7,009 research outputs found
Poisson Yang-Baxter maps with binomial Lax matrices
A construction of multidimensional parametric Yang-Baxter maps is presented.
The corresponding Lax matrices are the symplectic leaves of first degree matrix
polynomials equipped with the Sklyanin bracket. These maps are symplectic with
respect to the reduced symplectic structure on these leaves and provide
examples of integrable mappings. An interesting family of quadrirational
symplectic YB maps on with Lax
matrices is also presented.Comment: 22 pages, 3 figure
Traffic-responsive urban network control using multivariable regulators
The paper presents the philosophy, the aim, the development, the advantages, and the potential shortcomings of the TUC (Traffic-responsive Urban Control) strategy. Based on a store-and-forward modeling approach and using well-known methods of the Automatic Control Theory, the approach followed by TUC designs (off-line) and employs (on-line) a multivariable regulator for traffic-responsive co-ordinated network-wide signal control. Simulation investigations are used to demonstrate the efficiency of the proposed approach. Based on the presented investigations, summarising conclusions are drawn and future work is outlined
Average Case Tractability of Non-homogeneous Tensor Product Problems
We study d-variate approximation problems in the average case setting with
respect to a zero-mean Gaussian measure. Our interest is focused on measures
having a structure of non-homogeneous linear tensor product, where covariance
kernel is a product of univariate kernels. We consider the normalized average
error of algorithms that use finitely many evaluations of arbitrary linear
functionals. The information complexity is defined as the minimal number n(h,d)
of such evaluations for error in the d-variate case to be at most h. The growth
of n(h,d) as a function of h^{-1} and d depends on the eigenvalues of the
covariance operator and determines whether a problem is tractable or not. Four
types of tractability are studied and for each of them we find the necessary
and sufficient conditions in terms of the eigenvalues of univariate kernels. We
illustrate our results by considering approximation problems related to the
product of Korobov kernels characterized by a weights g_k and smoothnesses r_k.
We assume that weights are non-increasing and smoothness parameters are
non-decreasing. Furthermore they may be related, for instance g_k=g(r_k) for
some non-increasing function g. In particular, we show that approximation
problem is strongly polynomially tractable, i.e., n(h,d)\le C h^{-p} for all d
and 0<h<1, where C and p are independent of h and d, iff liminf |ln g_k|/ln k
>1. For other types of tractability we also show necessary and sufficient
conditions in terms of the sequences g_k and r_k
Reductions of lattice mKdV to -
This Letter presents a reduction of the lattice modified Korteweg-de-Vries
equation that gives rise to a -analogue of the sixth Painlev\'e equation.
This new approach allows us to give the first ultradiscrete Lax representation
of an ultradiscrete analogue of the sixth Painlev\'e equation.Comment: 4 page
A rolling-horizon quadratic-programming approach to the signal control problem in large-scale congested urban road networks
The paper investigates the efficiency of a recently developed signal control methodology, which offers a computationally feasible technique for real-time network-wide signal control in large-scale urban traffic networks and is applicable also under congested traffic conditions. In this methodology, the traffic flow process is modeled by use of the store-and-forward modeling paradigm, and the problem of network-wide signal control (including all constraints) is formulated as a quadratic-programming problem that aims at minimizing and balancing the link queues so as to minimize the risk of queue spillback. For the application of the proposed methodology in real time, the corresponding optimization algorithm is embedded in a rolling-horizon (model-predictive) control scheme. The control strategy’s efficiency and real-time feasibility is demonstrated and compared with the Linear-Quadratic approach taken by the signal control strategy TUC (Traffic-responsive Urban Control) as well as with optimized fixed-control settings via their simulation-based application to the road network of the city centre of Chania, Greece, under a number of different demand scenarios. The comparative evaluation is based on various criteria and tools including the recently proposed fundamental diagram for urban network traffic
Store-and-forward based methods for the signal control problem in large-scale congested urban road networks
The problem of designing network-wide traffic signal control strategies for large-scale congested urban road networks is considered. One known and two novel methodologies, all based on the store-and-forward modeling paradigm, are presented and compared. The known methodology is a linear multivariable feedback regulator derived through the formulation of a linear-quadratic optimal control problem. An alternative, novel methodology consists of an open-loop constrained quadratic optimal control problem, whose numerical solution is achieved via quadratic programming. Yet a different formulation leads to an open-loop constrained nonlinear optimal control problem, whose numerical solution is achieved by use of a feasible-direction algorithm. A preliminary simulation-based investigation of the signal control problem for a large-scale urban road network using these methodologies demonstrates the comparative efficiency and real-time feasibility of the developed signal control methods
Towards a Better System for Immigration Control
We study different methods of immigration control using a simple model of a congested world. Our main comparison involves quota, the predominant instrument of immigration control, and a proposed system of immigration tolls and emigration subsidies. We show that the equilibrium of the proposed system is Pareto superior to the quota system. This is consistent with the tolls and subsidies creating a market for international migrants. When countries are price-takers the market becomes perfect and the exploitation of gains from trade complete. From a normative perspective, an open-borders policy is preferred to both control methods but will meet political opposition because it hurts the residents of the rich country.
A hybrid strategy for real-time traffic signal control of urban road networks
The recently developed traffic signal control strategy known as traffic-responsive urban control (TUC) requires availability of a fixed signal plan that is sufficiently efficient under undersaturated traffic conditions. To drop this requirement, the well-known Webster procedure for fixed-signal control derivation at isolated junctions is appropriately employed for real-time operation based on measured flows. It is demonstrated via simulation experiments and field application that the following hold: 1) The developed real-time demand-based approach is a viable real-time signal control strategy for undersaturated traffic conditions. 2) It can indeed be used within TUC to drop the requirement for a prespecified fixed signal plan. 3) It may, under certain conditions, contribute to more efficient results, compared with the original TUC method
Additive noise effects in active nonlinear spatially extended systems
We examine the effects of pure additive noise on spatially extended systems
with quadratic nonlinearities. We develop a general multiscale theory for such
systems and apply it to the Kuramoto-Sivashinsky equation as a case study. We
first focus on a regime close to the instability onset (primary bifurcation),
where the system can be described by a single dominant mode. We show
analytically that the resulting noise in the equation describing the amplitude
of the dominant mode largely depends on the nature of the stochastic forcing.
For a highly degenerate noise, in the sense that it is acting on the first
stable mode only, the amplitude equation is dominated by a pure multiplicative
noise, which in turn induces the dominant mode to undergo several critical
state transitions and complex phenomena, including intermittency and
stabilisation, as the noise strength is increased. The intermittent behaviour
is characterised by a power-law probability density and the corresponding
critical exponent is calculated rigorously by making use of the first-passage
properties of the amplitude equation. On the other hand, when the noise is
acting on the whole subspace of stable modes, the multiplicative noise is
corrected by an additive-like term, with the eventual loss of any stabilised
state. We also show that the stochastic forcing has no effect on the dominant
mode dynamics when it is acting on the second stable mode. Finally, in a regime
which is relatively far from the instability onset, so that there are two
unstable modes, we observe numerically that when the noise is acting on the
first stable mode, both dominant modes show noise-induced complex phenomena
similar to the single-mode case
A proposal for a different chi-square function for Poisson distributions
We obtain an approximate Gaussian distribution from a Poisson distribution
after doing a change of variable. A new chi-square function is obtained which
can be used for parameter estimations and goodness-of-fit testing when
adjusting curves to histograms. Since the new distribution is approximately
Gaussian we can use it even when the bin contents are small. The corresponding
chi-square function can be used for curve fitting. This chi-square function is
simple to implement and presents a fast convergence of the parameters to the
correct value, especially for the parameters associated with the width of the
fitted curve. We present a Monte Carlo comparative study of the fitting method
introduced here and two other methods for three types of curves: Gaussian,
Breit-Wigner and Moyal, when each bin content obeys a Poisson distribution. It
is also shown that the new method and the other two converge to the same result
when the number of events increasesComment: 27 pages, 13 figure
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