Nonlinear and Complex Dynamics in Economics

This paper is an up-to-date survey of the state-of-the-art in dynamical systems theory relevant to high levels of dynamical complexity, characterizing chaos and near chaos, as commonly found in the physical sciences. The paper also surveys applications in economics and �finance. This survey does not include bifurcation analyses at lower levels of dynamical complexity, such as Hopf and transcritical bifurcations, which arise closer to the stable region of the parameter space. We discuss the geometric approach (based on the theory of differential/difference equations) to dynamical systems and make the basic notions of complexity, chaos, and other related concepts precise, having in mind their (actual or potential) applications to economically motivated questions. We also introduce specifi�c applications in microeconomics, macroeconomics, and �finance, and discuss the policy relevancy of chaos

Nonlinear and Complex Dynamics in Real Systems

This is the publisher's version, also available electronically from http://www.degruyter.com/view/j/ijnsns.2006.7.2/ijnsns.2006.7.2.191/ijnsns.2006.7.2.191.xml?format=INT.In this article we provide a review of the literature with respect to fluctuations in real systems and chaos. In doing so, we contrast the order and organization hypothesis of real systems to nonlinear chaotic dynamics and discuss some techniques used in distinguishing between stochastic and deterministic behavior. Moreover, we look at the issue of where and when the ideas of chaos could profitably be applied to real systems

A Complexity Analysis of Noise-like Activity in the Nervous System and its Application to Brain State Classification and Identification in Epilepsy

Complexity lies halfway between stochasticity and determinism, suggesting that brain activity is neither fully random nor fully predictable but lives by the rules of nonlinear high- and low-complexity dynamics. One important aspect of brain function is noise-like activity (NLA), defined as background, electrical potential fluctuations in the nervous system distinct from spiking rhythms in the foreground. The objective of this thesis was to investigate the neurodynamical complexity of NLA recorded at the cellular and local network scales in in vitro preparations of mouse and human hippocampal tissue, under healthy and epileptiform conditions. In particular, it was found that neuronal NLA arises out of the physiological contributions of gap junctions and chemical synaptic channels and is characterized by a spectrum of complexity, ranging from high- to low-complexity, that was measured using methods from nonlinear dynamical systems theory. Importantly, the complexity of background, neuronal NLA was shown to depend on the degree of cellular interconnectivity to the surrounding local network. In addition, the complexity and multifractality of NLA was further studied at the cellular and local network scales in epileptiform transitions to seizure-like events, identifying emergent low-complexity and reduced multifractality (bordering on monofractal-type dynamics) in the pathological ictal state. Finally, dual intracellular recordings of hippocampal epileptiform activity were analyzed to measure NLA synchronicity, showing evidence for increased same- and cross-frequency correlations and increased phase synchronization in the pathological ictal state. Convergence towards increased phase synchrony manifested in lower frequency regions including theta (4-10 Hz) and beta (12-30 Hz), but also in higher frequency bands (gamma, 30-80 Hz). In summary, there is evidence to suggest that background NLA captures important neurodynamical information pertinent to the classification and identification of brain state transitions in healthy and epileptiform hippocampal dynamics, using sophisticated neuroengineering analyses of these physiological signals.Ph

A Complexity Analysis of Noise-like Activity in the Nervous System and its Application to Brain State Classification and Identification in Epilepsy

Complexity lies halfway between stochasticity and determinism, suggesting that brain activity is neither fully random nor fully predictable but lives by the rules of nonlinear high- and low-complexity dynamics. One important aspect of brain function is noise-like activity (NLA), defined as background, electrical potential fluctuations in the nervous system distinct from spiking rhythms in the foreground. The objective of this thesis was to investigate the neurodynamical complexity of NLA recorded at the cellular and local network scales in in vitro preparations of mouse and human hippocampal tissue, under healthy and epileptiform conditions. In particular, it was found that neuronal NLA arises out of the physiological contributions of gap junctions and chemical synaptic channels and is characterized by a spectrum of complexity, ranging from high- to low-complexity, that was measured using methods from nonlinear dynamical systems theory. Importantly, the complexity of background, neuronal NLA was shown to depend on the degree of cellular interconnectivity to the surrounding local network. In addition, the complexity and multifractality of NLA was further studied at the cellular and local network scales in epileptiform transitions to seizure-like events, identifying emergent low-complexity and reduced multifractality (bordering on monofractal-type dynamics) in the pathological ictal state. Finally, dual intracellular recordings of hippocampal epileptiform activity were analyzed to measure NLA synchronicity, showing evidence for increased same- and cross-frequency correlations and increased phase synchronization in the pathological ictal state. Convergence towards increased phase synchrony manifested in lower frequency regions including theta (4-10 Hz) and beta (12-30 Hz), but also in higher frequency bands (gamma, 30-80 Hz). In summary, there is evidence to suggest that background NLA captures important neurodynamical information pertinent to the classification and identification of brain state transitions in healthy and epileptiform hippocampal dynamics, using sophisticated neuroengineering analyses of these physiological signals.Ph

Fungal osteomyelitis with vertebral re-ossification

AbstractIntroductionWe present a rare case of thoracic vertebral osteomyelitis secondary to pulmonary Blastomyces dermatitides.Presentation of caseA 27-year-old male presented with three months of chest pains and non-productive cough. Examination revealed diminished breath sounds on the right. CT/MR imaging confirmed a right-sided pre-/paravertebral soft tissue mass and destructive lytic lesions from T2 to T6. CT-guided needle biopsy confirmed granulomatous pulmonary Blastomycosis. Conservative management with antifungal therapy was initiated. Neurosurgical review confirmed no clinical or profound radiographic instability, and the patient was stabilized with TLSO bracing. Serial imaging 3 months later revealed near-resolution of the thoracic soft tissue mass, with vertebral re-ossification from T2 to T6.DiscussionFungal osteomyelitis presents a rare entity in the spectrum of spinal infections. In such cases, lytic spinal lesions are classically seen in association with a large paraspinous mass. Fungal infections of the spinal column may be treated conservatively, with surgical intervention reserved for progressive cases manifesting with neurological compromise and/or spinal column instability. Here, we found unexpected evidence for vertebral re-ossification across the affected thoracic levels (T2-6) in response to IV antibiotic therapy and conservative bracing, nearly 3 months later

Prostate carcinoma mimicking a sphenoid wing meningioma

AbstractIntroductionWe report here on a rare case of a large, lateral sphenoid wing tumor with radiographic and intraoperative findings highly suggestive of meningioma, yet pathology was in fact consistent with metastatic prostate adenocarcinoma.Presentation of caseAn 81 year-old male presented with expressive dysphasia, right-sided weakness and headaches. Imaging revealed a heterogeneously-enhancing lesion based on the left lateral sphenoid wing. The presumed diagnosis was strongly in favor of meningioma, and the patient underwent complete resection of the dural-based lesion. Final pathology confirmed the unexpected finding of a metastatic prostate adenocarcinoma. Although he tolerated surgery well, the patient was subsequently referred for palliative therapy given findings of widespread systemic disease.DiscussionIntracranial metastases may involve the dura, at times presenting with rare radiographic features highly suggestive for meningioma, as in our case here. This makes differentiation, at least based on imaging, a challenge. Elderly patients presenting with neurological deficits secondary to a newly-diagnosed, dural-based lesion should thus be considered for metastasis, prompting additional imaging studies (including body CT, MRI or PET) to rule out a primary lesion elsewhere. In some cases, this may affect the overall decision to proceed with surgical resection, or alternatively, to proceed directly to palliative therapy (the latter decision made in the context of widespread metastatic disease).ConclusionWe conclude that dural-based metastatic lesions may mimic meningiomas, warranting thorough pre-operative work-up to exclude the possibility of metastasis. In certain cases, identification of widespread disease might preclude surgery and favor palliation, instead