Organisational Values as "Attractors of Chaos": An Emerging Cultural Change to Manage Organisational Complexity

Business organisations are excellent representations of what in physics and mathematics are designated "chaotic" systems. Because a culture of innovation will be vital for organisational survival in the 21st century, the present paper proposes that viewing organisations in terms of "complexity theory" may assist leaders in fine-tuning managerial philosophies that provide orderly management emphasizing stability within a culture of organised chaos, for it is on the "boundary of chaos" that the greatest creativity occurs. It is argued that 21st century companies, as chaotic social systems, will no longer be effectively managed by rigid objectives (MBO) nor by instructions (MBI). Their capacity for self-organisation will be derived essentially from how their members accept a shared set of values or principles for action (MBV). Complexity theory deals with systems that show complex structures in time or space, often hiding simple deterministic rules. This theory holds that once these rules are found, it is possible to make effective predictions and even to control the apparent complexity. The state of chaos that self-organises, thanks to the appearance of the "strange attractor", is the ideal basis for creativity and innovation in the company. In this self-organised state of chaos, members are not confined to narrow roles, and gradually develop their capacity for differentiation and relationships, growing continuously toward their maximum potential contribution to the efficiency of the organisation. In this way, values act as organisers or "attractors" of disorder, which in the theory of chaos are equations represented by unusually regular geometric configurations that predict the long-term behaviour of complex systems. In business organisations (as in all kinds of social systems) the starting principles end up as the final principles in the long term. An attractor is a model representation of the behavioral results of a system. The attractor is not a force of attraction or a goal-oriented presence in the system; it simply depicts where the system is headed based on its rules of motion. Thus, in a culture that cultivates or shares values of autonomy, responsibility, independence, innovation, creativity, and proaction, the risk of short-term chaos is mitigated by an overall long-term sense of direction. A more suitable approach to manage the internal and external complexities that organisations are currently confronting is to alter their dominant culture under the principles of MBV.

Organisational values as "attractors of chaos": An emerging cultural change to manage organisational complexity

Business organisations are excellent representations of what in physics and mathematics are designated "chaotic" systems. Because a culture of innovation will be vital for organisational survival in the 21st century, the present paper proposes that viewing organisations in terms of "complexity theory" may assist leaders in fine-tuning managerial philosophies that provide orderly management emphasizing stability within a culture of organised chaos, for it is on the "boundary of chaos" that the greatest creativity occurs. It is argued that 21st century companies, as chaotic social systems, will no longer be effectively managed by rigid objectives (MBO) nor by instructions (MBI). Their capacity for self-organisation will be derived essentially from how their members accept a shared set of values or principles for action (MBV). Complexity theory deals with systems that show complex structures in time or space, often hiding simple deterministic rules. This theory holds that once these rules are found, it is possible to make effective predictions and even to control the apparent complexity. The state of chaos that self-organises, thanks to the appearance of the "strange attractor", is the ideal basis for creativity and innovation in the company. In this self-organised state of chaos, members are not confined to narrow roles, and gradually develop their capacity for differentiation and relationships, growing continuously toward their maximum potential contribution to the efficiency of the organisation. In this way, values act as organisers or "attractors" of disorder, which in the theory of chaos are equations represented by unusually regular geometric configurations that predict the long-term behaviour of complex systems. In business organisations (as in all kinds of social systems) the starting principles end up as the final principles in the long term. An attractor is a model representation of the behavioral results of a system. The attractor is not a force of attraction or a goal-oriented presence in the system; it simply depicts where the system is headed based on its rules of motion. Thus, in a culture that cultivates or shares values of autonomy, responsibility, independence, innovation, creativity, and proaction, the risk of short-term chaos is mitigated by an overall long-term sense of direction. A more suitable approach to manage the internal and external complexities that organisations are currently confronting is to alter their dominant culture under the principles of MBV.

Multiple correspondence analysis of a subset of response categories

In the analysis of multivariate categorical data, typically the analysis of questionnaire data, it is often advantageous, for substantive and technical reasons, to analyse a subset of response categories. In multiple correspondence analysis, where each category is coded as a column of an indicator matrix or row and column of Burt matrix, it is not correct to simply analyse the corresponding submatrix of data, since the whole geometric structure is different for the submatrix . A simple modification of the correspondence analysis algorithm allows the overall geometric structure of the complete data set to be retained while calculating the solution for the selected subset of points. This strategy is useful for analysing patterns of response amongst any subset of categories and relating these patterns to demographic factors, especially for studying patterns of particular responses such as missing and neutral responses. The methodology is illustrated using data from the International Social Survey Program on Family and Changing Gender Roles in 1994.

Australian Asian options

We study European options on the ratio of the stock price to its averageand viceversa. Some of these options are traded in the Australian StockExchange since 1992, thus we call them Australian Asian options. Forgeometric averages, we obtain closed-form expressions for option prices.For arithmetic means, we use dierent approximations that produce verysimilar results.

From correspondence analysis to multiple and joint correspondence analysis

The generalization of simple (two-variable) correspondence analysis to more than two categorical variables, commonly referred to as multiple correspondence analysis, is neither obvious nor well-defined. We present two alternative ways of generalizing correspondence analysis, one based on the quantification of the variables and intercorrelation relationships, and the other based on the geometric ideas of simple correspondence analysis. We propose a version of multiple correspondence analysis, with adjusted principal inertias, as the method of choice for the geometric definition, since it contains simple correspondence analysis as an exact special case, which is not the situation of the standard generalizations. We also clarify the issue of supplementary point representation and the properties of joint correspondence analysis, a method that visualizes all two-way relationships between the variables. The methodology is illustrated using data on attitudes to science from the International Social Survey Program on Environment in 1993.

Geometría flexible para las estructuras de barras

This article brings a geometric proposal which can be applied to the bar structures. The starting point is the substitution of the usual knots in a structural web by a system of combining the bars tivo by two, which is achieved by twisting the bars in each knot. The tensile forces that appear and the introduction of joints in each of these knots allow the transition from a rigid or undeformablegeometiy to a neiv flexible" one leading to the possibility of one and the same structural web adopting different sizes while preserving its original geometric form

Unified formalism for non-autonomous mechanical systems

We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (1983). The dynamical equations of motion and their compatibility and consistency are carefully studied, making clear that all the characteristics of the Lagrangian and the Hamiltonian formalisms are recovered in this formulation. As an example, it is studied a semidiscretization of the nonlinear wave equation proving the applicability of the proposed formalism.

Enhanced radar precipitation estimates using a combined clutter and beam blockage correction technique

Weather radar observations are currently the most reliable method for remote sensing of precipitation. However, a number of factors affect the quality of radar observations and may limit seriously automated quantitative applications of radar precipitation estimates such as those required in Numerical Weather Prediction (NWP) data assimilation or in hydrological models. In this paper, a technique to correct two different problems typically present in radar data is presented and evaluated. The aspects dealt with are non-precipitating echoes - caused either by permanent ground clutter or by anomalous propagation of the radar beam (anaprop echoes) - and also topographical beam blockage. The correction technique is based in the computation of realistic beam propagation trajectories based upon recent radiosonde observations instead of assuming standard radio propagation conditions. The correction consists of three different steps: 1) calculation of a Dynamic Elevation Map which provides the minimum clutter-free antenna elevation for each pixel within the radar coverage; 2) correction for residual anaprop, checking the vertical reflectivity gradients within the radar volume; and 3) topographical beam blockage estimation and correction using a geometric optics approach. The technique is evaluated with four case studies in the region of the Po Valley (N Italy) using a C-band Doppler radar and a network of raingauges providing hourly precipitation measurements. The case studies cover different seasons, different radio propagation conditions and also stratiform and convective precipitation type events. After applying the proposed correction, a comparison of the radar precipitation estimates with raingauges indicates a general reduction in both the root mean squared error and the fractional error variance indicating the efficiency and robustness of the procedure. Moreover, the technique presented is not computationally expensive so it seems well suited to be implemented in an operational environment.

Super-resolution of remotely sensed images with variable-pixel linear reconstruction

This paper describes the development and applications of a super-resolution method, known as Super-Resolution Variable-Pixel Linear Reconstruction. The algorithm works combining different lower resolution images in order to obtain, as a result, a higher resolution image. We show that it can make significant spatial resolution improvements to satellite images of the Earth¿s surface allowing recognition of objects with size approaching the limiting spatial resolution of the lower resolution images. The algorithm is based on the Variable-Pixel Linear Reconstruction algorithm developed by Fruchter and Hook, a well-known method in astronomy but never used for Earth remote sensing purposes. The algorithm preserves photometry, can weight input images according to the statistical significance of each pixel, and removes the effect of geometric distortion on both image shape and photometry. In this paper, we describe its development for remote sensing purposes, show the usefulness of the algorithm working with images as different to the astronomical images as the remote sensing ones, and show applications to: 1) a set of simulated multispectral images obtained from a real Quickbird image; and 2) a set of multispectral real Landsat Enhanced Thematic Mapper Plus (ETM+) images. These examples show that the algorithm provides a substantial improvement in limiting spatial resolution for both simulated and real data sets without significantly altering the multispectral content of the input low-resolution images, without amplifying the noise, and with very few artifacts.

Induced aggregation operators in decision making with the Dempster-Shafer belief structure

We study the induced aggregation operators. The analysis begins with a revision of some basic concepts such as the induced ordered weighted averaging (IOWA) operator and the induced ordered weighted geometric (IOWG) operator. We then analyze the problem of decision making with Dempster-Shafer theory of evidence. We suggest the use of induced aggregation operators in decision making with Dempster-Shafer theory. We focus on the aggregation step and examine some of its main properties, including the distinction between descending and ascending orders and different families of induced operators. Finally, we present an illustrative example in which the results obtained using different types of aggregation operators can be seen.

The induced generalized OWA operator

[spa] Se presenta el operador OWA generalizado inducido (IGOWA). Es un nuevo operador de agregación que generaliza al operador OWA a través de utilizar las principales características de dos operadores muy conocidos como son el operador OWA generalizado y el operador OWA inducido. Entonces, este operador utiliza medias generalizadas y variables de ordenación inducidas en el proceso de reordenación. Con esta formulación, se obtiene una amplia gama de operadores de agregación que incluye a todos los casos particulares de los operadores IOWA y GOWA, y otros casos particulares. A continuación, se realiza una generalización mayor al operador IGOWA a través de utilizar medias cuasi-aritméticas. Finalmente, también se desarrolla un ejemplo numérico del nuevo modelo en un problema de toma de decisiones financieras.

Induced aggregation operators in decision making with the Dempster-Shafer belief structure

We study the induced aggregation operators. The analysis begins with a revision of some basic concepts such as the induced ordered weighted averaging (IOWA) operator and the induced ordered weighted geometric (IOWG) operator. We then analyze the problem of decision making with Dempster-Shafer theory of evidence. We suggest the use of induced aggregation operators in decision making with Dempster-Shafer theory. We focus on the aggregation step and examine some of its main properties, including the distinction between descending and ascending orders and different families of induced operators. Finally, we present an illustrative example in which the results obtained using different types of aggregation operators can be seen.

An axiomatization of the nucleolus of the assignment game

[cat] En el domini dels jocs bilaterals d’assignació, es presenta una axiomàtica del nucleolus com l´unica solució que compleix les propietats de consistència respecte del joc derivat definit per Owen (1992) i monotonia de les queixes dels sectors respecte de la seva cardinalitat. Com a conseqüència obtenim una caracterització geomètrica del nucleolus mitjançant una propietat de bisecció més forta que la que satisfan els punts del kernel (Maschler et al, 1979).

The induced generalized OWA operator

[spa] Se presenta el operador OWA generalizado inducido (IGOWA). Es un nuevo operador de agregación que generaliza al operador OWA a través de utilizar las principales características de dos operadores muy conocidos como son el operador OWA generalizado y el operador OWA inducido. Entonces, este operador utiliza medias generalizadas y variables de ordenación inducidas en el proceso de reordenación. Con esta formulación, se obtiene una amplia gama de operadores de agregación que incluye a todos los casos particulares de los operadores IOWA y GOWA, y otros casos particulares. A continuación, se realiza una generalización mayor al operador IGOWA a través de utilizar medias cuasi-aritméticas. Finalmente, también se desarrolla un ejemplo numérico del nuevo modelo en un problema de toma de decisiones financieras.

Origin of a restraining bend in an evolving strike-slip system: The Cenozoic As Pontes basin (NW Spain)

The As Pontes basin (12 km2), NW Iberian Peninsula, is bounded by a double restraining bend of a dextral strike-slip fault, which is related to the western onshore end of the Pyrenean belt. Surface and subsurface data obtained from intensive coal exploration and mining in the basin since the 1960s together with additional structural and stratigraphic sequence analysis allowed us to determine the geometric relationships between tectonic structures and stratigraphic markers. The small size of the basin and the large amount of quality data make the As Pontes basin a unique natural laboratory for improving our understanding of the origin and evolution of restraining bends. The double restraining bend is the end stage of the structural evolution of a compressive underlapping stepover, where the basin was formed. During the first stage (stepover stage), which began ca. 30 Ma ago (latest Rupelian) and lasted 3.4 My, two small isolated basins bounded by thrusts and normal faults were formed. For 1.3 My, the strike-slip faults, which defined the stepover, grew towards each other until joining and forming the double restraining bend, which bounds one large As Pontes basin (transition stage). The history of the basin was controlled by the activity of the double restraining bend for a further 3.4 My (restraining bend stage) and ended in mid-Aquitanian times (ca. 22 Ma).