Representation Failure

Democracy has failure built into its DNA. The ideals of which it is composed are almost all aspirational, meaning that they cannot be met fully, partly because their full pursuit would conflict with other ideals in the package we mean when we ask what ought to be entailed when the people rule. The obligation involved in pursuing these ideals is therefore not to meet them, but to strive toward them, recognizing the impossibility of their full attainment and making the best accommodations one can to the conflicts with other ideals that arise in the process of that striving. In this process, pursuing the most direct path to the ideal may allow one to capture less of what is important about its meaning than letting the ideal inform democratic practices indirectly. Representation, for example, is on its face antithetical to the democratic ideal of giving a law to oneself. Yet without adopting direct democracy it is possible to capture the shards, threads, and intimations of the ideal of autonomy in certain practices of representation in the elected, administrative, and societal realms. Those practices include “recursive representation,” or mutually responsive, communication between constituent and representative, itself an aspirational ideal.

Infinite Paths of Minimal Length on Suborbital Graphs for Some Fuchsian Groups

In this study, we work on the Fuchsian group Hm where m is a prime number acting on mℚ^ transitively. We give necessary and sufficient conditions for two vertices to be adjacent in suborbital graphs induced by these groups. Moreover, we investigate infinite paths of minimal length in graphs and give the recursive representation of continued fraction of such vertex.

Optimal Term Structure in a Monetary Economy with Incomplete Markets

In a stochastic economy, the rebalancing of short and long term government debt positions can have real effects when markets are incomplete. This paper analyzes both stationary and dynamic policy rules for the term structure of interest rates. After proving the existence of a recursive representation of equilibrium, necessary conditions for Pareto efficiency are characterized. The necessary conditions are equivalent for both stationary and dynamic policy rules.

PARAMETRIC COMPLEXITY REDUCTION OF DISCRETE-TIME LINEAR SYSTEMS HAVING A SLOW INITIAL ONSET OR DELAY

This paper is concerned with an optimal expansion of linear discrete time systems on Meixner functions. Many orthogonal functions have been widely used to reduce the model parameter number such as Laguerre functions, Kautz functions and orthogonal basis functions. However, when the system has a slow initial onset or delay, Meixner functions, which have a slow start, are more suitable in terms of providing a more accurate approximation to the system. The optimal approximation of Meixner model is ensured once the pole characterizing the Meixner functions is set to its optimal value. In this paper, a new recursive representation of Meixner model is proposed. Further we propose, from input/output measurements, an iterative pole optimization algorithm of the Meixner pole functions. The method consists in applying the Newton-Raphson’s technique in which their elements are expressed analytically by using the derivative of the Meixner functions. Simulation results show the effectiveness of the proposed optimal modeling method.

Identification of a linear parameter varying system based on Meixner-like model

In this article, the Meixner-like model is used to represent the linear discrete-time system in comparison with the Laguerre model. Furthermore, we propose from input/output measurements a new recursive representation of the Meixner-like model. However, a significant approximation of this model is subject to an optimal choice of Meixner-like parameters: pole, order of generalization and Fourier coefficients. The present research yields a series of computational experiments, through a simulation example of a linear parameter varying (LPV) system. This study tests this approach, verifies the theoretical results and points out the positive outcomes of using the Meixner-like model in comparison with the Laguerre model.