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

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-

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

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

Early stages of pediatric bipolar disorder: retrospective analysis of a Czech inpatient sample

Michal Goetz,1 Tomas Novak,2 Marie Vesela,1 Zdenek Hlavka,3 Martin Brunovsky,2 Michal Povazan,4 Radek Ptacek,5 Antonin Sebela21Department of Child Psychiatry, Second Faculty of Medicine, Motol University Hospital, Charles University in Prague, Prague, Czech Republic; 2National Institute of Mental Health, Klecany and Third Faculty of Medicine, Charles University in Prague, Prague, Czech Republic; 3Department of Probability and Mathematical Statistics, Faculty of Mathematics and Physics, Charles University in Prague, Prague, Czech Republic; 4Children’s Department, Bohnice Psychiatric Hospital, Prague, Czech Republic; 5Department of Psychiatry, First Faculty of Medicine, General Teaching Hospital, Charles University in Prague, Czech RepublicBackground: Approximately 30%–60% of adults diagnosed with bipolar disorder (BD) report onset between the ages 15 and 19 years; however, a correct diagnosis is often delayed by several years. Therefore, investigations of the early features of BD are important for adequately understanding the prodromal stages of the illness.Methods: A complete review of the medical records of 46 children and adolescents who were hospitalized for BD at two psychiatric teaching centers in Prague, Czech Republic was performed. Frequency of BD in all inpatients, age of symptom onset, phenomenology of mood episodes, lifetime psychiatric comorbidity, differences between very-early-onset (<13 years of age) and early-onset patients (13–18 years), and differences between the offspring of parents with and without BD were analyzed.Results: The sample represents 0.83% of the total number of inpatients (n=5,483) admitted during the study period at both centers. BD often started with depression (56%), followed by hypomania (24%) and mixed episodes (20%). The average age during the first mood episode was 14.9 years (14.6 years for depression and 15.6 years for hypomania). Seven children (15%) experienced their first mood episode before age 13 years (very early onset). Traumatic events, first-degree relatives with mood disorders, and attention deficit hyperactivity disorder were significantly more frequent in the very-early-onset group vs the early-onset group (13–18 years) (P≤0.05). The offspring of bipolar parents were significantly younger at the onset of the first mood episode (13.2 vs 15.4 years; P=0.02) and when experiencing the first mania compared to the offspring of non-BD parents (14.3 vs 15.9 years; P=0.03). Anxiety disorders, substance abuse, specific learning disabilities, and attention deficit hyperactivity disorder were the most frequent lifetime comorbid conditions.Conclusion: Clinicians must be aware of the potential for childhood BD onset in patients who suffer from recurrent depression, who have first-degree relatives with BD, and who have experienced severe psychosocial stressors.Keywords: children, adolescents, inpatient