Likelihood Ratio Tests in Random Graph Models with Increasing Dimensions by Ting Yan (521258)

“…<p>We explore the Wilks phenomena in two random graph models: the <math><mrow><mi>β</mi></mrow></math>-model and the Bradley–Terry model. For two increasing dimensional null hypotheses, including a specified null <math><mrow><msub><mrow><mi>H</mi></mrow><mn>0</mn></msub><mo>:</mo><msub><mrow><mi>β</mi></mrow><mi>i</mi></msub><mo>=</mo><msubsup><mrow><mi>β</mi></mrow><mi>i</mi><mn>0</mn></msubsup></mrow></math> for <math><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>r</mi></mrow></math> and a homogenous null <math><mrow><msub><mrow><mi>H</mi></mrow><mn>0</mn></msub><mo>:</mo><msub><mrow><mi>β</mi></mrow><mn>1</mn></msub><mo>=</mo><mo>⋯</mo><mo>=</mo><msub><mrow><mi>β</mi></mrow><mi>r</mi></msub></mrow></math>, we reveal high dimensional Wilks’ phenomena that the normalized log-likelihood ratio statistic, <math><mrow><mo>[</mo><mn>2</mn><mo>{</mo><mi>l</mi><mo>(</mo><mrow><mrow><mi>β</mi><mo>̂</mo></mrow></mrow><mo>)</mo><mo>−</mo><mi>l</mi><mo>(</mo><mrow><mrow><mrow><mrow><mi>β</mi><mo>̂</mo></mrow></mrow></mrow></mrow><mn>0</mn><mo>)</mo><mo>}</mo><mo>−</mo><mi>r</mi><mo>]</mo><mo>/</mo><mrow><mrow><mo>(</mo><mn>2</mn><mi>r</mi><mo>)</mo></mrow></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></mrow></math>, converges in distribution to the standard normal distribution as <i>r</i> goes to infinity. …”

Linear interpolated slope of frequency vs intensity increase ratio. by Birthe Marie Steensen (21212520)

“…<p>The slope of observations and models with the percent increase in intensity and percent increase in frequency ratio (same as <a href="/article/info:doi/10.1371/journal.pclm.0000442#pclm.0000442.g005" target="_blank">Fig 5</a>) for the 99^th, 99.9^th and 9.97^th percentile, CMIP6 models are shown in green with green shading between the minimum and maximum slope, and CORDEX models are shown in blue with blue shading between the minimum and maximum slope.…”

Ratio of forward scatter (FSC) and side scatter (SSC) to control in <i>M</i>. <i>aeruginosa</i> exposed to H₂O₂ and UV, blue, and green light. by Emma T. Brentjens (17295999)

“…Among the light and H₂O₂-treated samples, the highest H₂O₂ concentration (750 μg/mL) generally exhibited the lowest FSC and SSC values relative to the control. FSC and SSC also generally decreased over time, with a few exceptions. …”

Mean values of participants’ heart rate. by Ezel Üsten (16548547)

Mean values of participants’ heart rate. by Ezel Üsten (16548547)

Mean values of participants’ heart rate. by Ezel Üsten (16548547)

Mean values of participants’ heart rate. by Ezel Üsten (16548547)

The <i>λ</i>_<i>i−j</i> values for different VC and freeze‒thaw cycle test conditions. by Ruihong Wang (1932328)

Impact of large choroidal vessels (LCV) and topographical orientation on percentage of flow deficit (FD%) values. by Valentin Hacker (9956024)

The structural equation model showed the direct and indirect effects of plant factors and soil factors on plant species diversity and plant functional diversity. (a) Structural equ... by Xuemei Xiang (20756894)

An initial investigation into the increase in the fishing mortality species ratio (Fparadoxus/Fcapensis) in recent hake assessments by Rebecca A Rademeyer (10107625)

Endocardial to epicardial wall thickness ratio by histology. There was a progressive increase over gestational weeks (GW). by Biagio Castaldi (20673392)

“…<p>Endocardial to epicardial wall thickness ratio by histology. There was a progressive increase over gestational weeks (GW).…”

BPCA ratios and proxies with a generally negative correlation with increasing pyrolysis temperature (with the exception of average CAS). by Ivy Notterpek (21368133)

A-B. Hazard ratios per 1 SD–increase in Lean BMI or FMI for Primary endpoint. by Wen Su (332346)

Measurement of Na⁺ ratio in the TE and blastocyst cross-sectional area in Group A. by Ayaka Fujishima (21221913)

“…Group A included 11 embryos (Embryo Nos. 1–11) and demonstrated an initial decrease in Na⁺ concentration within the ROI (correspomding to theTE), followed by either a plateau or a gradual increase. …”

Schematic for measuring <i>D</i> and <i>D</i>′ values. by Hong Zhang (25820)

“…The measured <i>I</i>_s decreases following a power-law trend as <i>β</i> and <i>D</i> increase, with weathering reducing the sensitivity of <i>I</i>_s to <i>β</i> but not significantly altering its sensitivity to <i>D</i>. …”

Random forest model variable importance ranking by mean decrease in Gini value in the derivation dataset (<i>N</i> = 2,771). by Andrew F. Auld (8967719)

Correlation analysis between the odorant concentration ratio and PNs response ratio, <i>R</i>^<i>PN</i>, for different values of stimulus duration (from 10 to 200ms) and... by Mario Pannunzi (553941)

Distal ratio across tissues and in COPD. by Lela Lackey (815515)

Subjects:

A visual comparison of the associated resistance data from Table 1 with the values of <i>k</i>_cat, <i>K</i>_M, catalytic efficiency (<i>k</i>_cat/<i>... by J. Roadnight Sheehan (20141887)