On the invariants of coloured Petri Nets

In this paper, we develop a theorem that enables computation of the place invariants of the union of a finite collection of coloured Petri Nets when the individual nets satisfy certain conditions and their invariants are known. We consider the illustrative examples of the Readers-Writers problem, a resource sharing system, and a network of databases and show how this theorem is a valuable tool in the analysis of concurrent systems.

Reflexive Incidence Matrx (RIM) Representation of Petr Nets

Although incidence matrix representation has been used to analyze the Petri net based models of a system, it has the limitation that it does not preserve reflexive properties (i.e., the presence of selfloops) of Petri nets. But in many practical applications self-loops play very important roles. This paper proposes a new representation scheme for general Petri nets. This scheme defines a matrix called "reflexive incidence matrix (RIM) c which is a combination of two matrices, a "base matrix Cb,,, and a "power matrix CP." This scheme preserves the reflexive and other properties of the Petri nets. Through a detailed analysis it is shown that the proposed scheme requires less memory space and less processing time for answering commonly encountered net queries compared to other schemes. Algorithms to generate the RIM from the given net description and to decompose RIM into input and output function matrices are also given. The proposed Petri net representation scheme is very useful to model and analyze the systems having shared resources, chemical processes, network protocols, etc., and to evaluate the performance of asynchronous concurrent systems.

Gear selectivity of large-mesh nets and drumlines used to catch sharks in the Queensland Shark Control Program.

Catches of sharks and bycatch in large-mesh nets and baited drumlines used by the Queensland Shark Control Program were examined to determine the efficacy of both gear types and assess fishing strategies that minimise their impacts. There were few significant differences in the size of both sharks and bycatch in the two gear types, apart from significantly smaller (p < 0.05) tiger sharks Galeocerdo cuvier being taken on drumlines and smaller green turtles Chelonia mydas in nets. Catch per unit effort showed orders of magnitude differences among species, even within the same family. Hammerhead sharks and rays were particularly vulnerable to net capture, whereas higher catch rates of tiger sharks were observed for drumlines. Nets caught more marine mammals, teleost fish and rays, whereas drumlines exhibited higher catch rates of the threatened loggerhead turtle Caretta caretta. Survival of most taxa (particularly obligate ram ventilators) was lower in nets than drumlines. Bycatch species (turtles and marine mammals) were able to swim to the surface to breathe when they were hooked on drumlines, enhancing their survival potential. Fishing strategies that recognise the different selectivity patterns of the gear can be developed to suit local biotic and abiotic conditions, although it is recognised that quantification of both ecological risk and risk to bathers is not a simple task.

Thiol-Disulfide Interchange Mediated Reversible Dendritic Megamer Formation and Dissociation

We report the formation of dynamic, reversible cross-linked dendritic megamers and their dissociation to monomeric dendrimers, through a thiol-disulfide interchange reaction. For this study, poly(alkyl aryl ether) dendrimers up to three-generations presenting thiol functionalities, were prepared. The series from zero to three generations of dendrimers were installed with 3, 6, 12, and 24 thiol functionalities at their peripheries. Upon synthesis, cross-linking of the dendrimer was accomplished through disulfide bond formation. The cross-linking of dendrimers was monitored through optical density changes at 420 nm. Dense cross-linking led to visible precipitation of dendritic megamers and the morphologies of the megamers were characterized by transmission electron microscopy. The disulfide cross-links between megamer monomers could be dissociated readily upon reduction of disulfide bond by dithiothreitol reagent. Preliminary studies show that dendritic megamers encapsulate C-60 and the efficiency of encapsulation increased with increasing generation of dendritic megamer.

Graphical simulation of Petri Nets

An interactive graphics package for modeling with Petri Nets has been implemented. It uses the VT-11 graphics terminal supported on the PDP-11/35 computer to draw, execute, analyze, edit and redraw a Petri Net. Each of the above mentioned tasks can be performed by selecting appropriate items from a menu displayed on the screen. Petri Nets with a reasonably large number of nodes can be created and analyzed using this package. The number of nodes supported may be increased by making simple changes in the program. Being interactive, the program seeks information from the user after displaying appropriate messages on the terminal. After completing the Petri Net, it may be executed step by step and the changes in the number of tokens may be observed on the screen, at each place. Some properties of Petri Nets like safety, boundedness, conservation and redundancy can be checked using this package. This package can be used very effectively for modeling asynchronous (concurrent) systems with Petri Nets and simulating the model by “graphical execution.”

Amine-Templated Aluminoborates Exhibiting Graphite and Diamond Nets

A solvothermal reaction of Al2O3, H3BO3, pyridine, and H2O at 180 degrees C/7 days in the presence of organic amine molecules gave rise to four new aluminoborates, [(C6H18N2)(AlB6O13H3)], I; [(C5H16N2) (AlB5O10)]center dot 2H(2)O, II; [(C5H16N2)-(AlB5O10)], III; and [(C5H17N3)(AlB5O10)] center dot H2O, IV, with two- and three-dimensional structures. All the structures have been formed by the connectivity involving Al3+ ions and [B5O10] cyclic pentaborate units. In 1, the 3-connected trigonal nodes form a layer that resembles a graphite structure has been observed. The compounds II, III, and IV, have 4-connected nodes that forms a diamond related three-dimensional structure. The formation of solvatomorphs in II and III is noteworthy and has been observed first time in a family of amine template aluminoborates. A comparison of the various aluminoborate structures reveals subtle relationships between the organic amines (length of the amines) and the final framework structures. The compounds have been characterized using a variety of techniques including IR, second-order optical behavior, and MAS NMR studies.

A new methodology for analyzing distributed systems modeled by petri nets

Distributed computing systems can be modeled adequately by Petri nets. The computation of invariants of Petri nets becomes necessary for proving the properties of modeled systems. This paper presents a two-phase, bottom-up approach for invariant computation and analysis of Petri nets. In the first phase, a newly defined subnet, called the RP-subnet, with an invariant is chosen. In the second phase, the selected RP-subnet is analyzed. Our methodology is illustrated with two examples viz., the dining philosophers' problem and the connection-disconnection phase of a transport protocol. We believe that this new method, which is computationally no worse than the existing techniques, would simplify the analysis of many practical distributed systems.

S-nets: A Petri net based model for performance evaluation of real-time scheduling algorithms

A new class of nets, called S-nets, is introduced for the performance analysis of scheduling algorithms used in real-time systems Deterministic timed Petri nets do not adequately model the scheduling of resources encountered in real-time systems, and need to be augmented with resource places and signal places, and a scheduler block, to facilitate the modeling of scheduling algorithms. The tokens are colored, and the transition firing rules are suitably modified. Further, the concept of transition folding is used, to get intuitively simple models of multiframe real-time systems. Two generic performance measures, called �load index� and �balance index,� which characterize the resource utilization and the uniformity of workload distribution, respectively, are defined. The utility of S-nets for evaluating heuristic-based scheduling schemes is illustrated by considering three heuristics for real-time scheduling. S-nets are useful in tuning the hardware configuration and the underlying scheduling policy, so that the system utilization is maximized, and the workload distribution among the computing resources is balanced.

Small strong epsilon nets

Let P be a set of n points in R-d. A point x is said to be a centerpoint of P if x is contained in every convex object that contains more than dn/d+1 points of P. We call a point x a strong centerpoint for a family of objects C if x is an element of P is contained in every object C is an element of C that contains more than a constant fraction of points of P. A strong centerpoint does not exist even for halfspaces in R-2. We prove that a strong centerpoint exists for axis-parallel boxes in Rd and give exact bounds. We then extend this to small strong epsilon-nets in the plane. Let epsilon(S)(i) represent the smallest real number in 0, 1] such that there exists an epsilon(S)(i)-net of size i with respect to S. We prove upper and lower bounds for epsilon(S)(i) where S is the family of axis-parallel rectangles, halfspaces and disks. (C) 2014 Elsevier B.V. All rights reserved.

Interpenetrated and Catenated Zinc Thiosulfates Frameworks with dia and qtz Nets: Synthesis, Structure, and Properties

Reactions between Zn(NO3)(2)center dot 6H(2)O, Na2S2O3, 4,4'-bipyridine (bpy), 1,2-bis(4-pyridyl)ethene (bpe), 1,2-bis (4-pyridyl) ethane (bpa), and 1,3-bis(4-pyridyl)propane (bpp) under solvothermal conditions resulted in four new zinc thiosulfate hybrid compounds. Compound I has four-membered zinc thiosulfate rings connected by the ligand, 1,3-bis(4-pyridyl)propane (bpp) forming a two-dimensional structure. Compounds II-IV have one-dimensional zinc thiosulfate chains connected by the ligands, bpy (II), bpe (III), and bpa (IV) giving rise to three-dimensional structures. All the four-structures exhibit 3-fold interpenetration. Proton conductivity studies indicate reasonable proton mobility at 34 degrees C and at 98% relative humidity. The compounds also exhibit Lewis acid character and good photocatalytic activity for the decomposition of cationic dyes.