A model and simulation for homeorhesis in the motion of a single individual

In contrast to nonliving systems, all living systems perform homeorhesis. The system state tends to the so-called necessary path, or creode, when the exogenous signals are in a certain system-relevant range. The present work develops the homeorhesis-aware dynamical model for the motion of a single individual (e.g., human). The model allows for the purposeful behaviour of the individual, the creode, the exogenous forces, and the individual-specific sensitivity to their influences. The model also describes the homeorhetic-dysfunction movements. The transparency of the model is such that it allows a physical analogue in the form of electronic circuits. The model is a first step towards the construction of sociologically relevant models for the prediction of human behaviour. It is indispensable for the analyses of dangerous scenarios where the experiments are impossible, for example when predicting the behaviour of panic-stricken crowds in life-threatening situations. The work illustrates the corresponding numerical-simulation results with a series of figures and suggests topics for future research.     

Robust weighted vertex p-center model considering uncertain data: An application to emergency management

This paper presents a generalized weighted vertex p-center (WVPC) model that represents uncertain nodal weights and edge lengths using prescribed intervals or ranges. The objective of the robust WVPC (RWVPC) model is to locate p facilities on a given set of candidate sites so as to minimize worst-case deviation in maximum weighted distance from the optimal solution. The RWVPC model is well-suited for locating urgent relief distribution centers (URDCs) in an emergency logistics system responding to quick-onset natural disasters in which precise estimates of relief demands from affected areas and travel times between URDCs and affected areas are not available. To reduce the computational complexity of solving the model, this work proposes a theorem that facilitates identification of the worst-case scenario for a given set of facility locations. Since the problem is NP-hard, a heuristic framework is developed to efficiently obtain robust solutions. Then, a specific implementation of the framework, based on simulated annealing, is developed to conduct numerical experiments. Experimental results show that the proposed heuristic is effective and efficient in obtaining robust solutions. We also examine the impact of the degree of data uncertainty on the selected performance measures and the tradeoff between solution quality and robustness. Additionally, this work applies the proposed RWVPC model to a real-world instance based on a massive earthquake that hit central Taiwan on September 21, 1999.     

An approximation algorithm for scheduling trees of malleable tasks

This work presents an approximation algorithm for scheduling the tasks of a parallel application. These tasks are considered as malleable tasks (MT in short), which means that they can be executed on several processors. This model receives recently a lot of attention, mainly due to their practical use for implementing actual parallel applications. Most of the works developed within this model deal with independent MT for which good approximation algorithms have been designed. This work is devoted to the case where MT are linked by precedence relations. We present a 4(1+ϵ) approximation algorithm (for any fixed ϵ) for the specific structure of a tree. This preliminary result should open the way for further investigations concerning arbitrary precedence graphs of MT.     

Approximate maximizers of intricacy functionals

G. Edelman, O. Sporns, and G. Tononi introduced in theoretical biology the neural complexity of a family of random variables. A previous work showed that this functional is a special case of intricacy, i.e., an average of the mutual information of subsystems with specific mathematical properties. Moreover, its maximum value grows at a definite speed with the size of the system. In this work, we compute exactly this speed of growth by building “approximate maximizers” subject to an entropy condition. These approximate maximizers work simultaneously for all intricacies. We also establish some properties of arbitrary approximate maximizers, in particular the existence of a threshold in the size of subsystems of approximate maximizers: most smaller subsystems are almost equidistributed, most larger subsystems determine the full system. The main ideas are a random construction of almost maximizers with a high statistical symmetry and the consideration of entropy profiles, i.e., the average entropies of sub-systems of a given size. The latter gives rise to interesting questions of probability and information theory.     

Well-posedness of an infinite system of partial differential equations modelling parasitic infection in an age-structured host

We study a deterministic model for the dynamics of a population infected by macroparasites. The model consists of an infinite system of partial differential equations, with initial and boundary conditions; the system is transformed in an abstract Cauchy problem on a suitable Banach space, and existence and uniqueness of the solution are obtained through multiplicative perturbation of a linear C₀-semigroup. Positivity and boundedness are proved using the specific form of the equations.     

A hypercube queueing loss model with customer-dependent service rates

This paper is concerned with the solution of a specific hypercube queueing model. It extends the work that was described in a related paper by Atkinson et al. [Atkinson, J.B., Kovalenko, I.N., Kuznetsov, N., Mykhalevych, K.V., 2006. Heuristic methods for the analysis of a queuing system describing emergency medical services deployed along a highway. Cybernetics & Systems Analysis, 42, 379–391], which investigated a model for deploying emergency services along a highway. The model is based on the servicing of customer demands that arise in a number of distinct geographical zones, or atoms. Service is provided by servers that are positioned at a number of bases, each having a fixed geographical location along the highway. At each base a single server is available. Demands arising in any atom have a first-preference base and a second-preference base. If the first-preference base is busy, service is provided by the second-preference base; and, if both bases are busy, the demand is lost. In practice, because of differences in travel times from the first and second-preference bases to the atom in question, the service rate may be significantly different in the two cases. The model studied here allows for such customer-dependent service rates to occur, and the corresponding hypercube model has 3ⁿ states, where n is the number of bases. The computational intractability of this model means that exact solutions for the long-run proportion of lost demands (p_loss) can be obtained only for small values of n. In this paper, we propose two heuristic methods and a simulation approach for approximating p_loss. The heuristics are shown to produce very accurate estimates of p_loss.     

Large deviations and estimation in infinite-dimensional models

Consider a random sample from a statistical model with an unknown, and possibly infinite-dimensional, parameter - e.g., a nonparametric or semiparametric model - and a real-valued functional T of this parameter which is to be estimated. The objective is to develop bounds on the (negative) exponential rate at which consistent estimates converge in probability to T, or, equivalently, lower bounds for the asymptotic effective standard deviation of such estimates - that is, to extend work of R.R. Bahadur from parametric models to more general (semiparametric and nonparametric) models. The approach is to define a finite-dimensional submodel, determine Bahadur's bounds for a finite-dimensional model, and then ‘sup’ or ‘inf’ the bounds with respect to ways of defining the submodels; this can be construed as a ‘directional approach’, the submodels being in a specified ‘direction’ from a specific model. Extension is made to the estimation of vector-valued and infinite-dimensional functionals T, by expressing consistency in terms of a distance, or, alternatively, by treating classes of real functionals of T. Several examples are presented.     

A study of repairable parts inventory system operating under performance-based contract

Performance-Based Logistics (PBL) is becoming a dominant logistics support strategy, especially in the defense industry. PBL contracts are designed to serve the customer’s key performance measures, while the traditional contracts for after-sales services, such as Fixed-price (FP) and Cost-plus (C+), only provide insurance or incentive. In this research, we develop an inventory model for a repairable parts system operating under a PBL contract. We model the closed-loop inventory system as an M/M/m queue in which component failures are Poisson distributed and the repair times at the service facility are exponential. Our model provides the supplier and the customer increased flexibility in achieving target availability. Analysis of key parameters suggests that to improve the availability of the system with repairable spare parts, the supplier should work to improve the components reliability and efficiency of repair facility, rather than the base stock level, which has minimal impact on system availability.     

Instability of equilibrium points of some Lagrangian systems

In this work we show that, if L is a natural Lagrangian system such that the k-jet of the potential energy ensures it does not have a minimum at the equilibrium and such that its Hessian has rank at least n−2, then there is an asymptotic trajectory to the associated equilibrium point and so the equilibrium is unstable. This applies, in particular, to analytic potentials with a saddle point and a Hessian with at most 2 null eigenvalues.The result is proven for Lagrangians in a specific form, and we show that the class of Lagrangians we are interested can be taken into this specific form by a subtle change of spatial coordinates. We also consider the extension of this results to systems subjected to gyroscopic forces.     

Evaluation of time-varying availability in multi-echelon spare parts systems with passivation

The popular models for repairable item inventory, both in the literature as well as practical applications, assume that the demands for items are independent of the number of working systems. However this assumption can introduce a serious underestimation of availability when the number of working systems is small, the failure rate is high or the repair time is long. In this paper, we study a multi-echelon repairable item inventory system under the phenomenon of passivation, i.e. serviceable items are passivated (“switched off”) upon system failure. This work is motivated by corrective maintenance of high-cost technical equipment in the miltary. We propose an efficient approximation model to compute time-varying availability. Experiments show that our analytical model agrees well with Monte Carlo simulation.     

Qualitative analysis of steady states to the Sel'kov model

In this work, we are concerned with a reaction-diffusion system well known as the Sel'kov model, which has been used for the study of morphogenesis, population dynamics and autocatalytic oxidation reactions. We derive some further analytic results for the steady states to this model. In particular, we show that no nonconstant positive steady state exists if 0<p?1 and θ is large, which provides a sharp contrast to the case of p>1 and large θ, where nonconstant positive steady states can occur. Thus, these conclusions indicate that the parameter p plays a crucial role in leading to spatially nonhomogeneous distribution of the two reactants. The a priori estimates are fundamental to our mathematical approaches.     

A combination of time-scale calculus and a cross-validation technique used in fitting and evaluating fractional models

In this work, we demonstrate how fractional calculus and time-scale calculus can be combined beautifully to solve and fit a modeling problem. In addition, a cross-validation technique is used to evaluate the fitted model. The specific application that we consider is the one-compartment model. The one-compartment model is a first-order differential equation that describes drug concentration over time. It turns out that approximating the solution by using a fractional model allows us to get more accurate results for model fitting. To quantitatively verify this insight, we compare between a first-order model and anα-order fractional model using real data for drug concentration. Then the mean squared error and a cross-validation method are used to determine the model that provides the best fit and predictions for unseen data.     

Properties of certain zero column-sum matrices with applications to the optimization of chemical reactors

This work is motivated by linear chemical reactor systems. The mathematical model of these systems employs a finite dimensional concentration vector which yields the properties of a discrete probability distribution. Central in the response of the system is a rate matrix. The properties of these matrices are analyzed in terms of the theories of Markoff and M-matrices. A linear objective function is selected and the optimization of a cascade system relative to changes of the sizes of the tanks is pursued. This amounts to the optimization of the objective function on R₊^m. The global optimum is shown to lie on the diagonal of the domain. Hence, the search for optimum can be simplified to a single dimension. Other related topics such as the effect of the number of tanks in the cascade on the optimum, conditions for off-diagonal stationary points and the constrained optimization are also considered.     

Modeling traffic flow interrupted by incidents

A steady-state M/M/c queueing system under batch service interruptions is introduced to model the traffic flow on a roadway link subject to incidents. When a traffic incident happens, either all lanes or part of a lane is closed to the traffic. As such, we model these interruptions either as complete service disruptions where none of the servers work or partial failures where servers work at a reduced service rate. We analyze this system in steady-state and present a scheme to obtain the stationary number of vehicles on a link. For those links with large c values, the closed-form solution of M/M/∞ queues under batch service interruptions can be used as an approximation. We present simulation results that show the validity of the queueing models in the computation of average travel times.     

Reliable compartmental models for double-pipe heat exchangers: An analytical study

In this work, the analytical properties of the heat exchanger infinite-dimensional dynamic model are discussed. More importantly, those of a 2nd-order lumped-parameter model using the logarithmic mean temperature difference (LMTD) as driving force are derived and shown to agree with those of the former. Three essential aspects are focused: existence and uniqueness of solutions, equilibrium states, and stability properties. The results developed in this work are intended to supply a solid support for the reliability on the use of the kind of simple compartmental model that is treated. This is specially addressed to works where it is not the quantitative solutions but the qualitative behavior that is important, like modelling and simulation of heat exchanger networks and complex industrial processes where heat exchangers are involved.     

The General Two-Server Queueing Loss System: Discrete-Time Analysis and Numerical Approximation of Continuous-Time Systems

The Erlang Loss formula is a widely used model for determining values of the long-run proportion of customers that are lost (p_loss values) in multi-server loss systems with Poisson arrival processes. There is a need for models that are less restrictive. Here, the general two-server loss system is investigated with no restrictions on the form that the renewal type input process takes; i.e. the underlying model is based on the GI/G/2 model of queueing theory. The analysis is carried out in discrete time leading to a compact system of equations that can be solved numerically, or in special cases exactly, to obtain p_loss values. Exact results are obtained for some specific loss systems involving geometric distributions and, by taking appropriate limits, these results are extended to their continuous-time counterparts. A simple numerical procedure is developed to allow systems involving arbitrary continuous distributions to be approximated by the discrete-time model, leading to very accurate results for a set of test problems.     

Conversion estimates for gas-solid reactions

Many chemical engineering processes involve a reaction between a diffusing substance and an immobile solid phase. The usual treatments are based on the assumptions that either diffusion or reaction dominates. Instead, we shall model an isothermal process in which reaction and diffusion are of the same order as would occur, for instance, in low temperature coke burning. Mass balances then lead to a parabolic system for the concentrations of the two phases. The system can be reduced to a scalar parabolic problem for the cumulative gas concentration. The popular pseudo-steady-state approximation is then obtained by setting the porosity ∈ equal to zero. This pseudo-steady-state problem is an elliptic problem in which time appears only as a parameter in the boundary condition. In previous work, we have shown that the pseudo-steady-state solution provides an O(∈) approximation to the exact concentration, uniformly in space and time. The present paper is concerned with estimates for the conversion, that is, the fraction of solid that has been converted to products by time t. We obtain bounds for the conversion in terms of a similar quantity (explicity calculable in some cases) for the pseudo-steady-state problem.     

The effect of variability in a closed-loop conveyor system

A production system consisting of a work station, a loading and unloading stations linked by a closed-loop material-handling system is considered. The material-handling system consists of two continuous line conveyors. Each conveyor is assumed to have a specified constant velocity, length and capacity. The work station is assumed to have a single machine, an unloading station and no local storage. In this production system the work pieces, which at their instant of arrival find the work station busy, are blocked. Those work pieces bypass the work station and are transported by the conveyor to the loading station to merge with the incoming work pieces to be transported to the work station again. The above production system is modeled by a G/G/1/0 queueing loss system with retrials, stationary counting arrival process, generally distributed service times, a single server and no waiting room. The flow of work pieces inside the system is modeled by a point process and is approximated by a renewal process. To analyze the asymptotic performance of the above system, a recursive procedure is developed. Furthermore, an expression for the asymptotic distribution of the number of work pieces along each conveyor is derived and is used to control the congestion along the material handling system. Finally numerical results are provided and compared against those from a simulation study.     

Models for products

This paper explores how models can support productive thinking. For us a model is a thing, a tool to help make sense of something. We restrict attention to specific models for whole-number multiplication, hence the wording of the title. They support evolving thinking in large measure through the ways their users redesign them. They assume new forms, come to be seen and understood in different ways. We show how work that learners do with models can help them to transform, not simply their understanding of key concepts, but also how they come to view themselves as thinkers and learners, as collaborators in a social process that their work and thinking help to constitute. We draw on recent research on core knowledge, especially by Carey, Spelke, and Tomasello, to clarify how models, as we view them here, can underpin specific actions that support emerging understanding.