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heterogeneous media and related fields.
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TOP 10 Most Read Articles in NHM, October 2016
1 
Recognition of crowd behavior from mobile sensors with pattern analysis and graph clustering methods
Volume 6, Number 3, Pages: 521  544, 2011
Daniel Roggen,
Martin Wirz,
Gerhard Tröster
and Dirk Helbing
Abstract
References
Full Text
Related Articles
Mobile onbody sensing has distinct advantages for the analysis and understanding of crowd dynamics: sensing is not geographically restricted to a specific instrumented area, mobile phones offer onbody sensing and they are already deployed on a large scale, and the rich sets of sensors they contain allows one to characterize the behavior of users through pattern recognition techniques.
In this paper we present a methodological framework for the machine recognition of crowd behavior from onbody sensors, such as those in mobile phones.
The recognition of crowd behaviors opens the way to the acquisition of largescale datasets for the analysis and understanding of crowd dynamics.
It has also practical safety applications by providing improved crowd situational awareness in cases of emergency.
The framework comprises: behavioral recognition with the user's mobile device, pairwise analyses of the activity relatedness of two users, and graph clustering in order to uncover globally, which users participate in a given crowd behavior.
We illustrate this framework for the identification of groups of persons walking, using empirically collected data.
We discuss the challenges and research avenues for theoretical and applied mathematics arising from the mobile sensing of crowd behaviors.

2 
Numerical network models and entropy principles for isothermal junction flow
Volume 9, Number 1, Pages: 65  95, 2014
Gunhild A. Reigstad
Abstract
References
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We numerically explore network models which are derived for the isothermal Euler equations.
Previously we proved the existence and uniqueness of solutions to the generalized Riemann problem at a junction under the conditions of monotone momentum related coupling constant and equal crosssectional areas for all connected pipe sections.
In the present paper we extend this proof to the case of pipe sections of different crosssectional areas.
We describe a numerical implementation of the network models, where the flow in each pipe section is calculated using a classical highresolution Roe scheme.
We propose a numerical treatment of the boundary conditions at the pipejunction interface, consistent with the coupling conditions. In particular, mass is exactly conserved across the junction.
Numerical results are provided for two different network configurations and for three different network models.
Mechanical energy considerations are applied in order to evaluate the results in terms of physical soundness.
Analytical predictions for junctions connecting three pipe sections are verified for both network configurations.
Long term behaviour of physical and unphysical solutions are presented and compared, and the impact of having pipes with different crosssectional area is shown.

3 
Constructing setvalued fundamental diagrams from Jamiton solutions in second order traffic models
Volume 8, Number 3, Pages: 745  772, 2013
Benjamin Seibold,
Morris R. Flynn,
Aslan R. Kasimov
and Rodolfo R. Rosales
Abstract
References
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Fundamental diagrams of vehicular traffic flow are generally multivalued in the congested flow regime. We show that such setvalued fundamental diagrams can be constructed systematically from simple second order macroscopic traffic models, such as the classical PayneWhitham model or the inhomogeneous AwRascleZhang model. These second order models possess nonlinear traveling wave solutions, called jamitons, and the multivalued parts in the fundamental diagram correspond precisely to jamitondominated solutions. This study shows that transitions from functionvalued to setvalued parts in a fundamental diagram arise naturally in wellknown second order models. As a particular consequence, these models intrinsically reproduce traffic phases.

4 
Computational models for fluid exchange between microcirculation and tissue interstitium
Volume 9, Number 1, Pages: 135  159, 2014
Laura Cattaneo
and Paolo Zunino
Abstract
References
Full Text
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The aim of this work is to develop a computational model able to capture the interplay between microcirculation and interstitial flow. Such phenomena are at the basis of the exchange of nutrients, wastes and pharmacological agents between the cardiovascular system and the organs. They are particularly interesting for the study of effective therapies to treat vascularized tumors with drugs. We develop a model applicable at the microscopic scale, where the capillaries and the interstitial volume can be described as independent structures capable to propagate flow. We facilitate the analysis of complex capillary bed configurations, by representing the capillaries as a onedimensional network, ending up with a heterogeneous system characterized by channels embedded into a porous medium. We use the immersed boundary method to couple the onedimensional with the threedimensional flow through the network and the interstitial volume, respectively. The main idea consists in replacing the immersed network with an equivalent concentrated source term. After discussing the details for the implementation of a computational solver, we apply it to compare flow within healthy and tumor tissue samples.

5 
Liquidity generated by heterogeneous beliefs and costly estimations
Volume 7, Number 2, Pages: 349  361, 2012
Min Shen
and Gabriel Turinici
Abstract
References
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We study the liquidity, defined as the size of the trading volume, in a situation where an infinite number of agents
with heterogeneous beliefs reach a tradeoff between the cost of a precise estimation (variable depending on the agent) and the expected wealth from trading. The "true" asset price is not known and the market price is set at a level that clears the market. We show that, under some technical assumptions, the model has natural properties such as monotony of supply and demand functions with respect to the price, existence of an equilibrium and monotony with respect to the
marginal cost of information. We also situate our approach within the Mean Field Games (MFG) framework of Lions and Lasry which allows to obtain an interpretation as a limit of Nash equilibrium for an infinite number of agents.

6 
Archimedean copula and contagion modeling in epidemiology
Volume 8, Number 1, Pages: 149  170, 2013
Jacques Demongeot,
Mohamad Ghassani,
Mustapha Rachdi,
Idir Ouassou
and Carla Taramasco
Abstract
References
Full Text
Related Articles
The aim of this paper is first to find interactions between compartments of hosts in the RossMacdonald Malaria transmission system. So, to make clearer this association we introduce the concordance measure and then the Kendall's tau and Spearman's rho. Moreover, since the population compartments are dependent, we compute their conditional distribution function using the Archimedean copula. Secondly, we get the vector population partition into several dependent parts conditionally to the fecundity and to the transmission parameters and we show that we can divide the vector population by using $p$th quantiles and test the independence between the subpopulations of susceptibles and infecteds. Third, we calculate the $p$th quantiles with the Poisson distribution. Fourth, we introduce the proportional risk model of Cox in the RossMacdonald model with the copula approach to find the relationship between survival functions of compartments.

7 
Asymptotic synchronous behavior of Kuramoto type models with frustrations
Volume 9, Number 1, Pages: 33  64, 2014
SeungYeal Ha,
Yongduck Kim
and Zhuchun Li
Abstract
References
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We present a quantitative asymptotic behavior of coupled Kuramoto oscillators with frustrations and give some sufficient conditions for the parameters and initial condition leading to phase or frequency synchronization.
We consider three Kuramototype models with frustrations.
First, we study a general case with nonidentical oscillators; i.e., the natural frequencies are distributed.
Second, as a special case, we study an ensemble of two groups of identical oscillators. For these mixture of two identical Kuramoto oscillator groups, we study the relaxation dynamics from the mixed stage to the phaselocked states via the segregation stage. Finally, we consider a Kuramototype model that was recently derived from the Van der Pol equations for two coupled oscillator systems in the work of Lück and Pikovsky [27]. In this case, we provide a framework in which the phase synchronization of each group is attained.
Moreover, the constant frustration causes the two groups to segregate from each other, although they have the same natural frequency. We also provide several numerical simulations to confirm our analytical results.

8 
Forcebased models of pedestrian dynamics
Volume 6, Number 3, Pages: 425  442, 2011
Mohcine Chraibi,
Ulrich Kemloh,
Andreas Schadschneider
and Armin Seyfried
Abstract
References
Full Text
Related Articles
Forcebased models describe the interactions of pedestrians in terms
of physical and social forces. We discuss some intrinsic problems of
this approach, like penetration of particles, unrealistic
oscillations and velocities as well as conceptual problems related
to violations of Newton's laws. We then present the generalized
centrifugal force model which solves some of these problems.
Furthermore we discuss the problem of choosing a realistic driving
force to an exit. We illustrate this problem by investigating
the behaviour of pedestrians at bottlenecks.

9 
Adaptive and nonadaptive
model predictive control of an irrigation channel
Volume 4, Number 2, Pages: 303  324, 2009
João M. Lemos,
Fernando Machado,
Nuno Nogueira,
Luís Rato
and Manuel Rijo
Abstract
Full Text
Related Articles
The performance achieved with both adaptive and nonadaptive Model Predictive Control (MPC) when applied to a pilot irrigation channel is evaluated. Several control structures are considered, corresponding to various degrees of centralization of sensor information, ranging from local upstream control of the different channel pools to multivariable control using only proximal pools, and centralized multivariable control relying on a global channel model.
In addition to the nonadaptive version, an adaptive MPC algorithm based on redundantly estimated multiple models is considered and tested with and without feedforward of adjacent pool levels, both for upstream and downstream control. In order to establish a baseline, the results of upstream and local PID controllers are included for comparison. A systematic simulation study of the performances of these controllers, both for disturbance rejection and reference tracking is shown.

10 
Selforganized network flows
Volume 2, Number 2, Pages: 193  210, 2007
Dirk Helbing,
Jan Siegmeier
and Stefan Lämmer
Abstract
Full Text
Related Articles
A model for traffic flow in street networks or material flows in supply networks is presented, that takes into account the conservation of cars or materials and other significant features of traffic flows such as jam formation, spillovers, and loaddependent transportation times. Furthermore, conflicts or coordination problems of intersecting or merging flows are considered as well. Making assumptions regarding the permeability of the intersection as a function of the conflicting flows and the queue lengths, we find selforganized oscillations in the flows similar to the operation of traffic lights.

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