Shapes in vector fields : methods for continuous deformations and surface-based flow visualizations

Magdeburg, Univ., Fak. für Informatik, Diss., 2013

Magnetic control of flexoelectric domains in a nematic fluid

Aus: Soft matter, Vol. 10.2014, H. 25, S. 4487 - 4497

Continuous fluidized bed crystallization

Magdeburg, Univ., Fak. für Verfahrens- und Systemtechnik, Diss., 2015

Some remarks on the class of continuous (Semi-) strictcly quasiconvex functions

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Clarke critical values of subanalytic Lipschitz continuous functions

We prove that any subanalytic locally Lipschitz function has the Sard property. Such functions are typically nonsmooth and their lack of regularity necessitates the choice of some generalized notion of gradient and of critical point. In our framework these notions are defined in terms of the Clarke and of the convex-stable subdifferentials. The main result of this note asserts that for any subanalytic locally Lipschitz function the set of its Clarke critical values is locally finite. The proof relies on Pawlucki's extension of the Puiseuxlemma. In the last section we give an example of a continuous subanalytic function which is not constant on a segment of "broadly critical" points, that is, points for which we can find arbitrarily short convex combinations of gradients at nearby points.

Forecasting volatility using a continuous time model

This paper evaluates the forecasting performance of a continuous stochastic volatility model with two factors of volatility (SV2F) and compares it to those of GARCH and ARFIMA models. The empirical results show that the volatility forecasting ability of the SV2F model is better than that of the GARCH and ARFIMA models, especially when volatility seems to change pattern. We use ex-post volatility as a proxy of the realized volatility obtained from intraday data and the forecasts from the SV2F are calculated using the reprojection technique proposed by Gallant and Tauchen (1998).

The possibility for continuous growth with exhaustible resources: unknowingly an agreement has been reached, but it may not be correct

It is the size of the elasticity of substitution that has been the central issue in the long debate over the possibility of continuous growth in the presence of exhaustible resources. This paper reviews the debate and comes to the surprising conclusion that , unnoticed by the pessimists, the optimist position has gradually evolved so that it now approximates that of the pessimists. The paper also summarises some preliminary work by the author that indicates that this common position may not be correct

Long-term outcome after cognitive and behavioral regression in nonlesional epilepsy with continuous spike-waves during slow-wave sleep.

PURPOSE: To present the long-term follow-up of 10 adolescents and young adults with documented cognitive and behavioral regression as children due to nonlesional focal, mainly frontal, epilepsy with continuous spike-waves during slow wave sleep (CSWS). METHODS: Past medical and electroencephalography (EEG) data were reviewed and neuropsychological tests exploring main cognitive functions were administered. KEY FINDINGS: After a mean duration of follow-up of 15.6 years (range, 8-23 years), none of the 10 patients had recovered fully, but four regained borderline to normal intelligence and were almost independent. Patients with prolonged global intellectual regression had the worst outcome, whereas those with more specific and short-lived deficits recovered best. The marked behavioral disorders resolved in all but one patient. Executive functions were neither severely nor homogenously affected. Three patients with a frontal syndrome during the active phase (AP) disclosed only mild residual executive and social cognition deficits. The main cognitive gains occurred shortly after the AP, but qualitative improvements continued to occur. Long-term outcome correlated best with duration of CSWS. SIGNIFICANCE: Our findings emphasize that cognitive recovery after cessation of CSWS depends on the severity and duration of the initial regression. None of our patients had major executive and social cognition deficits with preserved intelligence, as reported in adults with early destructive lesions of the frontal lobes. Early recognition of epilepsy with CSWS and rapid introduction of effective therapy are crucial for a best possible outcome.

Quantifying consistency of Event Related Potentials across subjects based on single-trial topographic analysis

Introduction: Non-invasive brain imaging techniques often contrast experimental conditions across a cohort of participants, obfuscating distinctions in individual performance and brain mechanisms that are better characterised by the inter-trial variability. To overcome such limitations, we developed topographic analysis methods for single-trial EEG data [1]. So far this was typically based on time-frequency analysis of single-electrode data or single independent components. The method's efficacy is demonstrated for event-related responses to environmental sounds, hitherto studied at an average event-related potential (ERP) level. Methods: Nine healthy subjects participated to the experiment. Auditory meaningful sounds of common objects were used for a target detection task [2]. On each block, subjects were asked to discriminate target sounds, which were living or man-made auditory objects. Continuous 64-channel EEG was acquired during the task. Two datasets were considered for each subject including single-trial of the two conditions, living and man-made. The analysis comprised two steps. In the first part, a mixture of Gaussians analysis [3] provided representative topographies for each subject. In the second step, conditional probabilities for each Gaussian provided statistical inference on the structure of these topographies across trials, time, and experimental conditions. Similar analysis was conducted at group-level. Results: Results show that the occurrence of each map is structured in time and consistent across trials both at the single-subject and at group level. Conducting separate analyses of ERPs at single-subject and group levels, we could quantify the consistency of identified topographies and their time course of activation within and across participants as well as experimental conditions. A general agreement was found with previous analysis at average ERP level. Conclusions: This novel approach to single-trial analysis promises to have impact on several domains. In clinical research, it gives the possibility to statistically evaluate single-subject data, an essential tool for analysing patients with specific deficits and impairments and their deviation from normative standards. In cognitive neuroscience, it provides a novel tool for understanding behaviour and brain activity interdependencies at both single-subject and at group levels. In basic neurophysiology, it provides a new representation of ERPs and promises to cast light on the mechanisms of its generation and inter-individual variability.

Intraoperative cerebral perfusion and postoperative cognitive dysfunction in geriatric patients

Background: Inadequate intraoperative cerebral perfusion has been suggested as a possible cause of postoperative cognitive dysfunction (POCD). Methods: We investigated 35 patients aged 65 or older undergoing elective major non-cardiac surgery under standardized general anaesthesia (thiopental, sevoflurane, fentanyl, atracurium). Intraoperative cerebral perfusion was monitored with transcranial Doppler, and near-infrared spectroscopy (NIRS). Arterial blood pressure was monitored continuously with a Finapres device. Mx, an index allowing continuous monitoring of cerebrovascular autoregulation based on the changes in mean arterial blood pressure (MAP) and cerebral blood flow velocity was calculated. Mx >0.5 was defined as disturbed cerebrovascular autoregulation. Cognitive function was measured preoperatively and 7 days postoperatively using the CERAD-NAB Plus test battery. A postoperative decline >1 z-score in at least two of the tested domains was defined as POCD. Data are shown as mean } SD. Results: Mean age was 75 } 7 yrs. Sixteen patients (46%) developed POCD. These patients were older (77 } 8 vs 73 } 7 yrs), had lower MAP (77 } 12 vs 81 } 11 mm Hg), lower cerebral tissue oxygenation indices measured by NIRS (66.8 } 6.0 vs 68.6 } 4.3%) and less efficient cerebrovascular autoregulation (Mx 0.54 } 0.17 and 0.44 } 0.22) than patients without POCD. Disturbed intraoperative cerebrovascular autoregulation was found more often (56 vs 37%) in patients with POCD. However, none of these differences reached statistical significance. Conclusions: Our data show a trend towards subtle changes in intraoperative cerebral perfusion in elderly patients who develop POCD. However, a cause effect relationship must not be assumed and a greater number of patients needs to be investigated patients. However, more patients need to be investigated to confirm and characterize these differences.

Adaptive Continuous time Markov Chain Approximation Model to General Jump-Diusions

We propose a non-equidistant Q rate matrix formula and an adaptive numerical algorithm for a continuous time Markov chain to approximate jump-diffusions with affine or non-affine functional specifications. Our approach also accommodates state-dependent jump intensity and jump distribution, a flexibility that is very hard to achieve with other numerical methods. The Kolmogorov-Smirnov test shows that the proposed Markov chain transition density converges to the one given by the likelihood expansion formula as in Ait-Sahalia (2008). We provide numerical examples for European stock option pricing in Black and Scholes (1973), Merton (1976) and Kou (2002).

A Simple Characterization of Dynamic Completeness in Continuous Time

This paper investigates dynamic completeness of financial markets in which the underlying risk process is a multi-dimensional Brownian motion and the risky securities dividends geometric Brownian motions. A sufficient condition, that the instantaneous dispersion matrix of the relative dividends is non-degenerate, was established recently in the literature for single-commodity, pure-exchange economies with many heterogenous agents, under the assumption that the intermediate flows of all dividends, utilities, and endowments are analytic functions. For the current setting, a different mathematical argument in which analyticity is not needed shows that a slightly weaker condition suffices for general pricing kernels. That is, dynamic completeness obtains irrespectively of preferences, endowments, and other structural elements (such as whether or not the budget constraints include only pure exchange, whether or not the time horizon is finite with lump-sum dividends available on the terminal date, etc.)

Integer Programming on Domains Containing Inseparable Ordered Paris

Using the integer programming approach introduced by Sethuraman, Teo, and Vohra (2003), we extend the analysis of the preference domains containing an inseparable ordered pair, initiated by Kalai and Ritz (1978). We show that these domains admit not only Arrovian social welfare functions \without ties," but also Arrovian social welfare functions \with ties," since they satisfy the strictly decomposability condition introduced by Busetto, Codognato, and Tonin (2012). Moreover, we go further in the comparison between Kalai and Ritz (1978)'s inseparability and Arrow (1963)'s single-peak restrictions, showing that the former condition is more \respectable," in the sense of Muller and Satterthwaite (1985).