Current Fluctuations for Independent Random Walks in Multiple Dimensions

Consider a system of particles evolving as independent and identically distributed (i.i.d.) random walks. Initial fluctuations in the particle density get translated over time with velocity [(v)\vec]\vec{v}, the common mean velocity of the random walks. Consider a box centered around an observer who starts at the origin and moves with constant velocity [(v)\vec]\vec{v}. To observe interesting fluctuations beyond the translation of initial density fluctuations, we measure the net flux of particles over time into this moving box. We call this the “box-current” process.     

Density Delay and Organizational Survival: Computational Models and Empirical Comparisons

Research on the ecological dynamics oforganizational populations has demonstrated that competitiveconditions at the time of founding have enduring effects onorganizational survival. According to ecological theories,organizational life chances are systematically affected by density (the number of organizations in a population) at thetime of founding because the lower resource endowments thatcharacterize organizations appearing in periods of highpopulation density tend to become self-reinforcing, and—over time—amplify differences in mortality rates oforganizations founded under different conditions. However,credible arguments have been offered that could justify both positive and negative effects of the delayed effectsof population density on organizational mortality rates, andreceived empirical research in part reflects this ambiguity.To develop new insight into this issue and to explore theboundaries of received empirical results, in this study wepresent a computational model of organizational evolutionaccording to which the global dynamics of organizationalpopulations emerge from the iteration of simple rules oflocal interaction among individual organizations. We use the synthetic data produced by simulation to estimate eventhistory models of organizational mortality, and compare theparameter estimates with those reported in the most recentempirical studies of actual organizational populations. Theconclusions supported by the model qualify and extendreceived empirical results, and suggest that delayed effectsof density are highly sensitive the details of local structure of connections among members of organizationalpopulations.     

The Dynamics of Cultural Influence Networks

This article investigates the behavior of cultural influence networks over time, using a computer simulation based on a formal model of cultural transmission in organizations. In the formal model, every organizational member exerts some cultural influence on, and is influenced by, every other member; these influence paths constitute a dense social network and the weights of paths (ties) vary throughout the network. Over time, each organizational member's enculturation level changes in response to influence from other members, and the influence weight of each path changes in relationship to the cultural similarity of the individuals connected by the path. Virtual experiments explore the configuration and evolution of the cultural influence network under varying demographic conditions and influence principles. Demographic effects are studied by varying organizational size, hiring selectivity and turnover rates. Two principles for determining initial influence path weights are examined, cohort-based influence and random influence. The simulations show that the cultural influence network evolves over time to a robust configuration, fluctuating around a stable dynamic equilibrium as individuals enter and leave the organization. As turnover rates rise, cohort-based influence strengthens the influence network and reduces network inequality. In this model, cohort-based influence processes promote cultural stability in organizations.     

A Model of Obsolescence of Organizational Rules

The phenomenon of obsolescence has found little attention in past research on organizational change. Most research on organizational change has instead been concerned with the opposite of obsolescence, that is, with mechanisms which render organizational structures increasingly persistent. However, everyday experience teaches that organizational structures become outdated as surrounding conditions shift. This article explores obsolescence by means of mathematical modeling and empirical analysis. Obsolescence is conceptualized as a result of flows of conditions in, out, and between two states: consistent conditions and inconsistent conditions. The model predicts that the obsoleteness curve rises with decreasing increments over time. This is tested with empirical data on organizational rule change. The results confirm the obsolescence model. This revised version was published online in August 2006 with corrections to the Cover Date.     

Unifying temporal and organizational scales in multiscale decision-making

In enterprise systems, making decisions is a complex task for agents at all levels of the organizational hierarchy. To calculate an optimal course of action, an agent has to include uncertainties and the anticipated decisions of other agents, recognizing that they also engage in a stochastic, game-theoretic reasoning process. Furthermore, higher-level agents seek to align the interests of their subordinates by providing incentives. Incentive-giving and receiving agents need to include the effect of the incentive on their payoffs in the optimal strategy calculations. In this paper, we present a multiscale decision-making model that accounts for uncertainties and organizational interdependencies over time. Multiscale decision-making combines stochastic games with hierarchical Markov decision processes to model and solve multi-organizational-scale and multi-time-scale problems. This is the first model that unifies the organizational and temporal scales and can solve a 3-agent, 3-period problem. Solutions can be derived as analytic equations with low computational effort. We apply the model to a service enterprise challenge that illustrates the applicability and relevance of the model. This paper makes an important contribution to the foundation of multiscale decision theory and represents a key step towards solving the general X-agent, T-period problem.     

Temperature fluctuations superimposed on background temperature change

Proxy data allows the temperature of the Earth to be mapped over long periods of time. In this work the temperature fluctuations for over 200 proxy data sets were examined and from this set 50 sets were analyzed to test for periodic and quasi-periodic fluctuations in the data sets. Temperature reconstructions over 4 different time scales were analyzed to see if patterns emerged. Data were put into four time intervals; 4,000 years, 14,000 years, 1,000,000 years, and 3,000,000 years and analyzed with a goal to understanding periodic and quasi-periodic patterns in global temperature change superimposed on a “background” average temperature change. Quasi-periodic signatures were identified that predate the Industrial Revolution, during much of which direct data on temperature are not available. These data indicate that Earth temperatures have undergone a number of periodic and quasi-periodic intervals that contain both global warming and global cooling cycles. The fluctuations are superimposed on a background of temperature change that has a declining slope during the two periods, pre-ice age and post ice age with a transition about 12,000 BCE. The data are divided into “events” that span the time periods 3,000,000 BCE to “0” CE, 1,000,000 BCE to “0” CE, 12,000 BCE to 2,000 CE and 2,000 BCE to 2,000 CE. An equation using a quasi-periodic (frequency modulated sine waves) patterns was developed to analyze the date sets for quasi-periodic patterns. “Periodicities” which show reasonable agreement with the predictions of Milankovitch and other investigators were found in the data sets.     

Trapped modes for periodic structures in waveguides

The Laplace operator is considered for waveguides perturbed by a periodic structure consisting of N congruent obstacles spanning the waveguide. Neumann boundary conditions are imposed on the periodic structure, and either Neumann or Dirichlet conditions on the guide walls. It is proven that there are at least N (resp. N‐1) trapped modes in the Neumann case (resp. Dirichlet case) under fairly general hypotheses, including the special case where the obstacles consist of line segments placed parallel to the waveguide walls. Copyright © 2004 John Wiley & Sons, Ltd.     

Circadian rhythm and tumour growth

We address the following question: can one sustain, on the basis of mathematical models, that for cancer cells, the loss of control by circadian rhythm favours a faster growth? This question, which comes from the observation that tumour growth in mice is enhanced by experimental disruption of the circadian rhythm, may be tackled by mathematical modelling of the cell cycle. For this purpose we consider an age-structured population model with control of death (apoptosis) rates and phase transitions, and two eigenvalues: one for periodic control coefficients (via a variant of Floquet theory in infinite dimension) and one for constant coefficients (taken as the time average of the periodic case). We show by a direct proof that, surprisingly enough considering the above-mentioned observation, the periodic eigenvalue is always greater than the steady state eigenvalue when the sole apoptosis rate is concerned. We also show by numerical simulations when transition rates between the phases of the cell cycle are concerned, that, without further hypotheses, no natural hierarchy between the two eigenvalues exists. This at least shows that, if such models are to take account of the above-mentioned observation, control of death rates inside phases is not sufficient, and that transition rates between phases are a key target in proliferation control. To cite this article: J. Clairambault et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Existence Theorems for Periodic Differential Inclusions in IR^N

We study the periodic problem for differential inclusions in R~N.First we look for extremal periodicsolutions.Using techniques from multivalued analysis and a fixed point argument we establish an existencetheorem under some general hypotheses.We also consider the“nonconvex periodic problem”under lowersemicontinuity hypotheses,and the“convex periodic problem”under general upper semicontinuity hypotheseson the multivalued vector field.For both problems,we prove existence theorems under very general hypotheses.Our approach extends existing results in the literature and appear to be the most general results on the nonconvexperiodic problem.     

Protective capacity positioning: Impact on manufacturing cell performance

Protective capacity is the `extra' capacity placed at non-bottleneck resources to absorb random disruptions in planned levels of performance so that the bottleneck resource is more effectively utilized. Although informative, the research related to protective capacity offers little insight into the preferred placement of protective capacity. By building on the existing research, our study develops hypotheses related to protective capacity positioning and then tested them by using a simulation model of a manufacturing cell. The results indicate that the placement of the protective capacity has no practical influence on mean flow time, but it strongly influences bottleneck shiftiness. Specifically, the study's results may indicate that under conditions of high work center utilization, the placement of protective capacity immediately before and after the bottleneck with a higher proportion distributed to the upstream work centers may significantly lower bottleneck shiftiness. Several future research needs are discussed.     

Modeling centralized organization of organizational change

Organizations change with the dynamics of the world. To enable organizations to change, certain structures and capabilities are needed. As all processes, a change process has an organization of its own. In this paper it is shown how within a formal organization modeling approach also organizational change processes can be modeled. A generic organization model (covering both organization structure and behavior) for organizational change is presented and formally evaluated for a case study. This model takes into account different phases in a change process considered in Organization Theory literature, such as unfreezing, movement and refreezing. Moreover, at the level of individuals, the internal beliefs and their changes are incorporated in the model. In addition, an internal mental model for (reflective) reasoning about expected role behavior is included in the organization model.     

The performance of numerical methods for elliptic problems with mixed boundary conditions

We consider solving linear, second order, elliptic partial differential equations with boundary conditions of types Dirichlet (DIR), mixed (MIX), and nearly Neumann (Neu) by using software modules that implement five numerical methods (one finite element and four finite differences). They represent both the new generation of improved methods and the traditional ones; they are: Hermite collocation plus band Gauss elimination (HC), ordinary finite differences plus band Gauss elimination (5P), ordinary finite differences with Dyaknov iteration (DY), DY with Richardson extrapolation to achieve fourth order convergence (D4), and ordinary finite differences with multigrid iteration (MG). We carry out a performance evaluation in which we measure the grid size and the computer time needed to achieve three significant digits of accuracy in the solution. We compute the changes in these two measures as we change boundary condition types from DIR to MIX and MIX to NEU and then test the following hypotheses: (i) the performance of all the modules is degraded by introducing the derivative terms into the boundary conditions; (ii) finite element collocation (HC) is least affected; (iii) the fourth order modules (HC and D4) are less affected than the other second order modules; and (iv) the traditional 5-point finite differences (5P) are most affected. We establish these hypotheses with high levels of confidence by using several sample problems. The most significant conclusion is that a high order collocation method is preferred for problems with general operators and derivatives in the boundary conditions. We also establish with considerable confidence that these modules have the following rankings in absolute comparative time performance: MG (best), HC and D4, DY, and 5P (worst).     

Performance bounds for hierarchical systems under partial dynamic information

This paper discusses a general approach to obtain optimum performance bounds for (N+1)-person deterministic decision problems,N+1>2, with several levels of hierarchy and under partial dynamic information. Both cooperative and noncooperative modes of decision making are considered at the lower levels of hierarchy; in each case, it is shown that the optimum performance of the decision maker at the top of the hierarchy can be obtained by solving a sequence of open-loop (static) optimization problems. A numerical example included in the paper illustrates the general approach.     

The polynomial hierarchy for some structures over the binary words

For each k > 0 we construct an algebraic structure over which the polynomial hierarchy collapses at level k. We also find an algebraic structure over which the polynomial hierarchy does not collapse. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non-linear near-resonance oscillations of an elastic incompressible layer

Plane one-dimensional waves of small amplitude, propagating transverse to an incompressible elastic layer and reflected successively from its boundaries, are considered. The oscillations are caused by small periodic (or close to periodic) external action on one of the layer boundaries, when the period of the external action is close to the period of natural oscillations of the layer. One of the boundaries of the elastic layer is fixed, while the other performs small specified two-dimensional motion in its plane. In such a near-resonance situation, non-linear effects occur which may build up over time. A system of equations is obtained which describes the slow change in the functions characterizing the oscillations of the medium in each period of the external action. It is assumed that all the quantities depend both on real time, any change of which in the approach considered is limited to one period, and on “slow” time, for which one period of real time serves as a small quantity. It is assumed that the evolution of the solution occurs when the slow time changes, while the role of real time is similar to the role of a spatial variable. This system of equations is obtained by the method of averaging over a period of the quantities representing nonlinear terms and the effect of the boundary conditions in the equations. It contains derivatives with respect to the real and slow times and also values of the functions characterizing the solution averaged over a period of the real time. If the averaged values are known, the equations have a hyperbolic form and their solutions can be both continuous and contain weak and strong discontinuities.     

On a Mathematical Comparison between Hierarchy and Network with a Classification of Coordination Structures

This paper proposes a mathematical model to compare a network organization with a hierarchical organization. In order to formulate the model, we define a three-dimensional framework of the coordination structure of a network and of other typical coordination structures. In the framework, we can define a network structure by contrasting it with a hierarchy, in terms of the distribution of decision making, which is one of the main features of information processing. Based on this definition, we have developed a mathematical model for evaluating coordination structures. Using this model, we can derive two boundary conditions among the coordination structures with respect to the optimal coordination structure. The boundary conditions help us to understand why an organization changes its coordination structure from a hierarchy to a network and what factors cause this change. They enable us, for example, to find points of structural change where the optimal coordination structure shifts from a hierarchy to a hierarchy with delegation or from a hierarchy with delegation to a network, when the nature of the task changes from routine to non-routine. In conclusion, our framework and model may provide a basis for discussing the processes that occur when coordination structures change between a hierarchy and a network.     

The Effect of Organizational Communication Media on Organizational Culture and Performance: An Agent-Based Simulation Model

This paper examines the mutual relationship between the communication richness of media used for conducting organizational communication and organizational culture. The richness of the media influences how well the organization might maintain its culture. On the other hand, a strong organizational culture allows a more effective use of the media by providing members with some of the necessary common ground to better understand the information exchanged. These relationships are investigated using an agent-based simulation model (ABM). Our ABM incorporates many partial theories into a coherent and fully defined model, which helps formalize and integrate those theories. Our model allows us to analyze non-linearities and interaction effects, which are difficult to investigate using other techniques. Additionally, the ABM allows us to investigate the dynamics of the phenomenon and generate hypotheses that could then be tested using empirical studies. Given the substantial resources necessary to conduct empirical studies, we think that the present ABM is valuable in helping guide data collection efforts. In this paper, we present results that show that organizational culture can influence the effectiveness of the media used for organizational communication and that a high media richness can help maintain and stabilize a culture. The effect of media richness on organizational culture depends on the initial strength of the culture. In general, for a given richness of the media, an initially strong culture stabilizes faster and becomes stronger through time than an initially weak culture. Additionally, the model suggests that a stable network of contacts among agents fosters a high achievement of organizational tasks. Conversely, when agents are forced to establish contacts with agents outside the usual network for doing their work, the accomplishment of tasks decreases.     

DEA-based predictors for estimating fleet size changes when modelling the introduction of rights-based management

The introduction of individual transferable quotas (ITQs) into a fishery is going to change not only the amount of catch a fleet can take, but often also changes the fleet structure, particularly if total allowable catches are decreased. This can have an impact on the economic, social and environmental outcomes of fisheries management. Management Strategy Evaluation (MSE) modelling approaches are recognised as the most appropriate method for assessing impacts of management, but these require information as to how fleets may change under different management systems. In this study, we test the applicability of data envelopment analysis (DEA) based performance measures as predictors of how a fishing fleet might change under the introduction of ITQs and also at different levels of quota. In particular, we test the assumption that technical efficiency and capacity utilisation are suitable predictors of which boats are likely to exit the fishery. We also consider scale efficiency as an alternative predictor. We apply the analysis to the Torres Strait tropical rock lobster fishery that is transitioning to an ITQ-based management system for one sector of the fishery. The results indicate that capacity utilisation, technical efficiency and scale efficiency are reasonable indicators of who may remain in the fishery post ITQs. We find that the use of these measures to estimate the impacts of lower quota levels provides consistent fleet size estimates at the aggregate level, but which individual vessels are predicted to exit is dependent on the measure used.     

A hybrid evolutionary algorithm for the periodic location-routing problem

The well-known vehicle routing problem (VRP) has been studied in depth over the last decades. Nowadays, generalizations of VRP have been developed for tactical or strategic decision levels of companies but not both. The tactical extension or periodic VRP (PVRP) plans a set of trips over a multiperiod horizon, subject to frequency constraints. The strategic extension is motivated by interdependent depot location and routing decisions in most distribution systems. Low-quality solutions are obtained if depots are located first, regardless of the future routes. In the location-routing problem (LRP), location and routing decisions are tackled simultaneously. Here for the first time, except for some conference papers, the goal is to combine the PVRP and LRP into an even more realistic problem covering all decision levels: the periodic LRP or PLRP. A hybrid evolutionary algorithm is proposed to solve large size instances of the PLRP. First, an individual representing an assignment of customers to combinations of visit days is randomly generated. The evolution operates through an Evolutionary Local Search (ELS) on visit day assignments. The algorithm is hybridized with a heuristic based on the Randomized Extended Clarke and Wright Algorithm (RECWA) to create feasible solutions and stops when a given number of iterations is reached. The method is evaluated over three sets of instances, and solutions are compared to the literature on particular cases such as one-day horizon (LRP) or one depot (PVRP). This metaheuristic outperforms the previous methods for the PLRP.