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The first method built and designed for blind zero-shot denoising is S2S {{cite:60200c297dc9d94eaf4bedba6355fd8ed2ce8c72}}. It is a blind-spot network that uses partial convolutions {{cite:efaa332fab265d5c48f2d2971a6a950f16f4d44e}} to mask out pixels, which is computationally expensive and slow.
| m | 058b7d3e97438d8e20978937829b048f |
When the network is restricted to be a branching, that is, adirected tree in which every
vertex has indegree at most one, then an optimal network can be computed in polynomial
time {{cite:2777601e4a47b813e5c5575891762b62df914f75}}, {{cite:507b115fa77431a270434295eacf7c89c22ad17a}}. Note that learning a more restricted Bayesian network is not necessarily easier: While learning a branching is solvable in polynomial time, the problem becomes NP-hard if we aim to learn a directed path {{cite:b32e730c1b0af90dd7df710c2dc024b889d9d033}}.
| r | 9cae64b51f9215c748aeabfe1bf70bea |
The results reveal not only the new degree of freedom in the experiments
with nonlinear dissipative systems in photonics, but also allow encoding
data in the form of multiple stable SMs with different TSs, and SMs with
fixed TS but different colors (central wavelengths). Such multiple states
may be toggled in a controllable fashion, which is important for
applications of SMs to communications {{cite:31684617509979c5f3dc90d115c9849a3338b9db}},
optical switching {{cite:a98cef62f88c292da0a29211ff320a621af51e53}}, and storage {{cite:d97b9908a328f1e5b59bdb52e75b8cbb4586ab5f}}, {{cite:93366ad08655ef907fa7da4e46fddc8fed3c46d3}}. Also, these findings offer potential for
the use of the optical SMs in high-capacity schemes for optical data
processing {{cite:fdc334e6bbb506d68e4a5e8c86f840f175655440}}, {{cite:b5360c73ada43cb9619dff41a260b143d390fb76}}, machine learning based
on ultrafast photonics {{cite:5df26dbdf4171970e79a79630185b4e10f50e9fb}}, {{cite:6a2b4466d21d7d4f84c54bac439a53cb01b9ce51}}, {{cite:0d6ff7beb0239c0a31a83561fe987a22b8d89e33}}, {{cite:2b215279b1dbdfb8cabcedbd9b15fcde67cd8a2a}},
and operations with high dimensional temporal quantum information {{cite:adfa02c946e7f3e92e88cbfcf591a435aa1b2509}}, {{cite:3315d02d7ea7abe697655187da70be326b7baa44}}.
| d | 589725d9c0db6d3f574568248c869141 |
3. Why we are often unlucky to have {{formula:3bfcbc64-d127-4e48-8acf-c107ce57595d}}
(1) First, the test sets are almost surely outside the convex hull of the training set because “`interpolation almost surely never occurs in high-dimensional ({{formula:a103ec6e-c630-4f24-8f95-cce3b0ed4abe}} ) cases”' {{cite:cb334fbb86726096ae2a9d77884f2c6607abc1a2}}. As a result, the variability of (train + test) sets is almost surely larger than the variability of (train) set. Since {{formula:e2641114-5feb-471a-8680-ce16cc530c07}} increases with data variability (see point 4 below), we have {{formula:7ab7c658-6d33-42c9-94f6-9d18e54b3e0c}} almost surely.
(2) Second, we don’t know the value of {{formula:a7c4764d-0580-4c62-bef1-0bce79d0485b}} and can only guess it. In practice, we often guess a small value because training often diverges with large {{formula:084cc93f-4ffd-44c1-a62c-0a2d27cececf}} (as observed in {{cite:961ddd8fd4ac4bae958fc01d4cc23588a545a383}}, {{cite:17d36ec4d810add8b1be7acd3854f030a0e9e33c}}).
| d | 7c8ed1dd65fa3468097aa671309bc0f2 |
where {{formula:5fd89d34-a858-4225-b3f8-b95f6271e9d9}} is called a moment order. The multifractal analysis consists of determining whether statistical moments of {{formula:0c56f12b-dcd6-493f-964d-2331d04a548a}} -series of {{formula:40a5730a-3761-4af5-8740-afc52f9b635c}} have power-law scaling with {{formula:7f49db4d-5a10-462e-8a2b-4d73d28140e1}} . If all moments have identical power-low scaling the urban morphology is fractal (monofractal), if they have power-law scaling but with different exponents the urban morphology is multifractal, and if they don't have the power-law scaling the urban morphology is nonfractal. Assuming that the urban structure is either monofractal or multifractal, the results of the multifractal analysis is summarized by the Renyi's generalized dimensions (RGD) spectrum {{cite:0a76269e057a799db6f028a5155a022e2bebe770}}.
| m | c0359d84bd7db17ff857728b021bdbd2 |
Can SBP work with other efficient training strategies?
We validate if SBP is complementary with other memory saving methods.
As gradient checkpoint {{cite:dc186b64d3c146691290e4f5e74121b9f4f505f5}} is widely used to save memory, we report the memory and speed of SBP when integrated with gradient checkpoint.
As shown in Table REF , the memory consumption of SBP without checkpoint is similar to the standard end-to-end training with checkpoint, but is {{formula:492db14b-3498-464d-a9e4-7017f04ec47c}} 30% faster. When applying gradient checkpoint to SBP, additional {{formula:15cfca73-90f6-4792-9033-a79e23163455}} 40% the memory can be saved comparing to using SBP alone.
Furthermore, we test to incorporate Mixed Precision (w/ opt_level as O1) into SBP. The results show that this can lead to {{formula:527785c4-807b-4b4e-b17b-aaf8fc9d60e6}} 50% more savings of GPU memory on Swin-T without accuracy loss.
| r | 0914069a6b381aff1aa78ffdeadba5e7 |
The area-based registration methods, also called intensity-based methods, register images by directly using correlation of pixel values, mutual information, or transform domain of the image pairs. Usually, the global image or a predefined local window is used to search for matching {{cite:23a54a74b7c70396c83c5ff392ebab2baeeeb6e6}}. By establishing the similarity relationship of the original pixel values {{cite:2c0c540013d3b946dc05aa1b8a57482dc573dfda}}, {{cite:115e040d16c9bb8bc6466ed715af06244cec1cf7}}, statistical properties {{cite:acd3bf558e36037fd131c7c6d13f187af1a29902}}, {{cite:89170a4cb53f5823bfc98b0e8ca247b6d9920881}}, {{cite:29c9e938c7347374107fcc7d45ce150753d69b7b}}, or transform domain, such as Fourier transformation {{cite:bfd550c55b3c4c62e0043097a8ebf7c58d8cb3a7}}, {{cite:f0f1cf8b2a0c0df9340fbe2db7b38f62ed3b3758}}, and wavelet transformation {{cite:9d0bec11158d762d3a26a9849b30ee1cca2723fc}}, the optimal spatial transformation model between the image pairs is found through parameter optimization methods. The advantage of the area-based methods lies in high registration accuracy, but the drawbacks are particularly obvious. The drawbacks of the area-based methods mainly lie in three aspects.
| m | e855cd9a88919036a43cc72aeb357558 |
In this paper, we introduce a modular neural network architecture that divides the task into several sub-tasks, each handling a different type of information in a specific manner. Our approach is similar to {{cite:8f1da6c68dcdbd873e52fd89bdd2521ec00d6bf2}}, {{cite:14d1093b89230f3930f01f3cbe9c7286b3a876a6}} and {{cite:6a1cb43d7e404dfb16d7044c4f17010cdedde7c7}} in that we extract visual and natural language information in an independent manner by employing networks commonly used for these types of data, i.e., CNNs and RNNs, and then focus on processing this multi-domain information by means of another neural network, yielding an end-to-end trainable architecture. However, our method also introduces the usage of Simple Recurrent Units (SRUs) for efficient segmentation based on referring expressions, a Synthesis Module that processes the linguistic and visual information jointly, and an Upsampling Module that outputs highly detailed segmentation maps.
| i | 7612c2b4d7ef455db699252fa96f18ec |
The first term is the symmetric exchange energy density
{{formula:125a73ee-ff04-4bd1-af80-adc4cb3a12d3}}
with exchange stiffness material parameter {{formula:c35a953f-36db-46aa-97bf-0edc842819bb}} , where {{formula:64c49ab3-fdc6-49e5-a7e1-d07ea536ea73}} , {{formula:a3093f21-c977-40fd-b29b-3cb7bbb61b77}} , and
{{formula:cf058741-0c8a-4c4f-9db3-8b5d6dfc2c78}} are the Cartesian components of the vector {{formula:8bce8905-1b07-4360-a154-447a048ef06f}}
that describes the magnetisation {{formula:bb3dd50f-f529-4945-906d-ac920967b2ba}} , with
{{formula:0fc05662-8cce-44d0-8f2f-8844ffaccf44}} being the saturation magnetisation. The second term
is the Dzyaloshinskii-Moriya Interaction (DMI) energy density
{{formula:3e0741d7-5f15-4620-89e4-ea66fed048c0}} , obtained by
constructing the allowed Lifshitz invariants for the crystallographic class
T {{cite:d48515949652bab9489ee235df53cf6e113459af}}, {{cite:bc25bc194d9a8b17e60a0bbe1b81c533401d41ea}}, where {{formula:8cc4c415-c12a-4d66-a687-6dad4a3a1e3a}} is the material parameter. The third
term is the Zeeman energy density term {{formula:fb47a892-ae22-46f3-b28d-6e98c44ae464}}
which defines the coupling of magnetisation to an external
magnetic field {{formula:9a052193-e850-46e1-8446-1ff5d39834f4}} . The {{formula:f0f09336-051f-4982-af9a-a3baa27e591c}} term represents the
demagnetisation (magnetostatic) energy density. The last term
{{formula:49cba99f-af1e-4614-b307-c18cb218c7a9}} is the magnetocrystalline anisotropy energy density, and because
the simulated material is assumed to be isotropic, we neglect it throughout
this work. Neglecting this term also allows us to determine whether the
magnetocrystalline anisotropy is a crucial mechanism allowing the stability of
skyrmionic textures in confined helimagnetic nanostructures.
| m | c0d7f15ad40c020881693c9f6cce1daa |
Since Ads/CFT correspondence calls the duality between the type IIB superstring theory
formulated on {{formula:6cc57f9c-8ad8-498a-b935-41033093cf9d}} and {{formula:aa352dc1-76e2-476b-a6a3-64239525ffdf}} SYM in four dimensions ( which realize
a construction that is coupled with the U(1) gauge field {{cite:eab5702ee6b3b4a9df15dde068ad27806002ba4d}}, {{cite:718b802afd88178c7d58245e783fa9e19b84ab3b}}, {{cite:c9396909f74424c4d67056016438bee32ce72c42}} ), it is interesting
to consider the Schwinger effect in the context of the AdS/CFT correspondence.
| i | c3b1616af7fcf86b062e277fcec9d40e |
If {{formula:3d81fa1e-82e5-4461-af9e-d6f0a5e0c62e}} , then {{formula:ae1d9b6b-8e0c-4ad9-aebc-f5dfd76626ee}} is a CG-group. Next, suppose {{formula:6569bc88-d835-456e-bc11-1c86a73705cc}} . In view of {{cite:94f66902ee22a5216660975a47c79da122143c39}}), the proper centralizers of {{formula:73d73d92-fc93-414d-b52c-ef8863002dae}} are precisely the members of the family {{formula:d1c9801f-b052-4af6-9d2c-0218ddf93fd6}} , where
(a)
{{formula:1840a5a2-7903-456e-b07b-bebdc74f39d2}} is the subgroup of all diagonal matrices in {{formula:f110cf53-a6e7-4fe6-860c-0c9019e03aff}} , and the number of conjugates of {{formula:88fef906-d95c-4203-90b5-c7942cad5cc8}} in {{formula:bdc86db4-1e8a-49e8-a8bf-9362624c6602}} is {{formula:5d3d9e44-ff51-49ea-b431-3fa68fb6fa94}} ,
(b)
{{formula:0c69a874-543c-4ae8-ba87-f31818df7c24}} is a cyclic subgroup of {{formula:395058e5-4db1-408d-8637-c6966ddd5157}} , and the number of conjugates of {{formula:186d7b64-0aa4-4507-8b0a-c04cb28658da}} in {{formula:25f2cf70-9b6a-4192-b19d-9899a5c3fb31}} is {{formula:b4d1ba9c-cf5a-4aab-9f30-68829b20961e}} ,
(c)
{{formula:97d3e016-392b-450b-ab62-1791160f00d9}} is the Sylow {{formula:d22607f2-cb20-4b48-ae06-3929448c1d4b}} -subgroup of {{formula:2bf26422-d14f-4c7b-8322-92f6bf8c6c79}} consisting of all upper triangular matrices with 1 in the diagonal, and the number of conjugates of {{formula:ceda3c61-9c11-45ec-b3b3-28ce9990eeaf}} in {{formula:d002fb7e-c0d6-4706-80f1-394ec80f6113}} is {{formula:282915d7-08ed-41c5-bacf-7bcaa8fe23e3}} .
Therefore {{formula:19d66f79-dc48-4603-9ff7-0ff801d91d88}} . Also by {{cite:21a0c9ab4f4f50f29524640733707ee3e78df6a5}}, for {{formula:01cc48aa-8df4-4d9f-9eca-5f339a39197d}} , we have {{formula:dccc3363-03f9-48b5-b1a3-49ba4a05e297}} having order {{formula:3de06fd5-d728-4db4-aa27-13210ec2e9f9}} . In the present scenario, one can easily verify that {{formula:41b6f21e-6423-44e4-9168-408208520b44}} is not a CG-group.
Proposition 2.10
The group {{formula:97c110b2-b8a9-4763-8521-ee2a40490316}} is a CG-group if and only if {{formula:233c4644-1961-4c50-a677-fbc03391d43b}} or 3.
It is easy to verify that {{formula:604202a9-5e88-46fb-8ef3-be23c40a016e}} and {{formula:3782f60d-10a0-4d19-86a2-be6cec81cbcc}} are CG-groups. On the otherhand, if {{formula:a250b8cd-3ef7-4d40-b3e3-522a809ac0f4}} , then by {{cite:a99eb6b29560a892136d6e7f916780c8b1a9fc5f}}, we have {{formula:ae36b916-0a6a-43b0-84e4-a679a9ff704b}} and consequently using {{cite:43782893a747d2d54153b7d42f7aea8ecac81fa1}}, {{formula:aa895c4b-faa8-474b-8849-235077217588}} is not a CG-group.
We now compute the number of distinct element centralizers of {{formula:3f30cb05-92f5-4030-8566-92d297870edd}} .
Proposition 2.11
Let {{formula:bf691376-b3b0-4a19-a120-c49dea942775}} . Then
{{formula:150aa8a9-4284-4fb3-895d-8c59da376f01}}
5 if {{formula:4f1b71b3-853b-4e12-95d4-27aa6159ab24}}
14 if {{formula:89569a10-4e41-4135-88cc-fcb7bad7b38f}}
22 if {{formula:534b1a7f-de4d-49f6-a01d-e3c3fd127701}}
{{formula:c56deb67-8d37-4ac0-859b-780a77c35802}}
If {{formula:17645e5a-10ac-43e1-8228-53b9ec003896}} is even, then {{formula:c592ac37-cd7f-4be1-8d37-fdd80fed81de}} (see {{cite:bf193bffa94320acc84b5b8f3b8b5bcc2a971840}}). Now, the result follows from {{cite:c27c33ed603560443e61721bdc17408078247a0d}}.
Now, suppose {{formula:3e4c0b26-5654-4d38-95cf-43d865a1999f}} is odd. We have {{formula:bb39263b-a444-4b97-b052-0b8b1584a62f}} and {{formula:d165b41d-1651-4613-8f0e-0394eff6e5aa}} . Next, suppose {{formula:48e22e74-5260-47ca-9500-f3148b9207cd}} . In view of {{cite:b5723072d5e04edd5f0c3910515d3705617ccc5a}}, it follows that the centralizer of any involution (element of order 2) in {{formula:ab6c2300-d195-49ac-a7c9-d10d5cb8a0af}} is either {{formula:b1fddbbe-4759-44bb-8fb2-4dbfd56d1b85}} or {{formula:fe788eaf-a518-4f76-9ac8-1ad1d1f289be}} . Hence by {{cite:7097b5a9e069df88196ed9d1e6979bb3f4423049}}, {{formula:24c9c68e-fa26-4fd9-9e4b-0ad2aa80fbb9}} , noting that the size of element centralizers in {{formula:04d8ddcc-3445-4edd-90e3-dd2d666e44c9}} are {{formula:f2823c9e-997b-494e-8313-d100997cc8a5}} and 12. On the other hand, if {{formula:e20a29aa-fe80-48ea-ba4b-8ebd76e5f978}} , then using {{cite:a66af4865732c00f23740d871d769f6fc5a2b0a7}}, it follows that the size of the proper element centralizers of {{formula:df7d2b2d-ff61-47c8-a477-31a4c80a8cb1}} are {{formula:7eb421c3-bb6d-43d1-88b3-56b46dde494e}} and {{formula:f088fbec-0f25-42e3-94f3-767447b6e7ea}} . Again, let {{formula:76adeeb0-72e5-4c58-960d-7dc7ffdd6963}} and {{formula:dcbf38ab-6219-4da1-9718-559db86d443c}} be any two distinct involutions in {{formula:d8d6eb2e-ab20-485e-a562-ba5dcbafbe2b}} . Suppose {{formula:d9755687-0f1c-476e-af4d-17e803fd2b99}} . Since {{formula:7b7b5ad2-0901-4a12-b76c-36fd74f41390}} , therefore {{formula:2c70111b-e778-436e-a580-6309564d523d}} noting that {{formula:63f5349a-e75a-4a4d-a48b-20f9ebce71f7}} , which is a contradiction. Therefore {{formula:ab3965fe-7463-4c3e-a799-7876e7b74430}} . In the present scenario, in view of {{cite:7097b5a9e069df88196ed9d1e6979bb3f4423049}},
{{formula:cfc58263-fbad-4abc-b81a-69ad81c70b25}} .
As an immediate corollary, we have the following results, noting that {{formula:8210fa66-289c-4c63-9165-113dbc97197f}} for {{formula:82bcdc2c-c974-4df6-8b0c-0d1d91d1fab8}} (see {{cite:bf193bffa94320acc84b5b8f3b8b5bcc2a971840}}):
Corollary 2.12
{{formula:fef322d3-f766-49f8-87bd-645d46f26010}} is a CG-group if and only if {{formula:2deb8b6e-9b87-4d2a-a1bd-1c9a88ad84e4}} or 3.
Corollary 2.13
{{formula:709be054-dcab-4766-9cf5-55ff9c3ba23f}} is not a CG-group.
For {{formula:4d47cba5-b484-43d7-baab-bba09156edd6}} , we have the following result:
Proposition 2.14
{{formula:c1efbdee-b059-486b-aa53-83c064591544}} is a CG-group if and only if {{formula:a84563dd-db22-40a5-a95b-e144ad6ed780}} or 3.
For {{formula:48f8edb3-1b0f-42f1-bf01-782d4ed851cd}} we have {{formula:4556855c-a43b-4f9d-a1dd-0e36ed88ea2e}} is a simple group (see {{cite:bf193bffa94320acc84b5b8f3b8b5bcc2a971840}}) and hence by {{cite:43782893a747d2d54153b7d42f7aea8ecac81fa1}}, {{formula:ea5f3fa0-9824-4d28-a7fc-d50015bdae71}} is not a CG-group. On the otherhand {{formula:bf29bcf4-f84a-4450-87c3-b583c5711979}} and {{formula:17080347-d19d-4c0b-977a-bf8fb3f84df6}} are CG-groups.
We conclude the section with the following lemmas:
Lemma 2.15
Let {{formula:a6fb98b2-6ea2-46c7-b205-64b9c1e8ed3b}} be a finite group such that {{formula:2f19f6dc-65a2-49cc-8b50-24afe86634d2}} . Then {{formula:68fc9be1-3acb-47b1-a258-5362dee30ac4}} is a CG-group if and only if {{formula:ad13296d-8429-4e8d-a30d-3c6100b7c6fd}} is a CG-group.
The proof follows using {{cite:1fdf5b6faff220d1a58e763bc0dbd346f1ab2941}}, noting that if {{formula:b8ff4483-19c0-4210-af6f-6b3bf1176566}} , then {{formula:2edf6c00-bfc9-4418-98f9-1c9d643437c6}} .
Lemma 2.16
Let {{formula:463e44e4-b26d-4963-a183-a44542b7c585}} be a finite group such that all sylow subgroups are abelian. Then {{formula:516f7716-cb83-4dc5-b5c9-9c5e75c47f58}} is a CG-group if and only if {{formula:0b67d892-92a0-4120-a6f7-54a7002ec6d7}} is a CG-group.
In the present scenario, we have {{formula:187d3e46-4c7e-4a5c-8ea3-3e237f60c4d8}} (see {{cite:16f7ae3aa48ad06029c4354fca983f0ea73b0356}}). Therefore the result follows from the previous lemma.
The main results
In this section, we prove the main results of the paper. However, we begin with the following lemma.
Lemma 3.1
Let {{formula:081ee1b3-240f-4cf0-af7a-c9a9ee58b3b7}} be any group. If {{formula:cde02750-3db8-4cbe-bd18-165847b081c9}} where {{formula:5fd5d8bb-4a4d-4cf9-a75f-6808cf50db7e}} are primes (not necessarily distinct), then {{formula:5ab5f94d-f813-4ecc-9244-fd081bc12ce3}} is abelian for any {{formula:6d01ff08-005e-4a62-81b9-0a12d5cdf58d}} .
Let {{formula:0fb3e782-564b-48c0-9480-83bf4dc7b746}} . If {{formula:bc1ec827-6e43-4a6c-a6f8-a3bfeca0a272}} is cyclic, then {{formula:67d6706d-231d-433f-8faf-0652af44424b}} is abelian. Now, suppose {{formula:369cc57b-8780-4b07-955f-0b3d82ce475b}} . Then {{formula:e7bc80e4-c4f5-4d7d-acd5-c6481b0bb4f9}} or {{formula:b57394a6-e412-4324-b4ff-cfde4bd43adb}} . If {{formula:8b5fe668-5347-4584-935e-9b2a29160826}} , then {{formula:fb9fbb45-fd3c-4cf6-98db-d50727b3504c}} is abelian. Next suppose {{formula:59fbbb5a-26da-45fd-a2ea-b79a7d485564}} . Then there exists some {{formula:692d648d-36af-4b0f-913b-96bf6b76ef99}} such that
{{formula:bf4dda3d-b777-4d90-8bf9-9f745aea9d83}} . Consequently, {{formula:0b0cdf57-fa98-4b62-b83a-3c6a0e119913}} and hence {{formula:e25aff26-8ee3-4486-ba85-26d1c57f4ace}} is abelian. If {{formula:569faf9f-ec4c-4ff4-be43-ad1c508e7854}} or {{formula:6d09dd06-0a38-44a5-9c66-ca173969f1ee}} , then using similar arguments we can show that {{formula:a95cafc9-8c1d-4770-b229-fee8d33af7d0}} is abelian.
Remark 3.2
Recall that a group {{formula:51d67012-2b85-4d46-a18a-15f5f10dde6a}} is said to be a CA-group if {{formula:7196dbb8-3d2e-4d1f-ac54-f90004b0fba6}} is abelian for any {{formula:9f21b8b7-d01d-4a6c-ac0b-10e9f0f74f1d}} . It is easy to see that for such groups {{formula:4347b535-cf79-447f-86f1-63cef0d9aba7}} for any two distinct proper centralizers {{formula:e997946d-ce33-4e5b-8d87-338f06e14cd7}} and {{formula:9ee14268-3e15-4334-b9a6-af3cc0308b7b}} . Also we have seen that if {{formula:5f11a231-89e6-4db8-afbf-badecbfc75c2}} where {{formula:28f1d5fe-b445-4cd1-bbf3-28718dc691f5}} are primes (not necessarily distinct), then {{formula:37c7d48c-73e6-44f4-8900-4da3f1125830}} is a CA-group.
The authors in {{cite:4ca88ad1aafbf8f458c6f6f38f423e610e3b8ed7}} showed that if {{formula:dfab1dad-5048-4118-b0cb-d60224650a76}} is a finite group such that {{formula:6ff8bd82-551f-465c-ace2-38a43d894ad9}} is isomorphic to a simple group, then then {{formula:1cc5c3c2-d429-4645-aaf8-05ea06e109d0}} and {{formula:7d9b8f10-fd3f-4e60-ad66-cb7ad0f5af73}} are isoclinic groups.
In the following we generalize this result as follows:
Proposition 3.3
Let {{formula:8cce8d84-39cf-418f-afc0-b2aeedbc0d3c}} be a finite group such that {{formula:cb1fb3c7-9afc-412e-9d3c-2d7123cddd8b}} is perfect. Then {{formula:ae3e5a88-ef69-427f-a087-d1ef3117b7e4}} and {{formula:7ab672a5-b516-482c-ada2-c84e77d67c5c}} are isoclinic groups.
Suppose {{formula:031ac3db-f860-43b8-b41c-0db29e6b71e6}} is perfect. Then {{formula:6eeebee0-2692-4c84-939e-55b4445848ab}} and consequently, {{formula:b8cf4e7a-7422-4eb2-a06e-50dfd9a96e18}} . Therefore in view of {{cite:b871c894c53eabd04e3584b5e3beee1e8312b197}}, {{formula:8dba2dca-97b2-4d06-b6c5-4478d0b6a1e9}} is isoclinic to {{formula:24c6c2e1-fecb-4682-82af-7fa310c271d7}} .
As an immediate consequence we have the following necessary condition for a finite CG-group.
Proposition 3.4
Let {{formula:e52ac542-ed3b-4fa6-bcbe-7944a8cf071d}} be a finite group such that {{formula:412aa37d-b2c6-4b05-927f-50288dd4b50e}} is perfect. Then {{formula:a42798b2-8664-4353-b2b0-36736646d399}} is not a CG-group.
Suppose {{formula:5c40d10f-fe6b-4962-b0fc-cd228bff0fe6}} is perfect. Then by Proposition REF , {{formula:6425324f-4489-4df2-83ae-af1b90694906}} is isoclinic to {{formula:b9b0504e-5385-44da-8768-13e88a607997}} and consequently, using {{cite:d2a9993d61ca74b5f09812224a74393e576af65b}}, we have {{formula:fecef36e-5369-4bc7-8970-d0a2ccc9fad4}} . Now, if {{formula:6fc29f5f-f626-49dd-8df1-9755dca09786}} is a CG-group, then {{formula:c6a94db7-240e-4b3b-8041-f4b5f62f7f37}} , which is impossible by {{cite:43782893a747d2d54153b7d42f7aea8ecac81fa1}}.
The following result follows using technique similar to {{cite:1fdf5b6faff220d1a58e763bc0dbd346f1ab2941}}.
Proposition 3.5
Let {{formula:de839f61-1934-48e7-a291-451a350dfa14}} be the smallest prime divisor of the order of a group {{formula:6a531518-83ed-4d6f-8a3f-f7c3f510f4a4}} and {{formula:b1cc89a7-b2b0-4854-b00f-51114762889a}} . Then {{formula:abef5a52-2c9a-4785-91ea-91a49a3441e4}} is a CG-group if and only if {{formula:5b3661f3-4780-4a17-bcbc-3bffb9518db9}} .
As an application to this we have the following result. Given a group {{formula:6de4f8c0-89b2-4183-9318-3be635934b29}} , {{formula:4fec24f8-0991-4fc3-9a19-7befec5d5625}} denotes the size of a maximal set of pairwise non-commuting elements of {{formula:ce0c2f15-dae6-4c23-ac6f-9fbfa8348a38}} .
Proposition 3.6
Let {{formula:632789dc-9525-4bff-bad5-af1e68164f5f}} be a finite non-abelian metacyclic {{formula:e8f2b766-14c0-4482-b748-c843627f40a6}} -group, where {{formula:94289822-5b8e-4634-9951-1f448bd499b7}} is a prime. Then {{formula:1e24baf6-334f-4843-973f-1e7bc7a2d0f3}} is a CG-group if and only if {{formula:4ec08079-556c-41dd-a213-467575df9994}} .
In view of {{cite:9e69c109fbebcaa114db94e4dc02d5afefaa8dc2}}, we have {{formula:c0890d51-06bf-430b-9400-a4217ebcf915}} . Now, suppose {{formula:0da8dc14-6053-4160-8ba5-9aa3d6fb1a64}} is a CG-group. Then {{formula:cc94ffad-5ce8-418f-84fb-52411c3e7f0b}} . Consequently, we have {{formula:d1bf77a5-96fa-4313-b2b5-37b951fc49a7}} . Now, the result follows using Proposition REF .
The following proposition gives a sufficient condition for a finite group to be a CG-group.
Proposition 3.7
Let {{formula:b80dc129-d725-4f90-856d-c3cc3ef1e509}} be a finite non-abelian group with an abelian normal subgroup of prime index. Then
(a)
{{formula:1c67573b-b5e9-4e2d-ad56-5d4d95c82c52}} is a CG-group.
(b)
If {{formula:e176604d-a88a-404b-ac5f-1e502145c049}} is abelian, then {{formula:3175ecdf-d407-4be4-b78b-f75ce5ce31d9}} is elementary abelian.
(c)
If {{formula:17134065-6a2a-4b2c-a1f9-a162782ec0bf}} is non-abelian, then {{formula:dcf08a8c-002a-4f86-bfc2-42b27f751a91}} a CG-group. In particular, if {{formula:98ef6355-752f-49a3-9d45-6229187f74a7}} is of order {{formula:41ff3621-8101-4d25-b640-7fcdd0440063}} for some prime {{formula:5896fdbf-82f5-4859-b2a1-c93865e226e7}} , then {{formula:d854c4e5-1a53-4d79-b95c-cbbf21de858e}} .
.
a) See {{cite:56f04fbca1f7a86cc6871bea5e6fa8ddfdd6dca8}}. It may be mentioned here that {{cite:cfe2da6ddc48d0732ce23fead38f065f136ba543}}) is a particular case of this result, where the author obtained the result for {{formula:82ec1f11-802b-401e-ac9b-a55a7fe29dc9}} -groups ({{formula:8f206b09-715a-4d2f-886b-4cbc87ef011c}} a prime )only, noting that {{formula:bcd12e28-c6cb-4464-9d48-6762fbad44b2}} if and only if {{formula:3628e752-441c-41a8-a33f-e0d86133f417}} is a CA-group ({{cite:55fbab336a0b482d77bb06366eba7c8b55729d7c}}).
b) By {{cite:e4464462bd2acddf1264d313e060ad3a641c329d}}, {{formula:4b45b357-22ed-47b8-9b7a-5715ca744629}} is a CA-group and consequently, {{formula:9cb8e144-1e41-4dd5-87e5-4819f709f1da}} is a partition of {{formula:7e355395-ac9b-42fd-be59-b651322344ee}} (see {{cite:55fbab336a0b482d77bb06366eba7c8b55729d7c}}). Therefore if {{formula:5a89baee-af70-4594-9152-414be0951496}} is abelian, by {{cite:648cdfa164f94d1e5358205e7d477a68b6ad95e1}}, we have {{formula:4369c1a0-4e19-4515-888c-7e870bc08757}} is elementary abelian.
c) Suppose {{formula:ddd6e8b3-5223-479d-94d7-7601942d8586}} is non-abelian. Let {{formula:93900568-f5cd-4ca0-ba68-4fbcb050a124}} be an abelian normal subgroup of {{formula:77880008-38b6-422a-8445-259292a96c65}} of prime index. Then {{formula:34caea11-9f8a-4898-8ae5-5d6edde3f757}} for some {{formula:b43fb1f3-2ace-4b41-97ad-324775a1dfb3}} . In the present scenerio, we have {{formula:b310db20-460c-478a-9398-cbe0cf34d702}} , and consequently, {{formula:19514d4c-6766-48de-a838-7bc03b2e5366}} is an abelian normal subgroup of {{formula:80b6d534-d951-4b51-8936-d4a4a5adcee0}} of prime index. Therefore by {{cite:56f04fbca1f7a86cc6871bea5e6fa8ddfdd6dca8}}, {{formula:61238d9c-f04b-4451-9f6a-5d1ced68f07e}} is a CG-group.
Again, suppose {{formula:63d22553-e860-47e1-9f27-9ba7d53b1ae6}} is non-abelian of order {{formula:fb28b780-0812-4f12-8a22-3e84e9322405}} for some prime {{formula:b7909a46-8d42-4ea0-ab3a-c396db8642ca}} . By {{cite:e4464462bd2acddf1264d313e060ad3a641c329d}}, {{formula:402ffd05-5913-401a-93b8-1807f440840f}} is a CA-group. Therefore {{formula:447191e2-bbeb-482a-838d-666330464d31}} for any {{formula:46715563-9987-41eb-8fc4-7631f7c76f55}} . Now, {{formula:b9560feb-00b5-4928-a75e-7785fe0c6c8c}} is a centralizer of {{formula:6a45c32a-2de6-468f-944d-585ab97ebd77}} of index {{formula:a1c11090-982a-4069-9098-2067b9032519}} . Clearly {{formula:a23bbc57-15f4-4260-b960-09ca8787526a}} will contain exactly {{formula:e881a21d-05b6-4fa8-b137-2b095e5899c3}} distinct right cosets of {{formula:5a70f768-1554-4ebf-94a5-4f843b36c72d}} . Therefore the number of right cosets of {{formula:5481aa70-ebce-4b77-8786-aa7806eb5f86}} (other than {{formula:062702ee-1814-416f-8213-96ada8802f5a}} ) left for the remaining proper centralizers is {{formula:21d1afa0-cdd8-4348-b6af-7f6194adcba1}} . In the present scenario, one can verify that any proper centralizer other than {{formula:37447ac2-270a-4361-9b95-0331f6e540a9}} will contain exactly {{formula:c98c4a73-e9b0-4d3b-a741-1dbe75ff84c7}} distinct right cosets of {{formula:ef531fbb-e936-4327-9b6b-4dff578bf67d}} . Hence {{formula:e9bb69cd-e628-495d-a86e-948062198813}} .
As an application of the above proposition, we have the following result for minimal non-abelian group. Recall that a minimal non-abelian group is a non-abelian group all of whose proper subgroups are abelian. By {{cite:de0626d18a2d9e8effead94d2c621e487938101b}}, we have if {{formula:e09cc6bb-4f77-458a-bf08-19eed01510ae}} is a finite minimal non-abelian group, then {{formula:06a442c6-8516-4206-9230-5d76744fef8b}} can have at the most two distinct prime divisors and if {{formula:633649da-2a7e-4813-a383-10f4a4ecdb8e}} is not a prime power group, then {{formula:deed22b6-b4c7-4d36-9ae6-95c62aee5fc8}} , where {{formula:38afb1e1-c3a4-443b-9bef-1aa3bdee1635}} is a cyclic {{formula:4deb29a3-4002-4e14-a91b-53325f5de401}} -Sylow subgroup of {{formula:e88988fd-3a6f-4dca-90d3-0e7b6a19e7df}} and {{formula:d4150095-f7d7-4a5e-bddc-f75e6a016b9c}} is the elementary abelian minimal normal {{formula:391bbc4c-b753-47b1-8ef1-78af4fa78fed}} -Sylow subgroup of {{formula:228da241-29b5-46f9-9e89-e8dd1a45cf51}} .
Proposition 3.8
Let {{formula:46d48313-dcb9-4919-9d78-977587822964}} be a finite minimal non-abelian group. Then
(a)
{{formula:9571cad1-c828-4876-9c48-572e6b8d1516}} is a CG-group. In particular, (see {{cite:f44a022fd8bb762f69f395b8e90d573cb7428de3}}) if {{formula:e5a75b70-9835-40c8-9c46-00ab66e91d7b}} is a {{formula:cde19bf4-8de4-4ab3-868d-3c78b71ce27e}} -group ({{formula:3086ff71-9cf0-4b62-8da0-95689a1ef0fd}} a prime), then we have {{formula:02087989-ab62-4fd1-baa7-a28be11c4229}} . Otherwise, {{formula:d823148a-daad-48a4-860a-ea3b5e7aaed4}} is a primitive {{formula:e5790cca-5003-47af-8fb1-8cd0d154d1d3}} centralizer group, where {{formula:6b2c6a61-5846-4888-b497-55f260259c9f}} is the normal Sylow subgroup of {{formula:fc01a73f-b7d9-448c-a20b-61dd4643fff4}} .
(b)
If {{formula:4d096a92-effe-42d3-8704-e20e87228c6f}} is a {{formula:ab42d413-c568-4f26-a6d6-4d0b487aa483}} -group ({{formula:a2041895-2b0e-4495-8df3-e58a7a3b32e0}} a prime), then {{formula:91fb9ff4-d399-4696-8ccf-f8b4f0079c33}} . Otherwise, {{formula:96b4be70-5c54-4c30-ac49-f93ef76a9044}} is a CG-group.
.
a) Let {{formula:27144ec2-2901-4f0a-84ca-99afc6db618e}} be a finite minimal non-abelian group. If {{formula:6497126e-9381-458a-93a3-aff2085244b7}} is a {{formula:e384c081-5ca0-434c-a85e-950cb2c865f4}} -group, for some prime {{formula:b66ab70a-0f3f-4515-9124-d2e7c7d12081}} , then {{formula:2724d10b-2618-49a4-a759-f246fe1492d1}} has an abelian normal subgroup of prime index and hence by Proposition REF , {{formula:156c3d28-4a9a-4f44-a804-a036c14555ec}} is a CG-group.
Next, suppose {{formula:303585a6-25da-4b69-b189-d85b6a962d55}} is not a {{formula:4d1abe85-d164-495a-8f31-3c51bd6afff1}} -group. Let {{formula:6d0e4702-3206-4363-bf66-dca719308129}} be a cyclic Sylow subgroup and {{formula:bf47f11f-05a2-4b2c-ba4c-941ebf96100f}} be the elementary abelian Sylow subgroup of {{formula:38c39366-0066-4946-b9bc-4097e3b9d616}} respectively. Then {{formula:10bd3e71-f2a8-4ad7-b114-480616cdd780}} has a normal subgroup {{formula:72d0feb1-4a8d-4f01-a43a-04f8b6e44dc4}} of prime index and consequently, {{formula:32f9332d-b577-4ab6-9484-9951ef1e45f2}} is an abelian normal subgroup of {{formula:f4cf8129-ff14-4301-afea-617ed3315796}} of prime index. Therefore by Proposition REF , {{formula:305c3982-ffb2-4fdb-92b4-646cffe6d0e9}} is a CG-group.
Now, if {{formula:bda98a04-20f3-4208-842f-fbe8072ea543}} is a {{formula:713861b2-58e5-478d-a8e5-ad133f487fc5}} -group, then {{formula:937bec5f-faa1-4e71-a091-93877539abf8}} , noting that we have {{formula:524c4c31-4dc2-49e9-aa49-3844d77b16d3}} by {{cite:80a065c0bd3864a9dadd67efd0040cb3a0800688}}. On the otherhand, in view of {{cite:1fdf5b6faff220d1a58e763bc0dbd346f1ab2941}}, we have {{formula:82901b8d-1f62-4510-afc5-718ceff8c8ef}} is a primitive {{formula:9be4ca7a-d568-451f-9c85-f8dd54aec9cb}} centralizer group, where {{formula:ef39eaf8-11d2-499a-af2e-ffbe26cd9091}} is the normal Sylow subgroup of {{formula:5ceb6f6a-87dc-49a9-98f1-119137662aeb}} , niting that in the present scenario, we have {{formula:27f36113-ef1d-4802-9091-9b0c1d12865e}} and {{formula:9cf7a402-2811-484f-aeb4-6495b5ee37bd}} .
b) If {{formula:c7a17895-6db2-4de1-a0fd-5c917c1b62b4}} is a {{formula:ca46aae6-d031-4053-8380-95c56a9b2a95}} -group, then the result follows from Peoposition REF , noting that we have {{formula:3e3b951c-2d3c-47bc-9b0c-f911d774d8d3}} by {{cite:80a065c0bd3864a9dadd67efd0040cb3a0800688}}. On the other hand, if {{formula:66a3e348-80c7-4bba-b675-74355b0a155a}} is not a prime power group, then {{formula:f93fe275-35a0-4d4b-a33c-152172b120f0}} is not a prime power group, noting that in the present scenario, we have {{formula:ea46f793-8e83-4fc6-9b24-08b972174a6c}} , where {{formula:1737a568-147a-47c5-890d-c6bf3ad3beb6}} is a cyclic Sylow subgroup of {{formula:6aafcea2-5a26-4b86-9245-e69361bd011b}} . Now, the result follows from Proposition REF .
Recall that a Frobenius group {{formula:70778916-8ce9-49bd-a1dd-190debb544d9}} is said to be minimal if no proper subgroup of {{formula:f7faf088-26d2-4aa7-bab2-cd6a39991ead}} is Frobenius. In this connection we have the following result:
Proposition 3.9
Let {{formula:26560cda-3057-4fd3-9f8e-9a52271e6a8b}} be a Frobenius group with kernel {{formula:c1a96fee-6212-4848-9733-0ae043ea1eda}} and complement {{formula:08bd9e83-8888-43c2-aaa6-5bac4af83ede}} .
(a)
If {{formula:f72a88da-f36f-4be6-b11e-2e7c32d78c12}} is minimal Frobenius, then {{formula:633b946a-81cd-4e7a-91c9-235ded4ba19f}} is a CG-group,
(b)
If {{formula:ff4a7563-a958-491d-8bfc-32b7e5845ac4}} is cyclic, then {{formula:31551cf9-eea2-4cb4-b6ea-1cf7b89efc1c}} is a CG-group,
(c)
If {{formula:ba7b6191-c23a-4f53-9a09-f356508d0dfc}} is abelian, then {{formula:102972dc-184c-49ad-abf3-f5860a699b59}} is a CG-group if and only if {{formula:7b3777e8-b903-43dd-990d-2d253c4db55d}} is abelian.
.
a) If {{formula:f23e5331-101d-4c00-895c-bed7968faffb}} is a minimal Frobenius group, then by {{cite:ef76a7477244dfc986e70117022a3c38e821c5cd}}, {{formula:ec5a0500-1b12-4113-97dd-00bcd7397e1d}} is elementary abelian and {{formula:ebeb9776-45bc-4ee4-8155-402fa4b72082}} has prime order. Again, by {{cite:8e0eec9fef377b19f1608f0166a8e7ad23d66882}}, {{formula:8332a7d1-ed6b-4422-9727-0917ad3eee9e}} . Therefore from the definition of Frobenius group, {{formula:e3f1f0f8-dc45-4056-b293-b40cc5b5a3b2}} is a CG-group.
b) If {{formula:a04f94c1-8811-4b04-a7b9-8ce031e5558b}} is cyclic, then in view of {{cite:be3474c71440ca7841d9e76544a18ad189baef51}}, {{formula:91bd4750-65ef-404b-9110-a25934dda286}} is cyclic. In the present scenario, by {{cite:8e0eec9fef377b19f1608f0166a8e7ad23d66882}}, we have {{formula:8fa03d16-9fa7-4691-b103-691767836a21}} . Therefore from the definition of Frobenius group, {{formula:b03ef868-a37b-4973-919f-ab5e9b540a24}} is a CG-group.
c) If {{formula:fb7e061f-33f9-4ea9-9cd0-17c2025cf47f}} is abelian, then by {{cite:8e0eec9fef377b19f1608f0166a8e7ad23d66882}}, we have {{formula:604945cd-5002-4cf3-b89b-054c7acc0f79}} . Now, if {{formula:2c5941e0-0bdf-4f66-a6e0-53548d44f9dd}} is a CG-group, then {{formula:bf8c24b6-9e1a-4789-b02e-968367cf5d60}} must be abelian.
Again, if {{formula:ad52ec4c-b659-4787-8ea1-9b164fd40cbf}} is abelian, then from the definition of Frobenius group, {{formula:0fd788e7-697b-4be8-8372-a05b25bb7d01}} is a CG-group.
Remark 3.10
If {{formula:32ec6ffb-1cd7-4d6f-ad97-52edddca2ea2}} is a finite solvable group in which centralizers of non-identity elements are abelian, then {{formula:ed0a3841-3eae-4e0e-9952-9a7aa86a0aad}} is a Frobenius group with abelian kernel and cyclic complement (see {{cite:9c93c12d9954b4283b868d853b95a80c07944108}}). In this connection we have the following result:
Proposition 3.11
Let {{formula:c0cf31c7-af7b-40ef-918b-223fb3ae3c44}} be a finite group such that {{formula:635d240a-3001-466c-a0ac-f96acb48d470}} is abelian for every non-identity element {{formula:2160f86c-a75f-4f4c-bfa1-8a72b1dc84a7}} . Then {{formula:4d547a8a-178a-448b-ad84-f5eaec838410}} is a CG-group if and only if {{formula:2cc2e1de-a84d-41f3-ad5e-578c947cff32}} is a Frobenius group with abelian kernel and cyclic complement.
Suppose {{formula:15aeea6e-a61a-4eca-928c-33f323b35a22}} is a CG-group. If {{formula:b766db72-c0ab-4d92-856b-afd8f41a2c1b}} is non-solvable, then by {{cite:94f66902ee22a5216660975a47c79da122143c39}}, {{formula:dcef7ce0-e006-4b5c-aa8a-b67c68fedab5}} is simple and consequently using {{cite:43782893a747d2d54153b7d42f7aea8ecac81fa1}}, {{formula:be313bd2-4c9f-47ca-aa36-66fbeb020768}} is not a CG-group. Therefore {{formula:de837c85-1543-4b71-af10-eabe0f73e57f}} is solvable. Now, the result follows from Remars REF .
Conversely, suppose {{formula:18e18711-c89f-4735-a8f5-a57d303dcb3f}} is a Frobenius group with abelian kernel {{formula:bdd5b6f9-67e2-4237-a6be-e252a215a849}} and cyclic complement. By {{cite:8e0eec9fef377b19f1608f0166a8e7ad23d66882}}, we have {{formula:38ad7f8a-84d8-4f3b-8c8f-4c5002d8b39b}} . Therefore from the definition of Frobenius group, {{formula:67ebf0bf-5732-4541-93c3-d1c26827924b}} is a CG-group.
As an immediate consequence we have the following result:
Proposition 3.12
If {{formula:4f0f10ea-728b-4646-a21f-4768bdfac96c}} is a non-abelian group of order {{formula:b811d1e5-a3ab-4030-8a49-3080c4ba6bde}} , {{formula:4d7796a7-e875-4519-98a6-011809f61fe0}} being primes (not necessarily distinct), then {{formula:79304446-9195-4f03-86a6-9f7cbb3ae152}} is a CG-group.
If {{formula:d5e3fad8-e83b-48a1-b73a-7d59cd68a156}} , then in view of Remark REF , {{formula:0127bcd9-76ff-41d8-af5f-9694ef44e40a}} is a solvable CA-group and therefore by Proposition REF , {{formula:6088d67d-3600-4a40-af74-95cd1f4fe795}} is a CG-group. Again, if {{formula:4f9dfce6-f3b6-40d7-9f1d-7ae7edc1641a}} , then {{formula:7bcfcbe4-bab5-4a1d-8670-b63b764eb418}} is a product of two primes and hence by {{cite:56f04fbca1f7a86cc6871bea5e6fa8ddfdd6dca8}}, {{formula:afaeb6ef-1b85-4244-bdee-2811ed1bc753}} is a CG-group.
Proposition 3.13
If {{formula:3855ebf0-62ed-4e1b-ba82-60a7c393c6b2}} is a non-abelian group of order {{formula:8a5e15b3-b25c-4762-9529-5672c381ef09}} , {{formula:e362caa6-5550-4086-a693-3c4690cc505c}} being prime, then {{formula:43f262cc-9153-4db1-b5f2-a475bbc73783}} is a CG-group.
It is well known that if {{formula:11278861-339b-46af-a331-6cac141cee9e}} is a non-abelian group of order {{formula:0c1aaeb6-81a6-45f2-872d-bb4225f992f2}} , {{formula:d6d5d5c6-46bc-4be9-8190-68c5414ede24}} being prime, then {{formula:19ad6b47-c36d-4fde-9a97-eabb9e64ab82}} has an abelian normal subgroup of prime index and hence by Proposition REF , {{formula:a46f62ad-ed3a-46df-a19b-1248e0fecce4}} is a CG-group.
We need the following result to prove our next proposition:
Proposition 3.14 (Lemma 12.12 {{cite:cb06cd868a6b83d4eb75c17c481f7814b5580a26}})
Let {{formula:89198009-1b0d-469a-88bd-1aa67474c9c1}} be a finite group. If {{formula:fe918c31-0d63-4f41-a02d-0a64a47d0808}} with {{formula:859114e6-1068-46a1-b6d4-bed7cc35a5b8}} abelian and {{formula:cbe09d5b-0df2-41a0-b27a-6f70b7e51ccb}} cyclic, then {{formula:4e0ad100-347c-4007-bd60-ccefd1f28dc3}} .
We now give another sufficient condition for a finite group to be a CG-group.
Proposition 3.15
Let {{formula:cc5de3c3-1a7b-46f1-9352-001a50be2d06}} be a finite group such that {{formula:a10ca134-da2b-40e0-aa37-ff45f00ff304}} is a Frobenius group with {{formula:0c799e40-230b-4e6a-a7ad-28039cee9b86}} and {{formula:4b778258-45a0-4e4e-a676-379be2877556}} abelian. Then {{formula:3d79cde5-8d0d-476f-a521-f709fad17b01}} is a CG-group.
Using the third isomorphic theorem, we get {{formula:4b1b74f2-81b2-4ab2-898f-7b60fa6a2fdd}} . Consequently, we have {{formula:d308a465-4c50-48cc-bcad-a19e5db3c827}} is an abelian normal subgroup of {{formula:5f7c6f1c-c098-4693-9c20-3a68a06809f4}} such that {{formula:7d971f1e-cd63-448d-bdc4-dae83e6df965}} is cyclic. In the present scenario, in view of Proposition REF , {{formula:787b349f-7c89-4934-9895-c3d35b53a0ac}} which forces {{formula:7c1bb992-45f2-4cf3-b835-5af17b732706}} . Therefore by {{cite:1de1e783f1ea3fd7ec01eac24a4f70f2be79e64d}}, {{formula:cbeedf48-6fcd-488e-835c-547ca959a8ab}} is a CG-group.
As a consequence we have the following corollaries:
Corollary 3.16
Let {{formula:282a1c75-610b-492a-a1e6-fab796377889}} be a finite group such that {{formula:020d2851-3d3c-4033-8f03-8c0df4e98dda}} is a Frobenius group with {{formula:e1e657c6-9991-4dba-b320-082f537897e1}} abelian. If {{formula:b9d6343a-6717-42d0-9a4e-71018c2a9050}} is abelian, then {{formula:80a9040a-f433-465e-8653-9001ea02bcd6}} is a CG-group.
Note that {{formula:3b9c5e58-d954-463a-9acf-24b5a2e8808b}} is abelian implies {{formula:f6dc3134-27a2-4449-946c-3ec951d02f93}} is cyclic and consequently, using {{cite:8e0eec9fef377b19f1608f0166a8e7ad23d66882}}, we have {{formula:5f022790-7a81-4bd7-ad60-229562a26b02}} . Now, if {{formula:cdadf4f8-d59d-4d30-88c8-b916f031a80d}} is abelian, then {{formula:3dd7c102-4d7c-4e2f-ae2d-9a3f4219235f}} is abelian and therefore, by Proposition REF , {{formula:acbb3c6a-6277-4804-bccb-304495028f49}} is a CG-group.
Corollary 3.17
Let {{formula:db44c328-f6be-43af-9484-d1f642659b67}} be a finite group such that {{formula:20ebc621-aa70-412a-a5c4-89e62b8e365c}} is minimal Frobenius group. If {{formula:04819f5e-1207-4946-aba9-ded8c84e1dd0}} is abelian, then {{formula:c76da1ae-0126-41ed-9f74-4043040b6b78}} is a CG-group.
In view of {{cite:ef76a7477244dfc986e70117022a3c38e821c5cd}}, {{formula:6cca73f7-71cb-4d94-9e5f-83d3296e4c41}} is a Frobenius group with cyclic complement and therefore, the result follows from Corollary REF .
Corollary 3.18
Let {{formula:9b56706d-832a-46fa-bacd-7da9194e4080}} be a finite group such that {{formula:b468a0ce-6929-4e22-9cbe-b0d5aa5e6b90}} is a Frobenius group with cyclic kernel. Then {{formula:4c6442e0-2483-4fca-9b26-0beda2601bfb}} is a CG-group.
In view of {{cite:be3474c71440ca7841d9e76544a18ad189baef51}}, {{formula:6cd80bb1-1de9-410d-80ad-e55895d557d9}} has cyclic Frobenius complement and therefore the result follows from Proposition REF .
In this connection we would like to mention the following three lemmas:
Lemma 3.19
Let {{formula:5409694b-3bd1-4781-9d74-1d4a36418a26}} be a finite group such that {{formula:f028551c-2010-4613-a821-2d8ec18faf87}} is a Frobenius group with {{formula:c752bd7a-c1a0-403b-a43d-44de7c103c39}} and {{formula:4ebb7f4f-979d-47d8-a3d7-50d073b04b22}} abelian. Then {{formula:d2bf0555-ff6e-4bd7-bcf9-4c37b832a373}} .
In the present scenario, from Proposition REF and {{cite:8e0eec9fef377b19f1608f0166a8e7ad23d66882}}, we have {{formula:8906fb1a-ffee-400e-8e44-c19aff98c994}} and hence the result follows.
Lemma 3.20
Let {{formula:1290599c-4c38-428f-8a42-6a9c2e939729}} be a finite group such that {{formula:c6890a99-129f-45d2-9ecc-8f5b96d12897}} is a Frobenius group with cyclic kernel. Then {{formula:fbc16811-9f79-4007-8de3-2451a0a9b703}} .
In view of {{cite:be3474c71440ca7841d9e76544a18ad189baef51}}, {{formula:352f770f-0696-452e-b745-62e6aec0d1d1}} has cyclic Frobenius complement and therefore the result follows from Lemma REF .
Lemma 3.21
Let {{formula:d2428ef6-cb44-4ea7-a50a-4bafa9982fbb}} be a finite group such that {{formula:f89b5577-ff49-464f-aa64-d7020c94cbf9}} is a Frobenius group with {{formula:3a079f4f-54ab-420e-aa19-1cce82c6b8e3}} abelian. If {{formula:2f75655a-2ffe-4487-80a7-dffcbbe7a502}} is abelian, then {{formula:3a0f5f61-8985-434e-ac8b-0ba07b76775e}} .
Using arguments similar to Corolary REF and Lemma REF we get the result.
As a consequence of Proposition REF , we have the following three results:
Proposition 3.22
Let {{formula:98fc6c8b-b010-4702-b81a-92b38646af07}} be a finite group such that {{formula:8b9b121c-5280-43f7-a84d-1defb6b826d8}} is of prime order {{formula:08bf16a5-8ff2-489c-870f-3ba9fbc163ab}} and {{formula:9dab3d86-70c9-407f-8199-bb808395a61e}} . Then {{formula:595fa264-e3c7-4d18-90aa-43657caadadf}} is a CG-group.
In the present scenario, we have {{formula:fed6c5b6-e8fc-4f57-a490-f16882350d04}} is of prime order {{formula:6ad386d0-f86b-45e3-8e0c-f1de500cf83f}} and {{formula:b18d427f-dda1-4e67-8630-962f2fd49f43}} is of order 1. Therefore in view of {{cite:53911179d74b39602728970e9256b85c45d25b7a}}, {{formula:e9b6834e-5059-49b5-bbea-2c9862f9694c}} is a Frobenius group with cyclic kernel and cyclic complement. Therefore {{formula:613500f2-8f44-4471-8ae9-d57a469a8c88}} is a CG-group by Corollary REF .
Proposition 3.23
If {{formula:6a6feae4-853a-4f08-89fa-ce4fea8f1a85}} is a finite group such that {{formula:9cd4df64-c5d9-4ad9-b95b-675ac23c61bc}} or {{formula:5878d980-2d56-4624-a17b-097b1aa45bf8}} for any primes {{formula:b73f04c8-7894-492d-8b35-c16ea2057696}} , then {{formula:f4b87a0f-3d57-4889-8958-4bcf829bc840}} is a CG-group.
Suppose {{formula:19befd43-de9a-4854-809f-40826f6b5f11}} . By {{cite:5e409999a6faa00a5cae739113f35ff3d61d83d9}}, we have {{formula:a90fff6e-b1fa-48d5-94d6-f554871cdc5a}} and therefore in view of Remark REF , {{formula:5c60dd0b-2045-4ee6-8bfd-1101ec9749ca}} is a solvable CA-group. But then using Remark REF , we have {{formula:216c3d09-1085-4904-88ac-8f9999c2b464}} is a Frobenius group with cyclic kernel and cyclic complement. Now, the result follows using Proposition REF .
Next, suppose {{formula:57b8505f-3a1b-43fb-be16-9bfaf659809b}} . For {{formula:29a58642-793a-47a2-981e-5e8d6afe1478}} , we have {{formula:fdd7743a-e114-4d4a-9b60-65fa3b92a69e}} or {{formula:04e30e0c-e05e-411c-9848-5361d0ecd527}} . If {{formula:daf6e3de-67df-47d8-868d-c3337c687feb}} , then
{{formula:b52e4e62-4b1d-4b6f-b939-a056c163391d}} is a Frobenius group with kernel of order 4 and complement of order 3. In the present scenario, we have {{formula:3efc97ce-0a32-452e-8269-dfbbc9f4c9fe}} and {{formula:82445b80-5e30-46ec-8796-1db25fe74c9f}} both are abelian, and therefore by Proposition REF , {{formula:b96a5a47-bd60-4fc9-b98c-abfe8c388dd1}} is a CG-group. On the otherhand if {{formula:8b74557e-436a-4497-93b5-a315bd236c47}} , then by {{cite:56f04fbca1f7a86cc6871bea5e6fa8ddfdd6dca8}}, {{formula:ee0c657d-897a-4043-a7c7-4e00b49cfc47}} is a CG-group.
Now, we consider the case when {{formula:308a5675-2964-4c52-bd72-2086b3ad2f96}} . Using {{cite:5e409999a6faa00a5cae739113f35ff3d61d83d9}}, we have
{{formula:1f53e1e3-a283-40ef-a8f5-bbc1fcf7fa22}} or {{formula:797cd485-1e4e-4604-8d50-ee56562b5a98}} . Now, If {{formula:97436f56-669d-4fa0-9d62-bb7870283aa1}} , then by {{cite:5e409999a6faa00a5cae739113f35ff3d61d83d9}}, {{formula:b88bcb04-ed88-49ee-98bc-4414ab4dd4ce}} and so {{formula:89dbbe96-5d1b-42c0-8d1e-fccab226f9ac}} is a CG-group by {{cite:56f04fbca1f7a86cc6871bea5e6fa8ddfdd6dca8}}.
Again, if {{formula:0dbefb33-f9a6-4fc7-acfa-26f0e3fcf0f0}} , then in view of Remark REF and Remark REF , {{formula:0ae39a93-b714-4e3f-a2c4-2fab86e17dff}} is a Frobenius group with cyclic kernel and cyclic complement of order {{formula:23d3bc2d-29fc-4d6e-93ee-9c3f04ac132f}} . Now, the result follows using Corollary REF .
Proposition 3.24
If {{formula:64490677-4523-4bf6-b25c-e1950709ca28}} is a finite group such that {{formula:fe6f60dc-b30b-4c36-b155-d8afe0eab4b8}} or {{formula:9e3780a4-ac26-4d09-a905-4f7fcb847d49}} , {{formula:880520dc-e3b5-4103-9dbc-b4f7b659f385}} be primes, then {{formula:9e729308-4246-438d-ad0b-8846a1d1caeb}} .
By {{cite:5e409999a6faa00a5cae739113f35ff3d61d83d9}}, we have {{formula:35130c4d-edba-4873-b55c-68c3927b0cb5}} and hence in view of Remark REF and Remark REF , {{formula:cbbf86a5-c85c-4500-8957-5921c3a0607f}} is a Frobenius group with abelian kernel and cyclic complement. In the present scenario, one can verify that {{formula:43c917cc-71b7-4ebd-a2aa-76df483162fc}} and {{formula:7cf31132-81d5-4ce0-b27c-e46f2c3cfaf6}} both are abelian. Therefore the result follows using Lemma REF .
For finite groups with central quotient of order {{formula:587c0f30-f3e6-4021-b5c5-615be92f1add}} , {{formula:e6f17a86-6c5e-445a-8b8e-19ddc43875e6}} being prime, we have the following result:
Proposition 3.25
Let {{formula:6bcc9bd4-70e0-47bd-81f1-8a9e1dc8db92}} be a finite group such that {{formula:b0e95370-0488-4cda-b583-1aff13e5cb2f}} , {{formula:d9459930-4681-4acb-a0ff-bed9bbb56f9e}} being prime. Then {{formula:7067d4f2-01d7-43f4-ad8c-fe814afc697d}} is a CG-group if and only if {{formula:a22e8243-0d2e-47aa-b5e9-aeea4babe3f6}} has an abelian normal subgroup of prime index.
Let {{formula:810b1a8f-de8d-4834-a77d-1220cfc5d03d}} be a CG-group. In view of Remark REF , we have {{formula:c2749e0f-477e-47d6-af27-7ba48d34cace}} is a CA-group and {{formula:25a4e087-8894-443e-beb9-e5223f060c14}} for any {{formula:1f8d5348-410e-473e-9f87-64623788dce4}} . Now, suppose {{formula:fc072dd7-a268-47f4-b4e2-575f8d3886a4}} has no centralizer of index {{formula:fe025731-36aa-4bf3-88a9-a5c6c4168e5f}} . Then {{formula:2aec1229-b8d7-4a3e-8f28-d09125a4fd0d}} for all {{formula:b1f25417-6f39-4849-906d-5128d189840c}} and consequently by {{cite:3b1db7733525e21baa5011d66b433f092a0c790b}}, {{formula:56a50eb1-d66a-4ac0-9405-35ca96304ef3}} , where {{formula:43a4d157-b9fc-4ee7-a50b-d52953e318a1}} is an abelian group and {{formula:080b0ec6-b122-481b-a030-34a77aa09fcb}} is a {{formula:2b3c5f6b-0858-46ad-9c00-4e6b35456fdb}} -group. In the present scenario, each proper centralizer of {{formula:d66bdb81-6247-4ab9-ba41-58cdcb5d33d7}} will contain exactly {{formula:4e3c09a4-be99-4392-83a8-fdea86538246}} distinct right coset of {{formula:9f13a099-7270-4431-a144-338a59df7e87}} . Therefore {{formula:3013f138-2212-45a9-a52e-1108592d15cc}} . But then {{formula:9620a304-1538-493a-a286-4de83b2d5e2f}} , which is impossible. Therefore {{formula:a3def4e1-2dda-430d-8554-90bbb7cbe328}} must have a centralizer of prime index {{formula:db3c40fa-4529-4d4a-ae5f-0c944f0f5b00}} , say, {{formula:bf1134d4-1bc1-43b9-a217-9e016c04988d}} for some {{formula:2c81d529-2b12-47be-a245-4ad2cc6f75cf}} . Clearly, in view of {{cite:7313ee7e80b71434dbb1c2c98a6c7a342cd902c5}}, {{formula:976cfe60-456b-4b17-9228-0d00c37a622d}} cannot have another centralizer of index {{formula:16cfa71e-7610-4fc2-a3ce-da42248c1175}} and consequently {{formula:02ca9bca-a4fb-4294-b764-3e78db6da16f}} . Thus {{formula:e147afe7-2775-4004-a79a-4f0116b7c210}} has an abelian normal subgroup of prime index.
Conversely, if {{formula:d48ef442-ac04-46db-954b-13dae2b56bf6}} has an abelian normal subgroup of prime index, then by Proposition REF , {{formula:1c780efe-ef79-4f07-9475-48cce3523490}} is a CG-group.
As an application of Proposition REF , we also have the following result:
Proposition 3.26
Let {{formula:242429f1-b9b8-470b-9f63-073bdfebe50f}} be a finite non-abelian solvable group. If {{formula:edb4ab05-c0fc-493b-ad35-fabb62a82952}} for all non-abelian {{formula:a5baff5e-f82e-4780-8033-98a44fda856a}} , then {{formula:82361ecd-556f-48ae-b1b9-f22511ee7e95}} is a CG-group.
If {{formula:5600c4e7-fdf4-4193-8ef9-091f96ae6a35}} is a nilpotent group, then in view of {{cite:80a065c0bd3864a9dadd67efd0040cb3a0800688}}, {{formula:998c2df1-04fb-4590-8607-4ad2e60ffacf}} is a minimal non-abelian {{formula:8aea8560-7163-4932-8efb-ea2d731f74eb}} -group for some prime {{formula:ac3c645a-2c2a-43f4-9af6-0e00d046056c}} and therefore by Proposition REF , {{formula:1d1a6972-3a62-484a-8b6d-5389b67b41f2}} is a CG-group.
Next, suppose {{formula:104196f0-f477-487b-93f2-72ed801961e2}} is non-nilpotent. Then by {{cite:80a065c0bd3864a9dadd67efd0040cb3a0800688}}, we have {{formula:86d86cd8-24ec-40a8-b0c0-779826b7062c}} is a Frobenius group with complement of prime order {{formula:4cf1ee3a-a936-49ae-8837-754a7419e1e8}} . Moreover, by {{cite:80a065c0bd3864a9dadd67efd0040cb3a0800688}}, we have {{formula:bf7340b0-860a-4901-8a8d-972381bd055d}} is abelian. Therefore by Corollary REF , {{formula:2f15be1d-cae2-4899-bd98-11b1aca43090}} is a CG-group.
It may be mentioned here that all the examples of CG-groups given in the earlier section are CA-groups. However, there exists CG-groups which are not CA-groups. For example, it can be verify that {{formula:89ab8d4b-a1fb-49fc-a684-2ba4df2b8d1f}} is a CG-group but not a CA-group. In this connection, we give the following result on CG-groups whose central quotient is {{formula:53dfc556-8275-486f-b1b5-95c7c948e923}} .
Proposition 3.27
Let {{formula:f36a9545-5208-4629-9996-775af921d14d}} be a finite group such that {{formula:7ac128cb-5b1c-4c3a-ac71-7f615e0a5b24}} . Then {{formula:b3174208-b88a-4498-baf4-eb43892c8b86}} is a CG-group if and only if {{formula:2da342ed-0b54-43fe-bbbc-ef8ff621c481}} .
If {{formula:5f0a3d9e-33ac-40d2-9fda-7f17a57c5d12}} , then we have {{formula:f7245f5a-156b-4466-b628-026783c18064}} noting that {{formula:e8a71fb1-3d2e-478b-a3c5-62e8f7b37ce0}} . Therefore by {{cite:1fdf5b6faff220d1a58e763bc0dbd346f1ab2941}}, {{formula:2c869720-39b5-467c-afdd-935a7866779f}} .
Conversely, suppose {{formula:212c32f0-8d0c-49c8-886d-3caf2b91ea45}} . In view of {{cite:f44a022fd8bb762f69f395b8e90d573cb7428de3}}, we have {{formula:f9333fe0-022f-43bc-995e-789bbd3c2e1b}} and consequently, {{formula:7a1a2052-0845-48a9-99b9-b1e9caa10278}} , forcing {{formula:5268e0a2-1cca-4667-a06b-4d03625ccf3a}} . Therefore we have {{formula:899f7f3e-a533-49c9-8c21-8c6c378c2d39}} .
Remark 3.28
Recall that a minimal non-nilpotent group is a non-nilpotent group all of whose proper subgroups are nilpotent. If {{formula:e026b551-1620-4995-b4e5-332ab7c37be8}} is a finite minimal non-nilpotent group then {{formula:3b074c47-93db-4481-890b-69a1f9711d5e}} is a solvable group of order {{formula:43e5a096-173e-45e7-b10a-21b393f715ce}} ({{formula:8ba71d4a-403c-4602-9b85-6a18c200270a}} are distinct primes) with a unique Sylow {{formula:dba97779-8e2f-479f-8172-97ef9a5ffe49}} -subgroup {{formula:0c14cf0c-7772-4348-bbd8-94731eeaf34e}} and a cyclic Sylow {{formula:b22e634e-100e-4970-b134-30df04ebfcab}} -subgroup {{formula:a6de6502-6bbf-4ac6-9367-4abd989ac45c}} . Moreover, we have {{formula:83d4b1b3-eb23-4080-895f-7abeda3f1fc1}} (see {{cite:62d8f72361971e58aaff8e3b6ca757b11072a7db}}).
Proposition 3.29
Let {{formula:a0aaab50-bcad-4284-ad7b-f0952ff264f2}} be a finite minimal non-nilpotent group.
(a)
If {{formula:209fa39c-39ef-4a64-99c7-1675cef9a38e}} is abelian, then {{formula:204f8af4-7eb3-4b19-876b-f56be0c420f7}} is a CG-group.
(b)
{{formula:2a5bc080-ca27-4954-a249-1c5d3e01e2ab}} is a CG-group.
.
a) By Remark REF , we have {{formula:c9b59e1a-7b65-4086-9628-306ef9e536ed}} . Again, by {{cite:707f45fa9021bbebc6625571e39c9660b2d82ce5}}, we have {{formula:cfbb1244-fd7c-4445-88d9-0f62f15db841}} is a Frobenius group with cyclic complement. Now, if {{formula:4249b067-442a-4231-b394-f187063cef2f}} is abelian, then {{formula:29d1fdda-4782-471e-a6dc-ab09c43c32f8}} will be abelian and hence {{formula:6f03aea4-0e87-41f2-8773-c697f0ced040}} is a CG-group by Proposition REF .
b) Let {{formula:2a2ab664-8302-4b8e-ad3d-8611d34fa38e}} be a minimal non-nilpotent group. By {{cite:707f45fa9021bbebc6625571e39c9660b2d82ce5}}, {{formula:b67ffa02-7246-41fb-bb97-27c358d30727}} is a Frobenius group with elementary abelian kernel {{formula:09b6b31d-c14e-4a44-9107-5dfcf731c6d0}} and complement of prime order. Again, by {{cite:8e0eec9fef377b19f1608f0166a8e7ad23d66882}}, {{formula:756fd9da-0f8a-4e7a-9766-7a4629514fce}} . Therefore from the definition of Frobenius group, {{formula:f434c993-00a2-46cf-abf6-20d01f912172}} is a CG-group.
Proposition 3.30
Let {{formula:cf898f0f-81a4-466a-80b8-e959bc19c28f}} be a finite group such that {{formula:6213b0d6-4028-4fc6-a670-dfdfcb729cf8}} is minimal non-nilpotent. If {{formula:67e719e2-61c5-4b4b-9249-a04a68446a6c}} is abelian, then {{formula:0cd44f44-11b2-43ef-b526-cfbfedddf0a4}} is a CG-group.
In view of Remark REF , we have {{formula:76afaea6-9946-4c18-87e7-a9a6cff0915b}} , where {{formula:a9c03c2b-adfc-478e-be5e-93cc559d8a76}} is a subgroup of {{formula:29101218-2c0f-440e-a1be-c6751b4b2ce6}} such that {{formula:3030e7e3-e61c-447b-af50-3795c72784b3}} is cyclic. Now, if {{formula:9cf4847b-a930-4c2c-84f4-a9c32093671e}} is abelian, then {{formula:df8acc0e-5913-4fb3-9be6-873f02cf71b6}} will be abelian and consequently, by third isomprphic theorem, we have {{formula:4a833d28-f85a-4ecf-b6ef-84f812705d0c}} . Therefore in view of Proposition REF , we have {{formula:77693525-3c1a-4af5-bd4f-edf98f035154}} and hence {{formula:63c853de-ec32-461b-8bcf-68dc01883b4c}} . Therefore using {{cite:1fdf5b6faff220d1a58e763bc0dbd346f1ab2941}} and Proposition REF , we have
{{formula:0c8026cb-a833-4b69-a2d0-0abd24b072a9}} .
Proposition 3.31
Let {{formula:7aac2ca0-71da-4173-8a1e-9ce8d79bc075}} be a finite group such that {{formula:4624c70c-67bc-4ac6-8e75-8e07890076f4}} is minimal non-abelian which is not a {{formula:18fe57db-ade5-4401-826a-ebeceba19f23}} -group, {{formula:6b7f5ba2-1bb8-4908-a761-2a01105ce73d}} being prime. If {{formula:2726995b-d104-46cb-9cc8-e6d1a87764df}} is abelian, then {{formula:7221fa3d-bb20-40a3-8ed6-1aa313a4d3f4}} is a CG-group.
In the present scenario, in view of {{cite:f44a022fd8bb762f69f395b8e90d573cb7428de3}}, {{formula:81d6d9cc-2ebe-4cc3-be11-75636883ce45}} is a Frobenius group with cyclic complement. Now, the result follows using Corollary REF .
Finally, we conclude the paper with a counterexample to the following conjecture {{cite:4ca88ad1aafbf8f458c6f6f38f423e610e3b8ed7}} which is also a counterexample to {{cite:4ca88ad1aafbf8f458c6f6f38f423e610e3b8ed7}} :
Conjecture 3.32
Let {{formula:104df858-2e8b-48de-90bb-e3e664bb85a0}} and {{formula:416f333d-3344-4f14-a56b-e2a1edfac331}} be finite groups. Is it true that if {{formula:b0f46c57-0e03-4ef1-9b43-f3e00b8e4e47}}
and {{formula:19766e72-40c4-4cd8-9234-eec04bb987c3}} , then {{formula:1cbba90a-c833-4c6b-9b1b-3c8bc456af08}} is isoclinic to {{formula:1b00b918-3c0e-48d5-bca9-352ef61c1ac4}} ?
Consider any non-abelian group {{formula:18b2f11c-e577-4855-b60d-ea6b2080dfbd}} of order 27 and {{formula:5c725b0e-ad5e-47a9-ad98-f452c4fef225}} . In view of {{cite:56f04fbca1f7a86cc6871bea5e6fa8ddfdd6dca8}}, we have {{formula:1c73b8b9-f1d8-4205-b58b-5c9296d759f8}} and {{formula:c2c60a5d-cc8e-4a39-a843-21e5fd6171dd}} . But {{formula:0acb5540-3e82-426c-97af-71473550be47}} is not isoclinic to {{formula:cbe075dc-1f4e-4ed4-ba60-017501b1e634}} .
| r | 383e401b73825b56378a900131b01c97 |
In this work, we demonstrate a striking result: model scale and chain-of-thought (CoT) prompting are alone enough to achieve SOTA accuracy across a variety of arithmetic and commonsense reasoning tasks. Most previous work combines domain-specific architectures, task-specific finetuning, and task-specific verifiers to achieve strong results on reasoning tasks. In this work, the tasks are simply represented via few-shot prompting. Like {{cite:943fb00004afb8a180689c2e546cbecf104f107a}}, for arithmetic reasoning datasets, we augment model predictions using a post-hoc external calculator, though we find that using such a calculator did not improve performance by more than 5% on any dataset.
| r | c1cede31430d3cb1f295560df90afcd2 |
The massive scalability of our approach comes at the price of not being able to recover a transport plan or transport maps. This is because averaging maps/plans of high-dimensional measures projected on {{formula:37c7e3d1-cd54-42d5-9ba9-03b77dfa81ca}} is not meaningful, and is a common limitation of sliced OT {{cite:adae9c3e601d38d7b85394c4f8dc16f0224fbcd3}}, {{cite:2114dbbffa4dc8791cb416228d06f4bf53ef3d64}}, {{cite:80031c22bef663a825e3f9977080eaf4bb172066}}. Still, the amount of applications of evaluating scalably a multi-marginal distance is extensive as demonstrated in the experiments section.
| d | 968b65d6457a0c1acb214c39fc8b4761 |
Dataset.
We used samples from the Autism Brain Imaging Data Exchange (ABIDE) Preprocessed dataset {{cite:d3de3f42011ff3d8ae6e30c6443fe868efa07078}} for our experiments. It contains data from 16 imaging sites, preprocessed by five different teams using four pipelines: the Connectome Computation System (CCS), the Configurable Pipeline for the Analysis of Connectomes (CPAC), the Data Processing Assistant for rs-fMRI (DPARSF) and the NeuroImaging Analysis Kit. The preprocessed data sets are available onlinehttp://preprocessed-connectomes-project.org/abide/. To account for possible biases due to differences in sites, we used randomly sampled subsets of the available data for both cohorts; the same sets were also used by {{cite:a8cd8585264d9b0fff1bbf3f59fd4016ee4e0a71}}. The NT cohort consisted of 226 subjects (with mean age = (15 {{formula:a45e6e45-1ab1-4d25-ba66-3bbfd235c58a}} 3.6)), while the ASD cohort was made up of 202 subjects (with mean age = (15.4 {{formula:e0bf626d-5174-4652-988a-13303ce18e41}} 3.8)). FIQ and VIQ scores in the NT cohort have means 111.573 {{formula:91c4719e-3445-4bdc-b895-8865dd65fe77}} 12.056 and 112.787 {{formula:cc0ff088-2822-493a-b636-5238ed63dd69}} 12.018, whereas FIQ and VIQ scores in the ASD cohort have means 106.102 {{formula:cdd5f27d-4aea-4baf-8f84-0a8f92f62f2a}} 15.045 and 103.005 {{formula:315048db-ad63-48f9-97a0-58a22d925f11}} 16.874, respectively. The brain connectomes were obtained from resting-state functional magnetic resonance imaging using the parcellation from {{cite:5e29c2e52fb3384378517648d1680aab89793bf9}} with 116 ROIs. The functional connectomes are represented by 116-by-116 matrices, whose entry in row {{formula:dd6a5faf-e16f-4f5f-9c07-786fd3498ebb}} and column {{formula:5e54e972-9a07-474d-a006-efb50d2d5ebb}} is the Pearson correlation between the average rs-fMRI signal measured in ROI {{formula:a3870d81-092e-447b-9751-25f9796ae93a}} and ROI {{formula:19e6e8ed-115b-4c28-9b70-5a59d70cdc06}} .
| r | d95e81b7cfff7071dcd76b9a98428d51 |
To further valid the performance of our proposed prior, we compare the tilted prior to a variety of recent methods that achieve top performance in OOD detection for VAE's. The methods we compare against are Likelihood Regret (Regret) {{cite:62ebd7d6058a4750fb0772e76df8b6ab254a9bee}}, Likelihood Ratios (Ratio) {{cite:c5c91f156cf5a22e702e033e17c2ab698d09e55a}}, Input Complexity (IC (png)), (IC (jp2)) {{cite:e1c5d3f6044335fd95f03854b1d9a171e9aa495e}} and a VAE with a standard Gaussian prior (LL). The results from this analysis are summarized on Table 1.
| m | c1fcfc4e4d412ce4f7e7ed4aa5c956b8 |
Recently, some works have considered the sensing model to proposed a mixed approach which considers the hand crafted as well as the data-driven CS reconstruction. In particular, these methods use a deep network or denoiser to replace the hand-crafted prior, then, this non-linear prior is employed in the optimization algorithm {{cite:cc80578cba0f46920ee665ee0e93369c2a945e7d}}. For instance, Plug-and-play priors (PnP) use pre-existing denoisers as a proximal step {{cite:4fc4bde3e3f25ded8832a9482b70d1f13c52dc81}}, {{cite:6e32b7b44449ce94f9c14a9538811054b6318357}}, {{cite:745302c24c8c3509c2ac3ff58c5db72184bd49c4}} learns the proximal mapping using a convolutional network, and {{cite:522e11205ab18497b6cc6429c1bdbe83247dd962}} learns a SI prior, through a convolutional autoencoder, which is then incorporated into the optimization problem. More recently, D-AMP {{cite:ce2edbfefccc52c59d8ab833266f5c8f9150e208}}, ISTA-Net {{cite:4e7fa72a0a630b207aede85351857b9de9c57dfb}}, ADMM-Net {{cite:785dc08c2c7573c9a731740c59a2f9d6af13718b}}, and DNU {{cite:1a663ee84ffd2c9b1886a20644c7d0f4834f2828}} use the unrolled based method that incorporates the optimization steps into the deep network architecture using residual networks; consequently, they can learn the prior and the parameters via end-to-end training. This strategy is also employed for CSI in {{cite:79a73a5d1608a58026a4052148054974b5817b27}}, {{cite:1c99731382288bd7e643b2eb1245d3e34a80bdbd}}. Although these methods have proven to be more general, they still depend on training data, which is limited in SI.
| m | e1ae4b8a948455fd1477fb9ab69245da |
where {{formula:1e56ab4e-695c-4dd3-9553-b061ed88d03f}} refers to the entropy in the supremum norm, see, e.g, Lemma 2.1 of {{cite:a6e58cd1726641a71c4ef5cd14ac0c43b6bba093}}. Now, by the triangle inequality,
{{formula:b5cd65b0-7839-4440-80a8-83cc5d0efe40}}
| r | 34ee0440a08fdb6688307a1e2d1b88f0 |
Arguing optimality of an algorithm is a two step process: {{formula:f5912e3e-2406-48dc-926d-bb37221a16a8}} estimate the performance of the specific algorithm and {{formula:99d38477-6f42-4c74-9378-c2f9be84a470}} derive a matching lower-bound that is valid among all possible estimation procedures. Beginning with the former, we build on the seminal work of Polyak and Juditsky {{cite:f94fd66dc14c94d8cee756f15569d2c6345ec3d5}}. Letting {{formula:088e213c-1117-4eb4-85a2-966b01abb9d3}} denote the average iterate, we show that the deviation {{formula:fdaf3b82-cb28-43e1-bb05-94f02b288fd1}} is asymptotically normal with an appealingly simple covariance. See Figure REF for an illustration.The code can be found at https://github.com/mateodd25/Asymptotic-normality-in-performative-prediction.
| r | 6cfeb8503fccb7d0c8f011835fe65c40 |
The observability of the truncated problem is the novel ingredient here for which we trigger some microlocal analysis tools such as microlocal defect measures. Indeed, Hörmander {{cite:62d30e2142069d609008c003c860dcfd4b9fc5a7}} and Duistermaat and Hörmander {{cite:0e6583990ee40618d21e26ac981f69bb5deb9c50}} described the propagation of singularities to a partial differential equation {{formula:1fbefe5b-64d9-4d7c-95fc-d016dcead924}} in {{formula:855f3d3c-12cb-4823-90f9-deee32dfb826}} in a domain without boundary. In particular, they defined the wave front set {{formula:bfcea2f0-55c7-47eb-9c31-cd0e695d1918}} of a distribution {{formula:8773ded4-7ada-47f7-9277-10d9a2c7e2aa}} , the subset of the cotangent bundle in which singularities may move, and showed that the wave front set is invariant under the Hamiltonian flow {{formula:f2a8e238-af7d-4932-a088-e886ef7d3f20}} of the principal symbol {{formula:be2c082c-90ba-4450-8a66-776f340de6d3}} of {{formula:752b2d23-27a8-4105-ba54-1516a667c9ea}} . Later, Hörmander {{cite:cc559149cc282dcd8980cf85e9056c6eb9891aab}} incorporated his own work and that of others into his magnum opus The Analysis of Linear Partial Differential Operators. Chapter 24 in Volume III of that work remains a standard reference on the subject. It is well-known that if {{formula:ee618527-b881-48bb-8d12-5b155e20af30}} is a proper, classical pseudo-differential operator and {{formula:e8024607-0687-4d2c-b700-210ac73a83d7}} is such that {{formula:5420d265-b0ef-4c65-ac13-09efb255f9d5}} , then {{formula:c27ceeb5-8542-44c2-8ce8-0027aafcb75d}} is a union of integral curves of the Hamiltonian of {{formula:8a6f6d68-8228-461d-aeca-7ab8430c957b}} . Inspired by the works mentioned above, {{cite:e66535dfe2f1b5fb0437b54689e395671c980054}}, {{cite:7ccbf15e0c054ad8fda70617f00da594e9eb014b}}, and {{cite:a6e2e0ebf66d28bb5ff3f587347f7d3ece040108}} proved an analogous result related to a microlocal defect measure {{formula:9e728cf3-4848-4647-880d-c903d413f168}} (a Radon measure) associated with a bounded sequence in {{formula:2e749b69-d6c0-425a-a8cf-8d32d210d5d5}} which weakly converges to zero. Roughly speaking, the {{formula:c4db11e9-64f4-4c0c-bdc3-e1e7d39aee7d}} is also invariant under the Hamiltonian flow {{formula:5db1463b-3bdd-4fc7-a8fb-a2ae3e0a3a41}} of the principal symbol {{formula:24cbcf8f-77e2-4924-b536-ef551c9792fa}} of a differential operator {{formula:6914c24e-d008-466d-b793-d9caddc5fc78}} which satisfies certain properties. The main result reads as follows: Let {{formula:a1f4c436-8b84-4114-b0b7-184a9b042397}} be a self-adjoint differential operator of order {{formula:2974ba47-0ff2-4277-9891-7265f7556487}} on an open set {{formula:e157c4dc-9f88-4a81-8eff-e7a94ebddc92}} and {{formula:b43e5bd9-f047-47a1-83b6-c46aad809053}} be a bounded sequence in {{formula:2db8f1b8-247f-494d-bbf2-58644ad61e3d}} weakly converging to 0 with a microlocal defect measure {{formula:aedc90d7-5170-4d92-80cb-a16ffe265c4e}} . Suppose that {{formula:a2a5e6bf-ce61-48f8-acd0-0b34544a65be}} converges to 0 in {{formula:86ff0f17-de63-465b-bd49-3d96047927c1}} . Then the support of {{formula:d38a56d9-e553-42f4-a033-f6d649afa8ce}} , {{formula:bed60cd5-78dc-47a7-aa27-cab5606c6284}} , is a union of curves like {{formula:1f9a0bc0-8ff0-4816-a0ac-d6b99416d5d4}} , where {{formula:516e4a96-d17a-4c13-b64b-3f46cf6172e4}} is a null-bicharacteristic of {{formula:db0696c4-06f4-47af-b685-96f28c413f1f}} where {{formula:654790e7-52f7-4f7d-94e1-642731966446}} is the principal symbol of {{formula:806aa2e0-2ab9-4b4b-9495-65cae3dc2ae7}} (see Theorem REF below). This result is crucial to establish the control and stabilization of waves, which we will discuss later. The idea for proving the above result is found in the unpublished lecture notes of Burq and Gérard {{cite:7ccbf15e0c054ad8fda70617f00da594e9eb014b}}. To make this article self-contained, we supplement details to the proof of this remarkable result and give other related preliminaries in the appendix.
| i | 0ffe0ac289e2f79cbcaad966a7e93ecb |
with {{formula:79dcfa96-e6bc-4f45-bc64-d000fb03284c}} . An algebraic measure tree {{formula:17f6e749-3f42-49b3-a984-ff4a2c82b13f}} consists of a separable algebraic tree {{formula:004e3013-96d0-4fc6-855e-0481265ac5e2}} together with a probability measure {{formula:987f7e90-b66b-4e98-8398-6d513c24d17f}} on the Borel {{formula:ac7f5212-0ec7-487c-b4d9-9545cac3d6a9}} -algebra {{formula:921bc424-7963-4eff-9b28-4accbc5d3015}} . Associating each algebraic measure tree to the metric measure space where the intrinsic metric is defined with the help of the distribution of branch points (see Definition REF ), we can use the Gromov-weak topology (see {{cite:e75b142c92221736b14b24a07b5b3e675e29670d}}, {{cite:435681a0662e27d5d0ac745d11524c6f43b3025a}}, {{cite:eff8295116fa8b044e09871d1d59da8a009c83f4}}) to define a metrizable topology on the set {{formula:7cc00912-23a9-4b3d-ae9c-26696c83dfdf}} 2{{formula:f14809b3-4fdd-468b-8e1c-60058d9e10d4}} 2{{formula:c639eae7-aa00-4d4f-b848-c4f3a4001ae1}} 2{{formula:cf8c52f1-fd82-4343-b816-2b014d4852f8}} This state space 2 has served to construct and study in {{cite:4a4673794d8070bba52cbc212756589f3c1148ac}} the Aldous diffusion ({{cite:435fa91a8bb046c45f07fb68a3079a8c9bf517ca}}), and more generally in {{cite:2226036a232e23fdc4eed1ff7f99e795341cceae}} the {{formula:02ec22f2-eadc-4d9d-a088-b646115cd6a9}} -Ford diffusion (see {{cite:50b8472e500def0abd21a6d4a74ec1c792c6261d}}), which are Markov processes on binary trees without edge lengths. The compactness of 2 allows to get around tightness issues in these construction. Also, the sample shape convergence gives rise to a family of convergence determining classes of functions which are very useful when one wants to study tree-valued stochastic processes.
| i | 64ef91d6fc7b834d9d1d5b0f0c4fadf0 |
In Refs. {{cite:2eebdc6223d8c30b9ef582199f640eb4ab46591b}}, {{cite:4a7b81e64d9c3e6b7b66ab02eb7908125f72f2a8}}, the authors study the analogous heavy meson systems.
In Ref. {{cite:2eebdc6223d8c30b9ef582199f640eb4ab46591b}}, Liu, Luo and Zhu study the S-wave {{formula:5966f158-caa7-43fb-973e-7c1564fcfec3}} system
through the heavy meson chiral perturbation theory,
considering the {{formula:32c81f9d-73fb-4abc-a4d0-7b9c437aad23}} meson exchange between {{formula:ad931039-a688-42fb-8efe-2a22f62926c4}} and {{formula:1cb95630-3ddc-4268-b673-cf3bebbdf2fd}} , which generates a potential to bind them,
and observe that there exists the {{formula:7c143504-f431-4539-9dc1-f023d62ad2ea}} molecular state.
In Ref. {{cite:4a7b81e64d9c3e6b7b66ab02eb7908125f72f2a8}}, similarly, using the heavy meson chiral perturbation theory,
Sanchez et al study the S-wave {{formula:48a8f79b-9ee7-41c7-8d87-c21ceb1547a3}} and {{formula:6404b0d9-8582-4171-8896-b3bc4c190471}} systems
exchanging a kaon to bind {{formula:7f045373-eb13-4284-8306-a601826ffc02}} ({{formula:0c74f462-4f3c-4e47-be59-b3ae9c4f2578}} ) and {{formula:9bca8e17-0e67-405a-9dc6-00034863878f}} ({{formula:87479418-f5f6-4212-9745-6f0eef7e4d0f}} ),
and predict the existence of {{formula:b63ee466-99ac-4ae2-990d-94a5e9eca6d9}} and {{formula:41826e67-3daf-4e68-8a68-e13f76d53365}} bound states.
Differently, in this article,
we construct the color singlet-singlet molecule-type interpolating currents {{formula:3b4ed0be-d6db-4371-a3e7-885253b38dea}}
in Eqs. (REF )–(REF )
to study the {{formula:93176e30-21ed-4aec-aa2d-a97f5124bb7e}} and {{formula:2bb530d4-b040-4e46-9baf-6f2c2ed25125}} systems with QCD sum rules,
and give the prediction that
the {{formula:c5079d03-b322-420a-89ab-a1d46a67ed63}} and {{formula:a72f50ac-9d67-4475-85fe-df00c2c25119}}
are difficult to form bound state molecular states.
| r | 19bd53e2284dedf02b4ae2d3e1690fc7 |
being unnormalised kernels. By convention, {{formula:bdadc592-876b-48de-897c-a4abe96de950}} .
Note that each {{formula:51efc1c5-aeb7-47e2-9063-a0651c83f60f}} is a probability measure, while {{formula:ea84ec76-cee4-4c41-b316-53497a609b2a}} is not normalised.
For every {{formula:1a7fd2fb-b18f-45a7-8835-17b07c126ee9}} we also define the marginal distribution
{{formula:5327ebbd-a953-4a0e-87e0-96f1c03e92f8}} .
In the context of nonlinear filtering in general state-space hidden Markov models, {{formula:b67a8737-f112-4f73-b45f-7e8e1d89354f}} is the joint-smoothing distribution and {{formula:b02e8768-7d61-4ce4-ac0f-b4e9571c8caf}} is the filter distribution; see {{cite:7580909fd888e4d68067b378b0d50bdf8ffcff60}}, {{cite:c337fec33f1faab0522e105550cbd443a9bf40e5}}, {{cite:b747e8a5c358a6864a3722597a830b852ed4daf7}}.
| i | 2b25b57b163a576a7fc8506fa7ea14e9 |
Generally speaking, the analysis of black hole X-ray observations requires fitting the data with some theoretical model in order to measure the properties of the system. Some of these theoretical models rely on assumptions that may be violated in the presence of new physics. In General Relativity, we have {{cite:ca74421cfb1d355a86f019f5b82d017730800ac1}}:
| i | 9aadc8d0dd368f12459d6ec04aa187b0 |
RSC has two other main advantages in comparison with other classifiers. Firstly, by using prototypical vectors the model is intuitively understandable (see for example REF E). This is a desirable feature to protect against overfitting or flaws in uninterpretable "black box" models like DNNs {{cite:4f42619e55449c96c1df7bbfc00b4f0a8e2e6a14}}. Secondly, by using ranks of features we utilise many of the advantages of nonparametric statistics {{cite:6c9470b772908c5772e9c1a614552802a7821eef}}, namely that we do not need to make an assumption about the distribution of the underlying data, and that the filters are scale invariant. This means that data preprocessing, which is used extensively in machine learning, will often not be necessary for RSF thereby increasing its efficiency and ease-of-use.
| d | ff8d4a18386567b13b651d5e54665da7 |
The precision-recall curves of all methods are reported in
Fig. REF -a. As shown, our method significantly outperforms the
state-of-the-art both on the FBMS dataset {{cite:a5c8db5e2c4752cbfcb4c292835bf0652ecc791d}}, and the DAVIS dataset {{cite:d5203c1e90cbbe45f0fd1266eb5e307a87bef355}}. Our saliency
method achieves the best precision rates, which demonstrates our saliency
maps are more precise and responsive to the actual salient information.
The F-scores are depicted in Fig. REF -b, in which our model achieves better scores than other methods.
Similar conclusions can be drawn from the MAE. In
Fig. REF -c, our method achieves the lowest MAE
among all compared methods.
| r | 6c9a05136776cefcd4378b5cc56d8574 |
Other research has pointed out that neural networks also demonstrate an over-reliance on superficial regularities {{cite:c7380f1af31e529ed53f0f4b9f996a33d26a8b3f}} and textual cues {{cite:188f2c0958521edfa296543488b4da8322184641}}.
We observe that the color-shifting procedure proposed in {{cite:44086298b996dc866b4999cb5ffaf2e36aabd702}} also causes structural distortion when the saturation channel is clipped (Figure REF ).
This is because when saturation is changed unevenly, minor features might gain salience relative to others while salient features might become unrecognizable. Therefore, the drop of performance observed in {{cite:44086298b996dc866b4999cb5ffaf2e36aabd702}} should be interpreted as the reaction of neural networks to color and structural noise.
In this paper, we have eliminated such structural distortion to focus on color.
However, it is possible that robust edge detection also plays a role in increasing structural robustness and shape bias in neural networks.
| d | d123664a86faed405b0d6ba3fdc01b80 |
The aim of the work presented in this paper is to design sparse, low-complexity neural networks by reducing the number of parameters while keeping performance degradation negligible. Memory and computational requirements in particular complicate the deployment of deep neural networks on low-power embedded platforms as they have limited computing and power budget. The energy efficiency challenge of large models motivates model compression. Several algorithm-level techniques have been proposed to compress models and accelerate DNNs, such as quantization to 16-bit {{cite:8f50e1f2e9ba6d6ce01483ce15c50c575e66d7da}}, group L1 or L2 regularization {{cite:bb0b2bc88ac6b54fddfeffa33df62f206f2e0d67}}, node pruning {{cite:46d0d0941d66644bdbe7990a2342742c36a28786}}, {{cite:8e2f5b7ed64eefeffdb1b980c3af919c11d68da7}}, {{cite:2c7e69e523019bc81dc72d78406da4c2f85f3964}}, filter pruning for CNNs ({{cite:5f0b2f4afbfdc4f75aff3d147fd402e730eb0ae0}}, {{cite:2c7e69e523019bc81dc72d78406da4c2f85f3964}}, {{cite:69fad2b7556b92440efd5b186a557a8490965cc4}}, {{cite:8d7f41453061f144be1885b0765f69709e41b4dd}}, weight pruning using magnitude-based methods {{cite:c9e088488e4fa92d0763ef93ea9bc9cf22c1850f}}, weight quantization {{cite:4a02585188ffe035fc0d9a7fa6820eeb4afe0dc4}}, {{cite:d0ad9cc357e66aa587ad0cb22af7c214b9ed4bb0}}, connection pruning {{cite:c9e088488e4fa92d0763ef93ea9bc9cf22c1850f}}, and low-rank approximation {{cite:088603800a4b67accf0420065d1b218486c4e1fd}}.
| i | 56fef51fc7af0ac4613fde2c7640ebad |
Before concluding, we would like to point out how our model can be significant to quantum many-body systems.
Our intention is to indicate how broadly applicable the concept of quantum dissipative adaptation may become.
Firstly, we notice that the {{formula:a14c9181-8563-4ab3-aa1c-1a8b0d8586f1}} structure of energy levels can arise from the quantization of collective degrees of freedom describing many interacting atoms and electrons, as happens in the so-called artificial atoms (e.g., electron-hole pairs in semiconductor quantum dots {{cite:37436e3dbc2c7ff37ce7b810eac0fa57d231f06f}} and the quantized magnetic flux in superconducting rings {{cite:7830f5038d800f1166f7859f88cf78c0759efb18}}).
Lodahl et al. {{cite:37436e3dbc2c7ff37ce7b810eac0fa57d231f06f}} and Gu et al. {{cite:7830f5038d800f1166f7859f88cf78c0759efb18}} also discuss how these artificial atoms can be driven by single-photon pulses propagating in one-dimensional waveguides, building the closest possible scenario to that in our model.
| d | c4e446278c3f59fbc732baac3b758cd1 |
The value obtained for the mass-to-light ratio of the lens in
Section of {{formula:b39d7b6f-e093-40a5-814f-6238a1cc1784}} assumes a redshift of
{{formula:5ee7452a-892e-421a-b71c-cf12ac357cba}} based on non-detection of the lens in the {{formula:19823b9a-d579-4ac0-8a9e-e92372b53f65}} -band. As this
redshift is essentially a lower limit, we investigated the effect of
increasing it to {{formula:d64a4f3c-16d4-4b0e-9e25-e6d1690bfc12}} and derived {{formula:229d8e2d-b8de-46e8-9d68-a6273d4c0c55}} for
the lensing galaxy. This small change in {{formula:69158c1e-afaa-4c38-b5f6-91ce4a3c1978}} is due to
the fact that an increase in redshift results in larger values for both
luminosity and mass which tend to cancel out in the mass-to-light ratio.
Our value of {{formula:56ffa00c-dcf6-49ab-bcf3-5ab7497d484b}} lies quite close to the relation
between mass and mass-to-light found by {{cite:6e7c662f9cb29f6235e14f3666e0b5b029620727}}, and thus adds to a
consistent picture of the double quasar as a gravitational lens.
| d | 7b8f8b4febd9ed97c6072b8cfc0a4f77 |
Speech signals are corrupted considering SNRs values ranging from {{formula:9bfca399-6c8c-4aed-a806-3a4fcb995683}} dB up to {{formula:bf169000-79b3-45c3-a8bb-3205f7300268}} dB, where the SNRs are measured between the reverberant speech signal and the background noise.
For each reverberant signal, SNRs are selected in order to obtain STOI {{cite:e8a69434ae1ee2eacf4051fb96779a10be1bbd63}} objective intelligibility scores of {{{formula:7bf8209a-9af4-4f24-a6d0-6ecb6eedc45f}} , {{formula:1b2df6ce-7e57-40c6-9ddb-0ff517b502b2}} , {{formula:aec9aeea-fd9a-4129-98b2-9da91c6d83d7}} , {{formula:9767ba6f-2334-488c-8d68-b69d24480db7}} , {{formula:d76a8aaf-ef0c-4b6e-ab43-946d891630db}} and {{formula:ed16637b-e299-4e27-8277-748012e631a3}} }.
The limit values of {{formula:b68c8b58-f9fa-4ecb-b35d-b9a9c9281580}} and {{formula:a4956c89-424f-4bc5-819c-67fc61945b09}} are defined here as thresholds of poor and good intelligibility for the unprocessed (UNP) noisy-reverberant speech.
Results are organized considering the increasing value of {{formula:d8a2caa1-f0b7-429d-8b35-6abfd863a4ad}} , i.e., for each measure rooms LASP2 ({{formula:a675afe6-efbc-494c-a8a1-d7f7a34efad2}} s) and Stairway ({{formula:110435e0-57d3-4cb0-ae09-c2c607486697}} s) are presented consecutively with acoustic noises Babble and Cafeteria within each case.
| d | 072b120472e4b22b3430ebfcf45dc6a2 |
As widely known, due to the non-commutativity of the Hamiltonian with different times, the obtaining of desired evolution in two-level systems has still encountered great difficulties. Fortunately, there was already a few famous cases which has derived the exact solution with different restrictions, which may finding a way to make it solvable respected to some special forms of time-dependent Hamiltonian. The most famous solutions in the history may be Landau-Zener Transition
{{cite:da0ca5d09b41810d8d6f0a10e44fe4853e2ff02c}}, {{cite:f460c4dacbd066bc859fb752f900dc832cd79aa6}}, Rabi problems {{cite:fd90d59521c8fadd855ed82ddfe9d9c67aa012ef}} and hyperbolic secant pulse {{cite:972d543bb61579ad6d2e69f4bfd43b21c7ff8f33}}. Also in the past ten years, some different analytical schemes was proposed, like shortcuts scheme or single-shot shaped pulse {{cite:f0c3d87f4f2ca453f95b2938ccb6e4c36bfc7359}}, {{cite:8f03fb2093019bec150ee8a301dcf2cd8622da38}}, {{cite:2181efc5de477b11b0330af11d4d15c397db2d3b}}, {{cite:365b5da2d1814788e1411cdaa9ad0f2e546cb797}}, {{cite:931e8aac22534fad61321f709253cc92dcd9afb0}}, {{cite:700858c9159f66c7654876fa6735dc1707f49d75}}, {{cite:be3502cb467e91030116043cdc724008ce6bf434}} and others {{cite:aff51ba9885be882784c36bf964f94ccf4fdb01f}}, {{cite:e6772601f5d959e92d06fb878991a8f49e4dc801}}, {{cite:da4793496e8ba53d837deb8887a90f4436f5b366}}, {{cite:4b660850a57cea461877fd9bfc73bea453f87737}}, {{cite:1b8105502268c8becbf543d44f0c7af3d8b5288b}}, {{cite:ddeafae5626f01a7f9e60940fe2cd0f0a80993fb}}.
| i | 33706da34db3aea4d35ec42bca92268b |
The methods and results of this paper can be extended in different directions. We can apply the abstract framework presented in section to other examples of differential equations, for instance the Navier-Stokes equations of fluid dynamics. Although we showed that the curse of dimensionality is broken by DeepOnets for all the examples that we consider, it is unclear if our bounds on computational complexity of DeepOnets are sharp. We show almost sharpness for scalar conservation laws and given the sub-algebraic decay of DeepOnet size, we believe that the results for the pendulum and elliptic PDE are also optimal. However, there is certainly room for a sharp estimate for the Allen-Chan equation. Finally, one can readily extend DeepOnets, for instance by endowing them with a recurrent structure, to approximate the whole time-series for a time-parametrized operator, such as the solution operators of time-dependent PDEs. Extending the rigorous results of this paper to cover this recurrent case will also be considered in the future. Another possible avenue of future work is the extension of the approximation results in this paper to the case of multiple nonlinear operators (MNOs), already considered in {{cite:cc58ae97c28e7b9658a92387f4702fb10acbdd33}}, where the authors prove an universal approximation property, similar to {{cite:9b4dec58093331e11410f07c454cea484e34af42}} for these operators.
| d | 9231b43dca07d2e3f24909a8e3d0db22 |
The application and ubiquity of noble liquid detectors in the fields of high energy physics {{cite:84633d4ba4db830bd3f38f13beff3c18452fa4b9}}, {{cite:ac5fb2689fab0ee2e41d0dda02db3fb8bb17e087}}, {{cite:ec7a7fac39a58407935d9a928d1bccc13ab3fa9b}}, {{cite:3426d07f9994270fdc16c9fa915778fac9224f79}}, {{cite:0d3016e3df0fe3c2821df34925c3fa6cf5235f54}}, {{cite:50ad955050bb7ab2e8ae9e0659ce8008e699a872}}, {{cite:1580f8f106f682ad9058f4a91eee938e7f576aa8}}, {{cite:f4c17dad315e7251473fb5b953f75338e099adcd}}, medical imaging {{cite:26d5e223b5c9407b0f92938b5b7961fffcaaaaab}}, {{cite:f297487b7b2dfc649173387abf61018ee9ca28c9}}, {{cite:dd7a93912644316694565f5af599609b24ab4206}}, {{cite:6f852d8fdd94c67d29f70d8ce60c756ded1178f9}}, and rare event searches {{cite:652da94e97fe065f17d8f94545fb08eb13282d32}}, {{cite:fccbd0e19ae2681ad8abf15fe90f9db78fae4994}}, {{cite:0e8455c53a29c4f4da822d026539386e7ef4b0ed}}, {{cite:92a253098d078a9455c9fca4ac92814b6352c8c3}}, {{cite:aaef820da89e2ba5feb789c3bd2d4e193f99e6bb}}, {{cite:4f9b47e155ce6f0b520d465170e6966ac82a48e3}}, {{cite:61490841326488544e03b568d05cf96cb24a948d}} is due to the many attractive properties these media provide. Charged particles traversing noble liquids deposit energy in the form of scintillation light and the ionization charge. Depending on the application, an experiment may choose to apply an external electric field and collect ionization electrons. Given the anti-correlation between the collected ionization charge and the light yield, this comes with a loss in the overall detected scintillation light.
| i | c6831f49fce6695b1495c62556679f40 |
Recently, supervised deep hashing methods {{cite:e1e5b5e28b90ac86f622519f0a06ddd77fb7ce53}}, {{cite:eb2a858bc71ee622e2e4b641081104b29c1a669a}}, {{cite:5d69e4bd351fd94c67ebe7ceca09edf902c94c82}}, {{cite:f9277a66082d795a63e15a02b2d2efe6a082ad5c}}, {{cite:ddd21fd441a964be5f7704deb1624de3af4cbbd1}} show promising results for large-scale image retrieval systems. However, since binary hash codes cannot be directly applied to learn deep continuous representations, performance degradation is inevitable compared to the retrieval using real vectors. To address this problem, quantization-based deep image retrieval approaches have been proposed in {{cite:b7aaebbabe6e107095af7ecbb185d852b185c9ac}}, {{cite:319da7ff98b4fab07ca0285dcba5056961b55f13}}, {{cite:0f64456670d06cf28bf2ccf97d0fa81ad4f446e2}}, {{cite:59587f0386323f6b4e15a6284ef7781aa425563a}}, {{cite:5d696db7d4bee0293c565dde19e976b2e10e9757}}, {{cite:6da420cc07531d867434d844a899a23b05004447}}. By introducing differentiable quantization methods on continuous deep image feature vectors (deep descriptors), direct learning of deep representations is allowed in the real-valued space.
| i | 5464aaab344a9db0c74678aca8ae67e9 |
Datasets and Evaluation Metric. MS COCO 2017 {{cite:2237af9992594f5da9e693225e5426b3cd94a602}} is a challenging benchmark in object detection which contains 80 object classes. For experiments on the COCO dataset, we use train and validation set for training and test set for testing. The standard COCO protocols are used as an evaluation metric, i.e. {{formula:8b257399-93cb-401f-ac2e-869077629268}} , {{formula:1e090f0e-1263-4435-9c79-812a4168133a}} , {{formula:90ca384d-4a7d-4726-af0c-e7608f436cf2}} , {{formula:e02c8d72-a6ab-44bf-bb91-86735cee019e}} , {{formula:5096c99c-c9b0-4005-9bd8-6096881270be}} and {{formula:eab944b0-fb11-434c-8746-2d2cbdc2a523}} .
| d | 438b80036a9bf52b70aa0aef8b8dc000 |
Thus the aforementioned two classes of functions exhibit lower/subdifferential regularity, while the latter collection of extended-real-valued functions is much broader; see, e.g., {{cite:2b2c18bf7f06d7bea27446e33c9e5171248dd4cb}}, {{cite:01a2f8a5c2e789277b64d701f30be05929dd4966}}, {{cite:b647e02a3e5f8041d11b00cd6684806c55c05392}}.
| d | dc5da8d30f920bd1ca7017b901433a06 |
Contrastive Learning experiment: We next evaluate our HyperInvariance framework with a real-world contrastive learning experiment, taking SimCLR {{cite:5957acd12f0646ef757c1ea903d085cbb59ceb12}} as a representative state of the art learner to build upon. To define a set of invariances of interest, we borrow from {{cite:e773974253ddac701a3f40a507a1353bd316bce2}}
who extract two subsets of SimCLR augmentations denoted dorsal and ventral. {{cite:e773974253ddac701a3f40a507a1353bd316bce2}} showed that contrastive models trained to maximize similarity between images and their dorsal/ventral augmented counterparts learn representations invariant to corresponding transformations. Pre-train: We instantiate our framework with SimCLR (hereafter referred to as HyperSimCLR) and a ResNet18 architecture and train on STL-10 {{cite:31df110f3c236ac3e170e6eecce66afd4bf212fa}}. During training, we assign invariance hyper-parameters as {{formula:ba16f448-e1c4-4068-9ae6-9bde108e4918}} , {{formula:86b8c758-77ea-43a2-bfef-6e0b283aaad8}} and {{formula:2f778266-693b-4463-a440-43aa91aa8165}} for default, ventral and dorsal augmentations respectively. For every {{formula:099e53a7-7f3b-41a8-a0f2-7a21c414eb3b}} , the hypernetwork is trained to optimize the contrastive loss for an image and the counterpart with augmentation corresponding to {{formula:3193ab80-da90-4491-9dfb-0e4d84fc01b1}} . Downstream Given the learned frozen HyperSimCLR-ResNet18 feature, we train linear readout and hyperparameters for new tasks. For recognition we evaluate CIFAR10 classification, and for regression, we evaluate 300W facial interest point detection {{cite:b19d9ffee0ac5a4f576510d2fe6ee6919c455466}}.
| r | 84cc9882c636256900115531933d7209 |
It is relatively straightforward to interpret the scaling trends in terms of
the internal shock model in which the basic units of emission are assumed to
be pulses that are produced via the collision of relativistic shells emitted
by the central engine. In the case of the pulse-fitting method this is
essentially the default assumption. Indeed, {{cite:1ff062518da4fc5deb757441da089ed1dc8bd72b}} in their
study of the brightest BATSE bursts with {{formula:cb2cb28c-3e86-4c0c-8208-32cf46f12f84}} sec were the first to
demonstrate this explicitly by identifying and fitting distinct pulses and
showing a strong positive correlation between the number of pulses and the
duration of the burst. More recent studies, {{cite:e7fbb1eb986949dbdbe5790f4c29ddfe1f5f8a82}}, {{cite:9b45033f2ead856bce097e0ad49905487986e06b}}, {{cite:d546219d9dff1bbe3832e4ac8d70c124dcb20730}}
have provided further evidence for the pulse paradigm view of the prompt
emission in GRBs.
| r | 1888522046623aeebe2fe2450c821daa |
To incorporate the social preferences or personalities information into a multi-agent control framework,
some researchers draw ideas from sociology and psychology, for instance, the concept of Social Value Orientation (SVO) {{cite:05fa559743261d76f9ae2dd005fabe1c901e30c4}}, {{cite:2e68b7a2b5764c58bf0a839adf2d65bd00fb6a43}} as quantified selfishness to characterize egoistic and altruistic agents. These are promising potential solutions, as concepts like SVO provide a quantitative way to measure the agent choice over weighting its own rewards against the others in social dilemmas. There has been growing interest in leveraging these concepts to design heterogeneous multi-agent interaction mechanisms, e.g. {{cite:87f02524c6819c008552ec644a4ad891be6b42d7}}, {{cite:ac13bb512c1943f0595ccf1fbdac6725fa810b24}}, {{cite:9c47e9a2926da34df28e5411ccc925ec8e33610c}}.
| i | 8813443bfbac16fdf821deca3b6837e4 |
This variance is a measure of the uncertainty. Thus, we want to compute
the partition function. However, the partition function contains an
exponential number of terms and therefore is impossible to calculate
directly. In the next section, we present an algorithm that approximates
the value of this partition function using an importance sampling
technique; this technique gives a measure of the uncertainty with
respect to different cumulants. The partition function REF
corresponds exactly to the well-known grand canonical partition function{{cite:56fbca71a0c1d41d0a58be483864b81db1f5d382}},
establishing the relationship between the two fields. While the partition
function REF can generate moments to give a representation
of the uncertainty, obtaining this representation involves summing
over an exponential probability space. Sampling such a high dimensional
space is impractical; instead, we can use the partition function as
a scale. In the following sections, we present our algorithm, which
combines the probability measure REF with importance
sampling to obtain the variance in the loss {{formula:f22cbb09-b6cd-468d-9c85-d71fe97ff086}} and number
of units {{formula:8f6d6cdb-73cc-477a-91f8-371f7223210f}} . This allows us to estimate the uncertainty using the
above moments.
| m | a22cf9ea19bda19b7246a83f37862c39 |
Recent results ({{cite:1914bff9798abe992eeedf1795861af6ed90997a}}, {{cite:9689221389074d9b662bf0f7f1ed0e5f7db27af7}}) have shown qualitative differences between the adversarially robust boundaries of MNIST and CIFAR-10, which also impact the experimental findings in this work. In short, a robust decision boundary is in the MNIST case less spiky in comparison to CIFAR. For more details we refer to Appendix, Subsection REF . In Fig. REF we collect the statistics of the WRN and LeNet models on CIFAR10 and MNIST, respectively. On one hand, we confirm previous results ({{cite:1914bff9798abe992eeedf1795861af6ed90997a}}, {{cite:c90091f6ebbadcf407a7ddaa38cdc9c74ae2554d}}) implying the "flattening-of-boundary" phenomenon: noisy and adversarial training appear to improve and saturate isoperimetric bounds. Furthermore, the ball {{formula:dffc03bb-afb3-49ce-8e2a-2730386d326e}} realizing relative error volume {{formula:2c22db88-686f-4c61-94be-1f04a81596e9}} of {{formula:55465b4c-2ef2-44bf-8104-ffacc743741f}} is on average scaled up for adversarial and, especially, noisy training. On the other hand, an intriguing behaviour is observed for the decision boundary's heat diffusion traits. The isocapacitory saturation {{formula:eb4179a3-14ce-4e12-ac81-ce557e35cb7e}} does not appear to concentrate around the value corresponding to a flat hyperplane: defense training strategies, both FGSM and PGD-based, may not have a significant impact on the behaviour of {{formula:55af363c-2c9c-45e2-9433-468c184c1a21}} by forcing it to converge to the case of a flat decision boundary (shown as horizontal red punctured line). Put differently, the chance that a continuous Brownian perturbation will find an adversarial example (scaled to the appropriate ball {{formula:3c98ac94-6e13-42d9-a5dd-f9970cdd04ca}} ) will not be significantly altered on average (see Appendix, Subsection REF for a visual reference). However, it appears that noisy training consistently delivers lower values of {{formula:be55334f-2e03-4a0f-802b-ab88538badb5}} - intuitively, this is expected as the decision boundary is adjusted in terms of adding Gaussian "blobs", thus naturally being rounder. Geometrically, the sensitivity of {{formula:7d009ef0-13bb-44b1-9030-5799e14aaf17}} to small perturbations in almost flat surfaces (Subsection REF ) indicates that locally around clean (unperturbed) data points an amount of curvature and more complex geometry are still retained. Of course, this amount is not as large as to violate saturation of isoperimetric bounds and robustness comparability results in the sense of {{cite:c90091f6ebbadcf407a7ddaa38cdc9c74ae2554d}}. For example, in the case of CIFAR10 a simple geometric model surface that has a similar {{formula:da762784-4cf0-4618-9ffb-d1c5ac1cd810}} -behaviour (as for the adversarial and noisy training) is given in (Appendix, Subsections REF , REF ): considering a data point {{formula:3b79a841-273b-4e22-a318-354b273668c5}} , an almost flat decision boundary that is concavely bent w.r.t. {{formula:c55d292e-206f-4f1c-9984-c7837a55b892}} with approximate curvature of {{formula:8f77e3bd-7e9f-4853-9885-31476421158c}} . These observations reveal finer properties concerning decision boundary flattening due to defense training: in particular, noisy training appears to flatten decision boundaries and slightly bend them concavely w.r.t. to the clean data points. Further results for ResNet models and CNN are provided in (Appendix, Subsection REF ).
| r | 97b9024b23b775163568c9a36d4fa7b4 |
EASGD has been proven to be stable {{cite:5ffdfcd861f4866e388d6a128848a2fd689bbf54}} in cases of distributed deep learning. It induces an elastic force that does not allow the local model's weight matrix to deviate too much from the global weight matrix whereas also allowing some independence. The proposed method incorporates the concept of EASGD with the proposed adaptive focal loss [equation REF ]. The training of the network is done in two phases.
| m | cb7b4c58674884f734ebb0e8be184807 |
For this reason, we solely focus on the residual error between the solution of Koiter's model and the averaged solution of the original three-dimensional model. We use conforming finite element to discretize the three components of the displacement(cf. , e.g., {{cite:3110509f0970120be852c3d5e3ed4580abebad19}}). Apart from the transverse component of the solution of Koiter's model, which is discretized by means of HCT triangles (cf., e.g., Chapter 6 of {{cite:4a8120bd88f7bfb761466bd54d912dfa5903e9e7}}), all the other components of the solution of Koiter's model and of the solution of the three-dimensional model are approximated via a Lagrange finite element.
| r | c2e13838afc55ef958506d3cfca4a552 |
Now we have many different kinds of interpretation methods to choose when we want to analyze a neural model, although they are still in need of further improvement. At the current state of the art, which method we should choose still does not have a definite answer. The choice of the right interpretation method should depend on the specific model type we want to interpret; however, such a detailed and comprehensive guideline for all kinds of models to be analyzed is currently not available. Several recent studies started to look into this problem by benchmarking some popularly used interpretation methods applied to some neural models such as CNN, RNN, and transformer. For example, {{cite:772dfd49b9af1cbd440b145804e4d63d3dac85fd}} first use four interpretation methods, namely LRP, Gradient*Input, occlusion-based explanation {{cite:a3a099faf453fabb1fb1386e93287fd33ea0c288}}, and CD {{cite:9a22ccba65675f2aed1615cbd80797b5c7ec8eff}}, to obtain the relevance scores of each word in the text for the LSTM model for text classification tasks, and then measure the change of accuracy after removing two or three words in decreasing order of their relevance. By comparing the percentage of accuracy decrement, they observe that LRP and CD perform on-par with the occlusion-based relevance, with near 100% accuracy change, followed by Gradient*Input which leads to only 66% accuracy change. This experiment indicates that LRP, CD, and occlusion-based methods can better identify the most relevant words than Gradient*Input. As a counterpart, {{cite:4ad9aa36be65cbfd4fa7f446fea0269b6cf8956c}} argue that one should not compare interpretation methods solely on the loss of accuracy after masking since the removal of two or three features may not be sufficient for the model to behave incorrectly. Instead, they choose to measure the precision and recall of features identified as salient by comparing against ground truth important features and report the weighted precision and recall as the benchmarking metric. However, their annotations of which features are important are synthesized rather than collected by human annotation, which is not that convincing. In a more theoretical way, {{cite:7164825378021f0f89e8f339e5931f94f9dc6c7e}} propose several equations as quantitative evaluation criteria to measure and compare the sensitivity, faithfulness, and complexity of feature-based explanation methods.
| m | 7ab919c0d453b2e48d9995be47191e24 |
Our study and the previous work described above {{cite:5e4277fada4ceac3740db5f5001dc140cb47bf59}}, {{cite:f1241fb62743cd881bc3cc101ea4f1bbe7e3b530}} incorporates homeostatic synaptic plasticity, but does not account for any other of the wide variety of synaptic plasticity rules observed in neural recordings. Other work has shown that predictive coding can be learned in carefully constructed networks using learning rules that are not exclusively homeostatic {{cite:246ff4345d97471fc2f4aeac3d69624103bd6c31}}. Indeed, our approach of learning prediction errors in unstructured, randomly connected networks could potentially be made successful if the target rates, {{formula:150eb713-6bef-4a60-9f14-def5e342c403}} , were effectively modulated by the top-down or bottom-up input. Future work should consider the possibility of learning prediction errors in unstructured, random networks by combining these approaches.
| d | a840ee5abd0a57ffc3ebe56815b41f6f |
FID was adapted to assess fidelity of the generated audio in {{cite:7df7aac0b521e6a734a52f12a28537097bb7c0b5}}. This metric is designed for
very short sounds (<1 second) and, therefore, has limited applicability for long audio as it may miss long-term cues.
Another challenge in the visually guided sound generation is to reliably estimate the relevance of produced samples.
To mitigate both problems, we propose a family of metrics for fidelity and relevance evaluation based on a novel architecture called Melception, trained as a classifier on VGGSound {{cite:cdb3a345264ec9cdf475d748daa5dd801395219e}}, a large-scale open-domain dataset.
| i | d6756e1493eaf2f0918409715938d5a4 |
In summary, we have shown that recently developed methods for
calculating limits on sesquilinear electromagnetic
objectives {{cite:bccb6c3a8c0a767daa6a307efd3d1887a20cbc15}}, {{cite:8c8a71c89e03c70d7513aa489a637e7293b9e329}}, {{cite:e45e3e1bddadb7697c89ed7d435c8ef04b563c60}}, {{cite:95ec1e32f170debd16c5e5159e8c53e8a1c73509}}, {{cite:7c8095f6a170c9ff649a38b8b88868462c652bea}}, can be
applied to a wide variety of design problems, including spatial
multiplexing {{cite:7f3f026002207b84aac5a18de116bfb225966cd3}}, {{cite:234db1693384f21853ee89d1369bb4336abad108}}, {{cite:2e2a93c405cfda973d64dad10c3bc2abc6b989d8}},
metaoptics {{cite:690503890fcc0320731e0e4820dca26c7197ddce}}, {{cite:dc8e8f08ae737fa4de7ccbf395c2b940e6a2f899}}, {{cite:b74eca5ccc011c5f162bf19b00966ad7aa734807}}, {{cite:d1477bc5dc8af1c958b9dcc1ba9305e064986e53}}, linear
computation {{cite:c6aedc83dee4124d5ee998bbf76f8320bba138eb}}, {{cite:7592eeed35580eba3f420ee1a7ed6ac669840761}}, {{cite:4efb2e1f0284ee6469044c5508077069359c7d06}} and light
extraction {{cite:2c86d2746888f58546f61d1e3ba502a67f7e087c}}, {{cite:eda157dc30242fd2196a4250f83f1742f592acd2}}, {{cite:6457790f3f3d5395fbb172345e43e9f5c259fe40}}, {{cite:5807bcd0abeef52f5bcde7eef63b45d52783be59}}. Employing the language
of communication theory, this program stands as a significant
extension of prior work on channel-based electromagnetic
limits {{cite:9ac015c7cd7f127e62bbec39aaff19fd8e2a01a2}}, {{cite:dc2a345c3eee2ada71363eed966f9a86edf815ee}}, {{cite:81fc77d5a0d02624de3784417047ec981f8d5c86}}, {{cite:ebcdf2f2f04cb494fd12861180931815852b6174}}, {{cite:dc0660aa68732b1a3efca9a7fe95ad91009a72f9}}, {{cite:619c1ea4d93acea0b25402848e490ed2c9dbe28a}}, {{cite:5928a9758d19ac92a039e691f15bb07efb3f4213}}, {{cite:35f486803f3d08a7d02e4565c606630bf6f67588}}. Namely, although
highly insightful, the characteristics of the background Green's
function connecting the volumes containing particular sender and
receiver registers are generally insufficient for accurately assessing
whether the extent to which some desired communication can occur,
particularly in wavelength-scale devices. Rather, as may be confirmed
by a survey of the results presented in Sec. , the
degree to which communication between a predefined collection of
registers can occur may depend strongly on a range of other
environmental factors, such as the physical size and response
parameters available for designing the channels, and the spatial
profile of the register fields.
| d | cc91f0adebd5450668e78c52e3aca56d |
We extensively studied the vacuum structure of 4D effective
field theories arising from Type IIB flux compactifications
on the mirror of the rigid CY threefold.
Since all the closed string moduli can be stabilized by three-form
fluxes themselves due to the absence of Kähler structure
deformations, such a class of flux compactifications
plays a crucial role in revealing the vacuum structure of flux vacua
and in testing the swampland conjectures.
Remarkably, one can deal with more general fluxes than the
T-dual Type IIA flux compactification, namely the DGKT model {{cite:9235749777479d90454b2877e23ef0ceaec8b464}}.
| d | 39d1f826ac3f5eff80a74b0bf474d53e |
A comparison of the resolved and boosted channels (although corresponding to different phase-spaces) is possible at the parton level in the form of a ratio to the NNLO QCD predictions {{cite:c3d6c5614c9efcbd600942e1318a277d440b01a2}}, {{cite:d1da465b6e267ca064168bf8c1b122412a0941e3}}, {{cite:5ac1b274496feb1270708584cfcdc59367ea5674}}, as shown in Figure REF . The same figure also includes an example of the statistical correlation matrix between bins of all the spectra in the resolved topology, enabling correlated MC generators tuning of several observables at the same time.
| r | a88cd8925aeade7e5b61523ce2b0791d |
and {{formula:51dae330-b2ef-4b9a-b460-b59651a5bfa7}} denotes the weighting factor of the {{formula:27eee22c-5a78-4c14-9361-ee32fb3f7013}} -th user, {{formula:af4fb465-cc21-46ce-b4ea-7cb8b1a8a628}} , where {{formula:4fdbf210-d402-4fda-a945-c2fbbcebe014}} . Then, by exploiting the matrix derivative results in {{cite:47fc9e4ad0aff04ec21c4151d5cb924ff5413032}}, along with the complex matrix differentiation conclusions in {{cite:57ee282f9e0bf12f7618a48c34d5ab3d16c17a54}}, we can calculate the gradient of the WSR with respect to
{{formula:83d6fbd0-74b1-4220-9857-f4f690a1de8f}} asWe note that the derived gradient form here is a little different from {{cite:06a9f4dba1352e9c680100bda2bebfe894c239ad}}. This is because we rewrite the WSR expression in {{cite:06a9f4dba1352e9c680100bda2bebfe894c239ad}} only for notation simplicity. Mathematically, they are equivalent.
{{formula:f2975ec4-5bab-4293-a8b7-39183a569d92}}
| r | 9253e4efafe3da8fb09140470d9fc1f6 |
paragraph41ex plus1ex minus.2ex-1emImplementation Details.
For a fair comparison, we follow the baselines to use a 32-layer (respectively, 18-layer) ResNet {{cite:c5618754c631847611c3f5858ed4c9ba2a90c119}} as the feature extractor for CIFAR-100 (respectively, ImageNet), and a fully connected layer as the linear classifier. In particular, we remove the last ReLU layer for rectified cosine normalization. The memory size is fixed at 1000 or 2000, and the exemplars of old classes are chosen by the herd selection {{cite:f532e94ed842baf4a35d34413138b4bf61f31d10}} proposed in iCaRL {{cite:bbc3ea86e358e1d39809648d903b3d90e7e44982}}. At test time, we apply the same nearest-mean-of-exemplars classification strategy as iCaRL.
| r | 45d45bc8bc7ff430e7d80d641e8e9a15 |
The Expanded Wang-Landau (EWL) method {{cite:da153d9af33c5885d1c0bd827bc896c9d97ef386}}, {{cite:9f3f4b3e31c7baefe008604e04890fce5b2110ba}}, {{cite:3103715111c81b2af680a2103e90c66f40ec22a2}}, {{cite:2344ddc080e37d9281b92182765eaf25b3db0867}}, {{cite:0c9ddd98fad8faf4366306b33badcc13edabe6d5}} is a grand-canonical Monte Carlo (MC) simulation that was developed by combining a flat histogram sampling technique, known as Wang-Landau sampling {{cite:fd4266b0bb32a96dec31b22f063e4fef0d60eac3}}, {{cite:023bc0fb6e18e7705596616114345c1b7c423f67}}, {{cite:1122371b5b8b1f3ae62e26dea65913f64b587454}}, {{cite:b09521d1bd8a31a8a65770fd2995aa4d6cad43d9}}, {{cite:a25543fa55b40525755fb648dd6888abe8285245}}, {{cite:181344b4a5003877a0354fa9680cb4c9c68c79e3}} with a multi-stage (expanded ensemble) process for the insertion and deletion of molecules {{cite:09a44c6f3f1f25b147549d8f2be3787307592cea}}, {{cite:ef0408c46605155d4eeaeab4a067ae99aa6dfab3}}, {{cite:fb36dc947b83316b58c82acbbbe5f0325991419e}}, {{cite:f47776486b87974031b6b6812b95a53832bcc700}}, {{cite:55017fcc420fbf3898b6e28372795b4ea3b39fb6}}, {{cite:921cb095faf3878f7630fd9da4ef1eeed02a2370}}, {{cite:a533194e4dcc3b65219a4c23256a97206ba45a5c}}, {{cite:7094228c7490a4cfffb05872319388d5dda951d6}}, {{cite:184c2edb08f5d3e42d2b31fdaa72428899578bec}}, {{cite:d5a5c7ac32d44a77b8d47eb7a7a7913de6dea3b1}}, {{cite:1328774893c1e08e465dc81aa69ac29b482e71c5}}, {{cite:44942ba090a16120f810c72cf8222c16a9922811}}. During EWL simulations, the simulated system is composed of {{formula:4dc720d8-20f9-4084-a51e-7b715c44c1ae}} molecules and of a fractional molecule at stage {{formula:49a88fe0-2536-4f90-af2f-dce6cb3fa07b}} , where {{formula:f4e6d4b4-aff6-485a-8187-349b0b1454b2}} is an integer varying from 0 (void fractional molecule) to {{formula:6c96d0f1-c3ec-4806-bbb3-e948f7bd88f2}} , {{formula:fb982cc2-a626-4ad0-b947-5c31d9ffabde}} being the maximum number of stages. {{formula:266e358a-0dc5-4f4d-897c-aec3f10ead67}} characterizes the "size" of the fractional molecule and interacts with the full (regular) molecules accordingly, and the conventional insertion/deletion steps are replaced by steps consisting of changes in the stage value {{formula:10d2e0dc-5795-4e6d-ba35-d3f47d075b22}} for the fractional molecule. The Wang-Landau part of the method allows for the dynamic evaluation of the canonical partitions functions {{formula:71aface3-eee9-4482-9bf2-984036921bf3}} for the system. For any value of the chemical potential {{formula:e0ea604b-6f4f-42da-9388-f2a5e21e46a1}} , the grand-canonical partition function {{formula:767d9700-8a78-488c-aa6f-a0a31980e7a6}} is then obtained by summing up over {{formula:2258c72e-9b6d-4bf5-bca3-a615a0a1b2b8}} the functions {{formula:2f759ee2-4a07-4ab7-99f0-a815d6f8e94e}} (we drop the specification {{formula:3b81c9a1-5570-4db1-8bbd-8d01112da5ba}} in the rest of the paper) according to
{{formula:7c16808b-aa7e-4e87-80fc-35d508ce8fd8}}
| m | 5c0030369df72cb91d0eef59319040f8 |
It has been well realized in variational analysis that the subregularity properties (REF ) and (REF ) are equivalent to the following calmness and isolated calmness counterparts for inverse mappings; see, e.g., {{cite:a2e581a0ba2f1f9ba5e5a2dfb2a7cbd2dcc5080b}}, {{cite:227de480d6a7d26d8e4a27bdf89ea4d7cbe0e37e}}. Recall that {{formula:a4a8b4d6-5e73-4911-83f6-072a704f8eea}} is calm at {{formula:0424d50c-df3c-45cc-aef0-5468d5d75807}} if there exist {{formula:d47a4ba6-1ccb-410e-9a2c-08f724b0fdb7}} and neighborhoods {{formula:e3239616-8168-4fdf-b36a-50ad80b89337}} of {{formula:b391c390-1809-4b80-8832-1936218d99e8}} and {{formula:d98f570f-2641-42ad-9163-18d5008f8c2c}} of {{formula:99071aa5-eb75-4265-9ee0-8b74a72bccba}} such that
{{formula:f498e119-2017-4d26-9688-13e0fd62fe79}}
| d | fb49cabbf7fb0eb9498748d50d68ee05 |
To overcome the limitations of unknown sampling size and subspace dimensionality, the geodesic flow kernel (GFK) was proposed by Gong et al. {{cite:a7974642c4170712dc27c6d4abae1332278a95d3}}. They integrated all samples along the “geodesic" (the shortest distance between two points on the manifold), which is shown in the following equation.
{{formula:b1638221-bc3e-4376-92dd-5037123a1f74}}
| m | 823be0b84dee5bde123f30719771f52b |
The overall architecture of our method is illustrated in Fig. REF . Firstly, the input SAR image is fed as input of the ResNet-101 feature extraction backbone {{cite:9a1fe7bc1176415b0b4b7b966566ce5412f35f31}}, through which features of five different scales {{formula:596686bd-4acc-4c19-8888-7423a350310b}} are obtained. As the shallowest feature {{formula:50627e5e-cb9b-4505-8786-1ed67b5bb009}} contains little semantic information, {{formula:e9b18ab9-7c24-4038-a734-c243f20e0ba2}} are chosen to be combined through feature fusion module, and the resolution of the final output feature {{formula:902ce73e-49be-4f67-a0a0-b2ebb8908a80}} is 1/4 as the input image. {{formula:ea1b0e24-2faf-442b-b369-0347dd3d63c7}} is then processed by three network branches, from which we can obtain the center heatmap {{formula:2a72826e-9502-4ede-a60f-2b2c377a721c}} , the center offset map {{formula:2d456f03-0e3c-46c2-9596-355b3499a857}} and the encoding map {{formula:ac297c52-aadc-4a1f-be01-b15fa49ddd85}} , respectively. In the training stage, the multi-part loss function is calculated according to the center information of the ship targets and the polar encodings. The losses are combined to train the branches jointly. In the inference stage, the output of the branches is decoded through the polar decoding process. And the non-maximum suppression algorithm(NMS) is adopted to remove the duplicate detections and obtain the final detection results. In the polar encoding process, for each ship target, we sequentially sample the distances between the center point of the ship target and the boundary of the OBB every {{formula:62e6fe54-70bd-426c-9fe4-47d214e5ad01}} in the range of {{formula:f0d3602e-dbd8-4a7b-835a-5ffde3855984}} . The sampled N values are combined to form an encoding vector. Due to the central symmetry of the OBB, the encoding vector can represent the shape of the whole OBB. In the polar decoding process, the center points of the ship targets are first extracted from {{formula:bb141897-bb44-4416-bba1-b1403afb31be}} . Then the downsampling quantization errors are compensated in terms of the predictions from {{formula:67c68f46-4e17-4a0a-9586-b018bdc9de5b}} . The OBBs of the ship targets are finally restored through the processes of extracting the polar vectors from {{formula:b54209e3-4385-4d6c-adc2-5859e9d1d35a}} , converting the polar vectors into the boundary point sets, and finding the minimum bounding boxes of the point sets.
| m | be7e9922a5acd4c725a420152c5f94e6 |
Here, {{formula:ed6cefa6-b678-4d25-b80e-09ce049ac2cf}} is the discretisation error describing the discrepancy between the accurate forward model and the approximate model. The Bayesian approximation error method carries out an approximate marginalisation of the posterior over the error {{formula:0ce7ff80-51b5-4cf9-9679-59465a8fcf4a}} . Following {{cite:9b9a9f852486e2c2080a3825a74919f9687681eb}}, {{cite:70de268d79f18fb3a17b8887682186eb00314a80}}, the MAP estimate with the Bayesian approximation error model is obtained as
{{formula:d94c293f-ce25-43df-ae63-2c141e4ecc01}}
| m | cece2927491bb1003b52263ea5d90c06 |
The problem of finding the minimum number of fragments {{formula:718da555-8ec8-4747-b313-a51f51b40f6e}} representing
the Hamiltonian {{formula:11920503-3d0b-4e89-8834-b75f0b18faba}} has been shown to be equivalent to a Minimum
Clique Cover (MCC) problem for a graph representing the Hamiltonian. For this graph
each term of {{formula:c59f15da-9f7b-4f5b-a2d3-856637d0c3cd}} is a vertex and the commutativity condition determines connectivity.{{cite:7a90b6c72db4ddddf6e1f7dd68f6670faef9af2f}}, {{cite:736a3ba5004bf8e3c22eb86919204f7d52a4c16b}}
The MCC problem is NP-hard but it was found that different heuristic polynomial-in-time algorithms
can find good approximate solutions. In this work we specifically
consider the largest-first (LF) heuristic, whose name makes a reference
to the ordering which the algorithm uses to process the vertices of
the Hamiltonian graph;{{cite:7a90b6c72db4ddddf6e1f7dd68f6670faef9af2f}}, {{cite:736a3ba5004bf8e3c22eb86919204f7d52a4c16b}} as well as the Sorted
Insertion (SI) algorithm.{{cite:d75046f6a4942e0db6187904397f55e483cf128a}} The latter is a greedy algorithm introduced
to reduce the number of measurements required to attain a given level
of accuracy in the estimation of the energy expectation value (or
any other observable), rather than aiming at the minimization of the
number of groups in the Hamiltonian partition.
| m | 4f7b78496f5af23c2bc8ae40ffbfba7b |
We implemented 13 state-of-the-art methods, namely, Barlow Twins {{cite:fe29601180afb15311f35d7508555f78183482a9}}, BYOL {{cite:4dc6a39e1accab3708c1066675bf3da1d725f967}}, DeepCluster V2 {{cite:d2bbab22aad4bf113b091fb0b4eb46ac76b0d634}}, DINO {{cite:a2761055f0981734e7b4db882848b64e3af69e55}}, MoCo V2+ {{cite:60d83e06bff6708448a72e38310b9b3cce3084e8}}, NNCLR {{cite:6bac851f1349f2a748bcb84646b439fdc6d7492c}}, ReSSL {{cite:aa3042b8c2292b9260e2ae6aabfcc474e200d92e}}, SimCLR {{cite:c10576d686af37d96edddd90f7041bfd12ffe523}}, Supervised Contrastive Learning {{cite:d677379811564bea84c6836799896cb3f77f5760}}, SimSiam {{cite:1baf64f577348d455f41f484a6c1d971be8885d9}}, SwAV {{cite:d2bbab22aad4bf113b091fb0b4eb46ac76b0d634}}, VICReg {{cite:5a897da99607850643c099d4ed985f1c3d91bfec}} and W-MSE {{cite:b4d89e7022c31d93060b28e17a24200fb0d4650e}}.
| m | 948ee098a43a5601a19320c13dddbc77 |
The tools of fractal analysis provide a global description of the
heterogeneity of an object, such as its fractal dimension. This
approach is not adequate when the object may exhibit a
multifractal behavior. Multifractal analysis is a useful way to
systematically characterize the spatial heterogeneity of both
theoretical and experimental fractal patterns
{{cite:b0d06f7d0b260d2b9f62a72e20b5e3241be7bd1b}}, {{cite:ebe29c91a9450798d9c132b50e8990c6ddc275f4}}. It was initially proposed to
treat turbulence data, and has recently been applied successfully
in many different fields including time series analysis
{{cite:8d68a2ba5d0372688062b4fc275266f8fb97eee7}}, financial modelling {{cite:c9ae95fa18acb79597a9c0a6485a83a220a16a3c}}, biological
systems [21-28] and geophysical systems [29-34]. For complex
networks, Lee and Jung {{cite:bb548a50f2eee4b928f7dc12a0432d9efd6d1233}} found that their
behaviour is best described by a multifractal approach. As
mentioned above, through the recent works by Song et al.
{{cite:3598788e4653a867c933e2abe1172b9a5d4e073d}}, Guo and Cai {{cite:a972d4d14a189c2f53637a96bdc646791b0248dd}}, Kim et
al. {{cite:72c89fff15d7f367d70eaaf8b05db9aa56e82099}}, Zhou et al. {{cite:5ef363b1567978beb2e55ee5f14ccf9813051cce}},
Gao et al. {{cite:0c75768382f3aeb1f8c30101bcf1b3c405f8ae6b}}, it was already a big step
to go from the computation of the fractal dimension of a
geometrical object to that of a network via the box-counting
approach of fractal analysis. In this paper, we propose a new
box-covering algorithm to compute the generalised fractal
dimensions of a network. This is the next step to move from
fractal analysis to multifractal analysis of complex networks.
| i | c5116dff89dd07271cf693115e03b6ef |
Task A: diagnosis of chest X-rays. We use NIH chest X-ray datasethttps://nihcc.app.box.com/v/ChestXray-NIHCC and DenseNet-49 as the classification model. This dataset consists of 112,120 X-ray images with disease labels from 30,805 unique patients {{cite:e4134be9e4b55fb971a4c5a6afe4e09354d25600}}. We filter out patients whose ages are above 100 and resize the images to 256*256 pixels.Note that some samples may have multiple disease labels, therefore, this is a multi-class classification. We use Dense Convolutional Network (DenseNet) as the classifier, which connects layers to each other in a feed-forward fashion. DenseNets have several compelling advantages, including alleviating the vanishing-gradient problem, strengthening feature propagation, encouraging feature reuse, and substantially reducing parameters {{cite:ec69e5e056073bdcefaac99233871ee63736f4ac}}. The block sizes of DenseNet-49 are (4, 4, 8, 6). The batch size is 32. The dropout rate of the fully connected layer is 0.15. The initial learning rate is 1e-3, which decays every 40 epochs with the decay ratio {{formula:dc283577-a0ba-4022-bcfa-88e4cd97a111}} .
| m | 2a64824be16b5e936bef7edf01d3793b |
Finger gaiting is an inherently difficult task for a robot. Given a robot hand, the individual serial link fingers must work in proper unison without collision; maintaining stability while making and breaking contact with the object {{cite:0c651284521ba2ccba8a02e2ef68222398133e7e}}. The computational complexity of this problem has traditionally been very expensive–requiring the system to calculate and modulate forces and planned joint trajectories online during manipulation. We, conversely, are able to alleviate many of these complexities by leveraging compliance, i.e. safe modal transitions, in our system. The capabilities we present extend beyond what has been illustrated previously in the literature, some purely in simulation {{cite:9e484e170791c443b5cdfa59be8b9cf06966ff77}}, {{cite:179ae8a621a78fdf46d2328447c1a86ab8a9a73c}} and some demonstrated on a real robot, but with support surfaces {{cite:3220bff85883d0822d085bb8bd266c08db8c32e4}}, {{cite:f411a906afec054be64985b75e8773a52e301de3}}, {{cite:91fbadde1660829cf6a68517bf67a2fbcbcc85fb}} .
| i | bca0133349345ec188fc7b44392a51ce |
The main outflow of M 3-38 is aligned along its bipolar axis and has expansion velocities up to {{formula:65bd69c0-54e3-473d-a0eb-1543e32b25f6}} 225 km s{{formula:27b94f01-562b-4e34-9e85-cec68aa6f7b0}} (Fig. REF and REF ).
This makes the outflow in M 3-38 one of the fastest among PNe, only surpassed by those in M 1-16 and MyCn 18 and as fast as that in KjPn 8 {{cite:47554836cb540ccf0595fe39901fad540c842d3e}}.
The high velocity, linear PV diagram, and elongated morphology of this outflow makes it a “bona-fide” jet candidate.
The jet space velocity cannot be derived because its inclination angle with the line of sight is unknown.
If an inclination of 45{{formula:f3227d23-95dd-4908-8e08-fd543151213a}} were to be adopted, then the space velocity of the jet would be {{formula:010c589b-7226-4cf8-8c50-e39944d9bee5}} km s{{formula:d071224d-0a58-475d-9980-155df1f2fd19}} . The outermost fastest component of this jet is projected about 5{{formula:b07ac2eb-6ddb-4876-b391-c91a80d29011}} from the central star of M 3-38 (Fig. REF ).
Adopting the most recent distance estimate of 8 kpc to M 3-38Distance estimates to M 3-38 in the literature range from 5.3 to 14.1 kpc, with an average value very similar to the one adopted in the text.
derived from MSX MIR flux densities by {{cite:308a310284c205a05b95cc5ca660f344153e8d70}} and a similar {{formula:0760cafe-4fba-4a94-a8cd-abd7625fad85}} inclination angle, the projected distance from the PN center of 0.19 pc would imply a true linear radius of 0.27{{formula:448dc373-0d18-4462-9976-87738eabb887}} pc. This translates into a jet kinematic age of 860{{formula:69493f17-9f5f-4cd9-957b-5a4807db3846}} yr.
We remark that the values of the projected distance, true linear radius, and kinematic age given above scale with the distance, which has been adopted to be 8 kpc.
| d | 887227e555132c3d231b39e29d55c034 |
Most existing state-of-the-art object proposal methods mainly depend on bottom-up grouping and saliency cues to generate and rank proposals.
They commonly aim to generate class-agnostic proposals in a reasonable time consumption.
These object proposals methods have already been proven to achieve high recall performance and satisfactory detection accuracy in the popular ILSVRC {{cite:1d68014aeda91a2c3e9a5a5708be826b5713d395}} and PASCAL VOC {{cite:deef34b46ddaaa111feb2f4349cf7b2ede348ad2}} Detection Challenge Benchmark,
which require loose criteria, i.e. a detection is regarded as correct if the intersection over union (IoU) overlap is more than 0.5.
However, these object proposal methods fail under strict criteria (e.g IoU > 0.7) even if the state-of-the-art R-CNN {{cite:5a07e31fd4c721d68b80606af4ffd0353cced9a3}} object detection approach is employed.
Especially in the considerably challenge KITTI {{cite:a9ababe145b9c23e125cf8270e853dc4bb7b1857}} benchmark,
their performance is barely satisfactory since only low-level cues are considered.
| i | d757e45ba1686c02f9579798728d9620 |
Uncertainty estimation in deep neural networks with different Bayesian approximations was shown to improve model predictions, either by explaining this within the loss function or by aggregating predictions from ensembles {{cite:0e175437791395bd2713d643069df891f331926f}}.
Such estimations have been successfully applied to medical image segmentation {{cite:de87a7506b721d8ad1e2ee6fb2c4d9af70f98e47}}.
Epistemic uncertainty accounts for lack of confidence in the parameters of a model, i.e. uncertainty that can be reduced with additional labeled data. This can be estimated using so-called Dropout layers {{cite:c6bff50eb3d4abe89f9df2bf447fd4ba14b12a63}} both at training and inference time, known as Monte Carlo (MC) dropouts {{cite:2f72bbb0fd1a0adff539fa90e33e470968c4f896}}, {{cite:acf3d8bc691ed984bff0c9e53f9776f67ef5797a}}.
Aleatoric uncertainty captures the inherent noise in the observations, i.e. uncertainty that cannot be reduced with additional data; and it can be estimated with the inclusion of a stochastic loss as proposed in {{cite:0e175437791395bd2713d643069df891f331926f}}.
We herein study the use of the above uncertainty estimation tools to design a method for the estimation of segmentation quality in the above-described problem setting of heterogeneous FM marker combinations.
| i | ff44ee5b0b6db79a505c1230e9dd6a99 |
In the following, we report the classification performance of the individual pipeline components as well as the overall pipeline in our experimental evaluation. We use the Matthew's correlation coefficient (MCC) {{cite:3b50c2a4220971b039be155f60924dfe0616905b}} as the main metric of our evaluation due to its clear advantages over other metrics {{cite:456602d9767a6ac13f56fd5be730498ba53d979d}}, most prominently, its robustness to class imbalance. For the sake of completeness, we also report the binary accuracy (unweighted) as well as the area under the receiver-operator characteristic curve (AUC-ROC), however we stress that these results should be interpreted with caution as they are susceptible to class imbalance.
| r | 0f710799d8b22b95322e8759e877d7cd |
It would obviously be very interesting if we could directly observe the waterfall field(s) ({{formula:c94b763e-af12-46b8-8583-5fe426ff65d7}} ) via their mediation of primordial non-Gaussianity (NG), using the idea of “Cosmological Collider Physics” {{cite:b4aa4dbf70491b2735503bf2316c7adb291bb626}}, {{cite:879617ff8e92d075ce0e223175edcdd6484989b9}}. Ordinarily such signals would be strongly “Boltzmann”-suppressed by {{formula:3f88243d-866c-442c-8453-2bb8ca49d0f7}} , since {{formula:08ccc99a-ce84-4f4d-8df5-accfbde86917}} . However, the recently discussed “scalar chemical potential” mechanism {{cite:c61cdef920fa2cda0ac061df040f3dc2e5040065}} may eliminate this suppression and be compatible with our twin symmetry structure. We leave an exploration of this to future work.
| d | 3ec4c94ffe1306cdc894b8c581140380 |
In this section, the proposed method is compared with the SOTA methods,
including unsupervised methods :ReDO {{cite:f4353e3d91b14deea154ea0008539263e2c33b46}} and CAC {{cite:dc17fd6baa95780e5e5821524bdc41658383a68e}},
few-shot methods: SG-One {{cite:75eeed652a59e1d86836776ed1a93f0f231be086}}, PANet {{cite:7117fc470589f60c12eb7464a2834a6f8217fb20}}, SPNet {{cite:ac555f57bbb9d213b55f4f2f32822fe2e6679119}} and CANet {{cite:feb480daf98277af0c3086bd01c470b0ea30e6c5}},
weakly-/semi-supervised methods: USSS {{cite:0ecada4ca00a4b975ccb033aed1e4e5faac89862}} and ALSSS {{cite:03609f684d92823bea037ff8395721eefe02f2a2}},
and fully supervised methods: Unet {{cite:8aee960af4b284643866ea5675319f101b7c9fa6}}, FPN {{cite:081ad78bdecc24135a3c77d7224e86fa543e7374}}, LinkNet {{cite:3bb98e79241d9d0634e510c58078a9960c08b75a}}, PSPNet {{cite:701ed4033f4aed8a7ffaa3c8901ec9d84cbb205b}}, PAN {{cite:0cfed93ab1e0b48b0779fb7ffa41b046b41b5936}} and DeeplabV3+ {{cite:408b64f2f924c662225b1de54edeceb08280f623}} on four datasets.
Meanwhile, The Trans-Net is also compared with two boundary-aware methods: Gated-SCNN {{cite:d96ea62a1edce38f259e543e3b4a63b650111cd0}} and BFP {{cite:25f9ba209d2da8fb09002e8e529a7a3b47c0c5fd}}.
For the semi-supervised methods (USSS and ALSSS) and boundary-aware methods (Gated-SCNN and BFP), ten labeled samples are provided.
For {{formula:cc52cc21-cb34-44c4-81fc-b30b17563d2a}} , the visual boundary knowledge is translated from the {{formula:6dfa5edc-c81a-4116-90ba-a9c942e35f9d}} , which does not contain samples from the target category.
Fig. REF and Table REF show the quantitative and qualitative results, where we can see that most scores of proposed {{formula:4330200c-c3e0-4c4e-ad22-5b1e1c3f25e8}} achieve the state-of-the-art results on par with existing non-fully supervised methods on Birds and HumanMatting datasets.
Note that Flowers {{cite:85f6c67daba2a04fac2299af22fbfbd485786ccb}} dataset contains only 753 manually annotated samples, which leads to the inconsistent scores with Birds and HumanMatting.
The most likely reason is overfitting. More experiments on the algorithm pre-segmented Flowers (8189 samples) are given in the supplementary material.
Moreover, with only 10 labeled samples, {{formula:1715f8b5-2fea-47e7-ba99-f7afbe4fa957}} can achieve better results than some fully supervised methods and close results on par with the best fully supervised method. Meanwhile, with all the labeled samples of the target dataset, the {{formula:adcd0e36-be7b-486e-93ab-e69f107ad0e9}} achieves almost all the highest scores.
In sum, such experiments demonstrate the practicability of the BKT-Task and the proposed Trans-Net.
More visual results and experiment results on THUR15K and algorithm pre-segmented Flowers are given in the supplementary materials.
{{table:8dda89c5-0d30-46f0-b124-46ef5812c0b6}}{{table:20c62e28-162d-47f8-8158-6281f47c8be0}} | m | e011bdb61f7a7dec5c2ecc388c557354 |
Two well-known architectures, PointNet++ {{cite:b16ebf7845f8e745def52886b59155d6418011f4}}, and MeshCNN {{cite:bc56182e786fed9e3e388b701439dfb19a251faf}} are adapted for the face segmentation task. To compare performance between multiple representations we use per-face classification accuracy and IoU as our primary evaluation metrics. The triangles generated from each B-rep face inherit the label of that face and points inherit the labels of the triangles from which they were sampled. Triangle edges are considered to be owned by the first of the two triangles sharing the edge and edge labels are derived from the faces which generated the triangles. The per-face accuracy and IoU is then evaluated by averaging the segmentation scores for the points or edges derived from each face. This gives a prediction of the class for each face, from which the accuracy and mean IoU can be evaluated as described in Section REF . In addition to the per-face metrics we also report the per-point and per-edge accuracy and IoU for PointNet++ and MeshCNN respectively. As for the per-face metrics, the IoU values are computed by considering the points or edges from all bodies together.
| m | aa6ebc2d7cb53c88389678a1e8696fac |
Recently, continuous-time models based on differential equations and their discrete counterparts have been attracting attention to deal with extremely long (and possibly irregularly sampled) time series data {{cite:391b2bddae23d817a25268ba8cd61e3fc3e98c27}}, {{cite:bf4fbe9066bcd40e24fe58cae039942a4026ee21}}, {{cite:00f681fdad057503d9dfb36a85b905cff9280496}}, {{cite:486ab9644f124a67acb768af7d8bbaa2a914ffd3}}, {{cite:be492fad4a065747ff52b9e48f4a16ee2fba5a4b}}, {{cite:355369c77d11de6f64e4fcf8561a8328fa5f3d5a}}.
Some of these models utilize the sigmoid function to represent variable time steps for discretization.
Such use of the sigmoid function essentially has the same effect of the forget gate in LSTM and GRU in terms of time scales of models {{cite:7bb9c949ab3a4c972f8beefe018a0bc409ed7bf4}}, {{cite:00f681fdad057503d9dfb36a85b905cff9280496}}.
Thus, our method replacing gate function can be applied to the sigmoid function representing time steps to further enhance the learnability for wide range of time scales.
| d | 120a9f7a3f1d676c9fcc866645170a91 |
Before presenting our theoretical results, we briefly discuss about the available data from Au-Au collisions at {{formula:05e18a73-aa33-4125-bec0-31045fa0eaf9}} GeV on yield ratio based on Ref. {{cite:91ba5a4a775a439f9f4b2a66b93de42d5d6f98f2}} and Ref. {{cite:1daffa3a90f866013264de9ec60b32d37266b681}}. For {{formula:b471fe97-221b-4af0-9f25-13ae8bfc84f7}} hadrons, mid rapidity data ({{formula:4c9da26c-737f-4e38-ad92-4ca076d6d41f}} ) are available for five collision centralities; 0-5 %, 10-20 %, 20-40%, 40-60% and 60-80%. In case of {{formula:11c7bdfd-4b2f-4212-bb85-8818e0d8e2aa}} , the data are available in all those centralities apart from 10-20% and 60-80%. The {{formula:4915ab67-3f8e-4c5c-aaf1-06acec601654}} integrated yield, {{formula:26d9e5c4-cef8-44d0-ab84-e38458a5c28a}} , have been measured for {{formula:62923cf2-6483-4718-9cea-eed9f2993d00}} in Ref. {{cite:91ba5a4a775a439f9f4b2a66b93de42d5d6f98f2}} and for {{formula:7ae5a758-756c-4eea-aafb-9f5de1e228d5}} in Ref. {{cite:1daffa3a90f866013264de9ec60b32d37266b681}}. The rapidity windows for {{formula:5cc15a8d-841d-4344-b9d7-e1e422c94145}} is {{formula:32925efe-c02b-4ff3-9d00-ba56abce1a77}} , for {{formula:ce42725d-0162-4c12-8e6a-877aae3b70a7}} is {{formula:e0d816dd-ee26-4a93-b7ee-33120f1636f4}} and for {{formula:65a1394a-988a-4b8c-9ca6-a093daed651e}} is {{formula:e1ed9cef-50f7-477d-84af-6663d80ced25}} . The intergated yield {{formula:25826241-d8cb-45a7-9c99-87f62480396d}} is dominated by low {{formula:d509cc76-4587-48ca-bdc5-468ba617c304}} region of the spectra, that basically corresponds to soft production. {{formula:161a1719-920b-4618-bf80-0abe14494ce1}} of pions from Au-Au collisons at same energy is measured in {{cite:c80749c0db520eb38c92f5a17782afc29c5832d8}}. We take those experimental values and evaluate the ratios of the integrated yield of particles (plus anti-particles) to the pion yields, which are tabulated in the last columns of Tables- REF & REF . It may be reminded that there are minor differences in {{formula:493a8252-3ced-4c88-b170-0e6c2cecaa98}} values (at same centrality) in following references {{cite:91ba5a4a775a439f9f4b2a66b93de42d5d6f98f2}}, {{cite:c80749c0db520eb38c92f5a17782afc29c5832d8}}, {{cite:1daffa3a90f866013264de9ec60b32d37266b681}}. However the differences are very small as shown in Fig.REF . We consider {{formula:e5c695af-be56-4000-ac0f-130fa8d01ebf}} from Ref. {{cite:91ba5a4a775a439f9f4b2a66b93de42d5d6f98f2}} in our calculation of yield ratio of hyperons. While calculating yield ratio of {{formula:21a1eb50-82c5-4010-a156-59c2b7e971b1}} , we consider {{formula:741d59d5-0dbe-45ab-bf9a-9436714f75f9}} from Ref. {{cite:1daffa3a90f866013264de9ec60b32d37266b681}}.
| r | f26099e5ac714e7e072727f947f6b9a6 |
Our results primarily hold for convolutional networks such as ResNet-50 and ResNet-101 (data not shown) applied to computer vision tasks such as CIFAR-10 (data not shown) and ImageNet . Can the same approach be applied to NLP? Many recent scaling law papers find a linear boundary based on single, full training runs, where the scaling is based on model size {{cite:732493d8cb321f3ab557be7bda1c80509edfef5c}}. However, it is likely that each model size has an associated quality-time Pareto frontier. Is it possible to shift the scaling laws to have better exponents? Some of our preliminary experimentation is inconclusive. We hope to explore this in future work.
| d | 3c2306cbc05f51ec22be234671e48011 |
Medical image registration aims to learn a spatial deformation that identifies the correspondence between a moving image and a fixed image, which is a fundamental step in many medical image analysis applications such as longitudinal studies, population modeling, and statistical atlases {{cite:e93def7603658550f0d8b9476a857f0a2ddcccdb}}.
| i | 16e0731226a98ac0f519966b118d4dda |
Better numerical optimizers. The judicious choice of the numerical optimizer is probably the most
important factor. {{cite:d3ebf2f1394c9e81491e878fa396cf5ed582e95a}} provide a very useful overview of
derivative-free methods. Based on their recommendations, the first
step is to select the best known derivative-free methods such as
TOMLAB/MULTIMIN, TOMLAB/GLCCLUSTER, MCS or TOMLAB/LGO. The second
step is to employ meta-optimization techniques that combine different
approaches. Note that in our case the choice was limited due
to lack of availability of open source Python or C based
implementations. It is also worth considering building
ad-hoc optimizers for synthesis based on tensor networks and gradient descent. These have
the advantage of high GPU performance.
Better parallelization of the search algorithm. There are
two levels of parallelism within numerical optimization based algorithms. At
the inner level, the
first challenge is that the numerical
optimizer itself needs to have a good parallel implementation.This
does not seem to be the case with the publicly available
implementations which exploit it only in small matrix BLAS function
calls. There is an outer level of embarrassing parallelism across
optimizer invocations, given by the evaluation of the partial
solutions at a given search step. This is proportional with the number of
qubits in the algorithm. Since in our case the optimizer performs
best single threaded, shared memory parallelism is
sufficient. Implementations will eventually need to move to distributed memory
parallelism, given the availability of parallel numerical optimizers.
Synthesis for late NISQ (large) circuits: For circuits with
tens of qubits memory and computational requirements for synthesis
may be prohibitive, as unitaries scale exponentially with {{formula:1d2c7f52-1ad8-4c59-af87-dd2c832fee08}} . Given
an already existing circuit, a straightforward way to incorporate
synthesis is to partition it in manageable size blocks, optimize
these individually and recombine. For algorithm discovery, synthesis
will have to be incorporated into generative models for domain
science. For example, frameworks such as OpenFermion can already
generate arbitrary size circuits. We have already started exploring
these directions using the current algorithm.
Related Work
A fundamental result, which
spurred the apparition of quantum circuit synthesis is provided by the
Solovay Kitaev (SK) theorem.The theorem
relates circuit depth to the quality of the approximation and its
proof is by construction {{cite:30fc2eba7822ba24bd86f58e24d2db56773f6603}}, {{cite:1351bbbabd04d916f74b337e2ef516aef32aeea2}}, {{cite:3fa2b7243a0b8d2d7102aac2e76fa5c260e9a81f}}. Different approaches {{cite:30fc2eba7822ba24bd86f58e24d2db56773f6603}}, {{cite:354e7407fa76af0b82b4cc5765e3e0a2c9cf2aaf}}, {{cite:1612f3b547cb1a6a789aeebbf1dc4e784e470eb1}}, {{cite:9dbfe6c00077c0e7c7810beaacbd690a6c5934e7}}, {{cite:fabec14e5c8e6f9a7845856e91fd0d641fe308bf}}, {{cite:f15dc32f499500193c25140610f21ec48a010e06}}, {{cite:283b1826950f56b3f233533b93ac6aae05397ffe}}, {{cite:d5d5794446875715446d9eb691f9d7cece55d506}}, {{cite:da68077d3db4865f17886ed2edbb3e8996aa9e56}}, {{cite:b264fc551fc01ddda9399aa2f1f9863213362f2c}}, {{cite:c4042c75998520c116f28e346a4b15a39fd08c63}} to synthesis have been
introduced since, with the goal of generating shorter depth circuits.
These can be coarsely classified based on several
criteria: 1) target gate set; 2) algorithmic approach; and 3) solution distinguishability.
Target Gate Set: The SK algorithm is quite general in the sense that it is applicable to any
universal gate set. Synthesis can be improved in terms of both speed
and optimality by specializing the gate set. Examples include
synthesis of z-rotation unitaries with
Clifford+V approximation {{cite:871e1d22942e85604fd54fc19ebdd2be33127cd3}} or Clifford+T gates {{cite:3af59ab942b041e64e33fdbd14da8c365a8bdfe6}}. When ancillary qubits are allowed, one can synthesize
a single qubit unitaries with the Clifford+T gate set {{cite:3af59ab942b041e64e33fdbd14da8c365a8bdfe6}}, {{cite:c11d475f3eacd57959b5029810f3b16a4bed4a3e}}, {{cite:df4128fa92118df332467c11859dcaf223a3fd6e}}.
While these efforts propelled the field of synthesis, they are not
used on NISQ devices, which offer a different gate set
({{formula:3a3eb423-c0ab-4725-8979-b609a6530adf}} and Mølmer-Sørensen all-to-all).
Several {{cite:71857cc3d13291c43e9215e18cb7f23f013d9df8}}, {{cite:a0196b69ac9db17b32bce236502ed2e5d06d0857}}, {{cite:57217161c0f85243ab0699869b0e47f1f28ec39d}} other
algorithms, discussed below have since emerged.
Algorithmic Approaches: The earlier attempts inspired by
Solovay Kitaev use a recursive (or divide-an-conquer)
formulation, sometimes supplemented with search heuristics at the
bottom. More recent search based approaches are illustrated by the
Meet-in-the-Middle {{cite:9dbfe6c00077c0e7c7810beaacbd690a6c5934e7}} algorithm.
Several approaches use techniques from linear algebra for
unitary/tensor decomposition. {{cite:283b1826950f56b3f233533b93ac6aae05397ffe}} use QR matrix factorization via Given's rotation and Householder transformation
{{cite:d5d5794446875715446d9eb691f9d7cece55d506}}, but there are open questions as to the suitability
for hardware implementation because these algorithms are expressed
in terms of row and column updates of a matrix rather than in terms of qubits.
The state-of-the-art upper bounds on circuit depth are provided by
techniques {{cite:a0196b69ac9db17b32bce236502ed2e5d06d0857}}, {{cite:71857cc3d13291c43e9215e18cb7f23f013d9df8}} that use Cosine-Sine
decomposition. The Cosine-Sine decomposition was first
used by {{cite:03ec32956b6dd7b9ce24ab0b968e69d554bc06a7}} for compilation purposes. In practice,
commercial compilers ubiquitously deploy only
KAK {{cite:0894bcce271d2ebda0ec0481f222b97b6af0b636}} decompositions for two qubit unitaries.
The basic formulation of these techniques is topology
independent. Specializing for topology increases the upper bound by
rather large constants, {{cite:a0196b69ac9db17b32bce236502ed2e5d06d0857}} mention a factor of nine,
improved by {{cite:71857cc3d13291c43e9215e18cb7f23f013d9df8}} to {{formula:b7740831-b9ee-4318-8eed-d3f3ef13363f}} .
The published approaches are hard to extend to different qubit gate
sets and it remains to be seen if they can handle {{cite:00c550ff1fb9419375b07e8fcc6dc54ed8d6c198}} describes a method
using Givens rotations and Householder decomposition. qutrits. Furthermore, it seems that the numerical
techniques {{cite:c427228b3fa99f763cfdc210112017ae0b6f178c}} required for CSD still require
refinements as they cannot handle numerically challenging cases.
Several techniques use numerical optimization, much as we did. They
describe the gates in their variational/continuous representation and
use optimizers and search to find a gate decomposition and
instantiation.
The work closest to ours is by {{cite:57217161c0f85243ab0699869b0e47f1f28ec39d}} which use
numerical optimization and brute force search to synthesize circuits
for a processor using trapped ion qubits. Their main advantage is the
existence of all-to-all Mølmer-Sørensen gates, which allow a topology
independent approach. The main difference between our work and theirs
is that they use randomization and genetic algorithms to search the
solution space, while we show a more regimented way.
When Martinez et al. describe their results,
they claim that Mølmer-Sørensen counts are directly comparable to CNOT
counts. By this metric, we seem to generate comparable or shorter
circuits than theirs. It is not clear how their approach behaves when
topology constraints are present. The direct comparison is further limited due to
the fact that they consider only randomly generated unitaries, rather
than algorithms or well understood gates such as Toffoli or Fredkin.
Another topology independent numerical optimization technique is
presented by {{cite:f244968e89cb335498a4f508e8b28597ede69674}}. In this case, the main contribution is to
use a quantum annealer to do searches over sequences of increasing
gate depth. They report results only for two qubit circuits.
All existing studies focus on the quality of the solution, rather than
synthesis speed. They also report results for low qubit concurrency:
Khatri et al. {{cite:f244968e89cb335498a4f508e8b28597ede69674}} for two qubit systems, Martinez et al. {{cite:57217161c0f85243ab0699869b0e47f1f28ec39d}} for systems up to
four qubits.
Solution Distinguishability:
Synthesis algorithms are classified as exact or approximate based on
distinguishability. This is a subtle classification criteria, as most
algorithms can be viewed as either. For example, {{cite:9dbfe6c00077c0e7c7810beaacbd690a6c5934e7}}
proposed a divide-and-conquer algorithm called Meet-in-the-Middle
(MIM). Designed for exact circuit synthesis, the algorithm
may also be used to construct an {{formula:f2346429-3b34-45af-9de6-f598ccd94574}} -approximate circuit. The results seem to indicate that the algorithm failed
to synthesize a three qubit QFT circuit.
Furthermore, on NISQ devices, the target gate set of the algorithm
(e.g. T gate) may
be itself implemented as an approximation when using native gates.
We classify our approach as approximate since we accept solutions at a small distance from the original
unitary. In a sense, when algorithms move from design to
implementation, all algorithms are approximate due to numerical
floating point errors.
Conclusion
In this work we have shown methods to compile arbitrary quantum
unitaries into a sequence of gates native to several superconducting
qubit based architectures. The algorithm we develop is topology aware
and it is easily re-targeted to new gates sets or topologies. Results
indicate that we can match, or even improve on when topology is restricted,
the shortest depth
circuit implementation published for several widely used algorithms
and gates. We also show empirical evidence which supports an important
conjecture: the benefits of incorporating topology directly into
synthesis cannot be replicated if relying on all-to-all synthesis and
traditional (peephole base) optimizing quantum compilers or mappers.
The method is slow but it does produce good results in
practice. For the early NISQ era, which is likely to be characterized
by hero experiments, the overhead seems acceptable. Even when
superseded by faster algorithms, we believe our results provide a good
quality measure threshold for these implementations.
Looking forward,
better numerical optimizers are required for enhancing the
palatability of quantum circuit synthesis. These will alleviate some of the
need for developing better search algorithms.
| d | 5bd05b28706dedb8c34c36856f4f5b10 |
with {{formula:381c111e-af73-4466-8ded-0a9a6ece52cd}} .
Since {{formula:709ad536-c18e-4175-89db-eda972f5272c}} is a polyhedral cone, it follows from Proposition 4.1.4 of {{cite:f8e55bb6c10abf6d69321b99f26ae338d7c372e0}} that there exist {{formula:0cb0271e-5582-43fb-a8b5-449236cb6521}} orthogonal projectors {{formula:0878c008-9f92-4bf7-b873-cc5a729ad506}} such that
{{formula:5945ce20-7b49-4630-bf4d-320c55472b96}}
| r | f79fd1ed94d3380a48ad9f04f61062c3 |
Applying Theorem REF -REF to the graph {{formula:c434176e-66a9-46d2-abfe-5e319990b0de}} with the ECP, {{formula:03097a7f-4698-4dda-9390-f27ebe3c28c6}} , of Example REF , it
follows that its least eigenvalue {{formula:591b3108-9ec4-47ad-ae5f-9c72dc1fbbf2}} is not less than {{formula:30bd7b18-8d84-4bfa-b9d0-0717ca27e8fd}} . Furthermore, since the necessary and
sufficient conditions REF and REF of Theorem REF are not fulfilled in the ECP, {{formula:a65d6189-d8ec-4ca6-b031-ee343eb56d1e}} (actually, {{formula:ddb9163f-7fe9-4c8b-9458-39cb2f33b37d}} does not have an ECP fulfilling the necessary and sufficient conditions of Theorem REF -2), {{formula:7f1bf520-50c7-4637-8ae7-cfb61e6335e5}} . Additionally, there is no induced subgraph {{formula:37dedfe3-5595-4e9e-ace3-d9c0e9948a6a}} of {{formula:d2d65273-2925-4c36-be0c-25a860ca86db}} with an ECP, {{formula:967d6c10-ea17-42b5-8ef9-e86941e0923b}} , such that its least eigenvalue is {{formula:5b8c14b6-45ce-45c1-9d04-8920ddd1262c}} . Otherwise, taking into account that the eigenvalues of {{formula:358a901c-25f1-44c5-96ce-36ccfeec7a5c}} interlace the eigenvalues of {{formula:31215971-9e2a-49c7-bca6-7c6baefd5be4}} {{cite:afa39a8093c30c4b68dc898684a781f21b8d13a1}}, we obtain
{{formula:9e73d801-c902-400f-8995-8a2be9d2885a}}
| r | f9badeb7b2507c52b131fcd128e7eb1c |
We present a generic optimization framework, called ModelMix, which iteratively builds an envelope of training trajectories through post-processing historical updates, and randomly aggregates those model states before applying gradient descent.
We provide rigorous convergence and privacy analysis for ModelMix, which enables us to quantify {{formula:6d5eecce-22ce-4769-87ad-3b6836611a3f}} -DP budget of our protocol.
The refined privacy analysis framework proposed can also be used to capture the privacy amplification of a large class of training-purpose-oriented operations commonly used in deep learning.
This class of operations include data augmentation {{cite:290350e7798ef14498de32b2519258292d6a05ea}} and stochastic gradient Langevin dynamics (SGLD) {{cite:01d72f1558046b1b133cd187fff8c69c0f71beab}}, which cannot produce reasonable worst-case DP guarantees by themselves.
We study the influence of gradient clipping in private optimization and present the first generic convergence rate analysis of clipped DP-SGD in deep learning.
To our best knowledge, this is the first analysis of non-convex optimization via clipped DP-SGD with only mild assumptions on the concentration of stochastic gradient.
We show that the key factor in clipped DP-SGD is the sampling noise The noise corresponds to using a minibatch of samples to estimate the true full-batch gradient. of the stochastic gradient.
We then demonstrate why implementation of DP-SGD by clipping individual sample gradients can be unstable and sensitive to the selection of hyper-parameters. Those analyses can be used to instruct how to select hyper-parameters and improve network architecture in deep learning with DP-SGD.
ModelMix is a fundamental improvement to DP-SGD, which can be applied to almost all applications together with other advances in DP-SGD, such as low-rank or low-dimensional gradient embedding {{cite:9b6237f14d13d537fb8ab7f4c77c753c058d208f}}, {{cite:42c8a2d9c7278414872d9588c36f267fb385215d}} and fine-tuning based transfer learning {{cite:3df5630fdef7cca4277ccb3c18da1b52f5b8e55b}}, {{cite:a189d81d53080435c037162b606b4622d07e397d}} (if additional public data is provided).
In our experiments, we focus on computer vision tasks, a canonical domain for private deep learning.
We evaluate our methods on CIFAR-10, FMNIST and SVHN datasets using various neural network models and compare with the state-of-the-art results.
Our approach improves the privacy/utility tradeoff significantly. For example, provided a privacy budget {{formula:bed5b66e-7440-446d-b0f7-0f55c2ecce22}} , we are able to train Resnet20 on CIFAR10 with accuracy {{formula:69620384-539c-4705-9468-8a4b1fdfe146}} compared to {{formula:de8c71c6-580e-4913-b150-447a49c05e45}} when applying regular DP-SGD.
As for private transfer learning on CIFAR10, we can improve the {{formula:f9e6e88f-9bdd-434e-8156-7158509c74b2}} -DP guarantee in {{cite:3df5630fdef7cca4277ccb3c18da1b52f5b8e55b}} to {{formula:d94b298e-c94d-4642-a9fe-adeb3c445225}} producing the same {{formula:076cc745-c785-49df-a69e-2339e9529e99}} accuracy.
| r | ee1bb52d62db0ebc7f3ea874bc740f9e |
Partition methods for long-tailed FL
To create different federated (distributed) datasets according to the different patterns of local and global data distribution, different datasets and sampling methods are required.
Data distributions in Type 1 could be realized by IID sampling on long-tailed datasets.
Similarly, Type 2 could be achieved by Dirichlet-distribution {{cite:057cbaff0bc5b029d0d3477cb3885555704aae8c}} based generation method on the long-tailed datasets.
Specifically, the degree of the long-tail and the identicalness of local data distributions could be controlled by the global imbalance factor IF{{formula:80c3a918-1fb3-4352-8424-7ef38f66fa99}} and the concentration parameter {{formula:5cdda2d9-5235-4588-9606-fd8e15bc172e}} respectively. And Type 3 could be realized via the different long-tailed sampling (different head and tail pattern) on the balanced datasets.
| m | 88776699a0a9ae79de745999770927b9 |
As with any DML technique, our approach covers the following two major aspects of DML: 1. Constraint Mining: To appropriately mine constraints of examples (eg., pairs or triplets), and 2. DML Loss: An appropriate loss formulation to learn a metric using the mined constraints. In the recent years, a huge number of supervised, state-of-the-art DML techniques have been proposed: Tuplet Margin {{cite:659895afbaba1fc653ac5fdc3208919353a38213}}, Multi-Similarity {{cite:ff047f09a8f91b99446f6dedc2e2499e7b911845}}, SNR {{cite:d5c20cb07320fc4ab7763f62bcec1112b131fdb4}}, Circle Loss {{cite:3ae4a774ce7196ef616cb87c08089732357931f6}}, FastAP {{cite:c8309f7118697a1fe19ec777d8fd772f24fd3911}}, ArcFace {{cite:4f9ddf9058f86217a385af619fb2cc794b50ef05}}, Soft Triple {{cite:c8d53cacf5753e720103a533274f8be2ae5c0296}} etc. All of these approaches have made contributions either in terms of constraint mining, or a novel loss.
| i | 9ccd49f27e9e869682200ae2c6cd9616 |
We evaluated the anomaly segmentation performance between the proposed method and the existing SOTA methods mentioned in section 4.3.1 using the MVTec AD dataset. As shown in Table 1, the proposed method consistently outperformed all other existing methods evaluated in AUROC. The reconstruction-based methods such as {{formula:938fbebe-87a3-40f7-ad0e-309a326681d4}} used the reconstruction loss as the anomaly score. {{formula:c4d9096c-b782-4646-a291-c79c69504ac4}} had lower performance (0.82 AUROC) compared to the proposed method. CAVGA ({{cite:c410276dc6435fe7fece53b01dcff41ceb9a7b0d}}) and Cutpaste ({{cite:835489e4197c25dc08670d882d9eaa0e420ead6f}}) obtained anomaly maps using GradCAM ({{cite:95177c9c956e4d119e72f15306da20357d26e663}}), but these anomaly maps highly depend on the classification loss. In addition, compared to the methods using patch image representation such as US, the proposed method achieved higher performance. As a result, AnoSeg outperformed the conventional SOTA, such as Patch SVDD, SPADE, and Cutpaste, by {{formula:820b8ad3-0987-4900-a892-1a0471db9fb2}} AUROC in anomaly segmentation.
| r | 4e1386158f1f61b8ebe6f756ac14d4d3 |
Continuing to MIM, the advantages of HiViT become clearer.
With 800 epochs of MIM-based pre-training and 100 epochs of fine-tuning, HiViT-B reports {{formula:39646a7b-d071-4f29-b565-b04bd1acb710}} top-1 accuracy on ImageNet-1K, which is {{formula:a62cd601-8762-4792-b40a-dc67442220e8}} over ViT-B (using MAE {{cite:0b92cb27cb899a33569d0054e0d285bafa4d09a1}}, pre-training for 1600 epochs) and {{formula:56772df4-c46a-40a1-983c-530da47ea60d}} over Swin-B (using SimMIM {{cite:a1a4eb50becfc44b6b089d0741533d9d722427c8}}). More importantly, HiViT enjoys the efficient implementation that discards all masked patches (or tokens) at the input stage, and hence the training speed is {{formula:bea0f333-fd29-4ddd-8ff5-07e0059d040f}} as fast as that of SimMIM, since the original Swin Transformer must forward-propagate the full token set (Fig. REF ). The advantages persist to other visual recognition tasks, including linear probing ({{formula:84c6f8bd-dea1-470f-83f0-873afc34897f}} top-1 accuracy) on ImageNet-1K, semantic segmentation ({{formula:2efac518-30f9-47a7-afec-6d44787a77a9}} mIoU) on the ADE20K dataset {{cite:6f22fd952ada1220bfa79ba74181009a174975e9}}, and object detection ({{formula:7f5c18bf-acc6-4108-b910-76f4332fe633}} AP) and instance segmentation ({{formula:c22b6621-3616-4608-9e4e-627285088ae1}} AP) on the COCO dataset {{cite:2dd5ca925f7e84fedf436f548646f7d01d76d0fd}} ({{formula:b4d5c055-6ea8-466d-b5e0-f36266049429}} training schedule). These results validate that removing `local inter-unit operations' does not harm generic visual recognition.
| i | 0eb1c1dd9e911214b58db062b9670ca4 |
In recent years, a new class of higher derivative theories has been discovered that is ghost-free and in four dimensions neither topological nor trivial known as Generalized Quasi-Topological Gravity {{cite:f51fdfdde18dffb6e68aeb8345574446ab198910}}-{{cite:e06acbb576444f695d10e766c6eb9ebd694f1ca7}}.
One of the such higher-derivative gravity theories which in the four
dimensions is neither topological nor trivial is Einsteinian cubic
gravity. This theory of gravity, that has been recently proposed
in {{cite:a248788efd483a4333bd3f2fc23b88a3d5fe2d40}}, is the most general up to cubic order in
curvature dimension independent theory of gravity that shares its
graviton spectrum with Einstein's theory on constant curvature
backgrounds. The Einsteinian cubic gravity field equations admit
generalizations of the Schwarzschild solution, i.e. static,
spherically symmetric solutions with a single metric function
{{cite:2c68d6f6d0deca088964f864ac311de21c16da09}}, {{cite:66a6a065cb681f3c61704f986f658e1f60b4befc}}, {{cite:4a0e64ffd7cdfca1c09a279fe4bc04ec7d4f8a79}}. The
Lagrangian density of this theory is given by
{{cite:2c68d6f6d0deca088964f864ac311de21c16da09}}, {{cite:256d15cdc348868a856910541c648442adb8ee4d}}
{{formula:3d800a27-7697-459a-9a11-0219c549e48f}}
| i | e7ea1a9cb2ed2fe82a3c5a313e32739a |
The encoder in EDNet is a VGG-16 {{cite:d8363c5ecde3b05f75e9b2e1032d12d741a4ccfd}} with the pre-trained weight on ImageNet {{cite:4b8a12f427b5353da7b6c6947a705e6262ba3391}},
which has five Convolutional Blocks (CB) and thirteen convolutional layers. Each CB's output is an input to the next CB through a pooling layer with a stride of {{formula:00e330c9-7da3-4c75-bdfd-875763cb25e6}} . Hence, the encoder's output feature map has a resolution of {{formula:d655c521-fdf5-4dea-9cfe-a2ab6dea4611}} for an input resolution of {{formula:7be0518c-d03f-4cc1-b3f3-ee62d6e44779}} .
However, the decoder has five blocks to obtain the input resolutions of the output WHS masks ({{formula:d567d7ca-e8a4-4b98-ae82-69e8f447dc32}} ), where we apply 2D upsampling, with a stride of {{formula:69781d9f-a0c2-4d60-b9aa-38383578b9db}} , convolution with a kernel of {{formula:28721caf-f80b-4693-bc05-8c89f55a87a8}} , and a batch normalization {{cite:d87da151dd96ec4dbb8bc61cba12ed1929da4ee4}} in each decoder block.
| m | 7be1ef7d398dcfa78dfd1573f7794684 |
it leverages the functional oracles of the donor tests.
CraftDroid and AppTestMigrator explore a GUI model of the recipient app to find a sequence of events that maximize the semantic similarity with the events of the donor test.
They compute the semantic similarity of GUI events using word embedding {{cite:3a5bc58e32388bc60591a79cdb90122b5cca2fcf}} applied to the textual descriptors of events extracted from the GUI widgets.
Both techniques greedily explore a single test adaptation scenario, missing the many alternative adapted tests that could be generated starting from a same donor test.
Indeed, extensively exploring the execution space is often imperative to identify a sequence of events that well reflects the semantics of the donor test.
In this paper, we present AdaptDroid, a technique that formulates the GUI test adaptation problem as a search-problem using an evolutionary approach.
AdaptDroid explores the huge space of GUI tests with a fitness function that rewards the tests that are most similar to the donor test.
The AdaptDroid notion of similarity
considers both the semantics of the events and the capability of the adapted test to reach states where the donor oracle can be applied to.
We implemented AdaptDroid in a prototype tool, and evaluated with a human study involving 32 Android apps.
Our results show that AdaptDroid successfully adapts semantically relevant GUI tests in 11 out of 20 test adaptation scenarios. Thus confirming that test adaptation is a promising and complementary solution for generating GUI tests.
{{figure:089cf1e0-57c9-43a1-99b5-1ea9454d7027}}In summary, the main contributions of this paper are:
[leftmargin=*]
formulating the problem of adapting GUI tests across similar applications as an evolutionary approach,
proposing AdaptDroid, to adapt both GUI event sequences and oracle assertions across mobile apps,
presenting the results of a study showing that test adaptation of Android apps is a valuable opportunity,
presenting an empirical evaluation of AdaptDroid that highlights its effectiveness and limitations,
releasing the AdaptDroid tool and all experimental data {{cite:2785827261989008a5fa25a3b2b1d80e6b576364}}.
Adapting Tests Across GUI Applications
GUI applications interact with users through a Graphical User Interface (GUI) {{cite:10277907a9acc3a9ab1875095372d0447d18cd66}}.
A GUI is a forest of hierarchical windows (activities in Android),
where only one window is active at any time {{cite:0029a4078b6b717fc1f10ef716f883bad6375d91}}.
Windows host widgets, which are atomic GUI elements characterised by
properties: type, displayed text (if any) and xpath (a label that uniquely identifies the widget in the structural hierarchy of the window {{cite:c602bfca40e361669b919e3b9f0736e3ffea1a0c}}).
At any time, the active window has a state {{formula:1858ff52-bd8b-4547-8cca-62e79e474399}} that encompasses the state (properties values) of the displayed
widgets.
Some widgets expose user-actionable events that users can trigger to interact with the GUI.
For instance, users can click on widgets of type button or can fill widgets of type text field.
A GUI test {{formula:f95dc767-2311-4f0e-922e-0b840c9a4622}} is an ordered sequence of events {{formula:d2fbe083-1445-4b45-9a45-28397f6b82c3}} on widgets of the active windows. A test execution induces a sequence of observable state transitions {{formula:b932390e-78b0-4333-b371-2179f5178314}} , where {{formula:92d68da4-f65c-4560-b01b-d80cfd30f804}} and {{formula:97dcf2b6-28e4-4c38-bac1-1de767ba0a1f}} denote the states of the active window before and after the execution of event {{formula:82996894-bd78-4853-88fd-b103e47edbe6}} , respectively. An event is an atomic interaction on a widget. Events are typed. In this paper, we consider two common types of events
[-,leftmargin=*]
click({{formula:6aae7778-0a60-45b3-93e8-e176e8430d6b}} ): clicking a widget {{formula:1e7e4d46-3435-4e99-b3f8-430b8b5c39e5}} ;
fill({{formula:c4ef347c-4898-4a4e-b826-aa2b79a9e4ac}} , txt): filling a string txt in widget {{formula:df0c9cde-e844-4806-9832-b69283514f48}} .
Each test {{formula:7a587592-2d2f-460f-b160-f05d663fdb06}} is associated with one or more assertion oracles {{cite:3a29b0a4cdf38a782b41bb37091b3a175ac39c6c}} that check the correctness of the
state {{formula:1b9a49af-f11c-4842-b269-03e8956105ec}} obtained after the execution of {{formula:6f6862c6-bcf4-4d84-94fc-35265b52f7fd}} {{cite:8e0d2da0f336baa9d9f0f3a2c4adce1c7400835f}}.
We use {{formula:53dded41-d1cd-4d58-8ba3-127704b17cfe}} to denote the assertions associated with the test {{formula:d8c69f93-e12c-4718-9ff8-8292063d7576}} , and consider two types of assertions:
[-,leftmargin=*]
exists(txt) checks if {{formula:0a5d0ef7-a99e-4c53-b2dc-3fec9bb4ad16}} contains a widget with text txt: exists(txt) {{formula:24f598aa-5930-400b-8bec-40e62b44c0eb}} txt;
hasText(w, txt) checks if {{formula:581fb084-5f02-4d62-a7c6-eea2ac746196}} has a widget {{formula:9927c9e8-ccbf-49c7-b344-7432009be399}} with text txt: hasText(w, txt) {{formula:2144875f-b618-439a-91fd-cff68a3da76a}} {{formula:8cb8c85c-774f-4847-bfe1-7b20e9bcf64e}} {{formula:5e57c2a7-d7c4-406d-a532-3b1a5e6ffce0}} txt.
This paper presents AdaptDroid to adapt GUI tests (including oracles) across interactive applications that implement similar functionalities. Given two Android apps {{formula:d209907f-02a2-4c18-8d5a-f238e7b10d3c}} (donor), {{formula:0267d961-e17f-4d3b-98cd-448f31bf15d7}} (recipient), and a “donor” test {{formula:be7c3bad-3b3c-4cf2-bcb2-480740540f17}} for {{formula:f1ad60f7-256a-4033-9e11-f0ba7a917209}} , AdaptDroid generates a “recipient” test {{formula:8e22ee33-1a2c-4439-a5ad-1fa2366703fe}} that tests {{formula:17103a47-6b03-46fb-9f1e-85cadd2c3760}} as {{formula:42969547-15ad-416e-b684-e5505ef5509b}} tests {{formula:8a1d8cb5-ea63-4b53-b36d-d7a37ce443a7}} .
Working Example
Figure REF introduces a working example that illustrates the challenges of adapting GUI tests across similar applications.
Figure REF A shows a donor GUI test ({{formula:05a46a16-07a1-4f7f-90cb-1921bdd7972f}} ) designed for Splendo, an Android app to manage tasks lists.
The test adds a new task to a task list, and verifies that the task disappears once marked as done.
Figure REF B shows how AdaptDroid successfully adapts {{formula:25786d6e-57c7-4cfc-8ad1-3fe2858fbdb1}} to the recipient app Bills Reminder ({{formula:6cfe6b7f-0fe6-4473-be20-d5c5ad9b447e}} ), by generating {{formula:4019b4eb-668f-4034-aa56-8c9ab2086517}} that adds a new bill to the bill list and verifies that the bill disappears once marked as paid.
Although the two apps belong to different domains, they share
the logical operations of creating a new element (a task in {{formula:2425ba85-a213-4fa1-978c-1b807477c6aa}} , a bill in {{formula:2f20c953-baf1-4516-86e6-742e6280d4f1}} ) and marking it as completed (done in {{formula:f7c62b43-ca5e-4181-a073-e91b1013787c}} , paid in {{formula:52c318ee-3fd4-4e3e-a7ec-058ca597cecd}} ).
Automatically adapting GUI tests across apps presents three main challenges:
1) Huge space of GUI tests The space of the possible GUI tests grows exponentially
with both the length of the donor test and the number of widgets in the recipient app {{cite:4731dfd46e1b58b435b13760eed158092482ff2a}}.
Adapting tests requires an effective search strategy that recognizes the relevant GUI events in the recipient app.
2) GUI differences The donor test may exercise GUI widgets that are logically
equivalent but very different from the widgets of the recipient app.
For instance in Figure REF , semantically similar widgets are labelled ''What is to be done?''{{formula:a5dc6ddd-a6be-4906-983d-9ff96bcaccaf}} ({{formula:b652dd91-5b5b-47f4-9c1b-939434f65ffe}} ) and
''Payee/Item''{{formula:b2e1dc99-396f-4af9-8f64-d3783698a1dd}} ({{formula:78ab4f05-7a9f-425c-82d2-f747c3d000fd}} ), respectively. Also, Splendo uses a tick mark button ({{formula:e25cd37f-02c0-4f56-beaf-74f060fe9a00}} ) to save a task, while Bills Reminder uses a floppy disk image button ({{formula:b535bc0f-01b1-4603-a277-f7d197c51e28}} ).
3) No one-to-one GUI event matching The donor and adapted tests might have a different number of events.
For instance, in Figure REF the donor and recipient tests have four and seven events, respectively.
Creating a bill in Bills Reminder requires more events than
creating a task in Splendo.
Marking a bill as paid in Bills Reminder requires a date, while marking a task as done in Splendo does not.
The next Section presents AdaptDroid and discusses how it addresses these challenges.
AdaptDroid
{{figure:358d5e81-1caf-4b6f-b482-ebc7a248fcf1}}Figure REF overviews the AdaptDroid process.
AdaptDroid takes as an input the APK of a donor application {{formula:d2442fda-acc1-4bf5-9b09-5ad57521f5a7}} , a donor test {{formula:8a17adf2-cf92-49a7-9689-2f21d385cdcf}} and the APK of a recipient application {{formula:46cd6c9f-fb7f-40fc-8b26-614c00450185}} , and generates a test {{formula:5d1f574f-9df8-45c5-809a-0aa0ca3bad4d}} for {{formula:41e9543f-5100-4fac-999b-f6da84d02cfc}} .
AdaptDroid adapts tests in five phases. The Semantic Information Extraction phase executes {{formula:910a3693-80de-4648-afd9-5539706db46c}} on {{formula:edee03b9-efd9-46bc-844a-dabeb9e0e93f}} to extract semantic information relevant to the adaptation process, such as the semantic descriptors of the widgets exercised by {{formula:56e95b4a-af64-454f-b8ed-68c34f947f0d}} . The Initial Population Generation, Fitness Calculation and Population Evolution phases implement an evolutionary algorithm that evolves a population of GUI tests guided by a fitness function that steers the evolution towards a test {{formula:a72a7cb8-f8e4-4aab-955a-4545c8c5f3bd}} as similar as possible to {{formula:93a7ca90-efac-4ef6-9249-962e15883b75}} . The Population Evolution and Fitness Calculation phases iterate until they either perfectly adapt the test (fitness = 1.0) or a time-budget expires.
The Test Reduction and Oracle Injection phase removes irrelevant events in {{formula:cf4fae1c-a154-4ceb-86b4-c7c0411c497c}} and adds to {{formula:f0dc8172-3c0c-4961-98b7-208640ea1289}} the oracles adapted from {{formula:d798cf5f-b97a-4a6a-a0a0-18e07bd19f7a}} .
AdaptDroid faces Challenge 1 (huge space of GUI tests) with an evolutionary algorithm equipped with a proper set of evolution operators; Challenge 2 (GUI differences) with a matching strategy that takes into account the semantics of GUI events; Challenge 3 (no one-to-one GUI event matching) with a flexible fitness function that captures the different nature of the donor and recipient apps.
The following subsections describe the cross-app semantic matching of GUI events and the five AdaptDroid phases.
Cross-app Semantic Matching of GUI Events
AdaptDroid matches GUI events across applications according to their semantic similarity, regardless of syntactic differences, such as, widget types, positions and layouts.
This is because two similar apps may implement operations that are semantically similar but syntactically different.
AdaptDroid encodes the semantics of an event as an ordered sequence of one or more words, a sentence in natural language, that we call descriptor. AdaptDroid extracts the event descriptors from either the information shown in the GUI or the identifiers defined by the programmers (widget ids and file names).
Given an event {{formula:111c534b-77a9-4d6b-aa78-bfe20d6128b2}} , AdaptDroid extracts its descriptor {{formula:a63f0483-2d1d-449f-9659-df6e3414ba91}} as follows.
For click events {{formula:b7572935-ad0c-4ec6-8895-fdc81fb8b263}} click{{formula:d53decee-10a8-4a53-aab4-105526c204b7}}, {{formula:74a8c050-7967-4cbe-9612-1556c50e1175}} is the text displayed in the widget {{formula:00befd45-4965-449e-8bba-63984f63ec8d}}
(its text property). In the example of Figure REF , the label of widget {{formula:846a315e-2e74-4e80-82a3-6678a435d795}} ''Test''{{formula:c5a38c7c-96fc-4892-9015-fd092f8a16e3}} is the descriptor of {{formula:4a167844-a5f3-4b97-a7e9-a088714d9b97}} . Similarly, {{formula:52541962-8324-4fb2-a32b-fe8b06a26be0}} ''Test'', {{formula:f29167fe-b285-46b4-89cc-39feb6b7019e}} ''Mark as Paid''{{formula:253b5cd1-5d24-4637-a63e-ae2337dc55b7}} and {{formula:3b491000-2b53-4d60-84c5-0a5d952a9862}} ''8''.
If the text property is empty and the widget {{formula:692358a7-b2f9-456f-9caa-137b57af07b6}} includes an image, {{formula:0b8a7597-2971-4fd9-a79e-428b2990e62b}} is the file name
of the image.
In the example of Figure REF , the name of the image file associated with {{formula:bd9f0e48-5460-46ae-9557-17222b06aaca}} (''bs_add_task'') is the descriptor of {{formula:17bf5007-b515-46bb-b97c-ef0750ed7dad}} . Similarly, {{formula:935de943-c803-45d6-a52a-421ef2b3ff8f}} ''action_save_task'', {{formula:39e00e3f-e077-41e7-aa3f-e133060cb380}} ''action_add''{{formula:70b46906-c281-4d5f-8021-e30702d1bbf6}} and {{formula:4cc6ef78-9d62-49a7-9be4-9aa82e9c860a}} ''action_save''.
To facilitate the matching of descriptors, AdaptDroid splits words by underscore or camel-case ({{formula:0752d354-c0c6-490d-a7f4-ebb13bdcc191}} becomes ''bs add task''),
removes stop-words, and performs lemmatization {{cite:ff8ad5b816836492582ac5aa71fe51d08e22955a}}.
If the text property is empty and {{formula:99c25726-6bd3-41f1-8f21-f7ce9f7b5322}} does not include an image, {{formula:27c5b59a-f3f5-422b-beac-9d07a285d885}} is the {{formula:8364be77-43c3-4bb2-8d15-3fe7ee1223cd}} assigned by the developers to reference {{formula:cb903ec6-7913-4d0c-b1b6-13305aa8d29b}} in the GUI.
For fill events {{formula:9aa0df1c-38e2-4a44-8a1b-812b3228d3da}} fill({{formula:d57b12b3-3dcc-4798-a1f0-19a6e46a4e11}} , txt{{formula:9df64684-8c81-48e4-87fb-5bb90b181eb6}} ), {{formula:50eb34d5-458d-4de7-a8ab-2aa299a55949}} is
the text of the nearest widget from {{formula:514cfa70-3f1b-4d7a-9f2a-d7c88b905f2d}} .
We follow the approach of Becce et
al. {{cite:04f3d48fc61f953463b0554d62b39d17e0e9ece9}}, which is based on the observation that text fields
are normally described by near labels.
In the example of Figure REF , the text property of the label on top of {{formula:49bce311-6c96-4421-ae2f-1aeb6ce6ae7b}} ''Amount''{{formula:effab2e6-fc11-49cf-8963-46cd88c5fde8}} is the descriptor of {{formula:3c627d87-3aa0-4704-8a20-a7885e11957b}} . Similarly, {{formula:a8f71253-4026-481d-aa3e-76cfde87c5af}} ''What is to be done?''and {{formula:06609282-ee41-47d3-be31-86dd629ef59c}} ''Payee/Item''.
If there are no lables near {{formula:6289b826-3653-4c51-9d36-59f6e81fd27a}} , {{formula:62cf6bda-e026-4131-9f06-cb4d06403abe}} is the {{formula:42ce37d6-c4e2-458a-8995-1f3fc65c12a8}} assigned by the developers to reference {{formula:2cb5e0ce-742a-4f93-a0af-88207f9d9a0b}} in the GUI.
AdaptDroid identifies pairs of descriptors that represent the same concept
with a Boolean function IsSemSim(txt{{formula:fb1988ad-32ee-4582-ad2c-e70fbe2ce47c}} ,txt{{formula:61fc57f3-812c-42fa-87fa-691efb929339}} ) that returns ḭf the sentences txt{{formula:2277db9b-f1f8-4e69-ad6c-13cc6ee65492}} and txt{{formula:83725b64-1144-444f-9b93-6443042e1572}} are semantically similar, false otherwise.
The many available distances, such as Euclidean Distance, Cosine Distance and Jaccard Similarity, are ill-suited for our purposes.
This is because they are not designed to overcome the synonym problem,
that is, two sentences have the same semantics but no common words {{cite:3a5bc58e32388bc60591a79cdb90122b5cca2fcf}}.
We cannot expect that two distinct albeit similar apps use exactly the same words to express the same concepts.
Both CraftDroid {{cite:55caa99662f7fcc7520c3cfefa1489ff9ba5f7f2}} and AppTestMigrator {{cite:f69c67d9da399c73a673f8963d10f7a6f1501edb}} address the synonym problem with Word2vec {{cite:3a5bc58e32388bc60591a79cdb90122b5cca2fcf}}, a vector-based word embedding {{cite:3048f09f3b0731585819456565d34111d8e3ef85}}.
Word2vec trains a model that embeds words into a vector space, where words with similar semantics are close in the space {{cite:3a5bc58e32388bc60591a79cdb90122b5cca2fcf}}.
Word2vec matches single words, and thus it is inadequate when descriptors contain multiple words (as {{formula:7c2774e8-21ab-4dc9-a661-44167290a1bc}} ''Mark as Paid''{{formula:49f3888d-8cb7-4115-91d2-6ddbec81cb3c}} in Figure REF ).
Instead, AdaptDroid uses Word Mover's Distance (WMD) {{cite:a7a4706783cf3da05625e8e55554fb9dbb34233f}}, which calculates the distance between sentences composed of one or more words {{cite:3048f09f3b0731585819456565d34111d8e3ef85}}. Given two sentences txt{{formula:7eca7d53-e65e-4547-abf1-14dc78c8eff6}} and txt{{formula:84b3743d-674f-4bd0-9bd7-f4b6088a645b}}, WMD returns a number between 0 to 1 that expresses how close the sentences are
in the vector space {{cite:a7a4706783cf3da05625e8e55554fb9dbb34233f}}.
IsSemSim(txt{{formula:393c190f-3ce7-4527-b8f3-f4b1270c97d4}} , txt{{formula:ac19141d-1059-491a-a7c8-007962ca7670}} ) = if WMD(txt{{formula:c5b4a167-9fd8-4af0-a94c-7780ece69891}} , txt{{formula:653db59c-82a4-4434-89bb-aa615bb21722}} ) is greater than a given threshold {{formula:d8698bd8-c988-4662-8db2-9b9bbcf7fd14}} (0.65 in our experiments), false otherwise.
We implement IsSemSim as a Boolean function with a threshold,
because the WMD distances are not accurate enough to assume that the highest
similarity is the best one {{cite:a7a4706783cf3da05625e8e55554fb9dbb34233f}}, {{cite:3048f09f3b0731585819456565d34111d8e3ef85}}.
For example, two sentences with WMD 0.99 might not be more semantically similar than two sentences with WMD 0.88 {{cite:a7a4706783cf3da05625e8e55554fb9dbb34233f}}.
We now define the semantic matching of events, denoted by {{formula:0e51955a-6b52-4884-a9ec-b87ca4d6ea21}}. Given a donor test {{formula:dafd81fd-92cf-431c-a503-6c15257b7902}} , a recipient test {{formula:09e159e0-76f3-49be-b9c5-4cfb32bbc709}} , and two events {{formula:ac4ccad6-7009-4118-9676-18ea298560f2}} and {{formula:7a2fd0f6-f8da-4421-8738-9d934c418cdc}} , with descriptor {{formula:e93ee394-7712-4180-90be-4e5339da011d}} and {{formula:93eb27ef-77a8-492e-92a4-2f5309b03f7d}} , respectively, we say that {{formula:dd1219eb-eb3b-4311-a4ab-1ff66f6eeeab}} if one of the following cases holds.
Matching click events: {{formula:e72c0372-05da-4380-884e-714e75cee6b1}}
This is the case of clicks events that execute a similar functionality.
Matching fill events: {{formula:a14fde0a-c558-406a-850d-fe2aa19f8769}} {{formula:936c0b17-8f0c-47c3-9053-d8fc983433aa}} txti=txtj{{formula:a7c23b82-d17a-4637-a6db-10b066db1889}}
Matching fill-to-click events: {{formula:459cc09d-ad1c-4e5c-8874-b8c42cefbb17}}
This is the case of a fill event in {{formula:37cc6710-5174-4932-afb2-d8ffe5f02170}} that can be mapped to an equivalent click event in {{formula:c384b081-c7f8-4209-817e-08c19d95413e}} . For example, entering the value ''1''{{formula:3494452a-a2b5-42dc-a887-96e7759714cb}} in a calculator app can be mapped to clicking the button with text ''1'' in another calculator app.
The reader should notice that
we do not allow the opposite, that is, mapping click events of {{formula:a59f5386-aec7-47dc-a6d3-eec38eacb351}} to fill events of {{formula:b168a7e8-2970-4588-ae32-da71060e8ba4}} . Otherwise, AdaptDroid could easily (and incorrectly) map a button click in {{formula:031af4c4-221d-4877-9a7e-c46c388a996e}} with an event of {{formula:992ff028-e022-41dc-b4de-575f40b01d3c}} that enters the label of the clicked button in an input field.
In the example of Figure REF , AdaptDroid matches the events in {{formula:bd02ee1f-3cd6-4cbe-8718-849fb6b500b0}} with those in
{{formula:b5ec5a89-7ed6-428f-92f9-ada0519674e3}} as follows:
{{formula:0273d5ad-e7f6-4245-930b-185b657f8354}} {{formula:429e4391-6117-4f7a-9626-470e51b5d28f}} {{formula:8d56412a-d4bc-4fc8-9b8f-584934b7e1e1}}
{{formula:09d25188-28b3-414f-b741-448f363548b0}}
Semantic Information Extraction
This phase executes {{formula:b11abd6d-5c34-4e5e-97b4-17765d52c905}} in {{formula:93c76a22-fbb3-4cfa-becc-f9d3180c0236}} to collect the following information, which are required by the next phases.
- Oracle assertions. For each oracle assertion in {{formula:51666c5a-a07c-4f69-8136-168af954c20f}} , AdaptDroid logs both the state of the widgets, when each assertion is checked, and the expected value of the assertion.
- Events ordering. Obtaining a meaningful test adaptation that preserves the semantics of {{formula:74455094-5804-49bc-b176-6fe87d4eae38}} may require that some events are executed in a specific order. Conversely, certain events may follow alternative orders without affecting the semantics of the test (such as, the fill events that fill a form). AdaptDroid identifies such events to avoid unnecessary constraints on the events ordering while generating the adapted test.
To identify the opportunity of re-ordering events, AdaptDroid checks if each pair of consecutive events {{formula:33cd9230-b029-4721-8f71-6f1995946d48}} and {{formula:bfb7d6cd-99fd-4f5e-b029-d88fea11c37f}} in {{formula:57095f21-4dd2-4109-94f8-93d2020345dd}} could be potentially executed in the opposite order. Let us consider {{formula:cb4b3709-dfd3-4551-a96d-a9e29f32da9b}} {{formula:61416972-ff03-4061-bf8c-d1dd8f7401d9}} {{formula:523e9db8-2cc3-427c-a26a-7eb29b4716fa}} , which indicates the sequence of states traversed with the execution of events {{formula:2ebb3c2e-232a-4497-a218-a2c5d5702f39}} and {{formula:9f082a3a-d8b4-48dd-8531-986195166d50}} . We say that events {{formula:59258412-9c29-4d64-9984-fe7bfbf7b226}} and {{formula:b63fae36-6ecf-4aea-8fba-49326b338c84}} can be reordered, denoted by {{formula:2deac902-3fcf-4e2e-aff2-ffc8c649197f}} , iff {{formula:b09cef76-d072-40c2-8368-3095b051ac60}} is enabled in state {{formula:8d892b98-c7da-4dcd-a9c3-a487ee6febc1}} and {{formula:f38cb0ff-067d-4b8a-b28e-80a8afe30a5b}} is enabled in state {{formula:32fc2992-926d-4bdf-aa1c-0e42cd8153b6}} . We say that an event {{formula:1302004e-f6b4-4495-a3d1-0b2b8fed91f0}} that interacts with a widget {{formula:ac0c5061-5619-42a5-8004-5700dfd70c53}} is enabled in a state {{formula:a3e5c981-0c9b-4aa1-bd2c-e4c5800ea75c}} iff {{formula:c04ae8d8-40c0-46bb-a97f-37209ac10e74}} contains a widget {{formula:a239df75-5d58-44f6-8828-ecb4991a582c}} with the same xpath of the widget {{formula:f8cdcd56-3283-415f-af6d-26f63d0d832c}} and {{formula:0835b836-7091-4920-bb0e-614feacf876f}} is interactable.
We define the cluster of the events that can be arbitrarily reordered as the set of consecutive events that can be reordered.
Formally, given {{formula:4b9c3676-4eee-4102-bb59-e3413e1a2d53}} {{formula:4bd5e4be-f8e2-4ebd-9d88-4b9443b56ba0}} , the corresponding cluster is {{formula:ce53226c-5a04-4dc8-839a-3f643257483b}} . We also say that {{formula:8c8ea7b4-186d-4f3c-8aea-d4134a76e65b}} . We build the clusters by checking each pair of consecutive events to guarantee a linear time complexity with respect to test length.
For instance, {{formula:b0ac1931-fe59-44f5-8a61-74bf44e269bc}} in Figure REF has
four clusters with a single event each, indicating that the prescribed order is the only possible one.
To facilitate the definition of the next phases, we introduce the Boolean function isBefore{{formula:bff4b4ab-17b0-48c4-9e31-5e8bd77f7d1f}} that returns ḭff {{formula:bbf3fadf-9fac-47e6-8798-28b7ce40a162}} ({{formula:fe0fda6e-b20c-4934-859f-e0f879b0286b}} must strictly precede {{formula:4bd995f2-3bcc-46b1-a03f-ee3829209a5f}} in {{formula:b9a9b6c6-a62e-4412-bafd-7ce12606071e}} ), false otherwise.
Initial Population Generation
Any evolutionary algorithm starts by generating {{formula:d025384a-50fd-44e8-b6fe-5a5d769d060b}} the initial population of {{formula:a32d5585-e45e-44ad-a4f6-7c2e48116112}} individuals {{cite:7a788681eeedba5cde162d01cf6b35b4023dceab}}.
An individual for AdaptDroid is a test {{formula:90009126-6e50-48b9-a635-35498b1523fb}} for the recipient application {{formula:e274ef6b-6af5-4c6d-a39e-5bea650e7aae}} .
AdaptDroid populates {{formula:731ef2cb-2e76-494a-bb7a-774a0646a405}} with {{formula:42e42f7a-9728-4c95-a6e4-649137675030}} randomly-generated tests (to guarantee
genetic diversity in {{formula:a9582c4e-399b-4423-9f23-df23291aac19}} ) and NG tests ({{formula:3259c2a9-dd3f-47d7-9def-971f15774872}} ) generated with a greedy algorithm that are similar to {{formula:df5bb5b1-8644-4bf8-91ea-4f6a3288eaa3}}
(to have “good” genetic material for evolution).
AdaptDroid generates random tests following standard random approaches {{cite:5e3014701c166f2a797ef600ce8bb52a5acb420a}}.
Specifically, AdaptDroid generates a random test {{formula:925d57d5-d501-46e4-a124-aee36581730b}} by opening/restarting {{formula:54df0302-c38c-46f1-a28d-80c1acc6f017}} to obtain the initial state {{formula:ddf15df7-019f-46f4-aa4e-c4d31406f4ae}} , and repeating the following three steps until {{formula:82296ba5-2c88-46c6-90c5-cd6d306ef568}} reaches the maximum length {{formula:c4047b25-07ac-432f-a520-74277bc927c8}} :
[(i)]
it randomly selects an event {{formula:a3f9d272-8c2f-496b-95a7-fe6a1734101b}} from those enabled in the current GUI state {{formula:a29a8a81-c67b-4470-aeb9-14fc09f2142c}} ;
it appends {{formula:c55bb1e9-a92d-46bb-940f-013be460eff0}} to {{formula:c938b68e-f4a1-495d-bc20-b27fc8de3f48}} ;
it executes {{formula:4590d5b2-3e6a-4d97-a6e1-9e209dd473bf}} obtaining the state {{formula:db050712-d78c-42e5-89ac-4490147673f7}} .
The greedy-algorithm chooses an event {{formula:6100296e-2f1f-4ac8-9b0a-2a1d47da6c15}} among the events that semantically match an event in {{formula:2397c529-e9e9-4116-8788-5a635068178b}} , and then executes step (ii) and (iii) of the random-algorithm.
In details, step (i) of the greedy-algorithm selects an event {{formula:4710d3e9-f823-4bae-9648-746760b720ac}} from the set {{formula:1e4d03eb-c4e9-4b7d-89f4-0794744cc9b2}} . If this set is empty, it selects an event at random.
Fitness Calculation
At each generation gen of the evolutionary algorithm, the Fitness Calculation computes a fitness score in [0,1] for each test {{formula:246f3bd8-fc1d-4288-ad53-bc063f70c946}} in {{formula:b760dcc2-2df3-47aa-88c2-96445c23e67c}} .
The score characterizes the similarity between {{formula:921ed0d2-8f59-4032-9a0c-619200b0dd38}} and {{formula:fb35c8aa-41c8-435e-9c83-e0cceec5f623}} , and guides the exploration of possible test adaptations. AdaptDroid computes the fitness score by executing each {{formula:7d6260ff-362f-4f97-b063-c8a8efd42ed0}} in {{formula:fe724c3e-5c01-4678-9546-11b4fab70d8f}} and extracting the event descriptors and state transitions.
While executing the tests, AdaptDroid also updates a GUI model {{cite:0029a4078b6b717fc1f10ef716f883bad6375d91}} that encodes the sequence of events that trigger window transitions.
The definition of such a model follows the one proposed by Memon et al. {{cite:0029a4078b6b717fc1f10ef716f883bad6375d91}}. AdaptDroid uses this model in the Population Evolution phase to repair infeasible tests.
We define the fitness function of a test {{formula:ed70457e-e103-4f22-92c1-8eeebe8e5165}} , by considering
[(i)]
the number of events in {{formula:06c245e0-a41f-4806-8829-7374952dbdc1}} that semantically match the events in {{formula:8d6950f1-4e7d-4cd2-8d29-454774dca6b0}} (similar events), and
the number of assertions in {{formula:55e16abb-2fbe-4938-b3f1-c4728dcbde57}} that are applicable to the states reached by {{formula:d4110711-9bee-4c51-9525-769790bb059b}} (applicable assertions). Intuitively, the higher these numbers are the more successful the adaptation is.
Similar Events
To compute the number of similar events for each test {{formula:b37280fe-850b-4e61-9e21-fa5d9b17083b}} , AdaptDroid maps the events in {{formula:48882146-1d43-4276-b93e-e700a7c448ea}} to those in {{formula:7edc227d-e69e-4b94-bd52-633b2f594c78}} using the semantic matching (see Section REF ).
Let {{formula:900dc69a-e594-4ccd-9a17-a5fa903c6db5}} denote a binary relation over {{formula:9a803e3b-08b9-4700-8389-a78533898107}} and {{formula:8c1c5694-43e6-46d4-beee-5a0bca6ffdaa}} , that we call mapping, such that each pair of events semantically match. That is, {{formula:6f1ad86d-57c0-4c67-a35b-9b30d925fa6a}} is a set of pairs of events {{formula:9f1da212-a93e-466a-a333-3a5e67049012}} .
An event in {{formula:398dcbbb-36c9-4fbb-87eb-71e4c5b263ee}} can be mapped to multiple events in {{formula:3b2456b1-7e5f-46d6-8ad6-0f72f8f2fad3}} .
For instance, in Figure REF {{formula:81c50342-ad1d-4ad4-96b8-f6183578057f}} maps both {{formula:8f7e41b9-28dd-4a78-8d96-f875b97f6f48}} and {{formula:d62595c6-e3bf-4e62-989a-7d9e0b33f783}} . We use {{formula:8674edc6-2dd9-4bfb-bec4-01baed5006d6}} to denote all the possible mappings between events in {{formula:12745dce-3037-4d43-81b0-074e378f3778}} and {{formula:b0aa225f-a344-49e0-afac-729c8ad315a9}} .
Many mappings in {{formula:29450b84-e02c-4002-b5bf-e69de850fe5f}} could be invalid. A mapping {{formula:6d90e7b1-f5dc-47e3-840f-d02e91262b9b}} is valid iff all the following three criteria are satisfied:
1) Injective matching {{formula:73137547-c12b-4ccf-9a29-b6153b53ca44}} does not contain any event in {{formula:ebc4eb1c-1563-4cc1-8910-6b30bddc40e9}} that relates with more than an event in {{formula:bc7e56b0-f44b-4be1-9edc-46cd95225e4c}} : {{formula:eb590791-3fb0-4b12-8a6b-71f8ef220aee}} and {{formula:eaebafd4-a7bd-4d91-9577-5260929118f2}} , if {{formula:efd45930-685b-4027-a60d-4366b2a3a41c}} , then {{formula:77c8738e-3635-407e-ac56-f21026568d78}} ({{formula:000d481f-6c06-4d6a-9d05-25d497e4773a}} and {{formula:50600de1-7003-408d-9bb9-d7fa55e276f4}} are the same event).
In the example of Figure REF , the mapping {{formula:0d25db87-6b29-463c-9fb0-4cb7c60749d3}} is invalid because it does not satisfy this criterion.
2) Valid ordering
All events in {{formula:63249933-b890-45ec-ab21-ea7d3ecbaf7f}} satisfy the ordering of {{formula:1046ec38-74f0-492e-8b1c-76d7ccef7042}} as extracted in the Semantic Information Extraction phase: {{formula:a580542c-9278-4121-8d36-92f7209fe033}} if isBefore{{formula:e2e8e0bc-7de0-4c5c-8630-8291ea058f38}}{{formula:17df50e0-1c39-4024-b23f-8e9ff5c53330}} {{formula:752c5e70-325c-4267-97c6-ef81c6f0ffb4}}{{formula:1f6b20c6-b461-4a81-ae76-6142fe34f826}}{{formula:2c383c76-0362-4928-9123-e8b027a5d352}} ({{formula:61252535-2167-4b76-963d-8125864fa832}} precedes {{formula:04b86666-ac4c-4e15-8a05-bd11256883de}} in {{formula:94edd341-4f65-4b8d-9a88-000f62cfe58f}} ).
3) Consistent matching
Two events in {{formula:49db4ed6-9219-4667-b993-0668941bb8a7}} that are associated with the same event descriptor must be matched to consistent recipient events in {{formula:1fd65ff7-acf1-4be2-9b76-3ab44640c2e0}} :
{{formula:efd21f59-665f-4372-a50b-42723eeade02}} if {{formula:f7d3cbd2-3541-4ff4-9c54-da41d8f0ca9b}} and {{formula:e981061b-209d-4929-965c-b29ecef10c64}} have identical descriptors ({{formula:a4fff3ae-0723-4d3a-bc94-cf88dfb5b937}} ), then also {{formula:fbed5c72-f49b-4fa9-8e8f-5e9b5ffd48d0}} and {{formula:b6a40e80-07eb-467e-9b39-edbebb58df17}} must have identical descriptors ({{formula:8deb25c5-7b9c-4b77-b1e1-8e59537236ed}} ).
This constraint avoids mapping two equivalent events in {{formula:f349ff7c-b6c9-4e15-b483-de371f6fe713}} (such as clicking the same button) to different widgets in {{formula:f360e64a-1fad-4872-9151-10a95e77f695}} .
AdaptDroid selects the valid mapping {{formula:b061acd6-7ba1-4eb0-b569-3692ec94e621}} that maximizes the number of matched events, and uses {{formula:cd7f3c2e-8a4d-4b50-b921-0281a6b9f9bd}} to compute the event similarity between the two tests. Intuitively, {{formula:8300e554-28af-4930-9f9d-4f5197e023ec}} is the mapping that best captures the similarity of {{formula:0efa473f-737e-4bac-8fa0-b74dff818b62}} and {{formula:b8d0f486-bf51-452b-9d04-52071777f957}} .
More formally, {{formula:84356382-0989-4230-b1a6-d5923406bb7e}} such that {{formula:cd2a4d58-95f8-4513-a66f-a1cebf16e1f8}} is valid and {{formula:56798bf8-e134-4a63-9f94-bb0f1ed42d7a}} a valid {{formula:73035add-d921-4723-8f2e-9ad3d3b02dc0}}{{formula:d0e9c22d-cc93-437c-983e-c57c6a8fcdc0}}{{formula:cdeb9ded-86fa-43da-a088-e59a2dae851d}}{{formula:8d5fc349-f791-4fcf-b454-e11a4ff8f186}}{{formula:9eb3aa1d-3a72-49f8-9838-11fb7285bb71}} .
{{formula:49cb1151-de96-48b3-83c2-bd2766777c45}}{{formula:1b80bf67-84d4-4707-a779-892e5980028d}}{{formula:2d0c2f01-b25a-4979-a7e7-75b165017531}} indicates the number of pairs in a mapping {{formula:be94fc9a-8ca5-44dd-8294-5184eff80f21}} .
If there are multiple valid mappings with the highest cardinality, AdaptDroid selects one randomly.
In the example of Figure REF , {{formula:0173ebbc-d396-4e16-b1df-39e7253396d9}} .
Because of the huge number of possible mappings ({{formula:bd37013b-9bbc-4505-a4be-b69cf0d28fb6}} ), AdaptDroid does not enumerate {{formula:09a4dc7c-eca5-4137-bf3f-a8842f6ce0c4}} and then remove all invalid mappings.
Instead, AdaptDroid efficiently identifies {{formula:3c87a9f8-e95c-4536-b585-82bd88f89105}} by applying the three validity criteria while building {{formula:cd413cc3-8919-48ec-8ca4-5b9795e7c19a}} .
Applicable Assertions
AdaptDroid fitness function also considers the number of assertions in {{formula:57e2494b-46e6-492a-b10b-1c9f6820fba3}} that “can be applied to” {{formula:9c1ab6f3-d430-4950-84ce-0922d025b7dc}} . This is because a good adaptation of the donor test {{formula:cb66ab3f-7a9d-4dfe-8c69-745ebec54938}} must reach a state of the recipient app with widgets that are compatible with the ones checked by the donor assertions.
Intuitively, an assertion {{formula:07e5b9a5-8e6a-4144-8e05-7134ced92048}} is applicable in {{formula:c185dd18-5f01-4a4c-9010-a0a225aa347f}} if {{formula:c5dd64fa-338c-4c74-86ca-05b961139d3e}} can be applied to at least a state reached after the execution of the last event in the mapping {{formula:2f62a790-6199-4c4e-80a8-7b6acf3e89ff}} (we recall that we only consider assertions at the end of the tests).
The applicability of an assertion in a state depends on the existence (or absence) of widgets in the recipient app that are semantically similar to the widgets checked by the donor assertion in the donor app.
AdaptDroid supports four types of assertions: {{formula:f928dd36-ebdb-4aa4-8561-adc361e99c01}} exists(txt) and {{formula:72c9a919-b6b2-4429-92cf-78a8c95b84cf}} hasText(w,txt)), and their negative counterparts: {{formula:ad523a25-8844-4a29-8e4f-8e1f79e1a3f1}} not(exists(txt)) and {{formula:2419a467-4287-48e0-bd75-13a22b2f7673}} not(hasText(w,txt)).
For the positive assertion types {{formula:18900371-4044-45ce-a89e-8f666f6ec6d9}} and {{formula:6b8b5f4a-3117-45bc-87e2-a04d8ea87abe}} , the Boolean function {{formula:4978c4fd-7756-403a-8145-c5ef057b5828}} returns ḭff {{formula:9df03fa8-6b13-43ea-b981-1c8273e50822}} is applicable in the state reached after executing the last event of {{formula:d9ec588a-4443-46f9-9beb-aad50a68ced1}} in {{formula:b88b4376-c32a-4882-b488-4536a784af9d}} , false otherwise.
An assertion {{formula:c79aed22-a50d-4a66-bee7-426973dd7a9f}} is applicable in a state {{formula:8a51790d-ad13-4786-8ab6-8387c1c9edc4}} if there exists a widget {{formula:4ca71858-9bc0-4117-a20d-313ece18e077}} such that isSemSim{{formula:ae8a5ce7-dce1-4b40-9df1-19930b49ecba}} where {{formula:48eee200-7d90-435f-b66b-d6d348331ec9}} is the descriptor of the widget {{formula:f19e57c5-a02a-414d-91c3-557263a76378}} extracted with the rules in Section REF .
The descriptor of an assertion of type {{formula:95dc0b8f-706a-4b56-982b-fc4bfbd5ef3b}} exists(txt) is {{formula:a16d1960-abb9-431b-b0b8-56e645f7221c}} = txt , while for type {{formula:33e41ab0-43f5-4887-8198-d894e60a74f4}} hasText({{formula:bf26650a-602f-474e-a1fa-a5679d52056a}} ,txt) is {{formula:cc0a91f7-06e0-413a-bf88-662b164022f4}} .
For the negated assertion types {{formula:e1e289f9-03d8-4aaa-8bbf-17b46366b736}} and {{formula:55336247-9158-4df0-adf2-51f8bcef2fdd}} , we define the {{formula:3e2541f6-53f4-40ae-9b7d-3c2b18b03de3}} function differently.
This is because it is trivial to find a state that does not contain a certain widget/text. Indeed, most
of the states traversed by an adapted test satisfy this condition.
To better capture the semantics of negated assertions, we force {{formula:da736887-aa1d-4c38-85e3-ed64d0b0ff36}} to explicitly move the recipient app from a state that does not satisfy the assertion to a state that satisfies it.
Since we check for the absence of a certain widget/text, we also require {{formula:c9dfeffa-a23b-4872-a109-9eeb5f615c77}} to satisfy this constraint on the same window.
Otherwise, the constraint could be easily satisfied by changing the current window of the app.
More formally, given a negated assertion {{formula:28e68d1b-31d6-491a-954c-a4bfd9756b44}} , {{formula:968798ba-411e-4b5d-b200-e2ba033f389c}} returns ḭff (i) the positive version of {{formula:3c746c90-d97b-4e41-8eef-7198c850e374}} (obtained by removing not) is applicable in a state {{formula:89c18df3-9c2e-4af2-9028-788b438aac64}} traversed by {{formula:8ca462d5-0b90-42ff-abda-f81902752992}} , (ii) the positive version of {{formula:c5f705a8-0363-42cc-a6fb-ccc791d27825}} is not applicable in a state {{formula:02bfc975-40f4-4c46-803b-ed2e45beb6a8}} traversed after the last event in the mapping {{formula:cc878bbc-f30e-4481-892c-663a9e742e10}} , (iii) {{formula:7874c6b5-d272-4a77-bbfd-1b32291f98b4}} is traversed before {{formula:87bf82ba-2465-4e33-8dfa-8bfa6bcfa4b9}} , and (iv) both {{formula:84394069-332c-44ab-85ef-525bf7feb371}} and {{formula:57b34939-59b8-442a-a111-ce17356ff156}} refer to the same window; false otherwise.
In the example of Figure REF , assertion {{formula:b408c5cc-f82c-4679-aac2-26c682f6807e}} in {{formula:27547145-96e9-4969-bdcb-56c28290a48c}} verifies that no widget with text ''Test''{{formula:25bf71ce-8a3b-4131-8df4-2f1fbfc50476}} exists. The assertion is applicable to {{formula:ff60ab06-1aaa-4102-8615-585a9d6f8f30}} because the last state of {{formula:1847b7e5-bd19-4de8-8451-9cc46fca0a6e}} does not contain such a widget ({{formula:e5276c45-a012-42c5-a69e-e2866453502f}} is , the state after the event {{formula:1bb03d64-52b9-483f-9e5a-d702729beb5b}} does ({{formula:27bd8241-844c-40e9-8c69-adc954bb323b}} is false), and these two states belong to the same window.
Let {{formula:8fd678e6-3236-441e-a18c-ddf6c3ae427c}} denote the set of assertions of {{formula:70f3c3ca-6db5-4c8b-b906-88fbccbabc8c}} such that {{formula:1aad96d9-b8c1-4aef-a7cc-65a02189af64}} returns As such, the cardinality of {{formula:f42d8ff0-6a69-4257-bc26-b57c61eebd7b}} ({{formula:edbc730c-0f7f-4047-9696-576c7e006453}} ) measures the number of assertions successfully adapted to the recipient app.
{{formula:67f377a8-1d23-46a9-95a6-5908a4096747}}
The fitness score is proportional to both the number of events and the number of assertions in {{formula:876b9352-d309-4e88-9a60-69216a64cac4}} .
That is, obtaining an applicable assertion contributes as much as successfully adapting an event.
The score is a value in [0, 1], with 1 representing a perfect adaptation.
Population Evolution
The Population Evolution phase combines and mutates the individuals (GUI tests) in the current population {{formula:dc5280d4-143e-4504-a39a-0cc1ab558214}} to
generate a new population {{formula:ca54f1c7-41e9-4ff3-8866-ec8e24616c59}} of size {{formula:91af9a1d-863d-4b63-bd1e-6d03000cf07b}} .
We follow the classic evolutionary algorithm {{cite:273214a0de7aaeee0181906a0571a52c6d6462d9}}, which works in four consecutive steps: elitism, selection, crossover and mutation.
Elitism
AdaptDroid adds in {{formula:72eeb705-c474-4460-96e9-7fce05303475}} the elite set E of observed individuals with the highest fitness score ({{formula:d42eff24-2ded-42ce-9efb-2b59af861e4d}} ).
This elitism process is a standard genetic algorithm step that avoids missing the best individuals during the evolution {{cite:273214a0de7aaeee0181906a0571a52c6d6462d9}}.
Selection
AdaptDroid selects {{formula:81c287f9-53fe-4a12-ad4c-fce1d7fdab2e}} pairs of individuals from {{formula:6c6aa4bf-b41d-46ee-8929-ffd83ac41c72}} as candidates for the crossover.
We use the standard roulette wheel {{cite:273214a0de7aaeee0181906a0571a52c6d6462d9}} selection that assigns at each individual a probability of being selected proportional to its
fitness.
Crossover
AdaptDroid scans each selected pair {{formula:33c0dade-591d-4a7a-a8d0-322214b0e078}} , {{formula:e531d0b5-7824-425c-861a-68da29ff34b6}} and with probability CP performs the crossover and
with probability {{formula:7870cc13-d455-485c-b5ef-58df185be14f}} CP adds the two tests as they are in {{formula:50b93146-abc1-40de-afff-1faf3d0d807e}} .
The crossover of two parents produces two offspring by swapping their events. AdaptDroid implements a single-point cut crossover {{cite:273214a0de7aaeee0181906a0571a52c6d6462d9}} as follows.
Given a selected pair {{formula:e04e5446-3a13-40a1-8646-d230a40a2d78}} , {{formula:b314a367-4903-498c-a2d5-d6a2b4783455}} , AdaptDroid chooses two random cut points that split both {{formula:36de1dc8-b930-4afa-ac9e-70ea8e8e510b}} and {{formula:32120337-aff3-4fb6-a82d-604e1a38815b}} in two segments. It then creates two new tests.
One concatenating the first segment of {{formula:1df08b9d-f0c7-44ae-b1d6-4928e61a398f}} and the second segment of {{formula:9a5869d0-bbdb-48f8-a23f-a93039a4d587}} .
The other concatenating the second segment of {{formula:84df3a50-d757-475e-a620-c54b57a608f2}} and the first segment of {{formula:c72dfaab-b270-44af-a8e4-b0608aa0516d}} .
The crossover likely yields infeasible tests, where executing the first segment leads to a window ({{formula:03a8580a-a39c-4a5d-aa3d-fed826d5a219}} ) different from the window ({{formula:c0a8137d-a6c7-4ced-bcee-4b45c82fb514}} ) that the first event in the second segment expects.
AdaptDroid repairs these tests
by interleaving the two segments with a sequence of events that move from {{formula:1c461004-a3f2-4815-8ec2-9f5777392821}} to {{formula:16b3b2ca-a34e-4a28-8572-c3ef6b8bcbf5}} .
AdaptDroid identifies such sequence by querying the GUI Model of {{formula:5a0e695c-813a-4924-9c69-ab1d46f3e93d}} (see Section REF ).
Mutation
When the crossover terminates ({{formula:6177b73d-5a9e-4c88-b4bb-da8174f5ba3c}} ), AdaptDroid mutates the tests in {{formula:c8b74466-33dc-4850-b64c-acd81e921d0b}} with a certain probability, aiming to both add genetic diversity and quickly converge to a (sub)optimal solution. As such, AdaptDroid uses two mutations types: random and fitness-driven.
Random Mutations mutate the tests in {{formula:230622a0-08ab-4f5a-be67-9b9d8c13f77e}} with a probability RM by applying any of these mutations:
[(i)]
adding an event in a random position;
removing a randomly selected event;
adding multiple random fill events in a window containing multiple text fields.
The rationale of the last mutation is that forms with several fields might require many generations to be entirely filled out. This mutation speeds up the evolution by filling all the text fields in a single mutation.
Fitness-Driven Mutations mutate a test to improve its fitness score. Each test in {{formula:b41c0280-f5c1-40de-9bfa-f358abd37a0c}} has a probability FM of being mutated using one of these two mutations:
[(i)]
removing an event in {{formula:2c42272f-ba6c-4b42-b397-a16a97df3d10}} that does not match (according to {{formula:e3af759e-7339-42c3-bac0-7c7c7a6db8ea}} ) any event in {{formula:e211784e-1ae5-4ce3-a4a4-05d8f1bddd9c}} ;
adding an event {{formula:e4e2e0b4-a4cd-4518-ae46-0a4e407f6cf0}} in {{formula:130b4e37-92a1-4d0d-aea9-0e98d5baa7bb}} such that {{formula:2c35dcfe-1e3d-470a-82b5-01e130256c54}} , where {{formula:bbbb4012-7906-4389-a2eb-6e3a28d7a08c}} is a randomly selected event in {{formula:5ffeaf03-1150-4d6c-b0b2-b663107f2a45}} that does not match {{formula:0a7215d3-4cc2-41d1-a744-a80bd3723cca}} events.
Like crossovers, also mutations could create infeasible tests.
AdaptDroid identifies them by checking if all the events in the mutated tests can be executed in the order prescribed by the test, and fixes the infeasible tests it by removing all non-executable events. Indeed, the fixed test could still have useful genetic material for the evolution {{cite:c8537c6258525123f3d14dcacc6c32a4bc36ff8c}}.
The search for an adapted test keeps evolving and evaluating populations of tests until either a predefined budget expires (# of generations or time) or AdaptDroid finds a test with fitness one.
When the search terminates, AdaptDroid post-processes the test with the highest fitness score by reducing the test length, and injecting the donor assertions (if possible).
AdaptDroid reduces the test length by removing one by one the events that are not part of the mapping {{formula:1208180b-c19c-4317-88f1-a2ffa9b3160e}} used to calculate the fitness score.
After removing an event, AdaptDroid executes the test and recalculates its fitness.
If the fitness decreases, AdaptDroid restores the event because,
even though it did not directly contribute to the fitness value, it
enabled other relevant events to be executed.
In the {{formula:e39b714f-a94d-4156-8850-8269e3fbf7f8}} of the example of Figure REF , events {{formula:7e51350d-19c9-4358-949e-5094d814d8b0}} , {{formula:0e3dd84e-9001-48f7-b058-e83ee580d2a1}} , {{formula:a103c023-10b3-4e7b-a43d-086fdd3e3a89}} , and {{formula:90fea195-82ed-46c2-983b-ad9bf9f52f1a}} of {{formula:cb7afa58-d844-46cd-8426-62ff512e5d38}} do not match any event in {{formula:0e035acc-cf26-4cb7-841a-7f649836adba}} , but the post-process keeps them because removing any event reduces the fitness.
If the fitness function finds some assertions in {{formula:21fedbdd-a77c-4594-923f-6b5c00b962e6}} that are applicable to {{formula:b4191038-b2fd-412b-9bc0-bbbbbfec50c0}} , AdaptDroid adds them at the end of {{formula:4d442efd-d863-49bb-8ca9-f69ee062c344}} . In the example of Figure REF , AdaptDroid injects the assertion {{formula:af482214-31dd-4054-89b7-02eff43da747}} not(exists(''Test'')) at the end of {{formula:245b8f03-23f6-41f2-a03e-6158c6f4b030}} .
Evaluation
We evaluated AdaptDroid by implementing a prototype tool for Android apps {{cite:2785827261989008a5fa25a3b2b1d80e6b576364}}. Our prototype uses the Appium 6.1.0 framework {{cite:79301a71130946c2ed76ae4b722b1bc738e6b271}} to read the GUI states
and Android emulators to execute the tests. We evaluated AdaptDroid considering two research questions:
RQ1:
Effectiveness Can AdaptDroid effectively adapt GUI tests and oracles across similar applications?
RQ2:
Baseline Comparison Is AdaptDroid more effective than baseline approaches?
To measure the quality of test adaptations we need human judgment, possibly involving the designers of the donor tests.
For this reason, we evaluated AdaptDroid with a human study that involved four PhD students majoring in Software Engineering, who were not related to this project. We asked each participant to design some donor tests and to evaluate the adaptations produced by AdaptDroid.
{{table:c7e32674-dd28-4e71-886f-9381dd9d8bc3}}Selecting Subjects and Collecting Donor Tests
We selected a total of 32 Android apps (8 donors and 24 recipients) from the Google Play Store by referring to four app categories that represent apps with recurrent functionalities {{cite:49d959f3e84aafb0fd2bded6e083e8fe72bda67e}}: Expense Tracking, To-Do List, Note Keeping, and Online Shopping. We avoided selection biases as follows.
We queried the Google Play Store by searching for each category name.
From the list of returned apps, we selected the first two that are free/freemium and do not require login credentials at start-up.
Thus, obtaining a total of eight donor apps.
For each donor app {{formula:57983f9a-09e6-489c-aa0b-1615d17d93eb}} , we identified three recipient apps by retrieving the list of similar apps suggested in the Google Play Web page of {{formula:19fe7f98-8b04-407d-a3b4-212cfd9188ae}} .
From this list, we selected the first three apps that were not selected as donors and have the same characteristics described above.
This process resulted in 24 pairs {{formula:4790a6a6-ac3e-41a6-be37-a8ee4e9efc21}} , {{formula:348ad1ac-cc27-4395-8732-e6e59ecb84dc}} of donor and recipient apps.
We randomly partitioned the eight donor apps among the testers, by assigning two donor apps of different categories to each tester.
In this way, we prevented that a tester could design similar donor tests.
We asked each tester to design a Selenium GUI test {{cite:72518cf285708d769d4bb783c205255a9b20d165}} (with an oracle assertion) to test the main functionality of the app.
We left up to the tester to identify the main functionality of the app.
After each tester implemented a donor test, we asked to evaluate whether the test could be adapted to the recipient apps. Each tester evaluated each adaptation on a scale ''Fully'' (the main functionality of {{formula:d4cda02f-6dae-48b1-8fb3-9ce845a54bab}} can be tested as in {{formula:31fa17ba-019a-4ec9-a4f6-2bed92469f6e}} ), ''Partially'' ({{formula:aeca82ec-2750-41b2-aa5b-f6e5cc896d94}} allows to replicate only some of the operations performed in {{formula:37023050-affe-4451-923d-f72067bccfb2}} ), ''No'' ({{formula:8c5f61ca-d8b9-4faf-b256-dcd49e163745}} implements no functionality that can be tested as in {{formula:b41b1aad-4460-46f3-ae0a-052e8e3cb9b4}} ). Column “{{formula:ce265626-fcc7-478e-a919-d4c61dc618a6}} Adaptable?” of Table REF reports the responses. The testers deemed fully adaptable 18 pairs of tests (75%) and partially 3 pairs of tests (12.5%). This result confirms the intuition that GUI tests can be adapted across similar applications. Tester {{formula:f24543e1-a111-4226-b702-156977ad98db}} deemed the pairs with ID 13, 14 and 15 as not adaptable, because the test executes functionalities available only in the donor Pocket Universe and not in the recipient apps.
We asked the four testers to manually adapt the fully and partially adaptable donor tests to the recipient apps.
{{table:40a0aa92-524d-450f-9862-358fc2225844}}Running AdaptDroid
We ran AdaptDroid with the 21 fully and partially adaptable donor tests
giving as input the pairs {{formula:b8ff6816-f9d0-4469-a920-c5ee801f3f84}} and the corresponding
manually-written test {{formula:bf7e863c-04e1-4db8-9011-d205a1ecdf42}} .
We used a popular WMD model trained on a Google News dataset (about 100 billion words) {{cite:51fdf5ee83e527c88bb2bb26250f7eb203d5f94a}}.
We ran AdaptDroid with a budget of 100 generations with the configuration parameters values shown in Table REF .
We selected these values by performing some trial runs and by following basic guidelines of genetic programming {{cite:7a788681eeedba5cde162d01cf6b35b4023dceab}}.
Special considerations can be made for the values {{formula:1a0aae1d-7d75-43de-945d-2857fc62612b}} and {{formula:afad5c1f-3911-4177-85b9-a4ff928468fb}} .
We chose {{formula:8111f388-c07f-48c9-bf85-9bb7da0d96f9}} as the threshold for the semantic similarity by evaluating the WMD model on a list of {{formula:a021bc82-4b82-4b5b-9a11-a8c6671b1be7}} 2.5 M synonyms {{cite:2eaccf44337beb934a8b9a6425f88b755bfd6a6a}}.
More specifically, {{formula:763ef434-788b-4eab-9be4-43a015c343b5}} is the threshold that achieves the best trade-off between matched synonyms and unmatched pair of randomly selected words.
We choose {{formula:3d6328b9-7521-4610-8878-bc4c95cefb49}} to obtain initial tests for {{formula:ea44fbce-98ee-4f8c-ab9f-5598a1024f1a}} with a max length proportional to the length of the donor test.
When dealing with the test pair with ID 21, we experienced some compatibility issues between the Appium framework and the recipient app {{formula:a14b418c-5450-4d60-bc2b-605deae76f71}} ,
issues that prevented AdaptDroid generating tests.
Thus, we exclude such a pair from our analysis.
The “AdaptDroid” columns of Table REF show information about the returned adapted test {{formula:3028c9b7-6646-4c6e-8e95-0117adce1b50}} (the one with the highest fitness score).
Column “{{formula:daeedcdb-0e81-44f1-8eb9-1264146ae2b7}} ” provides the number of events of the adapted test. Column “fitness” shows the fitness score of {{formula:61459705-d7b6-4f67-b4df-e7e4985be32e}} .
AdaptDroid never reached fitness score 1.0, thus it terminated after 100 generations.
Column “gen.” shows the generation in which AdaptDroid produced {{formula:5aa43a72-1b21-4469-b390-2365aab33a0f}} .
AdaptDroid completed 100 generations in 24 hours on average, and spent most of this time
in executing the generated tests on the emulator. Executing tests is expensive because AdaptDroid re-installs {{formula:c30949d9-32b8-4da4-b980-e2aeb8ff3a54}} in the emulator before each test execution to guarantee that each test executes from a clean state. This time could be reduced by running many emulators in parallel or using cloud platforms for mobile testing.
RQ1: Effectiveness
We asked the testers to judge the quality of each test case {{formula:8bf7fe44-a664-4c3a-b764-a32e7a33c1dd}} produced with AdaptDroid for their assigned pairs.
We used a score from 0 to 4, where 0 means that {{formula:a27c9e13-6154-4f39-9316-9e7bcf34c84a}} is completely unrelated to the donor test semantics, and 4 means that {{formula:59095daf-2c86-4fa8-ba53-a32552520c34}} is an adaptation as good as the one that they manually produced (Column “{{formula:3f619f9d-d584-455e-9d35-8004bdd268df}}” of Table REF ).
In 8 cases out of 20 (40%) the testers evaluated AdaptDroid adaptations as high quality ({{formula:4d8f1642-9140-4b53-b70a-eb0c83a42fd3}} ), with three of which considered perfect adaptations.
In three cases (15%), the adapted tests were evaluated as medium quality ({{formula:f75c1204-90b0-4f73-b3eb-6409b3b2f7ec}} ).
This suggests that in these eleven cases ({{formula:e3b686c2-d8e2-4bff-a37a-49fa089b781b}} ) the fitness function well describes the similarity with the donor test.
We asked the testers to indicate the spurious and missing events in the tests. Columns “{{formula:260f77e0-5c15-4c6b-9116-4eda655bda72}} spurious events” and “{{formula:fc0dd509-e699-48c5-9bf3-a3936ce415fd}} missing events” of Table REF report the number of events identified as spurious and missing to obtain a perfect adaptation, respectively.
Column “{{formula:2eadfa4c-d6ff-4342-b9fb-ba73706c98ed}} ” of Table REF reports a structural quality indicator of the completeness of the matched events:
{{formula:9bc84f04-b2b4-45d3-b375-5386ad0cde24}} , where {{formula:59fd1a9c-d877-497f-a3cc-8f843bab0f96}} is the manually adapted test.
{{formula:e5edcc6c-3bc0-4474-9714-9db970ccec26}} ranges in [0, 1], where 0 indicates no matching between the events in {{formula:440425d5-001d-4ae1-9476-24a0e0ebe4a3}} and {{formula:92faa44d-60f4-4849-9602-fe7e854bef00}} , and 1 indicates a perfect matching.
The average of {{formula:12b53c06-90af-41fe-92b8-6cef2c9ad3ae}} is f 0.53, indicating that overall AdaptDroid adapted 53% true event matches identified by the testers.
There is a moderate correlation between the two quality indicators {{formula:18991062-0d6c-4c35-9ec4-577dc4a6ba22}} and {{formula:39677614-0f56-4f05-aebc-4c9bdafb56f0}} (Pearson coefficient is 0.89). This confirms that it is important for the testers to adapt a large portion of a test.
Column “Oracle Adapted?” in Table REF reports whether {{formula:1e603260-d6e0-4230-bbed-980574f2d18c}} has an assertion that the tester evaluated to be correct (''Yes''), partially correct (''Partially''), or not applicable in the states reached by {{formula:29a35f6b-503c-4591-9332-cbe7f4780500}} (''No'').
Testers {{formula:577ed23a-08c5-418c-87dc-de2ed33cf40c}} and {{formula:ca1f53b1-081e-48af-92c7-afcdc6d29213}} attributed partial correctness to three adapted oracles because of marginal differences in the expected output. For instance, in the pair with ID 3, the oracle in the donor test checks if a widget with descriptor ''expenses'' has text ''100''. The corresponding widget in the recipient test has text ''-100'', which is semantically
equivalent (100 expenses = -100 balance)
but syntactically different.
Therefore, the oracle was deemed partially correct.
We identify two main issues that limited the effectiveness of AdaptDroid.
1) Significant differences between {{formula:4e0bf9fe-e80f-4cd1-8898-89f5be23c53a}} and {{formula:baf61262-a491-4d2f-9bb9-8fcd0e7e998b}} .
For instance, in the pair with ID 18, {{formula:d1ff5d7d-04cd-4057-b311-54f8c745a6f6}} searches in the Aliexpress app for a USB drive and adds it to the shopping basket.
Tester {{formula:e48397f4-57ad-4247-8435-9399b31bd5e4}} manually adapted {{formula:00708d67-0290-433c-8284-4bb10d25fa03}} searching in the Shein app for a t-shirt.
AdaptDroid failed to adapt this test to Shein, as searching for a USB drive in Shein results in an empty search.
As another example, in the pairs with ID 23 and 24, {{formula:f1a8ff9a-457d-487d-9796-8fc09617da2d}} adds a task to a pre-existing work task list.
AdaptDroid failed to adapt these tests, as the recipient apps do not have a task list.
2) Missed Event Matches. The semantic matching of the descriptors was not always precise due to (i) the
unsoundness of WMD; and (ii) the limited semantics information of the event descriptors.
For example, some of the considered apps have image buttons with file name ''fabButton.png'', which
does not describe the semantics of the widget.
The results of our study are promising: AdaptDroid produced eleven good quality test adaptations between apps with very different GUIs.
In the experiments, we configure AdaptDroid to report all adaptations.
We can improve the quality of the generated output, by reporting only adapted tests that reach a minimum fitness score.
RQ2: Baseline Comparison
We compare AdaptDroid with two baseline approaches
[(i)]
Random, to empirically assess the effectiveness of the evolutionary algorithm of AdaptDroid;
AdaptDroid-basic, a restrained version of AdaptDroid without the fitness-driven mutations and greedy-matching initialization, to assess their impact to the overall effectiveness.
We obtained Random from AdaptDroid by
[(i)]
replacing the roulette-wheel selection with random selection,
randomly generating the tests in the initial population (NR {{formula:ca199fb2-8104-4b20-b342-fa2f0ce59efd}} and NG {{formula:7210e441-3938-4877-ad68-b7cc1eb3d179}} , Table REF ),
setting the probability of the fitness-driven mutations to zero (FM{{formula:605e5160-2329-4b29-9a54-de2a5486c385}} Table REF ), and
disabling elitism.
As such, Random carries population initialization and evolution completely random.
We opted to use a random variant of AdaptDroid rather than an existing random generator {{cite:5e3014701c166f2a797ef600ce8bb52a5acb420a}}, for a meaningful evaluation. With an existing random generator, we cannot ensure that the differences are due to the search strategy and not to differences in other implementation details, such as the events and inputs types considered by the tools.
We obtained AdaptDroid-basic from AdaptDroid by applying only the modifications (ii) and (iii) described above.
We ran Random and AdaptDroid-basic with a budget of 100 generations as AdaptDroid. The last four columns in Table REF show the fitness score of the fittest test and the generation that created it (with the highest fitness value among the tools in bold).
AdaptDroid consistently achieves a higher fitness than Random, and the same fitness only in one case (ID 22).
The difference between the tools is statistically significant: a two-tailed t-test returns a p-value of 0.0002.
AdaptDroid achieves an average fitness of 0.48, while AdaptDroid-basic of 0.45. This shows a difference albeit small of the fitness score.
{{figure:87fc1dfa-9566-4193-8056-e0fad2ef44a6}}Figure REF illustrates the gain of AdaptDroid over the baseline approaches, by plotting the highest fitness score
per generation averaged over the 20 adaptations. The plot highlights three important aspects:
I.- the fittest test of the greedily generated initial population ({{formula:f31829be-7f10-44b9-90c9-3fad8f938ac4}} ) of AdaptDroid has a much lower fitness score than the final score.
This shows that the greedy algorithm used to initialize the population is inadequate, thus motivating the use of an evolutionary approach.
II.-
the highest fitness per generation of AdaptDroid steadily increases while the
fitness of Random saturates much faster.
This demonstrates that AdaptDroid evolutionary approach is effective in exploring the search space, and it confirms our hypothesis that AdaptDroid generates GUI tests that can hardly be generated at random.
III.-
AdaptDroid and AdaptDroid-basic reach similar fitness, but AdaptDroid reaches it faster.
This indicates that the greedy-match initialization and the fitness-driven
mutations help to converge faster to the fittest test.
Threats to Validity A main threat to the external validity concerns the generalizabilty of a small set of adaptations. The scale of the experiment is limited, due to the cost of involving human testers. However, it is comparable to the ones of the main related approaches {{cite:f69c67d9da399c73a673f8963d10f7a6f1501edb}}, {{cite:55caa99662f7fcc7520c3cfefa1489ff9ba5f7f2}}.
Another threat relates to the selection of testers. The four
testers have testing experience, but they are not the developers of the
apps. We mitigate this issue by letting
the testers get familiarity with the apps before asking them to design the tests.
A final threat relates to the statistical significance of the results. Since the evolutionary algorithm is inherently stochastic, multiple runs may yield different results. Since the evaluation of the results involved human participants, who can only evaluate few tests, we ask them evaluate a single result of AdaptDroid.
Related Work
GUI Test Generation Existing generators of GUI tests {{cite:d5e42e1f8be8de65f6038e3976b9e365b570c45b}}, {{cite:6e71ecf5ede140a9e9588333196f663bcf3b3b65}} have two major limitations: [(i)]
lack of domain knowledge {{cite:3d3b6821c751e7b10bf891abbe1d3d1c8c0637e8}}, and thus they may generate either unrealistic or semantically meaningless GUI tests {{cite:34588af6fb5ce03b7daf47e5d0bf25cf0e6d190b}},
lack of automated oracles, and thus they are able to only detect crashes or exceptions {{cite:539d22d2369d611e992b5bec539ed6601c9ea3b4}}, {{cite:b759bba961e016955f7ccac29d58b113ef834af6}}.
AdaptDroid addresses these limitations by generating semantic GUI tests and oracles adapted from manually-written GUI tests of similar apps.
Researchers have exploited usage data to
improve GUI test generation {{cite:3d3b6821c751e7b10bf891abbe1d3d1c8c0637e8}}, {{cite:5d4515ab92b326da0b59eed548d7071e7dbba27e}}, {{cite:fb780349890ece9c8eba01974f90af42a7f4d36b}}, {{cite:c4df04f9fc5737e0e58c4d73c2b5ae81e3c78aa5}}.
For example, Polariz {{cite:3d3b6821c751e7b10bf891abbe1d3d1c8c0637e8}} and MonkeyLab {{cite:5d4515ab92b326da0b59eed548d7071e7dbba27e}} generate Android tests using GUI interaction patterns extracted from app usage data. Differently, AdaptDroid fully adapts existing tests across apps maintaining the same semantics of the donor test.
Similarly to AdaptDroid, the GUI test generators Augusto {{cite:5bb22c67305e9ad8d2a565dedcbac4c260c1f32f}} and AppFlow {{cite:49d959f3e84aafb0fd2bded6e083e8fe72bda67e}}
exploit commonalities among GUI applications.
However, they do not aim to adapt tests across applications nor leverage
existing GUI tests. Instead, they rely on a set of manually-crafted GUI interaction patterns.
Moreover, AppFlow recognizes common widgets using a semi-automated machine learning approach. Conversely, AdaptDroid matches GUI events without requiring human intervention.
GUI Test Adaptation CraftDroid {{cite:55caa99662f7fcc7520c3cfefa1489ff9ba5f7f2}} and
AppTestMigrator {{cite:f69c67d9da399c73a673f8963d10f7a6f1501edb}}, {{cite:9284e6afd9f977f60f9f0b324d4864308d1a04b6}} are the first attempts to adapt GUI tests across mobile apps.
Both approaches explore a statically computed GUI model of the recipient app to “greedly” find a sequence of events that maximizes the semantic similarity with the events of the donor tests.
Similarly to AdaptDroid, they extract event descriptors from the GUI and match them across applications using word embedding {{cite:3a5bc58e32388bc60591a79cdb90122b5cca2fcf}}.
However, AdaptDroid differs substantially from these two techniques.
AdaptDroid shares the overall objective of adapting tests across applications, but introduces
substantial novelties.
Both CraftDroid and
AppTestMigrator use a greedy algorithm, which resembles the one that AdaptDroid uses to generate the initial population {{formula:8c2b0425-6016-4317-bb2d-5060b7f46141}} .
AdaptDroid uses an evolutionary algorithm to improve an initial set of greedy-matched tests.
As discussed in Section , AdaptDroid evolutionary approach largely improves over a greedy algorithm.
Indeed, AppTestMigrator and CraftDroid explore a single test adaptation, and do not consider alternative sequences of random events that could yield to a better adaptation.
The AdaptDroid evolutionary approach explores many possible test adaptations to find the sequence of events that yields the best adaptation.
As such, AdaptDroid can be used to improve the tests adapted with AppTestMigrator or CraftDroid.
GUI Test Repair
Test repair techniques fix tests that become invalid during software evolution {{cite:f40e33e4c0a6a3467f6b0063c772c6f23224eac7}}, {{cite:0c4dd184ca11144d1ab1f57fe7309fa49e659c8d}}, {{cite:60fe71c8abae12ea2dfa9a28d83977dd69b5bab2}}, {{cite:989b1ec38b0763b01884127b7e3a49fa478b8c78}}, {{cite:e28d2f3b9a6f6e4382145e2262d5ead89e36aeb2}}, {{cite:ea58a6ed04db05b5efb240cb20100a59ee9e2cc9}}.
These techniques assume that most widgets remain unmodified between versions of the same app {{cite:2874adb4c8254610dc28e63f4a0ff78e0c861305}}, {{cite:f40e33e4c0a6a3467f6b0063c772c6f23224eac7}}, and do not address the core challenge of semantically matching widgets across apps.
Conclusions
This paper presents AdaptDroid an evolutionary technique to adapt test cases across mobile apps that share similar functionalities.
Our empirical evaluation indicates that AdaptDroid can adapt useful and non-trivial GUI tests across semantically similar apps with very different GUIs.
This confirms that formulating the test adaptation problem with an evolutionary approach is a viable solution.
An important future work is to reduce the computational cost of AdaptDroid by implementing a distributed version of the tool that executes the evolutionary algorithm on the cloud.
Indeed, one of the key advantages of evolutionary algorithms is that are easily parallelizable.
Another interesting future work is to extend AdaptDroid to adapt tests across different platforms, for instance, to adapt GUI tests from Mobile to Web applications.
| i | 53f6de3309484ec036a90cc6a64492a8 |
By Implicit Function Theorem, proved in {{cite:f7c2cc631b806565c90ed411ab786f58be62796e}} for the Heisenberg group and in {{cite:95303ee6620e32d852ee107ccde318cbdbd204db}} for a general Carnot group (see also Theorem 1.3, {{cite:ace7a89b4a590f2d4f78936dd1e92afb8a18bc17}}) it follows
{{formula:190cc4e4-ee05-46d9-b1b4-3c30675e7b74}}
| i | 9cdbb69790ee0a80bd0f24c051ab5cd6 |
Since our work is heavily based on the chiral representation, it should naturally admit a twistor description in the spirit of {{cite:8571897b6c6f637fbe09f7fa3fb3d6a0d3b226ff}}. To wit, it may offer a new perspective to flat holography, and more specifically higher-spin celestial holography {{cite:4b9798d6778e1f89ab3a1ade62ecc3ae03ab3d3c}}, {{cite:a543243f0065236dc904083221be06008a752e75}}. In {{cite:91d5f10ffe5c5b3892350c8d59e483fb94e65d0e}}, a higher-spin generalization of colour-kinematics duality {{cite:cc521d9e4a1deff7ca0d3b38285e8cf98f3a8647}} has been studied in the light-cone gauge. It would be interesting to understand the result of {{cite:91d5f10ffe5c5b3892350c8d59e483fb94e65d0e}} from a twistor point of view.
| d | 255240f35cd269ca80dd33ebf160ce79 |
Extractive Question Answering is the task of extracting a span of text from a given context paragraph as the answer to a specified question. Question Answering is a task in natural language processing (NLP) that has seen considerable progress in recent years with applications in search engines, such as Google Search and chatbots, such as IBM Watson. This is due to the proposal of large pre-trained language models, such as BERT {{cite:d94c3361e82fb5578f017c9ea0eb32e75302bd36}}, which utilize the Transformer {{cite:84cfa83e7fad666555a1eaf6248c5d81fc77b2eb}} architecture to develop robust language models for a variety of NLP tasks specified by benchmarks, such as GLUE {{cite:c3db1242457efd083051b8a6a396f0a9f37c0c96}} or decaNLP {{cite:ece1129c4a9f6afe83f73f98b10f8ea2c63b695f}}. Additionally, new datasets, including SQuAD {{cite:239ea0804c65397245905c3b9db14c348cc6008f}} have introduced more complex questions with inference based context to the question answering task. Recent work has shown to be productive in tackling the task of question answering, but the task is nowhere near solved. With the introduction of datasets, such as QuAC {{cite:932b4bb6dc4c8c2da8ff5eaaafad8732dd5d58d8}} and NewsQA {{cite:88dce30f9f54f287ce97f3deeab1cc35ab36cad4}} that rely much more on reasoning, it becomes challenging to generalize previous well performing QA models to different datasets.
| i | 2656b041ae4d6f32b7317e5ef0970a87 |
We have mentioned that the smaller the widths of the intermediate exchange particles are, the sharper the peak of triangular singularity is.
However, through a detailed calculation, we find that if the widths of the intermediate particles in the loop are too small, some other problems may arise.
In the cases of this work, where the internal particles are {{formula:15a020d2-71d7-4d18-aff5-8117d5838e38}} , {{formula:eafdb4c1-40a2-46bb-ae3b-fa62c3dee9bc}} and {{formula:ebf03675-838c-4bf0-9616-211eba5e3886}} , whose widths are 92.9 keV, 1.31 keV and 0, respectively {{cite:d10c8c76e9077696e3950268c802b3b4bec1f3a5}}.
The result given above tells that the width of the pure triangle singularity is only about 1 MeV and it is enlarged to 5 MeV after including the interference with the tree diagram,.
From the parameters of BESIII {{cite:d61b8da575574a03680c74e6bf6b9fc2622cf31f}}, we can know that the resolution of BESIII experiment is about 4.3 MeV. Hence it is almost impossible to observe this structure from the BESIII detection currently, unless BESIII or other experiments, such as STCF, can improve their resolutions to 2-3 MeV in the future {{cite:47614b70aa289cb495d97d5e04e4eee89aa0ae96}}.
| d | 0bc05552cd4776b85a63a036f7ca6a35 |
As concrete applications of our work, we feel that knowledge intensive tasks that involve access to external knowledge will benefit most from our analysis {{cite:596c13bb6a7134cffde5792139f839e930ecd281}}, {{cite:7e03f0ef007c4133d6cbc4e3cffd3ac8a774d3ad}}.
Additionally, Web tasks that rely on triplified knowledge like tags and relations {{cite:484c676e6e70e290cd0e77d7d05e4cd53a3a552c}} can employ BERT-based models to store relational information without direct need for learning grammatical and fine-grained linguistic knowledge.
Information retrieval tasks like conversational search and Web search can use our observations to complement their ability to provide clarifications {{cite:45afc4f1aebcfe4f6bfb9d32c145f1d38b52b221}} or explanations {{cite:59c4bfc64ae411e92ebf0106eeb6decd53f45162}}, {{cite:2135b1142ca1131d6381988d8e86d381fa479eea}} .
| d | 60405f7e362779c7fd4225ae1c9f92b6 |
Nonlinear isa provides us with a simple yet principled framework for learning speech representations in the presence of auxiliary variables, which in the case of sequential data like speech can be “time". Learning unsupervised representations can be posed as a problem of recovering from entangled samples the non-stationary sources that are independent given the auxiliary variable (time frame sequence). The nce-hsic algorithm can be used to identify original factors of variation via distinct independent subspaces. In order to ensure that the independent subspaces are not only mutually exclusive but are also having a high mi with surface features like Mel-frequency cepstral coefficients (mfcc) or log Mel spectrograms (lms) we build on existing approaches based on predictive coding strategies {{cite:79eb2add7b46b6b2d9b1666563dac6143aaf757e}}, {{cite:d8da07574bb9232a3d2f61f1c8d03fe7bf0641d7}}. Although our algorithm can be seamlessly integrated into any of these methods, in this work we show empirical results that highlight the performance improvements gained by incorporating the nce-hsic criterion into the apc model.
| m | e5a28725a22c0ea7ae6595e6c73f94ca |
In fact, a standard coupling argument with site percolation on {{formula:26f88847-719f-46b2-a0c2-9a6e55d2a85a}} (see {{cite:8cbeb17c1a632f8df257456a881c72672b3d4695}}, {{cite:6f338dfdf87a1772578827bd27e9e852a5729fe1}}) shows that {{formula:d5172521-cacb-4293-833f-7cfe1da50ea4}} . In a similar way, for every {{formula:748a9dc9-1188-43e6-8f52-4a31b9841e08}} we define
{{formula:1954bfc4-0d44-4009-a835-71972a49a3a4}}
| r | c47809f4b067ade58677b52304c66245 |
Here we evaluate the results in the table REF quantitatively. We couldn't compare out per class binary classification results with the MulT{{cite:32464d6745d4e758221a202f7f0054472b70e2b7}} model as they hadn't reported it, so it's unfair to claim that this model can outperform MulT on per class basis. We can still observe a couple of things from the all class classification accuracy {{formula:3c47b87f-b1bb-4d47-a14c-b35cd719f8e7}} and the {{formula:fbd2959e-ef69-40b5-ac85-2e9ab80cbb34}} score: 1) Our model is giving very competative results to the MulT model. We had only used 3 base attention modules in place of 6 in the MulT model. This would significantly reduce the computation requirement. 2) We can see that this multi-modal fusion has been effective in capturing the context of the situation because of its superior performance over uni-modal models. 3) Given that the model is performing on-par for unaligned data, we can prove our hypothesis that attention would indeed naturally provide the alignment and thus we do not explicitly need to align the sequences as a pre-processing step.
{{table:2008a51a-c720-43a5-a763-3679697ecab5}} | r | 19aca3aa065f3ef78d1a8eb0ca60d14e |
In this paper, we assume that we are given the data of a modular or super-modular fusion category {{cite:84146fe2ef414a7ecade23000dbf9e728da41f51}}, {{cite:ca64a4db19afe0db88cb9d8de63df6850764d805}}, {{cite:b5a6a6ba7a1ec17e9c92dc77b483c0b9f6de6ffc}} {{formula:ec314406-c384-4119-9bf2-992d3091d487}} in the bosonic or fermionic case respectively. In addition to {{formula:3ac3a072-fa78-41dd-b590-b19b6ba5baae}} , we are given the data that specifies the symmetry fractionalization {{cite:f30dd0043eb973909c81cd54af85eeb6530ff834}}, {{cite:d963aa6b179ce02263d3cc011d9ec3d731c0f64a}}, {{cite:eebe3bc58acadaef65e9470e683c84bed311aadf}}. This data consists of a group homomorphism {{formula:a34eb262-a259-4188-8094-91bb0a3b1a87}} , which specifies how the symmetry {{formula:35b9c6a2-e52e-47b3-b85f-e0ada4648079}} permutes the anyons, and a set of U(1) phases {{formula:bf571408-561a-416e-b393-09a214c454c3}} for each anyon {{formula:02b926c5-1c0b-4740-8e5d-5693f5696803}} , which must obey certain consistency equations and which are defined up to certain gauge transformations. We review this data in Appendix . The data {{formula:b568a3e8-f558-4a14-b699-9c5ab4f9fdb8}} in particular specify the {{formula:073d67d5-5ed6-4a5f-a9e7-2660f531a951}} fractional charges {{formula:bb271fc8-5153-4d8b-9123-5583124ba92a}} of each anyon {{formula:a9dfb006-0fde-4348-a4dc-adc94eb941e5}} , that specifies how the {{formula:4140def8-cc60-4260-a05d-9af4a9efbcb3}} symmetry is fractionalized.
| r | 16fa99eb0dc999ca75fb4ab8e2d626a8 |
Dynamical system view of deep learning has recently also gained a significant recognition {{cite:20d9150bb2fbd8577714928ab39ce6be9d5f45cb}}, {{cite:6bdab9547096545566ce3a7b4dacbd99fb6fb520}}, {{cite:221aee2924a8848ea4b9c92b37e31c4ad544f67f}}. Structure-preserving, in particular, Hamiltonian dynamics inspired neural network architectures have been put forward to improve stability of feed-forward propagation {{cite:eb9eb404526dac461543ab03470b8fca54532b63}}, {{cite:85bd92cffacf8974bd57a3cbaa045a13fc25b5bb}} and to address the problem of exploding and vanishing gradients in deep learning {{cite:029d790f2ba0b8f78b46155f831176f475f80dcf}}, {{cite:2b3abd3bef2ee17cd2b0c78efa530390a6d91897}}, where non-vanishing gradients are achieved by design, while exploding gradients can be controlled through regularization or avoided for special neural network architectures. Neural network architectures for learning dynamical systems have also been derived from structure-preserving numerical integrators {{cite:e6d06b2cbbe329d4866d41293feff0337e8d1376}}, {{cite:a60dfb0f4486f66bebe5c620e903b7d6c509f16a}}, {{cite:bc8154f3cb1230ba6a1be8b47809544971dd1559}}, such as symplectic Euler and Verlet numerical methods {{cite:916d0047d958212c50f3e7d3043bf320768e6c4e}}. Deep learning based integrators may provide competitive alternatives to conventional numerical integrators by allowing use of larger time steps {{cite:54af520deb3503164162b2061a96f63914dba24e}}. In addition to {{cite:2b3abd3bef2ee17cd2b0c78efa530390a6d91897}}, volume-preservation is also considered in {{cite:d6a82a0ca5d3df6bd4db5dd9ffdc2363d42d5896}}, where {{formula:b8d77ac2-331f-4146-9e89-dc9216eb6dfa}} may be considered as one of the most known efficient framework for learning bijective transformations of continuous probabilities.
| i | 58274c265c7fa62c2d2b423f750fb2d2 |
Two established methods for inferring causal relations between variable groups are multivariate LiNGaM {{cite:cbb94c3df0f846ceed8360717507d7bbaa338e9d}} {{cite:73d17798a50240d917ada605b72fafbcc8d3bffa}} and the trace method {{cite:326930bd95fa72604a9694ae02389df7d72b7e8c}} {{cite:d5144cb715610e18538eab6b1febbfa1ed273856}}. In contrast to our methods, both of these techniques assume interactions to be linear and LiNGaM additionally requires non-Gaussian noise to be applicable. In simulations with linearly interacting groups and Gaussian noise, the trace method and both versions of 2G-VecCI perform comparably well for groups of size 30 of moderate density with 100 samples, see Figure 2, although the trace method is significantly faster. For large groups of 100 variables each, the trace method tends to be biased towards the wrong causal direction if the interaction matrix is sparse even at high sample size 500. We believe that this behaviour arises from the fact that the trace method is challenged by interaction matrices that do not have full rank as was already pointed out in {{cite:326930bd95fa72604a9694ae02389df7d72b7e8c}}. When group sizes are large and {{formula:440d777b-a555-4770-b95d-9eb7465f4250}} tis sparse, its rank is likely to be lowered by the large amount of zero entries. 2G-VecCI.Full on the other hand still infers the correct causal direction reliably, see Figure 3. We also analysed the performance of the PC algorithm by treating each component in the vector-valued variables as a separate node and counting the arrow directions from (nodes belonging to) one group to the other and found that it has very low power. We used {{formula:88bd1940-4866-4237-9fa7-963c9e0d6fa6}} as the sensitivity parameter to reject those results as indeterminate where the arrow counts in opposing directions were too close (see further details in the appendix).
| m | 052abf7655cc5b9c37071701cb56424a |
While semantic segmentation based on deep learning has achieved remarkable progress {{cite:3e774688236ac6ba69efc43c8c6a8184810526cf}}, {{cite:61f962ae25affff34bfef54a39af6b804828b6d9}}, {{cite:fc4fc5482d51db1a62ad325f00be46dd60429990}}, {{cite:9bfb5183f99a54e39134aa3207de2687f58a12b8}}, it entails a large amount of mask-annotated data for supervised learning which is extremely exhaustive and expensive. Few-shot semantic segmentation is posed to address this problem by adapting a pre-trained segmentation model on base classes to novel classes using only a few annotated samples, namely support samples.
| i | c55258c37c23a82b1bcb339824669995 |
Variational autoencoders {{cite:0c8136bb22a366221a1af6c3edff68fafdd3272f}}, {{cite:7b33bd60be42ee5217a01fe502b29db8233d7d53}} (VAEs) use a neural network to parameterize a probability distribution.
VAEs consists of an encoder which parameterizes posterior probabilities and a decoder which parameterizes the reconstruction likelihood given a latent variable.
VAEs inspire many interesting works {{cite:b7396c4a2009ff00a74a0b9dcaaac0cc150884d8}}, {{cite:7ce1e0096fa592457f83f3bdb51b050893318322}}, {{cite:13f4536fcf31a7461dd584b079788a058c8e37e9}}, {{cite:4e92015272fc16825271f250d8cba7d0cf688f61}}, {{cite:15e424b4d7268e57d3f344d2f60ea19e1be698c3}} which are slightly different from VAEs. Their encoders produce a discrete distribution while the encoder in VAEs yields a continuous latent variable.
{{cite:b7396c4a2009ff00a74a0b9dcaaac0cc150884d8}} aimed to solve semantic role labeling problem. The encoder is essentially a semantic role labeling model which predicts roles given a rich set of syntactic and lexical features. The decoder reconstructs argument fillers given predicted roles.
{{cite:7ce1e0096fa592457f83f3bdb51b050893318322}} aimed to solve unsupervised open domain relation discovery. The encoder is a feature-rich relation extractor, which predicts a semantic relation between two entities. The decoder reconstructs entities relying on the predicted relation.
{{cite:13f4536fcf31a7461dd584b079788a058c8e37e9}} tried to learn multi-sense word embeddings. The encoder uses bilingual context to choose a sense for a given word. The decoder predicts context words based on the chosen sense and the given word.
{{cite:4e92015272fc16825271f250d8cba7d0cf688f61}} aimed to solve knowledge graph powered question answering.
Three neural networks are used to parameterize probabilities of a topic entity given a query and an answer, an answer based on a query and a predicted topic, and the topic given the query.
{{cite:15e424b4d7268e57d3f344d2f60ea19e1be698c3}} aimed to infer missing links in a knowledge graph.
Three neural networks are used to parameterize probabilities of a latent path given two entities and a relation, a relation based on two entities and the chosen latent path, and the relation given the latent path.
Our method also uses neural networks to parameterize two discrete distributions but aims to solve the DMSC task.
| m | 93806df685098561d833a800577b3acc |
In 2010 we systematically studied decay properties of the {{formula:8d5c7940-9d3e-49c1-9022-fb0d6a707064}} ({{formula:2d900d2c-f5dc-4d0f-bb58-ef04756f93e0}} ) hybrid meson with {{formula:2059569e-7e23-40ed-b48c-53c4863700cd}} using the methods of QCD sum rules and light-cone sum rules, where we pointed out its {{formula:fc205ca8-7c4f-4ef0-91f0-ada798641fbd}} decay mode {{cite:93524f5c9ff67847e0fcfd4bc330705e23a92989}}, {{cite:6fb28f2c5deefd1d8c1a217c3d35573d5feae24a}}. This is just the discovery channel of the {{formula:51360d7e-954d-497d-a143-9f75a0e59507}} observed by BESIII {{cite:0c84a0f2f90b2488e41bb4a2d1b744627819ffcc}}, {{cite:f02bc42c74d032194f51ffd03298ec41cb54c5af}}. However, the partial width of this decay mode was calculated to be quite small in Ref. {{cite:6fb28f2c5deefd1d8c1a217c3d35573d5feae24a}}, where we only took into account the normal decay process depicted in Fig. REF (a) with one quark-antiquark pair excited from the valence gluon.
| i | 3ec07389f3a781900306fad9f62979da |
Continual learning (CL) and its extension to lifelong learning, represents one of the most desired functions in an artificial intelligence system, representing the capability of learning new concepts while preserving the knowledge of past experiences {{cite:291f7ada4b8e28a5550cc946df19c1837826d5fb}}. Such an ability can be used in many real-time applications such as robotics, health investigative systems, autonomous vehicles {{cite:428b8cd56381ec4610470439a21846491ddacf1b}} or for guiding agents exploring artificial (meta) universes, requiring adapting to a changing environment. Unfortunately, modern deep learning models suffer from a degenerated performance on past data after learning novel knowledge, a phenomenon called catastrophic forgetting {{cite:9f375c942f8228e5940db17d3aa9b2a0005d1842}}.
| i | ae87026d6ae4c75a9b2ec9512f1ede6e |
Regarding the emergent symmetry, our results are supportive of the statement
that it is exact at large {{formula:fa65cbfc-a669-49e2-bd22-051fdb01d408}} , as we have illustrated in section , where we demonstrated its presence for an entire set of correlators involving composite operators in {{formula:913928c6-2b55-4821-aa25-b03fa05f16d2}} . This may have important implications for the AdS/CFT correspondence, which states that the critical {{formula:0395fc43-7e86-42bf-81fc-0b36e6e8523e}} vector model in {{formula:75420374-a50d-4001-97be-03cb51b433e2}} is dual to a higher-spin Vasiliev theory on {{formula:7134be2e-4452-43b9-b60e-edced285fbd7}} . The AdS/CFT mapping suggests that the operator {{formula:fe21ef0a-4825-44bb-9c4e-0d4be2c431f4}} is dual to the spin zero field {{formula:cd00e0d6-2b1d-48cc-a1ac-811a713da1ed}} in AdS, and correspondingly all its polynomial powers correspond to the polynomial powers of {{formula:ad18d8cd-cc2b-40ee-bf6a-70a82bbc474e}} . Thus, any statement we make about large {{formula:ac0ba576-4b4c-4e0b-a668-01208a5974b0}} three-point correlators of {{formula:b438f15a-c273-430f-8480-b315c5b2493b}} operators in the boundary CFT, has a direct implication for the three-point correlators of {{formula:a511f0de-38b1-4763-bd5f-025b817f78be}} in the bulk theory. Correlations of composite currents in the AdS bulk, are hitherto
largely undiscussed in the literature to the best of our knowledge.
However, symmetries of the bulk action alone, known to exist at least
at the classical level, can demand some boundary correlators to vanish. For instance,
the cubic interaction {{formula:bcc4c76d-dbae-4c4e-86a0-b3bdccb28b0b}} is absent in the Vasiliev's theory in the bulk {{cite:de4c9a788a201ee34b0284e6a410426ee490a97b}}, {{cite:bac1f9d0d6490381c04cbd6f896a928ae0bd0fce}},
which translates to the statement that the boundary CFT possesses the {{formula:a1061483-e035-4f8d-827c-7f3510efc670}}
symmetry.
Next, the calculation of sub-leading corrections to such correlators in the large {{formula:e47ef302-f055-47d1-add2-855309f22f4c}} CFT has a direct implication on one-loop corrections in the AdS bulk, which are otherwise very hard to compute {{cite:594e8c4040ddde919e4862a64fc026714f775b78}}.
At the same time, the symmetry considerations might again indicate whether certain correlators can become non-zero
at sub-leading orders, due to an anomalous symmetry breaking mechanism in the bulk. An example
of the latter is furnished by the possible anomalous torsion term generated by loops in the bulk.See, e.g., {{cite:c3b5f4e779ee134e51cc6a9a2e037119d4c40b01}} for a holographic description of parity-breaking system via torsion deformation of the AdS bulk. We thank A. Petkou for the discussion and drawing our attention to relevant references.
| d | 0ad886ee0c38f053bf82b7e8a60005f8 |
Several new physics constructions have been put forward to simultaneously explain the tensions in {{formula:a3ce0e38-9fdc-4f6b-b803-ffa0a3a5a961}} and {{formula:18ee366d-63ff-438f-bcfe-d9795218278d}} (see, for example, {{cite:d0894df5618efc4f3ab629adb13ce0f97cb0ced6}}, {{cite:906a7c1eb2996d2a45025951471e675703320faa}}, {{cite:8076f167d69b6d31957c4eabd16edb2821363fdb}}, {{cite:0afe8ecf566d8540fdc22192d0bcc0b837f1bcef}}, {{cite:c4f268e7158df5ef0d16fce563ae3ab015b5a6d2}}, {{cite:0f2297819c47b3e78d0f5d5b62e4f6ceea971039}}, {{cite:0103d25a3be4fc4801f8ad4c48981a5e0f07ec2b}}, {{cite:1678cff3d5ac2a90d4726e6bdf17206805007d7c}}, {{cite:7819e5a78243d1e0fb3ce5966b4f45d90569c930}}, {{cite:8b250f9bbd0ca4353723e8b9a448b617090d99f6}}, {{cite:3246ce3143226fd76e8f28ac583d85f24726f5b9}}, {{cite:567f0963409404de97ccaafa81e4c74fb4a29dd2}}, {{cite:0a4a99cc8a843e8b231af6d342715b1ae33caad4}}, {{cite:83b5c3d0ccfb4b34150f45c5c8018ada6b331e4b}}, {{cite:830f21d8a4a865000044c31ad164fb6a35473c62}}, {{cite:cd698e3caf5c1649d50f69b839fb176527d1d657}}, {{cite:ed35af3581fe5fc0336b89043514751cfab08732}}, {{cite:b8c04c8b94b398e8c0117ba9c98d241700a7442f}}, {{cite:0363ba6c261908fe119efe7572d15985ac5281ee}}, {{cite:074324350472a550ba778f94a71422df0298a6ce}}, {{cite:fa72c263cec828870361b11e8d9b4a8a63aea39e}}, {{cite:d8611a96c8871907594b60cd17379d3e75ff6db9}}, {{cite:831cf2b6d4db8f556ce486e4631c27653d29929b}}, {{cite:deb0d8cbbcf9eeecfb0817ef362e7261787fe25e}}, {{cite:5cf39eda5807cb24a96f840f7e1d51bf82955352}}, {{cite:79339ed534e1092b77b5dca9ff126d773ee02742}}, {{cite:981d14ffb4df1951dbf635a0e0ac976f572f3d56}}, {{cite:a2b92afdc59be43f9c389720957d18b51dcd5d10}}, {{cite:10ae5c2a6f7b3cea1ff3ea60a37c34d447b5683f}}). Among the most minimal models, extensions of the SM gauge group via additional {{formula:1e382cde-5202-463c-9624-a7f8e49f457e}} groups have been intensively explored, as these offer several appealing features. The new (vector) boson (as well as other potentially present state) and new associated neutral currents can open the door to
extensive implications both for particle and astroparticle physics, across vast energy scales {{cite:54d75c50c616f5a326b8218a887ee6ba0f3864a6}}. In addition to their potential in what concerns well-motivated dark matter mediators see, for instance {{cite:caec5b3cc1a860abc33273e160d9f84b6e2cd679}}, {{cite:cda38cbd622e6a210ec8be4db4066dac4d802271}}, {{cite:95f01682cd1b8ef7a2fcd6cc77ba9313b3cca8fc}}, {{cite:775ef1c5d60d057850543dec5fa479104a2cf90e}}, {{formula:2e67f1e2-3aef-43d7-94b5-b68b7a9eff9a}} extensions of the SM have been considered in the context of flavour physics, in particular in what concerns {{formula:2c9c25c6-5537-4c17-ad9c-a6208cd3bb1f}} -meson decay observables (especially {{formula:d36f97f3-7688-4390-9c28-e65544976956}} transitions) {{cite:0a7cd40ddd26a178fd765a1e266ddddc2c7eb7b6}}, {{cite:a330d19d7b25487ac6e55943abaddc8486f7de62}}, {{cite:bf3649079be9e228c6a8209aae03496c1e4e446c}}, {{cite:ba57d19c3b52764a1e763992bd23076e813f90bc}}, {{cite:8264bcaca5e554d0972f037ec768b03e9057bd37}}, {{cite:2148d0747a669b04f3cab70cc87365268029407e}}, {{cite:caec5b3cc1a860abc33273e160d9f84b6e2cd679}}, {{cite:b5de6696cc7f687fa94d206f919c0dede39b812e}}, {{cite:72e33de798cc36e93faf77fced472f3a83dd0fa9}}, {{cite:1ec1d0b8186633d8c70a0e16b760693128110c64}}, {{cite:d603348ddee537756781d69fca921d820662b0cd}}, {{cite:812d85938b004a23a454ebfc2d4e88db0e52e889}}, {{cite:1f24f43216b031ef6692ce7e31459ef30d69d6c9}}, {{cite:ec417716665c7c1255d5a96b355db99beb3197a5}}, {{cite:a5e122d12d6e2d45291f1e1b8ca53dc0ec76481d}}, {{cite:6b426383c3b31f5e9e1e4ff42583d7e6e1196608}}, {{cite:20dcc62486e3d59736681a85dade1d92df6302b3}}.
| i | 821166b922a9bb653ab5787a1554490d |