Stochastic Setup Research Articles

Role Reversals in a Tri-Trophic Prey–Predator Interaction System: A Model-Based Study Using Deterministic and Stochastic Approaches

It is frequently observed that adult members of prey species sometimes use their predation mechanism on juvenile members of predator species. Ecological literature describes this phenomenon as prey–predator role reversal dynamics.Numerous authors have observed and described the biological development behind this feeding behaviour. However, the dynamics of this role reversal have hardly been illustrated in the literature in a precise way. In this regard, we formulated an ecological model using the standard prey–predator interactions, allowing for a reverse feeding mechanism. The mathematical model consisted of a three-species food-web structure comprising the common prey, intermediate predator, and top predator. Note that a role-reversal mechanism was observed between the intermediate and top predators based on the scarcity of the prey population. However, we observed the most critical parameters had a significant effect on this reverse feeding behaviour. The bifurcation analysis is the primary criterion for this identification. The proposed deterministic model is then extended to its stochastic analogue by allowing for environmental influences on the tri-trophic food web structure. The conditional moment approach is applied to obtain the equilibrium distribution of populations and their conditional moments in the system. The stochastic setup analysis also supports the stability of this food chain structure, with some restricted conditions. Finally, to facilitate the interpretation of our mathematical results, we investigated it using numerical simulations.

Instantaneous maturity rate: a novel and compact characterization of biological growth curve models.

Modeling and analysis of biological growth curves are an age-old study area in which much effort has been dedicated to developing new growth equations. Recent efforts focus on identifying the correct model from a large number of equations. The relative growth rate (RGR), developed by Fisher (1921), has largely been used in the statistical inference of biological growth curve models. It is convenient to express growth equations using RGR, where RGR can be expressed as functions of size or time. Even though RGR is model invariant, it has limitations when it comes to identifying actual growth patterns. By proposing interval-specific rate parameters (ISRPs), Pal et al. (2018) appeared to solve this problem. The ISRP is based on the mathematical structure of the growth equations. Therefore, it is not model invariant. The current effort is to develop a measure of growth that is model invariant like RGR and shares the advantages of ISRP. We propose a new measure of growth, which we call instantaneous maturity rate (IMR). IMR is model invariant, which allows it to distinguish growth patterns more clearly than RGR. IMR is also scale-invariant and can take several forms including increasing, decreasing, constant, sigmoidal, bell-shaped, and bathtub. A wide range of possible IMR shapes makes it possible to identify different growth curves. The estimation procedure of IMR under a stochastic setup has been developed. Statistical properties of empirical IMR estimators have also been investigated in detail. In addition to extensive simulation studies, real data sets have been analyzed to prove the utility of IMR.

A noble extended stochastic logistic model for cell proliferation with density-dependent parameters

Cell proliferation often experiences a density-dependent intrinsic proliferation rate (IPR) and negative feedback from growth-inhibiting molecules in culture media. The lack of flexible models with explanatory parameters fails to capture such a proliferation mechanism. We propose an extended logistic growth law with the density-dependent IPR and additional negative feedback. The extended parameters of the proposed model can be interpreted as density-dependent cell-cell cooperation and negative feedback on cell proliferation. Moreover, we incorporate further density regulation for flexibility in the model through environmental resistance on cells. The proposed growth law has similarities with the strong Allee model and harvesting phenomenon. We also develop the stochastic analog of the deterministic model by representing possible heterogeneity in growth-inhibiting molecules and environmental perturbation of the culture setup as correlated multiplicative and additive noises. The model provides a conditional maximum sustainable stable cell density (MSSCD) and a new fitness measure for proliferative cells. The proposed model shows superiority to the logistic law after fitting to real cell culture datasets. We illustrate both conditional MSSCD and the new cell fitness for a range of parameters. The cell density distributions reveal the chance of overproliferation, underproliferation, or decay for different parameter sets under the deterministic and stochastic setups.

A stochastic approach for the single-machine scheduling problem to minimize total expected cost with client-dependent tardiness costs

In the injection moulding process, a set-up containing positioning moulds, a cleaning raw material hopper and machine settings is required. The set-up is uncertain owing to random factors, such as the crew’s skill levels and unexpected breakdowns. The general version of this problem is known as the single-machine scheduling problem with stochastic sequence-dependent set-up times. In this specialized form of the problem, the objective function is defined so as to minimize the total expected cost, which includes set-up, tardiness and earliness costs. Moreover, the effect of the client-dependent tardiness cost on the optimal machine schedule under uncertainty is explored. As a solution approach, a two-stage stochastic programming method is used. For the solution of large-size problems, the harmony search algorithm is proposed, and its performance is compared with the exact solution approach. Finally, the value of the stochastic solution is assessed by comparing the results with the deterministic approach.

Stochastic single machine scheduling problem as a multi-stage dynamic random decision process

In this work, we study a stochastic single machine scheduling problem in which the features of learning effect on processing times, sequence-dependent setup times, and machine configuration selection are considered simultaneously. More precisely, the machine works under a set of configurations and requires stochastic sequence-dependent setup times to switch from one configuration to another. Also, the stochastic processing time of a job is a function of its position and the machine configuration. The objective is to find the sequence of jobs and choose a configuration to process each job to minimize the makespan. We first show that the proposed problem can be formulated through two-stage and multi-stage Stochastic Programming models, which are challenging from the computational point of view. Then, by looking at the problem as a multi-stage dynamic random decision process, a new deterministic approximation-based formulation is developed. The method first derives a mixed-integer non-linear model based on the concept of accessibility to all possible and available alternatives at each stage of the decision-making process. Then, to efficiently solve the problem, a new accessibility measure is defined to convert the model into the search of a shortest path throughout the stages. Extensive computational experiments are carried out on various sets of instances. We discuss and compare the results found by the resolution of plain stochastic models with those obtained by the deterministic approximation approach. Our approximation shows excellent performances both in terms of solution accuracy and computational time.

Improving Solvability for Procedurally Generated Challenges in Physical Solitaire Games Through Entangled Components

Challenges for physical solitaire puzzle games are typically designed in advance by humans and limited in number. Alternatively, some games incorporate rules for stochastic setup, where the human solver randomly sets up the game board before solving the challenge. These setup rules greatly increase the number of possible challenges, but can often generate unsolvable or uninteresting challenges. To better understand the compromises involved in minimizing undesirable challenges, we examine three games where component design choices can influence the stochastic nature of the resulting challenge generation algorithms. We evaluate the effect of these components and algorithms on challenge solvability and challenge engagement. We find that algorithms which control randomness through entangling components based on sub-elements of the puzzle mechanics can generate interesting challenges with a high probability of being solvable.

Fear factor in a prey–predator system in deterministic and stochastic environment

In this article, a prey–predator model has been studied where apart from direct predation the prey population is affected by the fear induced from predators. The basic reproduction of the prey population is reduced as a cost of fear. Biologically well posedness of the model system has been shown through positivity and boundedness of solutions. Existence criterion and stability analysis of the non-negative equilibrium points have been discussed and necessary conditions for uniform persistence have been derived for corresponding non-autonomous system. Also, sufficient conditions for the existence of positive periodic solution of the non-autonomous system have been established by utilizing the coincidence degree theorem. We further show that the positive periodic solution is global attractor under certain conditions. Next, we construct the stochastic model based upon the deterministic setup by perturbing the intrinsic growth rate of prey and natural mortality rate of predators. It has been shown that the stochastic system admits unique positive global solution initiates from anywhere in the interior of the positive quadrant. The sufficient conditions for extinction, non-persistence and weakly persistence of both the species have been derived along with the stochastic permanence of the system. We have verified our analytical results and make a comparison between the deterministic and stochastic setup by exhaustive numerical simulations.

Stochastic Geometry-Based Modeling and Analysis of Massive MIMO-Enabled Millimeter Wave Cellular Networks

Massive multiple-input multiple-output (MIMO) systems operating within the millimeter wave frequency range offer exciting opportunities for the future fifth-generation (5G) wireless networks. While the increased bandwidth and spectral efficiency are attractive, transitioning to millimeter massive MIMO presents significant challenges with respect to blockages, high attenuation, and channel estimation errors. To address these challenges, this paper evaluates the outage performance of a millimeter wave cellular network using massive MIMO under a stochastic set-up subject to pilot contamination and matched-filter precoding. We model the cellular users and base stations with Poisson point processes. Furthermore, we consider blockages from random objects, and employ different path loss and fading models for the line-of-sight (LOS) and non-line-of-sight scenarios. Moreover, both fixed power transmissions and path loss inversion-based power control are considered along with the sectored antenna patterns. Using stochastic geometry, we derive the moment generating function of the interference experienced by a typical cellular user and its outage probability. It is observed that the environments with different path loss exponents have varying behaviour for similar blockage sizes and densities. In addition, the ratio of the number of cellular users to that of base stations, and the antenna beamwidth are critical parameters affecting the outage performance.

Coherence-enhanced constancy of a quantum thermoelectric generator

The study shows that presence of the quantum coherent, unitary component of the evolution of the system can improve constancy of heat engines, i.e., decrease fluctuations of the output power, in comparison with purely stochastic setups. This enables to overcome the recently derived trade-off between efficiency, power and constancy, which applies to classical Markovian steady-state heat engines. The concept is demonstrated using a model system consisting of two tunnel-coupled orbitals (i.e., electronic levels), each attached to a separate electronic reservoir; such a setup can be realized, for example, using quantum dots. Electronic transport is studied by means of the exact Levitov-Lesovik formula in the case without the Coulomb interaction between electrons, as well as applying a quantum master equation in the interacting case. Constancy of the analyzed thermoelectric generator is increased due to the fact that tunneling between the orbitals is associated with a unitary evolution of the electron state instead of a stochastic Poisson transition. This reduces stochasticity of the system, thus suppressing the current and power fluctuations. Moreover, noise can be further reduced by the Coulomb interaction between electrons which prevents the double occupancy of the system.

A capacitated lot sizing problem with stochastic setup times and overtime

In this paper, we study a Capacitated Lot Sizing Problem with Stochastic Setup Times and Overtime (CLSP-SSTO). We describe a mathematical model that considers both regular costs (including production, setup and inventory holding costs) and expected overtime costs (related to the excess usage of capacity). The CLSP-SSTO is formulated as a two-stage stochastic programming problem. A procedure is proposed to exactly compute the expected overtime for a given setup and production plan when the setup times follow a Gamma distribution. A sample average approximation procedure is applied to obtain upper bounds and a statistical lower bound. This is then used to benchmark the performance of two additional heuristics. A first heuristic is based on changing the capacity in the deterministic counterpart, while the second heuristic artificially modifies the setup time. We conduct our computational experiments on well-known problem instances and provide comprehensive analyses to evaluate the performance of each heuristic.

The quasi-optimality criterion in the linear functional strategy

The linear functional strategy for the regularization of inverse problems is considered. For selecting the regularization parameter therein, we propose the heuristic quasi-optimality principle and some modifications including the smoothness of the linear functionals. We prove convergence rates for the linear functional strategy with these heuristic rules taking into account the smoothness of the solution and the functionals and imposing a structural condition on the noise. Furthermore, we study these noise conditions in both a deterministic and stochastic setup and verify that for mildly-ill-posed problems and Gaussian noise, these conditions are satisfied almost surely, where on the contrary, in the severely-ill-posed case and in a similar setup, the corresponding noise condition fails to hold. Moreover, we propose an aggregation method for adaptively optimizing the parameter choice rule by making use of improved rates for linear functionals. Numerical results indicate that this method yields better results than the standard heuristic rule.

Try-once-discard scheduling for stochastic networked control systems

ABSTRACTIn practical networked control systems (NCS), such as smart grids, cooperative robotics, and sensor networks, often multiple control applications share a communication infrastructure, requiring a smart and efficient scheduling mechanism to coordinate the access to the capacity-limited communication medium. In this article we consider the problem of event-based scheduling design for NCSs consisting of multiple control loops over a shared communication medium. We extend the notion of Try-Once-Discard (TOD), which is one of the basic deterministic event-based scheduling protocols for resource constrained NCSs, to the case of multiple stochastic control systems coupled via a shared communication medium subject to capacity limitation and stochastic packet delivery failure. Showing that the overall network-induced error is a homogeneous Markov chain in our stochastic set-up, we first study stability properties of such networked systems under the TOD scheduling scheme employing the concepts of stochastic stability. Then, we derive sufficient stability conditions under the TOD rule assuming that the communication channel is not ideal, i.e. a scheduled data packet for transmission might be lost in the communication channel with a non-zero probability. Furthermore, we derive analytic performance bounds by finding uniform upper-bounds for an average quadratic cost function. The numerical simulations are performed for variety of system parameters and NCS set-ups to strengthen our stability claim as well as illustrating performance bounds. Additionally, we show that the TOD scheduling rule outperforms the conventional time-triggered, and uniform and non-uniform random channel access arbitration mechanisms, in terms of efficient coordination of channel access in stochastic NCSs.

Stochastic Semantics

We consider stochastic systems of equations of tree series, i.e., systems of equations whose right-hand sides are stochastic tree polynomials. We obtain their least solutions in arbitrary substochastic algebras, using both the [IO]- and OI-substitution mode. In the term algebra, we show that the co nsistency problem of the least [IO]- and OI-solutions is decidable, by reducing it to the consistency problem of stochastic context-free grammars. We prove a Kleene type theorem for the components of the least OI-solutions. The folklore Mezei-Wright result stating the coincidence of the components of least OI-solutions and behaviors of tree automata fails in the stochastic setup. As an application of our theory, we prove a Kleene theorem for the class of series generated by stochastic context-free grammars.

Incorporating the Stochastic Process Setup in Parameter Estimation

Estimation problems within the context of stochastic processes are usually studied with the help of statistical asymptotic theory and proposed estimators are tested with the use of simulated data. For processes with stationary increments it is customary to use differenced time series, treating them as selections from the increments’ distribution. Though distributionally correct, this approach throws away most information related to the stochastic process setup. In this paper we consider the above problems with reference to parameter estimation of a gamma process. Using the derived bridge processes we propose estimators whose properties we investigate in contrast to the gamma-increments MLE. The proposed estimators have a smaller bias, comparable variance and offer a look at the time-evolution of the parameter estimation. Empirical results are presented.

Reliability optimization in stochastic domain via genetic algorithm

Purpose– The purpose of this paper is to formulate the reliability optimization problem in stochastic and interval domain and also to solve the same under different stochastic set up.Design/methodology/approach– Stochastic programming technique has been used to convert the chance constraints into deterministic form and the corresponding problem is transformed to mixed-integer constrained optimization problem with interval objective. Then the reduced problem has been converted to unconstrained optimization problem with interval objective by Big-M penalty technique. The resulting problem has been solved by advanced real coded genetic algorithm with interval fitness, tournament selection, intermediate crossover and one-neighbourhood mutation.Findings– A new optimization technique has been developed in stochastic domain and the concept of interval valued parameters has been integrated with the stochastic setup so as to increase the applicability of the resultant solution to the interval valued nonlinear optimization problems.Practical implications– The concept of probability distribution with interval valued parameters has been introduced. This concept will motivate the researchers to carry out the research in this new direction.Originality/value– The application of genetic algorithm is extended to solve the reliability optimization problem in stochastic and interval domain.

IMPACT OF RETAILER COMPETITION ON MANUFACTURER'S DECISIONS AND PROFITS AT EQUILIBRIUM

As most of the supply chains in practice are decentralized, a key issue in supply chain management is to study the coordination of supply chain. The interactions among players are typically of two types, viz. vertical competition and horizontal competition. We use a game theoretic framework to analyze a two-stage supply chain. The supply chain is modeled as a Stackelberg game with a manufacturer as leader and multiple retailers as followers. We consider multiple retailers competing on quantities (Cournot competition) and study its impact on manufacturer's equilibrium decisions and profits. We show that the wholesale price contract does not achieve Nash equilibrium when retailers offer uniform pricing. On the other hand, in case of perfect price discrimination we prove the existence of unique Nash equilibrium in both deterministic and stochastic demand set-up. Under stochastic demand set-up, we consider information asymmetry between the manufacturer and retailers with respect to demand signal. Furthermore, we show the retailers' selling effort boost up the sales. As variance of sales can hurt the manufacturer's production decisions badly, we conjecture that the manufacturer can offer a retailer incentive contract which can manipulate retailers' equilibrium decision.

Observability of a Linear System Under Sparsity Constraints

Consider an n-dimensional linear system where it is known that there are at most nonzero components in the initial state. The observability problem, that is the recovery of the initial state, for such a system is considered. We obtain sufficient conditions on the number of available observations to be able to recover the initial state exactly for such a system. Both deterministic and stochastic setups are considered for system dynamics. In the former setting, the system matrices are known deterministically, whereas in the latter setting, all of the matrices are picked from a randomized class of matrices. The main message is that one does not need to obtain full n observations to be able to uniquely identify the initial state of the linear system, even when the observations are picked randomly, when the initial condition is known to be sparse.

An integrated neural network–simulation algorithm for performance optimisation of the bi-criteria two-stage assembly flow-shop scheduling problem with stochastic activities

This paper presents an integrated computer simulation and Artificial Neural Network (ANN) algorithm for a stochastic Two-Stage Assembly Flow-Shop Scheduling Problem (TSAFSP) with setup times under a weighted sum of makespan and mean completion time (MCT) criteria, known as bi-criteria. Significantly, it should be noted that there is no mathematical model to analyse the stochastic model, therefore simulation is used to solve the problem. The simulation model enables decision makers to consider the influence of job scheduling on machines in order to examine both criteria simultaneously. Since it is not possible to evaluate all sequence combinations using the simulation model in a reasonable time, multilayered neural network meta-models have been trained and used to estimate objective function values composed of both makespan and mean completion time criteria for the stochastic TSAFSP. To the best of the authors’ knowledge, this is the first study that considers stochastic machine breakdown, processing times, setup times, makespan and mean completion time as objectives concurrently. The TSAFSP is modelled by Visual SLAM simulation software. The simulation output results are then given to the ANN as inputs to build the meta-model. This meta-model is then used to obtain the results with the optimum values. The advantage of these meta-model applications is a reduction in the number of simulation runs and consequently a reduced run time. Also, this is the first study that introduces an intelligent and flexible algorithm for handling stochastic TSAFSP.

Measuring Convergence Using Dynamic Equilibrium Models: Evidence from Chinese Provinces

We propose a model to study economic convergence in the tradition of neoclassical growth theory. We employ a novel stochastic set-up of the Solow (1956) model with shocks to both capital and labor. Our novel approach identifies the speed of convergence directly from estimating the parameters which determine equilibrium dynamics. The inference on the structural parameters is done using a maximum-likelihood approach. We estimate our model using growth and population data for China’s provinces from 1980 to 2009. We report heterogeneity in the speed of convergence both across provinces and time. The Eastern provinces show a higher tendency of convergence, while there is no evidence of convergence for the Central and Western provinces. We find empirical evidence that the speed of convergence decreases over time for most provinces.

Minimalistic behavioral rule derived from bacterial chemotaxis in a stochastic resonance setup

Animals are able to cope with the noise, uncertainties, and complexity of the real world. Often even elementary living beings, equipped with very limited sensory organs, are able to reach regions favorable to their existence, using simple stochastic policies. In this paper we discuss a minimalistic stochastic behavioral rule, inspired from bacteria chemotaxis, which is able to increase the value of a specified evaluation function in a similar manner. In particular, we prove that, under opportune assumptions, the direction that is taken with maximum probability by an agent that follows this rule corresponds to the optimal direction. The rule does not require a specific agent dynamics, needs no memory for storing observed states, and works in generic n-dimensional spaces. It thus reveals itself interesting for the control of simple sensing robots as well.