Finding the set of k-additive dominating measures viewed as a flow problem

n this paper we deal with the problem of obtaining the set of k-additive measures dominating a fuzzy measure. This problem extends the problem of deriving the set of probabilities dominating a fuzzy measure, an important problem appearing in Decision Making and Game Theory. The solution proposed in the paper follows the line developed by Chateauneuf and Jaffray for dominating probabilities and continued by Miranda et al. for dominating k-additive belief functions. Here, we address the general case transforming the problem into a similar one such that the involved set functions have non-negative Möbius transform; this simplifies the problem and allows a result similar to the one developed for belief functions. Although the set obtained is very large, we show that the conditions cannot be sharpened. On the other hand, we also show that it is possible to define a more restrictive subset, providing a more natural extension of the result for probabilities, such that it is possible to derive any k-additive dominating measure from it

Flexibility properties in Complex Analysis and Affine Algebraic Geometry

In the last decades affine algebraic varieties and Stein manifolds with big (infinite-dimensional) automorphism groups have been intensively studied. Several notions expressing that the automorphisms group is big have been proposed. All of them imply that the manifold in question is an Oka-Forstneri\v{c} manifold. This important notion has also recently merged from the intensive studies around the homotopy principle in Complex Analysis. This homotopy principle, which goes back to the 1930's, has had an enormous impact on the development of the area of Several Complex Variables and the number of its applications is constantly growing. In this overview article we present 3 classes of properties: 1. density property, 2. flexibility 3. Oka-Forstneri\v{c}. For each class we give the relevant definitions, its most significant features and explain the known implications between all these properties. Many difficult mathematical problems could be solved by applying the developed theory, we indicate some of the most spectacular ones.Comment: thanks added, minor correction

Searching for improvement

Engineering design can be thought of as a search for the best solutions to engineering problems. To perform an effective search, one must distinguish between competing designs and establish a measure of design quality, or fitness. To compare different designs, their features must be adequately described in a well-defined framework, which can mean separating the creative and analytical parts of the design process. By this we mean that a distinction is drawn between coming up with novel design concepts, or architectures, and the process of detailing or refining existing design architecture. In the case of a given design architecture, one can consider the set of all possible designs that could be created by varying its features. If it were possible to measure the fitness of all designs in this set, then one could identify a fitness landscape and search for the best possible solution for this design architecture. In this Chapter, the significance of the interactions between design features in defining the metaphorical fitness landscape is described. This highlights that the efficiency of a search algorithm is inextricably linked to the problem structure (and hence the landscape). Two approaches, namely, Genetic Algorithms (GA) and Robust Engineering Design (RED) are considered in some detail with reference to a case study on improving the design of cardiovascular stents

Analysis of Layered Social Networks

Prevention of near-term terrorist attacks requires an understanding of current terrorist organizations to include their composition, the actors involved, and how they operate to achieve their objectives. To aid this understanding, operations research, sociological, and behavioral theory relevant to the study of social networks are applied, thereby providing theoretical foundations for new methodologies to analyze non-cooperative organizations, defined as those trying to hide their structure or are unwilling to provide information regarding their operations. Techniques applying information regarding multiple dimensions of interpersonal relationships, inferring from them the strengths of interpersonal ties, are explored. A layered network construct is offered that provides new analytic opportunities and insights generally unaccounted for in traditional social network analyses. These provide decision makers improved courses of action designed to impute influence upon an adversarial network, thereby achieving a desired influence, perception, or outcome to one or more actors within the target network. This knowledge may also be used to identify key individuals, relationships, and organizational practices. Subsequently, such analysis may lead to the identification of exploitable weaknesses to either eliminate the network as a whole, cause it to become operationally ineffective, or influence it to directly or indirectly support National Security Strategy

The instanton method and its numerical implementation in fluid mechanics

A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent developments related to the application of instanton methods to turbulence. Instantons are saddle point configurations of the underlying path integrals. They are equivalent to minimizers of the related Freidlin-Wentzell action and known to be able to characterize rare events in such systems. While there is an impressive body of work concerning their analytical description, this review focuses on the question on how to compute these minimizers numerically. In a short introduction we present the relevant mathematical and physical background before we discuss the stochastic Burgers equation in detail. We present algorithms to compute instantons numerically by an efficient solution of the corresponding Euler-Lagrange equations. A second focus is the discussion of a recently developed numerical filtering technique that allows to extract instantons from direct numerical simulations. In the following we present modifications of the algorithms to make them efficient when applied to two- or three-dimensional fluid dynamical problems. We illustrate these ideas using the two-dimensional Burgers equation and the three-dimensional Navier-Stokes equations

Structural and Cyclical Unemployment: What Can Be Derived from the Matching Function? (in English)

We explain movements in the U-V (unemployment and vacancy) space – that is, the relation-ship between stocks of unemployment and job vacancies, known as the Beveridge curve – in the Czech Republic during 1995–2004. While the Beveridge curve is described by labor-market stocks, we explain shifts in the Beveridge curve using gross labor-market flows by estimating the matching function. We interpret parameter changes of the matching function during the business cycle, distinguishing cyclical and structural changes to the unemployment rate. We find that the labor-market flows are good coincidence predictors of business-cycle turning points. We show that the Czech economy suffers hysteresis (path dependency) on the labor market, which is common in many other developed market economies in the European Union.Beveridge curve, Czech Republic, matching function, panel data, structural unemployment

Exposure-Based Cash-Flow-at-Risk for Value-Creating Risk Management under Macroeconomic Uncertainty

A strategically minded CFO will realize that strategic corporate risk management is about finding the right balance between risk prevention and proactive value generation. Efficient risk and performance management requires adequate assessment of risk and risk exposures on the one hand and performance on the other. Properly designed, a risk measure should provide information on to what extend the firm's performance is at risk, what is causing that risk, the relative importance of non-value-adding and value-adding risk, and the possibilities to use risk management to reduce total risk. In this chapter, we present an approach – exposure-based cash-flow-at-risk – to calculating a firm's downside risk conditional on the firm's exposure to non-value-adding macroeconomic and market risk and to analyzing corporate performance adjusted for the impact of non-value-adding risk.Cash-flow-at risk; Value at risk; Risk management; Value creation; Total risk

Economies of scale and efficiency measurement in Switzerland's Nursing homes

This paper examines the cost efficiency in the nursing home industry, an issue of concern to Swiss policy makers because of the explosive growth of national expenditure on elderly care and the aging of the population. A stochastic cost frontier model with a translog function has been applied to a balanced panel data of 1780 observations from 356 nursing homes operating over five years (1998-2002) in Switzerland. We compare the estimation results from different panel data econometric techniques focusing on the various methods of specification of unobserved heterogeneity across firms. In particular, the potential effects of such unobserved factors on the estimation results and their interpretation have been discussed. The paper eventually addresses three empirical issues: (1) the measurement of economies of scale in the nursing home sector, (2) the assessment of the economic performance of the firms by estimating their cost efficiency scores, and (3) the role of unobserved heterogeneity in the estimation process. The findings suggest that the economies of scale are an important potential source of cost reduction in a majority of Swiss nursing homes. Taking the size as given the efficiency performance of most individual units is practically very close to the estimated best practice. Nevertheless, the efficiency estimates suggest that some of the nursing homes can significantly reduce their costs by improving their operations.COST EFFICIENCY, ECONOMIES OF SCALE, NURSING HOMES, STOCHASTIC FRONTIER, PANEL DATA