scholarly journals Why Are Algebra Word Problems Difficult? Using Tutorial Log Files and the Power Law of Learning to Select the Best Fitting Cognitive Model

2004 ◽  
pp. 240-250 ◽  
Author(s):  
Ethan A. Croteau ◽  
Neil T. Heffernan ◽  
Kenneth R. Koedinger
Keyword(s):  
Power Law ◽  
Word Problems ◽  
Cognitive Model ◽  
Log Files ◽  
Best Fitting ◽  
Power Law Of Learning

scholarly journals Constraints on the distribution of supernova remnants with Galactocentric radius

2015 ◽  
Vol 454 (2) ◽  
pp. 1517-1524 ◽  
Author(s):  
D A Green
Keyword(s):  
Cosmic Rays ◽  
Power Law ◽  
Supernova Remnants ◽  
Exponential Model ◽  
Galactic Centre ◽  
Selection Effects ◽  
The Galaxy ◽  
Best Fitting ◽  
Galactic Longitude ◽  
Galactic Distribution

Abstract Supernova remnants (SNRs) in the Galaxy are an important source of energy injection into the interstellar medium, and also of cosmic rays. Currently there are 294 known SNRs in the Galaxy, and their distribution with Galactocentric radius is of interest for various studies. Here I discuss some of the statistics of Galactic SNRs, including the observational selection effects that apply, and difficulties in obtaining distances for individual remnants from the ‘$\Sigma$–D’ relation. Comparison of the observed Galactic longitude distribution of a sample of bright Galactic SNRs – which are not strongly affected by selection effects – with those expected from models is used to constrain the Galactic distribution of SNRs. The best-fitting power-law/exponential model is more concentrated towards the Galactic Centre than the widely used distribution obtained by Case & Bhattacharya.

scholarly journals Stochastic Collusion and the Power Law of Learning

2002 ◽  
Vol 46 (5) ◽  
pp. 629-653 ◽  
Author(s):  
ANDREAS FLACHE ◽  
MICHAEL W. MACY
Keyword(s):  
Power Law ◽  
Power Law Of Learning

scholarly journals Modelling the Milky Way – I. Method and first results fitting the thick disc and halo with DES-Y3 data

2020 ◽  
Vol 497 (2) ◽  
pp. 1547-1562 ◽  
Author(s):  
A Pieres ◽  
L Girardi ◽  
E Balbinot ◽  
B Santiago ◽  
L N da Costa ◽  
...  
Keyword(s):  
Power Law ◽  
Globular Clusters ◽  
Milky Way ◽  
Synthetic Data ◽  
Real Data ◽  
Large Magellanic Cloud ◽  
Galactic Centre ◽  
Thick Disc ◽  
Disc Model ◽  
Best Fitting

ABSTRACT We present a technique to fit the stellar components of the Galaxy by comparing Hess Diagrams (HDs) generated from trilegal models to real data. We apply this technique, which we call mwfitting, to photometric data from the first 3 yr of the Dark Energy Survey (DES). After removing regions containing known resolved stellar systems such as globular clusters, dwarf galaxies, nearby galaxies, the Large Magellanic Cloud, and the Sagittarius Stream, our main sample spans a total area of ∼2300 deg2. We further explore a smaller subset (∼1300 deg2) that excludes all regions with known stellar streams and stellar overdensities. Validation tests on synthetic data possessing similar properties to the DES data show that the method is able to recover input parameters with a precision better than 3 per cent. We fit the DES data with an exponential thick disc model and an oblate double power-law halo model. We find that the best-fitting thick disc model has radial and vertical scale heights of 2.67 ± 0.09 kpc and 925 ± 40 pc, respectively. The stellar halo is fit with a broken power-law density profile with an oblateness of 0.75 ± 0.01, an inner index of 1.82 ± 0.08, an outer index of 4.14 ± 0.05, and a break at 18.52 ± 0.27 kpc from the Galactic centre. Several previously discovered stellar overdensities are recovered in the residual stellar density map, showing the reliability of mwfitting in determining the Galactic components. Simulations made with the best-fitting parameters are a promising way to predict Milky Way star counts for surveys such as the LSST and Euclid.

The Power Law of Learning in Transumbilical Single-Port Laparoscopic Subtotal Hysterectomy

2018 ◽  
Vol 25 (6) ◽  
pp. 994-1001 ◽  
Author(s):  
Shu-Han You ◽  
Chen-Ying Huang ◽  
Hsuan Su ◽  
Chien-Min Han ◽  
Chyi-Long Lee ◽  
...  
Keyword(s):  
Power Law ◽  
Single Port ◽  
Subtotal Hysterectomy ◽  
Laparoscopic Subtotal Hysterectomy ◽  
Power Law Of Learning

scholarly journals Modelling heterogeneous dust particles: an application to cometary polarization

2020 ◽  
Vol 501 (2) ◽  
pp. 1766-1781
Author(s):  
Prithish Halder ◽  
Shashikiran Ganesh
Keyword(s):  
Power Law ◽  
Wavelength Dependence ◽  
Phase Curve ◽  
Dust Particles ◽  
High Porosity ◽  
Carbonaceous Materials ◽  
Silicate Minerals ◽  
Long Period ◽  
Short Period ◽  
Best Fitting

ABSTRACT In this work, we introduce a comet dust model that incorporates multiple dust morphologies along with inhomogeneous mixture of silicate minerals and carbonaceous materials under power-law size distribution, to replicate the standard polarization-phase curve observed in several comets in the narrow-band continuum. Following the results from Rosetta/midas and COSIMA, we create high porosity hierarchical aggregates (HA) and low porosity (<10 per cent) Solids in the form of agglomerated debris. We also introduce a moderate porosity structure with solids in the core, surrounded by fluffy aggregates called fluffy solids (FS). We study the mixing combinations, (HA and Solids), (HA and FS), and (HA, FS, and Solids) for a range of power-law index n= 2.0 to 3.0 for different sets of mixing percentage of silicate minerals and carbonaceous materials. Polarimetry of the short period comets 1P/Halley and 67P/Churyumov-Gerasimenko match best with the polarization resulting from the combination of HA and Solids while the combinations (HA and FS) and (HA, FS, and Solids) provide the best-fitting results for the long period comets C/1995 O1 (Hale-Bopp) and C/1996 B2 (Hyakutake). The best-fitting model results also recreate the observed wavelength dependence of polarization. Our dust model agree with the idea that the long period comets may have high percentage of loose particles (HA and FS) compared to those in the case of short period comets as the short period comets experience more frequent and/or higher magnitude of weathering.

scholarly journals Spectropolarimetric observations of the CIZA J2242.8+5301 northern radio relic: no evidence of high-frequency steepening

2020 ◽  
Vol 498 (2) ◽  
pp. 1628-1637 ◽  
Author(s):  
F Loi ◽  
M Murgia ◽  
V Vacca ◽  
F Govoni ◽  
A Melis ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Power Law ◽  
High Frequency ◽  
Galaxy Cluster ◽  
Very High Frequency ◽  
Best Fitting ◽  
First Time ◽  
Polarization Fraction ◽  
Very High ◽  
Fitting Model

ABSTRACT Observations of radio relics at very high frequency (>10 GHz) can help to understand how particles age and are (re-)accelerated in galaxy cluster outskirts and how magnetic fields are amplified in these environments. In this work, we present new single-dish 18.6 GHz Sardinia Radio Telescope and 14.25 GHz Effelsberg observations of the well-known northern radio relic of CIZA J2242.8+5301. We detected the relic which shows a length of ∼1.8 Mpc and a flux density equal to $S_{14.25\, \mathrm{ GHz}}=(9.5\pm 3.9)\, \mathrm{ mJy}$ and $S_{18.6\, \mathrm{ GHz}}=(7.67\pm 0.90)\, \mathrm{ mJy}$ at 14.25 and 18.6 GHz, respectively. The resulting best-fitting model of the relic spectrum from 145 MHz to 18.6 GHz is a power-law spectrum with spectral index α = 1.12 ± 0.03: no evidence of steepening has been found in the new data presented in this work. For the first time, polarization properties have been derived at 18.6 GHz, revealing an averaged polarization fraction of $\sim\! 40{{\ \rm per\ cent}}$ and a magnetic field aligned with the ’filaments’ or ’sheets’ of the relic.

scholarly journals Revisiting the luminosity and redshift distributions of long gamma-ray bursts

2021 ◽  
Author(s):  
Guang-Xuan Lan ◽  
Jun-Jie Wei ◽  
Hou-Dun Zeng ◽  
Ye Li ◽  
Xue-Feng Wu
Keyword(s):  
Power Law ◽  
Gamma Ray ◽  
Information Criterion ◽  
Good Representation ◽  
Redshift Distribution ◽  
Model Free ◽  
Flux Limit ◽  
Best Fitting ◽  
Incomplete Sampling ◽  
Burst Alert Telescope

Abstract In this work, we update and enlarge the long gamma-ray burst (GRB) sample detected by the Swift satellite. Given the incomplete sampling of the faint bursts and the low completeness in redshift measurement, we carefully select a subsample of bright Swift bursts to revisit the GRB luminosity function (LF) and redshift distribution by taking into account the probability of redshift measurement. Here we also explore two general expressions for the GRB LF, i.e. a broken power-law LF and a triple power-law LF. Our results suggest that a strong redshift evolution in luminosity (with an evolution index of $\delta =1.92^{+0.25}_{-0.37}$) or in density ($\delta =1.26^{+0.33}_{-0.34}$) is required in order to well account for the observations, independent of the assumed expression of the GRB LF. However, in a one-on-one comparison using the Akaike information criterion, the best-fitting evolution model involving the triple power-law LF is statistically preferred over the best-fitting one involving the broken power-law LF with a relative probability of ∼94.3 per cent versus ∼5.7 per cent. Extrapolating our fitting results to the flux limit of the whole Swift sample, and considering the trigger probability of Swift/Burst Alert Telescope in detail, we find that the expectations from our evolution models provide a good representation of the observed distributions of the whole sample without the need for any adjustment of the model free parameters. This further confirms the reliability of our analysis results.

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