Empiricism in ecological economics: a perspective from complex systems theory

Economies are open complex adaptive systems far from thermodynamic equilibrium, and neo-classical environmental economics seems not to be the best way to describe the behaviour of such systems. Standard econometric analysis (i.e. time series) takes a deterministic and predictive approach, which encourages the search for predictive policy to ‘correct’ environmental problems. Rather, it seems that, because of the characteristics of economic systems, an ex-post analysis is more appropriate, which describes the emergence of such systems’ properties, and which sees policy as a social steering mechanism. With this background, some of the recent empirical work published in the field of ecological economics that follows the approach defended here is presented. Finally, the conclusion is reached that a predictive use of econometrics (i.e. time series analysis) in ecological economics should be limited to cases in which uncertainty decreases, which is not the normal situation when analysing the evolution of economic systems. However, that does not mean we should not use empirical analysis. On the contrary, this is to be encouraged, but from a structural and ex-post point of view.

Dynamic Criteria: a Longitudinal Analysis of Professional Basketball Players" Outcomes

This paper describes the fluctuations of temporal criteria dynamics in the context of professional sport. Specifically, we try to verify the underlying deterministic patterns in the outcomes of professional basketball players. We use a longitudinal approach based on the analysis of the outcomes of 94 basketball players over ten years, covering practically players" entire career development. Time series were analyzed with techniques derived from nonlinear dynamical systems theory. These techniques analyze the underlying patterns in outcomes without previous shape assumptions (linear or nonlinear). These techniques are capable of detecting an intermediate situation between randomness and determinism, called chaos. So they are very useful for the study of dynamic criteria in organizations. We have found most players (88.30%) have a deterministic pattern in their outcomes, and most cases are chaotic (81.92%). Players with chaotic patterns have higher outcomes than players with linear patterns. Moreover, players with power forward and center positions achieve better results than other players. The high number of chaotic patterns found suggests caution when appraising individual outcomes, when coaches try to find the appropriate combination of players to design a competitive team, and other personnel decisions. Management efforts must be made to assume this uncertainty.

Diferencias en la dimensionalidad electroencefalograma entre vigilia y sueño profundo

Differences in dimensionality of electroencephalogram during awake and deeper sleep stages. The nonlinear dynamical systems theory provides some tools for the analysis of electroencephalogram (EEG) at different sleep stages. Its use could allow the automatic monitoring of the states of the sleep and it would also contribute an explanatory level of the differences between stages. The goal of the present paper is to address this type of analysis, focusing on the most different stages. Estimations of dimensionality were compared when six subjects were awake and in a deep sleep stage. Greater dimensionality involves more complexity because the system receives more external influences. If this dimensionality is maximum, we can consider that the time series is a noisy one. A smaller dimensionality involves lower complexity because the system receives fewer inputs. We hypothesized that we would find greater dimensionality when subjects were awake than in a deep sleep stage. Results show a noisy time series during the awake stage, whereas in the sleep stage, dimensionality is smaller, confirming our hypothesis. This result is similar to the findings reached previously by other authors.

Dynamic patterns of flow in the workplace: characterizing within-individual variability using a complexity science approach

As a result of the growing interest in studying employee well-being as a complex process that portrays high levels of within-individual variability and evolves over time, this present study considers the experience of flow in the workplace from a nonlinear dynamical systems approach. Our goal is to offer new ways to move the study of employee well-being beyond linear approaches. With nonlinear dynamical systems theory as the backdrop, we conducted a longitudinal study using the experience sampling method and qualitative semi-structured interviews for data collection; 6981 registers of data were collected from a sample of 60 employees. The obtained time series were analyzed using various techniques derived from the nonlinear dynamical systems theory (i.e., recurrence analysis and surrogate data) and multiple correspondence analyses. The results revealed the following: 1) flow in the workplace presents a high degree of within-individual variability; this variability is characterized as chaotic for most of the cases (75%); 2) high levels of flow are associated with chaos; and 3) different dimensions of the flow experience (e.g., merging of action and awareness) as well as individual (e.g., age) and job characteristics (e.g., job tenure) are associated with the emergence of different dynamic patterns (chaotic, linear and random).

KAM theory for conformally symplectic systems

We present a KAM theory for some dissipative systems (geometrically, these are conformally symplectic systems, i.e. systems that transform a symplectic form into a multiple of itself). For systems with n degrees of freedom depending on n parameters we show that it is possible to find solutions with n-dimensional (Diophantine) frequencies by adjusting the parameters. We do not assume that the system is close to integrable, but we use an a-posteriori format. Our unknowns are a parameterization of the solution and a parameter. We show that if there is a sufficiently approximate solution of the invariance equation, which also satisfies some explicit non–degeneracy conditions, then there is a true solution nearby. We present results both in Sobolev norms and in analytic norms. The a–posteriori format has several consequences: A) smooth dependence on the parameters, including the singular limit of zero dissipation; B) estimates on the measure of parameters covered by quasi–periodic solutions; C) convergence of perturbative expansions in analytic systems; D) bootstrap of regularity (i.e., that all tori which are smooth enough are analytic if the map is analytic); E) a numerically efficient criterion for the break–down of the quasi–periodic solutions. The proof is based on an iterative quadratically convergent method and on suitable estimates on the (analytical and Sobolev) norms of the approximate solution. The iterative step takes advantage of some geometric identities, which give a very useful coordinate system in the neighborhood of invariant (or approximately invariant) tori. This system of coordinates has several other uses: A) it shows that for dissipative conformally symplectic systems the quasi–periodic solutions are attractors, B) it leads to efficient algorithms, which have been implemented elsewhere. Details of the proof are given mainly for maps, but we also explain the slight modifications needed for flows and we devote the appendix to present explicit algorithms for flows.

Second-order Møller-Plesset perturbation theory without basis set superposition error : II : open-shell systems

The basis set superposition error-free second-order MØller-Plesset perturbation theory of intermolecular interactions was studied. The difficulties of the counterpoise (CP) correction in open-shell systems were also discussed. The calculations were performed by a program which was used for testing the new variants of the theory. It was shown that the CP correction for the diabatic surfaces should be preferred to the adiabatic ones

Hamilton Jacobi theory for constrained systems

We extend the HamiltonJacobi formulation to constrained dynamical systems. The discussion covers both the case of first-class constraints alone and that of first- and second-class constraints combined. The HamiltonDirac equations are recovered as characteristic of the system of partial differential equations satisfied by the HamiltonJacobi function.

Canonical transformations theory for presymplectic systems

We develop a theory of canonical transformations for presymplectic systems, reducing this concept to that of canonical transformations for regular coisotropic canonical systems. In this way we can also link these with the usual canonical transformations for the symplectic reduced phase space. Furthermore, the concept of a generating function arises in a natural way as well as that of gauge group.

Hamilton-Jacobi theory for constrained systems

We extend the HamiltonJacobi formulation to constrained dynamical systems. The discussion covers both the case of first-class constraints alone and that of first- and second-class constraints combined. The HamiltonDirac equations are recovered as characteristic of the system of partial differential equations satisfied by the HamiltonJacobi function.

Extent and limitations of density functional theory in describing magnetic systems

The performance of density-functional theory to solve the exact, nonrelativistic, many-electron problem for magnetic systems has been explored in a new implementation imposing space and spin symmetry constraints, as in ab initio wave function theory. Calculations on selected systems representative of organic diradicals, molecular magnets and antiferromagnetic solids carried out with and without these constraints lead to contradictory results, which provide numerical illustration on this usually obviated problem. It is concluded that the present exchange-correlation functionals provide reasonable numerical results although for the wrong physical reasons, thus evidencing the need for continued search for more accurate expressions.

Extent and limitations of density functional theory in describing magnetic systems

The performance of density-functional theory to solve the exact, nonrelativistic, many-electron problem for magnetic systems has been explored in a new implementation imposing space and spin symmetry constraints, as in ab initio wave function theory. Calculations on selected systems representative of organic diradicals, molecular magnets and antiferromagnetic solids carried out with and without these constraints lead to contradictory results, which provide numerical illustration on this usually obviated problem. It is concluded that the present exchange-correlation functionals provide reasonable numerical results although for the wrong physical reasons, thus evidencing the need for continued search for more accurate expressions.

Weak systems of Gandy, Jensen and Devlin

In Part I, we formulate and examine some systems that have arisen in the study of the constructible hierarchy; we find numerous transitive models for them, among which are supertransitive models containing all ordinals that show that Devlin's system BS lies strictly between Gandy's systems PZ and BST'; and we use our models to show that BS fails to handle even the simplest rudimentary functions, and is thus inadequate for the use intended for it in Devlin's treatise. In Part II we propose and study an enhancement of the underlying logic of these systems, build further models to show where the previous hierarchy of systems is preserved by our enhancement; and consider three systems that might serve for Devlin's purposes: one the enhancement of a version of BS, one a formulation of Gandy-Jensen set theory, and the third a subsystem common to those two. In Part III we give new proofs of results of Boffa by constructing three models in which, respectively, TCo, AxPair and AxSing fail; we give some sufficient conditions for a set not to belong to the rudimentary closure of another set, and thus answer a question of McAloon; and we comment on Gandy's numerals and correct and sharpen other of his observations.

Reduction, Linearization and stability of relative equilibria for mechanical systems on riemannian manifolds

Consider a Riemannian manifold equipped with an infinitesimal isometry. For this setup, a unified treatment is provided, solely in the language of Riemannian geometry, of techniques in reduction, linearization, and stability of relative equilibria. In particular, for mechanical control systems, an explicit characterization is given for the manner in which reduction by an infinitesimal isometry, and linearization along a controlled trajectory "commute." As part of the development, relationships are derived between the Jacobi equation of geodesic variation and concepts from reduction theory, such as the curvature of the mechanical connection and the effective potential. As an application of our techniques, fiber and base stability of relative equilibria are studied. The paper also serves as a tutorial of Riemannian geometric methods applicable in the intersection of mechanics and control theory.