Asymptotic analysis of first passage time in complex networks

The first passage time (FPT) distribution for random walk in complex networks is calculated through an asymptotic analysis. For network with size $N$ and short relaxation time $\tau\ll N$, the computed mean first passage time (MFPT), which is inverse of the decay rate of FPT distribution, is inversely proportional to the degree of the destination. These results are verified numerically for the paradigmatic networks with excellent agreement. We show that the range of validity of the analytical results covers networks that have short relaxation time and high mean degree, which turn out to be valid to many real networks.Comment: 6 pages, 4 figures, 1 tabl

A novel discrete network design problem formulation and its global optimization solution algorithm

Conventional discrete transportation network design problem deals with the optimal decision on new link addition, assuming the capacity of each candidate link addition is predetermined and fixed. In this paper, we address a novel yet general discrete network design problem formulation that aims to determine the optimal new link addition and their optimal capacities simultaneously, which answers the questions on whether a new link should be added or not, and if added, what should be the optimal link capacity. A global optimization method employing linearization, outer approximation and range reduction techniques is developed to solve the formulated model.postprin

Identification of critical combination of vulnerable links in transportation networks – a global optimisation approach

This paper presents a global optimisation framework for identifying the most critical combination of vulnerable links in a transportation network. The problem is formulated as a mixed-integer non-linear programme with equilibrium constraints, aiming to determine the combination of links whose deterioration would induce the most increase in total travel cost in the network. A global optimisation solution method applying a piecewise linearisation approach and range-reduction technique is developed to solve the model. From the numerical results, it is interesting and counterintuitive to note that the set of most vulnerable links when simultaneous multiple-link failure occurs is not simply the combination of the most vulnerable links with single-link failure, and the links in the critical combination of vulnerable links are not necessarily connected or even in the neighbourhood of each other. The numerical results also show that the ranking of vulnerable links will be significantly affected by certain input parameters

Elastic demand dynamic network user equilibrium: Formulation, existence and computation

This paper is concerned with dynamic user equilibrium with elastic travel demand (E-DUE) when the trip demand matrix is determined endogenously. We present an infinite-dimensional variational inequality (VI) formulation that is equivalent to the conditions defining a continuous-time E-DUE problem. An existence result for this VI is established by applying a fixed-point existence theorem (Browder, 1968) in an extended Hilbert space. We present three computational algorithms based on the aforementioned VI and its re-expression as a differential variational inequality (DVI): a projection method, a self-adaptive projection method, and a proximal point method. Rigorous convergence results are provided for these methods, which rely on increasingly relaxed notions of generalized monotonicity, namely mixed strongly-weakly monotonicity for the projection method; pseudomonotonicity for the self-adaptive projection method, and quasimonotonicity for the proximal point method. These three algorithms are tested and their solution quality, convergence, and computational efficiency are compared. Our convergence results, which transcend the transportation applications studied here, apply to a broad family of VIs and DVIs, and are the weakest reported to date

A turning restriction design problem in urban road networks

Turning restriction is one of the commonest traffic management techniques and an effective low cost traffic improvement strategy in urban road networks. However, the literature has not paid much attention to the turning restriction design problem (TRDP), which aims to determine a set of intersections where turning restrictions should be implemented. In this paper, a bi-level programming model is proposed to formulate the TRDP. The upper level problem is to minimize the total travel cost from the viewpoint of traffic managers, and the lower level problem is to depict travelers' route choice behavior based on stochastic user equilibrium (SUE) theory. We propose a branch and bound method (BBM), based on the sensitivity analysis algorithm (SAA), to find the optimal turning restriction strategy. A branch strategy and a bound strategy are applied to accelerate the solution process of the TRDP. The computational experiments give promising results, showing that the optimal turning restriction strategy can obviously reduce system congestion and are robust to the variations of both the dispersion parameter of the SUE problem and the level of demand. © 2010 Elsevier B.V. All rights reserved.postprin

A distributionally robust joint chance constrained optimization model for the dynamic network design problem under demand uncertainty

This paper develops a distributionally robust joint chance constrained optimization model for a dynamic network design problem (NDP) under demand uncertainty. The major contribution of this paper is to propose an approach to approximate a joint chance-constrained Cell Transmission Model (CTM) based System Optimal Dynamic Network Design Problem with only partial distributional information of uncertain demand. The proposed approximation is tighter than two popular benchmark approximations, namely the Bonferroni’s inequality and second-order cone programming (SOCP) approximations. The resultant formulation is a semidefinite program which is computationally efficient. A numerical experiment is conducted to demonstrate that the proposed approximation approach is superior to the other two approximation approaches in terms of solution quality. The proposed approximation approach may provide useful insights and have broader applicability in traffic management and traffic planning problems under uncertainty.postprin

Spatially dependent Rabi oscillations: an approach to sub-diffraction-limited CARS microscopy

We present a theoretical investigation of coherent anti-Stokes Raman scattering (CARS) that is modulated by periodically depleting the ground state population through Rabi oscillations driven by an additional control laser. We find that such a process generates optical sidebands in the CARS spectrum and that the frequency of the sidebands depends on the intensity of the control laser light field. We show that analyzing the sideband frequency upon scanning the beams across the sample allows one to spatially resolve emitter positions where a spatial resolution of 65 nm, which is well below the diffraction-limit, can be obtained

Uncertainty Orientation: A Theory of Self-Regulation Within and Across Cultures as Related to Cognition

Erich Fromm once said “the quest for certainty blocks the search for meaning. Uncertainty is the very condition to impel man to unfold his powers.” For some, this quote is unmistakably true, impelling them to great discoveries of nature and the mind. For others, uncertainty is the very essence of confusion and ambiguity, offering nothing more than reason to retreat to more predictable and certain times. In this chapter, we explore the theory of uncertainty orientation as related to cognition and cognitive processes, including research that was conducted in Canada, Japan, and China. First, we discuss the characteristic uncertainty selfregulation styles that distinguish uncertainty-oriented individuals from certainty-oriented individuals. Next, we discuss the uncertainty orientation framework which integrates one’s uncertainty self-regulation style, the uncertainty present in the situation, and one’s characteristic motivations (e.g., achievement motivations) to predict performance outcomes in the related motivation domain. After discussing these basic tenants of our framework, we examine some of the cross-cultural research that has directly tested the predictions of the theory of uncertainty orientation. Concluding, we contrast our conceptualization of culture with how culture is commonly conceived in cross-cultural research

Topological correlations in soap froths

Correlation in two-dimensional soap froth is analysed with an effective potential for the first time. Cells with equal number of sides repel (with linear correlation) while cells with different number of sides attract (with NON-bilinear) for nearest neighbours, which cannot be explained by the maximum entropy argument. Also, the analysis indicates that froth is correlated up to the third shell neighbours at least, contradicting the conventional ideas that froth is not strongly correlated.Comment: 10 Pages LaTeX, 6 Postscript figure