A continuous network design model in stochastic user equilibrium based on sensitivity analysis

The continuous network design problem (CNDP) is known to be difficult to solve due to the intrinsic properties of non-convexity and nonlinearity. Such kinds of CNDP can be formulated as a bi-level programme, in which the upper level represents the designer's decisions and the lower level the travellers' responses. Formulations of this kind can be classified as either Stackelberg approaches or Nash ones according to the relationship between the upper level and the lower level parts. This paper formulates the CNDP for road expansion based on Stackelberg game where leader and follower exist, and allows for variety of travellers' behaviour in choosing their routes. In order to solve the problem by the Stackelberg approach, we need a relation between link flows and design parameters. For this purpose, we use a logit route choice model, which provides this in an explicit closed-form function. This model is applied to two example road networks to test and briefly compare the results between the Stackelberg and Nash approaches to explore the differences between them

Compensatory effects in the PI3K/PTEN/AKT signaling network following receptor tyrosine kinase inhibition

Overcoming de novo and acquired resistance to anticancer drugs that target signaling networks is a formidable challenge for drug design and effective cancer therapy. Understanding the mechanisms by which this resistance arises may offer a route to addressing the insensitivity of signaling networks to drug intervention and restore the efficacy of anticancer therapy. Extending our recent work identifying PTEN as a key regulator of Herceptin sensitivity, we present an integrated theoretical and experimental approach to study the compensatory mechanisms within the PI3K/PTEN/AKT signaling network that afford resistance to receptor tyrosine kinase (RTK) inhibition by anti-HER2 monoclonal antibodies. In a computational model representing the dynamics of the signaling network, we define a single control parameter that encapsulates the balance of activities of the enzymes involved in the PI3K/PTEN/AKT cycle. By varying this control parameter we are able to demonstrate both distinct dynamic regimes of behavior of the signaling network and the transitions between those regimes. We demonstrate resistance, sensitivity, and suppression of RTK signals by the signaling network. Through model analysis we link the sensitivity-to-resistance transition to specific compensatory mechanisms within the signaling network. We study this transition in detail theoretically by variation of activities of PTEN, PI3K, AKT enzymes, and use the results to inform experiments that perturb the signaling network using combinatorial inhibition of RTK, PTEN, and PI3K enzymes in human ovarian carcinoma cell lines. We find good alignment between theoretical predictions and experimental results. We discuss the application of the results to the challenges of hypersensitivity of the signaling network to RTK signals, suppression of drug resistance, and efficacy of drug combinations in anticancer therapy

Fault tolerant packet-switched network design and Its sensitivity

Reliability and performance for telecommunication networks have traditionally been investigated separately in spite of their close relation. A design method integrating them for a reliable packet switched network, called a proofing method, is presented. Two heuristic design approaches (max-average, max-delay-link) for optimizing network cost in the proofing method are described. To verify their effectiveness and applicability, they are compared numerically for three example network topologies. The sensitivity of these two methods is examined with respect to changes in traffic demand and in link reliability. The design sensitivity to variation of input data is examined by changing the predicted probability of link failure, and by increasing the network traffic over the predicted value. The resulting analysis shows relative insensitivity of solutions generated by the two design methods to input data</p

Selected reliability studies for the NERVA program

An investigation was made into certain methods of reliability analysis that are particularly suitable for complex mechanisms or systems in which there are many interactions. The methods developed were intended to assist in the design of such mechanisms, especially for analysis of failure sensitivity to parameter variations and for estimating reliability where extensive and meaningful life testing is not feasible. The system is modeled by a network of interconnected nodes. Each node is a state or mode of operation, or is an input or output node, and the branches are interactions. The network, with its probabilistic and time-dependent paths is also analyzed for reliability and failure modes by a Monte Carlo, computerized simulation of system performance

Model simplification of signal transduction pathway networks via a hybrid inference strategy

A full-scale mathematical model of cellular networks normally involves a large number of variables and parameters. How to effectively develop manageable and reliable models is crucial for effective computation, analysis and design of such systems. The aim of model simplification is to eliminate parts of a model that are unimportant for the properties of interest. In this work, a model reduction strategy via hybrid inference is proposed for signal pathway networks. It integrates multiple techniques including conservation analysis, local sensitivity analysis, principal component analysis and flux analysis to identify the reactions and variables that can be considered to be eliminated from the full-scale model. Using an I·B-NF-·B signalling pathway model as an example, simulation analysis demonstrates that the simplified model quantitatively predicts the dynamic behaviours of the network

Detection mechanism in highly sensitive ZnO nanowires network gas sensors

Metal-oxide nanowires are showing a great interest in the domain of gas sensing due to their large response even at a low temperature, enabling low-power gas sensors. However their response is still not fully understood, and mainly restricted to the linear response regime, which limits the design of appropriate sensors for specific applications. Here we analyse the non-linear response of a sensor based on ZnO nanowires network, both as a function of the device geometry and as a response to oxygen exposure. Using an appropriate model, we disentangle the contribution of the nanowire resistance and of the junctions between nanowires in the network. The applied model shows a very good consistency with the experimental data, allowing us to demonstrate that the response to oxygen at room temperature is dominated by the barrier potential at low bias voltage, and that the nanowire resistance starts to play a role at higher bias voltage. This analysis allows us to find the appropriate device geometry and working point in order to optimize the sensitivity. Such analysis is important for providing design rules, not only for sensing devices, but also for applications in electronics and opto-electronics using nanostructures networks with different materials and geometries

Mitigating Cascading Failures in Interdependent Power Grids and Communication Networks

In this paper, we study the interdependency between the power grid and the communication network used to control the grid. A communication node depends on the power grid in order to receive power for operation, and a power node depends on the communication network in order to receive control signals for safe operation. We demonstrate that these dependencies can lead to cascading failures, and it is essential to consider the power flow equations for studying the behavior of such interdependent networks. We propose a two-phase control policy to mitigate the cascade of failures. In the first phase, our control policy finds the non-avoidable failures that occur due to physical disconnection. In the second phase, our algorithm redistributes the power so that all the connected communication nodes have enough power for operation and no power lines overload. We perform a sensitivity analysis to evaluate the performance of our control policy, and show that our control policy achieves close to optimal yield for many scenarios. This analysis can help design robust interdependent grids and associated control policies.Comment: 6 pages, 9 figures, submitte

Applications of sensitivity analysis for probit stochastic network equilibrium

Network equilibrium models are widely used by traffic practitioners to aid them in making decisions concerning the operation and management of traffic networks. The common practice is to test a prescribed range of hypothetical changes or policy measures through adjustments to the input data, namely the trip demands, the arc performance (travel time) functions, and policy variables such as tolls or signal timings. Relatively little use is, however, made of the full implicit relationship between model inputs and outputs inherent in these models. By exploiting the representation of such models as an equivalent optimisation problem, classical results on the sensitivity analysis of non-linear programs may be applied, to produce linear relationships between input data perturbations and model outputs. We specifically focus on recent results relating to the probit Stochastic User Equilibrium (PSUE) model, which has the advantage of greater behavioural realism and flexibility relative to the conventional Wardrop user equilibrium and logit SUE models. The paper goes on to explore four applications of these sensitivity expressions in gaining insight into the operation of road traffic networks. These applications are namely: identification of sensitive, ‘critical’ parameters; computation of approximate, re-equilibrated solutions following a change (post-optimisation); robustness analysis of model forecasts to input data errors, in the form of confidence interval estimation; and the solution of problems of the bi-level, optimal network design variety. Finally, numerical experiments applying these methods are reported