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”.

Genetic association study of QT interval highlights role for calcium signaling pathways in myocardial repolarization

The QT interval, an electrocardiographic measure reflecting myocardial repolarization, is a heritable trait. QT prolongation is a risk factor for ventricular arrhythmias and sudden cardiac death (SCD) and could indicate the presence of the potentially lethal mendelian long-QT syndrome (LQTS). Using a genome-wide association and replication study in up to 100,000 individuals, we identified 35 common variant loci associated with QT interval that collectively explain ∼8-10% of QT-interval variation and highlight the importance of calcium regulation in myocardial repolarization. Rare variant analysis of 6 new QT interval-associated loci in 298 unrelated probands with LQTS identified coding variants not found in controls but of uncertain causality and therefore requiring validation. Several newly identified loci encode proteins that physically interact with other recognized repolarization proteins. Our integration of common variant association, expression and orthogonal protein-protein interaction screens provides new insights into cardiac electrophysiology and identifies new candidate genes for ventricular arrhythmias, LQTS and SCD.

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.

In search of the internal structure of the processes underlying interval timing in the sub-second and the second range: A confirmatory factor analysis approach

One of the earliest accounts of duration perception by Karl von Vierordt implied a common process underlying the timing of intervals in the sub-second and the second range. To date, there are two major explanatory approaches for the timing of brief intervals: the Common Timing Hypothesis and the Distinct Timing Hypothesis. While the common timing hypothesis also proceeds from a unitary timing process, the distinct timing hypothesis suggests two dissociable, independent mechanisms for the timing of intervals in the sub-second and the second range, respectively. In the present paper, we introduce confirmatory factor analysis (CFA) to elucidate the internal structure of interval timing in the sub-second and the second range. Our results indicate that the assumption of two mechanisms underlying the processing of intervals in the second and the sub-second range might be more appropriate than the assumption of a unitary timing mechanism. In contrast to the basic assumption of the distinct timing hypothesis, however, these two timing mechanisms are closely associated with each other and share 77% of common variance. This finding suggests either a strong functional relationship between the two timing mechanisms or a hierarchically organized internal structure. Findings are discussed in the light of existing psychophysical and neurophysiological data.

The effects of type of interval, sensory modality, base duration, and psychophysical task on the discrimination of brief time intervals

The present study was designed to investigate the influences of type of psychophysical task (two-alternative forced-choice [2AFC] and reminder tasks), type of interval (filled vs. empty), sensory modality (auditory vs. visual), and base duration (ranging from 100 through 1,000 ms) on performance on duration discrimination. All of these factors were systematically varied in an experiment comprising 192 participants. This approach allowed for obtaining information not only on the general (main) effect of each factor alone, but also on the functional interplay and mutual interactions of some or all of these factors combined. Temporal sensitivity was markedly higher for auditory than for visual intervals, as well as for the reminder relative to the 2AFC task. With regard to base duration, discrimination performance deteriorated with decreasing base durations for intervals below 400 ms, whereas longer intervals were not affected. No indication emerged that overall performance on duration discrimination was influenced by the type of interval, and only two significant interactions were apparent: Base Duration × Type of Interval and Base Duration × Sensory Modality. With filled intervals, the deteriorating effect of base duration was limited to very brief base durations, not exceeding 100 ms, whereas with empty intervals, temporal discriminability was also affected for the 200-ms base duration. Similarly, the performance decrement observed with visual relative to auditory intervals increased with decreasing base durations. These findings suggest that type of task, sensory modality, and base duration represent largely independent sources of variance for performance on duration discrimination that can be accounted for by distinct nontemporal mechanisms.

Synthesis and incorporation into a-DNA of a novel conformationally constrained alpha-nucleoside analogue

We describe the synthesis and incorporation into alpha-DNA of a novel conformationally constrained alpha-nucleoside analogue. The carbohydrate part of this analogue was prepared in 4 steps from the known bicyclic precursor 1 via a stereospecific, intramolecular, Et 3B mediated radical addition to a keto-function as the key step. The thus obtained intermediate 4 was transformed stereoselectively into the corresponding alpha-nucleoside analogues 7 and 8 containing the bases adenine and thymine, and were further elaborated into the phosphoramidite building blocks 11 and 12 . Both building blocks were incorporated into alpha-oligodeoxynucleotides and their pairing behavior to parallel complementary DNA studied by UV-melting experiments. Single substitutions of alpha-deoxyribnucleoside units by the new analogues in the center of duplexes were found to be thermally destabilizing by only -0.8 to -3.1›C.

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).

The deglaciation history of the Simplon region (southern Swiss Alps) constrained by 10Be exposure dating of ice-molded bedrock surfaces

The deglaciation history of the Swiss Alps after the Last Glacial Maximum involved the decay of several ice domes and the subsequent disintegration of valley glaciers at high altitude. Here we use bedrock exposure dating to reconstruct the temporal and spatial pattern of ice retreat at the Simplon Pass (altitude: ∼2000 m) located 40 km southwest of the ‘Rhône ice dome’. Eleven 10Be exposure ages from glacially polished quartz veins and ice-molded bedrock surfaces cluster tightly between 13.5 ± 0.6 ka and 15.4 ± 0.6 ka (internal errors) indicating that the Simplon Pass depression became ice-free at 14.1 ± 0.4 ka (external error of mean age). This age constraint is interpreted to record the melting of the high valley glaciers in the Simplon Pass region during the warm Bølling–Allerød interstadial shortly after the Oldest Dryas stadial. Two bedrock samples collected a few hundred meters above the pass depression yield older 10Be ages of 17.8 ± 0.6 ka and 18.0 ± 0.6 ka. These ages likely reflect the initial downwasting of the Rhône ice dome and the termination of the ice transfluence from the ice dome across the Simplon Pass toward the southern foreland. There, the retreat of the piedmont glacier in Val d’Ossola was roughly synchronous with the decay of the Rhône ice dome in the interior of the mountain belt, as shown by 10Be ages of 17.7 ± 0.9 ka and 16.1 ± 0.6 ka for a whaleback at ∼500 m elevation near Montecrestese in northern Italy. In combination with well-dated paleoclimate records derived from lake sediments, our new age data suggest that during the deglaciation of the European Alps the decay of ice domes was approximately synchronous with the retreat of piedmont glaciers in the foreland and was followed by the melting of high-altitude valley glaciers after the transition from the Oldest Dryas to the Bølling–Allerød, when mean annual temperatures rose rapidly by ∼3 °C.

Resource-Constrained Project Scheduling with Project Management Information Systems

Most commercial project management software packages include planning methods to devise schedules for resource-constrained projects. As it is proprietary information of the software vendors which planning methods are implemented, the question arises how the software packages differ in quality with respect to their resource-allocation capabilities. We experimentally evaluate the resource-allocation capabilities of eight recent software packages by using 1,560 instances with 30, 60, and 120 activities of the well-known PSPLIB library. In some of the analyzed packages, the user may influence the resource allocation by means of multi-level priority rules, whereas in other packages, only few options can be chosen. We study the impact of various complexity parameters and priority rules on the project duration obtained by the software packages. The results indicate that the resource-allocation capabilities of these packages differ significantly. In general, the relative gap between the packages gets larger with increasing resource scarcity and with increasing number of activities. Moreover, the selection of the priority rule has a considerable impact on the project duration. Surprisingly, when selecting a priority rule in the packages where it is possible, both the mean and the variance of the project duration are in general worse than for the packages which do not offer the selection of a priority rule.