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Figure
|
{
"x1": 326.88,
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|
Figure 1: Two “newsworthiness” signals that editors make to guide reader attention are shown above. (1) Position (i.e. articles that are placed above, ↑, and left, ← relative to other articles are more important Hays (2018)). (2) Size (i.e. articles that are larger than other articles are more important) (3) Graphics and Font (i.e. articles with graphics and images are more important). We release NewsHomepages, a large dataset of over 3,000 homepages, collected twice-daily over three years, study information prioritization in this setting. We show can model these decisions at scale and demonstrate the usefulness of these models on two downstream tasks.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00004v1_1763715268/figures/2501.00004v1-Figure1-1.png
|
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|
300
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3
| 13
|
Figure
|
{
"x1": 114,
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}
|
Figure 3: We show three sections of a sample homepage (from CBS News) where editorial decisions for different reasons. We highlight the “Breaking News” Section, “Section Fronts” and “The Footer”.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00004v1_1763715268/figures/2501.00004v1-Figure3-1.png
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300
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8
| 13
|
Table
|
{
"x1": 336,
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"y2": 635.04
}
|
Table 8: Countries of origin for the homepages we collect, based on where the organization is based.
|
[
"United",
"States",
"892",
"Brazil",
"37",
"United",
"Kingdom",
"32",
"Nepal",
"24",
"Canada",
"20",
"South",
"Africa",
"18",
"France",
"17",
"Spain",
"13",
"Mexico",
"13",
"India",
"10",
"Japan",
"9",
"Argentina",
"9",
"Israel",
"9",
"Germany",
"9",
"Russia",
"8",
"Norway",
"8",
"Ukraine",
"6",
"Ireland",
"6",
"Italy",
"5",
"New",
"Zealand",
"4",
"Austria",
"3",
"Taiwan",
"3",
"Colombia",
"2",
"Australia",
"2",
"Uruguay",
"1",
"Qatar",
"1",
"Belgium",
"1",
"Latvia",
"1",
"Bosnia",
"and",
"Herzegovina",
"1",
"Georgia",
"1",
"El",
"Salvador",
"1",
"Lebanon",
"1",
"Country",
"Count"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00004v1_1763715268/figures/2501.00004v1-Table8-1.png
|
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|
300
|
6
| 12
|
Table
|
{
"x1": 114.96,
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"y2": 328.08
}
|
Table 6: Our corpus comprises homepages from 18 different languages. We assign each news outlet to the language of the majority of it’s articles’ languages (e.g. the New York Times sometimes publishes Spanishlanguage articles, but is predominantly and Englishlanguage newspaper).
|
[
"English",
"975",
"Spanish,",
"Castilian",
"44",
"Portuguese",
"36",
"Nepali",
"24",
"French",
"21",
"German",
"10",
"Japanese",
"9",
"Norwegian",
"8",
"Hindi",
"7",
"Hebrew",
"7",
"Russian",
"7",
"Italian",
"5",
"Ukrainian",
"5",
"Chinese",
"3",
"Afrikaans",
"3",
"Zulu",
"2",
"Xhosa",
"1",
"Language",
"Count"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00004v1_1763715268/figures/2501.00004v1-Table6-1.png
|
{
"x1": 70.53700256347656,
"x2": 290.78887939453125,
"y1": 339.6805419921875,
"y2": 405.4590148925781
}
|
300
|
7
| 12
|
Table
|
{
"x1": 306,
"x2": 523.1999999999999,
"y1": 70.8,
"y2": 412.08
}
|
Table 7: Size of training and test sets, in terms of # of pairs, used in our experiments.
|
[
"ainonline",
"2159",
"540",
"3844",
"962",
"airwaysmagazine",
"1233",
"309",
"1669",
"418",
"arstechnica",
"9349",
"2338",
"17883",
"4471",
"bleacherreport",
"3849",
"963",
"6689",
"1673",
"breitbartnews",
"7824",
"1957",
"15199",
"3800",
"chessbase",
"2094",
"524",
"3151",
"788",
"cnet",
"3769",
"943",
"6521",
"1631",
"denverpost",
"18802",
"4701",
"36607",
"9152",
"foxnews",
"62170",
"15543",
"125096",
"31274",
"jaxdotcom",
"4100",
"1026",
"7206",
"1802",
"jessicavalenti",
"455",
"114",
"512",
"129",
"jezebel",
"6270",
"1568",
"10956",
"2740",
"motherjones",
"2443",
"611",
"3572",
"893",
"newsobserver",
"7538",
"1885",
"14078",
"3520",
"nytimes",
"38432",
"9608",
"74857",
"18715",
"phoenixluc",
"209",
"53",
"305",
"77",
"rollcall",
"6572",
"1643",
"12436",
"3109",
"seattletimes",
"20942",
"5236",
"40882",
"10221",
"sfchronicle",
"5600",
"1401",
"10952",
"2739",
"sinow",
"176",
"44",
"315",
"79",
"slate",
"23527",
"5882",
"45470",
"11368",
"startelegram",
"11964",
"2992",
"22932",
"5734",
"studyfindsorg",
"450",
"113",
"403",
"101",
"thealligator",
"3046",
"762",
"5432",
"1359",
"theathletic",
"22722",
"5681",
"44463",
"11116",
"thedailyclimate",
"7211",
"1803",
"13688",
"3423",
"thehill",
"30800",
"7700",
"59965",
"14992",
"weatherchannel",
"4551",
"1138",
"8094",
"2024",
"wired",
"2058",
"515",
"3196",
"800",
"wsj",
"15569",
"3893",
"30496",
"7625",
"yaledailynews",
"1378",
"345",
"2527",
"632",
"Domain",
"Position",
"x",
"Size",
"Outlet",
"Train",
"Test",
"Train",
"Test"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00004v1_1763715268/figures/2501.00004v1-Table7-1.png
|
{
"x1": 305.8330078125,
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"y1": 424.5625305175781,
"y2": 442.52001953125
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|
300
|
5
| 7
|
Table
|
{
"x1": 80.88,
"x2": 514.0799999999999,
"y1": 72,
"y2": 253.92
}
|
Table 5: Summaries of the top 10 most newsworthy policies published by the San Francisco Board of Supervisors, as ranked by models trained on 7 different homepages.
|
[
"WSJ",
"Economic",
"and",
"Infrastructure",
"Policies,",
"Governance",
"and",
"Legislative",
"Policies",
"Contract",
"modifications;",
"Bond",
"sales;",
"Ground",
"lease",
"agree-",
"ments;",
"Charter",
"amendments",
"concerning",
"commissions",
"and",
"departments",
"related",
"to",
"aging",
"and",
"adult",
"services",
"Commemorative",
"and",
"Awareness",
"Events;",
"Labor",
"Dispute",
"Hearings;",
"Affordable",
"Housing",
"Loans",
"Labor",
"&",
"Employment,",
"Economic,",
"Hous-",
"ing",
"policies",
"Daily",
"Climate",
"Environmental",
"and",
"Energy",
"Policies,",
"Ur-",
"ban",
"Planning",
"and",
"Development",
"Agreement",
"with",
"North",
"Star",
"Solar;",
"Building",
"code",
"enforce-",
"ment",
"Fox",
"News",
"Community",
"and",
"Public",
"Safety",
"Policy,",
"Education",
"and",
"Social",
"Policy,",
"Fiscal",
"and",
"Economic",
"Policy",
"Appointment",
"of",
"individuals",
"to",
"advisory",
"committees;",
"Ap-",
"propriating",
"funds",
"for",
"San",
"Francisco",
"Unified",
"School",
"Dis-",
"trict;",
"Developing",
"materials",
"on",
"domestic",
"violence",
"Mother",
"Jones",
"Social",
"Policies,",
"Environmental",
"and",
"Health",
"Policies",
"Sanctuary",
"City",
"Protection;",
"Urging",
"Pardons;",
"Edible",
"Food",
"Recovery",
"and",
"Organic",
"Waste",
"Collection",
"Ars",
"Technica",
"Infrastructure",
"Policies",
"System",
"Impact",
"Mitigation",
"Agreement;",
"6th",
"St.",
"Substation",
"NYTimes",
"Social",
"&",
"Cultural",
"Awareness",
"Policies,",
"Environmental",
"Policies,",
"Public",
"Health",
"and",
"Emergency",
"Response,",
"Infrastructure",
"and",
"Development",
"Reducing",
"nutrient",
"pollution",
"from",
"wastewater;",
"Accepting",
"grants",
"for",
"forensic",
"science",
"improvements",
"Outlet",
"Top",
"Policies",
"LLM",
"Summaries",
"Examples",
"of",
"Policies",
"Weather",
"Chan-",
"nel"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00004v1_1763715268/figures/2501.00004v1-Table5-1.png
|
{
"x1": 70.55699920654297,
"x2": 525.6533813476562,
"y1": 266.1095275878906,
"y2": 284.0670166015625
}
|
300
|
1
| 3
|
Table
|
{
"x1": 108.96,
"x2": 486.24,
"y1": 70.8,
"y2": 154.07999999999998
}
|
Table 1: Sample of News Homepages by Category
|
[
"Category",
"Example",
"Outlets",
"National",
"The",
"New",
"York",
"Times,",
"The",
"Wall",
"Street",
"Journal,",
"NPR,",
"Bloomberg",
"State-level",
"San",
"Francisco",
"Chronicle,",
"Miami",
"Herald,",
"Chicago",
"Tribune",
"Local",
"Sturgis-Journal,",
"The",
"Daily",
"Jeffersonian,",
"LAist,",
"The",
"Desert",
"Sun",
"Subject-specific",
"The",
"Weather",
"Channel,",
"Chessbase,",
"ESPN",
"International",
"India",
"Today,",
"Ukrinform,",
"BBC,",
"Prensa",
"Grafica,",
"Japan",
"Times"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00004v1_1763715268/figures/2501.00004v1-Table1-1.png
|
{
"x1": 196.65199279785156,
"x2": 398.31494140625,
"y1": 165.68551635742188,
"y2": 171.68798828125
}
|
300
|
2
| 3
|
Table
|
{
"x1": 94.8,
"x2": 500.15999999999997,
"y1": 186.72,
"y2": 240.95999999999998
}
|
Table 2: Error analysis of bounding box detection methods comparing the DOM-Tree algorithm and a Detectron2 model across two datasets: the challenge dataset and the clean dataset. The challenge dataset is formed by selecting the bottom 10% of articles based on the match between OCR-extracted text and retrieved link text (described in Section 3 Step 2), while the clean dataset contains well-matched articles. Error types are divided into false positives (FP #1: multiple articles in one box, FP #2: no articles in a box) and false negatives (FN #1: partially captured articles, FN #2: articles not captured). As can be seen, the our trained model performs at par on the DOM-Tree algorithm in the clean settings and is far more robust in noisy settings.
|
[
"Challenge",
"dataset",
"DOM-Tree",
"algorithm",
"117",
"137",
"127",
"265",
"646",
"61.3%Detectron2",
"Model",
"25",
"23",
"27",
"87",
"162",
"90.3%",
"Clean",
"dataset",
"DOM-Tree",
"algorithm",
"12",
"20",
"0",
"13",
"45",
"97.1%Detectron2",
"Model",
"15",
"24",
"0",
"18",
"57",
"96.3%",
"FP#1",
"FP",
"#2",
"FN",
"#1",
"FN",
"#2",
"Total",
"Errors",
"%",
"Correct"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00004v1_1763715268/figures/2501.00004v1-Table2-1.png
|
{
"x1": 70.53700256347656,
"x2": 524.4129028320312,
"y1": 253.40353393554688,
"y2": 331.13702392578125
}
|
300
|
8
| 16
|
Figure
|
{
"x1": 69.84,
"x2": 525.12,
"y1": 464.88,
"y2": 690.9599999999999
}
|
Figure 8: When sorting our sources to determine the ones most difficult for the DOM-Tree algorithm, we define the Average Similarity score to be a general measure as to how well the bounding box’s text match the article’s JSON file containing text/link pairs. High similarity score means high bounding box accuracy, and vice versa.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00004v1_1763715268/figures/2501.00004v1-Figure8-1.png
|
{
"x1": 70.50700378417969,
"x2": 524.4112548828125,
"y1": 703.1845703125,
"y2": 733.0970458984375
}
|
300
|
7
| 16
|
Figure
|
{
"x1": 69.84,
"x2": 525.12,
"y1": 106.8,
"y2": 352.08
}
|
Figure 7: This diagram is an overview of the data preparation and training of the Detectron2 model for predicting bounding box on websites.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00004v1_1763715268/figures/2501.00004v1-Figure7-1.png
|
{
"x1": 70.86599731445312,
"x2": 524.4083862304688,
"y1": 363.8665466308594,
"y2": 381.8240051269531
}
|
300
|
4
| 4
|
Table
|
{
"x1": 72.96,
"x2": 287.03999999999996,
"y1": 183.6,
"y2": 336
}
|
Table 4: Performance metrics on a sampling of outlets, including on ones we used for the downstream experiments in Section 5.
|
[
"phoenixluc",
"57.1",
"70.3",
"57.4",
"90.7",
"newsobserver",
"75.0",
"72.5",
"74.3",
"70.7",
"slate",
"72.4",
"61.6",
"66.2",
"57.7",
"jaxdotcom",
"75.2",
"63.4",
"65.5",
"61.4",
"arstechnica",
"64.7",
"17.5",
"41.4",
"11.1",
"airwaysmagazine",
"72.5",
"73.7",
"78.9",
"69.1",
"denverpost",
"73.7",
"67.8",
"70.5",
"65.4",
"thedailyclimate",
"82.0",
"80.9",
"81.3",
"80.6",
"breitbartnews",
"68.9",
"22.8",
"54.7",
"14.4",
"foxnews",
"67.3",
"38.6",
"55.6",
"29.5",
"motherjones",
"71.4",
"63.0",
"68.7",
"58.2",
"thehill",
"68.8",
"55.5",
"59.8",
"51.7",
"wsj",
"70.0",
"48.0",
"52.0",
"44.6",
"Outlet",
"Accuracy",
"F1",
"Recall",
"Prec."
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00004v1_1763715268/figures/2501.00004v1-Table4-1.png
|
{
"x1": 70.55699920654297,
"x2": 290.7888488769531,
"y1": 348.0495300292969,
"y2": 377.9620056152344
}
|
300
|
3
| 4
|
Table
|
{
"x1": 135.84,
"x2": 459.12,
"y1": 70.8,
"y2": 142.07999999999998
}
|
Table 3: Performance metrics on NYTimes data for different models
|
[
"Size",
"Position",
"x",
"Size",
"Model",
"Name",
"F1",
"Precision",
"Recall",
"F1",
"Precision",
"Recall",
"Flan-t5-base",
"91.9",
"91.8",
"92.0",
"70.7",
"80.5",
"63.1",
"Flan-t5-Large",
"66.6",
"51.1",
"95.4",
"54.9",
"43.4",
"74.7",
"Roberta",
"Base",
"91.0",
"91.7",
"90.4",
"64.9",
"78.1",
"55.6",
"Roberta",
"Large",
"85.4",
"85.9",
"84.9",
"47.2",
"74.4",
"34.6",
"Distilbert-Base-Uncased",
"93.1",
"93.3",
"92.9",
"75.2",
"81.8",
"69.6"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00004v1_1763715268/figures/2501.00004v1-Table3-1.png
|
{
"x1": 161.0659942626953,
"x2": 433.9017639160156,
"y1": 154.12954711914062,
"y2": 160.13201904296875
}
|
300
|
5
| 15
|
Figure
|
{
"x1": 69.84,
"x2": 525.12,
"y1": 81.84,
"y2": 287.03999999999996
}
|
Figure 5: Different analyses we run on bounding boxes across time: average locations of bounding boxes on a homepage, locations where articles are added first, locations where they are removed, and the average time articles in various locations spend.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00004v1_1763715268/figures/2501.00004v1-Figure5-1.png
|
{
"x1": 70.86599731445312,
"x2": 524.409912109375,
"y1": 298.6075134277344,
"y2": 328.52001953125
}
|
300
|
6
| 15
|
Figure
|
{
"x1": 115.92,
"x2": 480.24,
"y1": 361.68,
"y2": 727.92
}
|
Figure 6: With our suite of tools for parsing homepages, we can examine on a granular level the movement of an article across the homepage.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00004v1_1763715268/figures/2501.00004v1-Figure6-1.png
|
{
"x1": 70.86599731445312,
"x2": 524.4064331054688,
"y1": 740.0775756835938,
"y2": 758.0350341796875
}
|
300
|
2
| 5
|
Figure
|
{
"x1": 92.88,
"x2": 519.12,
"y1": 72,
"y2": 204.23999999999998
}
|
Figure 2: The Family Planning Estimation Tool (FPET) produces estimates of FP indicators, based on survey data and observations on estimated modern use (EMUs), obtained from service statistics. The graph shows survey data on modern contraceptive use for married women of reproductive age in Kenya, together with an FPET fit (point estimates are given by the solid black line, shaded areas represent 90% credible intervals).
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00007v1_1763715277/figures/2501.00007v1-Figure2-1.png
|
{
"x1": 72,
"x2": 540.0056762695312,
"y1": 221.3894500732422,
"y2": 281.041015625
}
|
300
|
5
| 10
|
Figure
|
{
"x1": 72,
"x2": 540,
"y1": 138,
"y2": 574.0799999999999
}
|
Figure 5: Data, estimates, and forecasts from 1970 until 2030 for FP indicators for married women in Angola, Bolivia, and Burundi. Graphs show mCPR, unmet need for modern methods, demand, and demand satisfied with modern methods. Survey data are shown in colored dots with 95% confidence intervals that reflect total error variance. FPET estimates are shown in black, with grey shaded areas representing 90% credible intervals.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00007v1_1763715277/figures/2501.00007v1-Figure5-1.png
|
{
"x1": 72,
"x2": 540.0057983398438,
"y1": 591.906494140625,
"y2": 651.5579833984375
}
|
300
|
9
| 24
|
Figure
|
{
"x1": 94.8,
"x2": 517.1999999999999,
"y1": 70.8,
"y2": 692.16
}
|
Figure 9: Married-women mCPR estimates for Cote d’Ivoire, Ethiopia, Mali, and Nepal based on a training set (green, including data up to and including 2017), and all survey data (red). Data points that were not included in the training set are shown in round circles. Shaded areas are 90% credibility intervals. 25
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00007v1_1763715277/figures/2501.00007v1-Figure9-1.png
|
{
"x1": 72,
"x2": 540.0037841796875,
"y1": 709.2184448242188,
"y2": 755.3209838867188
}
|
300
|
1
| 25
|
Table
|
{
"x1": 82.8,
"x2": 529.1999999999999,
"y1": 130.79999999999998,
"y2": 245.04
}
|
Table 1: Summary of prediction errors (in percentage) for the year 2020. An error refers to the difference between the estimate for the indicator based on the full data set and the indicator based on the training data, for the year 2020 (3 year forecast horizon). A positive (negative) error indicates that the prediction based on data up to 2018 underpredicted (overpredicted) the target value. Table columns: ME = mean error, MedE = median error, MAE = mean absolute error, MedAE = median absolute error, prop less2perc = proportion of errors less than 2 percentage point, prop less5perc = proportion of errors less than 5 percentage points.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00007v1_1763715277/figures/2501.00007v1-Table1-1.png
|
{
"x1": 71.99998474121094,
"x2": 540.0057983398438,
"y1": 262.3094177246094,
"y2": 349.05902099609375
}
|
300
|
2
| 25
|
Table
|
{
"x1": 72,
"x2": 540,
"y1": 477.84,
"y2": 596.16
}
|
Table 2: Percentage of estimates for 2020 based on data prior to 2018 that fall outside their respective uncertainty intervals based on all data.. Table columns: below90UI = percentage of estimates that fall below the 90% UI, above90UI = percentage of estimates that fall below the 90% UI.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00007v1_1763715277/figures/2501.00007v1-Table2-1.png
|
{
"x1": 72,
"x2": 540.0030517578125,
"y1": 613.6394653320312,
"y2": 659.740966796875
}
|
300
|
10
| 28
|
Figure
|
{
"x1": 164.88,
"x2": 447.12,
"y1": 198,
"y2": 514.0799999999999
}
|
Figure 10: Comparison of FPET2 and FPET1 prediction errors for left-out DHSs. FPET2 errors (y-axis) plotted again FPET1 errors (x-axis). An error refers to the difference between a left-out DHS observation and the estimate for the indicator based on the validation data. A positive (negative) error indicates that the prediction based on data up to 2018 underpredicted (overpredicted) the target value.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00007v1_1763715277/figures/2501.00007v1-Figure10-1.png
|
{
"x1": 72,
"x2": 540.0048217773438,
"y1": 531.4354858398438,
"y2": 591.0869750976562
}
|
300
|
6
| 13
|
Figure
|
{
"x1": 168,
"x2": 443.76,
"y1": 101.28,
"y2": 625.1999999999999
}
|
Figure 6: Data and estimates for mCPR among married women for Burundi, Ethiopia, and Niger. Data are shown in colored dots with 95% confidence intervals that reflect total error variance. FPET estimates are shown in black, with grey shaded areas representing 90% credible intervals.
|
[
"Niger",
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"National",
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"married",
"DHS",
"MICS",
"National",
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"co",
"nt",
"1980",
"2000",
"2020",
"year",
"0.6",
"0.4",
"0.2",
"0.0"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00007v1_1763715277/figures/2501.00007v1-Figure6-1.png
|
{
"x1": 71.99999237060547,
"x2": 540.0015258789062,
"y1": 646.2244873046875,
"y2": 692.3270263671875
}
|
300
|
8
| 17
|
Figure
|
{
"x1": 72,
"x2": 540,
"y1": 397.91999999999996,
"y2": 591.12
}
|
Figure 8: Bugs Bunny, Brainy Smurf, and Bayes. To obtain realistic model-based estimates for all settings of interest, models need to be built by a collaboration between “data crunching” Bugs Bunny and “this is how the world works” Brainy Smurf. The Bayesian framework can be considered for producing model-based findings.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00007v1_1763715277/figures/2501.00007v1-Figure8-1.png
|
{
"x1": 72,
"x2": 540.0048828125,
"y1": 608.8414916992188,
"y2": 654.9429931640625
}
|
300
|
4
| 27
|
Table
|
{
"x1": 72,
"x2": 541.1999999999999,
"y1": 128.88,
"y2": 244.07999999999998
}
|
Table 4: Summary of FPET1 prediction errors (in percentage) for the year 2020. An error refers to the difference between the estimate for the indicator based on the full data set and the indicator based on the training data, for the year 2020 (3 year forecast horizon). A positive (negative) error indicates that the prediction based on data up to 2018 underpredicted (overpredicted) the target value. Table columns: ME = mean error, MedE = median error, MAE = mean absolute error, MedAE = median absolute error, prop less2perc = proportion of errors less than 2 percentage point, prop less5perc = proportion of errors less than 5 percentage points.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00007v1_1763715277/figures/2501.00007v1-Table4-1.png
|
{
"x1": 72,
"x2": 540.0048828125,
"y1": 261.4514465332031,
"y2": 348.2010192871094
}
|
300
|
5
| 27
|
Table
|
{
"x1": 72,
"x2": 541.1999999999999,
"y1": 471.84,
"y2": 557.04
}
|
Table 5: Summary of FPET1 prediction errors (in percentage) for left-out DHSs. An error refers to the difference between a left-out DHS observation and the estimate for the indicator based on the validation data. A positive (negative) error indicates that the prediction based on data up to 2018 underpredicted (overpredicted) the target value. Table columns: ME = mean error, MedE = median error, MAE = mean absolute error, MedAE = median absolute error, prop less2perc = proportion of errors less than 2 percentage point, prop less5perc = proportion of errors less than 5 percentage points.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00007v1_1763715277/figures/2501.00007v1-Table5-1.png
|
{
"x1": 71.99996948242188,
"x2": 540.0059204101562,
"y1": 574.0904541015625,
"y2": 660.8399658203125
}
|
300
|
3
| 7
|
Figure
|
{
"x1": 72,
"x2": 541.1999999999999,
"y1": 78.96,
"y2": 649.1999999999999
}
|
Figure 3: Observed data on demand and demand satisfied for modern methods for selected countries over time. Observations refer to prevalence among married women of reproductive age. Countries are included in the selected main regions if they have more than 4 observations.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00007v1_1763715277/figures/2501.00007v1-Figure3-1.png
|
{
"x1": 72,
"x2": 540.0045776367188,
"y1": 666.8905029296875,
"y2": 712.9930419921875
}
|
300
|
3
| 26
|
Table
|
{
"x1": 72,
"x2": 541.1999999999999,
"y1": 144,
"y2": 232.07999999999998
}
|
Table 3: Summary of prediction errors (in percentage) for left-out DHSs. An error refers to the difference between a left-out DHS observation and the estimate for the indicator based on the validation data. A positive (negative) error indicates that the prediction based on data up to 2018 underpredicted (overpredicted) the target value. Table columns: ME = mean error, MedE = median error, MAE = mean absolute error, MedAE = median absolute error, prop less2perc = proportion of errors less than 2 percentage point, prop less5perc = proportion of errors less than 5 percentage points.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00007v1_1763715277/figures/2501.00007v1-Table3-1.png
|
{
"x1": 72,
"x2": 540.0059814453125,
"y1": 249.43443298339844,
"y2": 336.18402099609375
}
|
300
|
4
| 8
|
Figure
|
{
"x1": 97.67999999999999,
"x2": 515.04,
"y1": 176.88,
"y2": 337.2
}
|
Figure 4: Illustration of the transition model specification for indicator ηc,t. Left: Rate of change (black) as a function of the ηc,t, parameterized using B-splines. The gray lines illustrate a scaled version of the non-zero spline basis functions. Right: Transition of ηc,t from low to high levels, based on the rate of change from plot on left. Figure adapted from Susmann and Alkema [2023].
|
[
"Latent",
"Indicator",
"Value",
"η",
"ct",
"0",
"20",
"40",
"60",
"80",
"t",
"1.00",
"0.75",
"0.50",
"0.25",
"0.00",
"λc",
"Ωc",
"Transition",
"Function",
"f",
"0.0",
"0.3",
"0.6",
"0.9",
"ηc,t",
"0.075",
"0.050",
"0.025",
"0.000",
"λc"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00007v1_1763715277/figures/2501.00007v1-Figure4-1.png
|
{
"x1": 71.99996948242188,
"x2": 540.00146484375,
"y1": 359.5434265136719,
"y2": 419.19500732421875
}
|
300
|
1
| 4
|
Figure
|
{
"x1": 141.84,
"x2": 470.15999999999997,
"y1": 138,
"y2": 615.12
}
|
Figure 1: Data for mCPR among married women for Burundi. Data are shown in colored dots with 95% confidence intervals that reflect sampling errors.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00007v1_1763715277/figures/2501.00007v1-Figure1-1.png
|
{
"x1": 72,
"x2": 540.0053100585938,
"y1": 632.8004760742188,
"y2": 651.8040161132812
}
|
300
|
7
| 15
|
Figure
|
{
"x1": 72,
"x2": 540,
"y1": 135.84,
"y2": 535.1999999999999
}
|
Figure 7: Illustration of the effect of including EMUs when estimating mCPR. The top row shows observed EMUs (red) for the level (left) and rate of change (right). The vertical lines indicate the 95% confidence intervals based on sEMU,d,c,t alone. Survey-based estimates of mCPR are added in black. The blue dashed line indicates the most recent survey year. The top row illustrates that the EMU-based rates of change suggest a stall after the most recent survey year, with rates of change that are lower than survey-based predictions. Plots in bottom row illustrate the effect of including the EMUs in FPET estimates: the stall in EMUs past the most recent survey results in a slower mCPR growth, as compared to survey-only estimates.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00007v1_1763715277/figures/2501.00007v1-Figure7-1.png
|
{
"x1": 72,
"x2": 540.00390625,
"y1": 553.0075073242188,
"y2": 653.3070068359375
}
|
300
|
5
| 5
|
Figure
|
{
"x1": 60.239999999999995,
"x2": 287.52,
"y1": 59.76,
"y2": 662.64
}
|
Figure 5: Performance comparison of different methods. (a) RMSE versus SNR. (b) RMSE versus degree of impairment ρ. (c) Standard deviation versus epoch.
|
[
"(c)",
"25",
"20",
"15",
"10",
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"3",
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"0.6",
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"MUSIC",
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"CNN",
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"100",
"101",
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"E",
"[",
"d",
"eg",
"]",
"10-1",
"10-2",
"SNR",
"[dB]",
"-5",
"0",
"5",
"10",
"15",
"20"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00009v1_1763715289/figures/2501.00009v1-Figure5-1.png
|
{
"x1": 54,
"x2": 292.504638671875,
"y1": 675.8225708007812,
"y2": 703.7429809570312
}
|
300
|
6
| 5
|
Figure
|
{
"x1": 344.88,
"x2": 534.24,
"y1": 288,
"y2": 469.2
}
|
Figure 6: Setups for anechoic chamber experiments.
|
[
"10m",
"SRS",
"Array",
"broadside",
"Anechoic",
"Chamber",
"𝜃𝐿",
"𝜃𝑙",
"𝜃1",
"-60°",
"60°",
"Field",
"of",
"view",
"Signal",
"processing",
"RF",
"signal",
"estimation",
"FFTCSI",
"output",
"AoA",
"Antenna",
"1",
"to",
"4",
"RRU",
"BBU"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00009v1_1763715289/figures/2501.00009v1-Figure6-1.png
|
{
"x1": 334.92999267578125,
"x2": 542.5704956054688,
"y1": 478.34051513671875,
"y2": 484.3429870605469
}
|
300
|
2
| 6
|
Table
|
{
"x1": 320.88,
"x2": 556.0799999999999,
"y1": 387.84,
"y2": 438.24
}
|
Table 2: Training and testing times.
|
[
"training",
"[h]",
"-",
"30.8",
"1.6",
"15.6",
"testing",
"[ms]",
"9.4",
"31.6",
"1.8",
"14.9",
"MUSIC",
"DeepMUSIC",
"CNN",
"Ours"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00009v1_1763715289/figures/2501.00009v1-Table2-1.png
|
{
"x1": 368.2049865722656,
"x2": 509.2953186035156,
"y1": 448.9105224609375,
"y2": 454.9129943847656
}
|
300
|
7
| 6
|
Figure
|
{
"x1": 61.199999999999996,
"x2": 282,
"y1": 54,
"y2": 428.64
}
|
Figure 7: AoA estimation error performance of different methods. (a) CDF. (b)Boxplots for 4 subregions.
|
[
"(b)",
"CNN",
"MoD-DNN",
"MUSIC",
"DeepMUSIC",
"de",
"g]",
"ro",
"r",
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"Er",
"at",
"io",
"Es",
"tim",
"10",
"8",
"6",
"4",
"2",
"0",
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"-30",
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"[0",
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",",
"30",
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"[30",
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"AoA",
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"(a)",
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"[deg]",
"MoD-CNN",
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"F",
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"D",
"ic",
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"p",
"ir",
"E",
"m",
"1",
"0.8",
"0.6",
"0.4",
"0.2",
"0",
"10",
"1",
"10",
"0",
"10",
"-1"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00009v1_1763715289/figures/2501.00009v1-Figure7-1.png
|
{
"x1": 53.99999237060547,
"x2": 292.5046081542969,
"y1": 434.9125061035156,
"y2": 451.87396240234375
}
|
300
|
1
| 2
|
Figure
|
{
"x1": 55.919999999999995,
"x2": 549.12,
"y1": 54,
"y2": 159.84
}
|
Figure 1: Framework of MoD-DNN for AoA estimation.
|
[
"Preprocessing",
"MoD-DNN",
"Spatial",
"Spectrum",
"AoASpectrum",
"Peak",
"Search",
"Sample",
"…",
"and",
"SCG",
"CNN",
"between",
"Iteration",
"Sample",
"…",
"…",
"……",
"Input",
"Output",
"Sample",
"…",
"…",
"……",
"Covariance",
"Matrix",
"R",
"Sample",
"…",
"Sample",
"Antenna",
"…",
"5G",
"gNB",
"CFR",
"H",
"y",
"Subcarrier",
"Vectorizing",
"AoA"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00009v1_1763715289/figures/2501.00009v1-Figure1-1.png
|
{
"x1": 193.0050048828125,
"x2": 418.99652099609375,
"y1": 164.24154663085938,
"y2": 170.2440185546875
}
|
300
|
2
| 2
|
Figure
|
{
"x1": 63.839999999999996,
"x2": 546,
"y1": 183.84,
"y2": 300
}
|
Figure 2: Illustration of proposed iteration for MoD-DNN module. (a) Overall iteration in MoD-DNN module. (b) Alternative optimization between CNN-based calibrator and inverse problem-based SSR.
|
[
"(b)",
"iη",
"Sample",
"…",
"…",
"……",
"1i−η",
"Sample",
"1i−z",
"w−…",
"…",
"……",
"Calibrator",
"CNN-based",
"SSR",
"layer",
"SCG-based",
"w",
"(a)",
"Shared",
"Weights",
"…",
"…",
"η",
"SCG",
"layer",
"CNN",
"layer",
"SCG",
"layer",
"CNN",
"layer",
"st1",
"iteration",
"thiterationi",
"thiterationI",
"0z",
"w",
"w",
"1i−z",
"1I−z1η",
"iη",
"Iη",
"CNN",
"layer",
"SCG",
"layer",
"w",
"Iteration",
"between",
"CNN",
"and",
"SCG",
"η̂"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00009v1_1763715289/figures/2501.00009v1-Figure2-1.png
|
{
"x1": 54,
"x2": 557.9977416992188,
"y1": 306.1385192871094,
"y2": 323.0999755859375
}
|
300
|
3
| 3
|
Figure
|
{
"x1": 326.88,
"x2": 550.0799999999999,
"y1": 55.919999999999995,
"y2": 136.07999999999998
}
|
Figure 3: Structure of CNN-based calibrator.
|
[
"Layer",
"#p…",
"…",
"BN",
"z",
"ConV",
"ReLU",
"ConV",
"BN",
"ReLU",
"ConV",
"BN",
"w",
"Layer",
"#P-1",
"Layer",
"#P",
"ReLU",
"BN",
"ConV",
"ReLU",
"BN",
"η",
"ConV",
"Layer",
"#1",
"Layer",
"#2"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00009v1_1763715289/figures/2501.00009v1-Figure3-1.png
|
{
"x1": 349.6549987792969,
"x2": 527.8460693359375,
"y1": 145.51351928710938,
"y2": 151.5159912109375
}
|
300
|
1
| 4
|
Table
|
{
"x1": 67.92,
"x2": 278.15999999999997,
"y1": 601.92,
"y2": 681.12
}
|
Table 1: Simulation settings.
|
[
"M",
"4",
"θ",
"[−60◦,",
"60◦]",
"B",
"100",
"MHz",
"∆θ",
"0.1◦",
"∆f",
"60",
"KHz",
"PUE",
"23",
"dBm",
"fc",
"4.8498",
"GHz",
"R",
"10",
"m",
"Symbol",
"Value",
"Symbol",
"Value"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00009v1_1763715289/figures/2501.00009v1-Table1-1.png
|
{
"x1": 116.35900115966797,
"x2": 230.14186096191406,
"y1": 692.7095336914062,
"y2": 698.7119750976562
}
|
300
|
4
| 4
|
Figure
|
{
"x1": 61.68,
"x2": 556.56,
"y1": 54.48,
"y2": 317.52
}
|
Figure 4: Spatial spectrum results at different AoA. Red dashed lines denote the truth. (a) MUSIC, −45◦. (b) MUSIC, 45◦. (c) DeepMUSIC, −45◦. (d) DeepMUSIC, 45◦. (e) MoD-DNN, −45◦. (f) MoD-DNN, 45◦.
|
[
"(f)",
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"m",
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"l",
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"iz",
"N",
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"1",
"0.75",
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"[deg]",
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"0",
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"[deg]",
"-60",
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"-45",
"-37.5",
"-30"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00009v1_1763715289/figures/2501.00009v1-Figure4-1.png
|
{
"x1": 53.999969482421875,
"x2": 558.004638671875,
"y1": 324.7995300292969,
"y2": 341.760986328125
}
|
300
|
1
| 0
|
Figure
|
{
"x1": 324.96,
"x2": 553.1999999999999,
"y1": 217.92,
"y2": 295.44
}
|
Figure 1: Correlation of the performance of sequence generation (Left) and structure generation (Right) w.r.t amino acid position in CDR-H3 for different lengths L from SAbDab.
|
[
"L=15",
"L=20",
"L=25",
"(Å",
")",
"RM",
"SD",
"6",
"4",
"2",
"0",
"0",
"5",
"10",
"15",
"20",
"25",
"Position",
"in",
"CDR-H3",
"L=15",
"L=20",
"L=25",
"(%",
")",
"AA",
"R",
"80",
"60",
"40",
"20",
"0",
"0",
"5",
"10",
"15",
"20",
"25",
"Position",
"in",
"CDR-H3"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00013v1_1763715309/figures/2501.00013v1-Figure1-1.png
|
{
"x1": 319.5,
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"y1": 315.18353271484375,
"y2": 343.10302734375
}
|
300
|
1
| 5
|
Table
|
{
"x1": 54.96,
"x2": 293.03999999999996,
"y1": 338.88,
"y2": 451.2
}
|
Table 1: Mean results of 10-fold cross-validation for CDR sequence and structure modeling on the SAbDab, where bold and underline denote the best and second metrics.
|
[
"DiffAb",
"61.34",
"1.02",
"37.66",
"1.20",
"25.79",
"3.02",
"AbDiffuser",
"62.76",
"1.08",
"41.10",
"1.16",
"29.58",
"2.83",
"MEAN",
"58.29",
"0.98",
"47.15",
"0.95",
"36.38",
"2.21",
"dyMEAN",
"63.52",
"0.84",
"55.41",
"0.82",
"37.19",
"2.09",
"ADesigner",
"64.34",
"0.82",
"55.52",
"0.79",
"37.37",
"1.97",
"RADD",
"(ours)",
"67.64",
"0.77",
"58.87",
"0.72",
"37.71",
"1.91",
"∆dyMEAN",
"+6.49%",
"-8.33%",
"+6.24%",
"-12.20%",
"+1.67%",
"-8.61%",
"LSTM",
"49.98",
"-",
"28.50",
"-",
"15.69",
"-",
"C-LSTM",
"40.93",
"-",
"29.24",
"-",
"15.48",
"-",
"RefineGNN",
"39.40",
"3.22",
"37.06",
"3.64",
"21.13",
"6.00",
"C-RefineGNN",
"33.19",
"3.25",
"33.53",
"3.69",
"18.88",
"6.22",
"HERN",
"41.71",
"1.78",
"35.46",
"2.21",
"24.75",
"3.89",
"C-HERN",
"47.36",
"1.45",
"41.45",
"1.20",
"28.47",
"2.64",
"Model",
"CDR-H1",
"CDR-H2",
"CDR-H3",
"AAR",
"(↑)",
"RMSD",
"(↓)",
"AAR",
"(↑)",
"RMSD",
"(↓)",
"AAR",
"(↑)",
"RMSD",
"(↓)"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00013v1_1763715309/figures/2501.00013v1-Table1-1.png
|
{
"x1": 54,
"x2": 292.5046081542969,
"y1": 297.38751220703125,
"y2": 325.3080139160156
}
|
300
|
2
| 5
|
Table
|
{
"x1": 344.88,
"x2": 535.1999999999999,
"y1": 326.88,
"y2": 452.15999999999997
}
|
Table 2: Performance comparison of antigen-binding CDRH3 sequence and structure design on the RAbD dataset.
|
[
"LSTM",
"22.36",
"-",
"-",
"C-LSTM",
"22.18",
"-",
"-",
"RefineGNN",
"29.79",
"0.8308",
"7.55",
"C-RefineGNN",
"28.90",
"0.8317",
"7.21",
"HERN",
"32.83",
"0.9684",
"3.12",
"C-HERN",
"34.51",
"0.9734",
"2.79",
"MEAN",
"36.77",
"0.9812",
"1.81",
"dyMEAN",
"39.14",
"0.9825",
"1.66",
"ADesigner",
"40.94",
"0.9850",
"1.55",
"RAAD",
"(ours)",
"41.26",
"0.9874",
"1.46",
"∆dyMEAN",
"+5.42%",
"+0.50%",
"-12.05%",
"Model",
"AAR",
"(↑)",
"TM-score",
"(↑)",
"RMSD",
"(↓)",
"RosettaAD",
"22.50",
"0.9435",
"5.52"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00013v1_1763715309/figures/2501.00013v1-Table2-1.png
|
{
"x1": 319.5,
"x2": 558.0046997070312,
"y1": 297.3874816894531,
"y2": 314.34893798828125
}
|
300
|
6
| 5
|
Figure
|
{
"x1": 133.2,
"x2": 482.15999999999997,
"y1": 60,
"y2": 232.32
}
|
Figure 6: Case Study. The structures and sequences of the antigen-binding CDR-H3s designed by MEAN, dyMEAN, and RAAD for two complexes (pdb: 5l6y and 4lvn), as well as RMSD scores with the ground-truth CDR-H3 structures.
|
[
"ARDSSSSWARWFFDL",
"MEAN:",
"ARDGYGGGYYYYFDL",
"Ground-Truth:",
"Ground-Truth:",
"RAAD:",
"VRYRYGYYWVFDD",
"dyMEAN:",
"VRDGYDYYWVFDD",
"MEAN:",
"ARYRYYYYYYFDD",
"VIYRYDGEWVFDD",
"RAAD:",
"ARDSSSYWAYYAFDL",
"dyMEAN:",
"ARDSSGGGYWCFDDL",
"Antigen",
"Light",
"Chain",
"Heavy",
"Chain",
"CDR-H3",
"(Ground-Truth)",
"CDR-H3",
"(Generated)",
"rmsd:",
"1.124",
"rmsd:",
"1.458",
"rmsd:",
"1.765",
"rmsd:",
"1.164",
"rmsd:",
"1.851rmsd:",
"1.517",
"pdb:5l6y",
"pdb:4lvn",
"gege"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00013v1_1763715309/figures/2501.00013v1-Figure6-1.png
|
{
"x1": 54,
"x2": 557.997802734375,
"y1": 255.54452514648438,
"y2": 272.5059814453125
}
|
300
|
2
| 1
|
Figure
|
{
"x1": 54.72,
"x2": 293.03999999999996,
"y1": 54.96,
"y2": 113.03999999999999
}
|
Figure 2: Structure of an antigen-antibody complex, where the antibody is symmetrically Y-shape, and we mainly focus on three CDRs of the variable domain in the heavy chain.
|
[
"FRFRFR",
"FR",
"FR",
"FR",
"FR",
"FR",
"Light",
"Chain",
"Heavey",
"Chain",
"...Antigen",
"VL",
"VH",
"CDR-L1",
"CDR-L2",
"CDR-L3",
"CDR-H1",
"CDR-H2",
"CDR-H3",
"Antigen",
"Epitope",
"1",
"Epitope",
"2",
"Epitope",
"K",
"VHVH",
"VL",
"VL",
"CH3",
"CH3",
"CH2",
"CH2",
"CH1CH1",
"CL",
"CL"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00013v1_1763715309/figures/2501.00013v1-Figure2-1.png
|
{
"x1": 54,
"x2": 292.504638671875,
"y1": 130.72451782226562,
"y2": 158.64495849609375
}
|
300
|
4
| 6
|
Table
|
{
"x1": 320.88,
"x2": 559.1999999999999,
"y1": 86.88,
"y2": 153.12
}
|
Table 4: Ablation study on different model componens, where bold and gray denote the best and poorest metrics.
|
[
"full",
"model",
"67.64",
"0.772",
"39.86",
"0.9847",
"1.442",
"11.55",
"-",
"node",
"feature",
"66.12",
"0.794",
"38.49",
"0.9829",
"1.522",
"10.12",
"-",
"edge",
"feature",
"65.62",
"0.819",
"38.66",
"0.9825",
"1.517",
"9.75",
"-",
"relational",
"MMP",
"64.85",
"0.807",
"37.97",
"0.9804",
"1.596",
"8.94",
"-",
"edge",
"updating",
"66.73",
"0.798",
"39.14",
"0.9836",
"1.488",
"10.74",
"-",
"global",
"nodes",
"65.63",
"0.810",
"38.27",
"0.9817",
"1.549",
"9.60",
"Model",
"Modeling",
"Generation",
"Optimization",
"AAR↑",
"RMSD↓",
"AAR↑",
"TM-score↑",
"RMSD↓",
"SP-score↑"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00013v1_1763715309/figures/2501.00013v1-Table4-1.png
|
{
"x1": 319.5,
"x2": 558.0045776367188,
"y1": 55.66855239868164,
"y2": 72.6300048828125
}
|
300
|
3
| 6
|
Table
|
{
"x1": 54.96,
"x2": 293.03999999999996,
"y1": 86.88,
"y2": 193.2
}
|
Table 3: Average ∆∆G (kcal/mol) and average number of changed residues (∆L) after antibody optimization.
|
[
"RAAD",
"(w/o",
"LSP)",
"-12.163",
"-1.748",
"10.415",
"6.50",
"RAAD",
"(w/",
"LSP)",
"-11.787",
"-0.238",
"11.549",
"5.98",
"Model",
"∆∆Gpos",
"(↓)",
"∆∆Gneg",
"(↑)",
"SP-score",
"(↑)",
"∆L",
"(↓)",
"Random",
"+1.489",
"+1.518",
"0.029",
"15.64",
"LSTM",
"-2.183",
"-0.496",
"1.687",
"9.45",
"C-LSTM",
"-2.534",
"-0.784",
"1.750",
"10.24",
"RefineGNN",
"-4.684",
"-1.191",
"3.493",
"7.76",
"C-RefineGNN",
"-5.179",
"-1.392",
"3.787",
"8.56",
"MEAN",
"-6.104",
"-1.605",
"4.499",
"9.61",
"dyMEAN",
"-8.215",
"-1.543",
"6.672",
"6.24",
"ADesigner",
"-10.431",
"-1.624",
"8.807",
"6.82"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00013v1_1763715309/figures/2501.00013v1-Table3-1.png
|
{
"x1": 53.99999237060547,
"x2": 292.5024108886719,
"y1": 55.66855239868164,
"y2": 72.6300048828125
}
|
300
|
5
| 6
|
Table
|
{
"x1": 319.92,
"x2": 558,
"y1": 532.8,
"y2": 610.0799999999999
}
|
Table 5: Evaluation on different input contexts, ranging from light chains, heavy chains, full antigens, and epitopes. The performance gains and drops are marked as red and green.
|
[
"(⑤",
"-",
"③)",
"/",
"③",
"+2.31%",
"-5.16%",
"+2.71%",
"+0.21%",
"+1.46%",
"(⑤",
"-",
"④)",
"/",
"④",
"+1.65%",
"-3.02%",
"+4.67%",
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"-3.81%",
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"%",
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"Full",
"54.89",
"0.943",
"36.56",
"0.9795",
"1.818",
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"0.9783",
"1.774",
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"66.05",
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"66.54",
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"39.42",
"0.9839",
"1.521",
"⑤",
"!",
"!",
"Full",
"67.64",
"0.772",
"41.26",
"0.9874",
"1.463",
"Model",
"Modeling",
"Generation",
"Heavey",
"Light",
"Antigen",
"AAR",
"(↑)",
"RMSD",
"(↓)",
"AAR",
"(↑)",
"TM-score",
"(↑)",
"RMSD",
"(↓)"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00013v1_1763715309/figures/2501.00013v1-Table5-1.png
|
{
"x1": 319.5,
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"y1": 492.19122314453125,
"y2": 520.1116943359375
}
|
300
|
7
| 6
|
Figure
|
{
"x1": 78,
"x2": 268.08,
"y1": 406.8,
"y2": 571.1999999999999
}
|
Figure 7: 3D structures and ∆∆G of CDR-H3s (pdb: 2vis) optimized by MEAN, dyMEAN, RAAD, as well as the original and optimized sequences (altered are marked in red).
|
[
"dyMEAN:",
"AREYYDYDWYYYAMDY",
"Original:",
"ARDFYDYDVFYYAMDY",
"Antigen",
"Light",
"Chain",
"Heavy",
"Chain",
"CDR-H3",
"RAAD:",
"ARDFYDYYDFYYAMDY",
"MEAN:",
"YREVYDYDVYTYAMAV"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00013v1_1763715309/figures/2501.00013v1-Figure7-1.png
|
{
"x1": 54,
"x2": 292.50457763671875,
"y1": 590.069580078125,
"y2": 617.989990234375
}
|
300
|
4
| 2
|
Figure
|
{
"x1": 337.68,
"x2": 546,
"y1": 218.88,
"y2": 375.12
}
|
Figure 4: Each RA-EGN layer aggregates messages and jointly updates features, coordinates, and relations.
|
[
"Coordinate",
"Updating",
"Edge",
"Relation",
"Updating",
"Node",
"Feature",
"Updating",
"Edge",
"Feature",
"Updating",
"Message",
"Aggregation"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00013v1_1763715309/figures/2501.00013v1-Figure4-1.png
|
{
"x1": 319.5,
"x2": 558.0045776367188,
"y1": 391.7995300292969,
"y2": 408.760986328125
}
|
300
|
3
| 2
|
Figure
|
{
"x1": 60,
"x2": 552,
"y1": 54.96,
"y2": 143.04
}
|
Figure 3: A high-level overview of our RAAD framework. The antigen-antibody complex is constructed as an attributed heterogeneous graph, which is passed through multilayer Relation-Aware Equivariant Graph Networks (RA-EGN). The outputs are fed to sequence generation and structure predictor to generate both the sequence and structure of CDRs in the antibody.
|
[
"Relation-Aware",
"Antibody",
"Design",
"(RAAD)GLobal",
"Node",
"R",
"A-",
"EG",
"N",
"R",
"A-",
"EG",
"N...",
"Heavey",
"Chain",
"Antigen",
"Light",
"Chain",
"G",
"ra",
"ph",
"C",
"on",
"st",
"ru",
"ct",
"io",
"n",
"CDR",
"Structure",
"Generation",
"Sequence",
"Generation",
"R",
"A-",
"EG",
"N",
"?",
"?",
"?"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00013v1_1763715309/figures/2501.00013v1-Figure3-1.png
|
{
"x1": 54,
"x2": 557.997802734375,
"y1": 168.02755737304688,
"y2": 195.947998046875
}
|
300
|
8
| 7
|
Figure
|
{
"x1": 58.8,
"x2": 288,
"y1": 54.96,
"y2": 137.76
}
|
Figure 8: Performance comparison of three methods for sequence modeling (AAR) and structural modeling (RMSD) for CDR-H3 of different lengths on the SAbDab dataset.
|
[
"RAAD",
"dyMEAN",
"MEAN",
"***",
"*",
"**",
"*",
"*",
"(%",
")",
"AA",
"R",
"50",
"45",
"40",
"35",
"30",
"25",
"20",
"15",
"<10",
"10-15",
"15-20",
"20-25",
">25",
"CDR-H3",
"Length",
"***RAAD",
"dyMEAN",
"MEAN",
"*",
"**",
"*",
"*",
"6",
"7",
"RM",
"SD",
"(Å",
")",
"5",
"4",
"3",
"2",
"1",
"0",
"<10",
"10-15",
"15-20",
"20-25",
">25",
"CDR-H3",
"Length"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00013v1_1763715309/figures/2501.00013v1-Figure8-1.png
|
{
"x1": 54,
"x2": 292.5046081542969,
"y1": 156.01351928710938,
"y2": 183.9329833984375
}
|
300
|
5
| 4
|
Figure
|
{
"x1": 61.919999999999995,
"x2": 550.0799999999999,
"y1": 54.96,
"y2": 186
}
|
Figure 5: A comparison between RAAD and previous methods in antigen-antibody interaction modeling. Their main differences include whether the interactions are dynamically updatable and whether antigenic epitopes are pre-given or adaptively learned.
|
[
"Graph",
"Construction",
"Antigen-Antibody",
"Interactions",
"(Relations)",
"Antigenic",
"Epitopes",
"Antigen",
"Residues",
"RAAD",
"(ours)",
"Antibody",
"ResiduesPrevious",
"Method",
"Eq.(4)...",
"Edge",
"Relation",
"Updating",
"Graph",
"Construction",
"Known",
"Epitopes",
"...",
"...",
"...",
"...",
"D",
"A",
"G",
"D",
"G",
"F",
"Y",
"C",
"M",
"D",
"P",
"...",
"...",
"...",
"...",
"D",
"A",
"G",
"D",
"G",
"F",
"Y",
"C",
"M",
"D",
"P",
"...",
"...",
"...",
"...",
"D",
"A",
"G",
"D",
"G",
"F",
"Y",
"C",
"M",
"D",
"P",
"...",
"...",
"...",
"...",
"D",
"A",
"G",
"D",
"G",
"F",
"Y",
"C",
"M",
"D",
"P",
"...",
"...",
"...",
"...",
"D",
"A",
"G",
"D",
"G",
"F",
"Y",
"C",
"M",
"D",
"P",
"...",
"...",
"G",
"F",
"D",
"Y",
"C",
"M",
"D",
"P",
"D",
"...",
"...",
"...",
"...",
"A",
"G",
"D",
"G",
"F",
"Y",
"C",
"M",
"D",
"P",
"...",
"...",
"...",
"...",
"D",
"A",
"G",
"D",
"G",
"F",
"D",
"P",
"C",
"M",
"D",
"Y"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00013v1_1763715309/figures/2501.00013v1-Figure5-1.png
|
{
"x1": 54,
"x2": 557.9979248046875,
"y1": 203.87155151367188,
"y2": 220.8330078125
}
|
300
|
4
| 5
|
Figure
|
{
"x1": 150.96,
"x2": 447.12,
"y1": 283.92,
"y2": 618
}
|
Figure 4: Pictorial representation of the present technique
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00014v1_1763715318/figures/2501.00014v1-Figure4-1.png
|
{
"x1": 190.85699462890625,
"x2": 406.6881103515625,
"y1": 632.5899658203125,
"y2": 636.5750122070312
}
|
300
|
8
| 10
|
Figure
|
{
"x1": 159.6,
"x2": 437.28,
"y1": 155.28,
"y2": 454.56
}
|
Figure 8: a.) Fluid streamlines using the standard FD–PINNs with 100 × 100 grid points. Fluid streamlines using the present FD–PINNs with different sub–domain grid points: b.) 100× 100, c.) 50× 50, and d.) 25× 25.
|
[
"(c)",
"(d)",
"0.8",
"1",
"Y",
"0.6",
"0.4",
"0.2",
"0",
"X",
"0",
"0.2",
"0.4",
"0.6",
"0.8",
"1",
"Y",
"1",
"0.8",
"0.6",
"0.4",
"0.2",
"0",
"X",
"0",
"0.2",
"0.4",
"0.6",
"0.8",
"1",
"(a)",
"(b)",
"Y",
"1",
"0.8",
"0.6",
"0.4",
"0.2",
"0",
"X",
"0",
"0.2",
"0.4",
"0.6",
"0.8",
"1",
"0.8",
"1",
"Y",
"0.6",
"0.4",
"0.2",
"0",
"X",
"0",
"0.2",
"0.4",
"0.6",
"0.8",
"1"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00014v1_1763715318/figures/2501.00014v1-Figure8-1.png
|
{
"x1": 72,
"x2": 525.5455322265625,
"y1": 468.69097900390625,
"y2": 482.1410217285156
}
|
300
|
4.5
| 14
|
Table
|
{
"x1": 73.92,
"x2": 526.0799999999999,
"y1": 139.92,
"y2": 243.12
}
|
Table 4.5: The MSEv comparison between the present and the standard FD–PINNs for the velocity v at several horizontal lines in the domain [0, 1]× [0.1, 0.9] of the cavity for the Reynolds number Re = 1000.
|
[
"(25×",
"25",
"sub–domain",
"grid",
"points",
")",
"(50×",
"50",
"sub–domain",
"grid",
"points",
")",
"(100×",
"100",
"sub–domain",
"grid",
"points",
")",
"(100×",
"100",
"grid",
"points)",
"0.10",
"2.2068e-04",
"2.0980e-04",
"2.1148e-04",
"2.2793e-04",
"0.20",
"7.1743e-04",
"5.6499e-04",
"4.9633e-04",
"5.0475e-04",
"0.30",
"5.4955e-04",
"5.1492e-04",
"4.9534e-04",
"5.8147e-04",
"0.40",
"7.1272e-04",
"6.3413e-04",
"5.9404e-04",
"6.5140e-04",
"0.50",
"7.6007e-04",
"6.8193e-04",
"6.4887e-04",
"6.8080e-04",
"0.60",
"5.7655e-04",
"5.6974e-04",
"5.6812e-04",
"5.7609e-04",
"0.70",
"3.7940e-04",
"4.0006e-04",
"4.1461e-04",
"3.7729e-04",
"0.80",
"2.1730e-04",
"2.1654e-04",
"2.1934e-04",
"1.5156e-04",
"0.90",
"5.4900e-05",
"3.7537e-05",
"5.0653e-05",
"6.0027e-05",
"y",
"The",
"present",
"FD–PINNs",
"The",
"present",
"FD–PINNs",
"The",
"present",
"FD–PINNs",
"The",
"standard",
"FD–PINNs"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00014v1_1763715318/figures/2501.00014v1-Table4.5-1.png
|
{
"x1": 72,
"x2": 525.54638671875,
"y1": 115.85498046875,
"y2": 129.3050537109375
}
|
300
|
4.6
| 14
|
Table
|
{
"x1": 73.92,
"x2": 526.0799999999999,
"y1": 303.84,
"y2": 407.03999999999996
}
|
Table 4.6: The MSEv comparison between the present and the standard FD–PINNs for the velocity v at several horizontal lines in the domain [0, 1]× [0.01, 0.09] of the cavity for the Reynolds number Re = 1000.
|
[
"(25×",
"25",
"sub–domain",
"grid",
"points",
")",
"(50×",
"50",
"sub–domain",
"grid",
"points",
")",
"(100×",
"100",
"sub–domain",
"grid",
"points",
")",
"(100×",
"100",
"grid",
"points)",
"0.01",
"5.3276e-08",
"5.3765e-08",
"4.4931e-08",
"6.9460e-08",
"0.02",
"1.0930e-06",
"1.1612e-06",
"1.3284e-06",
"1.2693e-06",
"0.03",
"5.9607e-06",
"6.1540e-06",
"6.9235e-06",
"7.0389e-06",
"0.04",
"1.7196e-05",
"1.7545e-05",
"1.9367e-05",
"2.0372e-05",
"0.05",
"3.5943e-05",
"3.6378e-05",
"3.9491e-05",
"4.2277e-05",
"0.06",
"6.2047e-05",
"6.2281e-05",
"6.6581e-05",
"7.1912e-05",
"0.07",
"9.4607e-05",
"9.4023e-05",
"9.9039e-05",
"1.0737e-04",
"0.08",
"1.3252e-04",
"1.3009e-04",
"1.3505e-04",
"1.4645e-04",
"0.09",
"1.7481e-04",
"1.6908e-04",
"1.7297e-04",
"1.8717e-04",
"y",
"The",
"present",
"FD–PINNs",
"The",
"present",
"FD–PINNs",
"The",
"present",
"FD–PINNs",
"The",
"standard",
"FD–PINNs"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00014v1_1763715318/figures/2501.00014v1-Table4.6-1.png
|
{
"x1": 72,
"x2": 525.54638671875,
"y1": 279.25994873046875,
"y2": 292.7099914550781
}
|
300
|
4.7
| 14
|
Table
|
{
"x1": 73.92,
"x2": 526.0799999999999,
"y1": 466.79999999999995,
"y2": 579.12
}
|
Table 4.7: The MSEv comparison between the present and the standard FD–PINNs for the velocity v at several horizontal lines on [0, 1]× [0.91, .99] of the cavity for the Reynolds number Re = 1000.
|
[
"0.91",
"6.0343e-05",
"2.8282e-05",
"4.1387e-05",
"7.0913e-05",
"0.92",
"7.3488e-05",
"2.0961e-05",
"3.3037e-05",
"8.7717e-05",
"0.93",
"9.5251e-05",
"1.6014e-05",
"2.5434e-05",
"1.1124e-04",
"0.94",
"1.2577e-04",
"1.4475e-05",
"1.8597e-05",
"1.4240e-04",
"0.95",
"1.6351e-04",
"1.8090e-05",
"1.2792e-05",
"1.8296e-04",
"0.96",
"2.0897e-04",
"2.8808e-05",
"8.5852e-06",
"2.4448e-04",
"0.97",
"3.0069e-04",
"4.5176e-05",
"6.6566e-06",
"3.9274e-04",
"0.98",
"6.8093e-04",
"6.6661e-05",
"7.7844e-06",
"9.0327e-04",
"0.99",
"2.2000e-03",
"3.6345e-04",
"1.2136e-05",
"2.6000e-03",
"(25×",
"25",
"sub–domain",
"grid",
"points",
")",
"(50×",
"50",
"sub–domain",
"grid",
"points",
")",
"(100×",
"100",
"sub–domain",
"grid",
"points",
")",
"(100×",
"100",
"grid",
"points)",
"y",
"The",
"present",
"FD–PINNs",
"The",
"present",
"FD–PINNs",
"The",
"present",
"FD–PINNs",
"The",
"standard",
"FD–PINNs"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00014v1_1763715318/figures/2501.00014v1-Table4.7-1.png
|
{
"x1": 72,
"x2": 525.54638671875,
"y1": 442.6649475097656,
"y2": 456.114990234375
}
|
300
|
1
| 1
|
Figure
|
{
"x1": 212.88,
"x2": 384,
"y1": 108.47999999999999,
"y2": 267.84
}
|
Figure 1: Geometry of a 2D square lid–driven cavity.
|
[
"y",
"x",
"1",
"0",
"1"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00014v1_1763715318/figures/2501.00014v1-Figure1-1.png
|
{
"x1": 200.50100708007812,
"x2": 397.0421447753906,
"y1": 292.02996826171875,
"y2": 296.0150146484375
}
|
300
|
7
| 9
|
Figure
|
{
"x1": 142.79999999999998,
"x2": 455.52,
"y1": 104.39999999999999,
"y2": 584.88
}
|
Figure 7: a–d.) Error in velocity magnitude generated by the standard FD–PINNs for the Reynolds number Re=1000 with 100× 100, 120× 120, 150× 150 and 300× 300 grid points, respectively. e–h.) Error in the lop left corner of the cavity, i–l.) Error in the top right corner, m-p.) Error in the lower left corner, q–t.) Error in the lower right corner.
|
[
"0",
"0.002",
"0.004",
"0.006",
"0.008",
"0.01",
"0.012",
"0.014",
"0.016",
"0.018",
"0.02",
"(t)",
"0.1",
"0.05",
"(s)",
"0.9",
"0.95",
"1",
"0",
"0.1",
"0.05",
"(r)",
"0.9",
"0.95",
"1",
"0",
"0.1",
"0.05",
"(q)",
"0.9",
"0.95",
"1",
"0",
"0.1",
"0.05",
"0.9",
"0.95",
"1",
"0",
"0",
"0.001",
"0.002",
"0.003",
"0.004",
"0.005",
"0.006",
"0.007",
"0.008",
"0.009",
"0.01",
"(p)",
"0.1",
"0.05",
"0",
"(o)",
"0",
"0.05",
"0.1",
"0.1",
"0.05",
"0",
"(n)",
"0",
"0.05",
"0.1",
"0.1",
"0.05",
"0",
"(m)",
"0",
"0.05",
"0.1",
"0.1",
"0.05",
"0",
"0.05",
"0.1",
"0",
"0",
"0.005",
"0.01",
"0.015",
"0.02",
"0.025",
"0.03",
"0.035",
"0.04",
"0.045",
"0.05",
"(l)",
"1",
"0.95",
"0.9",
"(k)",
"0.9",
"0.95",
"1",
"1",
"0.95",
"0.9",
"(j)",
"0.9",
"0.95",
"1",
"1",
"0.95",
"0.9",
"(i)",
"0.9",
"0.95",
"1",
"1",
"0.95",
"0.9",
"0.95",
"1",
"0.9",
"0",
"0.005",
"0.01",
"0.015",
"0.02",
"0.025",
"0.03",
"(h)",
"1",
"0.95",
"0.9",
"(g)",
"0",
"0.05",
"0.1",
"1",
"0.95",
"0.9",
"(f)",
"0",
"0.05",
"0.1",
"1",
"0.95",
"0.9",
"(e)",
"0",
"0.05",
"0.1",
"1",
"0.95",
"0",
"0.05",
"0.1",
"0.9",
"0",
"0.02",
"0.04",
"0.06",
"0.08",
"0.1",
"0.12",
"0.14",
"0.16",
"0.18",
"0.2",
"(d)",
"1",
"0.5",
"0",
"(c)",
"0",
"0.5",
"1",
"1",
"0.5",
"0",
"(b)",
"0",
"0.5",
"1",
"1",
"0.5",
"0",
"(a)",
"0",
"0.5",
"1",
"1",
"0.5",
"0",
"0.5",
"1",
"0"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00014v1_1763715318/figures/2501.00014v1-Figure7-1.png
|
{
"x1": 72,
"x2": 525.5454711914062,
"y1": 601.7259521484375,
"y2": 624.6400146484375
}
|
300
|
4.2
| 13
|
Table
|
{
"x1": 73.92,
"x2": 526.0799999999999,
"y1": 284.88,
"y2": 388.08
}
|
Table 4.2: The MSEu comparison between the present and the standard FD–PINNs for the velocity u at several vertical lines in the domain [0.1, 0.9]× [0, 1] of the cavity for the Reynolds number Re = 1000.
|
[
"(25×",
"25",
"sub–domain",
"grid",
"points",
")",
"(50×",
"50",
"sub–domain",
"grid",
"points",
")",
"(100×",
"100",
"sub–domain",
"grid",
"points",
")",
"(100×",
"100",
"grid",
"points)",
"0.10",
"1.2580e-04",
"4.5056e-05",
"4.2668e-05",
"1.1368e-04",
"0.20",
"2.8696e-04",
"2.1169e-04",
"1.7691e-04",
"1.7548e-04",
"0.30",
"3.5200e-04",
"3.3698e-04",
"3.2870e-04",
"3.8018e-04",
"0.40",
"6.0982e-04",
"5.6828e-04",
"5.4786e-04",
"5.8704e-04",
"0.50",
"7.3985e-04",
"7.2464e-04",
"7.1864e-04",
"7.2638e-04",
"0.60",
"6.9562e-04",
"7.1852e-04",
"7.2616e-04",
"6.7338e-04",
"0.70",
"4.2846e-04",
"5.0746e-04",
"5.4958e-04",
"4.4032e-04",
"0.80",
"3.4818e-04",
"3.9585e-04",
"4.2006e-04",
"2.2768e-04",
"0.90",
"6.2537e-05",
"1.1024e-04",
"1.4756e-04",
"6.1209e-05",
"x",
"The",
"present",
"FD–PINNs",
"The",
"present",
"FD–PINNs",
"The",
"present",
"FD–PINNs",
"The",
"standard",
"FD–PINNs"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00014v1_1763715318/figures/2501.00014v1-Table4.2-1.png
|
{
"x1": 71.99993896484375,
"x2": 525.5390625,
"y1": 260.258056640625,
"y2": 273.7081298828125
}
|
300
|
4.4
| 13
|
Table
|
{
"x1": 73.92,
"x2": 526.0799999999999,
"y1": 611.76,
"y2": 714
}
|
Table 4.4: The MSEu comparison between the present and the standard FD–PINNs for the velocity u at several vertical lines in the domain [0.91, 0.99]× [0, 1] of the cavity for the Reynolds number Re = 1000.
|
[
"(25×",
"25",
"sub–domain",
"grid",
"points",
")",
"(50×",
"50",
"sub–domain",
"grid",
"points",
")",
"(100×",
"100",
"sub–domain",
"grid",
"points",
")",
"(100×",
"100",
"grid",
"points)",
"0.91",
"5.2390e-05",
"8.5608e-05",
"1.1784e-04",
"6.2531e-05",
"0.92",
"5.1543e-05",
"6.4429e-05",
"9.0233e-05",
"7.4399e-05",
"0.93",
"6.3472e-05",
"4.7954e-05",
"6.5841e-05",
"1.0014e-04",
"0.94",
"9.2744e-05",
"3.7542e-05",
"4.5487e-05",
"1.4368e-04",
"0.95",
"1.4582e-04",
"3.4622e-05",
"2.9523e-05",
"2.1055e-04",
"0.96",
"2.3412e-04",
"4.0939e-05",
"1.7890e-05",
"3.1160e-04",
"0.97",
"3.8481e-04",
"6.0207e-05",
"1.0457e-05",
"4.7553e-04",
"0.98",
"6.7765e-04",
"1.0414e-04",
"7.8566e-06",
"7.8704e-04",
"0.99",
"1.3000e-03",
"2.1098e-04",
"1.7036e-05",
"1.4000e-03",
"x",
"The",
"present",
"FD–PINNs",
"The",
"present",
"FD–PINNs",
"The",
"present",
"FD–PINNs",
"The",
"standard",
"FD–PINNs"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00014v1_1763715318/figures/2501.00014v1-Table4.4-1.png
|
{
"x1": 72,
"x2": 525.5391235351562,
"y1": 587.0679321289062,
"y2": 600.5180053710938
}
|
300
|
4.3
| 13
|
Table
|
{
"x1": 73.92,
"x2": 526.0799999999999,
"y1": 447.84,
"y2": 551.04
}
|
Table 4.3: The MSEu comparison between the present and the standard FD–PINNs for the velocity u at several vertical lines in the domain [0.01, 0.09]× [0, 1] of the cavity for the Reynolds number Re = 1000.
|
[
"(25×",
"25",
"sub–domain",
"grid",
"points",
")",
"(50×",
"50",
"sub–domain",
"grid",
"points",
")",
"(100×",
"100",
"sub–domain",
"grid",
"points",
")",
"(100×",
"100",
"grid",
"points)",
"0.01",
"1.9000e-03",
"1.6973e-04",
"5.3916e-05",
"2.5000e-03",
"0.02",
"3.6008e-04",
"2.4029e-05",
"2.3642e-06",
"6.9050e-04",
"0.03",
"6.6109e-05",
"2.0272e-05",
"1.7614e-06",
"1.1031e-04",
"0.04",
"1.1037e-04",
"1.4707e-05",
"3.7727e-06",
"6.4359e-05",
"0.05",
"1.6296e-04",
"1.4325e-05",
"7.4290e-06",
"1.2288e-04",
"0.06",
"1.7529e-04",
"1.7112e-05",
"1.2526e-05",
"1.5543e-04",
"0.07",
"1.6507e-04",
"2.1920e-05",
"1.8831e-05",
"1.5596e-04",
"0.08",
"1.4893e-04",
"2.8301e-05",
"2.6081e-05",
"1.4224e-04",
"0.09",
"1.3486e-04",
"3.6040e-05",
"3.4062e-05",
"1.2645e-04",
"x",
"The",
"present",
"FD–PINNs",
"The",
"present",
"FD–PINNs",
"The",
"present",
"FD–PINNs",
"The",
"standard",
"FD–PINNs"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00014v1_1763715318/figures/2501.00014v1-Table4.3-1.png
|
{
"x1": 72,
"x2": 525.5391235351562,
"y1": 423.6629638671875,
"y2": 437.1130065917969
}
|
300
|
11
| 12
|
Figure
|
{
"x1": 145.2,
"x2": 452.4,
"y1": 104.39999999999999,
"y2": 490.08
}
|
Figure 11: a–d.) Error in the velocity magnitude for the Reynolds number Re=1000 generated by the standard FD–PINNs in the top left corner of the cavity with 100× 100 grid points, the present FD–PINNs with 25× 25, 50× 50 and 100× 100 sub–domain grid points, respectively. e–h.) Error in the lop right corner of the cavity, i–l.) Error in the lower left corner, m–p.) Error in the lower right corner.
|
[
"0",
"0.005",
"0.01",
"0.015",
"(p)",
"0.1",
"0.05",
"(o)",
"0.9",
"0.95",
"1",
"0",
"0.1",
"0.05",
"(n)",
"0.9",
"0.95",
"1",
"0",
"0.1",
"0.05",
"(m)",
"0.9",
"0.95",
"1",
"0",
"0.1",
"0.05",
"0.9",
"0.95",
"1",
"0",
"10",
"-3",
"0",
"0.5",
"1",
"1.5",
"2",
"2.5",
"3",
"3.5",
"4",
"(l)",
"0.1",
"0.05",
"0",
"(k)",
"0",
"0.05",
"0.1",
"0.1",
"0.05",
"0",
"(j)",
"0",
"0.05",
"0.1",
"0.1",
"0.05",
"0",
"(i)",
"0",
"0.05",
"0.1",
"0.1",
"0.05",
"0",
"0.05",
"0.1",
"0",
"0",
"0.005",
"0.01",
"0.015",
"0.02",
"0.025",
"0.03",
"0.035",
"0.04",
"0.045",
"0.05",
"(h)",
"1",
"0.95",
"0.9",
"(g)",
"0.9",
"0.95",
"1",
"1",
"0.95",
"0.9",
"(f)",
"0.9",
"0.95",
"1",
"1",
"0.95",
"0.9",
"(e)",
"0.9",
"0.95",
"1",
"1",
"0.95",
"0.9",
"0.95",
"1",
"0.9",
"0",
"0.005",
"0.01",
"0.015",
"0.02",
"0.025",
"0.03",
"(d)",
"1",
"0.95",
"0.9",
"(c)",
"0",
"0.05",
"0.1",
"1",
"0.95",
"0.9",
"(b)",
"0",
"0.05",
"0.1",
"1",
"0.95",
"0.9",
"(a)",
"0",
"0.05",
"0.1",
"1",
"0.95",
"0",
"0.05",
"0.1",
"0.9"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00014v1_1763715318/figures/2501.00014v1-Figure11-1.png
|
{
"x1": 72,
"x2": 525.5444946289062,
"y1": 506.9839782714844,
"y2": 539.3619995117188
}
|
300
|
5
| 7
|
Figure
|
{
"x1": 86.16,
"x2": 509.03999999999996,
"y1": 396,
"y2": 544.56
}
|
Figure 5: a.) Fluid streamlines using the reference solution for the Reynolds number Re=1000, b.) Comparison of the horizontal component of the reference velocity along the vertical centerline of the cavity against the Ghia et al. [39], c.) Comparison of the vertical component of the reference velocity along the horizontal centerline of the cavity against the Ghia et al. [39].
|
[
"(a)",
"(b)",
"(c)",
"Ghia",
"et",
"al.",
"Reference",
"solution",
"x",
"1",
"0.8",
"0.6",
"0.4",
"0.2",
"0",
"v",
"-0.5",
"0",
"0.5",
"Ghia",
"et",
"al.",
"Reference",
"solution",
"y",
"1",
"0.8",
"0.6",
"0.4",
"0.2",
"0",
"u",
"-0.5",
"0",
"0.5",
"1",
"Y",
"1",
"0.8",
"0.6",
"0.4",
"0.2",
"0",
"X",
"0",
"0.2",
"0.4",
"0.6",
"0.8",
"1"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00014v1_1763715318/figures/2501.00014v1-Figure5-1.png
|
{
"x1": 72,
"x2": 525.5410766601562,
"y1": 558.6909790039062,
"y2": 591.0689697265625
}
|
300
|
2
| 3
|
Figure
|
{
"x1": 162.96,
"x2": 441.84,
"y1": 546,
"y2": 660
}
|
Figure 2: Neural networks with four hidden layers and eight neurons in each.
|
[
"P",
"V",
"U",
"Y",
"X"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00014v1_1763715318/figures/2501.00014v1-Figure2-1.png
|
{
"x1": 153.8419952392578,
"x2": 439.9390869140625,
"y1": 700.9639282226562,
"y2": 704.948974609375
}
|
300
|
14
| 16
|
Figure
|
{
"x1": 79.44,
"x2": 523.4399999999999,
"y1": 145.92,
"y2": 288.47999999999996
}
|
Figure 14: Final loss of the present FD–PINNs with 25× 25, 50× 50 and 100× 100 sub–domain grid points.
|
[
"100",
"100",
"sub-domain",
"grid",
"points",
"50",
"50",
"sub-domain",
"grid",
"points",
"25",
"25",
"sub-domain",
"grid",
"points",
"L",
"o",
"s",
"s",
"10",
"-8",
"10",
"-10",
"Index",
"of",
"subdomains",
"2",
"4",
"6",
"8",
"10",
"12",
"14",
"16"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00014v1_1763715318/figures/2501.00014v1-Figure14-1.png
|
{
"x1": 97.10800170898438,
"x2": 500.43353271484375,
"y1": 307.47296142578125,
"y2": 311.4580078125
}
|
300
|
4.1
| 11
|
Table
|
{
"x1": 73.92,
"x2": 526.0799999999999,
"y1": 542.88,
"y2": 693.12
}
|
Table 4.1: Comparison of the center of secondary vortices.
|
[
"Li",
"et",
"al.",
"[43]",
"0.0855",
"0.0797",
"0.8619",
"0.1125",
"Tian",
"and",
"Yu",
"[6]",
"0.0859",
"0.0781",
"0.8594",
"0.1094",
"Ghia",
"et",
"al.",
"[39]",
"0.0859",
"0.0781",
"0.8594",
"0.1094",
"Gupta",
"and",
"Kalita",
"[42]",
"0.0875",
"0.0750",
"0.8625",
"0.1125",
"Bruneau",
"and",
"Jouron",
"[32]",
"0.0859",
"0.0820",
"0.8711",
"0.1094",
"Reference",
"solution",
"0.0830",
"0.0780",
"0.8690",
"0.1110",
"Botella",
"and",
"Peyret",
"[41]",
"0.0833",
"0.0781",
"0.8640",
"0.1118",
"The",
"present",
"FD–PINNs",
"(25",
"×",
"25",
"sub–domain",
"grid",
"points)",
"0.0735",
"0.0753",
"0.8695",
"0.1210",
"The",
"present",
"FD–PINNs",
"(50",
"×",
"50",
"sub–domain",
"grid",
"points)",
"0.0731",
"0.0673",
"0.8750",
"0.1270",
"The",
"present",
"FD–PINNs",
"(100",
"×",
"100",
"sub–domain",
"grid",
"points)",
"0.0782",
"0.0535",
"0.8795",
"0.1330",
"The",
"standard",
"FD–PINNs",
"(100",
"×",
"100",
"grid",
"points)",
"0.0845",
"0.0249",
"0.8940",
"0.1470",
"Source",
"x",
"y",
"x",
"y",
"Lower",
"left",
"corner",
"Lower",
"right",
"corner"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00014v1_1763715318/figures/2501.00014v1-Table4.1-1.png
|
{
"x1": 188.7160186767578,
"x2": 408.8287353515625,
"y1": 528.2249145507812,
"y2": 532.2099609375
}
|
300
|
10
| 11
|
Figure
|
{
"x1": 75.11999999999999,
"x2": 523.92,
"y1": 336,
"y2": 452.64
}
|
Figure 10: a.) Fluid streamlines using the standard FD–PINNs with 100× 100 grid points in the lower right corner of the cavity. Fluid streamlines using the present FD–PINNs with different sub–domain grid points in the lower right corner of the cavity: b.) 100× 100, c.) 50× 50, and d.) 25× 25.
|
[
"(a)",
"(b)",
"(c)",
"(d)",
"Y",
"0.4",
"0.35",
"0.3",
"0.25",
"0.2",
"0.15",
"0.1",
"0.05",
"0",
"X",
"0.6",
"0.7",
"0.8",
"0.9",
"1",
"Y",
"0.4",
"0.35",
"0.3",
"0.25",
"0.2",
"0.15",
"0.1",
"0.05",
"0",
"X",
"0.6",
"0.7",
"0.8",
"0.9",
"1",
"Y",
"0.4",
"0.35",
"0.3",
"0.25",
"0.2",
"0.15",
"0.1",
"0.05",
"0",
"X",
"0.6",
"0.7",
"0.8",
"0.9",
"1",
"Y",
"0.4",
"0.35",
"0.3",
"0.25",
"0.2",
"0.15",
"0.1",
"0.05",
"0",
"X",
"0.6",
"0.7",
"0.8",
"0.9",
"1"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00014v1_1763715318/figures/2501.00014v1-Figure10-1.png
|
{
"x1": 72.00003051757812,
"x2": 525.5426025390625,
"y1": 466.89996337890625,
"y2": 489.8139953613281
}
|
300
|
9
| 11
|
Figure
|
{
"x1": 76.8,
"x2": 522.48,
"y1": 154.79999999999998,
"y2": 270.96
}
|
Figure 9: a.) Fluid streamlines using the standard FD–PINNs with 100 × 100 grid points in the lower left corner of the cavity. Fluid streamlines using the present FD–PINNs with different sub–domain grid points in the lower left corner of the cavity: b.) 100× 100, c.) 50× 50, and d.) 25× 25.
|
[
"(a)",
"(b)",
"(c)",
"(d)",
"Y",
"0.3",
"0.25",
"0.2",
"0.15",
"0.1",
"0.05",
"0",
"X",
"0",
"0.1",
"0.2",
"0.3",
"Y",
"0.3",
"0.25",
"0.2",
"0.15",
"0.1",
"0.05",
"0",
"X",
"0",
"0.1",
"0.2",
"0.3",
"Y",
"0.3",
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"0.2",
"0.15",
"0.1",
"0.05",
"0",
"X",
"0",
"0.1",
"0.2",
"0.3",
"Y",
"0.3",
"0.25",
"0.2",
"0.15",
"0.1",
"0.05",
"0",
"X",
"0",
"0.1",
"0.2",
"0.3"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00014v1_1763715318/figures/2501.00014v1-Figure9-1.png
|
{
"x1": 72.00003051757812,
"x2": 525.5419921875,
"y1": 285.094970703125,
"y2": 308.0090026855469
}
|
300
|
6
| 8
|
Figure
|
{
"x1": 159.6,
"x2": 437.28,
"y1": 105.83999999999999,
"y2": 405.12
}
|
Figure 6: Fluid streamlines for the Reynolds number Re=1000 using the standard FD–PINNs with a.) 100×100 grid points, b.) 120 × 120 grid points, c.) 150 × 150 grid points, and d.) 300 × 300 grid points. Note that the grid points mentioned throughout this section are referred to as the interior grid points of a domain or sub–domain.
|
[
"(c)",
"(d)",
"Y",
"1",
"0.8",
"0.6",
"0.4",
"0.2",
"0",
"X",
"0",
"0.2",
"0.4",
"0.6",
"0.8",
"1",
"Y",
"1",
"0.8",
"0.6",
"0.4",
"0.2",
"0",
"X",
"0",
"0.2",
"0.4",
"0.6",
"0.8",
"1",
"(a)",
"(b)",
"Y",
"1",
"0.8",
"0.6",
"0.4",
"0.2",
"0",
"X",
"0",
"0.2",
"0.4",
"0.6",
"0.8",
"1",
"Y",
"1",
"0.8",
"0.6",
"0.4",
"0.2",
"0",
"X",
"0",
"0.2",
"0.4",
"0.6",
"0.8",
"1"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00014v1_1763715318/figures/2501.00014v1-Figure6-1.png
|
{
"x1": 72,
"x2": 525.546630859375,
"y1": 419.3759765625,
"y2": 442.2900085449219
}
|
300
|
3
| 4
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Figure
|
{
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Figure 3: Framework for second–order central difference scheme
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[
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300
|
12
| 15
|
Figure
|
{
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|
Figure 12: a.) Fluid streamlines using the standard FD–PINNs in the lower left corner of the cavity with 120 × 120 grid points. b.) Fluid streamlines using the present FD–PINNs in the lower left corner of the cavity with 50×50 sub–domain grid points. c.) Fluid streamlines using the standard FD–PINNs in the lower right corner of the cavity with with 120× 120 grid points. d.) Fluid streamlines using the present FD–PINNs in the lower right corner of the cavity with 50× 50 sub–domain grid points.
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300
|
13
| 15
|
Figure
|
{
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|
Figure 13: a.) Fluid streamlines for the Reynolds number Re=400 using the standard FD–PINNs with 100 × 100 grid points. b.) Fluid streamlines for the Reynolds number Re=400 using the present FD–PINNs with 25× 25 sub–domain grid points.
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300
|
6
| 14
|
Figure
|
{
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|
Figure 6: (a) Schematic diagram of a current-mode digital to analog converter for providing the biasing current to a stochastic MTJ. (b) Variation of the Bernoulli parameter of the stochastic MTJ with bias current. Red triangles are data point obtained from micromagnetic simulations, while the grey dotted line is a theoretical fit (sigmoid function).
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00015v1_1763715332/figures/2501.00015v1-Figure6-1.png
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{
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300
|
8
| 20
|
Figure
|
{
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|
Figure 8: Back-of-the-envelope power consumption analysis in femtojoules (logarithmic scale) for 50 000 samples from rejection sampling (RJ) and the mixture-based sampling approach. RJ sampling assumes draws using mt19937arO3 according to benchmarks from Antunes & Hill (2024). Other operations of the S-MTJ approach refer to the normalization overhead.
|
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300
|
9
| 20
|
Figure
|
{
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|
Figure 9: Back-of-the-envelope power consumption analysis in femtojoules (logarithmic scale) for 50 000 samples from rejection sampling (RJ) and the mixture-based sampling approach. RJ sampling assumes draws using s-MTJs. Other operations of the S-MTJ approach refer to the normalization overhead.
|
[
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300
|
1
| 6
|
Figure
|
{
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|
Figure 1: Hardware setup for sampling one value from a uniform Float16 distribution.
|
[
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300
|
10
| 21
|
Figure
|
{
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|
Figure 10: Visualization of samples obtained with three different assumptions. Perfect Resolution Sampling assumes the precise values obtained from Equations 5-8 in Section 4.2. Control Bits Sampling v1 assumes the closest distance measure to actual obtainable control bits. Control Bits Sampling v2 assumes that each exponent bit should actually be different over closest distance, even if the physically closest distance would imply redundant values.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00015v1_1763715332/figures/2501.00015v1-Figure10-1.png
|
{
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|
300
|
2
| 9
|
Table
|
{
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|
Table 2: Approximation error comparison (mixture-based approach vs. closed-form solution)
|
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{
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|
300
|
4
| 13
|
Figure
|
{
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|
Figure 4: (a) Schematic illustration of the self-energy (E) of a nanomagnet with respect to the polar angle (θM ) of its magnetization (indicated by thick arrows). (b) Natural frequency of stochastic switching for a nanomagnet of a particular diameter at different temperatures.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00015v1_1763715332/figures/2501.00015v1-Figure4-1.png
|
{
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|
300
|
5
| 13
|
Figure
|
{
"x1": 127.92,
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|
Figure 5: Dynamics of the normalized resistance of a stochastic MTJ for different bias current densities. (a) Ibias = 0 produces equal probability of observing the high or low state. (b) Histogram of the observed resistance state for Ibias = 0. (c, d) Trace and histogram of the observed resistance for a bias current of 2 × 1011 A/m2. (e, f) Trace and histogram of the observed resistance for a bias current of -2 × 1011 A/m2.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00015v1_1763715332/figures/2501.00015v1-Figure5-1.png
|
{
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|
300
|
11
| 22
|
Figure
|
{
"x1": 148.79999999999998,
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"y2": 159.12
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|
Figure 11: Histogram of 100 000 samples with 400 bins over the full Float16 range obtained by Perfect Resolution Sampling.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00015v1_1763715332/figures/2501.00015v1-Figure11-1.png
|
{
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|
300
|
14
| 22
|
Figure
|
{
"x1": 148.79999999999998,
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|
Figure 14: Histogram of 100 000 samples with 400 bins spanning the full Float16 range obtained via Control Bits Sampling v1 with rejecting from the two most overrepresented bins around zero.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00015v1_1763715332/figures/2501.00015v1-Figure14-1.png
|
{
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|
300
|
12
| 22
|
Figure
|
{
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|
Figure 12: Histogram of 100 000 samples with 400 bins spanning the full Float16 range obtained via Control Bits Sampling v1. The values show a slight bias, favoring those near zero. Each bin represents 0.25% of the overall range. Flattening the distribution by rejecting samples from the two most overrepresented bins would affect only 0.5 % of samples.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00015v1_1763715332/figures/2501.00015v1-Figure12-1.png
|
{
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|
300
|
13
| 22
|
Figure
|
{
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|
Figure 13: Histogram of 100 000 samples with 400 bins spanning the full Float16 range obtained via Control Bits Sampling v2. The values show a slight bias, favoring those near zero. Each bin represents 0.25% of the overall range. Flattening the distribution by rejecting samples from the two most overrepresented bins would affect only 0.5% of samples.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00015v1_1763715332/figures/2501.00015v1-Figure13-1.png
|
{
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|
300
|
7
| 18
|
Figure
|
{
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|
Figure 7: Power consumption analysis in Joules (logarithmic scale) for 230 random numbers. Benchmarks were performed by Antunes & Hill (2024).
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"4O",
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"4O",
"2",
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"to",
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"e",
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"m",
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"M",
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"xA",
"tO",
"nc",
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"32",
"k3",
"aO",
"2",
"m",
"rg",
"32",
"k3",
"a",
"py",
"th",
"on",
"On",
"eB",
"yO",
"ne",
"py",
"th",
"on",
"Ta",
"sk",
"se",
"tA",
"tO",
"nc",
"e",
"py",
"th",
"on",
"At",
"On",
"ce",
"nu",
"m",
"py",
"On",
"eB",
"yO",
"ne",
"nu",
"m",
"py",
"M",
"tO",
"ne",
"By",
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"e",
"nu",
"m",
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"Ph",
"ilo",
"xO",
"ne",
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"By",
"On",
"e",
"ou",
"r",
"ap",
"pr",
"oa",
"ch",
"w",
"/o",
"t",
"ra",
"ns",
"fo",
"rm",
"ou",
"r",
"ap",
"pr",
"oa",
"ch",
"w",
"it",
"h",
"tr",
"an",
"sf",
"or",
"m",
"lo",
"xA",
"rP",
"hi",
"te",
"ge",
"py",
"In",
"nu",
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"e",
"m",
"t1",
"99",
"37",
"ar",
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"ge",
"rO",
"3",
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"flo",
"wI",
"nt",
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"At",
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"ce",
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"99",
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"ar",
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"2",
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"99",
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"rT",
"as",
"te",
"ge",
"py",
"In",
"nu",
"m",
"eg",
"er",
"2I",
"nt",
"pc",
"g3"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00015v1_1763715332/figures/2501.00015v1-Figure7-1.png
|
{
"x1": 108,
"x2": 503.998291015625,
"y1": 399.9245300292969,
"y2": 416.885986328125
}
|
300
|
16
| 23
|
Figure
|
{
"x1": 156.96,
"x2": 450.24,
"y1": 410.88,
"y2": 638.16
}
|
Figure 16: Sampling after Prior-Likelihood Transformation: Using a Beta(2, 5) prior and a N (0.1, 0.12) likelihood, the final distribution is derived by multiplying their densities.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00015v1_1763715332/figures/2501.00015v1-Figure16-1.png
|
{
"x1": 108,
"x2": 503.9961242675781,
"y1": 661.9335327148438,
"y2": 678.89501953125
}
|
300
|
15
| 23
|
Figure
|
{
"x1": 158.88,
"x2": 448.08,
"y1": 120,
"y2": 344.15999999999997
}
|
Figure 15: Sampling from the convolution of two Gaussian distributions, N (0.2, 0.12) and N (0.2, 0.12), resulting in N (0.4, √ 0.12 + 0.12).
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00015v1_1763715332/figures/2501.00015v1-Figure15-1.png
|
{
"x1": 107.99993896484375,
"x2": 503.99993896484375,
"y1": 368.0105285644531,
"y2": 386.5989990234375
}
|
300
|
3
| 8
|
Figure
|
{
"x1": 109.92,
"x2": 498,
"y1": 226.79999999999998,
"y2": 304.56
}
|
Figure 3: Physical approximation error comparison for the first three moments of the uniform distribution (s-MTJ-based approach vs. closed-form solution sampling). Second moment standard deviation omitted due to equivalence to the means.
|
[
"(a)",
"First",
"Moment",
"(Mean)",
"(b)",
"Second",
"Moment",
"(Variance)",
"(c)",
"Third",
"Moment",
"(Kurtosis)"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00015v1_1763715332/figures/2501.00015v1-Figure3-1.png
|
{
"x1": 108,
"x2": 504.00323486328125,
"y1": 317.8235168457031,
"y2": 345.74395751953125
}
|
300
|
2
| 8
|
Figure
|
{
"x1": 111.83999999999999,
"x2": 501.12,
"y1": 86.16,
"y2": 183.35999999999999
}
|
Figure 2: Possible Bernoulli resolutions for s-MTJ device with 4 control bits.
|
[
"33",
"0.",
"99",
"11",
"0.",
"99",
"82",
"0.",
"98",
"43",
"0.",
"98",
"92",
"0.",
"97",
"25",
"0.",
"97",
"37",
"0.",
"96",
"23",
"0.",
"95",
"74",
"0.",
"93",
"83",
"0.",
"91",
"41",
"0.",
"89",
"37",
"0.",
"86",
"64",
"0.",
"82",
"13",
"84",
"0.",
"78",
"82",
"0.",
"72",
"0.",
"66",
"=",
"1]",
"E[",
"b",
"i",
"1.0",
"0.8",
"0.6",
"0.4",
"0",
"5",
"10",
"15",
"20",
"Current",
"Bias(µA)"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00015v1_1763715332/figures/2501.00015v1-Figure2-1.png
|
{
"x1": 152.23800659179688,
"x2": 459.763427734375,
"y1": 199.09353637695312,
"y2": 205.09600830078125
}
|
300
|
1
| 4
|
Table
|
{
"x1": 210,
"x2": 402.24,
"y1": 102,
"y2": 150
}
|
Table 1: Required 1-bit occurrences in a 3-bit exponent representation
|
[
"1-Bit",
"Count",
"e3",
"0",
"0",
"0",
"0",
"24",
"25",
"26",
"27",
"e2",
"0",
"0",
"22",
"23",
"0",
"0",
"26",
"27",
"e1",
"0",
"21",
"0",
"23",
"0",
"25",
"0",
"27"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00015v1_1763715332/figures/2501.00015v1-Table1-1.png
|
{
"x1": 166.31500244140625,
"x2": 445.6861267089844,
"y1": 83.53055572509766,
"y2": 89.53302001953125
}
|
300
|
3
| 15
|
Table
|
{
"x1": 157.92,
"x2": 454.08,
"y1": 427.91999999999996,
"y2": 540
}
|
Table 3: Parameters Used in Micromagnetic Simulations With the MuMax3 Code.
|
[
"Saturation",
"magnetization",
"(MS)",
"3.95×",
"104",
"A/m",
"(Kajale",
"et",
"al.,",
"2024)",
"Effective",
"anisotropy",
"field",
"(KU",
")",
"3.02×",
"106",
"A/m",
"(Kajale",
"et",
"al.,",
"2024)",
"Permeability",
"of",
"free",
"space",
"(µ0)",
"1.26×",
"10−6",
"kg·m/s2·A2",
"Temperature",
"(T",
")",
"300",
"K",
"Gilbert",
"damping",
"constant",
"(α)",
"0.02",
"(typical)",
"Exchange",
"stiffness",
"(Aex)",
"1.3×",
"1013",
"J/m",
"Thickness",
"1",
"nm",
"Diameter",
"2",
"nm",
"Parameter",
"Value"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00015v1_1763715332/figures/2501.00015v1-Table3-1.png
|
{
"x1": 141.8670196533203,
"x2": 470.1346740722656,
"y1": 408.86431884765625,
"y2": 414.8667907714844
}
|
300
|
10
| 10
|
Figure
|
{
"x1": 84.96,
"x2": 527.04,
"y1": 92.88,
"y2": 476.88
}
|
Figure 10: Case 2: Comparison of the true phase and displacement fields with the fields predicted by the data-driven two-step DeepONet for three applied displacement values: Ut = 0.005, Ut = 0.145, and Ut = 0.2. In each plot, the first row shows the predictions, the second row shows the true values, and the bottom row illustrates the absolute error.
|
[
"(b)",
"Predicted",
"displacement",
"u",
"(c)",
"Predicted",
"displacement",
"v",
"(a)",
"Predicted",
"damage",
"α"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00016v2_1763715345/figures/2501.00016v2-Figure10-1.png
|
{
"x1": 85.0389404296875,
"x2": 526.9638671875,
"y1": 490.2819519042969,
"y2": 513.1959838867188
}
|
300
|
14
| 14
|
Figure
|
{
"x1": 86.88,
"x2": 525.12,
"y1": 410.88,
"y2": 522
}
|
Figure 14: Case 1: Basis functions generated by the trunk network for modes 1, 2, 21, and 45.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00016v2_1763715345/figures/2501.00016v2-Figure14-1.png
|
{
"x1": 129.218994140625,
"x2": 482.7821350097656,
"y1": 533.678955078125,
"y2": 537.6640014648438
}
|
300
|
3
| 14
|
Table
|
{
"x1": 86.88,
"x2": 525.12,
"y1": 55.919999999999995,
"y2": 125.03999999999999
}
|
Table 3: Data-driven two-step DeepONet: Training details for different data-driven cases using two-step DeepONet architectures. The number of sensor points used in the trunk network for each case is listed in Table 1. In all cases, 45 samples are used for training and 5 samples for testing. The results reported were obtained using an NVIDIA H100 GPU.
|
[
"Case",
"4",
"300000",
"epochs",
"600000",
"epochs",
"16018",
"s",
"1403",
"s",
"1395",
"s",
"Case",
"3",
"500000",
"epochs",
"700000",
"epochs",
"95621",
"s",
"2444",
"s",
"2444/2438",
"s",
"Case",
"2",
"700000",
"epochs",
"900000",
"epochs",
"22521",
"s",
"1063",
"s",
"1078/1082",
"s",
"Case",
"1",
"500000",
"epochs",
"500000",
"epochs",
"1381",
"s",
"378",
"s",
"386",
"s",
"Case",
"Trunk",
"Branch",
"Comp.",
"Time",
"(Trunk)",
"Comp.",
"Time",
"(α)",
"Comp.",
"Time",
"(u/v)"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00016v2_1763715345/figures/2501.00016v2-Table3-1.png
|
{
"x1": 85.03900146484375,
"x2": 526.96044921875,
"y1": 137.43994140625,
"y2": 169.8179931640625
}
|
300
|
7
| 20
|
Table
|
{
"x1": 228.95999999999998,
"x2": 383.03999999999996,
"y1": 55.919999999999995,
"y2": 112.08
}
|
Table 7: DeepOKAN: Training details for various data-driven cases using DeepOKAN architectures. In all cases, the branch network is trained with 45 samples and tested with 5 samples, while the number of points used in the trunk network for each case is provided in Table 1.
|
[
"Case",
"4",
"500000",
"5916",
"s",
"Case",
"2",
"100000",
"397",
"s",
"Case",
"1",
"300000",
"1239",
"s",
"Case",
"Epochs",
"Comp.",
"Time"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00016v2_1763715345/figures/2501.00016v2-Table7-1.png
|
{
"x1": 85.03900146484375,
"x2": 526.961669921875,
"y1": 123.89093017578125,
"y2": 146.80499267578125
}
|
300
|
3
| 6
|
Figure
|
{
"x1": 108.96,
"x2": 503.03999999999996,
"y1": 55.919999999999995,
"y2": 183.12
}
|
Figure 3: Schematic of the two-step DeepONet for predicting the phase field α and the components u and v of the displacement field u. During the training, first, the trunk network parameters, along with matrices Au, Av , and Aα, are optimized, followed by the QR factorization of Φ∗, and finally the training of the branch network.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00016v2_1763715345/figures/2501.00016v2-Figure3-1.png
|
{
"x1": 85.03897094726562,
"x2": 526.9599609375,
"y1": 194.865966796875,
"y2": 217.780029296875
}
|
300
|
8
| 9
|
Figure
|
{
"x1": 238.79999999999998,
"x2": 373.2,
"y1": 84.72,
"y2": 250.07999999999998
}
|
Figure 8: Case 2: SEN specimen under tensile loading: geometry and boundary conditions.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00016v2_1763715345/figures/2501.00016v2-Figure8-1.png
|
{
"x1": 134.7779998779297,
"x2": 477.2250671386719,
"y1": 261.8929443359375,
"y2": 265.87799072265625
}
|
300
|
9
| 9
|
Figure
|
{
"x1": 86.88,
"x2": 525.12,
"y1": 426.96,
"y2": 515.04
}
|
Figure 9: Case 2: The evolution of the loss during the training of the trunk and branch networks for the problem of the SEN specimens under tensile loading conditions. The middle figure shows the adjusted losses after applying λα, λu, and λv , which are modified to balance the contributions of each loss. Since lossu in the trunk network is relatively small, the corresponding weight λu controls its influence. Conversely, because lossα is larger than the other losses, λα is adjusted to ensure a balanced contribution across all components.
|
[] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00016v2_1763715345/figures/2501.00016v2-Figure9-1.png
|
{
"x1": 85.03900146484375,
"x2": 526.9627075195312,
"y1": 527.1649780273438,
"y2": 569.0079956054688
}
|
300
|
2
| 13
|
Table
|
{
"x1": 182.88,
"x2": 429.12,
"y1": 642.9599999999999,
"y2": 693.12
}
|
Table 2: Data-driven two-step DeepONet: MAE for u, v, and α for Case 2, Case 3, and Case 4.
|
[
"Case",
"MAE",
"u",
"MAE",
"v",
"MAE",
"α",
"Tensile",
"(Case",
"2)",
"1.60e-04",
"2.46e-03",
"1.09e-02",
"Shear",
"(Case",
"3)",
"6.87e-04",
"1.56e-04",
"6.80e-04",
"Branching",
"(Case",
"4)",
"1.23e-03",
"5.14e-04",
"4.60e-03"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00016v2_1763715345/figures/2501.00016v2-Table2-1.png
|
{
"x1": 113.41600036621094,
"x2": 498.5829162597656,
"y1": 705.4749755859375,
"y2": 709.4600219726562
}
|
300
|
13
| 13
|
Figure
|
{
"x1": 84.96,
"x2": 527.04,
"y1": 55.919999999999995,
"y2": 440.15999999999997
}
|
Figure 13: Case 4: Comparison of the predicted (top row) and true (middle row) fields for (a) damage α, (b) displacement u, and (c) displacement v at three applied displacement values: Ut = 0.1, Ut = 0.3, and Ut = 0.5, representing crack propagation with branching. The bottom row in each plot shows the absolute error between the predicted and true fields.
|
[
"(b)",
"Predicted",
"displacement",
"u",
"(c)",
"Predicted",
"displacement",
"v",
"(a)",
"Predicted",
"damage",
"α"
] |
/home/yz979/palmer_scratch/SciMolmo-LaTeX-Source-Processing-Toolkit/pdfparser/pdf2latex/2025_new/temp/figures_2501.00016v2_1763715345/figures/2501.00016v2-Figure13-1.png
|
{
"x1": 85.03897094726562,
"x2": 526.9644165039062,
"y1": 453.4759521484375,
"y2": 485.8539733886719
}
|
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