Prism model

Dyer, K.R., and Taylor, P.A. (1973) A simple segmented prism model of tidal mixing in well-mixed estuaries. Estuar. Coastal Shelf Sci. 1, 411—418. 

Analysis of BPMN models extended with stochastic properties has seen limited development with only two approaches identified of dealing with general models which exhibit both probabilistic and non-deterministic transitions. Prandi et al. (Prandi, Quaglia, Zannone 2008) have identified Probabilistic Symbolic Model Checker (PRISM) (Kwiatkowska, Norman, Parker 2011) as ideally suited to the analysis of stochastic PRISM business processes. This effort involves conversion of PRISM models into a model expressed in the Calculus for Orchestration of Web Services (COWS) (Pu iese Tiezzi 2012), which in turn is converted into a model that can be analysed using PRISM (Kwiatkowska, Norman, Parker... 

This approach adds unnecessary complexity in that it is possible to convert the notation of BPMN directly into the PRISM modelling language, and then allow PRISM to impose a semantic interpretation without the additional semantic restrictions of going via COWS. Further, the translations PRISM to COWS and in particular from COWS to PRISM is loosely defined and, in the form described by the authors, not amenable to algorithmic translation. This approach, however, does allow the use of rewards. Consequently, the PRISM model checker is potentially able to perform analysis of both quantitative and stochastic properties of a business process. However, details of how such properties will be included in the original BPMN models is not described. 

Figure 3. Illustration of interleaving semantics imposed by the PRISM model checker (extract of the statespace of the parallel processes of from Fig. 10). 

SBOAT is a Stochastic BPMN Optimisation and Analysis Tool, which allows a user to model, and annotate with rewards and stochastic branching, a business processes as a BPMN BPD. Analysis is specified using a PRISM style PCTL query and depending on the nature of the query one or number of results are calculated. At the core of SBOAT is the PRISM model checker (Kwiatkowska, Norman, Parker 2011) which performs analysis of individual models generated by the SBOAT. An overview of the design of SBOAT is shown in Figure 5. 

In line with PCTL model checking theory, the model checking problem is polynomial in the size of the system statespace S. Furthermore, the translation of BPDs to PRISM models while subject to polynomial growth, constitutes only a... 

In this paper, we propose a safety analysis technique, failure propagation and transformation analysis (FPTA), which follows the direction of FPTC [15]. The FPTA method integrates an automated failure analysis algorithm presented in [15], and it also allows the application of model checking technique as provided by the PRISM model checker [7]. The approach is therefore a probabilistic safety analysis technique for component-based system development. 

Our transformation from the failure model to input used by the PRISM tool is currently carried out manually this can potentially lead to errors in the PRISM input. In our experience, errors are often found by PRISM, but many of these could be avoided with an automated transformation from our failure models to PRISM. We are currently building a tool which is based on om previous work [11]. The idea is that once we model the failure behavLoms of aU components in the system architecture, we then transform the model to PRISM model using model transformation technology. We are also exploring using customised editors to visually represent feedback from PRISM on models of system architecture. 

PRISM (polymer reference interaction-site model) method for modeling homopolymer melts... 

Theliterature contains many publications on self-made magnetic EEL spectrometers [2.182-2.196], and such systems have also been commercially available for many years. Several companies have developed such spectrometers, but the 90° magnetic prisms of the firm Gatan (parallel-detection EELS model 666 and the new Enfma model) are the only ones recently offered for TEM/STEM. Because they can easily be attached to a transmission microscope below its camera chamber, they are widely used. 

Langmuir-Blodgett films (LB) and self assembled monolayers (SAM) deposited on metal surfaces have been studied by SERS spectroscopy in several investigations. For example, mono- and bilayers of phospholipids and cholesterol deposited on a rutile prism with a silver coating have been analyzed in contact with water. The study showed that in these models of biological membranes the second layer modified the fluidity of the first monolayer, and revealed the conformation of the polar head close to the silver [4.300]. 

A third permutation group of the graph of cyclopropane obtains if the regular prism discussed as a model for (a) is subjected to rotations as well as to reflections which leave it invariant. The six vertices are thus subject to a permutation group of order 12. We call it the extended group of the stereoformula. Its cycle index is... 

Mentally divide the cross section of a body into many elementary areas. Correspondingly we can treat the model as a system of many elementary prisms. The dimensions of every elementary cross section are much smaller than the distance between an observation point and any point in this area. 

Figure 7.14 The PRISMA Bobile phase optiaization model showing M the construction of the prism and the selection of selectivity points (Reproduced with permission from ref. 170. Copyright Marcel Dekker, Inc.) ...

Platinum forms a wide variety of clusters and these are of interest as models for metallic platinum surfaces and catalysis on such surfaces. Many of these clusters are based on stacked triangles23,571 or bicapped pentagonal prisms.571 Many smaller clusters are also derived from triplatinum building blocks.16... 

If each polymer is modeled as being composed of N beads (or sites) and the interaction potential between polymers can be written as the sum of site-site interactions, then generalizations of the OZ equation to polymers are possible. One approach is the polymer reference interaction site model (PRISM) theory [90] (based on the RISM theory [91]) which results in a nonlinear integral equation given by... 

The wall-PRISM theory has been extended to multiple site models [95], A simple example of a multiple-site model is a vinyl polymer (e.g., polypropylene) where there are three types of united-atom sites corresponding to CH2, CH, and CH3 groups. Ignoring end effects as before the PRISM equations take the form... 

The wall-PRISM equation has been implemented for a number of hard-chain models including freely jointed [94] and semiflexible [96] tangent hard-sphere chains, freely rotating fused-hard-sphere chains [97], and united atom models of alkanes, isotactic polypropylene, polyisobutylene, and polydimethyl siloxane [95]. In all implementations to date, to my knowledge, the theory has been used exclusively for the stmcture of hard-sphere chains at smooth structureless hard walls. 

For the united atom models of realistic polymers the wall PRISM theory predicts interesting structure near the surface [95]. For example, the side chains are found preferentially in the immediate vicinity of the surface and shield the backbone from the surface. This behavior is expected from entropic considerations. Computer simulations of these systems would be of considerable interest. 

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