Non-deterministic Modeling Research Articles

Aspects of Symmetry in Petri Nets

Symmetry is a fundamental mathematical property applicable to the description of various shapes both geometrical and representational. Symmetry is central to understanding the nature of various objects. It can be used as a simplifying principle when structures are created. Petri nets are widely covered formalisms, useful for modeling different types of computer systems or computer configurations. Different forms of Petri nets exist along with several forms of representation. Petri nets are useful for i) deterministic and ii) non-deterministic modeling. The aspect of symmetry in Petri nets requires in-depth treatment that is often overlooked. Symmetry is a fundamental property found in Petri nets. This work tries to briefly touch on these properties and explain them with simple examples. Hopefully, readers will be inspired to carry out more work in this direction.

Analysis of age-specific fertility in India: Deterministic and non-deterministic modeling approaches

The main objective of this study is to investigate the pattern of age-specific fertility rates (ASFRs) in India using deterministic and non-deterministic approaches. Toward this end, we proposed statistical polynomial regression models to study the distributional pattern of ASFRs for total, rural, and urban women in India. Further, a comparative study considering selected skewed regression models was undertaken. For this study, secondary data on ASFR were collected from Sample Registration System, Statistical Report-2020, and from National Family Health Survey 5 (NFHS-5; 2019 – 2021). It was found that all three subcategories of ASFRs, namely, the total, rural, and urban ASFRs, followed the reciprocal biquadratic polynomial model. On the other hand, all three subcategories of ASFR follow the skew-normal type 2 distribution. Similar findings were also obtained and validated based on NFHS-5 data. Further, the chosen statistical models’ validity and stability were tested using various model validation techniques and model selection criteria.

Reducing passenger waiting time and energy consumption for metro timetabling: A robust optimization approach

Urban subway scheduling is a quite complicated task as any small fluctuation could disturb the entire system. Subway companies need an efficient scheduling system that best serves passengers and optimizes the utilization of resources. They need, therefore, to include real-world problems in their schedule through non-deterministic modeling. A robust optimization approach is applied in real-world data to propose an optimum train schedule that minimizes passenger waiting time and maximizes electrical energy converted from kinetic energy. Three high, normal, and low travel demand scenarios are considered to optimize train running-time duration in all three interstation movement categories, namely acceleration, coasting, and braking. To find the optimal solution, a genetic algorithm (GA) model has been applied to real data from a subway line in Tehran Metro.

Quantitative Analysis of Safety Risks and Relationship with Delayed Project Completion Times

Dynamic work environments in construction and civil infrastructure sectors remain susceptible to safety risks. Although previous research has resulted in improvements, there is currently a gap in measuring temporal impacts of safety risks quantitatively. Precise modeling of potential delays caused by safety incidents is vital for efficient management of risks and making informed decisions on project contingency. Toward this aim, the current research adopts a nondeterministic modeling method to simulate and quantify safety incidents and find correlations with project delays. Using a deductive approach, three research questions were formulated, and investigations conducted on Australian data collected from 2016 onwards. Quantitative impacts of safety risks on project completion times were numerically measured. Furthermore, safety risks were ranked based on their significance of temporal impacts on project performance. This paper contributes to the theory of safety management by developing a nondeterministic method to model impacts of safety risks at both industry and project levels. Practical contributions and outcomes can facilitate using machine learning methods to plan proportionate time buffers to address safety risks.

Basins of Attraction, Commitment Sets, and Phenotypes of Boolean Networks

The attractors of Boolean networks and their basins have been shown to be highly relevant for model validation and predictive modeling, e.g., in systems biology. Yet, there are currently very few tools available that are able to compute and visualize not only attractors but also their basins. In the realm of asynchronous, non-deterministic modeling not only is the repertoire of software even more limited, but also the formal notions for basins of attraction are often lacking. In this setting, the difficulty both for theory and computation arises from the fact that states may be elements of several distinct basins. In this paper, we address this topic by partitioning the state space into sets that are committed to the same attractors. These commitment sets can easily be generalized to sets that are equivalent w.r.t. the long-term behaviors of pre-selected nodes which leads us to the notions of markers and phenotypes which we illustrate in a case study on bladder tumorigenesis. For every concept, we propose equivalent CTL model checking queries and an extension of the state of the art model checking software NuSMV is made available that is capable of computing the respective sets. All notions are fully integrated as three new modules in our Python package PyBoolNet, including functions for visualizing the basins, commitment sets, and phenotypes as quotient graphs and pie charts.

Nondeterministic computational fluid dynamics modeling of Escherichia coli inactivation by peracetic acid in municipal wastewater contact tanks.

Wastewater disinfection processes are typically designed according to heuristics derived from batch experiments in which the interaction among wastewater quality, reactor hydraulics, and inactivation kinetics is often neglected. In this paper, a computational fluid dynamics (CFD) study was conducted in a nondeterministic (ND) modeling framework to predict the Escherichia coli inactivation by peracetic acid (PAA) in municipal contact tanks fed by secondary settled wastewater effluent. The extent and variability associated with the observed inactivation kinetics were both satisfactorily predicted by the stochastic inactivation model at a 95% confidence level. Moreover, it was found that (a) the process variability induced by reactor hydraulics is negligible when compared to the one caused by inactivation kinetics, (b) the PAA dose required for meeting regulations is dictated equally by the fixed limit of the microbial concentration as well as its probability of occurrence, and (c) neglecting the probability of occurrence during process sizing could lead to an underestimation of the PAA dose required by as much as 100%. Finally, the ND-CFD model was used to generate sizing information in the form of probabilistic disinfection curves relating E. coli inactivation and probability of occurrence with the average PAA dose and PAA residual concentration at the outlet of the contact tank.

A three-level non-deterministic modeling methodology for the NVH behavior of rubber connections

Abstract Complex built-up structures such as vehicles have a variety of joint types, such as spot-welds, bolted joints, rubber joints, etc. Rubber joints highly contribute to the nonlinear level of the structure and are a major source of uncertainties and variability. In the general framework of developing engineering tools for virtual prototyping and product refinement, the modeling of the NVH behavior of rubber joints involve the computational burden of including a detailed nonlinear model of the joint and the uncertainties and variability typical of that joint in a full-scale system model. However, in an engineering design phase the knowledge on the joint rubber material properties is typically poor, and the working conditions a rubber joint will experience are generally not known in detail. This lack of knowledge often do not justify the computational burden and the modeling effort of including detailed nonlinear models of the joint in a full-scale system model. Driven by these issues a non-deterministic numerical methodology based on a three-level modeling approach is being developed. The methodology aims at evaluating directly in the frequency domain the sensitivity of the NVH behavior of a full-scale system model to the rubber joint material properties when nonlinear visco-elastic rubber material behavior is considered. Rather than including directly in the model a representation of the rubber nonlinear visco-elastic behavior, the methodology proposes to model the material nonlinear visco-elastic behavior by using a linear visco-elastic material model defined in an interval sense, from which the scatter on the full-scale system NVH response is evaluated. Furthermore the development of a multi-level solution scheme allows to reduce the computational burden introduced by the non-deterministic approach by allowing the definition of an equivalent linear interval parametric rubber joint model, ready to be assembled in a full-scale system model at a reasonable computational cost. By using a commercial finite element code the developed methodology is illustrated through a numerical case-study: the low-frequency dynamic analysis of automotive door weather-strip seals.

A Neural Network Based Method for Optical Patient Set-up Registration in Breast Radiotherapy

Patient set-up optimization is required in breast-cancer radiotherapy to fill the accuracy gap between personalized treatment planning and uncertainties in the irradiation set-up. Opto-electronic systems allow implementing automatic procedures to minimize the positional mismatches of light-reflecting markers located on the patient surface with respect to a corresponding reference configuration. The same systems are used to detect the position of the irradiated body surface by means of laser spots; patient set-up is then corrected by matching the control points onto a CT based reference model through surface registration algorithms. In this paper, a non-deterministic approach based on Artificial Neural Networks is proposed for the automatic, real-time verification of geometrical set-up of breast irradiation. Unlike iterative surface registration methods, no passive fiducials are used and true real-time performance is obtained. Moreover, the non-deterministic modeling performed by the neural algorithm minimizes sensitivity to intra-fractional and inter-fractional non-rigid motion of the breast. The technique was validated through simulated activities by using reference CT data acquired on four subjects. Results show that the procedure is able to detect and reduce simulated set-up errors and revealed high reliability in patient position correction, even when the surface deformation is included in testing conditions.

Action-based union of the temporal opposites and elastic activity network in scheduling

It is the time resource that one deals with in scheduling. The task is how one can achieve the optimal allocation of a given time resource over a set of assigned activities. Most of the existing scheduling methods use a parametric time by which the activities are orderly allocated in accordance with the order of events. The parametric methods however fail in incorporating a dynamic aspect of scheduling that unfolds itself as the project proceeds as well as inerasable uncertainty in activities whose starting and ending nodes fluctuate. This paper reformulates the concept of time to match to a dynamic scheduling through a non-deterministic modeling of scheduling as a “mapped/represented” and “transformed/processed” temporal movement. It will be shown that an elastic interpretation of activity fluctuation can be derived naturally from the model, which allows us to develop an elastic network method for scheduling.

Computational structures technology: leap frogging into the twenty-first century

The history, recent developments and trends in computational structures technology (CST) are summarized. Discussion focuses on development of CST software and goals of CST activities. Some recent advances in a number of CST areas are described, including discretization techniques and element technology; computational material modeling; modeling of composite, sandwich and smart structures; computational tools and methodologies for life management; transient response analysis; numerical simulation of frictional contact/impact response; articulated structural dynamics; non-deterministic modeling and analysis methods; qualitative analysis and simulation; neuro-computing; hybrid techniques; error estimation and adaptive improvement strategies; strategies for solution of coupled problems; sensitivity analysis; integrated analysis and design; strategies and numerical algorithms for new computing systems; model generation facilities; and application of object-oriented technology. Research areas in CST that have high potential for meeting the future technological needs are identified.

An introduction to the Millennium Project

The pace, complexity, and globalization of change requires attention to the future. The change of millennia — the coming of the year 2001 — provides an opportunity, a psychological focus, for a global review of past achievements and problems and a unique chance to assess and reflect on future issues and opportunities. Unfortunately, there is as yet no mechanism or information utility to support a worldwide effort to study past achievements and problems or future issues and opportunities. Although there are many individual, isolated, special purpose, and one-time study efforts underway, there is no international system that can provide coherence or continuity to these studies, including feedback and sharing of information, and, in particular, the systematic exploration of future possibilities and policy alternatives. With growing interest in the future, the spread of instantaneous and global communications, the advent of powerful new nondeterministic modeling techniques, the ability to evoke, capture, and share information and perceptions with systematic questioning techniques and software, the proliferation of data bases, and knowledge visualization, it is now possible for futurists, scholars and others around the world to interact globally and take a fresh look at the future possibilities and policies in ways not previously possible. As the World Bank provides an ongoing system for research and feedback to improve economic policy, so too the United Nations University could provide an ongoing system for the improvement of futures research and its application to the policy process. According to a series of interviews, questionnaires, and meetings with leading futurists and scholars around the world, the proposed “Millenium Project” has the potential to become such a system. This study had as its principal objective determining the design of an information system that could effectively tap contributors, worldwide, to focus on lessons of the past that bear on world issues and the potential of future developments for intensifying or mitigating these and future issues. The first phase of the feasibility study was both methodological and substantive. Worldwide panels of experts contributed their judgments about the method or process of organizing the project; and the system that emerged from this interaction was applied in a prototype study to the issues of growing world population and the environment. During the first phase of the feasibility study, we found that: 1. 1. The Millennium Project is feasible and likely to be helpful to many institutions in examining and resolving policy issues at several levels. An overview of the project design and objectives appears in Section 2 of this article. 2. 2. Organizations that have an issues scanning function, or have a mandate to keep abreast of a broad range of futures thinking, have a need for access to a non-political, scholarly, and international system of future studies. Such organizations have requested continued participation in the second and third phase of this feasibility study, as well as establishing formal relations with the full Millennium Project. 3. 3. While several questions remain, the design features of a system to collect judgments using the Delphi process that were suggested by the international panel (outlined elsewhere in this report) form a straight forward operational system. Among the remaining questions are the design and use of international information systems and data bases, integration with quantitative techniques such as system modeling, the requirements for special study teams, and institutionalization and financial support. The design of the operational system is described in detail in Section 3 of this report. 4. 4. Cost estimates have been made for establishing international panels and collecting and analyzing information they provide using the Delphi process. Several assumptions are required. If a maximum of four topics are addressed in a particular year, each of the four panels consists of 150–200 people, the staff is kept to a base of three people with an additional 1.5 per panel, and advisors are paid an honorarium of $1.500, then the cost of this element of the full scale Project is likely to be approximately $900,000 per year. While communications modes are important in terms of timing and information access, the costs of communications are the smallest of the Project's cost elements. Detail of our cost estimates appear in Section 7 of this report. This is not the final feasibility study report, but only a report on part of Phase I. As such, it contains our initial findings about how the Project might be organized. We welcome comments from the reader. Please consider this as work in progress.

On the Transient Solution of Non-Deterministic Systems

Through the use of formal expansions, a non-deterministic solution approach is developed for systems modeled by first order matrix differential equations with random coefficients and input conditions. The generality of the solution procedure is such that various statistical moments can be generated. In particular, this includes such moments as the mean and standard deviation vectors, the variance-covariance matrix etc. To ascertain the overall properties of such moments, various recursive generators as well as convergence and truncation criteria are developed. Due to the formal structure of the overall solution, the inherent algorithmic apparatus is concise and easily programmed. Because of this, the procedure can be applied equally well to both large and small systems of non-deterministic modeling equations. A further feature of the given procedure lies in the fact that it can be used to generate the statistical solution for a given element of the dependent variable vector without necessitating the development of the entire solution. To demonstrate the scope of the approach, several numerical experiments are included in the paper.