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2101.00098__body_000013__cite_0013__start_1576__ref_4f73c48736ce5f7ea6122853ea73b71c90f21940
2,101.00098
2,108.13004
2101.00098__body_000013
13
Single-View 3D Reconstruction
3
subsection
{{cite:4f73c48736ce5f7ea6122853ea73b71c90f21940}}
1,576
1,625
2101.00098__ref__4f73c48736ce5f7ea6122853ea73b71c90f21940
Single-view 3D reconstruction aims at generating the 3D model of an object based on a single 2D projection of it. Currently, deep Convolutional Neural Networks (ConvNets) based methods have achieved the highest accuracy in various benchmarks by using both low-level image cues, e.g., texture, and high-level semantic inf...
Single-view 3D reconstruction aims at generating the 3D model of an object based on a single 2D projection of it. Currently, deep Convolutional Neural Networks (ConvNets) based methods have achieved the highest accuracy in various benchmarks by using both low-level image cues, e.g., texture, and high-level semantic inf...
A few existing work <OTHER_CIT>, <OTHER_CIT>, <TARGET_CIT> explored teeth reconstruction from X-ray, however, they either targeted at single tooth or worked with synthesized images only, which cannot serve our propose of patient-specific modeling and demonstration.
Single-view 3D reconstruction aims at generating the 3D model of an object based on a single 2D projection of it. Currently, deep Convolutional Neural Networks (ConvNets) based methods have achieved the highest accuracy in various benchmarks by using both low-level image cues, e.g., texture, and high-level semantic inf...
CAD tools have been widely applied in dentistry to improve the design of dental restorations, e.g. crowns, dental implants and orthodontic appliances <OTHER_CIT>, <OTHER_CIT>. Specifically, models of patients' oral cavity are created from digital 3D scanning, based on which dentists produce a virtual design of restorat...
2101.00098__body_000012|2101.00098__body_000013|2101.00098__body_000014
[SECTION] Single-View 3D Reconstruction [CONTEXT] CAD tools have been widely applied in dentistry to improve the design of dental restorations, e.g. crowns, dental implants and orthodontic appliances <OTHER_CIT>, <OTHER_CIT>. Specifically, models of patients' oral cavity are created from digital 3D scanning, based on ...
Single-View 3D Reconstruction
21
4
21
4
2101.00318__body_000000__cite_0001__start_190__ref_bf13f619b2f5c5b48b1fce9303bfa625d0ec56d6
2,101.00318
2,101.00316
2101.00318__body_000000
0
Introduction
1
section
{{cite:bf13f619b2f5c5b48b1fce9303bfa625d0ec56d6}}
190
239
2101.00318__ref__bf13f619b2f5c5b48b1fce9303bfa625d0ec56d6
The goal of unsupervised domain adaptation (UDA) is to transfer knowledge learned from a label-rich domain to new unlabeled target domains {{cite:1acfae6bca3fdb27d8d59584061ffec7f03f6dbf}}, {{cite:bf13f619b2f5c5b48b1fce9303bfa625d0ec56d6}}, {{cite:80f1542b4f6be99c38124cf8d89f12c46f726db2}}, {{cite:f7f967ce275cef99377c2...
The goal of unsupervised domain adaptation (UDA) is to transfer knowledge learned from a label-rich domain to new unlabeled target domains <OTHER_CIT>, <TARGET_CIT>, <OTHER_CIT>, <OTHER_CIT>. The conventional adversarial training and maximum mean discrepancy (MMD) based methods propose to align the marginal distributio...
The goal of unsupervised domain adaptation (UDA) is to transfer knowledge learned from a label-rich domain to new unlabeled target domains <OTHER_CIT>, <TARGET_CIT>, <OTHER_CIT>, <OTHER_CIT>.
The goal of unsupervised domain adaptation (UDA) is to transfer knowledge learned from a label-rich domain to new unlabeled target domains <OTHER_CIT>, <TARGET_CIT>, <OTHER_CIT>, <OTHER_CIT>. The conventional adversarial training and maximum mean discrepancy (MMD) based methods propose to align the marginal distributio...
The goal of unsupervised domain adaptation (UDA) is to transfer knowledge learned from a label-rich domain to new unlabeled target domains <OTHER_CIT>, <TARGET_CIT>, <OTHER_CIT>, <OTHER_CIT>. The conventional adversarial training and maximum mean discrepancy (MMD) based methods propose to align the marginal distributio...
2101.00318__body_000000|2101.00318__body_000001
[SECTION] Introduction [CONTEXT] The goal of unsupervised domain adaptation (UDA) is to transfer knowledge learned from a label-rich domain to new unlabeled target domains <OTHER_CIT>, <TARGET_CIT>, <OTHER_CIT>, <OTHER_CIT>. The conventional adversarial training and maximum mean discrepancy (MMD) based methods propose...
Introduction
47
33
47
33
2101.00318__body_000007__cite_0004__start_713__ref_afc677dcb24bfbd1086d38328af76b63147eca49
2,101.00318
2,101.00317
2101.00318__body_000007
7
Related Work
2
section
{{cite:afc677dcb24bfbd1086d38328af76b63147eca49}}
713
762
2101.00318__ref__afc677dcb24bfbd1086d38328af76b63147eca49
In recent years, big data drives the fast development of deep learning, which has transformed many fields, such as computer vision and medical image analysis {{cite:d50524f3e7c6b16647d8937c77673179f212f5e1}}, {{cite:72d97836bc394a2fe9a10425616c367d56dd91dc}}, {{cite:ee125d0add2d5b4c2e8662674bf596030716d8af}}. Deep lear...
In recent years, big data drives the fast development of deep learning, which has transformed many fields, such as computer vision and medical image analysis <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. Deep learning has drastically transformed the way in which features are extracted and then fed into a prediction model into...
The effectiveness of deep learning has been demonstrated in many computer vision tasks, such as classification, detection, and segmentation <OTHER_CIT>, <TARGET_CIT>, <OTHER_CIT>, <OTHER_CIT>.
In recent years, big data drives the fast development of deep learning, which has transformed many fields, such as computer vision and medical image analysis <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. Deep learning has drastically transformed the way in which features are extracted and then fed into a prediction model into...
We propose to adaptively explore the subtype-wise conditional and label shifts in UDA without the subtype labels, and explicitly enforce the subtype-aware compactness. We systematically investigate the cases with or without the prior information on subtype numbers. Our reliability-path based sub-graph scheme can effec...
2101.00318__body_000006|2101.00318__body_000007|2101.00318__body_000008
[SECTION] Related Work [CONTEXT] We propose to adaptively explore the subtype-wise conditional and label shifts in UDA without the subtype labels, and explicitly enforce the subtype-aware compactness. We systematically investigate the cases with or without the prior information on subtype numbers. Our reliability-pat...
Related Work
38
18
38
18
2101.00318__body_000008__cite_0004__start_401__ref_bf13f619b2f5c5b48b1fce9303bfa625d0ec56d6
2,101.00318
2,101.00316
2101.00318__body_000008
8
Related Work
2
section
{{cite:bf13f619b2f5c5b48b1fce9303bfa625d0ec56d6}}
401
450
2101.00318__ref__bf13f619b2f5c5b48b1fce9303bfa625d0ec56d6
Compared with over one million images of the ImageNet dataset, the collection of large-scale medical data is challenging for clinical applications {{cite:8983ec628ed591cd40b890b1fbdb99b426b44ec2}}, {{cite:635670ba2af89d8ec96efc078523d4ce21c1b367}}, {{cite:880f4a590226730f16fbdab70c42d1262fcb329c}}. To counter this, UDA...
Compared with over one million images of the ImageNet dataset, the collection of large-scale medical data is challenging for clinical applications <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. To counter this, UDA has gradually become popular <OTHER_CIT>, <TARGET_CIT>, which aims to match covariate shift (i.e., only {{formula...
To counter this, UDA has gradually become popular <OTHER_CIT>, <TARGET_CIT>, which aims to match covariate shift (i.e., only {{formula:180c5693-c3ba-462a-a8d9-a2697cac2adb}} shift).
Compared with over one million images of the ImageNet dataset, the collection of large-scale medical data is challenging for clinical applications <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. To counter this, UDA has gradually become popular <OTHER_CIT>, <TARGET_CIT>, which aims to match covariate shift (i.e., only {{formula...
In recent years, big data drives the fast development of deep learning, which has transformed many fields, such as computer vision and medical image analysis <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. Deep learning has drastically transformed the way in which features are extracted and then fed into a prediction model into...
2101.00318__body_000007|2101.00318__body_000008|2101.00318__body_000009
[SECTION] Related Work [CONTEXT] In recent years, big data drives the fast development of deep learning, which has transformed many fields, such as computer vision and medical image analysis <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. Deep learning has drastically transformed the way in which features are extracted and the...
Related Work
47
33
47
33
2101.00318__body_000009__cite_0001__start_123__ref_bf13f619b2f5c5b48b1fce9303bfa625d0ec56d6
2,101.00318
2,101.00316
2101.00318__body_000009
9
Related Work
2
section
{{cite:bf13f619b2f5c5b48b1fce9303bfa625d0ec56d6}}
123
172
2101.00318__ref__bf13f619b2f5c5b48b1fce9303bfa625d0ec56d6
Recently, pseudo labels of a target domain have been widely used in UDA {{cite:f7f967ce275cef99377c211e705a86701255ac7d}}, {{cite:bf13f619b2f5c5b48b1fce9303bfa625d0ec56d6}}. The pseudo labels are used to estimate target class centers {{cite:df8bc75366f50351459e663e50d0e779e13bb912}}, and the results are enforced to mat...
Recently, pseudo labels of a target domain have been widely used in UDA <OTHER_CIT>, <TARGET_CIT>. The pseudo labels are used to estimate target class centers <OTHER_CIT>, and the results are enforced to match the source class centers. Contrastive Adaptation Network <OTHER_CIT> is proposed to estimate contrastive domai...
Recently, pseudo labels of a target domain have been widely used in UDA <OTHER_CIT>, <TARGET_CIT>.
Recently, pseudo labels of a target domain have been widely used in UDA <OTHER_CIT>, <TARGET_CIT>. The pseudo labels are used to estimate target class centers <OTHER_CIT>, and the results are enforced to match the source class centers. Contrastive Adaptation Network <OTHER_CIT> is proposed to estimate contrastive domai...
Compared with over one million images of the ImageNet dataset, the collection of large-scale medical data is challenging for clinical applications <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. To counter this, UDA has gradually become popular <OTHER_CIT>, <OTHER_CIT>, which aims to match covariate shift (i.e., only {{formula:...
2101.00318__body_000008|2101.00318__body_000009|2101.00318__body_000010
[SECTION] Related Work [CONTEXT] Compared with over one million images of the ImageNet dataset, the collection of large-scale medical data is challenging for clinical applications <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. To counter this, UDA has gradually become popular <OTHER_CIT>, <OTHER_CIT>, which aims to match cova...
Related Work
47
33
47
33
2101.00554__body_000029__cite_0004__start_333__ref_faa977effe6d97463e6555c0f15b8cd95d3f5478
2,101.00554
2,103.09959
2101.00554__body_000029
29
Discussion
4
section
{{cite:faa977effe6d97463e6555c0f15b8cd95d3f5478}}
333
382
2101.00554__ref__faa977effe6d97463e6555c0f15b8cd95d3f5478
The present approach can be extended to enforce physical constraints and properties {{cite:4ef32b9d307ee1ede0bffc475a658dc16d0f3eaf}}, {{cite:df5f49a88cac2d1ff898a179117f072a4d245888}}, {{cite:d79ccb85d3c4d51dfaea989591d2fd080e552f50}}, {{cite:1e0fb6dc211228badc19d12f59934dc2dad3bca6}}. For example, evolutional deep ne...
The present approach can be extended to enforce physical constraints and properties <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. For example, evolutional deep neural network <TARGET_CIT> has been able to enforce the divergence free constraint for incompressible flow. Another possible extension is the constructio...
For example, evolutional deep neural network <TARGET_CIT> has been able to enforce the divergence free constraint for incompressible flow.
The present approach can be extended to enforce physical constraints and properties <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. For example, evolutional deep neural network <TARGET_CIT> has been able to enforce the divergence free constraint for incompressible flow. Another possible extension is the constructio...
Since CNNs have a large collection of toolsets from the image processing community, the present reconstruction approach is significant from the point of view of merging image processing with sensor data analytics. This perspective now allows engineers and scientists to move through the wealth of local and global measur...
2101.00554__body_000028|2101.00554__body_000029|2101.00554__body_000030
[SECTION] Discussion [CONTEXT] Since CNNs have a large collection of toolsets from the image processing community, the present reconstruction approach is significant from the point of view of merging image processing with sensor data analytics. This perspective now allows engineers and scientists to move through the w...
Discussion
94
66
94
66
2101.00781__body_000020__cite_0002__start_700__ref_59a56bbc07457c008eb7195144de915f16217459
2,101.00781
2,101.04849
2101.00781__body_000020
20
Metric Learning for Recommendation
2
subsection
{{cite:59a56bbc07457c008eb7195144de915f16217459}}
700
749
2101.00781__ref__59a56bbc07457c008eb7195144de915f16217459
The pioneering work CML {{cite:e8affa40d3bd960293739b9730861caa2b93bde8}} learns a joint user-item metric space for capturing fine-grained user preference. It minimizes the distance between each user-item interaction in Euclidean space, i.e., {{formula:6701411e-0715-4e54-8610-fae56dcc9082}} , where {{formula:bb300fc4-9...
The pioneering work CML <OTHER_CIT> learns a joint user-item metric space for capturing fine-grained user preference. It minimizes the distance between each user-item interaction in Euclidean space, i.e., {{formula:6701411e-0715-4e54-8610-fae56dcc9082}} , where {{formula:bb300fc4-99a8-4801-8090-08a95703c669}} and {{fo...
PMLAM <TARGET_CIT> is presented to generate adaptive margins for the training triples in the metric space.
The pioneering work CML <OTHER_CIT> learns a joint user-item metric space for capturing fine-grained user preference. It minimizes the distance between each user-item interaction in Euclidean space, i.e., {{formula:6701411e-0715-4e54-8610-fae56dcc9082}} , where {{formula:bb300fc4-99a8-4801-8090-08a95703c669}} and {{fo...
The goal of metric learning is to learn a distance metric that assigns smaller distances between similar pairs, and larger distances between dissimilar pairs. Metric learning has also been adopted in recommender systems  <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT> to address the issue that inner product similarity violates t...
2101.00781__body_000019|2101.00781__body_000020|2101.00781__body_000021
[SECTION] Metric Learning for Recommendation [CONTEXT] The goal of metric learning is to learn a distance metric that assigns smaller distances between similar pairs, and larger distances between dissimilar pairs. Metric learning has also been adopted in recommender systems  <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT> to ad...
Metric Learning for Recommendation
83
53
83
53
2101.01484__body_000003__cite_0000__start_422__ref_61fafec3862656e9796f4cde22c8a1569c4b5492
2,101.01484
2,103.04479
2101.01484__body_000003
3
Introduction
1
section
{{cite:61fafec3862656e9796f4cde22c8a1569c4b5492}}
422
471
2101.01484__ref__61fafec3862656e9796f4cde22c8a1569c4b5492
The flexible and cost-effective wireless backhaul has become an attractive alternative to wired backhaul for small cell networks. However, wireless backhaul is vulnerable to wiretapping due to the intrinsic broadcasting nature of wireless channels. Therefore, the issue of secure backhaul links has aroused wide interest...
The flexible and cost-effective wireless backhaul has become an attractive alternative to wired backhaul for small cell networks. However, wireless backhaul is vulnerable to wiretapping due to the intrinsic broadcasting nature of wireless channels. Therefore, the issue of secure backhaul links has aroused wide interest...
Considering unreliable wireless backhaul connections, the authors in <TARGET_CIT> investigated the secrecy performance of cooperative single carrier HetNets.
The flexible and cost-effective wireless backhaul has become an attractive alternative to wired backhaul for small cell networks. However, wireless backhaul is vulnerable to wiretapping due to the intrinsic broadcasting nature of wireless channels. Therefore, the issue of secure backhaul links has aroused wide interest...
For the transmission security of wireless links from the EC servers to the users, the existing physical layer secure (PLS) mechanism, which has been studied intensively and extensively <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, is sufficient. However, the PLS mechanism is complicated because it could ensure th...
2101.01484__body_000002|2101.01484__body_000003|2101.01484__body_000004
[SECTION] Introduction [CONTEXT] For the transmission security of wireless links from the EC servers to the users, the existing physical layer secure (PLS) mechanism, which has been studied intensively and extensively <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, is sufficient. However, the PLS mechanism is comp...
Introduction
151
114
151
114
2101.01369__body_000005__cite_0000__start_213__ref_e2598720f43c44d89e6c5febd43b99e169e8454e
2,101.01369
2,101.01369
2101.01369__body_000005
5
Introduction
1
section
{{cite:e2598720f43c44d89e6c5febd43b99e169e8454e}}
213
262
2101.01369__ref__e2598720f43c44d89e6c5febd43b99e169e8454e
To tackle the aforementioned problems in the SDSD receiver, in a preliminary work, we proposed a splitting-detection joint-decision (SDJD) receiver for ultrasonic IBCs to lower the complexity of the SDSD receiver {{cite:e2598720f43c44d89e6c5febd43b99e169e8454e}}. We have numerically compared the performance of the SDSD...
To tackle the aforementioned problems in the SDSD receiver, in a preliminary work, we proposed a splitting-detection joint-decision (SDJD) receiver for ultrasonic IBCs to lower the complexity of the SDSD receiver <TARGET_CIT>. We have numerically compared the performance of the SDSD and SDJD receivers in the case of pe...
To tackle the aforementioned problems in the SDSD receiver, in a preliminary work, we proposed a splitting-detection joint-decision (SDJD) receiver for ultrasonic IBCs to lower the complexity of the SDSD receiver <TARGET_CIT>.
To tackle the aforementioned problems in the SDSD receiver, in a preliminary work, we proposed a splitting-detection joint-decision (SDJD) receiver for ultrasonic IBCs to lower the complexity of the SDSD receiver <TARGET_CIT>. We have numerically compared the performance of the SDSD and SDJD receivers in the case of pe...
This paper shows that the SDSD receiver can be used to improve the BER performance of either CD or ED receiver in IBCs, under perfect channel estimation. However, the SDSD receiver requires to implement both the CD and ED receivers, which lead to complicated hardware design for implanted devices. Additionally, the maxi...
2101.01369__body_000004|2101.01369__body_000005|2101.01369__body_000006
[SECTION] Introduction [CONTEXT] This paper shows that the SDSD receiver can be used to improve the BER performance of either CD or ED receiver in IBCs, under perfect channel estimation. However, the SDSD receiver requires to implement both the CD and ED receivers, which lead to complicated hardware design for implant...
Introduction
101
71
101
71
2101.01890__body_000007__cite_0000__start_272__ref_6d34e089f18e7434db18f5f7e023a81c003e408b
2,101.0189
2,101.00193
2101.01890__body_000007
7
Introduction
1
section
{{cite:6d34e089f18e7434db18f5f7e023a81c003e408b}}
272
321
2101.01890__ref__6d34e089f18e7434db18f5f7e023a81c003e408b
In other words, they provide an unified overview of “spectral intersection counting” via different perspectives. With these established, we can construct a boundary correction term for Toeplitz operators on manifolds with boundary with compact group actions in the sequel {{cite:6d34e089f18e7434db18f5f7e023a81c003e408b}...
In other words, they provide an unified overview of “spectral intersection counting” via different perspectives. With these established, we can construct a boundary correction term for Toeplitz operators on manifolds with boundary with compact group actions in the sequel <TARGET_CIT>. In particular, the correction term...
With these established, we can construct a boundary correction term for Toeplitz operators on manifolds with boundary with compact group actions in the sequel <TARGET_CIT>.
In other words, they provide an unified overview of “spectral intersection counting” via different perspectives. With these established, we can construct a boundary correction term for Toeplitz operators on manifolds with boundary with compact group actions in the sequel <TARGET_CIT>. In particular, the correction term...
{{formula:26f67d1f-7de9-4c65-a49c-5edd98a23f82}} In other words, they provide an unified overview of “spectral intersection counting” via different perspectives. With these established, we can construct a boundary correction term for Toeplitz operators on manifolds with boundary with compact group actions in the seq...
2101.01890__body_000006|2101.01890__body_000007|2101.01890__body_000008
[SECTION] Introduction [CONTEXT] {{formula:26f67d1f-7de9-4c65-a49c-5edd98a23f82}} In other words, they provide an unified overview of “spectral intersection counting” via different perspectives. With these established, we can construct a boundary correction term for Toeplitz operators on manifolds with boundary wit...
Introduction
116
99
116
99
2101.01890__body_000230__cite_0000__start_191__ref_6d34e089f18e7434db18f5f7e023a81c003e408b
2,101.0189
2,101.00193
2101.01890__body_000230
230
Equivariant {{formula:05a24012-e71e-4941-8e17-aff56c43b24c}} -invariants
9
section
{{cite:6d34e089f18e7434db18f5f7e023a81c003e408b}}
191
240
2101.01890__ref__6d34e089f18e7434db18f5f7e023a81c003e408b
Remark 9.11 A consequence of Theorem REF will be illustrated in forming the boundary correction terms of the equivariant Toeplitz index theorem on odd-dimensional manifolds with boundary in {{cite:6d34e089f18e7434db18f5f7e023a81c003e408b}}.
Remark 9.11 A consequence of Theorem REF will be illustrated in forming the boundary correction terms of the equivariant Toeplitz index theorem on odd-dimensional manifolds with boundary in <TARGET_CIT>.
Remark 9.11 A consequence of Theorem REF will be illustrated in forming the boundary correction terms of the equivariant Toeplitz index theorem on odd-dimensional manifolds with boundary in <TARGET_CIT>.
Remark 9.11 A consequence of Theorem REF will be illustrated in forming the boundary correction terms of the equivariant Toeplitz index theorem on odd-dimensional manifolds with boundary in <TARGET_CIT>.
Let {{formula:586906db-6990-4269-bd37-22deabbfce01}} Since {{formula:64865a05-7e2c-4510-b355-416b8b1d9a19}} is of trace class, it is compact and its equivariant Maslov triple index {{formula:3868943e-b7e1-4697-82b0-38b923109c13}} is well-defined for {{formula:2f6defca-477d-488f-af20-4bea67ddb80e}} For {{formula:abe...
2101.01890__body_000229|2101.01890__body_000230|2101.01890__body_000231
[SECTION] Equivariant {{formula:05a24012-e71e-4941-8e17-aff56c43b24c}} -invariants [CONTEXT] Let {{formula:586906db-6990-4269-bd37-22deabbfce01}} Since {{formula:64865a05-7e2c-4510-b355-416b8b1d9a19}} is of trace class, it is compact and its equivariant Maslov triple index {{formula:3868943e-b7e1-4697-82b0-38b923109...
Equivariant {{formula:05a24012-e71e-4941-8e17-aff56c43b24c}} -invariants
116
99
116
99
2101.01890__body_000319__cite_0000__start_191__ref_6d34e089f18e7434db18f5f7e023a81c003e408b
2,101.0189
2,101.00193
2101.01890__body_000319
319
Equivariant {{formula:05a24012-e71e-4941-8e17-aff56c43b24c}} -invariants
9
section
{{cite:6d34e089f18e7434db18f5f7e023a81c003e408b}}
191
240
2101.01890__ref__6d34e089f18e7434db18f5f7e023a81c003e408b
Remark 9.11 A consequence of Theorem REF will be illustrated in forming the boundary correction terms of the equivariant Toeplitz index theorem on odd-dimensional manifolds with boundary in {{cite:6d34e089f18e7434db18f5f7e023a81c003e408b}}.
Remark 9.11 A consequence of Theorem REF will be illustrated in forming the boundary correction terms of the equivariant Toeplitz index theorem on odd-dimensional manifolds with boundary in <TARGET_CIT>.
Remark 9.11 A consequence of Theorem REF will be illustrated in forming the boundary correction terms of the equivariant Toeplitz index theorem on odd-dimensional manifolds with boundary in <TARGET_CIT>.
Remark 9.11 A consequence of Theorem REF will be illustrated in forming the boundary correction terms of the equivariant Toeplitz index theorem on odd-dimensional manifolds with boundary in <TARGET_CIT>.
Let {{formula:586906db-6990-4269-bd37-22deabbfce01}} Since {{formula:64865a05-7e2c-4510-b355-416b8b1d9a19}} is of trace class, it is compact and its equivariant Maslov triple index {{formula:3868943e-b7e1-4697-82b0-38b923109c13}} is well-defined for {{formula:2f6defca-477d-488f-af20-4bea67ddb80e}} For {{formula:abe...
2101.01890__body_000318|2101.01890__body_000319
[SECTION] Equivariant {{formula:05a24012-e71e-4941-8e17-aff56c43b24c}} -invariants [CONTEXT] Let {{formula:586906db-6990-4269-bd37-22deabbfce01}} Since {{formula:64865a05-7e2c-4510-b355-416b8b1d9a19}} is of trace class, it is compact and its equivariant Maslov triple index {{formula:3868943e-b7e1-4697-82b0-38b923109...
Equivariant {{formula:05a24012-e71e-4941-8e17-aff56c43b24c}} -invariants
116
99
116
99
2101.02162__body_000018__cite_0003__start_2019__ref_f48e25a1fee8e81e446aecb88f279dd85c11ec4e
2,101.02162
2,101.03352
2101.02162__body_000018
18
Electronic structure
3
subsection
{{cite:f48e25a1fee8e81e446aecb88f279dd85c11ec4e}}
2,019
2,068
2101.02162__ref__f48e25a1fee8e81e446aecb88f279dd85c11ec4e
The electronic band structure and density of states (DOS) within GGA+{{formula:4dd2897c-873a-46d3-bd22-60e472601a4c}} are depicted in Fig. REF . The electronic band structure shows two key features: a Dirac cone at the {{formula:5ab0572b-bd48-4bec-bb14-6800566ca25e}} point and the existence of two flat-bands at {{form...
The electronic band structure and density of states (DOS) within GGA+{{formula:4dd2897c-873a-46d3-bd22-60e472601a4c}} are depicted in Fig. REF . The electronic band structure shows two key features: a Dirac cone at the {{formula:5ab0572b-bd48-4bec-bb14-6800566ca25e}} point and the existence of two flat-bands at {{form...
Within this understanding, it is clear that an increase of {{formula:ef366ab4-c604-4d60-a0a5-11f4cb4fb049}} will force the electrons into a more localized state implying an increased effect of the atomic SOC <TARGET_CIT>, <OTHER_CIT>. {{figure:e8434a24-7baf-420d-a118-5ca615b77a7d}}
The electronic band structure and density of states (DOS) within GGA+{{formula:4dd2897c-873a-46d3-bd22-60e472601a4c}} are depicted in Fig. REF . The electronic band structure shows two key features: a Dirac cone at the {{formula:5ab0572b-bd48-4bec-bb14-6800566ca25e}} point and the existence of two flat-bands at {{form...
The {{formula:dfd0b54b-4b92-4cc2-b2b9-0bffd6f63d0a}} , {{formula:2e89334d-6cb7-4fd4-9e1a-a8c7d515002e}} and {{formula:30c096fe-248d-4a22-b2ee-457f07c99d74}} values were found to be {{formula:5dbb8b54-2552-4372-a753-78c669a70864}} meV, {{formula:a63e6d03-6101-46ef-ad79-a55557a7fdc5}} meV and {{formula:48fe4cd8-b1c5-...
2101.02162__body_000017|2101.02162__body_000018|2101.02162__body_000019
[SECTION] Electronic structure [CONTEXT] The {{formula:dfd0b54b-4b92-4cc2-b2b9-0bffd6f63d0a}} , {{formula:2e89334d-6cb7-4fd4-9e1a-a8c7d515002e}} and {{formula:30c096fe-248d-4a22-b2ee-457f07c99d74}} values were found to be {{formula:5dbb8b54-2552-4372-a753-78c669a70864}} meV, {{formula:a63e6d03-6101-46ef-ad79-a55557...
Electronic structure
27
5
27
5
2101.02161__body_000061__cite_0003__start_2173__ref_fe3c100a31a4e7906fb7f23137fbe45f930bed45
2,101.02161
2,101.02169
2101.02161__body_000061
61
Results and Discussion
4
section
{{cite:fe3c100a31a4e7906fb7f23137fbe45f930bed45}}
2,173
2,222
2101.02161__ref__fe3c100a31a4e7906fb7f23137fbe45f930bed45
We would like to first discuss briefly about the previous calculated values of {{formula:61ae4ace-899c-48cf-ac1c-4971808450ca}} in both the Cl{{formula:eb54ef2d-b508-4e5d-a934-9c10e111a811}} and Au{{formula:e9a0dd66-eba2-4dcc-9f68-d671f78bd1e1}} ions to understand the need of doing new theoretical results by includi...
We would like to first discuss briefly about the previous calculated values of {{formula:61ae4ace-899c-48cf-ac1c-4971808450ca}} in both the Cl{{formula:eb54ef2d-b508-4e5d-a934-9c10e111a811}} and Au{{formula:e9a0dd66-eba2-4dcc-9f68-d671f78bd1e1}} ions to understand the need of doing new theoretical results by includi...
There are three major limitations of this calculation: (i) It uses NR theory, however, later theoretical studies have exhibited quite large relativistic effects in the determination of {{formula:b4a8067f-589f-4be1-9cd5-56ce4d858201}} values of the negative ions <OTHER_CIT>, <OTHER_CIT>, <TARGET_CIT>.
We would like to first discuss briefly about the previous calculated values of {{formula:61ae4ace-899c-48cf-ac1c-4971808450ca}} in both the Cl{{formula:eb54ef2d-b508-4e5d-a934-9c10e111a811}} and Au{{formula:e9a0dd66-eba2-4dcc-9f68-d671f78bd1e1}} ions to understand the need of doing new theoretical results by includi...
with the orbital quantum number {{formula:0a48c188-2eab-4b33-9fde-c605ab7b29b8}} of the system, {{formula:471305d6-c6d0-43b2-b193-df09226e3e6c}} , {{formula:b24dc853-3c26-4216-98b4-177d2e08fac5}} , and the exponential integral {{formula:fc406c9c-f428-4ec2-8411-6af5003a819d}} . {{table:63a9e284-9c28-4f9d-b177-c49abf346...
2101.02161__body_000060|2101.02161__body_000061|2101.02161__body_000062
[SECTION] Results and Discussion [CONTEXT] with the orbital quantum number {{formula:0a48c188-2eab-4b33-9fde-c605ab7b29b8}} of the system, {{formula:471305d6-c6d0-43b2-b193-df09226e3e6c}} , {{formula:b24dc853-3c26-4216-98b4-177d2e08fac5}} , and the exponential integral {{formula:fc406c9c-f428-4ec2-8411-6af5003a819d}}...
Results and Discussion
34
0
35
0
2101.02420__body_000009__cite_0002__start_274__ref_28b1e5ac3687aee2ebb56a84790717ee689d41f9
2,101.0242
2,101.08435
2101.02420__body_000009
9
Related Works
1
subsection
{{cite:28b1e5ac3687aee2ebb56a84790717ee689d41f9}}
274
323
2101.02420__ref__28b1e5ac3687aee2ebb56a84790717ee689d41f9
With the tremendous success of deep learning techniques on physical layer communications, significant improvement becomes possible for the aforementioned search strategies {{cite:0bac1ec62384252319ffabaacd581aa10d24a311}}, {{cite:87e438eeee958ef13f5a3148842e3d762801ccdf}}, {{cite:28b1e5ac3687aee2ebb56a84790717ee689d41f...
With the tremendous success of deep learning techniques on physical layer communications, significant improvement becomes possible for the aforementioned search strategies <OTHER_CIT>, <OTHER_CIT>, <TARGET_CIT>, <OTHER_CIT>. Regarding the ILS problem, researchers have proposed a deep learning based SD (DL-SD) algorithm...
With the tremendous success of deep learning techniques on physical layer communications, significant improvement becomes possible for the aforementioned search strategies <OTHER_CIT>, <OTHER_CIT>, <TARGET_CIT>, <OTHER_CIT>.
With the tremendous success of deep learning techniques on physical layer communications, significant improvement becomes possible for the aforementioned search strategies <OTHER_CIT>, <OTHER_CIT>, <TARGET_CIT>, <OTHER_CIT>. Regarding the ILS problem, researchers have proposed a deep learning based SD (DL-SD) algorithm...
Attempts that employ best-first search (BeFS) or stack algorithms to overcome the drawbacks of DFS and BrFS have been investigated in the literature <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. Among these variants, A* like BeFS is the most promising variant wh...
2101.02420__body_000008|2101.02420__body_000009|2101.02420__body_000010
[SECTION] Related Works [CONTEXT] Attempts that employ best-first search (BeFS) or stack algorithms to overcome the drawbacks of DFS and BrFS have been investigated in the literature <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>, <OTHER_CIT>. Among these variants, A* like Be...
Related Works
86
51
86
51
2101.02931__body_000003__cite_0003__start_2821__ref_7c521c2435aba614111e633170861b7e2461fefa
2,101.02931
2,101.02931
2101.02931__body_000003
3
Our contribution
1
subsection
{{cite:7c521c2435aba614111e633170861b7e2461fefa}}
2,821
2,870
2101.02931__ref__7c521c2435aba614111e633170861b7e2461fefa
In this paper, we also take a Bayesian approach, viewing the unknowns as random variables and tackling the problem as one of Bayesian modeling and inference . The idea is again (as in BTD-HIRLS) to impose column sparsity jointly on the factors in a hierarchical, two-level manner. This is achieved through a Bayesian hie...
In this paper, we also take a Bayesian approach, viewing the unknowns as random variables and tackling the problem as one of Bayesian modeling and inference . The idea is again (as in BTD-HIRLS) to impose column sparsity jointly on the factors in a hierarchical, two-level manner. This is achieved through a Bayesian hie...
A preliminary version can be found in <TARGET_CIT>.
In this paper, we also take a Bayesian approach, viewing the unknowns as random variables and tackling the problem as one of Bayesian modeling and inference . The idea is again (as in BTD-HIRLS) to impose column sparsity jointly on the factors in a hierarchical, two-level manner. This is achieved through a Bayesian hie...
where {{formula:57b0f811-f25e-4a7c-93cd-45396fcea60b}} is an {{formula:7849c8b9-6add-42f7-9dd4-e43d9b3f9404}} matrix of rank {{formula:e83ad186-37ba-409f-84f6-65e7ff98eeb5}} , {{formula:23dc6257-196f-4048-980f-8a04107661c7}} is a nonzero column {{formula:2ba0f658-6fd6-4d07-9a8d-c230dd525a51}} -vector and {{formula:9...
2101.02931__body_000002|2101.02931__body_000003|2101.02931__body_000004
[SECTION] Our contribution [CONTEXT] where {{formula:57b0f811-f25e-4a7c-93cd-45396fcea60b}} is an {{formula:7849c8b9-6add-42f7-9dd4-e43d9b3f9404}} matrix of rank {{formula:e83ad186-37ba-409f-84f6-65e7ff98eeb5}} , {{formula:23dc6257-196f-4048-980f-8a04107661c7}} is a nonzero column {{formula:2ba0f658-6fd6-4d07-9a8d-...
Our contribution
17
11
17
11
2101.02811__body_000579__cite_0001__start_752__ref_44d5058cfb73e8238686543bda977cf7bdf2567c
2,101.02811
2,102.11702
2101.02811__body_000579
579
Free abelian groups of finite rank
1
subsection
{{cite:44d5058cfb73e8238686543bda977cf7bdf2567c}}
752
801
2101.02811__ref__44d5058cfb73e8238686543bda977cf7bdf2567c
Now we turn to a specific example where the configurations have a simple geometric description. For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formula:e44a42dd-540b-4dbc-9301-2bea83c9bb26}} is the set of all rotations, translations, and scalings of a fixed tr...
Now we turn to a specific example where the configurations have a simple geometric description. For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formula:e44a42dd-540b-4dbc-9301-2bea83c9bb26}} is the set of all rotations, translations, and scalings of a fixed tr...
Ajtai and Szemerédi showed a related result:The lower bound in Theorem REF has recently been improved by Linial and Shraibman <OTHER_CIT> and by Green <TARGET_CIT>.
Now we turn to a specific example where the configurations have a simple geometric description. For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formula:e44a42dd-540b-4dbc-9301-2bea83c9bb26}} is the set of all rotations, translations, and scalings of a fixed tr...
Theorem REF guarantees such a set for sufficiently large {{formula:a08c0efa-fa0c-4f47-8126-f154c4c760cb}} . Now we turn to a specific example where the configurations have a simple geometric description. For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formul...
2101.02811__body_000578|2101.02811__body_000579|2101.02811__body_000580
[SECTION] Free abelian groups of finite rank [CONTEXT] Theorem REF guarantees such a set for sufficiently large {{formula:a08c0efa-fa0c-4f47-8126-f154c4c760cb}} . Now we turn to a specific example where the configurations have a simple geometric description. For the Gaussian integers ({{formula:d7e7471a-9932-4186-8...
Free abelian groups of finite rank
12
0
13
0
2101.02811__body_001127__cite_0001__start_752__ref_44d5058cfb73e8238686543bda977cf7bdf2567c
2,101.02811
2,102.11702
2101.02811__body_001127
1,127
Free abelian groups of finite rank
1
subsection
{{cite:44d5058cfb73e8238686543bda977cf7bdf2567c}}
752
801
2101.02811__ref__44d5058cfb73e8238686543bda977cf7bdf2567c
Now we turn to a specific example where the configurations have a simple geometric description. For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formula:e44a42dd-540b-4dbc-9301-2bea83c9bb26}} is the set of all rotations, translations, and scalings of a fixed tr...
Now we turn to a specific example where the configurations have a simple geometric description. For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formula:e44a42dd-540b-4dbc-9301-2bea83c9bb26}} is the set of all rotations, translations, and scalings of a fixed tr...
Ajtai and Szemerédi showed a related result:The lower bound in Theorem REF has recently been improved by Linial and Shraibman <OTHER_CIT> and by Green <TARGET_CIT>.
Now we turn to a specific example where the configurations have a simple geometric description. For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formula:e44a42dd-540b-4dbc-9301-2bea83c9bb26}} is the set of all rotations, translations, and scalings of a fixed tr...
Theorem REF guarantees such a set for sufficiently large {{formula:a08c0efa-fa0c-4f47-8126-f154c4c760cb}} . Now we turn to a specific example where the configurations have a simple geometric description. For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formul...
2101.02811__body_001126|2101.02811__body_001127|2101.02811__body_001128
[SECTION] Free abelian groups of finite rank [CONTEXT] Theorem REF guarantees such a set for sufficiently large {{formula:a08c0efa-fa0c-4f47-8126-f154c4c760cb}} . Now we turn to a specific example where the configurations have a simple geometric description. For the Gaussian integers ({{formula:d7e7471a-9932-4186-8...
Free abelian groups of finite rank
12
0
13
0
2101.02811__body_001611__cite_0001__start_752__ref_44d5058cfb73e8238686543bda977cf7bdf2567c
2,101.02811
2,102.11702
2101.02811__body_001611
1,611
Free abelian groups of finite rank
1
subsection
{{cite:44d5058cfb73e8238686543bda977cf7bdf2567c}}
752
801
2101.02811__ref__44d5058cfb73e8238686543bda977cf7bdf2567c
Now we turn to a specific example where the configurations have a simple geometric description. For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formula:e44a42dd-540b-4dbc-9301-2bea83c9bb26}} is the set of all rotations, translations, and scalings of a fixed tr...
Now we turn to a specific example where the configurations have a simple geometric description. For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formula:e44a42dd-540b-4dbc-9301-2bea83c9bb26}} is the set of all rotations, translations, and scalings of a fixed tr...
Ajtai and Szemerédi showed a related result:The lower bound in Theorem REF has recently been improved by Linial and Shraibman <OTHER_CIT> and by Green <TARGET_CIT>.
Now we turn to a specific example where the configurations have a simple geometric description. For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formula:e44a42dd-540b-4dbc-9301-2bea83c9bb26}} is the set of all rotations, translations, and scalings of a fixed tr...
Theorem REF guarantees such a set for sufficiently large {{formula:a08c0efa-fa0c-4f47-8126-f154c4c760cb}} . Now we turn to a specific example where the configurations have a simple geometric description. For the Gaussian integers ({{formula:d7e7471a-9932-4186-834c-fff00aeefd2c}} ), the set of configurations {{formul...
2101.02811__body_001610|2101.02811__body_001611|2101.02811__body_001612
[SECTION] Free abelian groups of finite rank [CONTEXT] Theorem REF guarantees such a set for sufficiently large {{formula:a08c0efa-fa0c-4f47-8126-f154c4c760cb}} . Now we turn to a specific example where the configurations have a simple geometric description. For the Gaussian integers ({{formula:d7e7471a-9932-4186-8...
Free abelian groups of finite rank
12
0
13
0
End of preview. Expand in Data Studio

Citation Contexts for Scientific Evidence Retrieval

Dataset Description

This dataset contains 9,920 citation occurrences extracted from English-language scientific papers. Each row represents one occurrence of a citation in a source paper and links it to the cited paper. It provides four increasingly broad representations of the citation context:

  1. the sentence containing the citation (context_c1_sentence);
  2. the complete source paragraph (context_c2_paragraph);
  3. a local window containing the source body item and available neighboring body items (context_c3_window); and
  4. the same wider context with section information (context_c4_section_aware).

In the processed context fields, the citation represented by the row is replaced with <TARGET_CIT>, while other citations are replaced with <OTHER_CIT>. The dataset is intended for experiments that compare citation-context scopes in passage retrieval, citation grounding, scientific claim verification, and related information-retrieval tasks.

Dataset summary

Property Value
Rows / citation occurrences 9,920
Unique source papers 3,198
Unique cited papers 2,637
Unique citation IDs 9,920
Data files 1 CSV file
Predefined splits Train only (no official evaluation split)
Approximate CSV size 163.8 MB

Dataset Structure

Data instance

{
    "citation_id": "2101.00098__body_000013__cite_0013__start_1576__ref_...",
    "source_paper_id": "2101.00098",
    "cited_paper_id": "2108.13004",
    "source_section": "Single-View 3D Reconstruction",
    "citation_marker": "{{cite:...}}",
    "paragraph_with_target_marker": "... <OTHER_CIT>, <TARGET_CIT> ...",
    "context_c1_sentence": "... <TARGET_CIT> ...",
    "context_c2_paragraph": "...",
    "context_c3_window": "...",
    "context_c4_section_aware": "[SECTION] Single-View 3D Reconstruction\n\n[CONTEXT]\n...",
    "candidate_atomic_passage_count": 21,
    "candidate_contextual_passage_count": 4
}

The example is abbreviated; the CSV contains all fields listed below.

Fields

Field Type Description
citation_id string Unique identifier for the citation occurrence.
source_paper_id string Identifier of the paper containing the citation.
cited_paper_id string Identifier of the cited paper.
source_body_item_id string Identifier of the source body item containing the citation.
body_item_order integer Position of the body item in the source paper.
source_section string, nullable Source section title. Missing for 321 rows.
source_sec_number string Section number as represented in the source data. Kept as text because section numbers can be hierarchical.
source_sec_type string, nullable Structural type: section, subsection, or subsubsection; missing for 598 rows.
citation_marker string Original normalized citation marker in {{cite:...}} form.
span_start integer Start offset of the target marker in raw_source_paragraph.
span_end integer End offset of the target marker in raw_source_paragraph.
reference_id string Identifier of the corresponding bibliography entry in the source paper.
raw_source_paragraph string Original extracted paragraph, retaining normalized citation markers and other extraction placeholders.
paragraph_with_target_marker string Paragraph in which the row's citation is <TARGET_CIT> and all other citations are <OTHER_CIT>.
context_c1_sentence string Sentence containing <TARGET_CIT>.
context_c2_paragraph string Full paragraph containing <TARGET_CIT>.
context_c3_window string Wider context assembled from the target body item and available neighboring body items.
context_c3_component_body_item_ids string Pipe-delimited body-item IDs used to construct context_c3_window.
context_c4_section_aware string Section-aware representation formatted with [SECTION] and [CONTEXT] labels.
context_c4_raw_section_title string, nullable Raw section title used for C4; missing for 321 rows.
candidate_atomic_passage_count integer Number of retrieval-eligible atomic passages associated with the cited paper for this instance.
candidate_contextual_passage_count integer Number of retrieval-eligible contextual passages associated with the cited paper for this instance.
candidate_total_atomic_passage_count integer Total atomic passage count associated with the cited paper before the relevant eligibility restriction.
candidate_total_contextual_passage_count integer Total contextual passage count associated with the cited paper before the relevant eligibility restriction.

Context representations

Name Scope Median length (characters) Range (characters)
C1 Citation sentence 208 12–2,772
C2 Citation paragraph 949 14–241,559
C3 Local body-item window 2,424 110–242,089
C4 Section-aware local window 2,464.5 110–242,280

Very long contexts reflect unusually long source body items in the extracted corpus and have not been truncated to a model-specific token limit.

Dataset Creation

Each input citation occurrence was matched to its source body item and bibliography reference. The four contexts were then constructed at sentence, paragraph, neighboring-body-item, and section-aware scopes. In processed contexts, the selected citation was replaced by <TARGET_CIT> and co-occurring citations by <OTHER_CIT>.

Candidate passage counts describe the retrieval pool linked to the cited paper. The dataset itself does not include passage text, relevance labels, or a gold supporting-passage identifier, so supervised evidence-ranking experiments require an accompanying candidate-passage resource or separately constructed labels.

Limitations and Biases

  • The dataset reflects the coverage and extraction quality of its source scientific-paper corpus; it should not be treated as representative of all disciplines, venues, languages, or publication periods.
  • Context text can contain extraction artifacts such as {{formula:...}}, {{figure:...}}, and normalized citation markers.
  • A citation context does not necessarily state a single factual claim, and a cited paper may support only part of the surrounding text.
  • The dataset does not provide citation-intent labels, entailment labels, or manually verified evidence annotations.
  • Multiple rows can come from the same source or cited paper. Evaluation without paper-level grouping may overestimate generalization.

Contact

sanaa.abril@gmail.com

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