Some models are replicas of the physical properties (relative shape, form,
and weight) of the object they represent. Others are physical models but
do not have the same physical appearance as the object of their
representation. A third type of model deals with symbols and numerical
relationships and expressions. Each of these fits within an overall
classification of four main categories: physical models, schematic models,
verbal models, and mathematical models.

- abstract model

Modeling is one of the most powerful tools available for understanding, documenting, and managing the complexity of the infrastructures required to operate the energy system of the future. It is far less expensive to construct a model to test theories or techniques than to construct an actual entity only to find out that one crucial technique is wrong and the entire entity must be re-constructed.Models have been used extensively by many industries as the basis to analyze and design complex systems. The telecommunications industries have made extensive use of modeling to develop the diverse communications infrastructure(s) in widespread use today. Physical models are used in many industries, ranging from airplanes and Mars Landers to circuit breakers and transformers. Building architects use paper models (blueprints) to capture all the complexity in a modern high-rise building. Virtual models are increasingly being used to model even more complex concepts, from weather patterns to cosmology and, of particular interest to IntelliGrid Architecture project, to information management. One can even make a simple abstract model of the IntelliGrid Architecture, see Figure 9 below.

simulation model

A simulation model is a mathematical model of a system or process that includes key inputs which affect it and the corresponding outputs that are affected by it. If the model explicitly includes uncertainty, we refer to it as a Monte Carlo simulation model. For example, it can calculate the impact of uncertain inputs and decisions we make on outcomes that we care about, such as profit and loss, investment returns, environmental consequences, and the like. Such a model can be created by writing code in a programming language, statements in a simulation modeling language, or formulas in a Microsoft Excel spreadsheet. Regardless of how it is expressed, a simulation model will include:**Model**that are uncertain numbers -- we'll call these uncertain variables*inputs*- Intermediate calculations as required
**Model**that depend on the inputs -- we'll call these uncertain functions*outputs*

It's essential to realize that model*outputs*that depend on uncertain*inputs*are uncertain themselves -- hence we talk about**uncertain variables**and**uncertain functions**. When we perform a simulation with this model, we will test many different numeric values for the uncertain variables, and we'll obtain many different numeric values for the uncertain functions. We'll use**statistics**to analyze and summarize all the values for the uncertain functions (and, if we wish, the uncertain variables).- heterogenous model

The homogeneity hypothesis implies that the substitution process ultimately reaches an equilibrium and it is also assumed that the process was already stationary at the very beginning,*i.e.*, at the root of the phylogeny. If the homogeneity and stationarity assumptions were true, equal nucleotide frequencies would be expected in past and present-day sequences. Actually, we can observe discrepancy's in nucleotide frequencies in many real data sets of present species: model assumptions are clearly violated when using real sequences.It has been noticed that sequences of similar composition tend to be grouped together irrespective of their real phylogenetic relationships (Lockhart et al., 1994; Tarrio et al., 2001, see*e.g.*, ). In an attempt to avoid this bias, we developed an**HETEROGENEOUS**model in a Bayesian framework which models coarsely the heterogeneity using a small pool of homogeneous processes. Each branch of the tree ``chooses'' a substitution model among them. The likelihood computation now depends on the position of the root which is why a heterogeneous rooted tree was implemented in*PHASE*(ultrametricity is optional). The composition observed at this root becomes a free parameter of the model (see,*e.g.*, Yang and Roberts, 1995; Galtier and Gouy, 1998).Algorithms developed in*PHASE*are very similar to those implemented in*P4*by Peter Foster.*PHASE*framework might be a bit more general since the full substitution model is allowed vary over the tree. However, you are strongly advised to limit yourself to variation of the composition vector as Foster (2004) did. Unfortunately, we did not have time to implement a way to use a single exchangeability matrix over the whole tree yet. There is a workaround (a bit unsatisfactory): you can start the MCMC chain from a model properly initialized and turn off the perturbation of rate ratios so that they have constant values. Use the same trick to fix the gamma shape parameter and the proportion of invariant sites to a single constant value. (Do not use a +I model with**HETEROGENEOUS**without constraining the proportion of invariant sites to a constant value).*PHASE*is missing an efficient MCMC proposal to modify the position of the root. You are advised to use an outgroup in the**TREE**block to constrain the position of the common ancestor. Remember that this outgroup can also be a monophyletic cluster.

- model building methodology

System performance evaluation techniques are of vital importance in the system design process. As depicted schematically in Figure 1, the selection of the design variables is generally accomplished by an iterative process in which the evaluation of the system cost and performance plays a crucial part.