More on the universal equation for Efimov states

Efimov states are a sequence of shallow three-body bound states that arise when the two-body scattering length is much larger than the range of the interaction. The binding energies of these states are described as a function of the scattering length and one three-body parameter by a transcendental equation involving a universal function of one angular variable. We provide an accurate and convenient parametrization of this function. Moreover, we discuss the effective treatment of range corrections in the universal equation and compare with a strictly perturbative scheme.Comment: 13 pages, 5 figure

Up or down? Reading direction influences vertical counting direction in the horizontal plane - a cross-cultural comparison

Most adults and children in cultures where reading text progresses from left to right also count objects from the left to the right side of space. The reverse is found in cultures with a right-to-left reading direction. The current set of experiments investigated whether vertical counting in the horizontal plane is also influenced by reading direction. Participants were either from a left-to-right reading culture (UK) or from a mixed (left-to-right and top-to-bottom) reading culture (Hong Kong). In Experiment 1, native English-speaking children and adults and native Cantonese-speaking children and adults performed three object counting tasks. Objects were presented flat on a table in a horizontal, vertical, and square display. Independent of culture, the horizontal array was mostly counted from left to right. While the majority of English-speaking children counted the vertical display from bottom to top, the majority of the Cantonese-speaking children as well as both Cantonese- and English-speaking adults counted the vertical display from top to bottom. This pattern was replicated in the counting pattern for squares: all groups except the English-speaking children started counting with the top left coin. In Experiment 2, Cantonese-speaking adults counted a square array of objects after they read a text presented to them either in left-to-right or in top-to-bottom reading direction. Most Cantonese-speaking adults started counting the array by moving horizontally from left to right. However, significantly more Cantonese-speaking adults started counting with a top-to-bottom movement after reading the text presented in a top-to-bottom reading direction than in a left-to-right reading direction. Our results show clearly that vertical counting in the horizontal plane is influenced by longstanding as well as more recent experience of reading direction

Constrained firms, not subsistence activities : Evidence on capital returns and accumulation in Peruvian microenterprises.

We present a multi-period model of capital accumulation in order to investigate microenterprise (ME) production dynamics in a developing country context characterized by credit constraints and risk. These constraints are reflected in marginal returns to capital above market interest rates and we show that capital accumulation is faster in MEs with higher productivity, higher initial wealth and less risk exposure. We test our predictions using panel data for Peruvian MEs from 2002 to 2006. We indeed find high marginal returns to capital and sizable effects of household non-business wealth and, in contrast to previous studies, risk on capital accumulation in MEs. The findings of this paper can serve as a basis for the promotion of combined credit and risk management devices to enhance private sector development

Representation of visual scenes by local neuronal populations in layer 2/3 of mouse visual cortex

How are visual scenes encoded in local neural networks of visual cortex? In rodents, visual cortex lacks a columnar organization so that processing of diverse features from a spot in visual space could be performed locally by populations of neighboring neurons. To examine how complex visual scenes are represented by local microcircuits in mouse visual cortex we measured visually evoked responses of layer 2/3 neuronal populations using 3D two-photon calcium imaging. Both natural and artificial movie scenes (10 seconds duration) evoked distributed and sparsely organized responses in local populations of 70–150 neurons within the sampled volumes. About 50% of neurons showed calcium transients during visual scene presentation, of which about half displayed reliable temporal activation patterns. The majority of the reliably responding neurons were activated primarily by one of the four visual scenes applied. Consequently, single-neurons performed poorly in decoding, which visual scene had been presented. In contrast, high levels of decoding performance (>80%) were reached when considering population responses, requiring about 80 randomly picked cells or 20 reliable responders. Furthermore, reliable responding neurons tended to have neighbors sharing the same stimulus preference. Because of this local redundancy, it was beneficial for efficient scene decoding to read out activity from spatially distributed rather than locally clustered neurons. Our results suggest a population code in layer 2/3 of visual cortex, where the visual environment is dynamically represented in the activation of distinct functional sub-networks

Automatic number priming effects in adults with and without mathematical learning disabilities

This study examined automatic number processing in adults with mathematical learning disabilities (MLDs). The performance of adults with MLD during an automatic symbolic and non-symbolic priming task was compared to gender-, age-, and IQ-matched controls. No difference in the priming distance effect was found between the adults with and without MLD, suggesting that adults with MLD have an intact magnitude representation. Moreover, the adults with MLD did not have problems in processing the numerical symbols 1-9, suggesting that this basic deficit which is experienced by children with MLD is resolved by adulthood

Constrained firms, not subsistence activities: evidence on capital returns and accumulation in Peruvian microenterprises

We investigate the returns to capital and capital accumulation using panel data of Peruvian micro enterprises (MEs). Marginal returns to capital are found to be very high at low levels of capital, but rapidly decreasing at higher levels. The dynamic analyses of capital accumulation in MEs suggest that credit constraints explain a major part of the variation in firm growth. We find a very large positive effect of household non-business wealth on capital stocks of MEs. We also show a sizable effect of risk on accumulation and pronounced interactions between wealth and risk. The presented evidence is consistent with poorly endowed entrepreneurs who operate in imperfect capital markets and a very risky environment

Packing Returning Secretaries

We study online secretary problems with returns in combinatorial packing domains with $n$ candidates that arrive sequentially over time in random order. The goal is to accept a feasible packing of candidates of maximum total value. In the first variant, each candidate arrives exactly twice. All $2n$ arrivals occur in random order. We propose a simple 0.5-competitive algorithm that can be combined with arbitrary approximation algorithms for the packing domain, even when the total value of candidates is a subadditive function. For bipartite matching, we obtain an algorithm with competitive ratio at least $0.5721 - o(1)$ for growing $n$, and an algorithm with ratio at least $0.5459$ for all $n \ge 1$. We extend all algorithms and ratios to $k \ge 2$ arrivals per candidate. In the second variant, there is a pool of undecided candidates. In each round, a random candidate from the pool arrives. Upon arrival a candidate can be either decided (accept/reject) or postponed (returned into the pool). We mainly focus on minimizing the expected number of postponements when computing an optimal solution. An expected number of $\Theta(n \log n)$ is always sufficient. For matroids, we show that the expected number can be reduced to $O(r \log (n/r))$, where $r \le n/2$ is the minimum of the ranks of matroid and dual matroid. For bipartite matching, we show a bound of $O(r \log n)$, where $r$ is the size of the optimum matching. For general packing, we show a lower bound of $\Omega(n \log \log n)$, even when the size of the optimum is $r = \Theta(\log n)$.Comment: 23 pages, 5 figure

Direct evidence for linguistic influences in two-digit number processing

Language-specific differences in number words influence number processing even in non-verbal numerical tasks. For instance, the unit-decade compatibility effect in two-digit number magnitude comparison (compatible number pairs [42_57: 42]) was shown to be influenced by the inversion of number words (e.g., in German the number word for 42 is zweiundvierzig [literally: two-and-forty]). In two studies, we used articulatory suppression to investigate whether previously observed cross-linguistic differences in two-digit number processing are indeed driven by differences in number word formation. In a two-digit number comparison task, German- and English-speaking participants had to identify the larger of two numbers presented in Arabic digits. In Study 1, participants performed the same task twice, with and without articulatory suppression. In Study 2, the percentage of within-decade filler items (36_39) was manipulated additionally. As expected, in both studies between-group differences in the compatibility effect disappeared under articulatory suppression irrespective of the percentage of fillers included. Furthermore, paralleling results of previous studies including 33% or less filler items, we found that the compatibility effect was larger in German compared to English speakers in the 20% filler condition. However, this pattern was reversed in the 50% filler condition in both studies. Thus, results provide first direct evidence for influences of verbal number word formation on symbolic number processing. Moreover, these new findings suggest that linguistic influences and those of cognitive control processes associated with characteristics of the stimulus set interact in symbolic number processing