Stochastic Setup Research Articles

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.

Designing of an Assembly Line based on Reliability Approach

The problem of Assembly Line Balancing is to assign a set of tasks to an ordered sequence of workstations without violating the precedence constraints. The efficiency of the line will increase when tasks are more evenly distributed. In general, the efficiency measure(s) should be optimized subject to cycle time restriction and precedence constraints. Under the deterministic setup, efficiency of the system can be measured in various ways. Research works, reported so far, mainly deal with balancing loss as an inverse measure of efficiency. As a result, in earlier works balancing loss has been minimized subject to precedence constraints. In case the work elements are best described in terms of stochastic time, the entire problem has to be addressed with a different measure of efficiency. Expected variance of the idle times of workstations can be viewed as an inverse measure of stability of the system. A more appropriate and direct measure could be the reliability of the system such that each workstation adheres to assigned cycle time with high chance. The present work defines the reliability of the assembly line in terms of cycle time and distribution of the tasks times and offers an optimization formulation for the problem under precedence constraints. For demonstration purpose, one well known example in the literature has been addressed under stochastic setup.

Designing of an Assembly Line based on Reliability Approach

The problem of Assembly Line Balancing is to assign a set of tasks to an ordered sequence of workstations without violating the precedence constraints. The efficiency of the line will increase when tasks are more evenly distributed. In general, the efficiency measure(s) should be optimized subject to cycle time restriction and precedence constraints. Under the deterministic setup, efficiency of the system can be measured in various ways. Research works, reported so far, mainly deal with balancing loss as an inverse measure of efficiency. As a result, in earlier works balancing loss has been minimized subject to precedence constraints. In case the work elements are best described in terms of stochastic time, the entire problem has to be addressed with a different measure of efficiency. Expected variance of the idle times of workstations can be viewed as an inverse measure of stability of the system. A more appropriate and direct measure could be the reliability of the system such that each workstation adheres to assigned cycle time with high chance. The present work defines the reliability of the assembly line in terms of cycle time and distribution of the tasks times and offers an optimization formulation for the problem under precedence constraints. For demonstration purpose, one well known example in the literature has been addressed under stochastic setup.

The Structure and Growth of International Trade

The paper develops a model of proportionate growth to describe the dynamics of international trade flows. We show that a large number of the empirical regularities characterizing international trade -such as the fraction of zero trade flows across pairs of countries, the positive relationship between intensive and extensive margins, the high concentration of trade with respect to both products and destinations, the core-periphery structure of exchanges- are well explained by this simple stochastic setup. This helps us to distinguish among economically relevant regularities and those simply resulting from the mechanical interactions among agents. Furthermore, our model can be used to describe the process of `self-discovery' that lie at the foundations of suc- cessful export-led growth and is thought to play a crucial role in the process of economic development. Our model correctly predicts that large export flows are rare events, as pointed out in the empirical literature: yet, countries characterized by large `discovery' efforts are much more likely to draw a `big hit' due to the (very skewed) shape of the distribution of bilateral export flows.

Coverage-Time Optimization for Clustered Wireless Sensor Networks: A Power-Balancing Approach

In this paper, we investigate the maximization of the coverage time for a clustered wireless sensor network by optimal balancing of power consumption among cluster heads (CHs). Clustering significantly reduces the energy consumption of individual sensors, but it also increases the communication burden on CHs. To investigate this tradeoff, our analytical model incorporates both intra- and intercluster traffic. Depending on whether location information is available or not, we consider optimization formulations under both deterministic and stochastic setups, using a Rayleigh fading model for intercluster communications. For the deterministic setup, sensor nodes and CHs are arbitrarily placed, but their locations are known. Each CH routes its traffic directly to the sink or relays it through other CHs. We present a coverage-time-optimal joint clustering/routing algorithm, in which the optimal clustering and routing parameters are computed using a linear program. For the stochastic setup, we consider a cone-like sensing region with uniformly distributed sensors and provide optimal power allocation strategies that guarantee (in a probabilistic sense) an upper bound on the end-to-end (inter-CH) path reliability. Two mechanisms are proposed for achieving balanced power consumption in the stochastic case: a routing-aware optimal cluster planning and a clustering-aware optimal random relay. For the first mechanism, the problem is formulated as a signomial optimization, which is efficiently solved using generalized geometric programming. For the second mechanism, we show that the problem is solvable in linear time. Numerical examples and simulations are used to validate our analysis and study the performance of the proposed schemes.

On Discrete‐Time Multiallelic Evolutionary Dynamics Driven by Selection

We revisit some problems arising in the context of multiallelic discrete‐time evolutionary dynamics driven by fitness. We consider both the deterministic and the stochastic setups and for the latter both the Wright‐Fisher and the Moran approaches. In the deterministic formulation, we construct a Markov process whose Master equation identifies with the nonlinear deterministic evolutionary equation. Then, we draw the attention on a class of fitness matrices that plays some role in the important matter of polymorphism: the class of strictly ultrametric fitness matrices. In the random cases, we focus on fixation probabilities, on various conditionings on nonfixation, and on (quasi)stationary distributions.

Parameter Identification in a Random Environment Exemplified by a Multiscale Model for Crystal Growth

We describe a framework for solving nonlinear inverse problems in a random environment. Such problems arise, for instance, in the identification of parameters in a stochastic process or in a differential equation where the parameters themselves are random variables. The corresponding inverse problems can be treated by Tikhonov regularization in a stochastic setup. Both the solution and the data in such inverse problems can be random variables. As an example, the inverse problem considered here concerns the identification of the parameter relating the nucleation rate to the temperature field in a mesoscale model for crystal growth. The derivation of the mesoscale model from a microscale model by geometric averages is outlined in the first sections. We formulate the corresponding inverse problem both for the “simply stochastic” case, which leads to a deterministic inverse problem, and for the “doubly stochastic” case yielding a stochastic inverse problem. We apply the stochastic version of the theory of Tikhonov regularization to prove convergence and convergence rates and outline how the stochastic regularization approach can be used to deal with scale-dependent modelling errors.

Stabilisation with feedback control utilising packet-dropping network links

The possibility of using networks, such as the Internet, for data transmission between physically distributed sensors and actuators in a system gives rise to several new challenges in control design. An approach is discussed for dealing with missing or delayed information because of packet drops or deteriorating network performance. More specifically, a stochastic set-up is used to find appropriate and optimal conditions for a system to remain stable despite packet drops. Both discrete-time and continuous-time systems are considered. Under reasonable assumptions on the behaviour of the network and the noise model, it is possible to characterise optimal control strategies in terms of the probability of a packet drop, the noise statistics, the instability of the open-loop system and, in the case of continuous-time systems, the sampling frequency.

A heuristic to control integrated multi-product multi-machine production-inventory systems with job shop routings and stochastic arrival, set-up and processing times

A heuristic to control integrated multi-product multi-machine production-inventory systems with job shop routings and stochastic arrival, set-up and processing times

Option Pricing under Stochastic Volatility and Trading Volume

This paper presents a pricing formula for European options that is derived from a model in which changes in the underlying price and trading volumes are jointly determined by exogenous events. The joint determination of volume and price changes provides a crucial link between volatility of the price process and an observable variable. The model works as follows: the process of information arrival (news) is taken to be a point process that induces simultaneous jumps in price and trading volume. In addition, price has a diffusion component that corresponds to background noise, and the parameter that governs the volatility of this component is a continuously weighted average of past trading volume. This specification makes increments to the volatility process depend on the current level of volatility and news and thereby accounts for the observed persistence in volatility. Moreover, it makes volatility an observable instead of a latent variable, as it is in the usual stochastic volatility setups. Options can be priced as in the Heston framework by inverting the conditional characteristic function of underlying price at expiration. We find that the model accounts well for time varying volatility smiles and term structures and that out-of-sample price forecasts for a sample of stock options are superior not only to those of standard stochastic volatility models but even to the benchmark ad hoc procedure of plugging current implicit volatilities into the Black-Scholes formula.

Improving ultrasound guided prostate radiation therapy using optimal stochastic setup corrections

Improving ultrasound guided prostate radiation therapy using optimal stochastic setup corrections

Stochastic equilibrium: learning by exponential smoothing

This article investigates the question of stability and the impact of learning in a stochastic setup, when only limited information is used to construct estimators. More precisely, we assume that the parameters are estimated by exponential smoothing, where past parameters are down-weighted and the weight of recent observations does not decrease with time. This situation is familiar from applications in finance where price and volatility forecasts are performed by using only some recent data. Even if time series of volatile stocks or bonds are available for a long time, only recent data is used in the analysis. In this situation the prices do not converge and remain a random variable. Already Muth (Econometrica 29 (1961) 315) designed the rational expectations concept to fit to stochastic equilibrium behavior as well. Moreover, e.g. in the work of Stokey and Lucas (Recursive Methods in Economic Dynamics (1989) Harvard University Press, Cambridge, MA), the idea of modeling stochastic equilibrium by the concepts of ergodicity and stationarity has become a familiar concept in economics. In this paper we provide tools to check for ergodicity and apply these tools to a capital market model where the agents learn by means of exponential smoothing. Furthermore, we check whether the implied law is consistent with the data observed by means of an econometric analysis. By applying advanced methods from the theory of stochastic dynamical systems this paper provides a useful example how modern mathematical tools can be used to investigate equilibrium behavior of stochastic models in economics.

Properties of Optimal-Weighted Flowtime Policies with a Makespan Constraint and Set-up Times

We characterize optimal policies for the problem of allocating a single server to a set of jobs from N families. Each job is an instance of demand for an item and is associated with a family, a holding cost rate, and a mean processing time. Set-up times are required to switch from one family to another, but are not required to switch within a family. We consider the case in which the order of jobs within the family is unconstrained, and a variation in which the order is fixed. The optimization is with respect to the weighted flowtime, and we treat problems both with and without a makespan-constraint. Practical examples based on this model are described. We partially characterize an optimal policy by means of a Gittins rewardrate index and a similar switching index derived from multi-armed bandit theory. For deterministic problems with a makespan constraint, we present an optimization algorithm for the special case of two families and at most three set-ups . Without a makespan constraint and without preemption, we prove that our analysis of a deterministic model extends to stochastic set-up and processing times without loss of optimality. Managerial insights based on our technical results are provided.

Monopolistic price setting and supply rigidities in a disequilibrium framework

A model of the firm with a delayed adjustment of prices and employment is analyzed. Prices and employment are determined under uncertainty about the location of the demand curve. Three models are distinguished: price setting with predetermined supply, employment determination with pre-determined prices, and a simultaneous price and employment determination. It is shown that many of the results of the deterministic case can be transfered to the stochastic set-up. The deterministic model is included as a special case. However, the model allows for supply rigidities and labour hoarding and permits the analysis of price adjustment.

Effect of set-up error on the dose across the junction of matching cranial-spinal fields in the treatment of medulloblastoma

Purpose : The effect of systematic and stochastic setup error on the dose delivered to the gap region for the three field radiation treatment of medulloblastoma is studied. The consequences of such setup error is discussed. Methods and Materials : The treatment of medulloblastoma is typically a 3 field technique, in which two lateral cranial fields are matched with a spine field. The x-ray dose delivered to the region between the matched fields depends upon the gap size. The choice of the gap width between the cranial and spinal fields is controversial. It is currently a compromise between minimizing the risk of dose hot spots to the spine, and the associated clinical complications, as well as the magnitude of cold spots (underdosing) across the gap, with the associated risk of disease recurrence. In this paper, we examine the effect of gap width with a moving junction, refered to as “field feathering”, on the dose across the field junction for a 6MV photon beam. In addition, we have studied 129 portal films and 40 simulation films to assess the accuracy and precision of patient setup during treatment with a plan involving feathered fields. Selected landmarks observable on both portal and simulation films were identified and the variation in the distances to the field edges measured. The distribution of patient setup error was convoluted with the beam profiles for a 6MV linac. These convoluted field edges were used to obtain dose profiles across the gap region as a function of gap separation. The consequences for therapy are discussed. In addition, analysis of patient setup error on an alternative treatment involving beam modifiers to broaden the beam penumbra is discussed. Results : The magnitude of the spatial stochastic and systematic setup error was determined to be approximately three and two millimeters respectively. The dosimetric consequences of patient setup error lead to over and under dosing in the spinal gap region for the three field technique. The degree of under or over dose depends on the nature and magnitude of the patient setup error. Conclusions : The effect of patient setup error can lead to significant dosimetric errors in the dose to the gap region depending on the magnitude of the setup errors. The effective over and under dose can be compensated by the use beams modifiers such as a beam spoiler or vibrating jaws.