Federal Dynamics in Times of Economic and Financial Crisis

The global economic and financial crisis is a challenge for all governments, but particularly for federal states because divided and/or shared territorial powers make federations susceptible to coordination problems in fiscal policy making. This article explores the effects of the ongoing crisis on federal relations. Three kinds of problems that may become the cause of federal tensions and conflicts are evoked: opportunism of subgovernments, centralisation and erosion of solidarity among members of the federation. Our analysis of fiscal policies and federal conflicts of 11 federations between 2007 and the present reveals three kinds of coordination problems: shirking in the use of federal government grants, rent-seeking in equalisation payments, and over-borrowing and over-spending. Our results show that shirking remained limited to few cases and occurred only in the first part of the crisis. However, rent-seeking and over-borrowing and over-spending led to a reduction of solidarity among subgovernments and to increased regulation of the fiscal discretion of the members of the federation. Subsequently, tensions in federal relations increased - although only in one case did this challenged the federal order.

Analysis of a finite volume method for a cross-diffusion model in population dynamics

The main goal of this paper is to propose a convergent finite volume method for a reactionâeuro"diffusion system with cross-diffusion. First, we sketch an existence proof for a class of cross-diffusion systems. Then the standard two-point finite volume fluxes are used in combination with a nonlinear positivity-preserving approximation of the cross-diffusion coefficients. Existence and uniqueness of the approximate solution are addressed, and it is also shown that the scheme converges to the corresponding weak solution for the studied model. Furthermore, we provide a stability analysis to study pattern-formation phenomena, and we perform two-dimensional numerical examples which exhibit formation of nonuniform spatial patterns. From the simulations it is also found that experimental rates of convergence are slightly below second order. The convergence proof uses two ingredients of interest for various applications, namely the discrete Sobolev embedding inequalities with general boundary conditions and a space-time $L^1$ compactness argument that mimics the compactness lemma due to Kruzhkov. The proofs of these results are given in the Appendix.

Balancing knowledge sharing and protection in collaborative innovation - The roles and dynamics of contracts, IPR's and trust

Pro-gradu tutkielman tavoitteena on tutkia, miten yritykset tasapainoilevat tiedon jakamisen ja suojaamisen välillä innovaatioyhteistyöprojekteissa, ja miten sopimukset, immateriaalioikeudet ja luottamus voivat vaikuttaa tähän tasapainoon. Yhteistyössä yritysten täytyy jakaa tarpeellista tietoa kumppanilleen, mutta toisaalta niiden täytyy varoa, etteivät ne menetä ydinosaamiseensa kuuluvaa tietoa ja kilpailuetuaan. Yrityksillä on useita keinoja tietovuodon estämiseen. Tutkielmassa keskitytään patenttien, sopimusten ja liikesalaisuuksien käyttöön tietoa suojaavina mekanismeina. Kyseiset suojamekanismit vaikuttavat luottamukseen kumppaneiden välillä, ja täten myös näiden halukkuuteen jakaa tietoa kumppaneilleen. Jos kumppanit eivät jaa tarpeeksi tietoa toisilleen, voi yhteistyö epäonnistua. Sopimusten, immateriaalioikeuksien ja luottamuksen rooleja ja vuorovaikutusta tutkitaan kahdenvälisissä yhteistyöprojekteissa. Tutkielmassa esitellään neljä case-esimerkkiä, jotka on koottu suomalaisen metsätoimialan yrityksen haastatteluista.

The Munc13 proteins differentially regulate readily releasable pool dynamics and calcium-dependent recovery at a central synapse.

The Munc13 gene family encodes molecules located at the synaptic active zone that regulate the reliability of synapses to encode information over a wide range of frequencies in response to action potentials. In the CNS, proteins of the Munc13 family are critical in regulating neurotransmitter release and synaptic plasticity. Although Munc13-1 is essential for synaptic transmission, it is paradoxical that Munc13-2 and Munc13-3 are functionally dispensable at some synapses, although their loss in other synapses leads to increases in frequency-dependent facilitation. We addressed this issue at the calyx of Held synapse, a giant glutamatergic synapse that we found to express all these Munc13 isoforms. We studied their roles in the regulation of synaptic transmission and their impact on the reliability of information transfer. Through detailed electrophysiological analyses of Munc13-2, Munc13-3, and Munc13-2-3 knock-out and wild-type mice, we report that the combined loss of Munc13-2 and Munc13-3 led to an increase in the rate of calcium-dependent recovery and a change in kinetics of release of the readily releasable pool. Furthermore, viral-mediated overexpression of a dominant-negative form of Munc13-1 at the calyx demonstrated that these effects are Munc13-1 dependent. Quantitative immunohistochemistry using Munc13-fluorescent protein knock-in mice revealed that Munc13-1 is the most highly expressed Munc13 isoform at the calyx and the only one highly colocalized with Bassoon at the active zone. Based on these data, we conclude that Munc13-2 and Munc13-3 isoforms limit the ability of Munc13-1 to regulate calcium-dependent replenishment of readily releasable pool and slow pool to fast pool conversion in central synapses.

Ruin problems under IBNR Dynamics

In this paper, we consider a discrete-time risk process allowing for delay in claim settlement, which introduces a certain type of dependence in the process. From martingale theory, an expression for the ultimate ruin probability is obtained, and Lundberg-type inequalities are derived. The impact of delay in claim settlement is then investigated. To this end, a convex order comparison of the aggregate claim amounts is performed with the corresponding non-delayed risk model, and numerical simulations are carried out with Belgian market data.

Artificial evolution on network structures : how time and space influence dynamics

Abstract The main objective of this work is to show how the choice of the temporal dimension and of the spatial structure of the population influences an artificial evolutionary process. In the field of Artificial Evolution we can observe a common trend in synchronously evolv¬ing panmictic populations, i.e., populations in which any individual can be recombined with any other individual. Already in the '90s, the works of Spiessens and Manderick, Sarma and De Jong, and Gorges-Schleuter have pointed out that, if a population is struc¬tured according to a mono- or bi-dimensional regular lattice, the evolutionary process shows a different dynamic with respect to the panmictic case. In particular, Sarma and De Jong have studied the selection pressure (i.e., the diffusion of a best individual when the only selection operator is active) induced by a regular bi-dimensional structure of the population, proposing a logistic modeling of the selection pressure curves. This model supposes that the diffusion of a best individual in a population follows an exponential law. We show that such a model is inadequate to describe the process, since the growth speed must be quadratic or sub-quadratic in the case of a bi-dimensional regular lattice. New linear and sub-quadratic models are proposed for modeling the selection pressure curves in, respectively, mono- and bi-dimensional regu¬lar structures. These models are extended to describe the process when asynchronous evolutions are employed. Different dynamics of the populations imply different search strategies of the resulting algorithm, when the evolutionary process is used to solve optimisation problems. A benchmark of both discrete and continuous test problems is used to study the search characteristics of the different topologies and updates of the populations. In the last decade, the pioneering studies of Watts and Strogatz have shown that most real networks, both in the biological and sociological worlds as well as in man-made structures, have mathematical properties that set them apart from regular and random structures. In particular, they introduced the concepts of small-world graphs, and they showed that this new family of structures has interesting computing capabilities. Populations structured according to these new topologies are proposed, and their evolutionary dynamics are studied and modeled. We also propose asynchronous evolutions for these structures, and the resulting evolutionary behaviors are investigated. Many man-made networks have grown, and are still growing incrementally, and explanations have been proposed for their actual shape, such as Albert and Barabasi's preferential attachment growth rule. However, many actual networks seem to have undergone some kind of Darwinian variation and selection. Thus, how these networks might have come to be selected is an interesting yet unanswered question. In the last part of this work, we show how a simple evolutionary algorithm can enable the emrgence o these kinds of structures for two prototypical problems of the automata networks world, the majority classification and the synchronisation problems. Synopsis L'objectif principal de ce travail est de montrer l'influence du choix de la dimension temporelle et de la structure spatiale d'une population sur un processus évolutionnaire artificiel. Dans le domaine de l'Evolution Artificielle on peut observer une tendence à évoluer d'une façon synchrone des populations panmictiques, où chaque individu peut être récombiné avec tout autre individu dans la population. Déjà dans les année '90, Spiessens et Manderick, Sarma et De Jong, et Gorges-Schleuter ont observé que, si une population possède une structure régulière mono- ou bi-dimensionnelle, le processus évolutionnaire montre une dynamique différente de celle d'une population panmictique. En particulier, Sarma et De Jong ont étudié la pression de sélection (c-à-d la diffusion d'un individu optimal quand seul l'opérateur de sélection est actif) induite par une structure régulière bi-dimensionnelle de la population, proposant une modélisation logistique des courbes de pression de sélection. Ce modèle suppose que la diffusion d'un individu optimal suit une loi exponentielle. On montre que ce modèle est inadéquat pour décrire ce phénomène, étant donné que la vitesse de croissance doit obéir à une loi quadratique ou sous-quadratique dans le cas d'une structure régulière bi-dimensionnelle. De nouveaux modèles linéaires et sous-quadratique sont proposés pour des structures mono- et bi-dimensionnelles. Ces modèles sont étendus pour décrire des processus évolutionnaires asynchrones. Différentes dynamiques de la population impliquent strategies différentes de recherche de l'algorithme résultant lorsque le processus évolutionnaire est utilisé pour résoudre des problèmes d'optimisation. Un ensemble de problèmes discrets et continus est utilisé pour étudier les charactéristiques de recherche des différentes topologies et mises à jour des populations. Ces dernières années, les études de Watts et Strogatz ont montré que beaucoup de réseaux, aussi bien dans les mondes biologiques et sociologiques que dans les structures produites par l'homme, ont des propriétés mathématiques qui les séparent à la fois des structures régulières et des structures aléatoires. En particulier, ils ont introduit la notion de graphe sm,all-world et ont montré que cette nouvelle famille de structures possède des intéressantes propriétés dynamiques. Des populations ayant ces nouvelles topologies sont proposés, et leurs dynamiques évolutionnaires sont étudiées et modélisées. Pour des populations ayant ces structures, des méthodes d'évolution asynchrone sont proposées, et la dynamique résultante est étudiée. Beaucoup de réseaux produits par l'homme se sont formés d'une façon incrémentale, et des explications pour leur forme actuelle ont été proposées, comme le preferential attachment de Albert et Barabàsi. Toutefois, beaucoup de réseaux existants doivent être le produit d'un processus de variation et sélection darwiniennes. Ainsi, la façon dont ces structures ont pu être sélectionnées est une question intéressante restée sans réponse. Dans la dernière partie de ce travail, on montre comment un simple processus évolutif artificiel permet à ce type de topologies d'émerger dans le cas de deux problèmes prototypiques des réseaux d'automates, les tâches de densité et de synchronisation.

Three essays on short-term macroeconomics : business fluctuations, large devaluations and inflation dynamics

Résumé: At least since the Great Depression, explaining why there are business fluctuations has been one of the biggest challenges that the science of economics has had to face. The hope is that if we could better understand recessions, then we could also be more successful in overcoming them. This dissertation consists of three papers that are part of the general endeavor of economists to understand these fluctuations. The first paper discusses, for a particular model, whether a result related to fluctuations would still hold if time were modeled as continuous rather than discrete. The two other papers focus on price stickiness. The second paper discusses why, after a large devaluation, prices of non-tradables may change by only a small amount in comparison to the magnitude of the devaluation. The third paper examines price adjustment in a model in which information is imperfect and it is costly to change prices.

Selective catalytic reduction of nitrogen oxides with ammonia in forced unsteady state reactors - Case based reasoning and mathematical model simulation reasoning

The application of forced unsteady-state reactors in case of selective catalytic reduction of nitrogen oxides (NOx) with ammonia (NH3) is sustained by the fact that favorable temperature and composition distributions which cannot be achieved in any steady-state regime can be obtained by means of unsteady-state operations. In a normal way of operation the low exothermicity of the selective catalytic reduction (SCR) reaction (usually carried out in the range of 280-350°C) is not enough to maintain by itself the chemical reaction. A normal mode of operation usually requires supply of supplementary heat increasing in this way the overall process operation cost. Through forced unsteady-state operation, the main advantage that can be obtained when exothermic reactions take place is the possibility of trapping, beside the ammonia, the moving heat wave inside the catalytic bed. The unsteady state-operation enables the exploitation of the thermal storage capacity of the catalyticbed. The catalytic bed acts as a regenerative heat exchanger allowing auto-thermal behaviour when the adiabatic temperature rise is low. Finding the optimum reactor configuration, employing the most suitable operation model and identifying the reactor behavior are highly important steps in order to configure a proper device for industrial applications. The Reverse Flow Reactor (RFR) - a forced unsteady state reactor - corresponds to the above mentioned characteristics and may be employed as an efficient device for the treatment of dilute pollutant mixtures. As a main disadvantage, beside its advantages, the RFR presents the 'wash out' phenomena. This phenomenon represents emissions of unconverted reactants at every switch of the flow direction. As a consequence our attention was focused on finding an alternative reactor configuration for RFR which is not affected by the incontrollable emissions of unconverted reactants. In this respect the Reactor Network (RN) was investigated. Its configuration consists of several reactors connected in a closed sequence, simulating a moving bed by changing the reactants feeding position. In the RN the flow direction is maintained in the same way ensuring uniformcatalyst exploitation and in the same time the 'wash out' phenomena is annulated. The simulated moving bed (SMB) can operate in transient mode giving practically constant exit concentration and high conversion levels. The main advantage of the reactor network operation is emphasizedby the possibility to obtain auto-thermal behavior with nearly uniformcatalyst utilization. However, the reactor network presents only a small range of switching times which allow to reach and to maintain an ignited state. Even so a proper study of the complex behavior of the RN may give the necessary information to overcome all the difficulties that can appear in the RN operation. The unsteady-state reactors complexity arises from the fact that these reactor types are characterized by short contact times and complex interaction between heat and mass transportphenomena. Such complex interactions can give rise to a remarkable complex dynamic behavior characterized by a set of spatial-temporal patterns, chaotic changes in concentration and traveling waves of heat or chemical reactivity. The main efforts of the current research studies concern the improvement of contact modalities between reactants, the possibility of thermal wave storage inside the reactor and the improvement of the kinetic activity of the catalyst used. Paying attention to the above mentioned aspects is important when higher activity even at low feeding temperatures and low emissions of unconverted reactants are the main operation concerns. Also, the prediction of the reactor pseudo or steady-state performance (regarding the conversion, selectivity and thermal behavior) and the dynamicreactor response during exploitation are important aspects in finding the optimal control strategy for the forced unsteady state catalytic tubular reactors. The design of an adapted reactor requires knowledge about the influence of its operating conditions on the overall process performance and a precise evaluation of the operating parameters rage for which a sustained dynamic behavior is obtained. An apriori estimation of the system parameters result in diminution of the computational efforts. Usually the convergence of unsteady state reactor systems requires integration over hundreds of cycles depending on the initial guess of the parameter values. The investigation of various operation models and thermal transfer strategies give reliable means to obtain recuperative and regenerative devices which are capable to maintain an auto-thermal behavior in case of low exothermic reactions. In the present research work a gradual analysis of the SCR of NOx with ammonia process in forced unsteady-state reactors was realized. The investigation covers the presentationof the general problematic related to the effect of noxious emissions in the environment, the analysis of the suitable catalysts types for the process, the mathematical analysis approach for modeling and finding the system solutions and the experimental investigation of the device found to be more suitable for the present process. In order to gain information about the forced unsteady state reactor design, operation, important system parameters and their values, mathematical description, mathematicalmethod for solving systems of partial differential equations and other specific aspects, in a fast and easy way, and a case based reasoning (CBR) approach has been used. This approach, using the experience of past similarproblems and their adapted solutions, may provide a method for gaining informations and solutions for new problems related to the forced unsteady state reactors technology. As a consequence a CBR system was implemented and a corresponding tool was developed. Further on, grooving up the hypothesis of isothermal operation, the investigation by means of numerical simulation of the feasibility of the SCR of NOx with ammonia in the RFRand in the RN with variable feeding position was realized. The hypothesis of non-isothermal operation was taken into account because in our opinion ifa commercial catalyst is considered, is not possible to modify the chemical activity and its adsorptive capacity to improve the operation butis possible to change the operation regime. In order to identify the most suitable device for the unsteady state reduction of NOx with ammonia, considering the perspective of recuperative and regenerative devices, a comparative analysis of the above mentioned two devices performance was realized. The assumption of isothermal conditions in the beginningof the forced unsteadystate investigation allowed the simplification of the analysis enabling to focus on the impact of the conditions and mode of operation on the dynamic features caused by the trapping of one reactant in the reactor, without considering the impact of thermal effect on overall reactor performance. The non-isothermal system approach has been investigated in order to point out the important influence of the thermal effect on overall reactor performance, studying the possibility of RFR and RN utilization as recuperative and regenerative devices and the possibility of achieving a sustained auto-thermal behavior in case of lowexothermic reaction of SCR of NOx with ammonia and low temperature gasfeeding. Beside the influence of the thermal effect, the influence of the principal operating parameters, as switching time, inlet flow rate and initial catalyst temperature have been stressed. This analysis is important not only because it allows a comparison between the two devices and optimisation of the operation, but also the switching time is the main operating parameter. An appropriate choice of this parameter enables the fulfilment of the process constraints. The level of the conversions achieved, the more uniform temperature profiles, the uniformity ofcatalyst exploitation and the much simpler mode of operation imposed the RN as a much more suitable device for SCR of NOx with ammonia, in usual operation and also in the perspective of control strategy implementation. Theoretical simplified models have also been proposed in order to describe the forced unsteady state reactors performance and to estimate their internal temperature and concentration profiles. The general idea was to extend the study of catalytic reactor dynamics taking into account the perspectives that haven't been analyzed yet. The experimental investigation ofRN revealed a good agreement between the data obtained by model simulation and the ones obtained experimentally.

Experimental insights into deformation dynamics and intermittency in rapid granular shear flows

This work concerns the experimental study of rapid granular shear flows in annular Couette geometry. The flow is induced by continuous driving of the horizontal plate at the top of the granular bed in an annulus. The compressive pressure, driving torque, instantaneous bed height and rotational speed of the shearing plate are measured. Moreover, local stress fluctuations are measured in a medium made of steel spheres 2 and 3 mm in diameter. Both monodisperse packing and bidisperse packing are investigated to reveal the influence of size diversity in intermittent features of granular materials. Experiments are conducted in an annulus that can contain up to 15 kg of spherical steel balls. The shearing granular medium takes place via the rotation of the upper plate which compresses the material loaded inside the annulus. Fluctuations of compressive force are locally measured at the bottom of the annulus using a piezoelectric sensor. Rapid shear flow experiments are pursued at different compressive forces and shear rates and the sensitivity of fluctuations are then investigated by different means through monodisperse and bidisperse packings. Another important feature of rapid granular shear flows is the formation of ordered structures upon shearing. It requires a certain range for the amount of granular material (uniform size distribution) loaded in the system in order to obtain stable flows. This is studied more deeply in this thesis. The results of the current work bring some new insights into deformation dynamics and intermittency in rapid granular shear flows. The experimental apparatus is modified in comparison to earlier investigations. The measurements produce data for various quantities continuously sampled from the start of shearing to the end. Static failure and dynamic shearing ofa granular medium is investigated. The results of this work revealed some important features of failure dynamics and structure formation in the system. Furthermore, some computer simulations are performed in a 2D annulus to examine the nature of kinetic energy dissipation. It is found that turbulent flow models can statistically represent rapid granular flows with high accuracy. In addition to academic outcomes and scientific publications our results have a number of technological applications associated with grinding, mining and massive grain storages.

Dynamics of Appropriability - Finding a Balance between Efficiency and Strength in the Appropriability Regime

Building and sustaining competitive advantage through the creation of market imperfections is challenging in a constantly changing business environment - particularly since the sources of such advantages are increasingly knowledge-based. Facilitated by improved networks and communication, knowledge spills over to competitors more easily than before,thus creating an appropriability problem: the inability of an innovating firm to utilize its innovations commercially. Consequently, as the importance of intellectual assets increases, their protection also calls for new approaches. Companies have various means of protection at their disposal, and by taking advantage of them they can make intangibles more non-transferable and prevent, or at leastdelay, imitation of their most crucial intellectual assets. However, creating barriers against imitation has another side to it, and the transfer of knowledge in situations requiring knowledge sharing may be unintentionally obstructed. Theaim of this thesis is to increase understanding of how firms can balance knowledge protection and sharing so as to benefit most from their knowledge assets. Thus, knowledge protection is approached through an examination of the appropriability regime of a firm, i.e., the combination of available and effective means ofprotecting innovations, their profitability, and the increased rents due to R&D. A further aim is to provide a broader understanding of the formation and structure of the appropriability regime. The study consists of two parts. The first part introduces the research topic and the overall results of the study, and the second part consists of six complementary research publications covering various appropriability issues. The thesis contributes to the existing literature in several ways. Although there is a wide range of prior research on appropriability issues, a lot of it is restricted either to the study of individual appropriability mechanisms, or to comparing certain features of them. These approaches are combined, and the relevant theoretical concepts are clarified and developed. In addition, the thesis provides empirical evidence of the formation of the appropriability regime, which is consequently presented as an adaptive process. Thus, a framework is provided that better corresponds to the complex reality of the current business environment.

On the origin of the inertia: the modified Newtonian dynamics theory

The sameness between the inertial mass and the gravitational mass is an assumption and not a consequence of the equivalent principle is shown. In the context of the Sciama’s inertia theory, the sameness between the inertial mass and the gravitational mass is discussed and a certain condition which must be experimentally satisfied is given. The inertial force proposed by Sciama, in a simple case, is derived from the Assis’ inertia theory based in the introduction of a Weber type force. The origin of the inertial force is totally justified taking into account that the Weber force is, in fact, an approximation of a simple retarded potential, see [18, 19]. The way how the inertial forces are also derived from some solutions of the general relativistic equations is presented. We wonder if the theory of inertia of Assis is included in the framework of the General Relativity. In the context of the inertia developed in the present paper we establish the relation between the constant acceleration a0 , that appears in the classical Modified Newtonian Dynamics (M0ND) theory, with the Hubble constant H0 , i.e. a0 ≈ cH0 .

Ehrenfest dynamics is purity non-preserving: a necessary ingredient for decoherence

We discuss the evolution of purity in mixed quantum/classical approaches to electronic nonadiabatic dynamics in the context of the Ehrenfest model. As it is impossible to exactly determine initial conditions for a realistic system, we choose to work in the statistical Ehrenfest formalism that we introduced in Alonso et al. [J. Phys. A: Math. Theor. 44, 396004 (2011)10.1088/1751-8113/44/39/395004]. From it, we develop a new framework to determine exactly the change in the purity of the quantum subsystem along with the evolution of a statistical Ehrenfest system. In a simple case, we verify how and to which extent Ehrenfest statistical dynamics makes a system with more than one classical trajectory, and an initial quantum pure state become a quantum mixed one. We prove this numerically showing how the evolution of purity depends on time, on the dimension of the quantum state space D, and on the number of classical trajectories N of the initial distribution. The results in this work open new perspectives for studying decoherence with Ehrenfest dynamics.

Using Pareto optimality to explore the topology and dynamics of the human connectome.

Graph theory has provided a key mathematical framework to analyse the architecture of human brain networks. This architecture embodies an inherently complex relationship between connection topology, the spatial arrangement of network elements, and the resulting network cost and functional performance. An exploration of these interacting factors and driving forces may reveal salient network features that are critically important for shaping and constraining the brain's topological organization and its evolvability. Several studies have pointed to an economic balance between network cost and network efficiency with networks organized in an 'economical' small-world favouring high communication efficiency at a low wiring cost. In this study, we define and explore a network morphospace in order to characterize different aspects of communication efficiency in human brain networks. Using a multi-objective evolutionary approach that approximates a Pareto-optimal set within the morphospace, we investigate the capacity of anatomical brain networks to evolve towards topologies that exhibit optimal information processing features while preserving network cost. This approach allows us to investigate network topologies that emerge under specific selection pressures, thus providing some insight into the selectional forces that may have shaped the network architecture of existing human brains.

Immigrant Families and the School in Spain: Dynamics and Factors that Influence their Relations

In Spain, academic debate and school administrations have evolved to the extent that relations between the school, the family and the surrounding environment are now considered as crucial to student achievement at school and to the good functioning of the educational system as a whole. Despite this development, change is slow in practice and often complicated due to the emerging resistance of families and schools, given that they have always maintained relations marked by an imbalance of power. Our theoretical and especially our empirical work has focused on the relations between immigrant families and the school system in Spain. In view of the above, the creation of what we call positive relational dynamics and communication in schools is conditioned by the attitudes and behaviour of the school administration, professionals and families. However, the physical space in which these relations take place must also be taken into consideration. Regarding school organisation, we have emphasised the role of the school’s administration. By differentiating the range of management models, we note the ones that facilitate more relations and communication with and among families (especially the one we have called the horizontal participative model) and those that discourage them. However, the multiple and complex range of attitudes among teachers and families must always be taken into account.