Fraction magnitude understanding and its unique role in predicting general mathematics achievement at two early stages of fraction instruction

Background Prior studies on fraction magnitude understanding focused mainly on students with relatively sufficient formal instruction on fractions whose fraction magnitude understanding is relatively mature. Aim This study fills a research gap by investigating fraction magnitude understanding in the early stages of fraction instruction. It extends previous findings to children with limited and primary formal fraction instruction. Sample(s) Thirty‐five fourth graders with limited fraction instruction and forty fourth graders with primary fraction instruction were recruited from a Chinese primary school. Methods Children's fraction magnitude understanding was assessed with a fraction number line estimation task. Approximate number system (ANS) acuity was assessed with a dot discrimination task. Whole number knowledge was assessed with a whole number line estimation task. General reading and mathematics achievements were collected concurrently and 1 year later. Results In children with limited fraction instruction, fraction representation was linear and fraction magnitude understanding was concurrently related to both ANS and whole number knowledge. In children with primary fraction instruction, fraction magnitude understanding appeared to (marginally) significantly predict general mathematics achievement 1 year later. Conclusions Fraction magnitude understanding emerged early during formal instruction of fractions. ANS and whole number knowledge were related to fraction magnitude understanding when children first began to learn about fractions in school. The predictive value of fraction magnitude understanding is likely constrained by its sophistication level

Essays on housing economics and real estate finance

This dissertation contains three chapters on topics in the field of housing economics and real estate finance. This first chapter examines the impact of mortgage credit supply contraction on the supply and pricing of rental housing in the wake of the 2008-2009 financial crisis. We provide estimates of (1) the size of mortgage credit supply shocks at the county-level across the United States; (2) the impact of mortgage credit supply shock on housing rents and housing supply. To estimate the size of the credit supply shock, we use non-parametric methods to identify lender specific supply-side shocks; we then use a shift-share approach to aggregate a measure of credit supply shock at county level. Using the county-level credit supply shock as instruments for changes in mortgage denial rates, we reveal that housing rents respond positively to the contraction of the mortgage supply. The impact on housing rents is heterogeneous among different income groups. Moreover, we also document that the contraction of the mortgage supply resulted in a decline in home sales, and increased the share of renter-occupied units. Moreover, households in the lowest income groups are most affected. The finding suggests that recent regulatory changes in mortgage lending may have unintended consequences, leading to reduced home ownership and increased rental housing prices for the lowest income households. The second chapter provides a comprehensive investigations into the heterogeneity of home improvement and maintenance activities that has not been well explored by literature. Using American Housing Survey data on home improvement and maintenance expenditure, we obtain the following empirical evidence: First, speculating buyers spend significantly higher amount on home improvement compared with non-speculating buyers, and are more likely to perform major improvement. Second, households spend significantly more following the home purchase rather than prior to resale. This could be attributed to search friction that prevent households from matching to the perfect home. Third, the spending of home improvement and maintenance exhibits considerable variation across housing segments. In addition, there is considerable regional variation. The third chapter studies housing demand inspired by the fact that housing’s relative price, share of expenditure, and “unaffordability” have all grown since 1970. We estimate housing demand using a novel compensated framework over space and an uncompensated framework over time. Our specifications pass tests imposed by rationality and household mobility. Housing demand is income and price inelastic, and appears to fall with household size. We provide a numerical non-homothetic constant elasticity of substitution utility function for improved quantitative modeling. An ideal cost-of-living index demonstrates that the poor have been disproportionately impacted by rising relative rents, which have greatly amplified increases in real income inequality

Wave attenuation and focusing by a parabolic arc pontoon breakwater

In the multifunctional system consisting of point absorber wave energy converters and a pontoon breakwater, the breakwater plays an essential role in attenuating waves on the lee side and amplifying waves for a better energy harvesting on the stoss side. The structure of breakwater is expectedly improved to enhance its wave attenuation and amplification at the same time. Here we present a novel parabolic arc breakwater and show that for a range of typical regular incident waves, it can attenuate more wave elevation and focus high waves in several regions in comparison to a straight breakwater. In further frequency-domain investigations, a special relatively-low frequency associated with the parabolic arc breakwater configuration is found and named as the critical frequency, closed to which splendid attenuation and focusing performance can be achieved. A systematic parametric study on the geometric factors (draft, width, and chord length) of the parabolic arc breakwater is thereafter carried out to examine their influence on the attenuation and focusing performance at the critical frequency. We find that an increase of the draft can reduce the critical frequency greatly so as to let it be within the real sea states, meanwhile slightly affecting the attenuation performance. An increase of the chord length has an uncertain but not large influence on the attenuation performance, whereas it enhances substantially the focusing performance. Simultaneously, an amplification rate up to 3.06 in two relatively-large focal areas in a prescribed deployment zone and an average attenuation rate of approximately 68% in a prescribed protection zone could be obtained in a commonly observed coastal wave.</p

Wave attenuation and focusing by a parabolic arc pontoon breakwater

In the multifunctional system consisting of point absorber wave energy converters and a pontoon breakwater, the breakwater plays an essential role in attenuating waves on the lee side and amplifying waves for a better energy harvesting on the stoss side. The structure of breakwater is expectedly improved to enhance its wave attenuation and amplification at the same time. Here we present a novel parabolic arc breakwater and show that for a range of typical regular incident waves, it can attenuate more wave elevation and focus high waves in several regions in comparison to a straight breakwater. In further frequency-domain investigations, a special relatively-low frequency associated with the parabolic arc breakwater configuration is found and named as the critical frequency, closed to which splendid attenuation and focusing performance can be achieved. A systematic parametric study on the geometric factors (draft, width, and chord length) of the parabolic arc breakwater is thereafter carried out to examine their influence on the attenuation and focusing performance at the critical frequency. We find that an increase of the draft can reduce the critical frequency greatly so as to let it be within the real sea states, meanwhile slightly affecting the attenuation performance. An increase of the chord length has an uncertain but not large influence on the attenuation performance, whereas it enhances substantially the focusing performance. Simultaneously, an amplification rate up to 3.06 in two relatively-large focal areas in a prescribed deployment zone and an average attenuation rate of approximately 68% in a prescribed protection zone could be obtained in a commonly observed coastal wave.</p

Determining the local dark matter density with LAMOST data

Measurement of the local dark matter density plays an important role in both Galactic dynamics and dark matter direct detection experiments. However, the estimated values from previous works are far from agreeing with each other. In this work, we provide a well-defined observed sample with 1427 G \& K type main-sequence stars from the LAMOST spectroscopic survey, taking into account selection effects, volume completeness, and the stellar populations. We apply a vertical Jeans equation method containing a single exponential stellar disk, a razor thin gas disk, and a constant dark matter density distribution to the sample, and obtain a total surface mass density of $\rm {78.7 ^{+3.9}_{-4.7}\ M_{\odot}\ pc^{-2}}$up to 1 kpc and a local dark matter density of$0.0159^{+0.0047}_{-0.0057}\,\rm M_{\odot}\,\rm pc^{-3}$. We find that the sampling density (i.e. number of stars per unit volume) of the spectroscopic data contributes to about two-thirds of the uncertainty in the estimated values. We discuss the effect of the tilt term in the Jeans equation and find it has little impact on our measurement. Other issues, such as a non-equilibrium component due to perturbations and contamination by the thick disk population, are also discussed.Comment: 11 pages, 10 figure

Effectiveness of external Sanjierupi Gao on mastalgia caused by mammary gland hyperplasia: a placebo controlled trial

AbstractObjectiveTo evaluate the curative effect of external application of the Chinese drug, Sanjierupi Gao, on mastalgia caused by mammary gland hyperplasia.MethodsThis randomized, double-blinded, and placebo controlled study enrolled 260 patients with mammary gland hyperplasia from five hospitals. Patients were randomly and equally divided into a Sanjierupi Gao treatment group and a placebo control group. An adhesive plaster was applied to the most painful area on either breast for 7 h a day. Treatment lasted for two menstrual cycles without application during menstruation. Mastalgia was used as the main index of curative effect. The change before and after treatment in days of mastalgia, the time to alleviate pain, pain extent, and severe pain scores were observed.ResultsCompared to the control group, the treatment group had significantly fewer days of mastalgia (P<0.01), a significantly lower severe pain score (P<0.01), and significantly less subjective pain and tenderness (P<0.05 and P<0.01, respectively). Three days before the follow-up visit, the pain score in the treatment group was significantly lower than that in the control group (P<0.05). A non-parametric test was used to compare the time to alleviate mastalgia between the two groups and found no statistical difference (Z=−0.313, P=0.754).ConclusionApplication of Sanjierupi Gao can decrease mastalgia duration in patients with mammary gland hyperplasia during menstruation and alleviate the extent of mastalgia. The time to alleviate pain is psychologically influenced

Contextual Biasing of Named-Entities with Large Language Models

This paper studies contextual biasing with Large Language Models (LLMs), where during second-pass rescoring additional contextual information is provided to a LLM to boost Automatic Speech Recognition (ASR) performance. We propose to leverage prompts for a LLM without fine tuning during rescoring which incorporate a biasing list and few-shot examples to serve as additional information when calculating the score for the hypothesis. In addition to few-shot prompt learning, we propose multi-task training of the LLM to predict both the entity class and the next token. To improve the efficiency for contextual biasing and to avoid exceeding LLMs' maximum sequence lengths, we propose dynamic prompting, where we select the most likely class using the class tag prediction, and only use entities in this class as contexts for next token prediction. Word Error Rate (WER) evaluation is performed on i) an internal calling, messaging, and dictation dataset, and ii) the SLUE-Voxpopuli dataset. Results indicate that biasing lists and few-shot examples can achieve 17.8% and 9.6% relative improvement compared to first pass ASR, and that multi-task training and dynamic prompting can achieve 20.0% and 11.3% relative WER improvement, respectively.Comment: 5 pages, 4 figures. Conference: ICASSP 202