Petri net equivalence

Determining whether two Petri nets are equivalent is an interesting problem from both practical and theoretical standpoints. Although it is undecidable in the general case, for many interesting nets the equivalence problem is solvable. This paper explores, mostly from a theoretical point of view, some of the issues of Petri net equivalence, including both reachability sets and languages. Some new definitions of reachability set equivalence are described which allow the markings of some places to be treated identically or ignored, analogous to the Petri net languages in which multiple transitions may be labeled with the same symbol or with the empty string. The complexity of some decidable Petri net equivalence problems is analyzed

Modeling and analysis of concurrent systems

A survey of modeling and analysis techniques in common use for modeling and analyzing concurrent systems. The models surveyed are CSP (Communicating Sequential Processes), Path Expressions, CCS (Calculus of Communicating Systems), CIRCAL, Petri Nets, Coloured Petri Nets, Predicate-Action Nets, Numerical Petri Nets, Contour-Transition Nets, and several varieties of Timed Petri Nets. The analysis techniques are state-space analysis, temporal logic, structural analysis, and inductive analysis

Mass Splitting and Production of Σc0\Sigma_c^0 and Σc++\Sigma_c^{++} Measured in 500GeV500 {GeV} π−−\pi^- -N Interactions

From a sample of $2722 \pm 78$ $\Lambda_c^+$ decaying to the $pK^-\pi^+$ final state, we have observed, in the hadroproduction experiment E791 at Fermilab, $143 \pm 20$ $\Sigma_c^0$ and $122 \pm 18$ $\Sigma_c^{++}$ through their decays to $\Lambda_c^+ \pi^{\pm}$. The mass difference $M(\Sigma_c^0) - M(\Lambda_c^+$) is measured to be $(167.38\pm 0.29\pm 0.15) {MeV}$; for $M(\Sigma_c^{++}) - M(\Lambda_c^+)$, we find $(167.76\pm 0.29\pm0.15) {MeV}$. The rate of $\Lambda_c^+$ production from decays of the $\Sigma_c$ triplet is (22\pm 2\pm 3) {%} of the total $\Lambda_c^+$ production assuming equal rate of production from all three, as measured for $\Sigma_c^0$ and $\Sigma_c^{++}$. We do not observe a statistically significant $\Sigma_c$ baryon-antibaryon production asymmetry. The $x_F$ and $p_t^2$ spectra of $\Lambda_c^+$ from $\Sigma_c$ decays are observed to be similar to those for all $\Lambda_c^+$'s produced.Comment: 15 pages, uuencoded postscript 3 figures uuencoded, tar-compressed fil

Modeling and analysis of concurrent systems

A survey of modeling and analysis techniques in common use for modeling and analyzing concurrent systems. The models surveyed are CSP (Communicating Sequential Processes), Path Expressions, CCS (Calculus of Communicating Systems), CIRCAL, Petri Nets, Coloured Petri Nets, Predicate-Action Nets, Numerical Petri Nets, Contour-Transition Nets, and several varieties of Timed Petri Nets. The analysis techniques are state-space analysis, temporal logic, structural analysis, and inductive analysis

Artificial neural networks can predict trauma volume and acuity regardless of center size and geography: A multicenter study.

BackgroundTrauma has long been considered unpredictable. Artificial neural networks (ANN) have recently shown the ability to predict admission volume, acuity, and operative needs at a single trauma center with very high reliability. This model has not been tested in a multicenter model with differing climate and geography. We hypothesize that an ANN can accurately predict trauma admission volume, penetrating trauma admissions, and mean Injury Severity Score (ISS) with a high degree of reliability across multiple trauma centers.MethodsThree years of admission data were collected from five geographically distinct US Level I trauma centers. Patients with incomplete data, pediatric patients, and primary thermal injuries were excluded. Daily number of traumas, number of penetrating cases, and mean ISS were tabulated from each center along with National Oceanic and Atmospheric Administration data from local airports. We trained a single two-layer feed-forward ANN on a random majority (70%) partitioning of data from all centers using Bayesian Regularization and minimizing mean squared error. Pearson's product-moment correlation coefficient was calculated for each partition, each trauma center, and for high- and low-volume days (>1 standard deviation above or below mean total number of traumas).ResultsThere were 5,410 days included. There were 43,380 traumas, including 4,982 penetrating traumas. The mean ISS was 11.78 (SD = 6.12). On the training partition, we achieved R = 0.8733. On the testing partition (new data to the model), we achieved R = 0.8732, with a combined R = 0.8732. For high- and low-volume days, we achieved R = 0.8934 and R = 0.7963, respectively.ConclusionAn ANN successfully predicted trauma volumes and acuity across multiple trauma centers with very high levels of reliability. The correlation was highest during periods of peak volume. This can potentially provide a framework for determining resource allocation at both the trauma system level and the individual hospital level.Level of evidenceCare Management, level IV