Symmetries and fixed point stability of stochastic differential equations modeling self-organized criticality

A stochastic nonlinear partial differential equation is constructed for two different models exhibiting self-organized criticality: the Bak-Tang-Wiesenfeld (BTW) sandpile model [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] and the Zhang model [Phys. Rev. Lett. 63, 470 (1989)]. The dynamic renormalization group (DRG) enables one to compute the critical exponents. However, the nontrivial stable fixed point of the DRG transformation is unreachable for the original parameters of the models. We introduce an alternative regularization of the step function involved in the threshold condition, which breaks the symmetry of the BTW model. Although the symmetry properties of the two models are different, it is shown that they both belong to the same universality class. In this case the DRG procedure leads to a symmetric behavior for both models, restoring the broken symmetry, and makes accessible the nontrivial fixed point. This technique could also be applied to other problems with threshold dynamics.

Examples of retracts in a free group that are not the fixed subgroup of any group of automorphisms

Let F be a free group of rank at least three. We show that some retracts of F previously studied by Martino-Ventura are not equal to the fixed subgroup of any group of automorphisms of F. This shows that, in F, there exist subgroups that are equal to the fixed subgroup of some set of endomorphisms but are not equal to the fixed subgroup of any set of automorphisms. Moreover, we determine the Galois monoids of these retracts, where, by the Galois monoid of a subgroup H of F, we mean the monoid consisting of all endomorphisms of F that fix H.

Stable coalition structures with fixed decision scheme

This paper studies the stability of a finite local public goods economy in horizontal differentiation, where a jurisdiction's choice of the public good is given by an exogenous decision scheme. In this paper, we characterize the class of decision schemes that ensure the existence of an equilibrium with free mobility (that we call Tiebout equilibrium) for monotone distribution of players. This class contains all the decision schemes whose choice lies between the Rawlsian decision scheme and the median voter with mid-distance of the two median voters when there are ties. We show that for non-monotone distribution, there is no decision scheme that can ensure the stability of coalitions. In the last part of the paper, we prove the non-emptiness of the core of this coalition formation game

Proper actions, fixed-point algebras and naturality in nonabelian duality

"Vegeu el resum a l'incici del document del fitxer adjunt."

The role of fixed delays in neuronal rate models

Fixed delays in neuronal interactions arise through synaptic and dendritic processing. Previous work has shown that such delays, which play an important role in shaping the dynamics of networks of large numbers of spiking neurons with continuous synaptic kinetics, can be taken into account with a rate model through the addition of an explicit, fixed delay. Here we extend this work to account for arbitrary symmetric patterns of synaptic connectivity and generic nonlinear transfer functions. Specifically, we conduct a weakly nonlinear analysis of the dynamical states arising via primary instabilities of the stationary uniform state. In this way we determine analytically how the nature and stability of these states depend on the choice of transfer function and connectivity. While this dependence is, in general, nontrivial, we make use of the smallness of the ratio in the delay in neuronal interactions to the effective time constant of integration to arrive at two general observations of physiological relevance. These are: 1 - fast oscillations are always supercritical for realistic transfer functions. 2 - Traveling waves are preferred over standing waves given plausible patterns of local connectivity.

Toward partial reorientation of land management for sustainability in view of material circulation: biophysical and historical analysis

This paper explores two major issues, from biophysical and historical viewpoints. We examine land management, which we define as the long-term fertility maintenance of land in relation to agriculture, fishery and forestry. We also explore humans’ positive role as agents aiming to reinforce harmonious materials circulation within the land. Liebig’s view on nature, agriculture and land, emphasizes the maintenance of long-term land fertility based on his agronomical thought that the circulation of matter in agricultural fields must be maintained with manure as much as possible. The thoughts of several classical economists, on nature, agriculture and land are reassessed from Liebig’s view point. Then, the land management problem is discussed at a much more fundamental level, to understand the necessary conditions for life in relation to land management. This point is analyzed in terms of two mechanisms: entropy disposal on the earth, and material circulation against gravitational field. Finally from the historical example of the metropolis of Edo, it is shown that there is yet another necessary condition for the sustainable management of land based on the creation of harmonious material cycles among cities, farm land, forests and surrounding sea areas in which humans play a vital role as agent.

Partial disjoint path for multi-layer protection in GMPLS networks

In this paper, different recovery methods applied at different network layers and time scales are used in order to enhance the network reliability. Each layer deploys its own fault management methods. However, current recovery methods are applied to only a specific layer. New protection schemes, based on the proposed partial disjoint path algorithm, are defined in order to avoid protection duplications in a multi-layer scenario. The new protection schemes also encompass shared segment backup computation and shared risk link group identification. A complete set of experiments proves the efficiency of the proposed methods in relation with previous ones, in terms of resources used to protect the network, the failure recovery time and the request rejection ratio

Application of the european customer satisfaction index to postal services. Structural equation models versus partial least squars

Customer satisfaction and retention are key issues for organizations in today’s competitive market place. As such, much research and revenue has been invested in developing accurate ways of assessing consumer satisfaction at both the macro (national) and micro (organizational) level, facilitating comparisons in performance both within and between industries. Since the instigation of the national customer satisfaction indices (CSI), partial least squares (PLS) has been used to estimate the CSI models in preference to structural equation models (SEM) because they do not rely on strict assumptions about the data. However, this choice was based upon some misconceptions about the use of SEM’s and does not take into consideration more recent advances in SEM, including estimation methods that are robust to non-normality and missing data. In this paper, both SEM and PLS approaches were compared by evaluating perceptions of the Isle of Man Post Office Products and Customer service using a CSI format. The new robust SEM procedures were found to be advantageous over PLS. Product quality was found to be the only driver of customer satisfaction, while image and satisfaction were the only predictors of loyalty, thus arguing for the specificity of postal services

Dynamic price competition with fixed capacities

Many revenue management (RM) industries are characterized by (a) fixed capacities in theshort term (e.g., hotel rooms, seats on an airline flight), (b) homogeneous products (e.g., twoairline flights between the same cities at similar times), and (c) customer purchasing decisionslargely influenced by price. Competition in these industries is also very high even with just twoor three direct competitors in a market. However, RM competition is not well understood andpractically all known implementations of RM software and most published models of RM donot explicitly model competition. For this reason, there has been considerable recent interestand research activity to understand RM competition. In this paper we study price competitionfor an oligopoly in a dynamic setting, where each of the sellers has a fixed number of unitsavailable for sale over a fixed number of periods. Demand is stochastic, and depending on howit evolves, sellers may change their prices at any time. This reflects the fact that firms constantly,and almost costlessly, change their prices (alternately, allocations at a price in quantity-basedRM), reacting either to updates in their estimates of market demand, competitor prices, orinventory levels. We first prove existence of a unique subgame-perfect equilibrium for a duopoly.In equilibrium, in each state sellers engage in Bertrand competition, so that the seller withthe lowest reservation value ends up selling a unit at a price that is equal to the equilibriumreservation value of the competitor. This structure hence extends the marginal-value conceptof bid-price control, used in many RM implementations, to a competitive model. In addition,we show that the seller with the lowest capacity sells all its units first. Furthermore, we extendthe results transparently to n firms and perform a number of numerical comparative staticsexploiting the uniqueness of the subgame-perfect equilibrium.

Fixed-term contracts and the duration distribution of unemployment

In the mid-1980s, many European countries introduced fixed-term contracts.Since then their labor markets have become more dynamic. This paper studiesthe implications of such reforms for the duration distribution ofunemployment, with particular emphasis on the changes in the durationdependence. I estimate a parametric duration model using cross-sectionaldata drawn from the Spanish Labor Force Survey from 1980 to 1994 to analyzethe chances of leaving unemployment before and after the introduction offixed-term contracts. I find that duration dependence has increased sincesuch reform. Semi-parametric estimation of the model also shows that forlong spells, the probability of leaving unemployment has decreased sincesuch reform.

Restless bandits, partial conservation laws and indexability

We show that if performance measures in a stochastic scheduling problem satisfy a set of so-called partial conservation laws (PCL), which extend previously studied generalized conservation laws (GCL), then the problem is solved optimally by a priority-index policy for an appropriate range of linear performance objectives, where the optimal indices are computed by a one-pass adaptive-greedy algorithm, based on Klimov's. We further apply this framework to investigate the indexability property of restless bandits introduced by Whittle, obtaining the following results: (1) we identify a class of restless bandits (PCL-indexable) which are indexable; membership in this class is tested through a single run of the adaptive-greedy algorithm, which also computes the Whittle indices when the test is positive; this provides a tractable sufficient condition for indexability; (2) we further indentify the class of GCL-indexable bandits, which includes classical bandits, having the property that they are indexable under any linear reward objective. The analysis is based on the so-called achievable region method, as the results follow fromnew linear programming formulations for the problems investigated.

On the performance of small-area estimators: Fixed vs. random area parameters

Most methods for small-area estimation are based on composite estimators derived from design- or model-based methods. A composite estimator is a linear combination of a direct and an indirect estimator with weights that usually depend on unknown parameters which need to be estimated. Although model-based small-area estimators are usually based on random-effects models, the assumption of fixed effects is at face value more appropriate.Model-based estimators are justified by the assumption of random (interchangeable) area effects; in practice, however, areas are not interchangeable. In the present paper we empirically assess the quality of several small-area estimators in the setting in which the area effects are treated as fixed. We consider two settings: one that draws samples from a theoretical population, and another that draws samples from an empirical population of a labor force register maintained by the National Institute of Social Security (NISS) of Catalonia. We distinguish two types of composite estimators: a) those that use weights that involve area specific estimates of bias and variance; and, b) those that use weights that involve a common variance and a common squared bias estimate for all the areas. We assess their precision and discuss alternatives to optimizing composite estimation in applications.

Financing constraints and fixed-term employment contracts

This paper studies the interactions between financing constraints and theemployment decisions of firms when both fixed-term and permanent employmentcontracts are available. We first develop a dynamic model that shows theeffects of financing constraints and firing costs on employment decisions. Oncecalibrated, the model shows that financially constrained firms tend to use moreintensely fixed term workers, and to make them absorb a larger fraction of thetotal employment volatility than financially unconstrained firms do. We testand confirm the predictions of the model on a unique panel data of Italian manufacturingfirms with detailed information about the type of workers employedby the firms and about firm financing constraints.

Fixed and random effects in Classical and Bayesian regression

This paper proposes a common and tractable framework for analyzingdifferent definitions of fixed and random effects in a contant-slopevariable-intercept model. It is shown that, regardless of whethereffects (i) are treated as parameters or as an error term, (ii) areestimated in different stages of a hierarchical model, or whether (iii)correlation between effects and regressors is allowed, when the sameinformation on effects is introduced into all estimation methods, theresulting slope estimator is also the same across methods. If differentmethods produce different results, it is ultimately because differentinformation is being used for each methods.