A Singular Differential Equation Stemming from an Optimal Control Problem in Financial Economics

We consider the ordinary differential equation x2u′′=axu′+bu−c(u′−1)2,x∈(0,x0), with a∈R,b∈R , c>0 and the singular initial condition u(0)=0, which in financial economics describes optimal disposal of an asset in a market with liquidity effects. It is shown in the paper that if a+b0 then there are infinitely many continuous solutions with indistinguishable asymptotics near 0. Moreover, it is proved that in the latter case there is precisely one solution u corresponding to the choice x 0=∞ which is such that 0≤u(x)≤x for all x>0, and that this solution is strictly increasing and concave

A cryogenic axial-centrifugal compressor for superfluid helium refrigeration

CERN's new project, the Large Hadron Collider (LHC), will use superfluid helium as coolant for its high-field superconducting magnets and therefore require large capacity refrigeration at 1.8 K. This may only be achieved by subatmospheric compression of gaseous helium at cryogenic temperature. To stimulate development of this technology, CERN has procured from industry prototype Cold Compressor Units (CCU). This unit is based on a cryogenic axial-centrifugal compressor, running on ceramic ball bearings and driven by a variable-frequency electrical motor operating under low-pressure helium at ambient temperature. The machine has been commissioned and is now in operation. After describing basic constructional features of the compressor, we report on measured performance

Guidelines for the recording and evaluation of pharmaco-EEG data in man: the International Pharmaco-EEG Society (IPEG)

The International Pharmaco-EEG Society (IPEG) presents updated guidelines summarising the requirements for the recording and computerised evaluation of pharmaco-EEG data in man. Since the publication of the first pharmaco-EEG guidelines in 1982, technical and data processing methods have advanced steadily, thus enhancing data quality and expanding the palette of tools available to investigate the action of drugs on the central nervous system (CNS), determine the pharmacokinetic and pharmacodynamic properties of novel therapeutics and evaluate the CNS penetration or toxicity of compounds. However, a review of the literature reveals inconsistent operating procedures from one study to another. While this fact does not invalidate results per se, the lack of standardisation constitutes a regrettable shortcoming, especially in the context of drug development programmes. Moreover, this shortcoming hampers reliable comparisons between outcomes of studies from different laboratories and hence also prevents pooling of data which is a requirement for sufficiently powering the validation of novel analytical algorithms and EEG-based biomarkers. The present updated guidelines reflect the consensus of a global panel of EEG experts and are intended to assist investigators using pharmaco-EEG in clinical research, by providing clear and concise recommendations and thereby enabling standardisation of methodology and facilitating comparability of data across laboratories

Controllability on infinite-dimensional manifolds

Following the unified approach of A. Kriegl and P.W. Michor (1997) for a treatment of global analysis on a class of locally convex spaces known as convenient, we give a generalization of Rashevsky-Chow's theorem for control systems in regular connected manifolds modelled on convenient (infinite-dimensional) locally convex spaces which are not necessarily normable.Comment: 19 pages, 1 figur

Probability of local bifurcation type from a fixed point: A random matrix perspective

Results regarding probable bifurcations from fixed points are presented in the context of general dynamical systems (real, random matrices), time-delay dynamical systems (companion matrices), and a set of mappings known for their properties as universal approximators (neural networks). The eigenvalue spectra is considered both numerically and analytically using previous work of Edelman et. al. Based upon the numerical evidence, various conjectures are presented. The conclusion is that in many circumstances, most bifurcations from fixed points of large dynamical systems will be due to complex eigenvalues. Nevertheless, surprising situations are presented for which the aforementioned conclusion is not general, e.g. real random matrices with Gaussian elements with a large positive mean and finite variance.Comment: 21 pages, 19 figure

Erratum to: A Singular Differential Equation Stemming from an Optimal Control Problem in Financial Economics

Erratum to: Appl Math Optim (2013) 68:255–274 DOI 10.1007/s00245-013-9205-

Subjective and objective evaluation of alertness and sleep quality in depressed patients

BACKGROUND: The reliability of the subjective statements reports on disturbed night sleep and alertness in the daytime was assessed by their correlation to the objective indicators in patients with mild deprsssion. METHOD: Among patients with depression, altogether 28 patients with insomnia were examined. Their answers to typical questions, as they are used during a psychiatric interview, were scored. In parallel, night sleep quality and alertness level in the daytime were objectively estimated by means of polygraphic recording. RESULTS: The subjective statements on the type of insomnia, the estimated time of falling asleep, frequent awakenings and occurrence of disturbing dreams seem to be unreliable. Similarly, the results were disappointing when the patients were asked about alertness disturbances in the daytime. An unexpected finding was the lack of any significant correlation to the scores obtained by means of Epworth's scale. Among the factors possibly influencing the patients' reports, age, sex, coffee intake and also chronic administration of sedatives or hypnotics showed a low correlation with the sleep and alertness indicators. CONCLUSION: The statistical evaluation indicated rather poor agreement between the subjective and objective items. The statistical evaluation suggested that anxiety and depression significantly influence reports on sleep quality and alertness disturbances in the daytime

The effectiveness of various potential predictors of response to treatment with SSRIs in patients with depressive disorder

IntroductionThe substantial non-response rate in depressive patients indicates a need to identify predictors of treatment outcome.Objective and aimsThe aim of the open-label, 6-week study was:– to compare efficacy of a priori defined predictors: ≥ 20% reduction in MADRS score at week 1, ≥ 20% reduction in MADRS score at week 2 (RM ≥ 20% W2), decrease of prefrontal theta cordance value (RC) and increase of serum/plasma brain-derived neurotrophic factor (BDNF) at week 1;– to assess whether the combination of these factors yield more robust predictive power than when used singly.MethodsAll patients (n = 38) were hospitalized and treated with various SSRIs. Areas under curve (AUC) as well as predictive values were calculated to compare predictive effect of single and combined predictor model.ResultsTwenty-one patients (55%) achieved response. The RM ≥ 20% W2 (AUC-0.83) showed better predictive efficacy compared to all other predictors with exception of RC. Other significant differences were not detected. The identified (logistic regression) combined predictive model (RM ≥ 20% W2 + RC) predicted response with accuracy of 82% (AUC-0.92) and was significantly better than other predictors but not RM ≥ 20% W2 and RC.ConclusionsOur findings indicate that the RM ≥ 20% W2 alone and in combination with RC may be useful in the prediction of response to SSRIs. Serum/plasma BDNF did not show strong predictive potential.Disclosure of interestThe authors have not supplied their declaration of competing interest.</jats:sec

Prefrontal Theta Cordance in the Prediction of Antidepressant Response to Various Classes of Antidepressants in Patients with Depressive Disorder

Introduction and objectivesPrevious studies demonstrated efficacy of reduction of QEEG prefrontal theta cordance (RC) after the first week of treatment in the prediction of antidepressant response.AimsThe study aimed to compare the ability of RC in the prediction of response to various antidepressant classes.MethodsAll patients (n = 142) were treated with antidepressants (SSRI-58, SNRI-47, NDRI-22, NaSSA-15) for ≥ 4 weeks. Response was defined as MADRS reduction ≥ 50%. EEG were performed at baseline and week 1 of treatment and cordance was calculated for 3 prefrontal electrodes (Fp1, Fp2, Fz).ResultsLogistic regression identified RC as a predictor of response to SSRI, SNRI and NDRI but not for NaSSA. Predictive parameters of RC for response to mentioned antidepressant classes are displayed in the Table 1.Areas under curves of ROC analysis (AUC) of RC for response prediction were not significantly different among antidepressant classes.ConclusionThe predictive efficacy of RC for response to SSRI, SNRI and NDRI was comparable.This study was supported by the grants of MH CZ nr.15-29900A, MH CZ – DRO (NIMH-CZ, 00023752) and by the project Nr. LO1611 from the MEYS under the NPU I program.</jats:sec