the national budget) between 1948 and 1968. Note how the trend curve (as defined by our linear difference model from the last post: see appendix for a fuller description) is a very poor predictor. Whatever is going on here isn’t a first-order process. Courtney Brown, Ph.D. Help! My model fits too well!