Exact Zero Vacuum Energy in twisted SU(N) Principal Chiral Field

We present a finite set of equations for twisted PCF model. At the special twist in the root of unity we demonstrate that the vacuum energy is exactly zero at any size L. Also in SU(2) case we numerically calculate the energy of the single particle state with zero rapidity, as a function of L.Comment: 5 pages, 3 figure

The Theory and Practice of a Dual Criteria Assignment Model with a continuously distributed Value-of-Time

24 pagesInternational audienceA dual criteria assignment model enables an analyst to represent disaggregate trade-offs between two cost criteria in the trip-makers' route choices, e.g. time and price in the cost vs. time model in which a continuously distributed value-of-time (VOT) is assumed. This paper develops the theory and practice of dual criteria assignment. First, the economic background of the model is set out: it enables the analyst to represent various route choice behaviors, variable demand, several user classes, flow-dependent travel time and capacity constraints. Second, the mathematical framework is introduced; due to a special transformation, the model is cast into a variational inequality which under some assumptions reduces to a convex minimisation program. Third, solution algorithms are introduced and compared. Fourth, econometric tools are provided to estimate the distribution of the VOT and to evaluate the uncertainty about the predicted revenue of a toll road, arising from the uncertainty about the distribution of the VOT. It is shown that these tools ensure the practicality of a dual criteria assignment in a medium-sized application

Modelling seat congestion in transit assignment

Submitted to Transportation Research Part B, manuscript TRB-D-08-00194 27 pagesSeating or standing make distinct on-board states for a transit rider, resulting in distinct discomfort costs, with potential influence on route choice on the transit network. The paper provides a model for seat congestion: from assumptions on seat capacity, travel behaviour and priority rules, a seat allocation process is described, resulting in the notion of service modes for a transit leg, making the leg cost a random variable. At the line level, line algorithms for flow loading and leg costing are provided, which are efficient. At the network level, a hyperpath formulation is provided for supply-demand equilibrium, with path-dependent segment cost, assignment algorithm and a property of existence. It is shown that multiple equilibria may arise. Model extensions by adding discomfort functions, taste differentiation, or discrete choice to compete or not for getting a seat, might induce uniqueness

Interval Prediction for Continuous-Time Systems with Parametric Uncertainties

The problem of behaviour prediction for linear parameter-varying systems is considered in the interval framework. It is assumed that the system is subject to uncertain inputs and the vector of scheduling parameters is unmeasurable, but all uncertainties take values in a given admissible set. Then an interval predictor is designed and its stability is guaranteed applying Lyapunov function with a novel structure. The conditions of stability are formulated in the form of linear matrix inequalities. Efficiency of the theoretical results is demonstrated in the application to safe motion planning for autonomous vehicles.Comment: 6 pages, CDC 2019. Website: https://eleurent.github.io/interval-prediction

Modelling a vehicle-sharing station as a dual waiting system: stochastic framework and stationary analysis

19 pagesA waiting system with two kinds of resources, say the vehicles and the docks in a vehicle-sharing service, is considered. Two arrival flows of customers are assumed, access customers who require a vehicle versus egress customers that bring back their vehicle and require a dock at the station. The total number of docks sets a limit capacity for the service. A stochastic, markovian, state-transition model is defined, which constitutes a bi-sided capacitated queuing system. The balance equations are stated and solved, yielding a stationary distribution under two conditions of compatibility. Indicators of service quality and system performance are defined and formulated under steady state

Multiple zeta functions and double wrapping in planar N=4 SYM

Using the FiNLIE solution of the AdS/CFT Y-system, we compute the anomalous dimension of the Konishi operator in planar N=4 SYM up to eight loops, i.e. up to the leading double wrapping order. At this order a non reducible Euler-Zagier sum, zeta(1,2,8), appears for the first time. We find that at all orders in perturbation, every spectral-dependent quantity of the Y-system is expressed through multiple Hurwitz zeta functions, hence we provide a Mathematica package to manipulate these functions, including the particular case of Euler-Zagier sums. Furthermore, we conjecture that only Euler-Zagier sums can appear in the answer for the anomalous dimension at any order in perturbation theory. We also resum the leading transcendentality terms of the anomalous dimension at all orders, obtaining a simple result in terms of Bessel functions. Finally, we demonstrate that exact Bethe equations should be related to an absence of poles condition that becomes especially nontrivial at double wrapping.Comment: 49 pages. Available online Mathematica packages contain routines for working with multiple Hurwitz zeta functions and weak coupling expansion of the FiNLIE, they are an important part of the article. The article has interactive symbols "#" (they work in pdf-viewers that support JavaScript); v2: terminology is made more precise, references added; v3: published versio

Curbing the computational difficulty of the logit equilibrium assignment model

26 pagesInternational audienceIn the past, research in traffic assignment modeling has been directed primarily towards improving the deterministic model. Alternative, more behavioral principles were thought to be too demanding computationally. This paper presents two mathematical contributions that enable one to solve a logit assignment model with flow-dependent travel times at a reduced cost. First, a convergence test for Fisk's minimization program is introduced, based on a duality gap principle. Second, a new definition of Dial's STOCH fixed-time logit assignment procedure is given, in which the set of available paths is defined only once and the computations are re-interpreted. A numerical experiment indicates that these tools make the logit assignment model very competitive compared to the procedures conventionally used for solving the deterministic model

On the Marginal Cost of Road Congestion: an Evaluation Method with Application to the Paris Region

The paper analyzes the sensitivity of the marginal congestion cost on a roadway network to the level of aggregation in space, from utmost disaggregate to utmost aggregate. Simulation and aggregation are based on a static network assignment model.Marginal cost ; Road congestion ; Cost aggregation ; Congestion indicator ; Assignment model

Six-loop Konishi anomalous dimension from the Y-system

We compute the Konishi anomalous dimension perturbatively up to six loop using the finite set of functional equations derived recently by Gromov, Kazakov, Leurent and Volin. The recursive procedure can be in principle extended to higher loops, the only obstacle being the complexity of the computation.Comment: 5 pages, 1 figure, version 2 : published versio

Une caractérisation de la mobilité quotidienne des Franciliens, à partir de l'EGT 2001-2002

International audienceNous décrivons la mobilité quotidienne des Franciliens en 2001-2002 en privilégiant les activités qui motivent les déplacements, l'organisation des activités et des déplacements sous la forme de boucles, et l'inscription des présences et des mouvements dans l'espace et dans le temps, et selon les moyens de transport. Nous montrons que le nombre de boucles par jour et par personne, ainsi que le nombre de déplacements par boucle, sont des indicateurs stables parmi la population, au sens que leurs variations selon le genre et l'âge, selon la catégorie socioprofessionnelle, selon le secteur géographique de résidence, demeurent réduites. La hiérarchisation des activités et des déplacements selon le motif principal et le mode principal de la boucle, révèle l'emprise des activités contraintes sur la vie quotidienne des habitants et sur le territoire, qu'il s'agisse de travail ou d'étude