Measuring and Controlling the Chaotic Motion of Profits

The study of economic systems has generated deep interest in exploring the complexity of chaotic motions in economy. Due to important developments in nonlinear dynamics, the last two decades have witnessed strong revival of interest in nonlinear endogenous business chaotic models. The inability to predict the behavior of dynamical systems in the presence of chaos suggests the application of chaos control methods, when we are more interested in obtaining regular behavior. In the present article, we study a specific economic model from the literature. More precisely, a system of three ordinary differential equations gather the variables of profits, reinvestments and financial flow of borrowings in the structure of a firm. Firstly, using results of symbolic dynamics, we characterize the topological entropy and the parameter space ordering of kneading sequences, associated with one-dimensional maps that reproduce significant aspects of the model dynamics. The analysis of the variation of this numerical invariant, in some realistic system parameter region, allows us to quantify and to distinguish different chaotic regimes. Finally, we show that complicated behavior arising from the chaotic firm model can be controlled without changing its original properties and the dynamics can be turned into the desired attracting time periodic motion (a stable steady state or into a regular cycle). The orbit stabilization is illustrated by the application of a feedback control technique initially developed by Romeiras et al. [1992]. This work provides another illustration of how our understanding of economic models can be enhanced by the theoretical and numerical investigation of nonlinear dynamical systems modeled by ordinary differential equations.

Assessment of data-driven modeling strategies for water delivery canals

The aim of this paper is to develop models for experimental open-channel water delivery systems and assess the use of three data-driven modeling tools toward that end. Water delivery canals are nonlinear dynamical systems and thus should be modeled to meet given operational requirements while capturing all relevant dynamics, including transport delays. Typically, the derivation of first principle models for open-channel systems is based on the use of Saint-Venant equations for shallow water, which is a time-consuming task and demands for specific expertise. The present paper proposes and assesses the use of three data-driven modeling tools: artificial neural networks, composite local linear models and fuzzy systems. The canal from Hydraulics and Canal Control Nucleus (A parts per thousand vora University, Portugal) will be used as a benchmark: The models are identified using data collected from the experimental facility, and then their performances are assessed based on suitable validation criterion. The performance of all models is compared among each other and against the experimental data to show the effectiveness of such tools to capture all significant dynamics within the canal system and, therefore, provide accurate nonlinear models that can be used for simulation or control. The models are available upon request to the authors.

Assessment of data-driven modeling strategies for water delivery canals

Conferência: CONTROLO’2012 - 16-18 July 2012 - Funchal

Generating timed trajectories foran autonomous robot

Tese de Doutoramento Programa Doutoral em Engenharia Electrónica e Computadores

Population pharmacokinetic-pharmacodynamic modelling of angiotensin receptor blockade in healthy volunteers.

OBJECTIVE: To compare the pharmacokinetic and pharmacodynamic characteristics of angiotensin II receptor antagonists as a therapeutic class. DESIGN: Population pharmacokinetic-pharmacodynamic modelling study. METHODS: The data of 14 phase I studies with 10 different drugs were analysed. A common population pharmacokinetic model (two compartments, mixed zero- and first-order absorption, two metabolite compartments) was applied to the 2685 drug and 900 metabolite concentration measurements. A standard nonlinear mixed effect modelling approach was used to estimate the drug-specific parameters and their variabilities. Similarly, a pharmacodynamic model was applied to the 7360 effect measurements, i.e. the decrease of peak blood pressure response to intravenous angiotensin challenge recorded by finger photoplethysmography. The concentration of drug and metabolite in an effect compartment was assumed to translate into receptor blockade [maximum effect (Emax) model with first-order link]. RESULTS: A general pharmacokinetic-pharmacodynamic (PK-PD) model for angiotensin antagonism in healthy individuals was successfully built up for the 10 drugs studied. Representatives of this class share different pharmacokinetic and pharmacodynamic profiles. Their effects on blood pressure are dose-dependent, but the time course of the effect varies between the drugs. CONCLUSIONS: The characterisation of PK-PD relationships for these drugs gives the opportunity to optimise therapeutic regimens and to suggest dosage adjustments in specific conditions. Such a model can be used to further refine the use of this class of drugs.

Plasma and cerebrospinal fluid population pharmacokinetics of temozolomide in malignant glioma patients

RESUME : Objectif: Le glioblastome multiforme (GBM) est la tumeur cérébrale maligne la plus agressive qui conduit au décès de la majorité des patients moins d'une année après le diagnostic. La plupart des agents chimiothérapeutiques actuellement disponibles ne traversent pas la barrière hémato¬encéphalique et ne peuvent par conséquent pas être utilisés pour ce type de tumeur. Le Temozolomide (TMZ) est un nouvel agent alkylant récemment développé pour le traitement des gliomes malins. A ce jour, très peu d'informations sont disponibles sur la pénétration intra-cérébrale de cet agent. Au cours d'une étude pilote de phase II menée auprès de 64 patients atteints de GBM, l'administration précoce de TMZ combinée à une radiothérapie standard (RT) afin d'intervenir au plus tôt dans l'évolution de la maladie, a permis de prolonger la survie de ces patients, résultat qui pu être confirmé par la suite lors de l'étude randomisée de phase III. L'objectif de cette étude a été de déterminer les paramètres pharmacocinétique du TMZ dans le plasma et le liquide céphalo-rachidien (LCR), d'évaluer l'influence de certains facteurs individuels (âge, sexe, surface corporelle, fonction rénale/hépatique, co-médications, RT concomitante) sur ces différents paramètres, et enfin d'explorer la relation existant entre l'exposition au TMZ et certains marqueurs cliniques d'efficacité et de toxicité. Matériel et Méthode: Les concentrations de TMZ ont été mesurées par chromatographie liquide à haute performance (HPLC) dans le plasma et le LCR de 35 patients atteints de GBM nouvellement diagnostiqués (étude pilote) ou de gliomes malins en récidive (étude récidive). L'analyse pharmacocinétique de population a été réalisée à l'aide du programme NONMEM. L'exposition systémique et cérébrale, définie par les AUC (Area Under the time-concentration Curve) dans le plasma et le LCR, a été estimée pour chaque patient et corrélée à la toxicité, la survie ainsi que la survie sans progression tumorale. Résultats: Un modèle à 1 compartiment avec une cinétique d'absorption et de transfert Kplasma -> LCR de ordre a été retenu afin de décrire le profil pharmacocinétique du TMZ. Les valeurs moyennes de population ont été de 10 L/h pour la clairance, de 30.3 L pour le volume de distribution, de 2.1 h pour la 1/2 vie d'élimination, de 5.78 hE-1 pour la constante d'absorption, de 7.2 10E4 hE-1 pour Kplasma->LCR et de 0.76 hE-1 pour KLCR plasma. La surface corporelle a montré une influence significative sur la clairance et le volume de distribution, alors que le sexe influence la clairance uniquement. L'AUC mesurée dans le LCR représente ~20% de celle du plasma et une augmentation de 15% de Kplasma->LCR a été observée lors du traitement concomitant de radiochimiothérapie. Conclusions: Cette étude est la première analyse pharmacocinétique effectuée chez l'homme permettant de quantifier la pénétration intra-cérébrale du TMZ. Le rapport AUC LCR/AUC Plasma a été de 20%. Le degré d'exposition systémique et cérébral au TMZ ne semble pas être un meilleur facteur prédictif de la survie ou de la tolérance au produit que ne l'est la dose cumulée seule. ABSTRACT Purpose: Scarce information is available on the brain penetration of temozolomide (TMZ), although this novel methylating agent is mainly used for the treatment of ma¬lignant brain tumors. The purpose was to assess TNIZ phar¬macokinetics in plasma and cerebrospinal fluid (CSF) along with its inter-individual variability, to characterize covari¬ates and to explore relationships between systemic or cere¬bral drug exposure and clinical outcomes. Experimental Design: TMZ levels were measured by high-performance liquid chromatography in plasma and CSF samples from 35 patients with newly diagnosed or recurrent malignant gliomas. The population pharmacoki¬netic analysis was performed with nonlinear mixed-effect modeling software. Drug exposure, defined by the area un¬der the concentration-time curve (AUC) in plasma and CSF, was estimated for each patient and correlated with toxicity, survival, and progression-free survival. Results: A three-compartment model with first-order absorption and transfer rates between plasma and CSF described the data appropriately. Oral clearance was 10 liter/h; volume of distribution (VD), 30.3 liters; absorption constant rate, 5.8 hE-1; elimination half-time, 2.1 h; transfer rate from plasma to CSF (Kplasma->CSF), 7.2 x 10E-4hE-1 and the backwards rate, 0.76hE-1. Body surface area signifi¬cantly influenced both clearance and VD, and clearance was sex dependent. The AU CSF corresponded to 20% of the AUCplasma. A trend toward an increased K plasma->CSF of 15% was observed in case of concomitant radiochemo-therapy. No significant correlations between AUC in plasma or CSF and toxicity, survival, or progression-free survival were apparent after deduction of dose-effect. Conclusions: This is the first human pharmacokinetic study on TMZ to quantify CSF penetration. The AUC CSF/ AUC plasma ratio was 20%. Systemic or cerebral exposures are not better predictors than the cumulative dose alone for both efficacy and safety.

Population pharmacokinetics of ganciclovir in solid-organ transplant recipients receiving oral valganciclovir.

Valganciclovir (VGC) is an oral prodrug of ganciclovir (GCV) recently introduced for prophylaxis and treatment of cytomegalovirus infection. Optimal concentration exposure for effective and safe VGC therapy would require either reproducible VGC absorption and GCV disposition or dosage adjustment based on therapeutic drug monitoring (TDM). We examined GCV population pharmacokinetics in solid organ transplant recipients receiving oral VGC, including the influence of clinical factors, the magnitude of variability, and its impact on efficacy and tolerability. Nonlinear mixed effect model (NONMEM) analysis was performed on plasma samples from 65 transplant recipients under VGC prophylaxis or treatment. A two-compartment model with first-order absorption appropriately described the data. Systemic clearance was markedly influenced by the glomerular filtration rate (GFR), patient gender, and graft type (clearance/GFR = 1.7 in kidney, 0.9 in heart, and 1.2 in lung and liver recipients) with interpatient and interoccasion variabilities of 26 and 12%, respectively. Body weight and sex influenced central volume of distribution (V(1) = 0.34 liter/kg in males and 0.27 liter/kg in females [20% interpatient variability]). No significant drug interaction was detected. The good prophylactic efficacy and tolerability of VGC precluded the demonstration of any relationship with GCV concentrations. In conclusion, this analysis highlights the importance of thorough adjustment of VGC dosage to renal function and body weight. Considering the good predictability and reproducibility of the GCV profile after treatment with oral VGC, routine TDM does not appear to be clinically indicated in solid-organ transplant recipients. However, GCV plasma measurement may still be helpful in specific clinical situations.

Sancho, et al. Reply

A Reply to the Comment by Jing-Dong Bao and Yan Zhou.

Chaotic, memory, and cooling rate effects in spin glasses: Evaluation of the Edwards-Anderson model

We investigate chaotic, memory, and cooling rate effects in the three-dimensional Edwards-Anderson model by doing thermoremanent (TRM) and ac susceptibility numerical experiments and making a detailed comparison with laboratory experiments on spin glasses. In contrast to the experiments, the Edwards-Anderson model does not show any trace of reinitialization processes in temperature change experiments (TRM or ac). A detailed comparison with ac relaxation experiments in the presence of dc magnetic field or coupling distribution perturbations reveals that the absence of chaotic effects in the Edwards-Anderson model is a consequence of the presence of strong cooling rate effects. We discuss possible solutions to this discrepancy, in particular the smallness of the time scales reached in numerical experiments, but we also question the validity of the Edwards-Anderson model to reproduce the experimental results.

Chaotic dynamics and team effectiveness: evidence from professional basketball

Considering teams as complex adaptive systems (CAS) this study deals with changes in team effectiveness over time in a specific context: professional basketball. The sample comprised 23 basketball teams whose outcomes were analysed over a 12-year period according to two objective measures. The results reveal that all the teams showed chaotic dynamics, one of the key characteristics of CAS. A relationship was also found between teams showing low-dimensional chaotic dynamics and better outcomes, supporting the idea of healthy variability in organizational behaviour. The stability of the squad was likewise found to influence team outcomes, although it was not associated with the chaotic dynamics in team effectiveness. It is concluded that studying teams as CAS enables fluctuations in team effectiveness to be explained, and that the techniques derived from nonlinear dynamical systems, developed specifically for the study of CAS, are useful for this purpose.

Chaotic dynamics and team effectiveness: evidence from professional basketball

Considering teams as complex adaptive systems (CAS) this study deals with changes in team effectiveness over time in a specific context: professional basketball. The sample comprised 23 basketball teams whose outcomes were analysed over a 12-year period according to two objective measures. The results reveal that all the teams showed chaotic dynamics, one of the key characteristics of CAS. A relationship was also found between teams showing low-dimensional chaotic dynamics and better outcomes, supporting the idea of healthy variability in organizational behaviour. The stability of the squad was likewise found to influence team outcomes, although it was not associated with the chaotic dynamics in team effectiveness. It is concluded that studying teams as CAS enables fluctuations in team effectiveness to be explained, and that the techniques derived from nonlinear dynamical systems, developed specifically for the study of CAS, are useful for this purpose.

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.

Chaotic dynamics of electric-field domains in periodically driven superlattices

Self-sustained time-dependent current oscillations under dc voltage bias have been observed in recent experiments on n-doped semiconductor superlattices with sequential resonant tunneling. The current oscillations are caused by the motion and recycling of the domain wall separating low- and high-electric-field regions of the superlattice, as the analysis of a discrete drift model shows and experimental evidence supports. Numerical simulation shows that different nonlinear dynamical regimes of the domain wall appear when an external microwave signal is superimposed on the dc bias and its driving frequency and driving amplitude vary. On the frequency-amplitude parameter plane, there are regions of entrainment and quasiperiodicity forming Arnold tongues. Chaos is demonstrated to appear at the boundaries of the tongues and in the regions where they overlap. Coexistence of up to four electric-field domains randomly nucleated in space is detected under ac+dc driving.

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).