Monodromy calculations for some differential equations

In vielen Teilgebieten der Mathematik ist es w"{u}nschenswert, die Monodromiegruppe einer homogenen linearen Differenzialgleichung zu verstehen. Es sind nur wenige analytische Methoden zur Berechnung dieser Gruppe bekannt, daher entwickeln wir im ersten Teil dieser Arbeit eine numerische Methode zur Approximation ihrer Erzeuger.rnIm zweiten Abschnitt fassen wir die Grundlagen der Theorie der Uniformisierung Riemannscher Fl"achen und die der arithmetischen Fuchsschen Gruppen zusammen. Auss erdem erkl"aren wir, wie unsere numerische Methode bei der Bestimmung von uniformisierenden Differenzialgleichungen dienlich sein kann. F"ur arithmetische Fuchssche Gruppen mit zwei Erzeugern erhalten wir lokale Daten und freie Parameter von Lam'{e} Gleichungen, welche die zugeh"origen Riemannschen Fl"achen uniformisieren. rnIm dritten Teil geben wir einen kurzen Abriss zur homologischen Spiegelsymmetrie und f"uhren die $widehat{Gamma}$-Klasse ein. Wir erkl"aren wie diese genutzt werden kann, um eine Hodge-theoretische Version der Spiegelsymmetrie f"ur torische Varit"aten zu beweisen. Daraus gewinnen wir Vermutungen "uber die Monodromiegruppe $M$ von Picard-Fuchs Gleichungen von gewissen Familien $f:mathcal{X}rightarrow bbp^1$ von $n$-dimensionalen Calabi-Yau Variet"aten. Diese besagen erstens, dass bez"uglich einer nat"urlichen Basis die Monodromiematrizen in $M$ Eintr"age aus dem K"orper $bbq(zeta(2j+1)/(2 pi i)^{2j+1},j=1,ldots,lfloor (n-1)/2 rfloor)$ haben. Und zweitens, dass sich topologische Invarianten des Spiegelpartners einer generischen Faser von $f:mathcal{X}rightarrow bbp^1$ aus einem speziellen Element von $M$ rekonstruieren lassen. Schliess lich benutzen wir die im ersten Teil entwickelten Methoden zur Verifizierung dieser Vermutungen, vornehmlich in Hinblick auf Dimension drei. Dar"uber hinaus erstellen wir eine Liste von Kandidaten topologischer Invarianten von vermutlich existierenden dreidimensionalen Calabi-Yau Variet"aten mit $h^{1,1}=1$.

Computing primal solutions with exact arithmetics in SCIP.

The research for exact solutions of mixed integer problems is an active topic in the scientific community. State-of-the-art MIP solvers exploit a floating- point numerical representation, therefore introducing small approximations. Although such MIP solvers yield reliable results for the majority of problems, there are cases in which a higher accuracy is required. Indeed, it is known that for some applications floating-point solvers provide falsely feasible solutions, i.e. solutions marked as feasible because of approximations that would not pass a check with exact arithmetic and cannot be practically implemented. The framework of the current dissertation is SCIP, a mixed integer programs solver mainly developed at Zuse Institute Berlin. In the same site we considered a new approach for exactly solving MIPs. Specifically, we developed a constraint handler to plug into SCIP, with the aim to analyze the accuracy of provided floating-point solutions and compute exact primal solutions starting from floating-point ones. We conducted a few computational experiments to test the exact primal constraint handler through the adoption of two main settings. Analysis mode allowed to collect statistics about current SCIP solutions' reliability. Our results confirm that floating-point solutions are accurate enough with respect to many instances. However, our analysis highlighted the presence of numerical errors of variable entity. By using the enforce mode, our constraint handler is able to suggest exact solutions starting from the integer part of a floating-point solution. With the latter setting, results show a general improvement of the quality of provided final solutions, without a significant loss of performances.

Sleep restriction attenuates amplitudes and attentional modulation of pain-related evoked potentials, but augments pain ratings in healthy volunteers

The experiment investigated the impact of sleep restriction on pain perception and related evoked potential correlates (laser-evoked potentials, LEPs). Ten healthy subjects with good sleep quality were investigated in the morning twice, once after habitual sleep and once after partial sleep restriction. Additionally, we studied the impact of attentional focussing on pain and LEPs by directing attention to (intensity discrimination) or away from the stimulus (mental arithmetic). Laser stimuli directed to the hand dorsum were rated as 30% more painful after sleep restriction (49+/-7 mm) than after a night of habitual sleep (38+/-7 mm). A significant interaction between attentional focus and sleep condition suggested that attentional focusing was less distinctive under sleep restriction. Intensity discrimination was preserved. In contrast, the amplitude of the early parasylvian N1 of LEPs was significantly smaller after a night of partial sleep restriction (-36%, p<0.05). Likewise, the amplitude of the vertex N2-P2 was significantly reduced (-34%, p<0.01); also attentional modulation of the N2-P2 was reduced. Thus, objective (LEPs) and subjective (pain ratings) parameters of nociceptive processing were differentially modulated by partial sleep restriction. We propose, that sleep reduction leads to an impairment of activation in the ascending pathway (leading to reduced LEPs). In contradistinction, pain perception was boosted, which we attribute to lack of pain control distinct from classical descending inhibition, and thus not affecting the projection pathway. Sleep-restricted subjects exhibit reduced attentional modulation of pain stimuli and may thus have difficulties to readily attend to or disengage from pain.

On a Microcomputer Implementation of an Intrusion-detection Algorithm

The main objective of this paper is to discuss various aspects of implementing a specific intrusion-detection scheme on a micro-computer system using fixed-point arithmetic. The proposed scheme is suitable for detecting intruder stimuli which are in the form of transient signals. It consists of two stages: an adaptive digital predictor and an adaptive threshold detection algorithm. Experimental results involving data acquired via field experiments are also included.

Taiji practice attenuates psychobiological stress reactivity - A randomized controlled trial in healthy subjects

Background: Stress reducing effects of Taiji, a mindful and gentle form of body movement, have been reported in previous studies, but standardized and controlled experimental studies are scarce. The present study investigates the effect of regular Taiji practice on psychobiological stress response in healthy men and women. Methods: 70 participants were randomly assigned to either Taiji classes or a waiting list. After 3 months, 26 (8 men, 18 women) persons in the Taiji group and 23 (9 men, 14 women) in the waiting control group underwent a standardized psychosocial stress test combining public speaking and mental arithmetic in front of an audience. Salivary cortisol and α-amylase, heart rate, and psychological responses to psychosocial stress were compared between the study groups. (ClinicalTrials.gov number, NCT01122706.) Results: Stress induced characteristic changes in all psychological and physiological measures. Compared to controls, Taiji participants exhibited a significantly lower stress reactivity of cortisol (p = .028) and heart rate (p = .028), as well as lower α-amylase levels (p = .049). They reported a lower increase in perceived stressfulness (p = .006) and maintained a higher level of calmness (p = .019) in response to psychosocial stress. Conclusion: Our results consistently suggest that practicing Taiji attenuates psychobiological stress reactivity in healthy subjects. This may underline the role of Taiji as a useful mind–body practice for stress prevention.

End-tidal CO(2). An important parameter for a correct interpretation in functional brain studies using speech tasks

The aim was to investigate the effect of different speech tasks, i.e. recitation of prose (PR), alliteration (AR) and hexameter (HR) verses and a control task (mental arithmetic (MA) with voicing of the result on end-tidal CO2 (PETCO2), cerebral hemodynamics and oxygenation. CO2 levels in the blood are known to strongly affect cerebral blood flow. Speech changes breathing pattern and may affect CO2 levels. Measurements were performed on 24 healthy adult volunteers during the performance of the 4 tasks. Tissue oxygen saturation (StO2) and absolute concentrations of oxyhemoglobin ([O2Hb]), deoxyhemoglobin ([HHb]) and total hemoglobin ([tHb]) were measured by functional near-infrared spectroscopy (fNIRS) and PETCO2 by a gas analyzer. Statistical analysis was applied to the difference between baseline before the task, 2 recitation and 5 baseline periods after the task. The 2 brain hemispheres and 4 tasks were tested separately. A significant decrease in PETCO2 was found during all 4 tasks with the smallest decrease during the MA task. During the recitation tasks (PR, AR and HR) a statistically significant (p < 0.05) decrease occurred for StO2 during PR and AR in the right prefrontal cortex (PFC) and during AR and HR in the left PFC. [O2Hb] decreased significantly during PR, AR and HR in both hemispheres. [HHb] increased significantly during the AR task in the right PFC. [tHb] decreased significantly during HR in the right PFC and during PR, AR and HR in the left PFC. During the MA task, StO2 increased and [HHb] decreased significantly during the MA task. We conclude that changes in breathing (hyperventilation) during the tasks led to lower CO2 pressure in the blood (hypocapnia), predominantly responsible for the measured changes in cerebral hemodynamics and oxygenation. In conclusion, our findings demonstrate that PETCO2 should be monitored during functional brain studies investigating speech using neuroimaging modalities, such as fNIRS, fMRI to ensure a correct interpretation of changes in hemodynamics and oxygenation.

Delayed response and lack of habituation in plasma interleukin-6 to acute mental stress in men

Acute mental stress induces a significant increase in plasma interleukin (IL)-6 levels as a possible mechanism for how psychological stress might contribute to atherosclerosis. We investigated whether the IL-6 response would habituate in response to a repetitively applied mental stressor and whether cortisol reactivity would show a relationship with IL-6 reactivity. Study participants were 21 reasonably healthy men (mean age 46+/-7 years) who underwent the Trier Social Stress Test (combination of a 3-min preparation, 5-min speech, and 5-min mental arithmetic) three times with an interval of 1 week. Plasma IL-6 and free salivary cortisol were measured immediately before and after stress, and at 45 and 105 min of recovery from stress. Cortisol samples were also obtained 15 and 30 min after stress. Compared to non-stressed controls, IL-6 significantly increased between rest and 45 min post-stress (p=.022) and between rest and 105 min post-stress (p=.001). Peak cortisol (p=.034) and systolic blood pressure (p=.009) responses to stress both habituated between weeks one and three. No adaptation occurred in diastolic blood pressure, heart rate, and IL-6 responses to stress. The areas under the curve integrating the stress-induced changes in cortisol and IL-6 reactivity were negatively correlated at visit three (r=-.54, p=.011), but not at visit one. The IL-6 response to acute mental stress occurs delayed and shows no adaptation to repeated moderate mental stress. The hypothalamus-pituitary-adrenal axis may attenuate stress reactivity of IL-6. The lack of habituation in IL-6 responses to daily stress could subject at-risk individuals to higher atherosclerotic morbidity and mortality.

Anticipatory cognitive stress appraisal and the acute procoagulant stress response in men

OBJECTIVE: Acute mental stress elicits blood hypercoagulability. Following a transactional stress model, we investigated whether individuals who anticipate stress as more threatening, challenging, and as exceeding their coping skills show greater stress reactivity of the coagulation activation marker D-dimer, indicating fibrin generation in plasma. METHODS: Forty-seven men (mean age 44 +/- 14 years; mean blood pressure [MBP] 101 +/- 12 mm Hg; mean body mass index [BMI] 26 +/- 3 kg/m(2)) completed the Primary Appraisal Secondary Appraisal (PASA) scale before undergoing the Trier Social Stress Test (combination of mock job interview and mental arithmetic task). Heart rate, blood pressure, plasma catecholamines, and D-dimer levels were measured before and after stress, and during recovery up to 60 minutes poststress. RESULTS: Hemodynamic measures, catecholamines, and D-dimer changed across all time points (p values <.001). The PASA "Stress Index" (integrated measure of transactional stress perception) correlated with total D-dimer area under the curve (AUC) between rest and 60 minutes poststress (r = 0.30, p = .050) and with D-dimer change from rest to immediately poststress (r = 0.29, p = .046). Primary appraisal (combined "threat" and "challenge") correlated with total D-dimer AUC (r = 0.37, p = .017), D-dimer stress change (r = 0.41, p = .004), and D-dimer recovery (r = 0.32, p = .042). "Challenge" correlated more strongly with D-dimer stress change than "threat" (p = .020). Primary appraisal (DeltaR(2) = 0.098, beta = 0.37, p = .019), and particularly its subscale "challenge" (DeltaR(2) = 0.138, beta = 0.40, p = .005), predicted D-dimer stress change independently of age, BP, BMI, and catecholamine change. CONCLUSIONS: Anticipatory cognitive appraisal determined the extent of coagulation activation to and recovery from stress in men. Particularly individuals who anticipated the stressor as more challenging and also more threatening had a greater fibrin stress response.

Low social support and poor emotional regulation are associated with increased stress hormone reactivity to mental stress in systemic hypertension

CONTEXT: There is strong evidence for a physiological hyperreactivity to stress in systemic hypertension, but data on associated or potentially moderating psychological factors are scarce. OBJECTIVE: The objective of the study was to identify psychological correlates of physiological stress reactivity in systemic hypertension. DESIGN: This was a cross-sectional, quasi-experimentally controlled study. Study participants underwent an acute standardized psychosocial stress task combining public speaking and mental arithmetic in front of an audience. SETTING: The study was conducted in the population in the state of Zurich, Switzerland. SUBJECTS: Subjects included 22 hypertensive and 26 normotensive men (mean +/- sem 44 +/- 2 yr). MAIN OUTCOME MEASURES: We assessed the psychological measures social support, emotional regulation, and cognitive appraisal of the stressful situation. Moreover, we measured salivary cortisol and plasma epinephrine and norepinephrine before and after stress and several times up to 60 min thereafter as well as blood pressure and heart rate. RESULTS: We found poorer hedonistic emotional regulation (HER) and lower perceived social support in hypertensives, compared with normotensives (P < 0.01). Compared with normotensives, hypertensives showed higher cortisol, epinephrine, and norepinephrine secretions after stress (P < 0.038) as well as higher systolic and diastolic blood pressure (P < 0.001). Cortisol reactivity and norepinephrine secretion were highest in hypertensive men with low HER (P < 0.05). In contrast, hypertensives with high HER did not significantly differ from normotensives in both cortisol and norepinephrine secretion after stress. Epinephrine secretion was highest in hypertensives with low social support but was not different between hypertensives with high social support and normotensives. CONCLUSIONS: The findings suggest that both low social support and low HER are associated with elevated stress hormone reactivity in systemic hypertension.

Intraobserver and interobserver variability of 64-row computed tomography abdominal aortic aneurysm neck measurements

BACKGROUND: Integrity of the abdominal aortic aneurysm (AAA) neck is crucial for the long-term success of endovascular AAA repair (EVAR). However, suitable tools for reliable assessment of changes in small aortic volumes are lacking. The purpose of this study was to assess the intraobserver and interobserver variability of software-enhanced 64-row computed tomographic angiography (CTA) AAA neck volume measurements in patients after EVAR. METHODS: A total of 25 consecutive patients successfully treated by EVAR underwent 64-row follow-up CTA in 1.5-mm collimation. Manual CTA measurements were performed twice by three blinded and independent readers in random order with at least a 4-week interval between readings. Maximum and minimum transverse aortic neck diameters were measured twice on two different levels within the proximal neck. Volumetry of the proximal aortic neck was performed by using dedicated software. Variability was calculated as 1.96 SD of the mean arithmetic difference according to Bland and Altman. Two-sided and paired t tests were used to compare measurements. P values <.05 were considered to indicate statistical significance. RESULTS: Intraobserver agreement was excellent for dedicated aneurysmal neck volumetry, with mean differences of less than 1 mL (P > .05), whereas it was poor for transverse aortic neck diameter measurements (P < .05). However, interobserver variability was statistically significant for both neck volumetry (P < .005) and neck diameter measurements (P < .015). CONCLUSIONS: The reliability of dedicated AAA neck volumetry by using 64-row CTA is excellent for serial measurements by individual readers, but not between different readers. Therefore, studies should be performed with aortic neck volumetry by a single experienced reader.

Intra-subject variability in attention-deficit hyperactivity disorder

BACKGROUND: This study is based on a comprehensive survey of the neuropsychological attention-deficit hyperactivity disorder (ADHD) literature and presents the first psychometric analyses of different parameters of intra-subject variability (ISV) in patients with ADHD compared to healthy controls, using the Continuous Performance Test, a Go-NoGo task, a Stop Signal Task, as well as N-back tasks. METHODS: Data of 57 patients with ADHD and 53 age- and gender-matched controls were available for statistical analysis. Different parameters were used to describe central tendency (arithmetic mean, median), dispersion (standard deviation, coefficient of variation, consecutive variance), and shape (skewness, excess) of reaction time distributions, as well as errors (commissions and omissions). RESULTS: Group comparisons revealed by far the strongest effect sizes for measures of dispersion, followed by measures of central tendency, and by commission errors. Statistical control of ISV reduced group differences in the other measures substantially. One (patients) or two (controls) principal components explained up to 67% of the inter-individual differences in intra-individual variability. CONCLUSIONS: Results suggest that, across a variety of neuropsychological tests, measures of ISV contribute best to group discrimination, with limited incremental validity of measures of central tendency and errors. Furthermore, increased ISV might be a unitary construct in ADHD.

Cognitive functioning, behavior, and quality of life after stroke in childhood

Rationale: To provide a better understanding of cognitive functioning, motor outcome, behavior and quality of life after childhood stroke and to study the relationship between variables expected to influence rehabilitation and outcome (age at stroke, time elapsed since stroke, lateralization, location and size of lesion). Methods: Children who suffered from stroke between birth and their eighteenth year of life underwent an assessment consisting of cognitive tests (WISC-III, WAIS-R, K-ABC, TAP, Rey-Figure, German Version of the CVLT) and questionnaires (Conner's Scales, KIDSCREEN). Results: Twenty-one patients after stroke in childhood (15 males, mean 11;11 years, SD 4;3, range 6;10-21;2) participated in the study. Mean Intelligence Quotients (IQ) were situated within the normal range (mean Full Scale IQ 96.5, range IQ 79-129). However, significantly more patients showed deficits in various cognitive domains than expected from a healthy population (Performance IQ p = .000; Digit Span p = .000, Arithmetic's p = .007, Divided Attention p = .028, Alertness p = .002). Verbal IQ was significantly better than Performance IQ in 13 of 17 patients, independent of the hemispheric side of lesion. Symptoms of ADHD occurred more often in the patients' sample than in a healthy population (learning difficulties/inattention p = .000; impulsivity/hyperactivity p = .006; psychosomatics p = .006). Certain aspects of quality of life were reduced (autonomy p = .003; parents' relation p = .003; social acceptance p = .037). Three patients had a right-sided hemiparesis, mean values of motor functions of the other patients were slightly impaired (sequential finger movements p = .000, hand alternation p = .001, foot tapping p = .043). In patients without hemiparesis, there was no relation between the lateralization of lesion and motor outcome. Lesion that occurred in the midst of childhood (5-10 years) led to better cognitive outcome than lesion in the very early (0-5 years) or late childhood (10-18 years). Other variables such as presence of seizure, elapsed time since stroke and size of lesion had a small to no impact on prognosis. Conclusion: Moderate cognitive and motor deficits, behavioral problems, and impairment in some aspects of quality of life frequently remain after stroke in childhood. Visuospatial functions are more often reduced than verbal functions, independent of the hemispheric side of lesion. This indicates a functional superiority of verbal skills compared to visuospatial skills in the process of recovery after brain injury. Compared to the cognitive outcome following stroke in adults, cognitive sequelae after childhood stroke do indicate neither the lateralization nor the location of the lesion focus. Age at stroke seems to be the only determining factor influencing cognitive outcome.

Statistical analysis of personal radiofrequency electromagnetic field measurements with nondetects

Exposimeters are increasingly applied in bioelectromagnetic research to determine personal radiofrequency electromagnetic field (RF-EMF) exposure. The main advantages of exposimeter measurements are their convenient handling for study participants and the large amount of personal exposure data, which can be obtained for several RF-EMF sources. However, the large proportion of measurements below the detection limit is a challenge for data analysis. With the robust ROS (regression on order statistics) method, summary statistics can be calculated by fitting an assumed distribution to the observed data. We used a preliminary sample of 109 weekly exposimeter measurements from the QUALIFEX study to compare summary statistics computed by robust ROS with a naïve approach, where values below the detection limit were replaced by the value of the detection limit. For the total RF-EMF exposure, differences between the naïve approach and the robust ROS were moderate for the 90th percentile and the arithmetic mean. However, exposure contributions from minor RF-EMF sources were considerably overestimated with the naïve approach. This results in an underestimation of the exposure range in the population, which may bias the evaluation of potential exposure-response associations. We conclude from our analyses that summary statistics of exposimeter data calculated by robust ROS are more reliable and more informative than estimates based on a naïve approach. Nevertheless, estimates of source-specific medians or even lower percentiles depend on the assumed data distribution and should be considered with caution.

Coagulation activity before and after acute psychosocial stress increases with age

OBJECTIVE: To assess whether stress further increases hypercoagulation in older individuals. We investigated whether acute stress-induced changes in coagulation parameters differ with age. It is known that hypercoagulation occurs in response to acute stress and that a shift in hemostasis toward a hypercoagulability state occurs with age. However, it is not yet known whether acute stress further increases hypercoagulation in older individuals, and thus may increase their risk for cardiovascular disease (CVD). METHODS: A total of 63 medication-free nonsmoking men, aged between 20 and 65 years (mean +/- standard error of the mean = 36.7 +/- 1.7 years), underwent an acute standardized psychosocial stress task combining public speaking and mental arithmetic in front of an audience. We measured plasma clotting factor VII activity (FVII:C), fibrinogen, and D-dimer at rest, immediately, and 20 minutes after stress. RESULTS: Increased age predicted greater increases in fibrinogen (beta = 0.26, p = 0.041; DeltaR(2) = 0.05), FVII:C (beta = 0.40, p = .006; DeltaR(2) = 0.11), and D-dimer (beta = 0.51, p < .001; DeltaR(2) = 0.18) from rest to 20 minutes after stress independent of body mass index and mean arterial blood pressure. General linear models revealed significant effects of age and stress on fibrinogen, FVII:C, and D-dimer (main effects: p < .04), and greater D-dimer stress reactivity with older age (interaction age-by-stress: F(1.5/90.4) = 4.36, p = .024; f = 0.33). CONCLUSIONS: Our results suggest that acute stress might increase vulnerability in the elderly for hypercoagulability and subsequent hemostasis-associated diseases like CVD.