Forcing for hat inductive definitions in arithmetic

By forcing, we give a direct interpretation of inline image into Avigad's inline image. To the best of the author's knowledge, this is one of the simplest applications of forcing to “real problems”.

Spatial biases during mental arithmetic: evidence from eye movements on a blank screen

While the influence of spatial-numerical associations in number categorization tasks has been well established, their role in mental arithmetic is less clear. It has been hypothesized that mental addition leads to rightward and upward shifts of spatial attention (along the “mental number line”), whereas subtraction leads to leftward and downward shifts. We addressed this hypothesis by analyzing spontaneous eye movements during mental arithmetic. Participants solved verbally presented arithmetic problems (e.g., 2 + 7, 8–3) aloud while looking at a blank screen. We found that eye movements reflected spatial biases in the ongoing mental operation: Gaze position shifted more upward when participants solved addition compared to subtraction problems, and the horizontal gaze position was partly determined by the magnitude of the operands. Interestingly, the difference between addition and subtraction trials was driven by the operator (plus vs. minus) but was not influenced by the computational process. Thus, our results do not support the idea of a mental movement toward the solution during arithmetic but indicate a semantic association between operation and space.

Unfolding Feasible Arithmetic and Weak Truth

In this paper we continue Feferman’s unfolding program initiated in (Feferman, vol. 6 of Lecture Notes in Logic, 1996) which uses the concept of the unfolding U(S) of a schematic system S in order to describe those operations, predicates and principles concerning them, which are implicit in the acceptance of S. The program has been carried through for a schematic system of non-finitist arithmetic NFA in Feferman and Strahm (Ann Pure Appl Log, 104(1–3):75–96, 2000) and for a system FA (with and without Bar rule) in Feferman and Strahm (Rev Symb Log, 3(4):665–689, 2010). The present contribution elucidates the concept of unfolding for a basic schematic system FEA of feasible arithmetic. Apart from the operational unfolding U0(FEA) of FEA, we study two full unfolding notions, namely the predicate unfolding U(FEA) and a more general truth unfolding UT(FEA) of FEA, the latter making use of a truth predicate added to the language of the operational unfolding. The main results obtained are that the provably convergent functions on binary words for all three unfolding systems are precisely those being computable in polynomial time. The upper bound computations make essential use of a specific theory of truth TPT over combinatory logic, which has recently been introduced in Eberhard and Strahm (Bull Symb Log, 18(3):474–475, 2012) and Eberhard (A feasible theory of truth over combinatory logic, 2014) and whose involved proof-theoretic analysis is due to Eberhard (A feasible theory of truth over combinatory logic, 2014). The results of this paper were first announced in (Eberhard and Strahm, Bull Symb Log 18(3):474–475, 2012).

Effects of exposure to physical factors on homeopathic preparations as determined by ultraviolet light spectroscopy

Clinical trials have reported statistically significant and clinically relevant effects of homeopathic preparations. We applied ultraviolet (UV) spectroscopy to investigate the physical properties of homeopathic preparations and to contribute to an understanding of the not-yet-identified mode of action. In previous investigations, homeopathic preparations had significantly lower UV light transmissions than controls. The aim of this study was to explore the possible effects of external factors (UV light and temperature) on the homeopathic preparations. Homeopathic centesimal (c) dilutions, 1c to 30c, of copper sulfate (CuSO(4)), decimal dilutions of sulfur (S(8)), 1x to 30x, and controls (succussed potentization medium) were prepared, randomized, and blinded. UV transmission was measured at six different time points after preparation (from 4 to 256 days). In addition, one series of samples was exposed to UV light of a sterilization lamp for 12 h, one was incubated at 37 degrees Celsius for 24 h, and one was heated to 90 degrees Celsius for 15 min. UV light transmission values from 190 or 220 nm to 340 nm were measured several times and averaged. After each exposure, UV transmission of the homeopathic preparations of CuSO(4) was significantly reduced compared to the controls, particularly after heating to 37 degrees Celsius. Overall, the nonexposed CuSO(4) preparations did not show significantly lower UV transmission compared to controls; however, the pooled subgroup of measurements at days 26, 33, and 110 yielded significant differences. UV light transmission for S(8) preparations did not show any differences compared to controls. Our conclusion is that exposure to external factors, incubation at 37 degrees Celsius in particular, increases the difference in light transmission of homeopathic CuSO(4) preparations compared to controls.

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.

Homeopathic Preparations of Quartz, Sulfur and Copper Sulfate Assessed by UV-Spectroscopy

Homeopathic preparations are used in homeopathy and anthroposophic medicine. Although there is evidence of effectiveness in several clinical studies, including double-blinded randomized controlled trials, their nature and mode of action could not be explained with current scientific approaches yet. Several physical methods have already been applied to investigate homeopathic preparations but it is yet unclear which methods are best suited to identify characteristic physicochemical properties of homeopathic preparations. The aim of this study was to investigate homeopathic preparations with UV-spectroscopy. In a blinded, randomized, controlled experiment homeopathic preparations of copper sulfate (CuSO(4); 11c-30c), quartz (SiO(2); 10c-30c, i.e., centesimal dilution steps) and sulfur (S; 11×-30×, i.e., decimal dilution steps) and controls (one-time succussed diluent) were investigated using UV-spectroscopy and tested for contamination by inductively coupled plasma mass spectrometry (ICP-MS). The UV transmission for homeopathic preparations of CuSO(4) preparations was significantly lower than in controls. The transmission seemed to be also lower for both SiO(2) and S, but not significant. The mean effect size (95% confidence interval) was similar for the homeopathic preparations: CuSO(4) (pooled data) 0.0544% (0.0260-0.0827%), SiO(2) 0.0323% (-0.0064% to 0.0710%) and S 0.0281% (-0.0520% to 0.1082%). UV transmission values of homeopathic preparations had a significantly higher variability compared to controls. In none of the samples the concentration of any element analyzed by ICP-MS exceeded 100 ppb. Lower transmission of UV light may indicate that homeopathic preparations are less structured or more dynamic than their succussed pure solvent.

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.