Finding Clusters in Petri Nets. An approach based on GPenSIM

Graph theory provides some methods for finding clusters in networks. Clusters reflect the invisible grouping of the elements in a network. This paper presents a new method for finding clusters in networks. In this method, the user can adjust a parameter to change the number of clusters. This method is newly added to the simulator General-purpose Petri Net Simulator (GPenSIM) as a function for network analysis. With this GPenSIM function, in addition to the usual performance analysis of a discrete-event system via a Petri net model, supplementary information about the grouping of the elements can also be found. Finding clusters in discrete-event systems provides valuable information such as the ideal location of the elements in a manufacturing network. This paper also presents an application example on a flexible manufacturing system

Resurgence in topological string theory

One of the main results of this theory describes, in a quantitative way, the relation between the perturbative and nonperturbative information of a system. Encoded in the asymptotic growth of the series coefficients of perturbation theory is the information necessary to reconstruct nonperturbative sectors. All these sectors can be put together in a formal object called the transseries, whose different coefficients are related to each other by resurgence relations. The resurgent approach has been applied succesfully to problems in mathematics, on differential and difference equations, and in physics, on quantum mechanics and even quantum field theory. It is currently a very active area of research merging the efforts of both physicists and mathematicians. This thesis performs a resurgent analysis of the perturbative topological string theory. Using the holomorphic anomaly equations it is possible to compute coefficients of the perturbative free energy to very high order and analyze their asymptotic growth. In agreement with resurgence, it is found that nonperturbative sectors coming from a transseries control this growth. It is shown that this transseries can be computed as a solution of a natural extension of the holomorphic anomaly equations. The first half of this thesis is concerned with the main properties of the theory of resurgence and with the computation of the perturbative topological string free energy. These results are then applied to a concrete topological string example. A careful study of the asymptotic growth of the perturbative free energies is performed and various resurgence relations are uncovered. These relations involve elements of the transseries describing the full nonperturbative free energy. General properties of the transseries satisfying the holomorphic anomaly equations are described, including the role of the instanton actions, the presence of holomorphic ambiguities and the possibility of resonance. The numerical results are found to match, to high precision, the elements of the computed transseries. The asymptotic nature of the higher instanton sectors is also studied and a complicated net of resurgence relations is found

A novel clustering methodology based on modularity optimisation for detecting authorship affinities in Shakespearean era plays

© 2016 Naeni et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. In this study we propose a novel, unsupervised clustering methodology for analyzing large datasets. This new, efficient methodology converts the general clustering problem into the community detection problem in graph by using the Jensen-Shannon distance, a dissimilarity measure originating in Information Theory. Moreover, we use graph theoretic concepts for the generation and analysis of proximity graphs. Our methodology is based on a newly proposed memetic algorithm (iMA-Net) for discovering clusters of data elements by maximizing the modularity function in proximity graphs of literary works. To test the effectiveness of this general methodology, we apply it to a text corpus dataset, which contains frequencies of approximately 55,114 unique words across all 168 written in the Shakespearean era (16th and 17th centuries), to analyze and detect clusters of similar plays. Experimental results and comparison with state-of-the-art clustering methods demonstrate the remarkable performance of our new method for identifying high quality clusters which reflect the commonalities in the literary style of the plays

Massless scalar free Field in 1+1 dimensions I: Weyl algebras Products and Superselection Sectors

This is the first of two papers on the superselection sectors of the conformal model in the title, in a time zero formulation. A classification of the sectors of the net of observables as restrictions of solitonic (twisted) and non-solitonic (untwisted) sector automorphisms of proper extensions of the observable net is given. All of them are implemented by the elements of a field net in a non-regular vacuum representation and the existence of a global compact Abelian gauge group is proved. A non-trivial center in the fixed-point net of this gauge group appears, but in an unphysical representation and reducing to the identity in the physical one. The completeness of the described superselection structure, to which the second paper is devoted, is shown in terms of Roberts' net cohomology. Some general features of physical field models defined by twisted cross products of Weyl algebras in non-regular representations are also presented.Comment: published final versio

Analysing Inflation: Monetary and Real Theories

The paper seeks to analyse the inflationary trends observed in Pakistan in the recent past by applying both the monetary and real theories. The former explains inflation in terms of changes in liquidity per unit of real output and velocity whereas the latter makes use of real variables, especially, the structure of economy. Since the ratio between money spending (quantity of money times velocity) and real GDP defines general price level, monetary theory offers a natural tool for analysing inflation. Even factors like raising utility prices by the government or higher expected inflation add to inflation only when the additional demand for money generated by these factors is met with an accommodating increase in money supply (with stable velocity). During FY86 to 96 in Pakistan, money supply grew by 15.4 percent, GDP by 5.3 percent, and velocity by –0.24 percent. This yields an estimated inflation of 9.4 percent, very close to the actual one of 9.2 percent. Interestingly enough, more than half of the money expansion during the 90s emanated from credit for budgetary support, rendering the latter an active source of inflation. Under the real theory, we focused on full-cost-pricing wherein the market value-added price is defined as a weighted sum of various primary costs, e.g., wages, profits, and net indirect taxes. To capture the impact of terms of trade, foreign trade flows were added. It has been estimated that the overall inflation of 9.4 percent during FY86–95 was contributed to the extent of 5.6 points by profits, 2.2 points by wages, 0.9 by net indirect taxes and 0.7 by terms of trade. From policy perspective, monetary analysis has an edge over real analysis as controlling inflation through monetary management is relatively easier than through regulating various costs elements which go into the formation of price

Scaling Algebras and Renormalization Group in Algebraic Quantum Field Theory

For any given algebra of local observables in Minkowski space an associated scaling algebra is constructed on which renormalization group (scaling) transformations act in a canonical manner. The method can be carried over to arbitrary spacetime manifolds and provides a framework for the systematic analysis of the short distance properties of local quantum field theories. It is shown that every theory has a (possibly non-unique) scaling limit which can be classified according to its classical or quantum nature. Dilation invariant theories are stable under the action of the renormalization group. Within this framework the problem of wedge (Bisognano-Wichmann) duality in the scaling limit is discussed and some of its physical implications are outlined.Comment: 47 pages, no figures, ams-late

COMPUTER SIMULATION AND COMPUTABILITY OF BIOLOGICAL SYSTEMS

The ability to simulate a biological organism by employing a computer is related to the ability of the computer to calculate the behavior of such a dynamical system, or the "computability" of the system.* However, the two questions of computability and simulation are not equivalent. Since the question of computability can be given a precise answer in terms of recursive functions, automata theory and dynamical systems, it will be appropriate to consider it first. The more elusive question of adequate simulation of biological systems by a computer will be then addressed and a possible connection between the two answers given will be considered. A conjecture is formulated that suggests the possibility of employing an algebraic-topological, "quantum" computer (Baianu, 1971b) for analogous and symbolic simulations of biological systems that may include chaotic processes that are not, in genral, either recursively or digitally computable. Depending on the biological network being modelled, such as the Human Genome/Cell Interactome or a trillion-cell Cognitive Neural Network system, the appropriate logical structure for such simulations might be either the Quantum MV-Logic (QMV) discussed in recent publications (Chiara, 2004, and references cited therein)or Lukasiewicz Logic Algebras that were shown to be isomorphic to MV-logic algebras (Georgescu et al, 2001)