64 research outputs found
Analysis of logistic growth models
A variety of growth curves have been developed to model both unpredated, intraspecific
population dynamics and more general biological growth. Most successful predictive models are
shown to be based on extended forms of the classical Verhulst logistic growth equation. We further
review and compare several such models and calculate and investigate properties of interest for
these. We also identify and detail several previously unreported associated limitations and restrictions.
A generalized form of the logistic growth curve is introduced which is shown incorporate these
models as special cases. The reported limitations of the generic growth model are shown to be addressed
by this new model and similarities between this and the extended growth curves are identified.
Several of its properties are also presented. We furthermore show that additional growth characteristics
are accommodated by this new model, enabling previously unsupported, untypical population dynamics to
be modelled by judicious choice of model parameter values alone
Analysis of reinforcement learning strategies for predation in a mimic-model prey environment
In this paper we propose a mathematical learning model for a stochastic automaton simulating the
behaviour of a predator operating in a random environment occupied by two types of prey:
palatable mimics and unpalatable models. Specifically, a well known linear reinforcement learning
algorithm is used to update the probabilities of the two actions, eat prey or ignore prey, at every
random encounter. Each action elicits a probabilistic response from the environment that can be
either favorable or unfavourable. We analyse both fixed and varying stochastic responses for the
system. The basic approach of mimicry is defined and a short review of relevant previous approaches in
the literature is given. Finally, the conditions for continuous predator performance improvement are
explicitly formulated and precise definitions of predatory efficiency and mimicry efficiency are
also provided
Deterministic and stochastic optimal inventory control with logistic stock-dependent demand rate
It has been suggested by many supply chain practitioners that in certain cases inventory can have a stimulating effect on the demand. In mathematical terms this amounts to the demand being a function of the inventory level alone. In this work we propose a logistic growth model for the inventory dependent demand rate and solve first the continuous time deterministic optimal control problem of maximising the present value of the total net profit over an infinite horizon. It is shown that under a strict condition there is a unique optimal stock level which the inventory planner should maintain in order to satisfy demand. The stochastic version of the optimal control problem is considered next. A bang-bang type of optimal control problem is formulated and the associated Hamilton-Jacobi-Bellman equation is solved. The inventory level that signifies a switch in the ordering strategy is worked out in the stochastic case. Copyright © 2014 Inderscience Enterprises Ltd
An optimal inventory pricing and ordering strategy subject to demand dependent on stock level and price
This article considers the deterministic singular optimal control problem of profit maximisation for inventory replenished at a variable rate and depleted by demand which is assumed to vary with price and stock availability. Optimal policies for the product order rate and price are derived using the maximum principle. Several initial inventory regions are identified as potential inventory states for feasible profit optimisation. Bounds on the maximum price for maximising net profit or minimising loss are obtained. Numerical simulations accompanied by phase diagrams are performed to support the theoretical findings
An Optimal Inventory Pricing and Ordering Strategy Subject to Stock and Price Dependent Demand
This article considers the deterministic optimal control problem of profit maximization for inventory replenished at a variable rate and depleted by demand which is assumed to vary with price and stock availability. Optimal policies for the inventor, product order rate and price are derived using the maximum principle. Bounds on the maximum price possible are also derived
Identification of Crisis Management Influencing Factors in the Abu Dhabi Police Force, United Arab Emirates
Through various disasters, due to both anthropological and natural causes, the development of effective crisis management (CM) mechanisms has become inevitably critical in order to reduce not only various types of losses, but also the potential magnitude of future calamities (Sahin, 2009). Although a number of researchers examined effective CM in organisations located in and/or managed by Western countries (Adams and Stewart, 2014), little has been conducted in the United Arab Emirates (UAE). In fact, to date, there has been no such research applied to any UAE police department. Thus, this study aims to review CM within the General Headquarters (GHQ) of Abu Dhabi Police in order to identify potential influencing factors contributing to effective CM in the organisation, and eventually develop a holistic framework based on global benchmarking
A nonlinear mixed-effects modeling approach for ecological data: Using temporal dynamics of vegetation moisture as an example
Increasingly, often ecologist collects data with nonlinear trends, heterogeneous variances, temporal correlation, and hierarchical structure. Nonlinear mixed-effects models offer a flexible approach to such data, but the estimation and interpretation of these models present challenges, partly associated with the lack of worked examples in the ecological literature. We illustrate the nonlinear mixed-effects modeling approach using temporal dynamics of vegetation moisture with field data from northwestern Patagonia. This is a Mediterranean-type climate region where modeling temporal changes in live fuel moisture content are conceptually relevant (ecological theory) and have practical implications (fire management). We used this approach to answer whether moisture dynamics varies among functional groups and aridity conditions, and compared it with other simpler statistical models. The modeling process is set out âstep-by-stepâ: We start translating the ideas about the system dynamics to a statistical model, which is made increasingly complex in order to include different sources of variability and correlation structures. We provide guidelines and R scripts (including a new self-starting function) that make data analyses reproducible. We also explain how to extract the parameter estimates from the R output. Our modeling approach suggests moisture dynamic to vary between grasses and shrubs, and between grasses facing different aridity conditions. Compared to more classical models, the nonlinear mixed-effects model showed greater goodness of fit and met statistical assumptions. While the mixed-effects approach accounts for spatial nesting, temporal dependence, and variance heterogeneity; the nonlinear function allowed to model the seasonal pattern. Parameters of the nonlinear mixed-effects model reflected relevant ecological processes. From an applied perspective, the model could forecast the time when fuel moisture becomes critical to fire occurrence. Due to the lack of worked examples for nonlinear mixed-effects models in the literature, our modeling approach could be useful to diverse ecologists dealing with complex data.Fil: Oddi, Facundo JosĂ©. Universidad Nacional de RĂo Negro. Sede Andina. Instituto de Investigaciones en Recursos Naturales, AgroecologĂa y Desarrollo Rural; Argentina. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; ArgentinaFil: Miguez, Fernando E.. University of Iowa; Estados UnidosFil: Ghermandi, Luciana. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - Patagonia Norte. Instituto de Investigaciones en Biodiversidad y Medioambiente. Universidad Nacional del Comahue. Centro Regional Universidad Bariloche. Instituto de Investigaciones en Biodiversidad y Medioambiente; ArgentinaFil: Bianchi, Lucas Osvaldo. Universidad Nacional de RĂo Negro. Sede Andina. Instituto de Investigaciones en Recursos Naturales, AgroecologĂa y Desarrollo Rural; Argentina. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; ArgentinaFil: Garibaldi, Lucas Alejandro. Universidad Nacional de RĂo Negro. Sede Andina. Instituto de Investigaciones en Recursos Naturales, AgroecologĂa y Desarrollo Rural; Argentina. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; Argentin
A Stochastic Differential Equation Inventory Model
© 2018, The Author(s). Inventory for an item is being replenished at a constant rate whilst simultaneously being depleted by demand growing randomly and in relation to the inventory level. A stochastic differential equation is put forward to model this situation with solutions to it derived when analytically possible. Probabilities of reaching designated a priori inventory levels from some initial level are considered. Finally, the existence of stable inventory states is investigated by solving the FokkerâPlanck equation for the diffusion process at the steady state. Investigation of the stability properties of the FokkerâPlanck equation reveals that a judicious choice of control strategy allows the inventory level to remain in a stable regime
The Epidemics of Donations: Logistic Growth and Power-Laws
This paper demonstrates that collective social dynamics resulting from individual donations can be well described by an epidemic model. It captures the herding behavior in donations as a non-local interaction between individual via a time-dependent mean field representing the mass media. Our study is based on the statistical analysis of a unique dataset obtained before and after the tsunami disaster of 2004. We find a power-law behavior for the distributions of donations with similar exponents for different countries. Even more remarkably, we show that these exponents are the same before and after the tsunami, which accounts for some kind of universal behavior in donations independent of the actual event. We further show that the time-dependent change of both the number and the total amount of donations after the tsunami follows a logistic growth equation. As a new element, a time-dependent scaling factor appears in this equation which accounts for the growing lack of public interest after the disaster. The results of the model are underpinned by the data analysis and thus also allow for a quantification of the media influence
A stochastic differential equation analysis of cerebrospinal fluid dynamics
<p>Abstract</p> <p>Background</p> <p>Clinical measurements of intracranial pressure (ICP) over time show fluctuations around the deterministic time path predicted by a classic mathematical model in hydrocephalus research. Thus an important issue in mathematical research on hydrocephalus remains unaddressed--modeling the effect of noise on CSF dynamics. Our objective is to mathematically model the noise in the data.</p> <p>Methods</p> <p>The classic model relating the temporal evolution of ICP in pressure-volume studies to infusions is a nonlinear differential equation based on natural physical analogies between CSF dynamics and an electrical circuit. Brownian motion was incorporated into the differential equation describing CSF dynamics to obtain a nonlinear stochastic differential equation (SDE) that accommodates the fluctuations in ICP.</p> <p>Results</p> <p>The SDE is explicitly solved and the dynamic probabilities of exceeding critical levels of ICP under different clinical conditions are computed. A key finding is that the probabilities display strong threshold effects with respect to noise. Above the noise threshold, the probabilities are significantly influenced by the resistance to CSF outflow and the intensity of the noise.</p> <p>Conclusions</p> <p>Fluctuations in the CSF formation rate increase fluctuations in the ICP and they should be minimized to lower the patient's risk. The nonlinear SDE provides a scientific methodology for dynamic risk management of patients. The dynamic output of the SDE matches the noisy ICP data generated by the actual intracranial dynamics of patients better than the classic model used in prior research.</p
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