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Table
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TABLE 1: Experiment I design: 20 participants are assigned to one of the five blocks and use all five bivariate pairs. Here, LyLy : lengthylengthy (splitVectors), LyLx: lengthylengthx, LC : lengthycolor, LT : lengthytexture, and LCL: lengthycolor/lengthx.
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Figure
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Fig. 8: Experiment II three task types. The callouts show the task-relevant feature-pair(s).
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Fig. 1: Illustration of five bivariate configurations of vector magnitudes ∈ (0, 9, 999]. Three examples show vector magnitudes 440 (4.4 × 102), 9, 999 (9.9 × 103), and 1 (1 × 100). Take 440 as an example, lengthylengthx (a) maps 4.4 (digit) and 2 (exponent) to lengths along the y and x axes accordingly ( lengthy lengthx); (b)-(e) have the same digitto-lengthy representation as (a). The exponent representations are manipulated to be (1) more integral or separable from lengthy and (2) more or less categorical. (b) lengthycolor/lengthx uses color to double-code exponent compared to (a). The exponents in (c), (d), and (e) use color, texture, or outer cylinder length accordingly. Our experimental results support that more separable dimensions lead to more perceptually accurate glyphs. The higher the separability, the higher the accuracy. Also, using a more categorical feature (e.g., color in (c)) of one of the variables benefited efficiency and accuracy.
|
[] |
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200
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2
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Table
|
{
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|
TABLE 2: Summary statistics by tasks. The significant main effects and the high effect size (ES) are in bold (none in these observations) and the medium effect size is in italic. Effect size is eta-square labeled “small” (0.01 − 0.06), “medium” [0.06 − 0.14), and “large” (≥ 0.14) effects following Cohen [39]. Post-hoc Tukey grouping results are reported for significant main effects, where > means statistically significantly better and enclosing parentheses mean they belong to the same Tukey group.
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200
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Figure
|
{
"x1": 47.879999999999995,
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|
Fig. 4: Experiment I task completion time and relative error or accuracy by tasks. The horizontal axis represents the mean task completion time while the vertical axis showing the accuracy or relative error. Same letters represent the same post-hoc analysis group. Colors label the feature-pair types. All error bars represent 95% confidence interval.
|
[
"(a)",
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"(b)",
"Task",
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"(RATIO)",
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"3",
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] |
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200
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5
| 6
|
Figure
|
{
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|
Fig. 5: Experiment I (Task MAG): All instances of correspondence errors by participant. The most separable lengthycolor glyph had no instances of correspondence error whilst the lengthylengthx had the most. The redundant color dimensions helped removed some correspondence errors (Two instances of lengthycolor/lengthx vs. five instances of lengthylengthx).
|
[] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00002_1762333113/figures/2301.00002-Figure5-1.png
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200
|
7
| 9
|
Figure
|
{
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|
Fig. 7: Density effects on color choices to justify the use of dense sampling and categorical colormap (c) in Experiment II. This example dataset shows two colormaps: ( segmented-continuous (a and b) and categorical (c and d) colormaps), at two different data densities. (a) and (c) show data with the raw density from the simulation results; (b) and (d) were produced by removing around 70% vector glyphs. The boundaries between the data categories are more recognizable when the data are dense in (a) and (c) (comparing the 1st column and the 2nd column). At the same density (comparing the 1st and 2nd row), the boundaries between levels are easier to recognize when spin vectors are rendered using a categorical colormap of (c) and (d). We thus use the raw dense and categorical colormaps (c) in Experiment II.
|
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200
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11
| 13
|
Figure
|
{
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|
Fig. 11: Contours of simulation data. Size from this viewpoint can guide visual grouping and size in 3D must take advantage of knowledge of the layout of the scene [45].
|
[
"(c)",
"Lengthytexture",
"feature-pair",
"(d)",
"Lengthycolor",
"feature-pair",
"(a)",
"Lengthylengthx",
"feature-pair",
"(b)",
"Lengthycolor/lengthx",
"feature-pair"
] |
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200
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2
| 2
|
Figure
|
{
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|
Fig. 2: Real-world large-magnitude-range quantum physics simulation results shown using (a)-(e) five bivariate featurepairs and (f) a traditional linear representation. LC, LCL, and LT can reveal scene spatial structures. We anticipate that two conditions determine the glyph efficiency: (1) the bivariate glyph uses two separable dimensions; and (2) one of the two dimensions uses a categorical representation thus can reveal global structures in data. The first condition is necessary for local tasks when a few items are compared. The second condition is needed for inspecting the entire scene.
|
[
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"(integral)",
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"(LCL)",
"(redun-",
"dant",
"encoding)"
] |
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200
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12
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|
Figure
|
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|
Fig. 12: Examples using different background colors: gray, white, and black. Figures on the top row are magnified views of region 1, marked by orange-box on the left image, and the bottom row shows region 2. With white background, the white cylinders would be washed out (top right image). With black background, the black cylinders would be washed out (bottom right image). In this study, the neutral stimulus-free gray background was chosen.
|
[] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00002_1762333113/figures/2301.00002-Figure12-1.png
|
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200
|
13
| 18
|
Figure
|
{
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|
Fig. 13: Experiment II: examples of selected exponent ranges of 3, 5, and 7 (from the second left to right). We could see that the pattern of magnitude distribution is more revealing by categorical colors than by texture glyphs. Coloring may show more steps with large exponent ranges and also give us a better understanding of data distribution. For example, we could quickly focus on the orange region.
|
[
"(c)",
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"(b)",
"Lengthycolor",
"(a)",
"Lengthylengthy",
"(splitVectors)"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00002_1762333113/figures/2301.00002-Figure13-1.png
|
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|
200
|
3
| 11
|
Table
|
{
"x1": 319.68,
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|
TABLE 3: Exp II: Summary statistics by tasks. The significant main effects and the high effect size are in bold and the medium effect size is in italic. Effect size is Cohen’s d for tasks SEARCH and MAX, and Cramer’s V for task NUMEROSITY (NUM). Post-hoc Tukey grouping results are reported for significant main effects, where > means statistically significantly better and enclosing parentheses mean they belong to the same Tukey group. Here, LC: lengthycolor and LT : lengthytexture.
|
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200
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10
| 11
|
Figure
|
{
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|
Fig. 10: Relative error for Tasks SEARCH and MAX was the percentage the reported value was away from the ground truth. Error rate for NUMEROSITY was the percentage of wrong answers of all trials for each participant. The vertical axis shows the relative error or error rate. Same letters represent the same post-hoc analysis group. All error bars represent 95% confidence intervals.
|
[] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00002_1762333113/figures/2301.00002-Figure10-1.png
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200
|
9
| 11
|
Figure
|
{
"x1": 64.8,
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|
Fig. 9: Experiment II (Tasks SEARCH and MAX): All instances of correspondence errors by participant. Again, the lengthycolor has the least instances of correspondence error whilst the lengthytexture had the most.
|
[] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00002_1762333113/figures/2301.00002-Figure9-1.png
|
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200
|
6
| 8
|
Figure
|
{
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|
Fig. 6: Visual mapping using color and texture in Experiment II. From the top to bottom, colors and texture segments are mapped to exponent values from the largest to the smallest. The three numbers next to the 7-level colormap are the RGB values. The numbers next to the texture columns are the proportion of black-on-white for the last 7-level texture configuration.
|
[] |
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|
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200
|
14
| 19
|
Figure
|
{
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|
Fig. 14: Experiment II: Search task. The spatial proximity of the locations of the identified targets, to the ground truth, for all trials in the study. Here the ground truth locations are translated to the origin (0, 0, 0). This task was timeconstrained. among the 810 trials (or 270 trials for each bivariate glyph type), participants completed 262 lengthycolor, 261 lengthytexture, and 251 lengthylengthy trials.
|
[
"(a)",
"lengthycolor",
"(b)",
"lengthytexture",
"(c)",
"lengthylengthy"
] |
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|
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200
|
15
| 19
|
Figure
|
{
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|
Fig. 15: Experiment II: Max task. The spatial proximity of the locations of the identified targets, to the ground truth (centered at the origin (0, 0, 0), for all trials in this task. The yellow dots show the closest points from other-than-target-exponent regions. Here the ground truth locations are translated to the origin (0, 0, 0). Among the 810 trials, participants gave an answer to 270 trials for each bivariate glyph type. Among each of these 270, participants completed 269 lengthycolor, 269 lengthytexture, and 259 lengthylengthy trials in total.
|
[
"(a)",
"lengthycolor",
"(b)",
"lengthytexture",
"(c)",
"lengthylengthy"
] |
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|
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200
|
8
| 20
|
Figure
|
{
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|
Figure 8. Mean squared errors in estimating the worker reliability vector p (left) and the task difficulty vector q (right), respectively.
|
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"error",
"1m∥q̂",
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"2",
"2"
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{
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|
200
|
1
| 6
|
Table
|
{
"x1": 60.839999999999996,
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|
Table 1. Parameters for synthetic data experiments under diverse scenarios.
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200
|
1
| 6
|
Figure
|
{
"x1": 78.84,
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"y1": 66.96,
"y2": 196.2
}
|
Figure 1. Prediction error in recovering the ordered top-two answers (g, h) for four different scenarios, summarized in Table 1, as the avg. number of queries per task changes. Our TopTwo2 algorithm achieves the best performance, near the oracle MLE for all the scenarios.
|
[] |
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{
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200
|
4
| 13
|
Table
|
{
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|
Table 4. Dataset information
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[
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{
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200
|
6
| 17
|
Figure
|
{
"x1": 54.72,
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|
Figure 6. Prediction error for (gj , hj) (top row), gj (middle) and hj (bottom) for four scenarios. Our algorithm (TopTwo2) achieves the best performance, near the oracle MLE for all the scenarios.
|
[] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00006_1762333129/figures/2301.00006-Figure6-1.png
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{
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200
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4
| 12
|
Figure
|
{
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|
Figure 4. Example tasks for ‘Color’ dataset where the ground truth g and the most confusing answer h are determined by the color distance from the reference color (top).
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200
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2
| 7
|
Figure
|
{
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|
Figure 2. (a) Prediction error for (gj , hj), gj and hj (from left to right) for color comparison task using real data collected by MTurk. TopTwo2 algorithm achieves the best performance. (b) Histogram of color distance gap for two task groups, the easy group with the highest qj(red) and the difficult group with the lowest qj(blue). The difficult group tends to have a smaller color distance gap.
|
[
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200
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7
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|
Figure
|
{
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|
Figure 7. Prediction error for (gj , hj) (first column), gj (second column), and hj (third column) for five different setups. The solid lines represent the mean prediction errors of each algorithm averaged over 10 runs, and the shaded regions represent the standard deviations.
|
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200
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5
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Table
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{
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|
Table 5. Comparison of performances for the corrupted CIFAR10H dataset with top2/full label training
|
[
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|
200
|
3
| 11
|
Table
|
{
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}
|
Table 3. Proportions of top-three dominating answers in public datasets
|
[
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"0.15±0.05",
"Adult2",
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"answer"
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{
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|
200
|
3
| 11
|
Figure
|
{
"x1": 54.72,
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|
Figure 3. Empirical distribution of the mean incidence of responses sorted by the dominant proportion, averaged over all tasks in each dataset. The i-th data point represents the average incidence of the i-th highest response in each task. The error bars indicate the standard deviation of the mean incidence of the i-th dominating answer over the tasks in the dataset.
|
[
"(e)",
"(f)",
"(g)",
"(a)",
"(b)",
"(c)",
"(d)"
] |
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{
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200
|
5
| 15
|
Figure
|
{
"x1": 68.75999999999999,
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|
Figure 5. Training images with (a) lowest and (b) highest confusion probabilities.
|
[
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"be",
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"(b)",
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{
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|
200
|
4
| 5
|
Figure
|
{
"x1": 320.76,
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"y1": 189.72,
"y2": 289.08
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|
Figure 4: Performance comparison of different VAEs for image generation on CelebA.
|
[
"(b)",
"KL(a)",
"Reconstruction",
"Loss"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00011_1762333142/figures/2301.00011-Figure4-1.png
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{
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|
200
|
3
| 5
|
Figure
|
{
"x1": 86.39999999999999,
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|
Figure 3: The information plane with the R − D curves of VAE, β-VAE, ControlVAE and eVAE on dSprites.
|
[
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{
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200
|
5
| 6
|
Figure
|
{
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|
Figure 5: Learning curves on dSprites1. (a,b) indicate that eVAE has the lowest reconstruction loss compared with VAE (β = 1), β-VAE (β = 4), and ControlVAE (KL = 19) under a fixed KL point KL=19. (c) is the element-wise KL divergence as a function of iterations in eVAE. We can observe that eVAE retains a stable and reasonable KL divergence of each generator dimension (factor): position-y (z2), scale (z3), shape (z4), position-x (z6), orientation (z7). More comparisons in terms of generated KL divergence can be found in Supplementary Material E.More comparisons in terms of generated KL divergence can be found in Supplementary Material E.
|
[
"(a)",
"Reconstruction",
"Loss",
"(b)",
"KL",
"(c)",
"Element-wise",
"KL",
"Divergence"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00011_1762333142/figures/2301.00011-Figure5-1.png
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{
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|
200
|
6
| 6
|
Figure
|
{
"x1": 59.04,
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"y1": 328.32,
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|
Figure 6: Latent traversal on dSprites. To distinguish the latent factors visually, we take the ellipse for illustration. Each row represents a latent factor in the traversal, while keeping others fixed. The first column refers to the seed image for initialization, and we then manipulate the latent dimension z across the range [-3, 3].
|
[
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200
|
7
| 6
|
Figure
|
{
"x1": 57.96,
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|
Figure 7: Learning curves on PTB for language modeling. The suffix of PID and VGA refer to a KL set point i.e., KL = 3; Cyc-8 indicates 8 iteration cycles where the weight increases linearly from 0 to 1; Cost-10k refers to 10k iterations during which the weight increases from 0 to 1 by a sigmoid function iteratively.
|
[
"(c)",
"Reconstruction",
"Loss(b)",
"KL(a)",
"Beta"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00011_1762333142/figures/2301.00011-Figure7-1.png
|
{
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|
200
|
1
| 3
|
Figure
|
{
"x1": 114.83999999999999,
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|
Figure 1: The framework of eVAE. The VAE results inform the chromosome sampling. The genes are then updated by variational V-crossover and V-mutation. The evolved results are checked per fitness for t+ 1 retraining, giving up, or converging.
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200
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1
| 11
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Table
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{
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"y2": 413.28
}
|
Table 1: Experimental settings for disentangled representation learning on dSprites, image generation on CelebA, and language generation on PTB.
|
[
"0.006",
"0.07",
"10",
"Mutation",
"Rate",
"Crossover",
"Rate",
"Individual",
"Number",
"init",
"lr:",
"0.001",
"threshold:100",
"decay",
"factor:",
"0.5",
"max",
"decay:",
"5",
"Input",
"Encoder",
"Latent",
"Decoder",
"PTB",
"(KL",
"=",
"3)",
"0.001",
"0.03",
"20",
"Mutation",
"Rate",
"Crossover",
"Rate",
"Individual",
"Number",
"Latent",
"Decoder",
"(128,128,3)",
"Conv(32,",
"32,",
"32),",
"ReLu,",
"Conv(32,16,16),",
"ReLu,",
"Conv(32,8,8),ReLu,",
"Conv(32,4,4),",
"Relu,",
"Linear(256),",
"Relu,",
"Linear(256),",
"Relu,",
"Linear(20)",
"10",
"Linear(256),",
"Relu,",
"Linear(256),",
"Relu,",
"Linear(512),",
"Relu,",
"Conv(32,4,4),",
"Relu,",
"Conv(32,8,8),",
"Relu,",
"Conv(32,16,16),",
"Relu,",
"Conv(32,32,32),",
"Relu,",
"(3,",
"64,64)",
"Input",
"Encoder",
"CelebA",
"(KL",
"=",
"200)",
"Adam(1e-4)",
"0.001",
"0.04",
"20",
"Latent",
"Decoder",
"(64,64,1)",
"Conv(32,",
"32,",
"32),",
"ReLu,",
"Conv(32,16,16),",
"ReLu,",
"Conv(32,8,8),",
"ReLu,Conv(32,4,4),",
"Relu,",
"Linear(256),",
"Relu,",
"Linear(256),",
"Relu,",
"Linear(20)",
"10",
"Linear(256),",
"Relu,",
"Linear(256),",
"Relu,",
"Linear(512),",
"Relu,",
"Conv(32,4,4),",
"Relu,",
"Conv(32,8,8),",
"Relu,",
"Conv(32,16,16),",
"Relu,",
"Conv(32,32,32),",
"Relu,",
"(1,",
"64,64)",
"Mutation",
"Rate",
"Crossover",
"Rate",
"Individual",
"Number",
"Input",
"Encoder",
"dSprites",
"Adam(1e-4)",
"Dataset",
"Optimiser",
"Architecture",
"eVAE",
"initialization"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00011_1762333142/figures/2301.00011-Table1-1.png
|
{
"x1": 54,
"x2": 557.998046875,
"y1": 424.54351806640625,
"y2": 441.5050048828125
}
|
200
|
8
| 11
|
Figure
|
{
"x1": 69.84,
"x2": 541.0799999999999,
"y1": 501.84,
"y2": 630
}
|
Figure 8: The element-wise KL divergence over iterations for β-VAE, ControlAVE, and eVAE on dSprites. It shows that each KL divergence of eVAE is larger than that of β-VAE, providing an enough space for generating disentangled representation. In addition, eVAE generates more stable KL divergence compared to ControlVAE.
|
[
"(c)",
"eVAE(b)",
"ControlVAE(a)",
"𝛽-VAE"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00011_1762333142/figures/2301.00011-Figure8-1.png
|
{
"x1": 53.99998474121094,
"x2": 558.000732421875,
"y1": 647.9955444335938,
"y2": 675.916015625
}
|
200
|
2
| 4
|
Figure
|
{
"x1": 68.75999999999999,
"x2": 280.08,
"y1": 57.96,
"y2": 232.2
}
|
Figure 2: eVAE - inner-outer joint evolutionary training process. The upper part shows the VAE training at time t, the objectives are then incorporated into the lower part - the outer training by variational genetic algorithm, whose fitness-based optimized results are fed to the VAE for further training.
|
[
"+",
"V-mutationVariational",
"GA",
"V-crossover",
"V-evaluation",
"Initialization",
"𝑓(𝜀",
"𝛽",
"∅𝑡,",
"𝜃𝑡",
",",
"ℒ(&)*\"",
"=",
"∆ℒ(&)*\"",
"+∥",
"𝐾𝐿𝑡",
"−",
"𝑐",
"∥",
"'",
"ℒ./01",
"=",
"𝑓𝑡(·)",
"𝛽t,",
"𝜃𝑡,",
"∅t,",
"ℒ(&)*\"",
"𝛽$+,",
"∗",
",",
"𝑓$+,∗",
"Encoder",
"Decoder",
"Outer",
"training",
"𝛽0",
"Inner",
"training",
"𝑥",
"−",
"𝑥.",
"'",
"𝑥.",
"𝐷%&(𝑞∅,\"||𝑝#,\")",
"z𝑡",
"𝑝#",
"𝑥𝑡|𝑧𝑡",
"𝛴!\"|#$",
"𝜇!\"|#$",
"𝜖",
"𝑥",
"𝑞",
"∅",
"𝑧𝑡|𝑥𝑡"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00011_1762333142/figures/2301.00011-Figure2-1.png
|
{
"x1": 53.999969482421875,
"x2": 292.504638671875,
"y1": 243.72653198242188,
"y2": 304.52294921875
}
|
200
|
1
| 6
|
Table
|
{
"x1": 133.92,
"x2": 503.28,
"y1": 132.84,
"y2": 215.28
}
|
Table 1. Datasets information.
|
[
"#",
"of",
"Graphs",
"1",
"1",
"4,337",
"4110",
"#",
"of",
"Edges",
"4110",
"1950",
"266,894",
"132,753",
"#",
"of",
"Nodes",
"700",
"871",
"131,488",
"122,747",
"#",
"of",
"Labels",
"4",
"2",
"2",
"2",
"BA-Shapes",
"Tree-Cycles",
"Mutagenicity",
"NCI1",
"Node",
"Classification",
"Graph",
"Classification"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00012_1762333150/figures/2301.00012-Table1-1.png
|
{
"x1": 243.9210205078125,
"x2": 371.43023681640625,
"y1": 117.57881164550781,
"y2": 122.06201171875
}
|
200
|
3
| 9
|
Figure
|
{
"x1": 133.92,
"x2": 481.32,
"y1": 362.88,
"y2": 588.24
}
|
Fig. 3. The explanation visualization on Mutagenicity when K = 15. Graph 3903 the label is 1, and the graph 3904 the label is 0. In this diagram, the first column is the original graph structure and the predicted label of the target GNN. The second to fourth columns are the explanation of graphs from GNNExplainer, Gem, and GANExplainer, respectively.
|
[] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00012_1762333150/figures/2301.00012-Figure3-1.png
|
{
"x1": 134.76499938964844,
"x2": 480.5947570800781,
"y1": 604.3427734375,
"y2": 652.6619873046875
}
|
200
|
2
| 9
|
Figure
|
{
"x1": 133.92,
"x2": 481.32,
"y1": 123.83999999999999,
"y2": 239.04
}
|
Fig. 2. The explanation visualization of Node 709, the label is 1, on Tree-Cycles when K = 6. In this diagram, the blue nodes mean the prediction label of the target GNN is 1, and the grey nodes mean the predictions of the target GNN for these nodes are 0. The red circle node is the node that needs to explain why the target GNN predicting label is 1. The first subfigure is the original graph structure, and the prediction of the target GNN is 1, which means the target GNN makes the right prediction. The second to fourth subfigures are the explanation of the node 709 from GNNExplainer, Gem, and GANExplainer, respectively.
|
[] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00012_1762333150/figures/2301.00012-Figure2-1.png
|
{
"x1": 134.76499938964844,
"x2": 480.59619140625,
"y1": 255.2868194580078,
"y2": 336.48291015625
}
|
200
|
2
| 7
|
Table
|
{
"x1": 133.92,
"x2": 482.03999999999996,
"y1": 438.84,
"y2": 505.08
}
|
Table 2. Results on Synthetic Datasets.
|
[
"GNNExplainer",
"0.7941",
"0.8824",
"0.9118",
"0.9118",
"0.9118",
"0.2000",
"0.5429",
"0.7143",
"0.8571",
"0.9429",
"Gem",
"0.9412",
"0.9412",
"0.9412",
"0.9412",
"0.9412",
"0.7429",
"0.7429",
"0.7714",
"0.8857",
"0.9143",
"GANExplainer",
"0.7647",
"1.000",
"0.9706",
"0.9853",
"0.9853",
"0.9143",
"1.0000",
"0.9714",
"1.0000",
"1.0000",
"K",
"(edges)",
"BA-Shapes",
"Tree-Cycles",
"5",
"6",
"7",
"8",
"9",
"6",
"7",
"8",
"9",
"10"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00012_1762333150/figures/2301.00012-Table2-1.png
|
{
"x1": 225.76699829101562,
"x2": 389.590087890625,
"y1": 420.77679443359375,
"y2": 425.2599792480469
}
|
200
|
1
| 3
|
Figure
|
{
"x1": 220.67999999999998,
"x2": 395.28,
"y1": 400.68,
"y2": 538.1999999999999
}
|
Fig. 1. The framework of GANExplainer. We generate ground truth through the Gem distillation process.
|
[] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00012_1762333150/figures/2301.00012-Figure1-1.png
|
{
"x1": 134.76499938964844,
"x2": 480.59246826171875,
"y1": 553.7877807617188,
"y2": 569.22998046875
}
|
200
|
3
| 8
|
Table
|
{
"x1": 160.92,
"x2": 452.15999999999997,
"y1": 311.76,
"y2": 378
}
|
Table 3. Results on Real-world Datasets.
|
[
"GNNExplainer",
"0.6981",
"0.7188",
"0.7442",
"0.7834",
"0.6909",
"0.7031",
"0.7566",
"0.8004",
"Gem",
"0.6705",
"0.7027",
"0.7741",
"0.7949",
"0.6253",
"0.7055",
"0.7956",
"0.8126",
"GANExplainer",
"0.6935",
"0.7442",
"0.7650",
"0.7857",
"0.6642",
"0.7494",
"0.7908",
"0.8273",
"K",
"(egeds)",
"Mutagenicity",
"NCI1",
"15",
"20",
"25",
"30",
"15",
"20",
"25",
"30"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00012_1762333150/figures/2301.00012-Table3-1.png
|
{
"x1": 223.0050048828125,
"x2": 392.352294921875,
"y1": 295.00396728515625,
"y2": 299.4871826171875
}
|
200
|
2
| 2
|
Figure
|
{
"x1": 55.8,
"x2": 556.1999999999999,
"y1": 54,
"y2": 171
}
|
Figure 2: Overall Architecture of PRI-GSL.
|
[
"Role",
"Characteriztion",
"…",
"t",
"ty",
"ab",
"ili",
"Pr",
"ob",
"…",
"QCW",
"EvolutionWavelets",
"Role-aware",
"Structure",
"Learner",
"+",
"t",
"Refined",
"GraphOriginal",
"Graph"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00015_1762333163/figures/2301.00015-Figure2-1.png
|
{
"x1": 218.91700744628906,
"x2": 393.0831298828125,
"y1": 182.71255493164062,
"y2": 188.71502685546875
}
|
200
|
1
| 5
|
Table
|
{
"x1": 69.84,
"x2": 542.16,
"y1": 62.64,
"y2": 220.32
}
|
Table 1: Accuracy ± standard deviation (%) of node classification. (Bold: best result; Underlined: runner up. )
|
[
"SDRF",
">1",
"day",
">1",
"day",
"41.05±1.17",
"69.97±0.28",
">1",
"day",
"81.94±0.59",
">1",
"day",
"SLAPS",
"25.29±1.06",
"23.10±3.39",
"40.24±1.80",
"68.58±1.46",
"75.64±0.77",
"79.27±1.54",
"88.48±2.47",
"PRI-GSL",
"33.87±2.08",
"28.55±2.04",
"51.83±2.44",
"69.34±2.64",
"76.77±3.20",
"83.67±2.09",
"92.40±1.15",
"IDGL",
"29.13±2.94",
"27.44±5.80",
"49.80±4.80",
"67.94±0.28",
"75.32±1.45",
"83.23±0.62",
"88.89±2.55",
"Pro-GNN",
"27.18±1.28",
"24.82±2.81",
"48.54±4.87",
"66.68±2.02",
"75.44±3.54",
"82.14±0.58",
"87.28±1.85",
"GCN",
"22.22±1.24",
"22.85±1.64",
"32.16±2.76",
"66.31±1.12",
"74.11±3.65",
"79.10±0.77",
"85.61±2.20",
"GAT",
"22.64±1.25",
"23.53±1.33",
"32.05±2.56",
"63.85±2.45",
"73.02±2.52",
"77.86±1.48",
"87.97±2.73",
"GraphSAGE",
"28.79±1.74",
"24.22±1.44",
"37.05±2.35",
"64.80±1.83",
"72.61±2.95",
"75.23±1.31",
"86.23±2.53",
"DropEdge",
"22.35±1.12",
"23.84±1.20",
"32.62±2.75",
"66.68±1.38",
"75.97±0.82",
"79.30±0.84",
"86.05±1.78",
"NeuralSparse",
"29.02±1.10",
"24.50±1.42",
"47.30±2.22",
"67.82±1.18",
"74.87±2.77",
"81.47±1.43",
"89.40±1.85",
"Graph-PRI",
"28.44±2.10",
"23.81±2.31",
"42.39±1.99",
"69.24±1.25",
"76.25±1.44",
"79.07±1.12",
"88.30±2.11",
"Photo",
"h=0.83",
"Cora",
"h=0.83",
"PubMed",
"h=0.79",
"CiteSeer",
"h=0.72",
"Chameleon",
"h=0.25",
"Actor",
"h=0.24",
"Method",
"Squirrel",
"h=0.22"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00015_1762333163/figures/2301.00015-Table1-1.png
|
{
"x1": 87.41699981689453,
"x2": 524.5834350585938,
"y1": 55.66855239868164,
"y2": 61.6710205078125
}
|
200
|
5
| 6
|
Figure
|
{
"x1": 56.879999999999995,
"x2": 555.12,
"y1": 54,
"y2": 142.2
}
|
Figure 5: Visualization of the original graph of Cora and learned graphs by Graph-PRI, Pro-GNN, IDGL, and PRI-GSL.
|
[
"(a)",
"Original",
"Graph.",
"(b)",
"Graph-PRI.",
"(c)",
"Pro-GNN.",
"(d)",
"IDGL.",
"(e)",
"PRI-GSL."
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00015_1762333163/figures/2301.00015-Figure5-1.png
|
{
"x1": 66.54501342773438,
"x2": 545.4571533203125,
"y1": 159.04953002929688,
"y2": 165.052001953125
}
|
200
|
6
| 6
|
Figure
|
{
"x1": 61.559999999999995,
"x2": 286.56,
"y1": 194.04,
"y2": 341.28
}
|
Figure 6: The variations of HvN(G̃) and DQJS(G̃||G).
|
[
"D",
"QJ",
"S(",
"G̃",
"||G",
")",
"2.9195",
"2.9190",
"2.9185",
"0",
"25",
"50",
"75",
"100",
"125",
"150",
"Epochs",
"converge",
"at",
"2.9187301",
"+2.9187",
"0.000029",
"0.000030",
"0.000031",
"0.000032",
"0.000033",
"H",
"vN",
"(G̃",
")",
"0",
"25",
"50",
"75",
"100",
"125",
"150",
"Epochs"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00015_1762333163/figures/2301.00015-Figure6-1.png
|
{
"x1": 64.44200134277344,
"x2": 282.05767822265625,
"y1": 360.3995361328125,
"y2": 367.8970031738281
}
|
200
|
7
| 6
|
Figure
|
{
"x1": 325.44,
"x2": 552.24,
"y1": 194.04,
"y2": 301.32
}
|
Figure 7: Parameter sensitivity of α and β.
|
[
"Cora",
"CiteSeer",
"69.11",
"69.11",
"69.56",
"70.11",
"69.67",
")",
"82.33",
"83.05",
"83.24",
"83.34",
"83.24",
"y",
"(%",
"ur",
"ac",
"A",
"cc",
"90",
"85",
"80",
"75",
"70",
"65",
"1",
"2",
"3",
"4",
"5",
"β",
"Cora",
"CiteSeer",
"69.67",
"69.03",
"70.42",
"69.03",
"69.03",
"83.28",
"83.22",
"83.33",
"84.1",
"83.28",
")",
"y",
"(%",
"ur",
"ac",
"A",
"cc",
"90",
"85",
"80",
"75",
"70",
"65",
"0.1",
"0.2",
"0.4",
"1.0",
"2.0",
"α"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00015_1762333163/figures/2301.00015-Figure7-1.png
|
{
"x1": 353.79998779296875,
"x2": 523.6996459960938,
"y1": 319.1485290527344,
"y2": 325.1510009765625
}
|
200
|
4
| 2
|
Figure
|
{
"x1": 65.88,
"x2": 287.28,
"y1": 51.839999999999996,
"y2": 207
}
|
FIG. 4. Maximum recoil velocity for different impact parameters b. For all the high spins studied here this peaks at b ≈ 2.38.
|
[] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00018_1762333172/figures/2301.00018-Figure4-1.png
|
{
"x1": 54,
"x2": 299.08392333984375,
"y1": 222.41578674316406,
"y2": 247.82000732421875
}
|
200
|
5
| 2
|
Figure
|
{
"x1": 65.88,
"x2": 287.28,
"y1": 261.71999999999997,
"y2": 418.32
}
|
FIG. 5. Display of peak velocity vs. γv and spin for merging holes.
|
[] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00018_1762333172/figures/2301.00018-Figure5-1.png
|
{
"x1": 54,
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|
200
|
6
| 2
|
Figure
|
{
"x1": 316.8,
"x2": 563.04,
"y1": 51.839999999999996,
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|
FIG. 6. Maximum recoil velocity for different initial momenta parameters γv and impact parameters b as a color map.
|
[] |
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{
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"y2": 225.916015625
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200
|
7
| 2
|
Figure
|
{
"x1": 316.8,
"x2": 563.04,
"y1": 243.72,
"y2": 417.24
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|
FIG. 7. Maximum recoil velocity versus the settled spins value sr and its extrapolation to maximal spin sr = 1. (Blue points are extrapolation to infinite resolution, red points are the n100 low resolution results).
|
[] |
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200
|
1
| 1
|
Figure
|
{
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FIG. 1. Evidence for the existence of a PeV bump in the diffuse flux of high-energy astrophysical neutrinos. The discovery potential is quantified via a Bayes factor (Section III) that compares the evidence for a two-component flux fit—a power law plus bump—vs. a one-component flux fit—a power law—after marginalizing over all flux parameters (Section II D). Present-day results (snapshot A) are obtained using the 7.5-year public IceCube HESE sample [7, 64]; the best-fit parameter values are in Table I. Projections (snapshots B, C, D) are obtained using scaled-up event rates, adopting the present-day best-fit two-component flux as the true flux. We assume that upcoming neutrino telescopes will have the same HESE-detection efficiency as IceCube. Left: Evolution of discovery potential with time, using combined detector exposure. Start times and sizes of upcoming telescopes are estimates for their final configurations (their vertical placements do not convey exposure or evidence). Right: Best-fit and 68% allowed ranges of the one- and two-component flux fits for snapshots A–D. A prominent PeV bump may be discovered decisively already by 2027, by combining IceCube, Baikal-GVD, and KM3NeT. (In contrast, constraining or discovering subdominant bumps will require adding more detectors; see Section V.) See Section IV for details.
|
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200
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I
| 9
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Table
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{
"x1": 53.64,
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TABLE I. Free model parameters, their priors, best-fit values and allowed ranges, from a fit to the IceCube 7.5-year HESE event sample [7, 64]. Allowed parameter ranges are 68% one-dimensional marginalized credible intervals. Results are for fits with a pure power law (“Pure PL”), a power law with an exponential cut-off (“PLC”), and a power law with a cut-off plus a bump (“PLC + B”). The former two serve as validation of our method; we find parameter values similar to Ref. [7]. For the latter, we only show the values of the parameters that maximize the posterior, Eq. (9). (We keep some nuisance parameters of the original HESE analysis[7] fixed to their nominal values.) See Sections III E and IV A for details.
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200
|
5
| 13
|
Figure
|
{
"x1": 320.03999999999996,
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|
FIG. 5. Upper limits on the height of a bump in the diffuse flux of high-energy astrophysical neutrinos. The bump flux component, Eq. (2), is centered at energy Eν,bump, has height E2ν,bumpΦν,bump, and width αbump = 1, and is overlaid on a power-law flux ∝ E−γν eEν/Eν,cut , with parameter values given by the best fit to the 7.5-year IceCube HESE sample [7] (“PLC” in Table I), shown for comparison. See Section II D and Fig. 3 for the definitions of the flux components. Today, IceCube limits the height of a bump centered at a few hundred TeV to be, at most, comparable to the size of the dominant power-law component. In the future, the upper limit may be tightened to tens of percent of the power-law component. Figure 6 shows how this translates into constraints on candidate neutrino source populations. See Section III for the statistical analysis and Section V A for details on this plot.
|
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200
|
4
| 12
|
Figure
|
{
"x1": 56.879999999999995,
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|
FIG. 4. Projected HESE event rates by the year 2035. The combined detector exposure is due to all the neutrino telescopes expected at that time (see Fig. 1): Baikal-GVD [70, 71], IceCube, IceCube-Gen2 [174], KM3NeT [72–74], P-ONE [175], TAMBO [176], and TRIDENT [177]. Events are distributed in reconstructed deposited energy (left) and reconstructed direction (right). Top: Assuming a power law with a high-energy cut-off, with flux parameters fixed at their present-day best-fit values (“PLC” in Table I). Bottom: Assuming a power law with a high-energy cut-off plus a PeV bump, with flux parameters fixed at their present-day best-fit values (“PLC + B” in Table I). The HESE-detection efficiency of upcoming detectors is assumed to be equal to that of IceCube today [7]; their combined exposure by 2035 is equivalent to 159 years of IceCube exposure.
|
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200
|
8
| 16
|
Figure
|
{
"x1": 319.68,
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|
FIG. 8. Illustration of the separation between a one-component vs. a two-component fit. We assume as the true flux, picked from Fig. 7 (marked with therein), a bump with normalization E2ν,bumpΦν,bump = 3.6× 10−8 GeV cm−2 s−1 sr−1, width αbump = 1, and centered at energy Eν,bump = 141 TeV. From top to bottom, the snapshots and corresponding combined detector exposure here are the same as in Figs. 5 and 7. See Section III for the statistical analysis and Section V C for details on this plot.
|
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200
|
7
| 16
|
Figure
|
{
"x1": 56.879999999999995,
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FIG. 7. Projected discovery potential of a bump in the diffuse flux of high-energy neutrinos. The bump flux component, Eq. (2), is centered at energy Eν,bump, has height E2ν,bumpΦν,bump, and width αbump = 1, and is overlaid on a power-law flux ∝ E−γν eEν/Eν,cut , with parameter values given by the best fit to the 7.5-year IceCube HESE sample [7] (“PLC” in Table I), shown for comparison. The Bayes factor that quantifies the discovery potential, Eq. (11), is obtained in a two-component flux fit to projected event distributions, and is marginalized over the power-law flux parameters. Figure 5 shows a corresponding plot of bump constraints; from top to bottom, the snapshots here are the same as in that figure. Decisive discovery of a subdominant bump may be achieved by 2035, using IceCube-Gen2 or, more prominently, using all planned upcoming neutrino telescopes available at the time (see Fig. 1). See Section III for the statistical analysis and Section V C for details on this plot. The white star ( ) marks the bump flux parameters chosen to make Fig. 8.
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200
|
6
| 15
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Figure
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{
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FIG. 6. Upper limits on the local (i.e., redshift z = 0) high-energy neutrino luminosity density of steady-state source candidates. Our new limits apply to pγ source populations that emit a diffuse neutrino spectrum with a bump centered at Eν,bump = 1 PeV and with width αbump = 1; they are interpretations of the limits from Fig. 5. Within a population, all sources are identical; they have the same neutrino luminosity in their rest frame. We show candidate source classes without distinction between mostly pp and mostly pγ sources. In each panel, the neutrino luminosity density evolves with redshift differently: no evolution (left), star-formation rate (SFR) evolution (center), and strong (FSRQ-like) evolution (right); see Appendix A. For each source class, its local luminosity density is chosen to saturate the present-day high-energy neutrino flux [185]. Our limits put this assumption to test. Limits from searches for point neutrino sources are from Ref. [174]. Our limits show that by 2035 the combined exposure IceCube plus IceCube-Gen2, or of all available detectors, could constrain the source luminosity density of pγ to a fraction of what is needed to saturate the diffuse flux at 1 PeV. See Section V B for details.
|
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|
{
"x1": 54,
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"y1": 272.63079833984375,
"y2": 371.260986328125
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|
200
|
1
| 0
|
Figure
|
{
"x1": 324.71999999999997,
"x2": 554.04,
"y1": 335.88,
"y2": 427.32
}
|
FIG. 1: Schematic diagram of GW echoes (stimulated Hawking radiation) from remnant of a BBH merger.
|
[] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00025_1762333195/figures/2301.00025-Figure1-1.png
|
{
"x1": 321.73199462890625,
"x2": 557.376220703125,
"y1": 439.4617004394531,
"y2": 455.8999938964844
}
|
200
|
6
| 5
|
Figure
|
{
"x1": 56.879999999999995,
"x2": 295.2,
"y1": 51.839999999999996,
"y2": 198
}
|
FIG. 6: Posterior for extracted parameters Ā and σ from target distribution P̄(A, Ā, σ) for 47 events conducted in this paper.
|
[] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00025_1762333195/figures/2301.00025-Figure6-1.png
|
{
"x1": 63.6150016784668,
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"y1": 211.68270874023438,
"y2": 239.57794189453125
}
|
200
|
7
| 5
|
Figure
|
{
"x1": 323.64,
"x2": 563.04,
"y1": 52.919999999999995,
"y2": 219.95999999999998
}
|
FIG. 7: Histograms to quantify false positive (GR injections) and true positive (GR+echo injections). Comparing to the GW190521 echo, we obtain their values as 1.46+1.17−0.875%, and 34.5± 7.3% respectively.
|
[
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|
{
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200
|
2
| 1
|
Figure
|
{
"x1": 59.76,
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|
FIG. 2: Boltzmann GW echoes template for GW150914 like signal with amplitude A = 1.
|
[] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00025_1762333195/figures/2301.00025-Figure2-1.png
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|
200
|
I
| 3
|
Table
|
{
"x1": 90.72,
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"y2": 504
}
|
TABLE I: Results of Bayes factor for GW echoes in GWTC-1, GWTC-2, and GWTC-3 events. Positive value of the log10 Bayes factor indicates a preference for the GR+echoes model over GR model, while the negative value suggests instead a preference for the GR model over the GR+echoes model. Here GW190521 shows loudest echo. Here based on [49] all the individual events appear as inconclusive to both GR or GR+echoes with GW190521 as exception! (see Fig. 4).
|
[
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{
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|
200
|
3
| 3
|
Figure
|
{
"x1": 59.76,
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"y2": 219.23999999999998
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|
FIG. 3: (a): Combined Bayes factor density in terms of amplitude for 47 events. Combined events give an overall
|
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|
{
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|
200
|
4
| 4
|
Figure
|
{
"x1": 60.839999999999996,
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|
FIG. 4: Histogram of log10 Bayes factors of 47 events in Table I. Vertical regions identify Jeffreys scale for interpretation of Bayes factor [49].
|
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|
{
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|
200
|
8
| 42
|
Table
|
{
"x1": 77.75999999999999,
"x2": 542.16,
"y1": 46.8,
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}
|
Table 8: The energies, E(R), of the lightest six flux tube states with length R in the sector q = 1 (+).
|
[
"0.4899(45)",
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"0.6680(73)",
"0.6693(192)",
"0.8066(195)",
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"0.5236(92)",
"0.6141(132)",
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"0.5905(93)",
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"75",
"0.5595(72)",
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"l⊥",
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"aE(R)",
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"q",
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"(+)",
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/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00034_1762333206/figures/2301.00034-Table8-1.png
|
{
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"y1": 628.0744018554688,
"y2": 648.5040283203125
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|
200
|
8
| 24
|
Figure
|
{
"x1": 82.08,
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"y1": 47.879999999999995,
"y2": 315.71999999999997
}
|
Figure 8: Energy differences with the ground state for q = 1 excited states in the (+) (blue dots) and (−) (brown dots) parity sectors as a function of string circumference at different string lengths. Blue curves show energies of the (1, 0), (2, 1) and (3, 2) GGRT levels. A red curve shows an estimate for the resonance state using the resonance mass (31).
|
[
"R/`s",
"∆E`s",
"10",
"9",
"8",
"7",
"6",
"5",
"2",
"3",
"4",
"5"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00034_1762333206/figures/2301.00034-Figure8-1.png
|
{
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|
200
|
9
| 25
|
Figure
|
{
"x1": 102.24,
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|
Figure 9: The effective mass computed as in formula (19) as a function of time, for the first, second and third excited states in the q = 0 (++) sector and compactification length R = 40a, represented as blue, yellow, green dots, and for the ground state, first and second excited states in the q = 0 (−+) sector and compactification length R = 60a, represented as blue, yellow and green “∗”. The horizontal solid lines in dark colors are the fitted value of the mass of the corresponding states. The shaded bands in light colors represents ±1 standard deviations.
|
[
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"*",
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|
{
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|
200
|
1
| 14
|
Figure
|
{
"x1": 166.68,
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"y1": 45.72,
"y2": 140.04
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|
Figure 1: Increasing the blocking level of a link by one.
|
[] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00034_1762333206/figures/2301.00034-Figure1-1.png
|
{
"x1": 167.8800048828125,
"x2": 451.3163146972656,
"y1": 153.15740966796875,
"y2": 159.1409912109375
}
|
200
|
2
| 14
|
Figure
|
{
"x1": 184.68,
"x2": 430.2,
"y1": 367.91999999999996,
"y2": 468.35999999999996
}
|
Figure 2: For an Abelian gauge group there is no sharp distinction between string excitations and additional glueballs.
|
[
"For",
"an",
"Abelian",
"gauge",
"group"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00034_1762333206/figures/2301.00034-Figure2-1.png
|
{
"x1": 86.1729965209961,
"x2": 533.022705078125,
"y1": 504.7804260253906,
"y2": 525.2100219726562
}
|
200
|
3
| 20
|
Table
|
{
"x1": 145.79999999999998,
"x2": 473.03999999999996,
"y1": 45.72,
"y2": 328.32
}
|
Table 3: The spectrum of Z2 glueballs in the 0+ sector at β = 0.756321 for different lattice sizes.
|
[
"Fitted",
"masses",
"0.2159(4)",
"0.3937(16)",
"0.5359(27)",
"25",
"0.1978(28)",
"0.2531(91)",
"0.3519(75)*",
"30",
"0.2075(30)",
"0.2992(87)",
"0.3726(110)*",
"35",
"0.2163(16)",
"0.3635(51)",
"0.4528(117)*",
"40",
"0.2170(15)",
"0.3804(81)",
"0.5097(95)",
"45",
"0.2144(17)",
"0.3896(54)",
"0.5329(100)",
"47",
"0.2118(14)",
"0.3865(96)",
"0.5319(115)",
"50",
"0.2159(20)",
"0.3742(62)",
"0.5019(166)",
"52",
"0.2131(22)",
"0.3920(52)",
"0.5237(93)",
"54",
"0.2182(12)",
"0.3899(89)",
"0.5141(93)",
"55",
"0.2141(20)",
"0.3990(40)",
"0.5326(108)",
"56",
"0.2169(18)",
"0.3953(44)",
"0.5462(59)",
"58",
"0.2152(22)",
"0.3849(66)",
"0.4947(158)",
"60",
"0.2178(20)",
"0.3998(52)",
"0.5080(154)",
"65",
"0.2138(20)",
"0.3906(64)",
"0.5153(182)",
"70",
"0.2168(11)",
"0.3984(61)",
"0.5497(67)",
"75",
"0.2159(17)",
"0.4025(44)",
"0.5541(66)",
"80",
"0.2175(17)",
"0.3886(73)",
"0.5216(144)",
"70×",
"70",
"(ly/a)×",
"(lt/a)",
"lx/a",
"aE;",
"0+"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00034_1762333206/figures/2301.00034-Table3-1.png
|
{
"x1": 86.1729965209961,
"x2": 533.0330810546875,
"y1": 341.7374267578125,
"y2": 362.1670227050781
}
|
200
|
12
| 29
|
Figure
|
{
"x1": 59.04,
"x2": 523.0799999999999,
"y1": 182.88,
"y2": 476.28
}
|
Figure 12: Energies in the q = 0 (−−) sector at R = 40a = 2.76ls as a function of inverse transverse size. Horizontal lines of different colors represent the GGRT spectrum starting with N = Ñ = 2.
|
[
"1/l⊥",
"√",
"σ",
"E/",
"√",
"σ",
"12",
"11",
"10",
"9",
"8",
"0.05",
"0.10",
"0.15",
"0.20",
"0.25"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00034_1762333206/figures/2301.00034-Figure12-1.png
|
{
"x1": 86.17300415039062,
"x2": 533.025146484375,
"y1": 490.49139404296875,
"y2": 525.3670043945312
}
|
200
|
11
| 28
|
Figure
|
{
"x1": 59.04,
"x2": 523.0799999999999,
"y1": 46.8,
"y2": 339.84
}
|
Figure 11: Energies in the q = 0 (−+) sector at R = 40a = 2.76ls as a function of the inverse transverse size. Horizontal lines of different colors represent the GGRT spectrum starting with N = Ñ = 2.
|
[
"1/l⊥",
"√",
"σ",
"E/",
"√",
"σ",
"10",
"9",
"8",
"7",
"6",
"0.05",
"0.10",
"0.15",
"0.20",
"0.25"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00034_1762333206/figures/2301.00034-Figure11-1.png
|
{
"x1": 86.1729736328125,
"x2": 533.0297241210938,
"y1": 354.1924133300781,
"y2": 389.0670166015625
}
|
200
|
4
| 38
|
Table
|
{
"x1": 126.72,
"x2": 493.2,
"y1": 47.879999999999995,
"y2": 516.24
}
|
Table 4: The energies, E(R), of the lightest seven flux tube states with length R in the sector q = 0 (++).
|
[
"40",
"55×",
"55",
"0.1731(19)",
"0.3514(57)",
"0.4407(90)",
"0.5443(86)",
"0.5715(177)",
"0.5694(118)",
"0.6240(146)",
"40",
"55×",
"70",
"0.1766(14)",
"0.3678(43)",
"0.4517(82)",
"0.5497(72)",
"0.5847(159)",
"0.5800(81)",
"40",
"65×",
"70",
"0.1772(17)",
"0.3662(70)",
"0.4162(133)",
"0.5506(69)",
"0.5665(136)",
"0.6653(87)",
"0.5415(176)",
"40",
"80×",
"70",
"0.1780(17)",
"0.3817(50)",
"0.4540(130)",
"0.5556(40)",
"0.4818(108)",
"0.6378(96)",
"0.6385(98)",
"40",
"160×",
"70",
"0.1768(15)",
"0.3772(44)",
"0.4660(61)",
"0.5607(41)",
"0.4972(94)",
"0.6469(57)",
"0.5515(104)*",
"40",
"300×",
"70",
"0.1770(13)",
"0.3767(21)",
"0.4557(63)",
"0.5449(48)",
"0.4928(96)",
"0.6332(122)",
"0.5611(103)*",
"0.7849(126)*",
"80",
"0.3745(64)",
"0.5093(75)",
"0.6069(132)",
"0.6197(157)",
"0.7463(152)*",
"0.6921(121)*",
"0.7561(118)*",
"75",
"0.3586(38)",
"0.5012(68)",
"0.6167(96)",
"0.6058(77)",
"0.7401(114)",
"0.6483(144)*",
"0.6858(174)*",
"70",
"0.3238(45)",
"0.4678(61)",
"0.5612(149)",
"0.5935(85)",
"0.6718(202)*",
"0.6567(137)*",
"0.6680(199)*",
"60",
"0.2819(29)",
"0.4404(72)",
"0.5412(138)",
"0.5701(75)",
"0.6386(207)",
"0.6543(88)",
"0.7048(96)",
"65",
"0.3085(31)",
"0.4640(60)",
"0.5683(116)",
"0.5850(83)",
"0.6663(122)",
"0.6375(113)*",
"25",
"0.0966(11)",
"0.3022(50)",
"0.3664(58)",
"0.4873(87)",
"0.5895(290)",
"0.5649(175)",
"0.5338(138)",
"30",
"0.1211(17)",
"0.3251(65)",
"0.3917(82)",
"0.5151(65)",
"0.5884(62)",
"0.4929(117)",
"0.5838(164)*",
"35",
"0.1506(13)",
"0.3456(134)",
"0.4167(126)",
"0.5460(60)",
"0.5479(135)",
"0.5542(117)",
"0.5416(161)",
"40",
"0.1785(14)",
"0.3766(60)",
"0.4318(124)",
"0.5439(80)",
"0.5123(161)",
"0.6392(117)",
"0.5854(80)*",
"45",
"0.2037(19)",
"0.3827(97)",
"0.4444(208)",
"0.5436(87)",
"0.5533(242)",
"0.6279(130)",
"0.5464(177)*",
"47",
"0.2143(12)",
"0.3969(35)",
"0.4737(101)",
"0.5448(69)",
"0.5596(147)",
"0.6539(64)",
"0.6010(69)",
"50",
"0.2255(34)",
"0.4002(58)",
"0.4997(108)",
"0.5599(52)",
"0.5850(154)",
"0.6507(96)",
"0.6282(109)",
"52",
"0.2339(19)",
"0.4118(65)",
"0.5009(92)",
"0.5634(59)",
"0.5813(198)",
"0.6407(139)",
"0.6327(67)*",
"54",
"0.2492(27)",
"0.4239(61)",
"0.5285(66)",
"0.5537(92)",
"0.6113(122)",
"0.6650(62)",
"0.6441(57)*",
"55",
"0.2500(29)",
"0.4106(100)",
"0.4715(280)",
"0.5600(61)",
"0.5612(242)",
"0.6571(100)",
"0.6259(72)",
"56",
"0.2571(26)",
"0.4214(66)",
"0.5043(117)",
"0.5583(45)",
"0.6008(169)",
"0.6671(46)*",
"58",
"0.2686(19)",
"0.4409(33)",
"0.5278(106)",
"0.5609(70)",
"0.6136(139)",
"0.0668(8)",
"0.2384(46)",
"0.3460(49)",
"0.4893(47)",
"0.4882(69)",
"0.4996(199)*",
"0.6339(109)",
"70×",
"70",
"20",
"R/a",
"l⊥",
"×",
"lt/a2",
"aE(R)",
";",
"q",
"=",
"0",
"(++)"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00034_1762333206/figures/2301.00034-Table4-1.png
|
{
"x1": 84.76200103759766,
"x2": 531.6190185546875,
"y1": 526.4443969726562,
"y2": 546.873046875
}
|
200
|
6
| 21
|
Figure
|
{
"x1": 77.03999999999999,
"x2": 511.2,
"y1": 46.8,
"y2": 317.52
}
|
Figure 6: Energy differences with the ground state for q = 0 excited states in the (++) parity sector as a function of string circumference at different string lengths. Blue curves are the (1, 1) and (2, 2) GGRT levels. The red horizontal line is the fitted resonance mass.
|
[
"R/`s",
"∆E`s",
"6",
"5",
"4",
"3",
"2",
"1",
"2",
"3",
"4",
"5",
"0"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00034_1762333206/figures/2301.00034-Figure6-1.png
|
{
"x1": 86.17301940917969,
"x2": 533.0321655273438,
"y1": 331.9294128417969,
"y2": 366.8050231933594
}
|
200
|
15
| 33
|
Figure
|
{
"x1": 59.04,
"x2": 523.0799999999999,
"y1": 160.92,
"y2": 454.68
}
|
Figure 15: Energies in the q = 0 (++) sector at R = 55a = 3.80ls as a function of inverse transverse size determined using an extended operator basis. Horizontal solid lines of different colors represent the GGRT spectrum starting from N = Ñ = 0. The lower dashed blue line represents the energy of the absolute ground state plus the glueball mass. The upper dashed blue line represents the absolute ground state plus the resonance mass as given by (31).
|
[
"1/l⊥",
"√",
"σ",
"E/",
"√",
"σ",
"10",
"8",
"6",
"4",
"2",
"0.05",
"0.10",
"0.15",
"0.20",
"0.25",
"0"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00034_1762333206/figures/2301.00034-Figure15-1.png
|
{
"x1": 86.17300415039062,
"x2": 533.0322265625,
"y1": 468.8224182128906,
"y2": 547.0350341796875
}
|
200
|
7
| 41
|
Table
|
{
"x1": 148.68,
"x2": 470.15999999999997,
"y1": 148.68,
"y2": 512.28
}
|
Table 7: The energies, E(R), of the lightest three flux tube states with length R in the sector q = 0 (−−).
|
[
"70×",
"70",
"0.7911(92)",
"0.8396(220)",
"0.8715(63)",
"25",
"0.6850(68)",
"0.7588(50)",
"0.7775(99)",
"30",
"0.6349(27)",
"0.7458(84)",
"0.9011(484)",
"35",
"0.6008(74)",
"0.6935(170)",
"40",
"0.5763(71)",
"0.6459(125)",
"0.6780(171)",
"45",
"0.5709(35)",
"0.6772(161)",
"0.7331(108)",
"47",
"0.5615(41)",
"0.6669(127)",
"0.7235(166)",
"50",
"0.5664(64)",
"0.6833(121)",
"0.7018(168)*",
"52",
"0.5707(69)",
"0.6595(131)",
"0.7488(163)",
"54",
"0.5704(51)",
"0.6867(87)",
"0.7153(130)*",
"55",
"0.5784(56)",
"0.6894(150)",
"0.7056(159)*",
"56",
"0.5827(51)",
"0.6697(186)",
"0.7709(76)*",
"58",
"0.5731(61)",
"0.7214(104)",
"0.7735(71)*",
"60",
"0.5838(62)",
"0.6984(169)",
"0.8113(54)*",
"65",
"0.5877(70)",
"0.7686(62)",
"0.7783(365)*",
"70",
"0.6121(77)",
"0.7115(210)*",
"75",
"0.6286(72)",
"0.6914(222)*",
"80",
"0.6424(80)",
"0.7357(326)*",
"40",
"55×",
"55",
"0.5763(50)",
"0.6136(100)",
"0.7731(133)",
"40",
"55×",
"70",
"0.5597(112)",
"0.6315(82)",
"0.7454(217)",
"40",
"65×",
"70",
"0.5768(47)",
"0.6218(129)",
"0.6967(191)",
"40",
"80×",
"70",
"0.5706(131)",
"0.6211(192)",
"0.7599(241)",
"40",
"160×",
"70",
"0.5805(47)",
"0.6568(103)",
"0.7938(270)",
"40",
"300×",
"70",
"0.5875(34)",
"0.6772(116)",
"0.8248(115)",
"R/a",
"l⊥",
"×",
"lt/a2",
"aE(R)",
";",
"q",
"=",
"0",
"(−−)",
"20"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00034_1762333206/figures/2301.00034-Table7-1.png
|
{
"x1": 86.17294311523438,
"x2": 533.0305786132812,
"y1": 525.7584228515625,
"y2": 546.18798828125
}
|
200
|
4
| 17
|
Figure
|
{
"x1": 108.72,
"x2": 474.12,
"y1": 45.72,
"y2": 548.28
}
|
Figure 4: The effective mass computed as in formula (19) as a function of time for the absolute ground states at string circumference R/a = 20, 40, 60, 80, represented as blue, yellow, green and red dots. The horizontal solid lines are the resulting fitted values of the state’s energies. The shaded bands represent the corresponding 1σ uncertainty intervals.
|
[
"t/a",
"aE(t)",
"0.5",
"0.4",
"0.3",
"0.2",
"0.1",
"0.0",
"0",
"2",
"4",
"6",
"8",
"10",
"12"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00034_1762333206/figures/2301.00034-Figure4-1.png
|
{
"x1": 86.17294311523438,
"x2": 533.0321044921875,
"y1": 562.6294555664062,
"y2": 626.39599609375
}
|
200
|
10
| 27
|
Figure
|
{
"x1": 59.04,
"x2": 523.0799999999999,
"y1": 76.67999999999999,
"y2": 370.08
}
|
Figure 10: Energies in the q = 0 (++) sector at R = 40a = 2.76ls as a function of the inverse transverse size. Horizontal lines of different colors represent the GGRT spectrum starting with N = Ñ = 0. The brown dashed line represents the resonance mass.
|
[
"1/l⊥",
"√",
"σ",
"E/",
"√",
"σ",
"10",
"8",
"6",
"4",
"2",
"0.05",
"0.10",
"0.15",
"0.20",
"0.25",
"0"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00034_1762333206/figures/2301.00034-Figure10-1.png
|
{
"x1": 86.1729736328125,
"x2": 533.0321655273438,
"y1": 384.2794189453125,
"y2": 419.1540222167969
}
|
200
|
5
| 39
|
Table
|
{
"x1": 201.95999999999998,
"x2": 417.24,
"y1": 148.68,
"y2": 512.28
}
|
Table 5: The energies, E(R), of the lightest flux tube state with length R in the sector q = 0 (+−).
|
[
"70×",
"70",
"0.9337(259)",
"25",
"0.8790(60)",
"30",
"0.8055(221)",
"35",
"0.7678(83)",
"40",
"0.7155(172)",
"45",
"0.7316(80)*",
"47",
"0.7392(99)*",
"50",
"0.7520(115)",
"52",
"0.7487(105)",
"54",
"0.6905(208)",
"55",
"0.7501(123)*",
"56",
"0.7272(85)",
"58",
"0.7644(55)*",
"60",
"0.7189(112)*",
"65",
"0.7264(132)*",
"70",
"0.7528(53)*",
"75",
"0.7401(159)*",
"80",
"0.7242(126)*",
"40",
"55×",
"55",
"0.7458(198)",
"40",
"55×",
"70",
"0.7513(183)",
"40",
"65×",
"70",
"0.7518(79)",
"40",
"80×",
"70",
"0.7478(80)",
"40",
"160×",
"70",
"0.7215(185)",
"40",
"300×",
"70",
"0.7389(79)",
"R/a",
"l⊥",
"×",
"lt/a2",
"aE(R)",
";",
"q",
"=",
"0",
"(+−)",
"20"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00034_1762333206/figures/2301.00034-Table5-1.png
|
{
"x1": 86.1729965209961,
"x2": 533.0309448242188,
"y1": 525.7584228515625,
"y2": 546.18798828125
}
|
200
|
16
| 35
|
Figure
|
{
"x1": 59.04,
"x2": 524.16,
"y1": 171,
"y2": 463.68
}
|
Figure 16: Energies in the q = 0 (−+) sector at R = 55a = 3.80ls as a function of the inverse transverse size determined using an extended operator basis. Horizontal solid lines of different colors represent the GGRT spectrum starting from N = Ñ = 2. The dashed green line represents the energy of absolute ground state plus glueball mass.
|
[
"1/l⊥",
"√",
"σ",
"E/",
"√",
"σ",
"10",
"9",
"8",
"7",
"0.05",
"0.10",
"0.15",
"0.20",
"0.25"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00034_1762333206/figures/2301.00034-Figure16-1.png
|
{
"x1": 86.1729736328125,
"x2": 533.0325317382812,
"y1": 477.9064025878906,
"y2": 527.22802734375
}
|
200
|
2
| 16
|
Table
|
{
"x1": 133.92,
"x2": 485.28,
"y1": 177.84,
"y2": 213.12
}
|
Table 2: Basic parameters of our simulation: the value of the coupling and its critical value, the range of the string circumference and its critical value, the string tension and the lightest glueball mass.
|
[
"0.756321",
"0.7614133(22)",
"[20,80]",
"∼",
"11.8",
"0.0691(1)",
"0.2159(4)",
"β",
"βc",
"R/a",
"Rc/a",
"a/`s",
"amG"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00034_1762333206/figures/2301.00034-Table2-1.png
|
{
"x1": 86.1729965209961,
"x2": 533.0297241210938,
"y1": 226.929443359375,
"y2": 261.80499267578125
}
|
200
|
14
| 31
|
Figure
|
{
"x1": 59.04,
"x2": 523.0799999999999,
"y1": 182.88,
"y2": 476.28
}
|
Figure 14: Energies in the q = 1 (−) sector at R = 40a = 2.76ls as a function of the inverse transverse size. Horizontal lines of different colors represent the GGRT spectrum starting from N = 1, Ñ = 0.
|
[
"1/l⊥",
"√",
"σ",
"E/",
"√",
"σ",
"10",
"8",
"6",
"4",
"2",
"0.05",
"0.10",
"0.15",
"0.20",
"0.25",
"0"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00034_1762333206/figures/2301.00034-Figure14-1.png
|
{
"x1": 86.17300415039062,
"x2": 533.02978515625,
"y1": 490.49139404296875,
"y2": 525.3670043945312
}
|
200
|
9
| 43
|
Table
|
{
"x1": 107.64,
"x2": 512.28,
"y1": 45.72,
"y2": 601.1999999999999
}
|
Table 9: The energies, E(R), of the lightest six flux tube states with length R in the sector q = 1 (−).
|
[
"65",
"0.4058(23)",
"0.5346(49)",
"0.6342(53)",
"0.6606(68)",
"0.6921(83)",
"0.6810(170)*",
"70",
"0.4230(26)",
"0.5555(52)",
"0.6418(222)",
"0.6895(86)",
"0.7063(61)*",
"75",
"0.4357(42)",
"0.5623(97)",
"0.6660(86)",
"0.7014(84)*",
"80",
"0.4572(45)",
"0.5701(84)",
"0.7048(69)",
"0.7088(93)*",
"40",
"55×",
"55",
"0.3424(17)",
"0.4991(64)",
"0.6044(67)",
"0.6363(98)",
"0.6713(104)",
"0.7215(61)",
"40",
"55×",
"70",
"0.3429(14)",
"0.4994(45)",
"0.6061(59)",
"0.6152(137)",
"0.6743(124)",
"0.6909(95)",
"40",
"65×",
"70",
"0.3420(19)",
"0.4876(47)",
"0.5947(123)",
"0.6052(27)",
"0.6154(93)",
"0.7075(118)",
"40",
"80×",
"70",
"0.3375(23)",
"0.4890(31)",
"0.5483(89)",
"0.6091(53)",
"0.6414(87)",
"0.7307(51)",
"40",
"160×",
"70",
"0.3426(11)",
"0.4855(31)",
"0.5294(73)",
"0.5975(59)",
"0.5975(32)",
"0.7095(98)",
"40",
"300×",
"70",
"0.3375(17)",
"0.4843(34)",
"0.5386(47)",
"0.5863(45)",
"0.5760(66)",
"0.7030(81)",
"0.6740(113)*",
"56",
"0.3741(24)",
"0.5116(38)",
"0.6230(35)*",
"0.6196(68)",
"0.6727(58)",
"0.6947(70)",
"58",
"0.3840(22)",
"0.5163(41)",
"0.6030(72)",
"0.6296(59)",
"0.6812(64)",
"0.6810(68)*",
"60",
"0.3899(20)",
"0.5221(54)",
"0.5940(135)",
"0.6431(77)",
"0.6850(56)",
"0.7166(110)*",
"54",
"0.3700(17)",
"0.5075(33)",
"0.6171(53)",
"0.6229(55)",
"0.6671(73)",
"0.6819(52)",
"55",
"0.3681(35)",
"0.5033(59)",
"0.6040(70)",
"0.6162(47)",
"0.6852(65)",
"0.6595(143)*",
"25",
"0.3621(16)",
"0.4946(58)",
"0.6232(78)",
"0.6326(65)",
"0.6182(84)",
"0.7189(66)",
"30",
"0.3448(16)",
"0.4861(50)",
"0.5896(73)",
"0.5737(180)",
"0.6070(159)",
"0.6968(108)",
"35",
"0.3382(19)",
"0.4886(37)",
"0.5600(89)",
"0.6152(71)",
"0.5959(140)*",
"0.6828(114)",
"40",
"0.3403(14)",
"0.4855(52)",
"0.5741(107)",
"0.6100(70)",
"0.6154(54)",
"0.7201(63)",
"45",
"0.3467(23)",
"0.4857(53)",
"0.5562(93)",
"0.6007(69)",
"0.6247(107)",
"0.6813(228)",
"47",
"0.3524(21)",
"0.4953(31)",
"0.5891(51)",
"0.6019(50)",
"0.6478(58)",
"0.6982(81)",
"50",
"0.3577(24)",
"0.4911(59)",
"0.5963(74)",
"0.5999(59)",
"0.6490(71)",
"0.6966(58)",
"52",
"0.3665(23)",
"0.5012(58)",
"0.6073(41)",
"0.6179(61)",
"0.6777(79)",
"0.4025(14)",
"0.5260(73)",
"0.6537(90)",
"0.6300(52)",
"0.6813(202)",
"0.7666(70)",
"70×",
"70",
"20",
"R/a",
"l⊥",
"×",
"lt/a2",
"aE(R)",
";",
"q",
"=",
"1",
"(−)"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00034_1762333206/figures/2301.00034-Table9-1.png
|
{
"x1": 84.51300048828125,
"x2": 531.3681030273438,
"y1": 612.6714477539062,
"y2": 633.1010131835938
}
|
200
|
6
| 40
|
Table
|
{
"x1": 72,
"x2": 547.1999999999999,
"y1": 148.68,
"y2": 512.28
}
|
Table 6: The energies, E(R), of the lightest four flux tube states (for 40× 160× 70 it is five) with length R in the sector q = 0 (−+).
|
[
"70×",
"70",
"0.4497(43)",
"0.6023(116)",
"0.6516(268)",
"0.9297(72)",
"25",
"0.4572(88)",
"0.5693(87)",
"0.7823(110)",
"0.8336(357)",
"30",
"0.4634(65)",
"0.5525(107)",
"0.7294(197)",
"0.7506(230)*",
"35",
"0.4784(45)",
"0.5851(41)",
"0.7281(41)",
"0.7736(329)",
"40",
"0.4686(65)",
"0.5666(73)",
"0.7019(137)",
"0.7166(222)*",
"45",
"0.4925(54)",
"0.5682(177)",
"0.6753(100)",
"0.7935(123)",
"47",
"0.5095(46)",
"0.5961(98)",
"0.6698(121)",
"0.7487(241)*",
"50",
"0.5261(52)",
"0.5991(87)",
"0.6866(71)",
"0.7826(102)",
"52",
"0.5364(59)",
"0.6139(58)*",
"0.6904(88)",
"0.7770(115)",
"54",
"0.5310(64)",
"0.6063(100)*",
"0.6897(69)",
"0.8138(53)",
"55",
"0.5405(56)",
"0.6393(63)",
"0.6994(91)",
"0.7418(258)*",
"56",
"0.5561(57)",
"0.6405(58)",
"0.6923(84)",
"0.7685(137)*",
"58",
"0.5467(39)",
"0.6314(62)",
"0.6979(83)",
"0.7007(83)",
"60",
"0.5717(44)",
"0.6331(78)",
"0.6604(148)*",
"0.8186(61)",
"65",
"0.5795(60)",
"0.6652(71)*",
"0.6964(108)*",
"70",
"0.6059(40)",
"0.7006(330)",
"0.7084(104)*",
"75",
"0.6259(38)",
"0.6874(218)*",
"0.7141(98)*",
"80",
"0.6177(125)",
"0.7305(118)*",
"0.7384(73)*",
"40",
"55×",
"55",
"0.5278(42)",
"0.6653(115)",
"0.7093(101)",
"40",
"55×",
"70",
"0.5308(62)",
"0.6988(136)",
"0.7007(83)",
"40",
"65×",
"70",
"0.5052(53)",
"0.5939(80)",
"0.7149(90)",
"0.7571(208)",
"40",
"80×",
"70",
"0.4801(83)",
"0.5430(71)",
"0.7136(66)",
"0.6882(161)",
"40",
"160×",
"70",
"0.4848(53)",
"0.4733(55)",
"0.5400(80)*",
"0.7147(142)",
"0.5930(135)*",
"40",
"300×",
"70",
"0.4836(32)",
"0.4694(82)",
"0.5325(92)*",
"0.6608(146)",
"R/a",
"l⊥",
"×",
"lt/a2",
"aE(R)",
";",
"q",
"=",
"0",
"(−+)",
"20"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00034_1762333206/figures/2301.00034-Table6-1.png
|
{
"x1": 86.1729736328125,
"x2": 533.0252075195312,
"y1": 525.7584228515625,
"y2": 546.18798828125
}
|
200
|
7
| 23
|
Figure
|
{
"x1": 82.08,
"x2": 511.2,
"y1": 46.8,
"y2": 314.64
}
|
Figure 7: Energy differences with the ground state for q = 0 excited states in the (−+) (blue dots) and (−−) (brown dots) parity sectors as a function of string circumference at different string lengths. The blue curve is the energy of the (2, 2) GGRT level.
|
[
"R/`s",
"∆E`s",
"10",
"8",
"6",
"4",
"2",
"3",
"4",
"5"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00034_1762333206/figures/2301.00034-Figure7-1.png
|
{
"x1": 86.17294311523438,
"x2": 533.027587890625,
"y1": 328.94842529296875,
"y2": 363.82403564453125
}
|
200
|
1
| 8
|
Table
|
{
"x1": 113.75999999999999,
"x2": 508.32,
"y1": 114.83999999999999,
"y2": 562.3199999999999
}
|
Table 1: Table with the states of the lowest GGRT levels with q = 0, 1 and Nl+Nr ≤ 6.
|
[
"+",
"a3a−2|0〉",
"+",
"a2a1a−1a−1|0〉",
"+",
"a1a1a1a−2|0〉",
"−",
"a3a−1a−1|0〉",
"−",
"a2a1a−2|0〉",
"−",
"a1a1a1a−1a−1|0〉",
"Nl",
"=",
"3,",
"Nr",
"=",
"2",
"Nl",
"=",
"2,",
"Nr",
"=",
"1",
"+",
"a2a−1|0〉",
"−",
"a1a1a−1|0〉",
"Nl",
"=",
"1,",
"Nr",
"=",
"0",
"−",
"a1|0〉",
"Nl,",
"Nr",
"Pt",
"GGRT",
"States",
"q",
"=",
"1",
"++",
"a3a−3|0〉",
"++",
"a2a1a−2a−1|0〉",
"++",
"a1a1a1a−1a−1a−1|0〉",
"++",
"(a1a1a1a−3",
"+",
"a3a−1a−1a−1)|0〉",
"+−",
"(a1a1a1a−3",
"−",
"a3a−1a−1a−1)|0〉",
"−+",
"(a3a−2a−1",
"+",
"a2a1a−3)|0〉",
"−−",
"(a3a−2a−1",
"−",
"a2a1a−3)|0〉",
"−+",
"(a2a1a−1a−1a−1",
"+",
"a1a1a1a−2a−1)|0〉",
"−−",
"(a2a1a−1a−1a−1",
"−",
"a1a1a1a−2a−1)|0〉",
"Nl",
"=",
"Nr",
"=",
"3",
"++",
"a2a−2|0〉",
"++",
"a1a1a−1a−1|0〉",
"−+",
"(a2a−1a−1",
"+",
"a1a1a−2)|0〉",
"−−",
"(a2a−1a−1",
"−",
"a1a1a−2)|0〉",
"Nl",
"=",
"Nr",
"=",
"2",
"Nl",
"=",
"Nr",
"=",
"1",
"++",
"a1a−1|0〉",
"Nl",
"=",
"Nr",
"=",
"0",
"++",
"|0〉",
"Nl,",
"Nr",
"Pt,",
"Pr",
"GGRT",
"States",
"q",
"=",
"0"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00034_1762333206/figures/2301.00034-Table1-1.png
|
{
"x1": 86.1729965209961,
"x2": 533.028076171875,
"y1": 588.7904052734375,
"y2": 596.5679931640625
}
|
200
|
13
| 30
|
Figure
|
{
"x1": 59.04,
"x2": 523.0799999999999,
"y1": 182.88,
"y2": 476.28
}
|
Figure 13: Energies in the q = 1 (+) sector at R = 40a = 2.76ls as a function of the inverse transverse size. Horizontal lines of different colors represent the GGRT spectrum starting from N = 2, Ñ = 1.
|
[
"1/l⊥",
"√",
"σ",
"E/",
"√",
"σ",
"10",
"9",
"8",
"7",
"0.05",
"0.10",
"0.15",
"0.20",
"0.25"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00034_1762333206/figures/2301.00034-Figure13-1.png
|
{
"x1": 86.17300415039062,
"x2": 533.02978515625,
"y1": 490.49139404296875,
"y2": 525.3670043945312
}
|
200
|
5
| 19
|
Figure
|
{
"x1": 168.12,
"x2": 428.03999999999996,
"y1": 45.72,
"y2": 211.32
}
|
Figure 5: The absolute ground state energy at different string lengths in string units. The solid line is the GGRT approximation for the ground state energy.
|
[
"R/`s",
"E`s",
"5",
"4",
"3",
"2",
"1",
"0",
"1",
"2",
"3",
"4",
"5",
"0"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00034_1762333206/figures/2301.00034-Figure5-1.png
|
{
"x1": 86.17298889160156,
"x2": 533.0275268554688,
"y1": 225.55145263671875,
"y2": 245.98004150390625
}
|
200
|
3
| 15
|
Figure
|
{
"x1": 142.92,
"x2": 476.28,
"y1": 45.72,
"y2": 235.07999999999998
}
|
Figure 3: The set of operators used in our simulation.
|
[] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00034_1762333206/figures/2301.00034-Figure3-1.png
|
{
"x1": 171.5189971923828,
"x2": 447.6866149902344,
"y1": 248.242431640625,
"y2": 254.22601318359375
}
|
200
|
1
| 2
|
Figure
|
{
"x1": 50.76,
"x2": 544.3199999999999,
"y1": 54.36,
"y2": 172.79999999999998
}
|
Figure 1: Diagram of the mQE-CGAN framework.
|
[] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00036_1762333216/figures/2301.00036-Figure1-1.png
|
{
"x1": 196.40199279785156,
"x2": 398.8725280761719,
"y1": 180.3448944091797,
"y2": 190.177978515625
}
|
200
|
1
| 4
|
Table
|
{
"x1": 307.8,
"x2": 541.0799999999999,
"y1": 550.8,
"y2": 693
}
|
Table 1: Generator evaluation metrics of the selected dataset of companies. Company names are replaced with placeholders as C. To provide further context; Company 1 (C1) is a Turkey-based cosmetics company, Company 2 (C2) and 4 (C4) are fashion retailers originated in Turkey, and Company 3 (C3) is a worldwide technology company.
|
[
"TF-IDF",
"1.218",
"3.39",
"1.20",
"(0.686,",
"0.272)",
"Word",
"Sim.",
"1.285",
"3.626",
"1.02",
"(0.736,",
"0.209)",
"Document",
"Sim.",
"1.28",
"3.605",
"1.15",
"(0.721,",
"0.203)",
"C4",
"Baseline",
"Generator",
"1.292",
"3.650",
"1.26",
"(0.709,",
"0.217)",
"TF-IDF",
"0.33",
"1.391",
"0.74",
"(0.819,",
"0.162)",
"Word",
"Sim.",
"0.337",
"1.401",
"0.84",
"(0.81,",
"0.169)",
"Document",
"Sim.",
"0.344",
"1.411",
"0.98",
"(0.809,",
"0.171)",
"C3",
"Baseline",
"Generator",
"0.34",
"1.405",
"1.07",
"(0.662,",
"0.173)",
"TF-IDF",
"0.267",
"1.307",
"0.46",
"(0.894,",
"0.146)",
"Word",
"Sim.",
"0.27",
"1.311",
"0.45",
"(0.911,",
"0.14)",
"Document",
"Sim.",
"0.272",
"1.313",
"0.46",
"(0.902,",
"0.1412)",
"C2",
"Baseline",
"Generator",
"0.267",
"1.307",
"0.46",
"(0.898,",
"0.144)",
"TF-IDF",
"1.288",
"3.644",
"1.15",
"(0.606,",
"0.176)",
"Word",
"Sim.",
"1.328",
"3.792",
"1.02",
"(0.696,",
"0.169)",
"Document",
"Sim.",
"1.258",
"3.536",
"0.99",
"(0.659,",
"0.178)",
"C1",
"Baseline",
"Generator",
"1.266",
"3.650",
"1.07",
"(0.602,",
"0.173)",
"Dataset",
"Condition",
"CE",
"Loss",
"Perplexity",
"WC",
"SS",
"(",
",",
")"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00036_1762333216/figures/2301.00036-Table1-1.png
|
{
"x1": 306.60400390625,
"x2": 543.971435546875,
"y1": 700.9558715820312,
"y2": 739.718994140625
}
|
200
|
4
| 4
|
Figure
|
{
"x1": 50.76,
"x2": 274.32,
"y1": 172.44,
"y2": 339.84
}
|
Figure 4: Statistics of the query and the document datasets utilized in the study. For each dataset, bars at the top display the maximum, average, and minimum number of words in queries. Similarly, bottom bars display statistics of the document corpus. For all datasets, the average number of words in user searches are almost four times less than their matching product equivalents, suggesting further ways to employ semantic information to be extracted from document data.
|
[] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00036_1762333216/figures/2301.00036-Figure4-1.png
|
{
"x1": 51.30699920654297,
"x2": 288.6759033203125,
"y1": 348.1768798828125,
"y2": 441.6968994140625
}
|
200
|
2
| 7
|
Table
|
{
"x1": 52.919999999999995,
"x2": 541.0799999999999,
"y1": 65.52,
"y2": 176.76
}
|
Table 2: Randomly selected generated samples and their corresponding query and reference document pairs. Generated sequences are obtained after the adversarial learning The generator of the framework was selected as Word Similarity model. For each different company dataset, three examples are displayed in the table. Whenever the company name is included in the generated sequence, they are marked as {company name}. {brand name} is added to not reveal specific brand names in the C3 dataset. {model name} is added to hide specific product models in the C3 to not reveal the further information about the company.
|
[
"kareli",
"gömlek",
"slim",
"fit",
"gömlek",
"slim",
"fit",
"kareli",
"gömlek",
"polo",
"yaka",
"tisort",
"{company",
"name}",
"polo",
"yaka",
"cepsiz",
"regular",
"fit",
"polo",
"yaka",
"tisort",
"C4",
"mont",
"{company",
"name}",
"klasik",
"regular",
"fit",
"standart",
"fit",
"mont",
"{company",
"name}",
"{model",
"name}",
"{company",
"name}",
"{model",
"name}",
"128",
"gb",
"{company",
"name}",
"{model",
"name}",
"128",
"gb",
"kulaklık",
"{company",
"name}",
"{model",
"name}",
"kablolu",
"mikrofonlu",
"{company",
"name}",
"{model",
"name}",
"kulaklık",
"C3",
"şarj",
"{company",
"name}",
"{model",
"name}",
"c-type",
"hızlı",
"seyahat",
"{company",
"name}",
"{model",
"name}",
"siyah",
"krem",
"ceket",
"kapüşonlu",
"siyah",
"ceket",
"kapüşonlu",
"beyaz",
"ceket",
"{company",
"name}",
"black",
"jake",
"jake",
"{company",
"name}",
"black",
"jean",
"pantolon",
"jake",
"{company",
"name}",
"black",
"gölgeli",
"jean",
"pantolon",
"C2",
"bandana",
"siyah",
"parka",
"sarı",
"bucket",
"çanta",
"yıpranma",
"krem",
"yıpranmış",
"nemlendirici",
"krem",
"50",
"brand",
"name",
"yıpranma",
"karşıtı",
"nemlendirici",
"krem",
"50",
"ml",
"C1",
"saçlar",
"saçlar",
"nemlendirici",
"krem",
"50",
"water",
"nemlendirici",
"şampuan",
"köpük",
"karma",
"köpük",
"150",
"vitaminli",
"150",
"ml",
"yüz",
"köpüğü"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00036_1762333216/figures/2301.00036-Table2-1.png
|
{
"x1": 51.30699920654297,
"x2": 543.9644775390625,
"y1": 184.71182250976562,
"y2": 215.5048828125
}
|
200
|
3
| 3
|
Figure
|
{
"x1": 82.8,
"x2": 257.03999999999996,
"y1": 276.48,
"y2": 491.03999999999996
}
|
Figure 3: LSTM based discriminator model of the mQECGAN framework.
|
[] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00036_1762333216/figures/2301.00036-Figure3-1.png
|
{
"x1": 51.30699920654297,
"x2": 288.67169189453125,
"y1": 498.421875,
"y2": 520.2109375
}
|
200
|
2
| 3
|
Figure
|
{
"x1": 99.72,
"x2": 495,
"y1": 54.36,
"y2": 223.92
}
|
Figure 2: Diagram of the Monte Carlo rollouts. At each step, a batch of sequences are generated by the decoder of the network. These batches are evaluated by the discriminator to guide the generation process of the generator model.
|
[] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00036_1762333216/figures/2301.00036-Figure2-1.png
|
{
"x1": 51.30699920654297,
"x2": 543.9675903320312,
"y1": 231.9119110107422,
"y2": 253.70098876953125
}
|
200
|
5
| 25
|
Figure
|
{
"x1": 200.88,
"x2": 399.24,
"y1": 146.88,
"y2": 240.12
}
|
Figure 5: Moving a monopole of magnetic charge p from one boundary to another creates a Wilson line of electric charge kp.
|
[
"≈"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00038_1762333224/figures/2301.00038-Figure5-1.png
|
{
"x1": 124.80198669433594,
"x2": 468.5150451660156,
"y1": 270.341552734375,
"y2": 288.56304931640625
}
|
200
|
4
| 20
|
Figure
|
{
"x1": 124.92,
"x2": 469.08,
"y1": 124.56,
"y2": 187.92
}
|
Figure 4: The bulk monopole Mp is connected by a Wilson line of charge kp to the Dirichlet boundary. In the Q-cohomology, due to the topological invariance in the t direction, this is equivalent to the boundary monopole Mp.
|
[
"Mp",
"Wkp",
"⇐⇒",
"Mp"
] |
/home/yz979/palmer_scratch/chengye/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2023_new/temp/figures_2301.00038_1762333224/figures/2301.00038-Figure4-1.png
|
{
"x1": 124.80203247070312,
"x2": 468.5137939453125,
"y1": 214.87152099609375,
"y2": 246.54302978515625
}
|
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