On factorially balanced sets of words

AbstractA set of words is factorially balanced if the set of all the factors of its words is balanced. We prove that if all words of a factorially balanced set have a finite index, then this set is a subset of the set of factors of a Sturmian word. Moreover, characterizing the set of factors of a given length n of a Sturmian word by the left special factor of length n−1 of this Sturmian word, we provide an enumeration formula for the number of sets of words that correspond to some set of factors of length n of a Sturmian word

Borel Summation of the Derivative Expansion and Effective Actions

We give an explicit demonstration that the derivative expansion of the QED effective action is a divergent but Borel summable asymptotic series, for a particular inhomogeneous background magnetic field. A duality transformation B\to iE gives a non-Borel-summable perturbative series for a time dependent background electric field, and Borel dispersion relations yield the non-perturbative imaginary part of the effective action, which determines the pair production probability. Resummations of leading Borel approximations exponentiate to give perturbative corrections to the exponents in the non-perturbative pair production rates. Comparison with a WKB analysis suggests that these divergence properties are general features of derivative expansions and effective actions.Comment: 18 pp, Revtex, 2 fig

AGL StimSelect: Software for automated selection of stimuli for artificial grammar learning

Artificial Grammar Learning (AGL) is an experimental paradigm that has been used extensively in cognitive research for many years to study implicit learning, associative learning, and generalization based either on similarity or rules. Without computer assistance it is virtually impossible to generate appropriate grammatical training stimuli along with grammatical or non-grammatical test stimuli that control relevant psychological variables. We present the first flexible, fully automated software for selecting AGL stimuli. The software allows users to specify a grammar of interest, and to manipulate characteristics of training and test sequences, and their relationship to each other. The user thus has direct control over stimulus features that may influence learning and generalization in AGL tasks. The software enables researchers to develop AGL designs that would not be feasible without automatic stimulus selection. It is implemented in Matlab

Three-dimensional simplicial gravity and combinatorics of group presentations

We demonstrate how some problems arising in simplicial quantum gravity can be successfully addressed within the framework of combinatorial group theory. In particular, we argue that the number of simplicial 3-manifolds having a fixed homology type grows exponentially with the number of tetrahedra they are made of. We propose a model of 3D gravity interacting with scalar fermions, some restriction of which gives the 2-dimensional self-avoiding-loop-gas matrix model. We propose a qualitative picture of the phase structure of 3D simplicial gravity compatible with the numerical experiments and available analytical results.Comment: 24 page

Saccade launch site as a predictor of fixation durations in reading: Comments on Hand, Miellet, O’Donnell, and Sereno (2010).

An important question in research on eye movements in reading is whether word frequency and word predictability have additive or interactive effects on fixation durations. A fair number of studies have reported only additive effects of the frequency and predictability of a target word on reading times on that word, failing to show significant interactions. Recently, however, Hand, Miellet, O'Donnell, and Sereno (see record 2010-19099-001) reported interactive effects in a study that included the distance of the prior fixation from the target word (launch site). They reported that when the saccade into the target word was launched from very near to the word (within 3 characters), the predictability effect was larger for low frequency words, but when the saccade was launched from a medium distance (4-6 characters from the word) the predictability effect was larger for high frequency words. Hand et al. argued for the importance of including launch site in analyses of target word fixation durations. Here we describe several problems with Hand et al.'s use of analyses of variance in which launch site is divided into distinct ordinal levels. We describe a more appropriate way to analyze such data-linear mixed-effect models-and we use this method to show that launch site does not modulate the interaction between frequency and predictability in two other data sets

Evolution from few- to many-body physics in one-dimensional Fermi systems: One- and two-body density matrices, and particle-partition entanglement

We study the evolution from few- to many-body physics of fermionic systems in one spatial dimension with attractive pairwise interactions. We determine the detailed form of the momentum distribution, the structure of the one-body density matrix, and the pairing properties encoded in the two-body density matrix. From the low- and high-momentum scaling behavior of the single-particle momentum distribution we estimate the speed of sound and Tan's contact, respectively. Both quantities are found to be in agreement with previous calculations. Based on our calculations of the one-body density matrices, we also present results for the particle-partition entanglement entropy, for which we find a logarithmic dependence on the total particle number.Comment: 14 pages, 9 figures, published versio