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An important issue when large-scale mathematical models are used to support decision makers is their reliability. Sensitivity analysis of model outputs to variation or natural uncertainties of model inputs is very significant for improving the reliability of these models. A comprehensive experimental study of Monte Carlo algorithm based on adaptive Monte Carlo approach for multidimensional numerical integration has been done. A comparison with Latin Hypercube Sampling and a particular quasi-Monte Carlo lattice rule based on generalized Fibonacci numbers has been presented. Such comparison has been made for the first time and this motivates the present study. The concentration values have been generated by the specialized modification SA-DEM of the Unified Danish Eulerian Model. Its parallel efficiency and scalability will be demonstrated by experiments on some of the most powerful supercomputers in Europe. The algorithms have been successfully applied to compute global Sobol sensitivity measures corresponding to the influence of six chemical reaction rates and four different groups of pollutants on the concentrations of important air pollutants.

Sensitivity analysis is a powerful tool for studying and improving the reliability of mathematical models. Air pollution and meteorological models are in front places among the examples of mathematical models with a lot of natural uncertainties in their input data sets and parameters. In this work some results of the global sensitivity study of the Unified Danish Eulerian Model (UNI-DEM) have been presented. One of the most attractive features of UNI-DEM is its advanced chemical scheme – the Condensed CBM IV, which consider a large number of chemical species and numerous reactions between them, of which the ozone is one of the most important pollutants for its central role in many practical applications of the results. A comprehensive experimental study of quasi-Monte Carlo algorithms based on lattice sequences with different generating vectors for multidimensional numerical integration has been done. The Fibonacci based lattice rule is compared with other types of lattice rules. The performance of a lattice rule depends on the choice of the generator vectors. When the integrand is sufficiently regular the lattice rules outperform not only the standard Monte Carlo methods, but also other types of methods using low discrepancy sequences.

The large-scale air pollution model UNI-DEM (the Unified Danish Eulerian Model) was used together with several carefully selected climatic scenarios. It was necessary to run the model over a long time-interval (sixteen consecutive years) and to use fine resolution on a very large space domain. This caused great difficulties because it was necessary to (a) perform many runs with different input parameters, (b) use huge input files containing the needed meteorological and emission data, (c) resolve many problems related to the computational difficulties, (d) develop and apply carefully prepared parallel codes, (e) exploit efficiently the cache memories of the available computers and (f) store in a proper way huge output files for visualization and animation. It will be described how these difficult tasks have been resolved and many results related to some potentially harmful ozone levels will be presented.

Sensitivity analysis of the results of large and complicated mathematical models is rather tuff and time-consuming task. However, this is quite an important problem as far as their critical applications are concerned. There are many such applications in the area of air pollution modelling. On the other hand, there are lots of natural uncertainties in the input data sets and parameters of a large-scale air pollution model. Such a model, the Danish Eulerian Model with its up-to-date high-performance implementations, is under consideration in this work. Its advanced chemical scheme (the Condensed CBM IV) takes into account a large number of chemical species and numerous reactions between them.

Sensitivity analysis is a powerful tool for studying and improving the reliability of large and complicated mathematical models. Air pollution and meteorological models are in front places among the examples of such models, with a lot of natural uncertainties in their input data sets and parameters. We present here some results of our global sensitivity study of the Unified Danish Eulerian Model (UNI-DEM). One of the most attractive features of UNI-DEM is its advanced chemical scheme – the Condensed CBM IV, which consider in detail a large number of chemical species and numerous reactions between them.

This paper demonstrates implementation of virtual prototyping approach in early stage of design concept evaluation. Examined structure is of contemporary smart pole design with integrated telecommunication equipment. The combination of integrated design (inside poles) and contemporary electronic equipment thermal management leads to the need of careful examination of thermal behaviour of entire structure. Most important issue is connected to the problem how to transfer generated heat to the environment. Presented study is performed through multiphysics analyses – thermal CFD (Computational Fluid Dynamics) – using virtual prototyping techniques to assess several design variants performance parameters. Used virtual prototypes enable to view in detail heat transfer process and to reach a better solution for cooling components placement. Each design parameter is assessed and further recommendations are formed for design improvement. Final design uses fans placed on the top of the pole structure leading to allowable thermal loads over electronic equipment.

Efficient implementation of the Two-times Repeated Richardson Extrapolation is studied in this paper under the assumption that systems of ordinary differential equations (ODEs) are solved numerically by Explicit Runge-Kutta Methods (ERKMs). The combinations of the Two-times Repeated Richardson Extrapolation with the ERKMs are new numerical methods. The computational cost per step of these new numerical methods is higher than the computational cost per step of the underlying ERKMs. However, the order of accuracy of the combined methods becomes very high: if the order of accuracy of the underlying ERKM is p, then the order of accuracy of its combination with the Two-times Repeated Richardson Extrapolation is at least \(p+3\) when the right-hand-side function of the system of ODEs is sufficiently many times continuously differentiable. Moreover, the stability properties of the new methods are always better than those of the underlying numerical methods when \(p=m\) and \( m=1,2,3,4\) (where m is the number of stage vectors in the chosen ERKM). These two useful properties, higher accuracy and better stability, are often giving a very reasonable compensation for the increased computational cost per step, because the same degree of accuracy can be achieved by applying a large stepsize which leads to a considerable reduction of the number of steps when the Two-times Repeated Richardson Extrapolation is used. This fact is verified by several numerical experiments.

The study aims to present virtual prototyping applicability for design and evaluation of complex system of automotive industry. It presents a new principle design solution and illustrates design development, based entirely on virtual prototyping. The design concept is to provide solution for radiators fan and its shroud for high speeds when the fan acts like resistance. Multiple design variants are examined using virtual prototype of radiators, fan, shroud and all engine components. Developed design variants are compared by their performance both at low and high speeds.

Repeated Richardson Extrapolation can successfully be used in the efforts to improve the efficiency of the numerical treatment of systems of ordinary differential equations (ODEs) mainly by increasing the accuracy of the computed results. It is assumed in this paper that Implicit Runge-Kutta Methods (IRKMs) are used in the numerical solution of systems of ODEs. If the order of accuracy of the selected IRKM is p, then the order of accuracy of its combination with the Repeated Richardson Extrapolation is at least \(p+2\) (assuming here that the right-hand-side of the system of ODEs is sufficiently many times continuously differentiable). However, it is additionally necessary to establish that the absolute stability properties of the new numerical methods (that are combinations of the Repeated Richardson Extrapolation and the selected IRKMs) are preserved, and this is an extremely difficult problem. Results related to the stability of the computations are derived and numerical tests with a two-parameter system of three ODEs and an atmospheric chemical scheme with 56 compounds, which is defined mathematically by a very stiff and ill-conditioned system of non-linear ODEs, are presented. The research results described in this paper can be considered as a continuation of the study carried out in Zlatev et al.: Richardson Extrapolation: Practical Aspects and Applications. De Gruyter, Berlin (2017).

UNI-DEM is a large-scale environmental model described by a non-linear system of partial differential equations (PDEs) and used in many studies of air pollution levels in different European countries. The discretization of UNI-DEM leads to a long series of huge computational tasks, because it is necessary to run the discretized model with many different scenarios during long time-periods of many consecutive years. Therefore, both the storage requirements and the computational work are enormous. We had to resolve four difficult problems in the efforts to perform successfully the required simulations. More precisely, we had to do the following: (a) to implement fast numerical methods, (b) to select suitable splitting procedures, (c) to exploit efficiently the cache memories of the available high-speed computers (d) to parallelize the computer codes.

This paper analyzes the operational reliability assessment of systems containing electronic element supplied in medicine. The analysis is based on the probability modeling through a Markov process. The identification of the system states is conducted from the system workability point of view. The possibilities for transitions from one system state to another are also analyzed. The analysis performed is illustrated by a case study of operational reliability indices estimation in regard to a type of semi-automatic blood pressure monitor. The basis of the case study are statistical data obtained regarding operational events occurred during the system operation. As a result of the analysis and the case study some prescriptions are suggested to be considered for to increase the operational system reliability.

This chapter focuses on the growth of trade and economy in USA and Mexico as compared to the world trade relative to income growth since 2001. The spatial and temporal analysis has been done in reference to manufacturing, services, and corporate social responsibility of large companies. This chapter critically examines the six global trade slowdowns and analyzes its structural and cyclical nature among the North American countries. The available evidence suggests that the explanation may lie in the slowing pace of international vertical specialization rather than increasing protection or the changing composition of trade and GDP. This chapter discusses the structural growth in business in reference to the product portfolio, market share, international trade, investment, and contribution of corporate business to GDP in the manufacturing sector. The chapter holds discussions on the impact of corporate social responsibilities on the structural growth of international trade within cross-cultural and socio-political relations.

Growth in international trade is not linear, but often discrete and unpredictable. Companies engaged in cross-border trade in the North American region need both the strategic directions and ability to shift their approach to drive on a sustainable growth path in the long term. It has been observed that companies are leaning toward venture collaborations in the international markets to gain global–local push in business and enhance their performance in the competitive marketplace. The discussions in this chapter outline the shifts of corporate mind-set need to make the business strategies effective and the patterns of common venture collaborations. This chapter discusses corporate and human resources management followed by the companies in doing business in North America. How trade moves with corporate alliances, partnerships, acquisitions, mergers, and joint ventures in most companies as a part of the core international business strategy have been critically examined in this chapter.

The local market competition is targeted toward the customers, and the competitors strive to win the customer, temporarily or permanently. However, in business-to-business process, the competition may turn more tactical and strategic in order to outperform the rivals firms. In this way, competition can be seen as regulated struggle. This chapter addresses the new opportunities in international trade by cooperating with the local industries in the trade region. Restructuring the contract manufacturing policies, updating investment and joint venture strategies, mergers, and acquisition, and building strategic alliances have been categorically discussed in this chapter. There is a need for the companies to work out the process of diagnosing, designing, implementing, and evaluating an effective method of resolving conflicts in the business projects as well as within an organization. This chapter critically examines the drivers and attributes of market chaos, complexities in technology growth, and dynamics of organizational work culture that affect the building and implementation of business projects.

Volatility in consumer markets is different than primary markets. It largely depends on the functional factors in the market such as demand, consumer preferences, supply chain efficiency, innovation and technology, and pricing strategies. The chapter argues that as the thinking is changing, increasing globalization of the markets and technological interventions in business, there is both pragmatic and philosophical shifts in the international trade models. As such, the products and services life cycles and investment benchmarks in the international trade are changing frequently causing the volatility in business models. While addressing these factors, this chapter also analyzes the risk factors in international business toward new product development, brand equity, price volatility, and the ubiquitous role of consumer credit in doing business in the destination markets. The chapter argues that the market volatility and evolution of international market space is governed by the forces that are beyond the control of any company or investor that include government policies, availability of capital, international economic indicators such oil price volatility, and geopolitical conflicts.

The North American Free Trade Agreement has given leverage to the USA and Mexico to gain a competitive advantage in manufacturing by offering infrastructure and services required to turn the industrial production cost effective. It has been estimated by the World Trade Organization that about 50% of global trade flows emerge through the preferential trade agreements between the countries. This trend indicates the growing importance of the regional agreements over the preferential or bilateral trade agreements between the countries as they are comprehensive and offer wider benefits. This chapter discusses the fundamentals of the integration process in the North American trade and economy and delineates how the market integration has been driven through exports, imports, and manufacturing investment made by the member countries which, taken together, have been responsible for 90% of regional imports during 2002–2012. The chapter analyzes the impact of market integration on the economy responding the pertinent questions that remain unresolved, whether the market integration through regional trade agreements delivers the desired benefits to the developing nations as compared to the one with the develop trade and economic conditions.

Corporate success depends on breaking through the clutter of market information and competitive intervention by conducting meticulously the marketing research facing consumers in the marketplace. As the competition is growing continuously in the global market, the risk on traditional decision-making tools and techniques is also falling in jeopardy. This chapter discusses the impact of advanced marketing-mix, operations and logistics, brand management, investments, and transfer of technology toward developing international trade in the North American marketplace. The discussions on approaches for cost-effective trade management, technology breakthroughs, and running real-time business decisions to gain a competitive advantage in the international marketplace are significant contributions in this chapter.

The role of government in promoting international trade is more significant than the entrepreneurial efforts. The diplomatic relations, fiscal and monetary policies, and public economics strategies largely affect international trade dynamics. Governments of developing nations have become cautious of opening more industries to multinational companies. This chapter discusses the role of government from macro to micro perspectives in reference to the North American region countries. Most developing nations prioritize national security more broadly and narrow the scope of foreign companies from entering the domestic marketplace and often favor promoting state-owned enterprises. The chapter argues that the rise of capitalism in international trade has driven globalization’s new risks in managing trade-related public policies in most emerging markets. The political ideology in regional and international economy, the US–Mexico trade support policies, potential conflicts and bilateral conflict resolutions, and the role of international organizations such as WTO, OECD, and the like in bilateral trade development have been discussed critically in this chapter.

Globalization promotes transformations in the business environment and consumer culture along the dimensions of economic geography which can be evidenced with the growth in the urban areas, shorter travel distances as businesses migrate closer to denser population, and generate competition among firms to take advantage of scale and trade in specialized products. The discussion in the chapter demonstrates that multinational firms have been slow to understand consumers in the developing world, and as a result, they have been vulnerable to local competitors that know how their shoppers think, what they crave, and how they buy. This chapter examines critical shifts in political ideology, reengineering bilateral business, business process engineering for higher growth and profit, and corporate dynamics among the US–Mexico firms for mutual growth.

Globalization has driven competition and new challenges among the firms to sustain in the marketplace. The innovation business projects in most companies follow a boom–bust cycle. As the economy prospers companies invest substantial resources in developing innovative projects to lead in the competitive markets while they rethink their priorities in view of the cost-benefit ratios when the markets sour. Growing firms are engaged in developing competitive strategies and innovative differentiations in staying sustainable and competitive in the global marketplace. North American trade and economy had suffered a severe setback after the financial downturn during 2007–2011 that crashed the international trade dynamics and reversed the booming business cycles. The regional agreement among the Canada, Mexico, and the USA had been driving the international trade faster in the region since its implementation in 1994. However, North American Free Trade Agreement (NAFTA) continues to be of interest to boost the regional balance of trade among the member countries as partners and also because this agreement plays a significant role in the US trade policy. This chapter discusses an overview of North American trade liberalization effects in reference to NAFTA and international trade policy perspectives to extend cooperation for rebuilding the trade and economy during the post-economic recession period.

Industrial policy and trade development are interrelated indicators that affect the economic growth of a country. In North America, the USA and Canada have well realized such symbiotic relationship in driving the national economic development. Mexico, being a country following the protectionism for a substantial period in the past and having several economic setbacks, has yet to overcome the black holes in low financial integration, industrial growth, and international trade competitiveness. This chapter critically examines the approach of Mexico and the USA on industrial policy, financial integration, and spending on research and development as an impetus for augmenting the industrial production and trade competitiveness. However, the growing threat of disruptive innovation on the international business has also been discussed in this chapter.

The climatic changes are already causing more and more extreme weather events in many different areas of the Earth. One of the most important consequences of these changes, which has different impacts, is the clear trend for global increase of the temperature. This increase has also some influence on the pollution levels, mainly because (a) many of the damaging pollutants participate in chemical reactions which depend strongly on the temperature and (b) the pollution levels depend also on the natural (biogenic) emissions, which in general are increased when the temperature becomes higher. Therefore, some pollution levels, which are not very dangerous at present, could become harmful in the near future. This is why the influence of the climate changes on the pollution levels should be studied carefully.Some results related to the influence of the climatic changes on some critical levels related to ozone concentrations are reported in this chapter. The mathematical tool applied in this investigation is a large-scale air pollution model developed and used to study pollution levels in Europe. The model is described by a system of partial differential equations. The discretization of this system leads to huge computational tasks and it is difficult to handle it even when some of the fastest computers are used. Several difficult tasks must be resolved in the efforts to make the model tractable on the computers available at present. It is necessary to resolve the following four tasks: (A) to apply advanced numerical methods, (B) to introduce some splitting techniques, (C) to parallelize the computational process and (D) to exploit the cache memories efficiently.Some results, which are obtained when the four requirements (A)–(D) are satisfied, are presented and analysed in the chapter. The results show clearly that the climatic changes will lead to some increase of pollution levels, thus these could become dangerous for human beings.

Explicit Runge-Kutta methods can efficiently be used in the numerical integration of initial value problems for non-stiff systems of ordinary differential equations (ODEs). Let m and p be the number of stages and the order of a given explicit Runge-Kutta method. We have proved in a previous paper [8] that the combination of any explicit Runge-Kutta method with \(m=p\) and the Richardson Extrapolation leads always to a considerable improvement of the absolute stability properties. We have shown in [7] (talk presented at the NM&A14 conference in Borovets, Bulgaria, August 2014) that the absolute stability regions can be further increased when \(p

Crowd evacuation management at large venues such as airports, stadiums, cruise ships or metro stations requires the deployment and access to a Common Operational Picture (COP) of the venue, with real-time intelligent contextual interpretation of crowd behaviour. Large CCTV and sensor network feeds all provide important but heterogeneous observations about crowd safety at the venue of interest. Hence, these observations must be critically analyzed and interpreted for supporting security managers of crowd safety at venues. Specifically, the large volume of the generated observations needs to be interpreted in context of the venue operational grounds, crowd-gathering event times and the knowledge on crowd expected behaviour. In this paper, a new context ontology modelling approach is introduced. It is based on knowledge about venue background information, expected crowd behaviours and their manifested features of observations. The aim is to improve situation awareness about crowd safety in crisis management and decision-support.

The chapter reviews evidence for the bodily mimesis hypothesis, which states that the evolution of language was preceded by an adaptation for improved volitional control of the body, giving our ancestors advantages in the domains of imi- tation, empathy, and gestural communication. Much of this evidence is also shared by other gesture-first theories of language origins, but they face the problem of explaining the "switch" from a gestural (proto) language to a spoken one. The bodily mimesis hypothesis fares better with this objection, since it (a) emphasizes the non- conventionality and non-systematicity of bodily mimetic signaling, (b) posits a long biocultural spiral of conventionalization and adaptation for speech, and (c) insists that the transition to speech should be seen as only partial. Following Brown (2012), a cognitive-semiotic explanation can further be given as to why speech has eventually taken on increasingly higher communicative load: Vocalization is intrinsically less capable of iconic representation, and given a multimodal gestural-vocal communica- tive signal, the vocal element is bound to eventually take on the role of symbolic rep- resentation, involving higher levels of conventionality and systematicity.

Large-scale environmental models can successfully be used in different important for the modern society studies as, for example, in the investigation of the influence of the future climatic changes on pollution levels in different countries. Such models are normally described mathematically by non-linear systems of partial differential equations, which are defined on very large spatial domains and have to be solved numerically on very long time intervals. Moreover, very often many different scenarios have also to be developed and used in the investigations. Therefore, both the storage requirements and the computational work are enormous. The great difficulties can be overcome only if the following four tasks are successfully resolved: (a) fast and sufficiently accurate numerical methods are to be selected, (b) reliable and efficient splitting procedures are to be applied, (c) the cache memories of the available computers are to be efficiently exploited and (d) the codes are to be parallelized.