Modeling transmission of directly transmitted infectious diseases using colored stochastic Petri nets

In order to improve our understanding of directly transmitted pathogens within host populations, epidemic models should take into account individual heterogeneities as well as stochastic fluctuations in individual parameters. The associated cost results in an increasing level of complexity of the mathematical models which generally lack consistent formalisms. In this paper, we demonstrate that complex epidemic models could be expressed as colored stochastic Petri nets (CSPN). CSPN is a mathematical tool developed in computer science. The concept is based on the Markov Chain theory and on a standard well codified graphical formalism. This approach presents an alternative to other computer simulation methods since it offers both a theoretical formalism and a graphical representation that facilitate the implementation, the understanding and thus the replication or modification of the model. We explain how common concepts of epidemic models--such as the incidence function--can be easily translated into an individual based point of view in the CSPN formalism. We then illustrate this approach by using the well documented susceptible-infected model with recruitment and death.     

Steady state analysis of metabolic pathways using Petri nets

Computer assisted analysis and simulation of biochemical pathways can improve the understanding of the structure and the dynamics of cell processes considerably. The construction and quantitative analysis of kinetic models is often impeded by the lack of reliable data. However, as the topological structure of biochemical systems can be regarded to remain constant in time, a qualitative analysis of a pathway model was shown to be quite promising as it can render a lot of useful knowledge, e. g., about its structural invariants. The topic of this paper are pathways whose substances have reached a dynamic concentration equilibrium (steady state). It is argued that appreciated tools from biochemistry and also low-level Petri nets can yield only part of the desired results, whereas executable high-level net models lead to a number of valuable additional insights by combining symbolic analysis and simulation.     

Structural description of the human eye using Petri nets

Petri nets are a tool for analysing and modelling processes and systems. Here they are used to describe the human visual canal for the first time. A dynamic net describes the formation of a glaucoma.     

Modeling biological systems with uncertain kinetic data using fuzzy continuous Petri nets

Background

Uncertainties exist in many biological systems, which can be classified as random uncertainties and fuzzy uncertainties. The former can usually be dealt with using stochastic methods, while the latter have to be handled with such approaches as fuzzy methods.

Results

In this paper, we focus on a special type of biological systems that can be described using ordinary differential equations or continuous Petri nets (CPNs), but some kinetic parameters are missing or inaccurate. For this, we propose a class of fuzzy continuous Petri nets (FCPNs) by combining CPNs and fuzzy logics. We also present and implement a simulation algorithm for FCPNs, and illustrate our method with the heat shock response system.

Conclusions

This approach can be used to model biological systems where some kinetic parameters are not available or their values vary due to some environmental factors.

     

Modular synthesis of Petri nets for modeling flexible manufacturing systems

This paper proposes a modular Petri net synthesis method for modeling flexible manufacturing systems based on synchronization among control processes of the manufacturing resources (such as robots and machines). In the method, the target system is modeled in a bottom-up and uniform manner by first describing the system's control processes using strongly connected state machines (SCSMs) as the basic modules. Each SCSM may contain multiple tokens to represent resources from the same type such as spaces in a buffer. Next, the common transitions and common transition subnets of the modules are merged to represent their synchronization. The system model constructed is proven to be conservative and thus bounded. Moreover, a restricted class of merged nets is proven to be live and reversible. For general classes of merged nets, this paper shows theorems that easily calculateP-invariants of the final net without solving the linear system equations. TheseP-invariants can be used to help in verifying the model's qualitative properties such as liveness.     

Design of a neurofuzzy controller with simplified architecture

This work presents the design of a neurofuzzy controller with simplified architecture that minimizes the processing time used in several stages associated with systems and processes modelling. The basic procedures of fuzzification and defuzzification are very simplified, whereas the inference procedures are computed in a direct way. The simplified architecture has allowed a fast and easy configuration of the neurofuzzy controller, as consequence, the control rules that define the control actions are obtained automatically. To validate the proposed approach, this neurofuzzy system is used in an industrial application for fluid flow control.     

Modelling and simulation of signal transductions in an apoptosis pathway by using timed Petri nets

This paper first presents basic Petri net components representing molecular interactions and mechanisms of signalling pathways, and introduces a method to construct a Petri net model of a signalling pathway with these components. Then a simulation method of determining the delay time of transitions, by using timed Petri nets — i.e. the time taken in firing of each transition — is proposed based on some simple principles that the number of tokens flowed into a place is equivalent to the number of tokens flowed out. Finally, the availability of proposed method is confirmed by observing signalling transductions in biological pathways through simulation experiments of the apoptosis signalling pathways as an example.     

An insoluble colored substrate for dextranase assay

An assay of dextranase (EC 3.2.1.11) was developed by using Sephadex G-200 coupled with Remazol Brilliant Blue (RBB) as an insoluble substrate. The assay procedure included incubation of suspension of the colored substrate in buffer containing enzyme under study, removal of residual insoluble substrate, and measurement of the absorbance of supernatant fluid containing colored soluble hydrolysis products at 595 nm. The procedure was examined in the screening of dextranase-forming bacilli from the microbial collection of the Institute of Biology, Ufa Research Center, RAS.     

XPN-FMS: A CAD tool for FMS modeling,analysis, animation,and simulation using Petri nets and X window

Flexible Services and Manufacturing Journal - We propose a CAD tool, XPN-FMS, which is primarily based on a unique Petri net (PN) synthesis method, called the knitting technique, developed by the...     

Magnetophoretic position detection for multiplexed immunoassay using colored microspheres in a microchannel

This paper demonstrates a new magnetophoretic position detection method for multiplexed immunoassay using colored microspheres as an encoding tool in a microchannel. Colored microspheres conjugated with respective capture molecules are incubated with a mixture of target analytes, followed by reaction with the probe molecules which had been conjugated with superparamagnetic nanoparticles (SMNPs). Under the magnetic field gradient, the resulting microspheres are deflected from their focused streamlines in a microchannel, and respective colored microspheres are detected using color charge-coupled device (CCD) in a specific detection region of the microchannel. The color and position of respective colored microspheres are automatically decoded and analyzed by MATLAB program, and the position was correlated with the concentration of corresponding target analytes. As a proof-of-concept, we attempted to assay simultaneously three types of biotinylated immunoglobuline Gs (IgGs), such as goat, rabbit and mouse IgGs, using colored microspheres (red, yellow and blue, respectively). As the capture molecules, corresponding anti-IgGs were employed and target analytes were probed using streptavidin-modified superparamagnetic nanoparticles. As a result, three analytes were simultaneously assayed using colored microspheres with high accuracy, and detection limits of goat IgG, rabbit IgG and mouse IgG were estimated to be 10.9, 30.6 and 12.1fM, respectively. In addition, with adjustment of the flow rate and detection zone, the dynamic range could be controlled by more than one order of magnitude.     

Motion planning with complete knowledge using a colored SOM

The motion planning problem requires that a collision-free path be determined for a robot moving amidst a fixed set of obstacles. Most neural network approaches to this problem are for the situation in which only local knowledge about the configuration space is available. The main goal of the paper is to show that neural networks are also suitable tools in situations with complete knowledge of the configuration space. In this paper we present an approach that combines a neural network and deterministic techniques. We define a colored version of Kohonen's self-organizing map that consists of two different classes of nodes. The network is presented with random configurations of the robot and, from this information, it constructs a road map of possible motions in the work space. The map is a growing network, and different nodes are used to approximate boundaries of obstacles and the Voronoi diagram of the obstacles, respectively. In a second phase, the positions of the two kinds of nodes are combined to obtain the road map. In this way a number of typical problems with small obstacles and passages are avoided, and the required number of nodes for a given accuracy is within reasonable limits. This road map is searched to find a motion connecting the given source and goal configurations of the robot. The algorithm is simple and general; the only specific computation that is required is a check for intersection of two polygons. We implemented the algorithm for planar robots allowing both translation and rotation and experiments show that compared to conventional techniques it performs well, even for difficult motion planning scenes.     

Model validation of biological pathways using Petri nets--demonstrated for apoptosis

This paper demonstrates the first steps of a new integrating methodology to develop and analyse models of biological pathways in a systematic manner using well established Petri net technologies. The whole approach comprises step-wise modelling, animation, model validation as well as qualitative and quantitative analysis for behaviour prediction. In this paper, the first phase is addressed how to develop and validate a qualitative model, which might be extended afterwards to a quantitative model. The example used in this paper is devoted to apoptosis, the genetically programmed cell death. Apoptosis is an essential part of normal physiology for most metazoan species. Disturbances in the apoptotic process could lead to several diseases. The signal transduction pathway of apoptosis includes highly complex mechanisms to control and execute programmed cell death. This paper explains how to model and validate this pathway using qualitative Petri nets. The results provide a mathematically unique and valid model enabling the confirmation of known properties as well as new insights in this pathway.     

An electromic controller for maintaining low dissolved oxygen levels in a bench-top fermentor

An electronic dissolved oxygen controller for use with a bench-top fermentor is described. It was designed to give an accurate control of low dissolved oxygen levels by continuous regulation of the agitation speed.     

Outline of a matrix calculus for neural nets

The activity of a neural net is represented in terms of a matrix vector equation with a normalizing operator in which the matrix represents only the complete structure of the net, and the normalized vector-matrix product represents the activity of all the non-afferent neurons. The activity vectors are functions of a quantized time variable whose elements are zero (no activity) or one (activity). Certain properties of the structure matrix are discussed and the computational procedure which results from the matrix vector equation is illustrated by a specific example.     

An architecture for biological information extraction and representation

Motivations: Technological advances in biomedical research are generating a plethora of heterogeneous data at a high rate. There is a critical need for extraction, integration and management tools for information discovery and synthesis from these heterogeneous data. RESULTS: In this paper, we present a general architecture, called ALFA, for information extraction and representation from diverse biological data. The ALFA architecture consists of: (i) a networked, hierarchical, hyper-graph object model for representing information from heterogeneous data sources in a standardized, structured format; and (ii) a suite of integrated, interactive software tools for information extraction and representation from diverse biological data sources. As part of our research efforts to explore this space, we have currently prototyped the ALFA object model and a set of interactive software tools for searching, filtering, and extracting information from scientific text. In particular, we describe BioFerret, a meta-search tool for searching and filtering relevant information from the web, and ALFA Text Viewer, an interactive tool for user-guided extraction, disambiguation, and representation of information from scientific text. We further demonstrate the potential of our tools in integrating the extracted information with experimental data and diagrammatic biological models via the common underlying ALFA representation. CONTACT: aditya_vailaya@agilent.com.     

An evolutionary Wolff's law for trabecular architecture.

A continuum model is proposed to describe the temporal evolution of both the density changes and the reorientation of the trabecular architecture given the applied stress state in the bone and certain material parameters of the bone. The data upon which the proposed model is to be based consist of experimentally determined remodeling rate coefficients and quantitative stereological and anisotropic elastic constant measurements of cancellous bone. The model shows that the system of differential equations governing the temporal changes in architecture is necessarily nonlinear. This nonlinearity is fundamental in that it stems from the fact that, during remodeling, the relationship between stress and strain is changing as the stress and strain variables themselves are changing. In order to preserve the remodeling property of the model, terms that are of the order strain times the changes in density and/or microstructural properties must be retained. If these terms were dropped, there would be no feedback mechanism for architectural adaptation and no adaptation of the trabecular architecture. There is, therefore, no linearized version of the model of the temporal evolution of trabecular architecture. An application of the model is illustrated by an example problem in which the temporal evolution of homogeneous trabecular architecture is predicted. A limitation of the proposed continuum model is the length scale below which it cannot be applied. The model cannot be applied in regions of cancellous bone where the trabecular bone architecture is relatively inhomogeneous or at a bone-implant interface.     

PUNCH: An architecture for Web-enabled wide-area network-computing

This paper addresses the architectural issues that arise in the design of a universally accessible wide-area network-computing system that is capable of making automatic cost/performance tradeoff decisions at run-time. The core system is designed around a three-level hierarchically distributed architecture, a choice driven by the dynamic, incremental, and distributed nature of the information associated with run-time cost/performance tradeoff decisions. Support for independent replication of each component in the hierarchy contributes to the overall scalability and reliability of the architecture. Meta-information is managed in a scalable manner by employing self-encoded resource identifiers that allow O(1) access to all managed information. Security and access control across administrative domains are provided by partitioning the infrastructure into independently-managed cells, and by giving administrators the ability to customize user-views directly at the location at which the request is processed. Demand-driven resource management is achieved by predicting the run-specific resource usage characteristics of tools via machine learning techniques. The concepts described in this paper are embodied in the Purdue University Network-Computing Hubs (PUNCH), a demand-based network-computing system that allows users to access and run unmodified tools via standard World Wide Web browsers. Tools do not have to be written in any particular language, and access to the source or object code is not required. The PUNCH infrastructure can be distributed in a manner that allows tools to be (user-transparently) executed wherever they reside. Currently, PUNCH contains over thirty tools developed by eight universities and four vendors, and serves more than five hundred users. During the past three years, PUNCH users have logged more than one million hits and have performed over seventy thousand simulations. This revised version was published online in July 2006 with corrections to the Cover Date.     

An exact method for the computation of the connectivity of random nets

The problem of finding the “weak connectivity” of a random net is reduced to one involving a Markov process. This provides a mathematically exact treatment of the problem which had previously been treated by an approximation, whose justification was not rigorous. The exact method allows in principle not only the calculation of the “weak connectivity”, but also of the “strong connectivity”, and, in general, the probability that from a randomly selected neuron in the net there exist paths to a specified number of neurons. The computations become exceedingly involved for large nets.