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.

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).

Left, right and interval bivariate censored data: Evaluating screening mammography in the presence of lead -time bias, length bias and over-detection

Of the large clinical trials evaluating screening mammography efficacy, none included women ages 75 and older. Recommendations on an upper age limit at which to discontinue screening are based on indirect evidence and are not consistent. Screening mammography is evaluated using observational data from the SEER-Medicare linked database. Measuring the benefit of screening mammography is difficult due to the impact of lead-time bias, length bias and over-detection. The underlying conceptual model divides the disease into two stages: pre-clinical (T0) and symptomatic (T1) breast cancer. Treating the time in these phases as a pair of dependent bivariate observations, (t0,t1), estimates are derived to describe the distribution of this random vector. To quantify the effect of screening mammography, statistical inference is made about the mammography parameters that correspond to the marginal distribution of the symptomatic phase duration (T1). This shows the hazard ratio of death from breast cancer comparing women with screen-detected tumors to those detected at their symptom onset is 0.36 (0.30, 0.42), indicating a benefit among the screen-detected cases. ^

Analysis of interval -censored events in hypertension studies: Evaluation of treatment of coronary heart disease

Many statistical studies feature data with both exact-time and interval-censored events. While a number of methods currently exist to handle interval-censored events and multivariate exact-time events separately, few techniques exist to deal with their combination. This thesis develops a theoretical framework for analyzing a multivariate endpoint comprised of a single interval-censored event plus an arbitrary number of exact-time events. The approach fuses the exact-time events, modeled using the marginal method of Wei, Lin, and Weissfeld, with a piecewise-exponential interval-censored component. The resulting model incorporates more of the information in the data and also removes some of the biases associated with the exclusion of interval-censored events. A simulation study demonstrates that our approach produces reliable estimates for the model parameters and their variance-covariance matrix. As a real-world data example, we apply this technique to the Systolic Hypertension in the Elderly Program (SHEP) clinical trial, which features three correlated events: clinical non-fatal myocardial infarction, fatal myocardial infarction (two exact-time events), and silent myocardial infarction (one interval-censored event). ^

Dinoflagellate cyst assemblages, oxygen isotope records of foraminifera, and alkenone and Mg/Ca-based SST estimates for the time interval 3.40-3.18 Ma (Late Pliocene) from five North Atlantic and Caribbean sediment cores

The early Late Pliocene (3.6 to ~3.0 million years ago) is the last extended interval in Earth's history when atmospheric CO2 concentrations were comparable to today's and global climate was warmer. Yet a severe global glaciation during marine isotope stage (MIS) M2 interrupted this phase of global warmth ~3.30 million years ago, and is seen as a premature attempt of the climate system to establish an ice-age world. Our geochemical and palynological records from five marine sediment cores along a Caribbean to eastern North Atlantic transect show that increased Pacific-to-Atlantic flow via the Central American Seaway weakened the North Atlantic Current (NAC) and attendant northward heat transport prior to MIS M2. The consequent cooling of the northern high latitude oceans permitted expansion of the Greenland ice sheet during MIS M2, despite near-modern atmospheric CO2 concentrations. Before and after MIS M2, heat transport via the NAC was crucial in maintaining warm climates comparable to those predicted for the end of this century.