Semi-supervised Deep Learning with Memory

© 2018, Springer Nature Switzerland AG. We consider the semi-supervised multi-class classification problem of learning from sparse labelled and abundant unlabelled training data. To address this problem, existing semi-supervised deep learning methods often rely on the up-to-date “network-in-training” to formulate the semi-supervised learning objective. This ignores both the discriminative feature representation and the model inference uncertainty revealed by the network in the preceding learning iterations, referred to as the memory of model learning. In this work, we propose a novel Memory-Assisted Deep Neural Network (MA-DNN) capable of exploiting the memory of model learning to enable semi-supervised learning. Specifically, we introduce a memory mechanism into the network training process as an assimilation-accommodation interaction between the network and an external memory module. Experiments demonstrate the advantages of the proposed MA-DNN model over the state-of-the-art semi-supervised deep learning methods on three image classification benchmark datasets: SVHN, CIFAR10, and CIFAR100

Intuitive and Informal Knowledge in Preschoolers’ Development of Probabilistic Thinking

Preschoolers develop a wide range of mathematical informal knowledge and intuitive thinking before they enter formal, goal-oriented education. In their everyday activities young children get engaged with situations that enhance them to develop skills, concepts, strategies, representations, attitudes, constructs and operations concerning a wide range of mathematical notions. Recently there is scientific interest in linking children’s informal and formal knowledge in order to provide them with opportunities to avoid biases aiming at formulating, perceiving, reflecting on and exercising probabilistic notions. The current study investigates preschoolers’ (N=90) intuitive understanding of the likelihood of events in a probabilistic task with spinners. Participants, at the age of 4 to 6, are tested on their predictions of the most probable outcome prior to and after an instructive session of reasoning. The probabilistic task, based on constructivist principles, includes methodological alterations concerning the sample space and the themes of the stimuli. Educational implications are further discussed under the general point of view that in order to link informal to formal mathematical learning in preschool classroom, the subject content and the cognitive capacity of children are important to match

ALMA Uncovers Highly Filamentary Structure toward the Sgr E Region

We report on the discovery of linear filaments observed in the CO(1-0) emission for a ∼2′ field of view toward the Sgr E star-forming region, centered at (l, b) = (358.°720, 0.°011). The Sgr E region is thought to be at the turbulent intersection of the “far dust lane” associated with the Galactic bar and the Central Molecular Zone (CMZ). This region is subject to strong accelerations, which are generally thought to inhibit star formation, yet Sgr E contains a large number of H ii regions. We present 12CO(1-0), 13CO(1-0), and C18O(1-0) spectral line observations from the Atacama Large Millimeter/submillimeter Array and provide measurements of the physical and kinematic properties for two of the brightest filaments. These filaments have widths (FWHMs) of ∼0.1 pc and are oriented nearly parallel to the Galactic plane, with angles from the Galactic plane of ∼2°. The filaments are elongated, with lower-limit aspect ratios of ∼5:1. For both filaments, we detect two distinct velocity components that are separated by about 15 km s−1. In the C18O spectral line data, with ∼0.09 pc spatial resolution, we find that these velocity components have relatively narrow (∼1-2 km s−1) FWHM line widths when compared to other sources toward the Galactic center. The properties of these filaments suggest that the gas in the Sgr E complex is being “stretched,” as it is rapidly accelerated by the gravitational field of the Galactic bar while falling toward the CMZ, a result that could provide insights into the extreme environment surrounding this region and the large-scale processes that fuel this environment

CMZoom: Survey Overview and First Data Release

We present an overview of the CMZoom survey and its first data release. CMZoom is the first blind, high-resolution survey of the Central Molecular Zone (CMZ; the inner 500 pc of the Milky Way) at wavelengths sensitive to the pre-cursors of high-mass stars. CMZoom is a 500-hour Large Program on the Submillimeter Array (SMA) that mapped at 1.3 mm all of the gas and dust in the CMZ above a molecular hydrogen column density of 10^23 cm^-2 at a resolution of ~3" (0.1 pc). In this paper, we focus on the 1.3 mm dust continuum and its data release, but also describe CMZoom spectral line data which will be released in a forthcoming publication. While CMZoom detected many regions with rich and complex substructure, its key result is an overall deficit in compact substructures on 0.1 - 2 pc scales (the compact dense gas fraction: CDGF). In comparison with clouds in the Galactic disk, the CDGF in the CMZ is substantially lower, despite having much higher average column densities. CMZ clouds with high CDGFs are well-known sites of active star formation. The inability of most gas in the CMZ to form compact substructures is likely responsible for the dearth of star formation in the CMZ, surprising considering its high density. The factors responsible for the low CDGF are not yet understood but are plausibly due to the extreme environment of the CMZ, having far-reaching ramifications for our understanding of the star formation process across the cosmos

Early Geometrical Thinking in the Environment of Patterns, Mosaics and Isometries

This book discusses the learning and teaching of geometry, with a special focus on kindergarten and primary education. It examines important new trends and developments in research and practice, and emphasizes theoretical, empirical and developmental issues. Further, it discusses various topics, including curriculum studies and implementation, spatial abilities and geometric reasoning, as well as the psychological roots of geometrical thinking and teacher preparation in geometry education. It considers these issues from historical, epistemological, cognitive semiotic and educational points of view in the context of students' difficulties and the design of teaching and curricula

Angular and Current-Target Correlations in Deep Inelastic Scattering at HERA

Correlations between charged particles in deep inelastic ep scattering have been studied in the Breit frame with the ZEUS detector at HERA using an integrated luminosity of 6.4 pb-1. Short-range correlations are analysed in terms of the angular separation between current-region particles within a cone centred around the virtual photon axis. Long-range correlations between the current and target regions have also been measured. The data support predictions for the scaling behaviour of the angular correlations at high Q2 and for anti-correlations between the current and target regions over a large range in Q2 and in the Bjorken scaling variable x. Analytic QCD calculations and Monte Carlo models correctly describe the trends of the data at high Q2, but show quantitative discrepancies. The data show differences between the correlations in deep inelastic scattering and e+e- annihilation.Comment: 26 pages including 10 figures (submitted to Eur. J. Phys. C

Measurement of the Bottom-Strange Meson Mixing Phase in the Full CDF Data Set

We report a measurement of the bottom-strange meson mixing phase \beta_s using the time evolution of B0_s -> J/\psi (->\mu+\mu-) \phi (-> K+ K-) decays in which the quark-flavor content of the bottom-strange meson is identified at production. This measurement uses the full data set of proton-antiproton collisions at sqrt(s)= 1.96 TeV collected by the Collider Detector experiment at the Fermilab Tevatron, corresponding to 9.6 fb-1 of integrated luminosity. We report confidence regions in the two-dimensional space of \beta_s and the B0_s decay-width difference \Delta\Gamma_s, and measure \beta_s in [-\pi/2, -1.51] U [-0.06, 0.30] U [1.26, \pi/2] at the 68% confidence level, in agreement with the standard model expectation. Assuming the standard model value of \beta_s, we also determine \Delta\Gamma_s = 0.068 +- 0.026 (stat) +- 0.009 (syst) ps-1 and the mean B0_s lifetime, \tau_s = 1.528 +- 0.019 (stat) +- 0.009 (syst) ps, which are consistent and competitive with determinations by other experiments.Comment: 8 pages, 2 figures, Phys. Rev. Lett 109, 171802 (2012

CMZoom IV. Incipient High-Mass Star Formation Throughout the Central Molecular Zone

In this work, we constrain the star-forming properties of all possible sites of incipient high-mass star formation in the Milky Way's Galactic Center. We identify dense structures using the CMZoom 1.3mm dust continuum catalog of objects with typical radii of ~0.1pc, and measure their association with tracers of high-mass star formation. We incorporate compact emission at 8, 21, 24, 25, and 70um from MSX, Spitzer, Herschel, and SOFIA, catalogued young stellar objects, and water and methanol masers to characterize each source. We find an incipient star formation rate (SFR) for the CMZ of ~0.08 M⊙ yr^{-1} over the next few 10^5 yr. We calculate upper and lower limits on the CMZ's incipient SFR of ~0.45 M⊙ yr^{-1} and ~0.05 M⊙ yr^{-1} respectively, spanning between roughly equal to and several times greater than other estimates of CMZ's recent SFR. Despite substantial uncertainties, our results suggest the incipient SFR in the CMZ may be higher than previously estimated. We find that the prevalence of star formation tracers does not correlate with source volume density, but instead ~>75% of high-mass star formation is found in regions above a column density ratio (NSMA/NHerschel) of ~1.5. Finally, we highlight the detection of ``atoll sources'', a reoccurring morphology of cold dust encircling evolved infrared sources, possibly representing HII regions in the process of destroying their envelopes

CMZoom II: Catalog of Compact Submillimeter Dust Continuum Sources in the Milky Way's Central Molecular Zone

In this paper we present the CMZoom Survey's catalog of compact sources (< 10'', ~0.4pc) within the Central Molecular Zone (CMZ). CMZoom is a Submillimeter Array (SMA) large program designed to provide a complete and unbiased map of all high column density gas (N(H$_2$) $\geq$ 10$^{23}$ cm$^{-2}$) of the innermost 500pc of the Galaxy in the 1.3mm dust continuum. We generate both a robust catalog designed to reduce spurious source detections, and a second catalog with higher completeness, both generated using a pruned dendrogram. In the robust catalog, we report 285 compact sources, or 816 in the high completeness catalog. These sources have effective radii between 0.04-0.4 pc, and are the potential progenitors of star clusters. The masses for both catalogs are dominated by the Sagittarius B2 cloud complex, where masses are likely unreliable due to free-free contamination, uncertain dust temperatures, and line-of-sight confusion. Given the survey selection and completeness, we predict that our robust catalog accounts for more than ~99% of compact substructure capable of forming high mass stars in the CMZ. This catalog provides a crucial foundation for future studies of high mass star formation in the Milky Way's Galactic Center

Preschoolers' Precision of the Approximate Number System Predicts Later School Mathematics Performance

The Approximate Number System (ANS) is a primitive mental system of nonverbal representations that supports an intuitive sense of number in human adults, children, infants, and other animal species. The numerical approximations produced by the ANS are characteristically imprecise and, in humans, this precision gradually improves from infancy to adulthood. Throughout development, wide ranging individual differences in ANS precision are evident within age groups. These individual differences have been linked to formal mathematics outcomes, based on concurrent, retrospective, or short-term longitudinal correlations observed during the school age years. However, it remains unknown whether this approximate number sense actually serves as a foundation for these school mathematics abilities. Here we show that ANS precision measured at preschool, prior to formal instruction in mathematics, selectively predicts performance on school mathematics at 6 years of age. In contrast, ANS precision does not predict non-numerical cognitive abilities. To our knowledge, these results provide the first evidence for early ANS precision, measured before the onset of formal education, predicting later mathematical abilities