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An important challenge in hadron physics is to understand the nature of excited nucleon resonances. These excitations are coupled to some meson-baryon and {{formula:5bedaf68-8b7f-4f89-a1d1-32bc83d0a418}} channels {{cite:5179e9578867a963b6122a9ba602f414c6aca08e}}, {{cite:e7d5c0f631dd75959bf5e91382f312bdb166c7d4}}. Extensive data are accumulated from photoproduction, electroproduction, and meson-nucleon scattering for decades efforts, which can help us disclose the structure of these resonances and furthermore the properties of QCD in the non-perturbative region.
| i | c8ce5e395e43876da6fe7f9b94a0c960 |
Our approach is related to deformable convolution {{cite:649307182a7ef8765f427074027826171dd6d1f5}}, {{cite:ef85cda305b966ce91e83f63ed05490621c9cdcc}} and Non-local {{cite:bfd5fd0985b54d08685f0584f5ea0a649b92c1d0}}, but has several key differences:
| d | 1b753f0fbe42c5fcab1ff005016f96f4 |
However we know how to construct correctly the path integral
formalism only in the restricted case of canonical variables {{cite:ed82573efd5a2064de3b79156b50b953bc4cc301}}. At first sight the path integrals in terms of generalized
coordinates can be defined through the corresponding transformation.
But there is an opinion that it is impossible to perform the
transformation of path-integral variables: the naive transformation
of coordinates give wrong results because of their stochastic nature
in quantum theoriesOne can find corresponding examples in
{{cite:ed82573efd5a2064de3b79156b50b953bc4cc301}}, {{cite:f69906734e21a93d0c65cdff953941918f10f2a9}}. The mostly popular method of transformation of the
path-integral variables is a "time-sliced" method {{cite:79cacb71449ab3fa4339e269478eacef2d39920b}}, which
induces corrections to the interaction Lagrangian proportional at
least to {{formula:8233dc2d-8434-4225-91da-538fca16e6f0}} {{cite:203f4071fcd8f4c0ef24058c0537d64cc052ad47}}, i.e. the problem of transformation is
of a quantum nature. For this reason the usage of the "time-sliced"
method in general case is cumbersome, see also {{cite:b25bca06b37788e375a7ff8b9fe2c304e00d15d5}}.. That is
why such general principle as the conservation of total probability
(REF ) should play important role. Indeed, it is evident that
{{formula:cd64de32-d1c3-434d-ac7f-389abdd829a3}} -like Dirac measure (REF ) allows to perform arbitrary
transformation {{cite:4570bcb306640fad5cd285ad6ece3193960ea854}} just as in the classical mechanics.
| i | b1805f9120df6a60ddcbf12a0a8e9d9f |
A semigroup {{formula:7dbd0e07-c114-436a-9301-0cec020f6097}} is an ordered semigroup if there is a partial order {{formula:2b931e53-ff27-4a78-afda-fc3d91a5b0ba}} on {{formula:922182d9-15ee-4753-8a5a-f72a590f912f}} such that, for any {{formula:594f3a46-15b1-42b3-b8ea-31c2efd03df1}} with {{formula:d902d671-c573-4614-8540-6cce6129268f}} , we have {{formula:9b6b9a2e-d6d4-4c40-994f-649744d9b9cc}} and {{formula:b40175f9-5048-481c-ba8d-a41ed2a9485a}} for all {{formula:9643c209-a887-4cdd-8057-0a8ba6522d58}} . The partial order {{formula:fd8c9827-c552-4651-9229-ca1e203e9b5b}} on {{formula:4605c944-191e-4f40-a4a2-89a9d34aa5eb}} is a total order if, further, for each pair {{formula:775165f4-f344-42c5-8358-72ac7fd92510}} , either {{formula:310f16c5-3f95-4ad6-a0c6-d3cbf3a90916}} or {{formula:5f896082-64db-439c-b93b-b2498dd2122a}} holds {{cite:16d0219764cfee9ea047a6ab2891af3a967e64e8}}.
| r | 8cdae5f68c5e80f0df34c0d7dfe93b5d |
Several research directions seem appealing on the basis of these results. Scaling in object and scene complexity could be handled by incorporating object priors based on hierarchical shape decompositions or infinite mixtures of piecewise GPs. The explicit 3D scenes could be augmented with physical information, with kinematic and physical constraints integrated via undirected potentials; it may begin to be practical to build systems that perform rich physical reasoning directly from real-world visual data. Image comparison could be improved by using richer appearance models such as Epitomes {{cite:f4d6533ed364be50e0ef518a233677d9418d6f38}}. It could also be fruitful to experiment directly modeling reflectance and illumination via an approach like SIRFS {{cite:2fc924f612db63e2ae7a80f22b0807fc17a4f621}}, though choosing the right resolution for comparison may be difficult. It seems natural to explore richer bottom-up proposal mechanisms that integrate state-of-the-art discriminative techniques, including modern artificial neural networks {{cite:143780ae711799b7614fd74b7bbe6b910362a3e3}}. Many of these directions, as well as the exploration of alternative inference strategies, may be simplified by implementation as generative probabilistic graphics programs atop general-purpose probabilistic programming systems {{cite:7bd31c6174039e4dfcc4fa8695a7a63cb5e9d3bb}}.
| d | 354defb73b20a60aa7e69f82075999e8 |
On the other hand, non-Hermitian systems sparked a great interest both in experimental and theoretical fields {{cite:b171e33f62356e874c4d4e03900070397a18722e}}, {{cite:05b4c0162785da2c21262eefad0a7bde9ae6d109}}, {{cite:ad66744477227502e3a907062f46048779c3421c}}, {{cite:45ce8a2bfadb45e89d0cde5720c2a74b65ef712c}}, {{cite:d6ad56f1aef690a9becec50e755811ac27b51184}}, {{cite:926ef838e6686019f90f5d3531bab8aacbcb30fa}}, {{cite:5f8f3bdadd30b73603bf5811bcab55ec77a2483b}}, {{cite:6fae143c6cd4836a21680f00d4cef49c6a7c3c38}}, {{cite:c0c07a17f24c99adb60e74e99778f494de6cae56}}, {{cite:cb596afd222a3286afc89b41bfa2365b83d218b9}}, {{cite:aba1dd5e93a18ce91b92b72e8eef271cdd1f955b}}, {{cite:3b4d39e9f7db76376059d15040e59d5b236dbe5c}}, {{cite:0db5b6ed767fa9b4ac4a198d3f5b97a5ac304ca6}}, {{cite:bf16c86fcedeae1bdc94ebf658e74eba72023ff4}}, {{cite:bd2b75f49a4f0592e57534f3096a9189e000effc}}, {{cite:242751587ee91f75b1c2d9ce377095c5ed27f282}}, {{cite:ee57d9aa1bb12ccf43177ed4ed61d2506c7d74ed}}, {{cite:83a7b5969bbd8da1fc685ae11c4a6f258ef90f5e}}, {{cite:f5e0919cb040911fb39f3edfa87a3836baec947c}}, {{cite:8e8fa258b64f15f29e1658b293dd19017a40ebc9}}, {{cite:ad39add4c15ae3e35f280ef7192fa29def9b540c}}, {{cite:0205514f1a8cf320454cdadd8fe864429029606d}}, {{cite:94f5229e6af3fb79e228d3703c74c88bcb105f64}}, {{cite:0dbb9f2dad7790db8f70a549396aaadf0877fac4}}, {{cite:15c36098fc0267aca870dc03d23739b72f03d6b6}}, {{cite:6baf08b780093602c084a3cb8f36e6cca7164d21}}, {{cite:0376b803f777e863c08dd9080a22773051cd4a49}}, {{cite:775255cd093f8e78307985e182c950c81408d36a}}, {{cite:ef80511b068215281a37a51ec4b4b2290987cf6d}}, {{cite:945868825d1fa6166e6be6529afa17f1673155fc}}, {{cite:4e67cca46b80ebbc7d219dd1532deaa895adc9c9}}, {{cite:4009c228340eef54eff6a3a22d24441cc76519a4}}, {{cite:bd130c3bf0e7f9d232de1735582f23c50725eda8}}, {{cite:ef1961b3820e08e285aff48111d24a9d25dde452}}, {{cite:6d42a3259546855627d4b2e8640b368e42dcc6da}}, {{cite:e9cd839e97aa3464e2ea7c6fb92af3d5e6b2f59e}}, {{cite:d87b550b10afd62c059ba55d3e32bbd54802dedf}}, {{cite:9e455a379a91c001fa6081d4fac86089e83f8d0c}}, {{cite:4d42a7a6bab84dfd213429a89acb435348c01fc3}}, {{cite:ffcc1ac9d4cc2bfd10201639da0d6157d2bad44b}}, {{cite:a5607d556df74f22dc5eb7aced52e90e0f406c50}}, {{cite:6118936054f5156b53d411d8d9dc33eb0b6daf77}}, {{cite:3b8b832562a672dec7aae613947159eda4c32c45}}, {{cite:40a5fdeb527b904ffea17e203b6e9d0e98dcc01f}}, {{cite:f8a7a100ab436e66352631b15e7e2d6068ded856}}, {{cite:7d83184ee5d0ebf04d86a0f1ee0395348f42b552}}, {{cite:0fa3b80983b5d6046db79d220dfe093b21de9416}}, {{cite:4b63051c18bf5b03e10ad3bc633dae431f549f24}}, {{cite:383c9d785d9cb43215c61b878050c521265b21b8}}. Striking feathers are the failure of the bulk-boundary correspondence {{cite:cb596afd222a3286afc89b41bfa2365b83d218b9}}, {{cite:aba1dd5e93a18ce91b92b72e8eef271cdd1f955b}}, {{cite:3b4d39e9f7db76376059d15040e59d5b236dbe5c}}, {{cite:0db5b6ed767fa9b4ac4a198d3f5b97a5ac304ca6}}, {{cite:bf16c86fcedeae1bdc94ebf658e74eba72023ff4}}, {{cite:4e67cca46b80ebbc7d219dd1532deaa895adc9c9}}, the non-Hermitian skin effect {{cite:926ef838e6686019f90f5d3531bab8aacbcb30fa}}, {{cite:c0c07a17f24c99adb60e74e99778f494de6cae56}}, {{cite:aba1dd5e93a18ce91b92b72e8eef271cdd1f955b}}, {{cite:3b4d39e9f7db76376059d15040e59d5b236dbe5c}}, {{cite:0db5b6ed767fa9b4ac4a198d3f5b97a5ac304ca6}}, the sensitivity of the spectra on boundary conditions {{cite:45ce8a2bfadb45e89d0cde5720c2a74b65ef712c}}, {{cite:945868825d1fa6166e6be6529afa17f1673155fc}}, and the non-Hermitian-induced topology {{cite:4e67cca46b80ebbc7d219dd1532deaa895adc9c9}}, {{cite:4009c228340eef54eff6a3a22d24441cc76519a4}}. Recently, the interplay of non-Hermiticity and disorder has brought a new perspective of the localization properties {{cite:ad66744477227502e3a907062f46048779c3421c}}, {{cite:45ce8a2bfadb45e89d0cde5720c2a74b65ef712c}}, {{cite:d6ad56f1aef690a9becec50e755811ac27b51184}}, {{cite:5f8f3bdadd30b73603bf5811bcab55ec77a2483b}}, {{cite:6fae143c6cd4836a21680f00d4cef49c6a7c3c38}}, {{cite:c0c07a17f24c99adb60e74e99778f494de6cae56}}, {{cite:83a7b5969bbd8da1fc685ae11c4a6f258ef90f5e}}, {{cite:0db5b6ed767fa9b4ac4a198d3f5b97a5ac304ca6}}, {{cite:e3399c16bc0910ca8f8277b9fdc95d43c2604a73}}, {{cite:10822c84754a1fd89385c080227d117b22383e08}}, {{cite:d5f9d47afa4a291425238dfdc75e980c809ab5c5}}, {{cite:a9fba0579a7f1538931ac805ae4c9aedba317332}}, {{cite:4e2ef9fcc422d6140da8d7738079ba8c2d32eebd}}, {{cite:dcf3a2ddc6931b34fc2179df916b5e501cc1fe2f}}, {{cite:13c89ef0294e18eb20b033585fa5703e26118729}}, {{cite:079140f90061789dbb469c5e13690d8dc547fe30}}, {{cite:2543106484966251c10c14e65a7b9a2b18abc83c}}, {{cite:383c9d785d9cb43215c61b878050c521265b21b8}}. The famous Hatano-Helson model describing the interplay of the random disorder and the nonreciprocal hopping in 1D lattices displays a finite metal-insulator transition {{cite:ad66744477227502e3a907062f46048779c3421c}}, {{cite:45ce8a2bfadb45e89d0cde5720c2a74b65ef712c}}, {{cite:d6ad56f1aef690a9becec50e755811ac27b51184}}, {{cite:0db5b6ed767fa9b4ac4a198d3f5b97a5ac304ca6}}. One found that the coincidence of the metal-insulator phase transition point with the {{formula:eae70102-a574-49fd-b447-15fe534d4b44}} symmetry breaking point is of topological nature for the {{formula:42e9a8fe-cd36-4fcb-94d3-b2ecf151a3a8}} symmetrical extension of the AA models both in 1D {{cite:5f8f3bdadd30b73603bf5811bcab55ec77a2483b}}, {{cite:6fae143c6cd4836a21680f00d4cef49c6a7c3c38}}, {{cite:c0c07a17f24c99adb60e74e99778f494de6cae56}}, {{cite:e3399c16bc0910ca8f8277b9fdc95d43c2604a73}}, {{cite:83a7b5969bbd8da1fc685ae11c4a6f258ef90f5e}} and 2D systems {{cite:10822c84754a1fd89385c080227d117b22383e08}}. The non-Hermitian Maryland model shows a localization-delocalization phase transition via topological mobility edges in the complex energy plane {{cite:d5f9d47afa4a291425238dfdc75e980c809ab5c5}}, {{cite:a9fba0579a7f1538931ac805ae4c9aedba317332}}, while there are not extended states in its Hermitian version {{cite:62c122d5db4052b2b96558160971009d75be7298}}, {{cite:84b7fe7836a8168fb3566b25c3bbf4ddd41e0e88}}. These surprising results in non-Hermitian disorder fields inspire us to study the non-Hermitian effect in the long-range AA models.
| i | 94da808103168f24e0c4ad98d5e8a68c |
In summary, we should have expected to have less confidence
in estimates of CIs of
{{formula:646b1c7e-4f76-41a6-a24d-6281b5650104}} at the outset of a EVD epidemic given process noise.
We hope that the current method, similar in intent to that of King et al. {{cite:79ee4ee4bffb2226b54ee2ff926442baa3f1cb58}},
provides an accessible route for estimating realistic CIs for {{formula:63649b7c-e113-496d-b1f8-1f14fd66676c}}
in epidemics. In practice, the 95% confidence
intervals in {{formula:c6ea88bc-1ca5-458b-9a0b-4d57801bd24b}} estimated from stochastic model fits
will be broader than that estimated from deterministic model
fits to cumulative case data.
Estimates of CIs using the current hybrid approach
represent a lower bound of uncertainty due to stochastic sources of noise.
As an epidemic continues and the number of infected individuals increases, observation noise contributes a relatively larger proportion of uncertainty as compared to process noise {{cite:35192489fa1c518bd8540a1d3c96189b3a185c72}}.
Remaining realistic about the limits to
confidence in model fits should also be incorporated
into public health practice, e.g.,
when projecting the necessary scope of intervention
based on “optimal” fits {{cite:adca16f3203750afa1f0c38a9bda20aa70353162}}.
We encourage the academic, governmental, and non-governmental
public health
communities to consider
incorporating unavoidable uncertainty into their decision making
pipelines when responding to emergent disease outbreaks.
Appendix
Generating function approach to link characteristic times and
transmission rates
The generalized SEIRD model includes {{formula:2d04021b-4cd8-4fe7-a859-9ec4fafc2858}} number of exposed classes each
of duration {{formula:eaf552af-51ed-44ff-b5e0-b210f6125ffa}} . Given a value of {{formula:84db0864-46cb-4fc0-bd1e-bf1195d97150}} and
{{formula:a4d82b1f-b9c8-41e9-a9da-2d7dff23fcdc}} , then the generating function approach of Wallinga
and Lipsitch {{cite:ab9a0266bb6b92dca3a81ba94c72867fed8ca54f}}, {{cite:74b3a02f67259bb6ce1ddc1d87e3fa54a8fb75f8}} can be used to derive
the following relationships:
{{formula:e23a7d26-d8e5-40f0-a05b-77c42affd6c3}}
Stochastic simulations of epidemic outbreaks
Stochastic realizations of the SEIRD model are simulated
using the Gillespie framework {{cite:0fd877e090c59b13c5ac27ecba0435bf6695d6f8}}, given the “reaction” events in the following table:
{{table:21f1dbd8-066f-431a-afab-d19025786767}}Processes transition individuals who are susceptible (S), exposed (E), infected (I), deceased (D), recovered (R), and buried (B).
The total population is fixed at {{formula:2634ce81-4e4e-4289-b4e7-359ecbf65c94}} .
Epidemics are initiated with one infectious individual in an otherwise susceptible population. Mathematically, the initial state is, in the respective ordering, {{formula:13ee15be-47ce-4181-b89d-21594114ba17}}
at {{formula:0b8700ef-5398-4d37-a644-536ec8e75936}} .
The total rate of outbreak-associated events is {{formula:86032384-9671-42d6-89c0-7bbbad81a085}} .
The time until next event is determined randomly such that
{{formula:1f06f9b1-48f1-4617-a064-66e194769f0a}}
where {{formula:f5ec92eb-03ce-4305-8dc7-fce9fd1e5757}} is a uniformly distributed number between 0 and 1. In this way,
the time between events follows an exponential distribution with rate {{formula:2afa74a2-4c33-48e9-b681-1457a9651005}} .
Then, the probability of each event is {{formula:16af2f5e-e736-47bf-bd45-458aeb7e926c}} . After selecting
an event and updating
the discrete number of individuals, the reaction rates are recalculated
and the process continues.
The same framework can be extended to include multiple {{formula:feecac88-2bb0-4ac9-9381-6f7cc85e0d5e}} subclasses
within the exposed class, to capture the peaked nature of
the exposed period (centered around 11 days for EVD).
Trajectories are complete when the epidemic dies out because
there are no more infectious individuals. In the present context,
we are interested in those trajectories that do not die out before the end of the simulation time.
{{figure:47a4596f-728c-4fde-9ace-63a25843986e}}
Pseudo-Bayesian approach for uncertainty in {{formula:a7b27fbf-dc1e-4ffe-8b71-33a9d5e7d444}}
The fraction of infections of EVD in west Africa due to transmissions from the deceased has been estimated to be between .01-0.3 {{cite:3956adb93f905f2e8d94386d11e04ee5e516a0c6}}. However an estimate from a prior EVD outbreak in Congo is even higher {{cite:949eda260c929adc690bfcb5ad333b2b057948b7}}. To address this treat {{formula:dc3f8a9b-ba66-4cc1-9a9c-3a4b78fc3f7f}} as uncertain with a uniform prior distribution between 0.1-0.4. We are interested with models that have a deterministic {{formula:5007b3d2-6969-4c18-912d-687e1db614d2}} . For each {{formula:2a24e1b5-0412-4dfe-9e4d-703d38ef96cc}} , we randomly, uniformly sample {{formula:d662d51d-4be7-4c21-9230-e48b2022b1ab}} from the prior distribution. Each sample of {{formula:18b8cbbb-0301-4f7c-8f2c-7658f687e936}} and {{formula:a12d6eff-7b5b-47d6-befe-3ec449a8f8fc}} determine the growth rate {{formula:8005cacf-1504-4426-971d-7ece249a22cf}} which in turn determines the infection parameters, {{formula:32536423-52a9-4428-9465-438e419290c7}} and {{formula:97daf445-17ee-4266-8b14-89777fabfa62}} .
An ensemble of {{formula:ba519605-465f-461c-b391-e15ef906809a}} trajectories are obtained for each value {{formula:2ce16054-373f-4167-adc0-b9e74fb6f758}} with {{formula:1e19e8b2-f155-42b9-a5d5-a114b952de4f}} sampled uniformly from [.1 .4] for each trajectory. The resulting distribution of measured characteristic times {{formula:90687635-d5f2-4ee9-9f45-9de4733ddcbf}} can be interpreted as a marginal distribution across {{formula:26525725-8607-4db8-984f-1320b364f620}} . Even with a fixed {{formula:a8740036-35e2-4dff-8849-317ee847fd63}} , as {{formula:cf544eaf-28bf-4809-9cf9-31f7bc736574}} varies the secondary infection distribution changes. Hence, the marginal distribution across {{formula:2dc9e839-9ab3-41dc-90ed-9d9b6ac931c7}} can also be interpreted as a marginal distribution across the time to secondary infection distributions that all correspond to the same reproductive number of the disease in the population {{formula:27fb0db8-697c-4e5f-a3f6-88b318f76075}} .
Comparing results from CCC and ICC data
There are a number of potential pitfalls of using CCCs rather than ICCs.
Yet, King and colleagues in their critique of CCCs noted
that the summary statistics of the epidemic growth for SEIR models
were functionally equivalent when
fitted to an ensemble of CCCs and ICCs given the same underlying
disease parameters {{cite:79ee4ee4bffb2226b54ee2ff926442baa3f1cb58}}. The difference, as they pointed out, was how to interpret
the quality of the fits in inferring CIs. Similarly, here we
find that the resulting distributions, {{formula:6bf1349a-71e8-4f17-b481-05c3bf22265c}} ,
measured using either the CCC or ICC are similar but not equivalent
(Figure REF ). Differences in the resulting CIs are minor, but the median of the ICC distribution is skewed larger than the theoretical value. These differences scale up to the overall analysis, but with minor effect on the {{formula:99468a2b-729d-4d7c-83e0-58e1a24391f4}} and {{formula:5254304b-fcd9-4896-a8b6-3662c86a27cc}} CIs. The resulting {{formula:572ee479-497d-4615-b283-f3c2067c73f0}} CIs from our synthetic data are 17.0–30.1 given fits to cumulative data and 16.6–28.5 given fits to incident data. The resulting CIs are approximately the same size.
This contrasts with prior results from profile likelihoods in which
the CIs as inferred from CCCs are contained within the CIs as inferred from ICCs {{cite:79ee4ee4bffb2226b54ee2ff926442baa3f1cb58}}.
{{figure:61fa7fb5-400a-42fc-935f-5100ce181d06}}We emphasize that our method does not utilize the quality of any individual fit to generate the CIs for {{formula:f5023506-f837-47c9-8368-68ff264bdb5f}} , for precisely the reasons cautioned by King and colleagues {{cite:79ee4ee4bffb2226b54ee2ff926442baa3f1cb58}}.
Estimating the growth rate, {{formula:f6ce8e16-10b9-48ab-a218-77fdd73918bb}} , from linear regression is uncertain due to the fitting procedure itself. Associated with each estimate of {{formula:4fb3293d-bd85-419a-b57a-bd05bac3e955}} are confidence intervals. We compare the distributions of errors due to fitting associated with the CCCs and ICCs of our simulated data in Figure REF . The errors associated with ICCs are larger than those associated with CCCs. It remains an open question as to whether/when
CCCs rather than ICCs are preferable when
leveraging regression fitting to estimate {{formula:f9f6465e-0d9d-4ccc-abc5-15b54cd57a87}} given process noise
alone, rather than observation noise.
{{figure:d0efcfa2-281c-4833-842b-d804a09fb4fa}}
Identifiability problem persists when inferring
relative fraction of post-death transmission from stochastic trajectories
The measured growth rate of
an epidemic, {{formula:69209151-aee3-4b06-9d4b-ddb03bb9a6db}} can be used to infer the basic
reproductive number, {{formula:15c06e00-e4ac-4091-b3c1-348e8da5d34f}} . Using a generating function
approach, it can be shown that {{formula:8a58339e-eaee-436f-af94-40c9ad92e06e}}
where {{formula:cd2619b7-9c02-4f7f-b53e-95d839e14130}} {{cite:ab9a0266bb6b92dca3a81ba94c72867fed8ca54f}}
where {{formula:e6ceebc2-5a76-43a8-aded-cbc1be257ceb}} is the normalized fraction of all secondary cases caused
by an infectious individual at “age” {{formula:4496db4d-0abf-42b2-a356-2601851de542}} since infection.
A range of values of
{{formula:9a2ee162-f230-4123-9015-0c2f0ea15bba}} may be compatible with a single estimate of {{formula:1b88a4e2-72da-4dee-b249-5978e23d62b8}} {{cite:74b3a02f67259bb6ce1ddc1d87e3fa54a8fb75f8}}.
This uncertainty is a consequence of an identifiability problem
given uncertainty in the relative fraction of transmission
events that could be attributed to post-death transmission.
Here we ask: what is the variation in the
growth rate, {{formula:c3fb16dd-7fea-4e21-aaae-7400acc1c66d}} , and characteristic time, {{formula:da7dc241-bebc-4374-b816-b92222589428}} ,
compatible with varying fraction of post-death transmission, {{formula:6f3ae843-73b6-4721-9236-52b5fe72f263}} .
Figure REF shows the measured variation in
the characteristic time, {{formula:1aaedb8a-b089-4eef-a0c6-5b143c6236d4}} for
5000 ensembles for three different expected growth rates
{{formula:32646ee1-1e57-4255-a09f-aa0772ba5b87}} , 1/21 and 1/28 days{{formula:fce8dec5-517b-4a01-9ac7-8d49d0d8310e}} . In each case, we varied
{{formula:d47177b8-f8c1-4121-8399-3844eb4762bf}} from 0 to 1 in increments of 0.2.
As in the prior section, we find that the
characteristic time of an epidemic can vary substantially
for a fixed value of {{formula:fed97432-218c-4d84-b452-9ff9fcf93c51}} . Here, we also expect
that a range of mechanistic models can all yield the same
expected characteristic time.
As is evident,
the identifiability problem highlighted in prior analyses
of deterministic models {{cite:74b3a02f67259bb6ce1ddc1d87e3fa54a8fb75f8}}, {{cite:e3676c541f9dd0e9e5deb754e777f1628e5de561}} also applies in
the case of stochastic models.
For SEIRD models, the expected value
of the basic reproductive number increases with {{formula:38e618cc-6241-4a94-babb-cfeeb826b469}} .
Therefore, efforts to constrain
estimates of {{formula:12cb1e64-573a-42ee-8d25-3e7037f1bebd}} from EVD case data will
be subject to inherent variability due, in part, to uncertainty
in mechanism, e.g., the relative fraction of post-death transmission,
and process, i.e., stochastic outbreak dynamics.
{{figure:57ae6788-624c-4dff-a5a4-bcb0b8aacaea}}
Acknowledgments
The work was funded by a grant to JSW from the Burroughs Wellcome Fund and from the Army Research Office grant #W911NF-14-1-0402. We would like to acknowledge Luis F. Jover for reviewing the manuscript.
| d | 3ab40ffb092565040a71e3182291248a |
(1) CCDN and the heatmap regression methods (HGs {{cite:e8cf7dad8f0889da427031265c83ea99e57036b1}}, SAN {{cite:5fc117aa50cbec8c5040100e553b564f085fd74d}}, Liu et al. {{cite:d534067f9b40b83a8be1b2ee787cb7dd63462c4b}} and LUVLi {{cite:181f72f3bf5ea4ce200c1a199264412f2a829f9e}}) enhance their robustness to the variations in facial poses, expressions and occlusions by effectively model the differences in facial local details and the correlations/relationships between different facial local details. The heatmap regression methods achieve this by utilizing the multi-scale features with larger receptive fields, while our method by proposing the cross-order cross-semantic deep network. However, our method outperforms the heatmap regression methods, which indicates that: 1) the well-designed cross-order two-squeeze multi-excitation module can effectively utilize the cross-order channel correlations to activate parts of interest and generate multiple attention-specific feature maps. 2) the proposed cross-order cross-semantic regularizer is able to drive the network to learn more fine and complementary cross-order cross-semantic features that are more robust to large poses and heavy occlusions from the generated multiple attention-specific feature maps. 3) by integrating the CTM module and COCS regularizer into a cross-order cross-semantic deep network with a seamless formulation, the robustness and accuracy of our method can be enhanced.
| r | 3b4103bdfa2475c51ac77c0bd55fd17a |
Our model is evaluated on robotic manipulation tasks - namely pick and place tasks - in simulation using multi-agent MuJoCo {{cite:0191f97433650694d925f1c647e32e4f78207162}} environments. Our evaluations investigate the following questions: (1) can our model perform new task instances (defined in REF ) previously unseen during training? And (2) what components (e.g. inverse loss, etc.) are most crucial for successful control?
{{figure:a9f7e050-7a89-4390-8b94-7007b82f8f2a}} | r | d53108e418894048f0b0f6c98db26390 |
In arithmetic statistics, other objects are frequently studied in this way. Given an ordering of the objects satisfying a Northcott property, one can ask for the asymptotic growth rate of the counting function
#{object order(object)X}
as {{formula:3e533f83-592b-4775-b284-e6960a685c33}} tends to {{formula:70de56b4-0ae2-4e6b-acad-b39de8f8617d}} . The standard examples are points on schemes (or stacks) bounded by height, whose asymptotic growth rates are predicted by the Batyrev-Manin conjecture {{cite:a19274dc7c8fdd3277084bc05af0e0a815e9c7bb}}, {{cite:66d8ecadbc4aa96396fda84b1fa03f5f64ebb6a7}}, and counting {{formula:eb665c01-a95f-4e8a-9e8c-e25ede304ffe}} -extensions of a global field {{formula:88320db4-55f9-461f-a159-3db8cc3a214d}} ordered by discriminant, whose asymptotic growth rates are predicted by Malle's conjecture {{cite:b1bb651780317a8e867465c7d9b83d39b4ecc499}}, {{cite:fd1e76eaf05ef417f9ac84e0c7ea876af0ed0d60}}.
| i | be78a55eeec115abb2360ac80f81685b |
We also want to highlight the importance of the principal tensor as reviewed in {{cite:aa577cd042bc720660bdff162fcba281de8965fb}}. Spacetimes
possessing a principal tensor are always algebraically special (type D). If they are vacuum solutions, then they
also have aligned fields: electromagnetic fields with the same components as the principal tensor. These fields have {{formula:ca348655-c0db-4f43-a5e5-f8c2637807ef}} free parameters; setting these charges proportional to the mass and {{formula:70785364-8b14-4e86-b4a9-3e85efd8f485}} NUT charges results in our single copy field. In some sense the principal tensor controls the form of the metric, so it is not too surprising that it is related so closely to the metric's single copy. A natural extension of our work would be to include non-vacuum metrics which still possess a principal tensor.
| d | ff9e0b9551a8231b3a0307861fe7a653 |
ROS: A method to build a more balanced dataset by over-sampling the minority samples{{cite:6b79ee2526958fe833c773a970b990bb666fabc4}}.
| m | 51f72e53cdb3845f472e58acf8e80363 |
After the realization of quantized conductance on quantum point contact (QPC), Y-junction structures on modulation-doped heterostructures have been proposed and fabricated{{cite:4f9a471211026bf6948a7bb7eb69fba6e3eb04f5}}, {{cite:88ee031fbcc65f0677e38784a414dbe7249dcbc3}}, {{cite:a222abf951f98a0c5ccb66d4ea994dc00d876c71}}. Different terminologies have been used to address similar devices such as Y-branch switch (YBS) and three-terminal ballistic junction (TBJ). A gate defined YBS hardly works in ballistic regime or in another world the quantization of conductance is rarely reported as a prominent characteristic of device{{cite:a222abf951f98a0c5ccb66d4ea994dc00d876c71}}. Whereas, peaks on the derivative of conductance on wet-etched version of YBS demonstrate the presence of quantization{{cite:ff49621d86fc3b38e779575ad5c28b5cd97b2379}}, {{cite:d8b8d3119504d797706cbb970e2c86ba0b6836a4}}. This is probably because subband-spacings in a gate defined 1D quantum wire are limited to the order of a few meV while larger energy spacing in a wet-etched GaAs/AlGaAs quantum wires, typically on the order of a few tens of meV, have been reported. Note that, the conductance of wet-etched YBS does not exhibits flat plateaus and an exact identical I-V characteristic have not been reported. On the other hand, carbon nanotube Y-junction (CNT-YJ), T-shaped GNR (T-GNR) and few Cross-shape GNR (C-GNR) have been widely studied theoretically{{cite:a8ed1c0e532c63e3d85e9d7edd4455ad37e688a8}}, {{cite:d1a24b3d411ff798b06e9db609754aae511cb240}}. The conductance of CNT-YJ shows oscillatory behavior in theoretical studies which merely depends on geometry of system. To the best our knowledge quantization of conductance does not report on chemically synthesized Y-junctions nanotube and both T-GNR and C-GNR do not exhibit quantization of conductance as well{{cite:804ded034f116a3a7c6b6236943245ae104b71ef}}, {{cite:df2bd2746e88c7dca5282968d5e6c15885d21ec3}}, {{cite:b287bf238e4c8719a75e3ccb6851fa59ec50a27b}}. A prominent benefit of the proposed structure is the flat plateaus on conductance of a smooth YJ-GWG, Fig. REF (d), which is not reported in other possible carbon base splitters so far. The optimization of the width of incoming path on a smooth-bended YJ-GWG can be considered as a viable method to achieve the goal of coherent splitting. YJ-GWG can be a gateway for the realization of possible carbon-base electron interference devices, as well as interconnect in graphene-based spintronic devices.
| d | e502e5ac21fa5df673f6b88a69614f6c |
First of all, if we willingly forgo covariance, then the light-front approach {{cite:57010ee00f8aeec9cdd7461f624b0ade7241f5cd}}, {{cite:605d6f2a32db5fe8318d3807799fd3b0910f46be}}, {{cite:8865ba1a33f9ccd5097ea3ea4b62747efdcb6232}}, {{cite:c0840c9e22786a138b99f4ee1832042eb6ecb7cd}}, {{cite:b9ae666df24a78804f93ba07b48156a6f5d893fc}}, {{cite:4e7cf2c96913f5dfdba43aac5878efd0d08cbc01}}, {{cite:0d82cb4f70d108cfec9bd092433fdbca9303cb9c}} is the very first approach that provides positive results on perturbatively local interacting higher-spin theories with propagating degrees of freedom. The chiral higher-spin theories {{cite:c0840c9e22786a138b99f4ee1832042eb6ecb7cd}}, {{cite:b9ae666df24a78804f93ba07b48156a6f5d893fc}}, {{cite:4e7cf2c96913f5dfdba43aac5878efd0d08cbc01}}, {{cite:d8ea9375d57b627696357b973673528f9b7d9ea8}}, {{cite:4658fcf7f8bf66412ee370be648558a66de44231}} are the first theories that can avoid No-go theorems in both flat and AdS spaces. The flat space chiral theories were shown to be integrable in {{cite:0d82cb4f70d108cfec9bd092433fdbca9303cb9c}} and proven to be UV finite at one-loop in {{cite:91f40c13ee7f037a7a3bb3e5275abb923364c5dd}}, {{cite:190292c32d48a72c2536d2c3bb47eaaaeb641b64}}, {{cite:2ddb74df0b054b1cf62d91168c5f735ec6cee52d}}. We expect that the chiral theories are one-loop exact.
Secondly, one can start with an auxiliary space where non-locality is under control, and find a map to spacetime with the requirement that the interacting vertices in spacetime should not be too non-local. In particular, twistor space provides such a framework to construct (covariant) theories of interacting higher-spin fields in spacetime. For instance, by deforming the complex structure on twistor space, one can obtain conformal higher-spin gravity in {{formula:605431b5-804b-46f5-bf76-7de2b5a125b4}} {{cite:828bf99d8d135af42296478fc125f1b16f4a1114}}, {{cite:5446f51bf8db1e379409e1d52430974696cb868e}}. The higher-spin extensions of (self-dual) Yang-Mills (HS-(SD)YM) {{cite:69b58a4e8cd5b63617356deafebef0e1cf6423be}}, {{cite:09580d7a80fd50e1194b59816e4cf5b7a1b6b6d4}} and self-dual gravity (HS-SDGRA) {{cite:69b58a4e8cd5b63617356deafebef0e1cf6423be}} were obtained recently, using also some methods with deep roots in twistor theory. The main advantage of constructing higher-spin theories using twistor theory is that we can carefully maintain the covariance.
| i | d92bca62f899777c41e4f52911f97c21 |
The dual norm is used to specify a suitable choice of the regularization parameter {{formula:18bde8f9-7812-43de-9fc9-c23ba280e65f}} . In particular, according to {{cite:2d99582b036ce5ee5bbae1f9d12a759541c2d0b0}}, {{cite:02334b88512920064654d8fd5665418032fcbd97}}, if we consider any optimal solution {{formula:26d02657-9c75-4431-a54c-0da668ddc835}} to the optimization problem (REF ), with {{formula:01892007-b215-415b-ab8f-b8c11c471281}} satisfying
{{formula:1e19438b-fce1-4cb3-9c07-8d618f60876c}}
| r | 39421cf6862d7e40b5b96e35a875991d |
We assume the reader's acquaintance with basic notions and results of the theory of inverse semigroups. All these can be found in the early chapters of the monographs {{cite:6ae6be46020338daeec1a7a9503a28d2c36132e0}}, {{cite:939258ff53e53dbe9588c93e93cbd5a902ae759f}}.
| r | afcfc6315423a68c8ea43214b47e26b2 |
Point set registration is a fundamental problem that has wide applications in computer vision {{cite:f2ec4f0dad8e15c05d5f9b47715c7b9c3bd4e799}}, robotics {{cite:0be840a4aeb61247e95482048989b5e7c686c821}}, computer graphics {{cite:543d4ceecc47916cf76a7d7f159b7dd180e9b914}}, medical image analysis {{cite:b88bc0ac207dc088ee69885b8d121e4c3eae2ced}} and so on. With the advent of sensors such as LiDAR (Light Detection and Ranging) and depth cameras, it becomes relatively easy to capture real-world 3D scene data. However, one usually attains partial point clouds at once due to the 3D nature of the objects. To accurately reconstruct the 3D model, it is necessary to align multiple point clouds acquired from multi views of the object into a unified coordinate system.
| i | bbd1c11423b71e57b4d2ab69b0f09194 |
Also in {{cite:422701780a7ee689e2f657f423820bcc540107db}} the singularities of the 6-point ziggurat were determined and found to comprise precisely those encoded in the “hexagon symbol alphabet” which is expected to suffice for expressing all 6-point amplitudes in SYM theory. Consequently, no massless planar 6-point Feynman integral, in any field theory, can have (first-type) Landau singularities anywhere other than on the vanishing locus of the hexagon symbol alphabet. In this paper we initiate a study of the singularities of the 7-point ziggurat and its connection to the “heptagon symbol alphabet” that, according to all evidence available to date {{cite:b32591acf176e3522c9c9f12eaa360a0ca49b25b}}, {{cite:c7b352e7e120d7377cf792e580c59d5578eccaad}}, {{cite:e8e65f972bf403e659c06ef3a7c4f23e4d267fc5}}, seems to suffice for expressing all 7-point amplitudes in SYM theory. However we emphasize that just like {{cite:422701780a7ee689e2f657f423820bcc540107db}}, our present analysis is completely general and is in no way tied to SYM theory.
| i | 37d9dfd26982def88b03f8b0866d6a93 |
We implemented the Fourier recurrent unit in Tensorflow {{cite:baecfa327cc2ce638bc18dab9fc47252802a84ed}}
and used the standard implementation of BasicRNNCell and BasicLSTMCell for RNN and LSTM, respectively.
We also used the released source code of SRU {{cite:c5602d50e48c5f797524f632322522cbae04d1e0}} and used the default configurations of {{formula:f6067e55-d0b2-48a0-8df1-fff5bf040453}} , {{formula:dfa6f4c4-2000-413c-b553-d226747f8224}} dimension of 60, and {{formula:a89fbebf-763d-4355-8deb-748ff256bd4f}} dimension of 200. We release our codes on githubhttps://github.com/limbo018/FRU.
For fair comparison, we construct one layer of above cells with 200 units in the experiments.
Adam {{cite:95aa6df70ba23d0dafcf39d25b301a8c6c425efd}} is adopted as the optimization engine.
We explore learning rates in {0.001, 0.005, 0.01, 0.05, 0.1} and learning
rate decay in {0.8, 0.85, 0.9, 0.95, 0.99}. The best results are reported
after grid search for best hyper parameters.
For simplicity, we use {{formula:eae5ad36-4ade-4c00-b0f9-4f6281fa286f}} to denote {{formula:a5073add-c721-4d8b-a4d3-724bc27cb67f}} sampled sparse
frequencies and {{formula:41d33e70-0c31-44b8-9355-4f0114763325}} dimensions for each frequency {{formula:e9473fc1-febf-47bd-802a-2031b999225b}} in a FRU cell.
| r | 9600553718c7724d2ee0ac8bb41076cc |
There are many network-based optimization problems that fall under the category of linear inequality constrained optimization, one of such problems is distributed support vector machines{{cite:06c8e1609e33058dd76197270eff6ecdd9445b19}}, {{cite:7394cf652554749f77ebd72d23c1f33725351fd3}} which is solved in a distributed manner over a network of nodes acquiring valuable statistics. The results of this paper can be further extended to such problems.
| d | b50bace4b5ab374656d214d7a210253e |
Each {{formula:548759b4-8c34-4c44-ab6d-bd85c769ae76}} is {{formula:ebf0ce03-4c26-4179-8649-16dc53b8ab60}} -subgaussian (because Bernoulli), and is conditionally independent of the other random variables conditioned and on {{formula:f1e1e60d-7217-4052-a73c-4d9843286bd9}} and {{formula:ecb94892-b57b-4ce4-aa4d-19fd73115593}} . The incremental linear regression of line 7 of Algorithm is the same as {{cite:19b26856895ed55b550781681deeaaf30372a1de}}. Our observation model satisfies the conditions of the analysis of confidence ellipsoids of {{cite:d3e701db0a73650f8c0c2afd5ad1863602688ef2}}, from which we obtain:
| r | 6e2a85bb32bac421316556748897ce35 |
Related Globally Normalized Models
There is a rich literature on the applications of globally normalized
models {{cite:b9c012756d0f665a3f7a0c97f73b456ce47abe0a}}, {{cite:236961d9d9a0537f6030820ebc1d94647cb75d55}}, {{cite:e4b250d0bbf84f2231848bebb609449cb0a47ed0}}, {{cite:96f98931574616367042bf5788c4d0f07e34829e}} as
well as detailed studies on the importance of global normalization in addressing the label bias problem
{{cite:96f98931574616367042bf5788c4d0f07e34829e}}, {{cite:9b0c9f81af98be72df4a000743bb7664b514215d}}, {{cite:861b5efa2dca1ae55da910b8f5e104d80b0fea64}}.
In the context
of ASR there is a lot of research on applying globally normalized models {{cite:1e0bcdf21edcf63e8c6e05f20568bc3c092b6777}}, {{cite:d8e4fd41065d36c0f5b563a9763c37a7ce6a15d9}}, {{cite:48d871ff12a433aadbcc60362b701ede3e58aa0e}}, {{cite:a322296426dfba9b0021df0ae1b6cb9eee000601}}, {{cite:174bf17314f20cbdda9c6b854bdeb4a748503804}}, {{cite:ba888615d70bbee107791ba0639903fda30be5d6}}, {{cite:3535c6ff4626e69d30f49b32092e8a9cd573596b}}. Among these, MMI {{cite:1e0bcdf21edcf63e8c6e05f20568bc3c092b6777}}, {{cite:d8e4fd41065d36c0f5b563a9763c37a7ce6a15d9}} is the most relevant
globally normalized criterion to
our work. In MMI a sequence level score is factorized by a likelihood score
which comes from an acoustic model and a prior score which is usually a word based
language model (LM). The denominator score is then approximated over a lattice
of hypotheses. More recently a lattice free version of this criterion has been
introduced {{cite:689cf41e7ca614934af4b9c28f32b13b2acf0cd0}} which replaces the word level LM with a 4-gram
phone LM.
Both the GNAT and MMI criteria are globally normalized.
The GNAT model differentiates itself from MMI in several ways. First unlike MMI it
does not require an external LM and it does not apply any constraint on how the sequence level
scores are defined. Second, in MMI the language model is kept frozen while the acoustic model parameters
are updated via optimization of the MMI criterion. In GNAT all the model parameters
are trained together.
Third, GNAT provides the exact computation
of the denominator while standard MMI only offers an approximation. Finally GNAT trains from scratch
without any need for initialization or special regularization techniques as used in the
lattice-free version of MMI {{cite:689cf41e7ca614934af4b9c28f32b13b2acf0cd0}}. In addition we were able to train
GNAT models with accelerators without any techniques discussed in {{cite:689cf41e7ca614934af4b9c28f32b13b2acf0cd0}}.
| d | 5cb3743ced5bb5f5f3038a6773b707d1 |
We finally comment on the consequences of our finding of the excess of the speed
of sound over the conformal bound for the modeling of the EoS of neutron stars.
With increasing amount of data on the masses and radii of the observed neutron stars
in the Universe, several groups started to extract information on the QCD
EoS at nonzero baryon density using this experimental data. In these approaches,
the EoS is typically constrained at small and large densities from effective
hadronic models (e.g. {{cite:58749e032702571ec0df19e1b8a40d6fd27fa550}}, {{cite:4e4187cc3e14b8838667f940513d9940a9f639ef}}) and perturbative
QCD (e.g. {{cite:66cc2e3ed3c25f46d83b31399f536693921faa7e}}), respectively and then interpolated using a set of
basis functions
(e.g. {{cite:1bef93f5d9bb38f1dca2ee6773a7512b32c04fee}}, {{cite:68b651d64833e84280a6a3dcaaf5c0a05decc7a0}}, {{cite:27bfb8a827f5500b9b5587fe7a518eb55b4956f5}}, {{cite:3825463d645be5e898b5f509586fb15e9ff12152}}).
Newer studies use a large set of different types of basic functions and millions
of different EoS
interpolations {{cite:d862d9dbe5d1fc8048e97c169e53271355cf7395}}, {{cite:80800954564c30230fbe3c54da888daa399d478c}}, {{cite:bdd4905bc6ff14a0aa900891a91bc89cf3a15abe}}, {{cite:57b81e6c8ed4cebf685fddfec690d5fc0dff364e}}, {{cite:f1875ad2e75cfcec5d1c26cb5f74d31b4354eb4f}}, {{cite:1d549560bfbd4a291418f4551bcf3c8c97cf133d}}.
While most recent studies indicate that experimental constraints
favour a stiff EoS with a speed of sound that exceeds the conformal
limit {{cite:80800954564c30230fbe3c54da888daa399d478c}}, {{cite:57b81e6c8ed4cebf685fddfec690d5fc0dff364e}}, {{cite:f1875ad2e75cfcec5d1c26cb5f74d31b4354eb4f}}, {{cite:1d549560bfbd4a291418f4551bcf3c8c97cf133d}},
it has often been considered as extreme for the EoS to develop large speeds of sound of
{{formula:40d4e9ee-2143-4148-9362-659b81c26197}} to 0.6 or even to have an EoS which exceeds the conformal bound. In our study
we provide direct evidence that an EoS with a speed of sound of this magnitude exists in QCD at small
temperatures. Thus, such conditions for the EoS of cold dense QCD matter are certainly not unrealistic.
| d | e39a04211e5f5be21843ef4d8084964c |
While the use of a Wald-type test statistic is reasonable for linear regression, for other regression models there are compelling reasons, at least in low dimensions, for preferring a likelihood ratio statistic. Indeed, the Wald statistic is often justified on the basis that it locally approximates the logarithm of the likelihood ratio. As noted by {{cite:bd59624692c5d592a9fa8a65e128464a8bebe5ea}}, the likelihood ratio statistic preserves any natural asymmetry in the confidence regions due to asymmetry of the log likelihood function. In simple contexts there are also more sophisticated arguments based on approximate conditioning {{cite:861880a5bc9d9832cbf4bd3d3b12df59c3ade80d}} that point to its use. This suggests an approach based on direct generalization of the ideas of {{cite:aa0609b16016b305f32c93a03568591cfeb48826}}. The possibility for this is apparent from equation (REF ), where the factor multiplying {{formula:7fcb2d25-2052-4b13-a92f-4b30a2d69ade}} is the least squares estimate of the coefficient vector in a regression of {{formula:7c5d666e-6794-414e-af74-119dd26626cb}} on {{formula:44cdfeae-c025-4d01-991f-d312bd042207}} . The introduction of {{formula:a514fc22-3bf6-42a9-b96d-77dbb181eae8}} would accommodate {{formula:69a266d4-a25b-4599-bafd-9a5b573dc9fa}} by replacing this least squares estimate by a ridge regression estimate {{cite:a8eaef56edaa67ed4907d94864e93fe11985cab5}} and would yield a parameter approximately orthogonal to {{formula:d5c34ee2-e9dd-4928-845c-e936700039e9}} when {{formula:dcf50dc4-5639-4d05-b3cf-97640bb8834c}} . Further analysis is needed to understand how far this idea generalizes. To be useful, any subsequent operation would have to exploit the resulting sparsity in the relevant column of the Fisher information matrix as in {{cite:085510280d0ab25f6d3c0d883460a3e67e6c6570}}, who assumed sparsity of the Fisher information without the preliminary approximate parameter-orthogonalizing step.
| d | baceedae899d16e516dbb9c204fc9ab0 |
The new training and learning strategies aim to gradually improve the quality of pseudo labels during training. For example, Bai et al. {{cite:38e9edac7d732543b35e25e628e9bcf245c5d066}} proposed an iterative training strategy, in which the network is first trained on labeled data, and then it predicts pseudo labels for unlabeled data, which are further combined with the labeled data to train the network again. During the iterative training process, a conditional random field (CRF) {{cite:b028c79a6779f0f4f30e642c5adb27ede92961c7}} was used to refine the pseudo labels.
Zeng et al. {{cite:7fc18b6b7757d594ff628c76e99672a89dddce98}} proposed a reciprocal learning strategy for their teacher-student architecture. The strategy contains a feedback mechanism for the teacher network via observing how pseudo labels would affect the student, which is omitted in previous teacher-student based models.
| m | 52bb89954377c795f83fccdd487b5d61 |
Most GNNs (such as {{cite:bb13ce57156126e7441f14ad45fcc313a4a1b46a}}, {{cite:f9d669f7c671547379124351c9a6c363ad5a367b}}, {{cite:b5226053340e329cf76bf8a426e4c1a1b42b8eb1}}, {{cite:6e1093f00444c35c4f16ef34bf7b0d5fc294c9ca}}, {{cite:5f11fcccfdd9a0f7b98255868a503d17da98bd8a}}, {{cite:b8dcefec33e2896a5af3308f19fed71971e933a7}}, {{cite:e2590f76ffefb6a4b61df0c2dd6e35c8143a98de}}, {{cite:b4e0d9fbeb121b4033e98bf3d83872a4ebf48b16}}) are designed with a message-passing mechanism {{cite:e068cf0ad17e9e5f2752e29031e31245e9bf76b0}} that builds node representation by aggregating local neighborhood information. It means that this class of GNNs is fundamentally structural, i.e. the node representation only depends on the local structure of the graph.
As such, two atoms in a molecule with the same neighborhood
are expected to have similar representation. However, it can be limiting to have the same representation for these two atoms as their positions in the molecule are distinct, and their role may be specifically separate {{cite:ad50d1162a4d19d4d3ed7014319e6e0d437909e6}}. As a consequence, the popular message-passing GNNs (MP-GNNs) fail to differentiate two nodes with the same 1-hop local structure. This restriction is now properly understood in the context of the equivalence of MP-GNNs with Weisfeiler-Leman (WL) test {{cite:e24f1828800e53d5aa56f60639ecfeca934c6a89}} for graph isomorphism {{cite:b4e0d9fbeb121b4033e98bf3d83872a4ebf48b16}}, {{cite:0c31efa8cc3e10faaaaf72a9420b11bb993cc79e}}.
| i | f3cd7969d7954c9b0d6a6570f92c2508 |
Our approach enjoys efficiency as the additional computational cost stems only from passing the intermediate features through the decoder.
Algorithmic complexity is kept simple as perturbations are randomly sampled within a moving range that is determined by a linear curriculum learning {{cite:8bc38cc3bde86da44e7fea1b1252757453bbd3cc}} scheme.
The FID is used only minimally to determine the maximum intensity value of each perturbation.
The model generalizability and robustness is improved as more parameter space of the perturbation is explored, and the fact that `denoising sensor input' grants `steering' to be learnt from the denoised, inner representations of the training data.
| i | 96cc81b746ef8c5580a95b1d43b15440 |
The following is a paraphrasing of Lemma 8 in {{cite:ad2a2234f0a1395d2283a88ef838c6ca38a7f9ad}} and is used in multiple proofs.
| d | bc8319200f01b01884c34c68ead7e283 |
Learning the similarity metrics between arbitrary images is a fundamental problem for a variety of tasks, such as image retrieval {{cite:8782ab1433dc116e3678f70cd563c7dc7ecf4de0}}, verification {{cite:d48618860ba2a09205eadf100e5a1dfa8d8f8673}}, {{cite:177ba44015e8ce5220888723d8e5198d98bc3fc5}}, localization {{cite:8331ae4d8e393165921111bc47c717c0a5bb88de}}, video tracking {{cite:d145b3a447d82195b2b270492594bcabc1efd377}}, etc. Recently the deep Siamese network {{cite:751f6288a27d2246dddd1ea09a6f99695cf5b75a}} based framework has become a standard architecture for metric learning and achieves exciting results on a wide range of applications {{cite:479308a9e85157539f05ddbc5bed7066e76ece66}}. However, there are surprisingly few works conducting visual analysis to explain why the learned similarity of a given image pair is high or low. Specifically, which part contributes the most to the similarity is a straightforward question and the answer can reveal important hidden information about the model as well as the data.
| i | 88a1cf7fd491ce31b40a261de49f7aa5 |
For the Carlini&Wagner (C&W) method {{cite:9c935ed68ecfe59255c4cd2867f298ebcad1c3e9}} has three versions, an {{formula:86dd551c-f0c8-4764-ad66-2be73abeeb77}} , an {{formula:a6f9b6a8-fa61-4fb0-86a7-49bf0218aa1d}} and an {{formula:8a8e14d4-f014-480c-9780-1eea77436e63}} attack. We will employ the most commonly used {{formula:1da41678-50f0-474d-8782-1558647c2657}} attack.
For a given image {{formula:3710d999-406a-44e7-b58d-83673469f84e}} this method generates an adversarial example {{formula:f1610f9e-a061-4f6e-96f1-f9f656c0d5e9}} by solving the following optimization problem:
{{formula:bede687f-330c-4542-b45f-eeff49c3e0af}}
| m | 56e2e76b3a132bc3dbc28a46ddd0a418 |
Both intra- and inter-class distances are normalized using the Frobenius norm to eliminate the difference caused by the scale of the node embedding matrix.
By the definition of over-smoothing in {{cite:6dfa5704e67de0b4aad952d9bff4488a464a43c0}}, the distance between intra- and inter-class pairwise distance should be decreasing sharply as the number of GCN layers increases.
| r | d70a8aeb3bb274369ebf7f91d532bdb9 |
We propose a novel factorized neural rendering framework that learns to encode outdoor scenes from Internet photo collection, which enables controllable scene re-rendering with user-desired lighting condition and photo extrapolation or extrapolated 3D photo generation that extends a narrow-view image to a broaden field of view.
We show an overview of our method in Fig. REF .
Unlike previous neural implicit methods {{cite:b79d500bc6248cae61164530d742719d78898f46}}, {{cite:e49713aa8f23ec9b635a0dfe3f20ed79b04fffa1}}, {{cite:7c36499bb540cd0ddc90dcd4ded10b2a7177b5c8}}, {{cite:85b80621f5ac85cceafe39229f1058f98b322a07}} that encode all the appearance variations (e.g., lighting condition, auto exposure, white balancing and filtering effects, etc.) in one latent space, we present the first attempt
to model outdoor scenes with a more controllable and explainable re-rendering pipeline (Sec. REF ).
To survive from the training with noisy Internet photos, we utilize a composited training scheme (Sec. REF ), which learns scene geometry with transient removal strategy from Martin-Brualla et al. {{cite:e49713aa8f23ec9b635a0dfe3f20ed79b04fffa1}}, and supervises re-rendering with distilled occlusion-free images.
Moreover, we apply a novel realism augmentation technique that propagates appearance details from tourist photos to the rendered views (Sec. REF ), which efficiently improves the photo-realism of the rendering results.
Please refer to our supplementary material for more technical background.
| m | 96683884186049c17d1ea65f78eee181 |
The effects of photoionisation may be diminished in our simulations also because we consider particularly dense regions. In relation to this we find that ionising feedback has greater impact in Region 2, in terms of the star formation rate, and in Figure REF we can see regions which are highly disrupted by feedback. Previous work has found that the effects of ionisation are less in higher surface density clouds {{cite:89545f17830d6b8e9c0c7ebaeccd6e074a7abbac}}, {{cite:7ba0ef8ed005ca5b0fcac128d03abf827ea264c5}}, {{cite:3f975527497164e473fe8a7adf63fb8c879cfc62}}. We also see that the efficiency of cluster formation, in terms of the mass of the clusters formed in the presence of ionising feedback compared to no feedback, is still quite high, comparable again to previous results for denser clouds {{cite:f933fe95a75f1687fdcdcf9ac680d6191855f5ad}}, {{cite:7ba0ef8ed005ca5b0fcac128d03abf827ea264c5}}. However we do see an indication that in some cases, ionisation is limiting the masses of resultant clusters (see also {{cite:7ba0ef8ed005ca5b0fcac128d03abf827ea264c5}}). This is in contrast to the work of {{cite:bfb958185d23055d2ca85500a023016b694e0b06}} which included solely radiation pressure and found that cluster masses continued to grow. However we have different initial conditions and look at the surrounding gas mass, rather than gas inflow rates so it is difficult to make a direct comparison. We note that even without feedback star formation may be quenched, for example due to the surrounding gas reservoir (which here can change due to the large scale dynamics), so we have directly compared equivalent clusters with and without ionising feedback to take this into account.
| d | 6004001e40ac90019f979b16c6f48d8d |
This paper is organized as follows. In section II, we introduce our
notations and equations in (3+1)D. We treat the QCD and QED gauge
interactions in a single U(3) framework which includes both the
subgroups of QCD SU(3) gauge interaction and the QED U(1) gauge
interaction with different coupling constants, for our problem with
cylindrical symmetry. We apply Polyakov's result of transverse
confinement in QCD and compact QED gauge interactions in (2+1)D
{{cite:bbaece72432ccf9e3dec02f85c269d24f87b99f4}}, {{cite:30d51a60a5330bf988103e776f71359ee9f102fc}} and study in section III the quark field part of
the action integral. We separate the action integral into the
transverse (2+1)D{{formula:344c729a-77dc-4289-8345-e55edd875073}} Lagrangian and the longitudinal
(1+1)D{{formula:66bb165c-f9a7-4ee6-902b-609548fdc2b9}} Lagrangian for a system with cylindrical
symmetry and transverse confinement as in a flux tube, with details
given in Appendix A. The relations between various quantities in 2D
and 4D are given in Appendix B. In section IV, we study the gauge
field part of the action integral and see how the transverse degrees
of freedom can be integrated to yield only the gauge fields in the
(1+1)D Lagrangian in the flux tube. In section V, we write down the
simplified action in the (1+1)D{{formula:b6e4b7a6-dca5-4789-9d29-aa353d1d64ea}} space-time which can
be the starting point for the description of the dynamics in the flux
tube environment. In section VI, we examine the dynamics of quarks
and gauge fields in the longitudinal (1+1)D space-time with an assumed
transverse lowest energy mode, and obtain the solution of the 4D Dirac
equation and its general solution. The solution is then used to
calculate the quark current to generate the gauge fields. We solve
the Maxwell equation and obtain the masses of bound mesons as a
function of the coupling constants. In section VII we present our
conclusions.
| i | 8ff1f34c9d993818373a45faa021ce0b |
In the end, we compare baseline methods and existing TL methods with our input-dependent skip connection method. Result can be seen in Table REF . We can observe that although our proposed method utilizes a model pre-trained on partially music-related datasets, AudioSet and ImageNet, it outperforms existing models pre-trained on music-specific datasets, such as MSD {{cite:9d0a2fbed7f4d51fbfa99162732cf7442561e6d8}}, {{cite:b2e3fa512161dda89d3e458a11174b13cc6af37c}}, music listening history dataset {{cite:a37e389e83185c9d9873b4736ec4b7ecdd091d58}} and model pre-trained on millions of music data {{cite:59bee6c7867f1a19a1a64c36f7231322cc3094c3}}. Our IDS-NMR method also outperforms fine-tuning method (BL-FT-AST). Although our methods perform on par with the representation method (BL-R-AST), our IDS-NMR method gives models the flexibility to learn task-specific information. As extra findings, our IDS-NMR method with jointly ImageNet and AudioSet pre-training could achieve one highest test accuracy (85.1%) and outperforms AudioSet-only pre-training by 2.8% within all the random seeds.
The representation from AST model (BL-R-AST) performs better than VGGish model (BL-R-VGGish). This result suggests that the utilization of the AST model could thus lead to improved results for a variety of MIR applications in the near future, replacing VGGish features which have been commonly used in many music downstream tasks.
{{table:fa7d8288-0848-4c3c-8d93-7aa530786fd8}} | d | eccad7c7aa375dd35d36facc56014d6a |
Another widely used marginal contribution-based method is the Shapley value {{cite:5762bfabc05b7a83077c84e89644d25369e78716}}, {{cite:129c990f680d337fee237089502c3d32c120c9dd}}. It summarizes the impact of one feature by taking a simple average across all marginal contributions. To be more specific, the Shapley value is defined as follows.
{{formula:12196b3f-e861-4698-8d7e-21647662baae}}
| m | aacbee279a5d75882a32a1a0c5ec2cd0 |
Using the fixed effects covariates, fit CART algorithm {{cite:62a4534ac260800688f4df0785040b65af703ac9}} for {{formula:76b5f34b-db11-4c4a-a52e-30b38c4dcc00}} and extract {{formula:f15aa531-8b31-45aa-97ad-95e7d1d4df33}} from the fitted tree.
Estimate {{formula:9806f788-95d5-4c70-b37e-45def80d643c}} {{formula:197f3ea0-681f-40f1-b77e-af4aafeba3d6}} and {{formula:9ade7d60-4cca-42a9-9c14-9fa3ef95381d}} using the following LMM model:
{{formula:f47d695b-8502-4bec-9019-0ec02b16c503}}
where {{formula:7eca1382-0ab9-4a47-b94a-ac2088bd9d8e}}
Given {{formula:7285ab3d-df1b-456a-bd0d-2a8b5a0532d8}} and {{formula:c173ad02-8ac0-4bb0-90e1-cc507e929c1b}} estimate {{formula:2901e866-4795-49b2-92f4-f74da9b120e3}} using the BLUP formula.
| m | 665cb120e8b9f6406c7e87fcf93560ab |
{{cite:a6c0d3c408b8f8253e856b2d2f671918fb295246}} proposed using Monte Carlo dropout to estimate predictive uncertainty by using dropout at test time. There has been work on approximate Bayesian interpretation of dropout {{cite:a6c0d3c408b8f8253e856b2d2f671918fb295246}}, {{cite:8f1ada8baf5a06046228e7745e7de09f1ba37dde}}, {{cite:0d92224e3b58cb8a5625048f5fad34c2a38f86dc}}. Specifically, {{cite:a6c0d3c408b8f8253e856b2d2f671918fb295246}} showed that Monte Carlo dropout is equivalent to a variational approximation in a Bayesian neural network. With this justification, they proposed a method to estimate predictive uncertainty through variational distribution. Monte Carlo dropout is relatively simple to implement leading to its popularity in practice. Interestingly, dropout may also be interpreted as ensemble model combination {{cite:65bf652f4c309fd5c0ee149b7bf2b0cdfa90577b}} where the predictions are averaged over an ensemble of neural networks. The ensemble interpretation seems more plausible particularly in the scenario where the dropout rates are not tuned based on the training data, since any sensible approximation to the true Bayesian posterior distribution has to depend on the training data. This interpretation motivates the investigation of ensembles as an alternative solution for estimating predictive uncertainty. Despite the simplicity of dropout implementation, we were not able to produce satisfying confidence interval for our crowd counting problem. Hence we consider a simple non-parametric bootstrap of functions which we discuss in Section REF .
| d | 3cf0aa63a894451f5d970413eb9c57ad |
Moreover, it could be interesting to identify the {{formula:56e48c5c-cfe7-4cd5-9ba8-a93e301bbdd3}} and {{formula:698a1693-0cb4-4b97-b4f6-e8eaf2893b3d}} SCFTs dual to the {{formula:46efd4ef-5686-4452-9b8f-0fb0f1c6f73e}} vacua and the two-dimensional conformal fixed points in the IR as well as the associated RG flows in the field theory context. Partial results along this direction have been given in {{cite:7c51afabb143a260a8246df3a0c6a52f2fb071e2}} in which the possible dual {{formula:2c48b0d2-138b-4049-9c95-078665cc1a8b}} and {{formula:d61f67a2-7a61-4776-80f3-e4291de0fbaa}} SCFTs have been identified. It would be useful to extend these results to the case with topological twists. Furthermore, constructing similar solutions in the form of {{formula:261ba626-f4bc-41ff-a81e-5ff57b89fabb}} with {{formula:ed5c8a91-a2b8-45d5-a3e9-11030b075b67}} being a spindle or a half-spindle along the line of recent results in {{cite:58131f6da3fcb36a08b60ca68ff3432c90ba9bf6}}, {{cite:08a3b8d07a5e21ec97c4f3d0061ef4383d32395c}}, {{cite:777fda24f1d4678984b75b994bbb6ce3afc0ab11}}, {{cite:6db9f9e6320354d26be70377aac7cc0d4e27eb4d}} is also worth considering. Finally, finding similar solutions within {{formula:a153d551-22e9-44d7-b355-ced4420256f8}} gauged supergravity with gauge groups identified in {{cite:debdc91d43d9be8f70983673d96e8c1971ec49f8}} as embeddable in eleven dimensions would lead to new holographic solutions in string/M-theory framework. We leave all these and related issues for future work.
| d | 5ad459cc08c61b54437757a41e9cc852 |
the scalar functions {{formula:3cdfbfb0-7925-4d58-af78-2f2d9299e772}} and {{formula:f1fb207e-6b04-43de-8802-0ab2862ed9c0}} are provided in Appendices B and C of Ref. {{cite:36c264ecc8be1897fa4892e9ecc98a3865a55b3a}}, respectively. Thus, the only missing inputs are the electromagnetic form factors (EFFs), {{formula:1c7e00e1-a58e-47e0-8b32-6d7a9c23479b}} , obtained from the process {{formula:a0857f50-b8de-43ad-9fe0-622f3f20debe}} .
| i | 137c2f40bac46497929aa5be9e965a37 |
Related work. RAVI builds on and generalizes
recent work from both the Monte Carlo and variational
inference literatures. For example, {{cite:d0c091826a84f7715b9657aab1336c0917fd5398}} and {{cite:536625e781fb7eef158921de6d65ce6065fe0a84}} showed how
auxiliary variables could be used to
construct and optimize variational bounds for
specific families of expressive variational approximations.
{{cite:d2a8542315a8631c0ca8a0ffcb2362d777d7bc52}} presented tighter bounds
in a more general setting. RAVI is a further
generalization, in two directions: first, we show
that these bounds arise from particular
choices of meta-inference strategy, and can be
tightened by improving meta-inference; and second, we
extend the results to the Monte Carlo setting, enabling
learned variational families to be used as IS, SMC, or MH proposals. We also provide general theorems about the
variance of RAVI samplers and the bias of RAVI variational bounds, which can be applied to analyze both new and existing algorithms.
| d | 3d73d4c94e814a41153570243a027fde |
The connection to coarse graining has implications for the generalization puzzle.
First only the relevant modes given by the large singular values need to be retained, implying a dramatic reduction in the
number of parameters, as pointed out in {{cite:0dca8e5ba146bc4a34bf41f8965ee5644f6525b8}}.
Second, relevant modes only have support at low Fourier modes, so that the coefficients of large momentum modes are
set to zero.
In addition, the coefficients appearing in the Fourier expansion of the hidden and visible singular vectors are not independent.
This implies a further dramatic decrease in the number of parameters, which has not previously been pointed out in the
literature and it is a direct consequence of the connection to the renormalization group.
| d | eba2f12658b7c8435e5f1ac83e7edc2b |
Our results show that any family of quantum circuits that both admits a classical poly-box and satisfies the poly-sparsity condition is in the complexity class SampP {{cite:4566a4735c59aa693d7bb4458d3a4872cb37c36e}}. In light of the multiple known constructions of poly-boxes (see Refs. {{cite:4ff82b8f7066308b5609c0b7bf02311e7c08cdd8}}, {{cite:6d62fdfc036bbf6ff5fb47865df044a2c0064fc4}}, {{cite:0f2dc76d92909f863c09e257e396971de13a99e2}}, {{cite:68fff50524db92fe929d43ef0494c1a56f960173}}, {{cite:c410f5324eff2f845c554632e122fb47f4cafbec}}) over restricted families of quantum circuits, and in particular Ref. {{cite:0f2dc76d92909f863c09e257e396971de13a99e2}}, this is a substantial new contribution to the understanding of the computational power of these families of quantum circuits not only in terms of decision problems but more generally, i.e., in terms of sampling and search problems.
| d | c9c0ef95a42d482831f66fecedaa36b1 |
Besides the case of {{formula:8be2137f-a76d-42bc-809b-e7e59eb94e76}} which has been studied in the previous works, we also explore the possible evolution of {{formula:4eee1be7-cc6b-4950-b572-2335cf7e9d25}} with the parametrization {{formula:7cfad895-78b5-443a-a68b-cbf96ad49fbe}} . The previous studies have conducted observational constraints on the scenario of {{formula:486cd7b7-1795-4640-926a-5d67d039d39a}} with several different cosmological probes {{cite:1b5be660f43ccc0a83b4cdeabd0e28df0ff6a9a0}}, {{cite:615d985e69b8959a1cc0f34a46e44f4103616f51}}, {{cite:54dda03f2f15cb24d99c6790ae59b9b1265a0443}}, {{cite:9b9fdaeca012d901ae2e6626fde7cf4f63ee03cf}}, {{cite:d715021f273928d9de91871a6685fb8af87f281e}}, including the SNe Ia, CMB, BAO, Hubble parameter {{formula:562fc3ae-574b-4033-b262-8ef8eab365df}} versus redshift and Sandage-Loeb test data sets.
In this work, by considering the cases of {{formula:5545f76c-cfb6-4250-bbba-de0b5f0a69f8}} and {{formula:c08a31df-4aa0-43ab-b848-44127461f604}} , we explore the cosmic coincidence problem and its possible evolution with the recent observations, including the SNe Ia data from the Pantheon sample {{cite:281994679f3f27a29fa4720652f0c93cf5a4aa33}}, the CMB power spectrum data from the Planck 2018 final analysis {{cite:2fd9ba820111064b8284a1381758034b14f59fef}}, and the BAO data from the measurements of 6dFGS survey{{cite:3c73bece1136c964f38ac3351a59f200c94c554f}}, SDSS DR7 MGS{{cite:c281ecf63cba3bd9305f4a774d73ae7e094aebdf}}, and BOSS DR12{{cite:3620e7786d0f2230b18be3bd704783a18285d7b4}}.
| i | f9c1dfb58c55331bfc71ed6b0b13b432 |
Meanwhile, tensor datasets are often high-dimensional, i.e., the ambient data dimension is substantially bigger than the sample size. It is thus crucial to exploit the hidden low-dimensional structures from the datasets to facilitate the follow-up analyses. In tensor data analysis, low-rankness is among the most commonly considered structural assumptions. In this paper, we assume the target parameter {{formula:e6235879-749c-4e5b-aa7c-fcb65a3ac55f}} has an intrinsic low Tucker (or multilinear) rank {{formula:5c94bd56-73a0-4b06-8584-b5f614a5342d}} , i.e., all fibersFibers are bar-shaped vectors and are counterpart of matrix columns and rows in a tensors {{cite:a3ae5e63d49484e0fcd88c3ca51c946e06d7967b}}. of {{formula:40978bf6-4e78-40bd-9767-2b550d8713de}} along mode-{{formula:fb8eb3bf-d1bf-4064-ac0a-6758644dc53d}} lie in a {{formula:33e97fe3-1aca-4f23-bf4d-b7ac6efb09a2}} dimensional subspace of {{formula:ba3a9cd1-257d-43e5-9787-ec2feb30a4b5}} for {{formula:17af730e-92fb-49c6-a5aa-23edb8de9756}} .
| i | 7b710fb99139c416145b8678179be5d3 |
Understanding the origins of giant planets remains elusive. Radial velocity surveys
have found giant planets to exist around roughly 10% of Sun-like stars {{cite:45d8fe3ba2e5d9b9e01ee2cfcc3761626a7e97bf}}, {{cite:44b79369fe9cc04ef0480387beb571e7cf4c1021}}. However, only {{formula:6eafaf89-b0ca-41d6-a1de-ae6045514c45}} % of Sun-like stars have hot Jupiters on very short-period
orbits {{cite:664e62a5413408a964a43d3e55c1b976d9085941}}. Very few stars have warm Jupiters with orbital radii of up
to 0.5-1 au {{cite:052c20ead96371cda0dacef59c2d375115ba7af7}}, {{cite:276c16ff46b151158a10d1507fd3106148a7528f}}. Instead, when considering the unbiased distribution, most giant planets are found between 1 and several au {{cite:052c20ead96371cda0dacef59c2d375115ba7af7}}, {{cite:276c16ff46b151158a10d1507fd3106148a7528f}}, {{cite:44b79369fe9cc04ef0480387beb571e7cf4c1021}}, {{cite:664e62a5413408a964a43d3e55c1b976d9085941}}, {{cite:45d8fe3ba2e5d9b9e01ee2cfcc3761626a7e97bf}}, while there are hints that their number decreases again farther
out {{cite:45d8fe3ba2e5d9b9e01ee2cfcc3761626a7e97bf}}, {{cite:6c68364fbddfb6afeea18123247163de1375d22f}}. In our Solar System, of course, there are no giant planets within 5 AU from the Sun, although Jupiter may have been at {{formula:bfdda3f6-a88f-4ecc-bb2f-31d11db36f01}} au in the past {{cite:bb44f1fe92cf9745ef4f037a9e5a9661c29d546e}}. The preference for giant planets to orbit relatively far from the parent star, in contrast to super-Earths for example, is puzzling because giant planets must have formed in the presence of gas in the protoplanetary disc and, consequently, they should have migrated towards the central star due to planet-disc interactions.
| i | af9da310abd5e0650261c95d329ff181 |
The F-test offers a potentially powerful way to
distinguish when it is necessary to use a more complicated two-component model. The
F-test can compare the {{formula:68cbad79-91cc-4297-93d7-55ea35c74135}} values
among nested linear models with Gaussian errors {{cite:25c258a590199484a554493e066aedd3131835e1}}. Although our
models are not linear and our error distribution is not strictly Gaussian, we
apply the F-test to our fits. Following {{cite:73655c494023d9f617a46091aa8217517958c539}}, we adopt an F-test
probability of 0.32 as the cutoff indicating a more complicated model is required.
When we find a low F-test probability, P{{formula:288b72d8-ecad-4efb-a375-c4dc01ba4027}} , the more
complicated model (i. e., going from a one-component to two-component fit, or allowing
the Sérsic index of the bulge to vary) provides a better fit to the
observed profile. In cases where a Ser fit is used rather than a SerExp fit, the improvement in fitting is large enough to justify using a model
with more free parameters. The improved fit is not merely the result of
using a more flexible model. A similar test was performed by {{cite:b04fff922a1a401100e6aa69a98fe6b873347788}}
to select among a pure disk or disk+bulge model.
| d | 1e7c2663c781ecfac736af7d06379197 |
Under the constant flow of liquid into the container a drastic change in the crystal facet kinetics is seen from the jump-like singularity of the derivative in the {{formula:6766f073-3734-469e-ae79-e829fc1d681c}} records. From the experimental data it follows that the transition from the slow to the fast kinetics occurs faster than 40 {{formula:6bb5f146-9b6a-4836-9242-8fdfe415ec5b}} s {{cite:c6180cfe8bc2ff912984e5d69e6a6c83162a70d9}}. The reverse transition, as it follows from the experimental results presented below, takes place faster than the measurement step 80 {{formula:b63fda85-f169-41a9-8b70-fb586d2cfb04}} s. For this time, the rate of increasing the helium mass in the container and the crystal surface area {{formula:0ec54ce0-c10a-47fc-bac8-e46bb9559de4}} vary negligibly. The incoming mass increases that of the crystal. We have
{{formula:7b0b859f-b3f1-4638-9457-6732b2602fad}}
| m | d132b0f2231f7ad8d99ec255795d01f9 |
Observations indicated on even more energetic phenomena which
might occur in the GC. Thus, a hot plasma with the temperature
about 10 keV was found in the GC which can be heated if there are
sources with a power {{formula:e5fdedf4-d3a7-4594-a99f-bac43d4a1d35}} erg s{{formula:4c8a8f04-90ee-4e31-96f9-b3094995806a}} (see e.g.
{{cite:0ca99cbeb221a20ff55224caba7750441e31bfe1}}), which could be generated by events of huge energy
release in the past. It was shown that the energy about {{formula:65deaacb-1f54-4f44-ac82-38a0db6d08e7}}
erg can be released if the central black hole captured a star (see
e.g. {{cite:c7447d5a75e808d8f9350ce413695ef1cc45e86e}}, {{cite:b1ba1aca97789dd2e1f2b6d62a3dd444dd067431}}, {{cite:1dbb7c344a167824cfb9c83a28600b15092b81ff}}). As a result, a flux of
subrelativistic protons is ejected from the GC, which heats the
central region {{cite:860222fa4e1204a1087dff41bde74860027df7c5}}. These protons can also produce
6.4 keV line emission from molecular clouds {{cite:17705bc2507ae9d2811fce0394522a48a0730beb}},
which is, however, stationary because the lifetime of these
protons {{formula:c0125ff8-8414-474a-81b7-1325cf3510f9}} yr {{cite:06556df3951e6c4ffd6fe4ad263119da63da4c9e}} is much longer than
the characteristic time of star capture by the central black hole
({{formula:ad4b275b-3031-4037-bb7b-8465946da89e}} yr) {{cite:c7447d5a75e808d8f9350ce413695ef1cc45e86e}}. This scenario assumed at
least two components of the X-ray line and continuum emission from
the clouds: the first is a time variable component generated by
X-rays from sources in the GC, and the second is a
quasi-stationary component produced by subrelativistic protons
interacting with the gas.
| i | 40aaec07135d423c73b0c6d37b45b811 |
This approach differs from other methods which use neural networks to generate painting-like images, such as style transfer {{cite:d80ef69276a7a7ac168adadd41715da739a5018f}} or GANs{{cite:205b545aa8917e1a19b25b634964fda4c8ff0a0d}}, which essentially map textures across pixel grids and do not model the physical process of drawing. Stroke based-rendering with some optimisation goal has been studied before the deep learning era {{cite:8dd915cee419f9b48c970b009b13bcfb74163fdd}}. In the field of robot art, Pix18 {{cite:853892fa41eb2d89dd0cb0eb7f87b3f903e16603}} excels at creating oil paintings with its own art subject, and with minimal human intervention.While recent advances to image generation have focused on reinforcement learning {{cite:9d009e050b31f02793a57f88ba738a0d9fb68c36}} or neural renderers {{cite:7245e522fe3e720bb9db801e799b782804d5bb49}}, {{cite:24aa77d505319232c1b57767e1a1b067a6dfde6d}}, the optimisation of brushstrokes against loss functions parameterised by deep networks, which can then be directly interpreted by a drawing robot has been missing from the field.
| i | 3ef50ef7891ccd6456a1ac31f1b5ee13 |
We will explain precisely what this means in Section , but vaguely, congested transport is a branch of optimal transport theory that seeks to model the optimal flow of mass under the effects of congestion. That is, like moving through a busy city, the concentration of mass in a region affects the minimal time required to move through that region. This is distinguished from the typical optimal transport model, where the cost of moving mass from some point {{formula:33b81d85-83a5-468a-ab16-c2fa7c8d7468}} to another {{formula:a3a2d680-0c6d-47ad-87e5-a14700695104}} does not take into account the traffic along the way. The theory of congested transport for the continuous case (as opposed to the discrete one) was developed by {{cite:749d80cc0d976f00e70a427a3355e5c4a059625e}} and {{cite:ff2c681ffa9a858e80a944d383057722757b43de}}; see also Chapter 4 of {{cite:b64cd6864dc1738b17e1c01315334da90577d176}}.
| i | af69fb329790fbb5d03f8b8edd3f4e99 |
Low convergence represents a major problem for triplet-based losses. Besides, given a set of samples, it is not trivial to find positive or negative instances to use as hard pairs, nor is it easy to fine-tune the margin that separates them {{cite:0efb8ecad54faf6a423768b0ebcda037088b9cda}}. Notwithstanding, tripled-based losses are still the most popular losses in the literature, despite their limitations.
| i | 700763808891285d6461cb17339b80dd |
The evaluated baselines are the classic 8-PA {{cite:12b2d04820213cb622689001ac71df6470dd879c}} in spherical projection and the GSM solution {{cite:e5483ba099cf61b0413ea64c03b953e641346d15}}. For the former, we compare with our normalized approach using the optimization (REF ), which we refer to as {{formula:59485f5e-07d0-451f-8a20-68e274bec9da}} . To compare with GSM, we use our proposed optimization (REF ), where we refer to {{formula:bee07e6e-120a-4a2a-bb85-589c16470055}} and {{formula:bfd912f4-ba36-4971-9e27-45669f0cf5e2}} as a weighting function evaluated by residuals from a camera pose {{formula:8c5d09bf-0507-4cf7-ab91-2e9e4e7540cd}} (computed by using the 8-PA{{cite:8ed9d26f6a1dd08d524d54b08f83bf0428043834}}) and residuals obtained from our normalization {{formula:efdfde77-ab70-46b6-b88d-b01d6144033b}} , respectively.
| r | 5a76d81cef124dee764c05019366cf27 |
The absorption probability {{formula:582c361a-76e1-420a-96a4-3ae8176aa78b}} can be expressed in terms of the total {{formula:988c3e65-d806-4ecd-9379-fd4c4a2291c5}} reaction cross section
{{formula:23461c73-437d-4227-84ca-c3d69801b486}} {{cite:f5d2e3c5b4e5d296ede247d2a1924d717b780e1f}} and the integrated skin density {{formula:84a00150-a344-4093-ace3-4cc45cf2f3bd}} of the additional neutron skin of nucleus (II) with respect to the reference nucleus (I):
{{formula:c337faf6-0675-4cd3-86f7-f9961bc18e00}}
| m | dc44084514e2997f86d87a9153f2ba89 |
The impending realization of scalable quantum computers has posed a great challenge for modern public key cryptosystems. As Shor's quantum algorithm {{cite:5a3980f2419dd1a8369b9d537eb2b38bc404c3b0}} can solve the prime factorization and discrete logarithm problems in polynomial time, conventional public-key cryptosystems based on these problems are no longer secure. Although making a prophesy for
when we can build a large
quantum computer is hard,
we should start preparing the next generation quantum-safe cryptosystem as soon as possible, because
historical experiences show that deploying modern public key cryptography infrastructures takes a long time.
| i | b87c5c13613f8f878676a85d671b7ca9 |
The neural network controlling the robot is based on the C. elegans connectome. The neurons in the nervous system of the worm can be divided into three categories according to their neuronal structural and functional properties: sensory neurons, interneurons and motor neurons {{cite:fccacb755f08b0b988291c016304817bc4495e33}}, {{cite:159aa73db72c2d7b286d134f7e020a5d856fea51}}. In the robot, the distance sensor activates a number of sensory neurons when the distance from the robot to an obstacle is below a given threshold. The wheels are controlled by the output of motor neurons. With this setup we conducted experiments where the robot was allowed to roam freely in a room with random obstacles, recording simultaneously the individual dynamics of all the neurons and also the actions of the robot
| r | f64050f8f2a1c714650a59f33d0f0518 |
While previous work has already sought to obtain more robust VAEs empirically {{cite:af45daf40bd9512f8f63c3b5f9f9d5cafb9376bf}}, {{cite:3dd1c4c705d6890e7b06578215fc19de593a7055}}, {{cite:b79dc0d53c51f8df0d359e61222d96b4eaa87a20}},
this work lacks formal guarantees.
This is a meaningful worry because in other model classes, robustification techniques showing promise empirically but lacking guarantees have later been circumvented by more sophisticated attacks {{cite:a38d26975141a91e1ff4558f1a59718fb0bbf1dc}}, {{cite:3d8436f03a69ae63b4924eca5500bb555b7c3678}}.
It stands to reason that existing techniques for robustifying VAEs might be similarly ineffectual.
Further, though previous theoretical work {{cite:fcbb86a38a538a26361bb90d80a1b357740a932c}} can ascertain robustness post-training, it cannot enforce and control robustness a priori, before training.
| i | 87716e8af3f0be3f84d71a6a2c1237e8 |
Metal hydrides have always been considered ideal
candidates for high-temperature (high-{{formula:83790254-adef-439a-ab6d-36431e2b06b5}} )
superconductors owing to their ultrahigh phonon
vibration frequency. {{cite:63175145c62701935302ba79d5ad840ae9669592}}, {{cite:add677a6d283919d0cbf6d7948dd721d9d030e50}}
However, realizing superconductivity
by keeping them under the metallicity gradient
often requires extremely high pressures. {{cite:63175145c62701935302ba79d5ad840ae9669592}}, {{cite:add677a6d283919d0cbf6d7948dd721d9d030e50}}, {{cite:5fb81384549ff26b0024b7c10f3e9d79547735c7}}, {{cite:98754a941910af079b863beac221c984d2e6c8fb}}, {{cite:575caa83fa9d2ff17ed6cd42988cd4c636841e47}}, {{cite:5a84465394d9f85555be8f6cc2ad02488a2d837d}}
Therefore, theoretical simulations play an extremely
important role in search for novel hydride superconductors. {{cite:c13b284f02ed1298309a34d4720004e7d6ca1b2f}}, {{cite:783da3add07928fbd9afa7404ec0d17f6e4832fe}}, {{cite:4c76c26eb592f8d0e9652338499ed0c29ed2500b}}
Through theoretical simulations, almost all the predictions
for binary hydrides have been completed, and studies have successfully predicted the room-temperature
superconductivity of YH{{formula:8306023b-d630-41f7-84a0-098249a478c4}} . {{cite:49ba82fbb0de5ff51cbb3c076464195ca90f8cfb}}, {{cite:c9c8a06230c1b7969cb9b1227e384964a5b0845a}}
The successful prediction of room-temperature superconductivity in
ternary Li{{formula:f561fc62-c07d-48f9-a2a5-aa1d042abf88}} MgH{{formula:c0fda537-8406-449e-8f98-46c5c5c51582}} {{cite:caabbe50879e8ca027897f453baf89ecc402d5ef}}
and the experimental discovery
of room-temperature superconductivity in the C–S–H system {{cite:d2cec5c903ee9d9c9a0f0ea518433b69806ea34e}}
have pushed research on
superconducting ternary hydrides system to a climax.
{{figure:600eef6c-af2e-4ba2-baf3-84d796ddf3a2}} | i | 87fea858887762ffdc38df84b59221d6 |
Despite the fact that these methods including AutoFE have achieved promising results in tabular data applications, they mainly focus on feature interactions, no matter by hand-craft crossing existing features {{cite:50a5c0af24ea049dbf9df5bbc2e987f6a104cc48}}, {{cite:6f2831a62698a635eab991010586299fb137469e}} or automatically computing higher-order feature interactions {{cite:48302bbfd74673f3bb129f43a6039060f43b1e7a}}, {{cite:5935cccc98699fc753918e2f1733eecd537429d3}}. In this work, we argue that existing methods ignore an important aspect for the TDP task: the sample relations, which can be very useful for the prediction performance.
We illustrate it by an example in Figure REF ,
when we want to predict whether user 35360 (6-th row) can repay the debt in time,
those with the same education level, e.g., user 12841 (1st row), 28877 (3rd row), and 40633 (5-th row),
can provide useful signals, since the repayment ability of people with the same education level may be similar.
In manifold learning {{cite:874fcaedcfffca334d5d68270561fca11498bf39}} and geometric deep learning {{cite:7b70a18106710b9a63ba58973c65e38ec1a6903c}},
modeling the relations between samples has been
shown beneficial to the empirical performance.
Moreover, the relations among samples can be in multiple facets in tabular data,
leading to a more challenging problem to capture them for the final prediction.
Take the user 35360 in Figure REF as an example again, those sharing similar ages, i.e., 40633, 28877, 35360, and 47533, can also provide useful signals. A real-world case in loan default analysis is given in {{cite:b979f1d5bac72bfa56f73450a3bcb3537dd31593}}, where the authors show that both the transaction and social relations among users can help predict users' loan default behavior. While loan default analysis can be naturally modeled as a TDP task, in real-world businesses, the scope of TDP is much more larger, e.g., sales prediction, commodity recommendation, etc. It lacks a solution to capture the sample relations in general tabular scenarios.
| i | c789d7bce79d2eb8f702811cc0aeedba |
Previous methods: CMN{{cite:298074f8ce9d67907cd91b772f3bdfbe73c743ac}}, DialogueRNN {{cite:95e11061049f47c73ed29c4798282af3615d7983}}, HiGRU{{cite:6096303146b1e06f58fbe1aceb7129cf97f121dc}}, DialogueGCN{{cite:0f8570d1dab1427a9153e1c8240de28bbcb8c2f1}}, TL-ERC{{cite:52aef3a931dc07a14786b995c454edc93ffbc114}},
and KET {{cite:48ac74c6f7ae6f23786f387b74b27d0432603492}}.
| m | 80e923f33ffce11a04a4094c1e906d29 |
To obtain a more comprehensive picture of apparent robustness we start from the rigorous evaluation methodology used by {{cite:17f372ee0baf92294c09c6106e30387ffe34c9d6}}, {{cite:5652a09d03cf9ea8d6cbf5af7d468bbeba23946c}}. We perform untargeted PGD attacks with 100 steps and 10 randomised restarts, as well as multi-targeted (MT) PGD attacks using 200 steps and 20 restarts. Anticipating the danger of obfuscated gradients skewing results, we also evaluate with the Square approach of {{cite:2652f3533a4a5bf042de6d4bbedf739ef0e32e86}}, a powerful gradient-free attack, with 10000 evaluations and 10 restarts. For precise comparisons with the broader literature we also report evaluations using the parameter-free AutoAttack (AA) strategy of {{cite:a20e6fe4bd4ff0ce2d6bc94d76d0bdf94bf8679d}}.
| m | d7ffa95ca0892602a4a904746ba14018 |
Much mathematical study of matrix recovery
{{cite:906105e0be76f4949a3d06bd3fc604ba706dc9db}}, {{cite:30e0cc15418ad7e90882d313a795bafb7111dc63}}, {{cite:61f1c0003086a053e97ad6df8233238e3965e39a}}, {{cite:b7055b04e888401963c78d303209710b4f3cde75}}
has focused on providing rigorous bounds which show the existence
of a region of success, without however establishing a phase
transition phenomenon, or determining its exact boundary.
A relatively accurate result by Candès and Recht (CR) for the case of Gaussian measurements
{{cite:b787664b0d14879080a08e600c2c4c74d127a308}}, implies that
{{formula:d88dcd92-cfd5-4d6b-abb2-e568fb7dc625}} measurements are sufficient.
Our formulas for the square case {{formula:c21f4ac0-8ca5-4be5-b683-b25253664946}} show that
{{formula:9f6bf509-8e00-4e3d-8e43-f445aa47cdcf}}
| d | be9d77f845f70920a6ca30cb2aaf68e1 |
A similar problem, often referred to as convex integration, consists in finding such functions by only specifying some subgradients but no function values; see {{cite:33a2d28b029774fd373143068d18bc5c70b0c9a2}}; for the case where {{formula:a683fca3-085f-46b9-9cac-26760af1df25}} is the class of (closed and proper) convex functions, this problem was also treated at length in {{cite:0aceac7212aed583b5bc452ac3be023c84a311a4}}.
Motivated by applications to performance estimation problems (see below), this problem was studied in {{cite:c150fd1713316d85a579ecbbc54a6adfaaf66d44}} for the cases where {{formula:b1b8c0a9-2235-4c3c-a81e-125b9080d7e5}} is the class of closed proper (possibly strongly) convex (possibly smooth) functions.
In this case, it is possible to obtain simple necessary and sufficient conditions for the set {{formula:fe5ab588-f01c-4846-b63b-4ba7dc3c03f1}} to be interpolable; we refer to those conditions as interpolation conditions.
Such conditions take the form of a set of inequalities on {{formula:b349382e-5503-46e9-a347-b776d6bcf441}} , and sometimes allow to conveniently deal with discrete versions of functions within a certain class {{formula:7483df8d-47fc-44b2-9410-de41d4348392}} (for which we have interpolation conditions at our disposal).
There exists a few classes of functions, typical for the analysis of first-order methods, for which such conditions exist, see, e.g., {{cite:11916605a6f41e2c3a90eaa6a0ba2d3b700fe543}}.
The next theorem provides interpolation conditions for the class of convex {{formula:a6c3c322-2a24-4fc9-acbe-c0af47bb3db7}} functions.
| r | 19887966321b85e7a0e920c1eb63e0cd |
Comparison with DMC {{cite:66c12408f6e0185989e7b85660e0e72f37508b75}}:
In the process of incrementally learning a new set of classes, Deep Model Consolidation (DMC) {{cite:66c12408f6e0185989e7b85660e0e72f37508b75}} trains a new object detector just for these classes as the first step. Next, a third object detector is trained by consolidating the base detector (trained on initial classes) and the model trained on new classes using unlabelled auxiliary data via distillation loss. In the experimental analysis on Pascal VOC dataset, {{formula:3ef4b3ad-afdb-44a7-8e19-34c86477d2d0}} images from Microsoft COCO are used as auxiliary data. Our proposed methodology requires only two models (base and incremental) to work and does not make use of any auxiliary data. For a fair comparison with DMC {{cite:66c12408f6e0185989e7b85660e0e72f37508b75}}, we also modify our methodology to make use of auxiliary data (without using any supervised labels) in a simple and naive way. We use the auxiliary data to define an additional constraint in the distillation loss as follows:
| d | 31dab80fb80977ff4e29c400ab9e5542 |
Even though the Bayesian approach to statistical inference is extremely beneficial, some challenges remain. In particular, we recommend consider alternative inference methods in order to account for “big data”, which is currently an active research area in computational statistics (e.g., variational methods). See for example {{cite:e28872a9b39b2e69733f6a324ca4d63ffb1516c3}}.
| d | 46ac1b0d7541baf731e9257664a7c345 |
There are two main lines of research to train DCNNs for face recognition. Those that train a multi-class classifier which can separate different identities in the training set, such by using a softmax classifier {{cite:25ceaf7511822fed5acbb24e4aec5d0fbdaadd8d}}, {{cite:7b9a0d519017b6788fdf949962e13c406d9b0d56}}, {{cite:66514df195e271a1ac92b8566bd88fc71604d42a}}, and those that learn directly an embedding, such as the triplet loss {{cite:fe6771429439f9b7818386c396af7d5c2082384d}}. Based on the large-scale training data and the elaborate DCNN architectures, both the softmax-loss-based methods {{cite:66514df195e271a1ac92b8566bd88fc71604d42a}} and the triplet-loss-based methods {{cite:fe6771429439f9b7818386c396af7d5c2082384d}} can obtain excellent performance on face recognition. However, both the softmax loss and the triplet loss have some drawbacks. For the softmax loss: (1) the size of the linear transformation matrix {{formula:5fbd4b9f-1432-4f15-bf0b-63b4de7c4ea3}} increases linearly with the identities number {{formula:52e88b99-ce5d-46d6-8f7c-d9d23d759061}} ; (2) the learned features are separable for the closed-set classification problem but not discriminative enough for the open-set face recognition problem. For the triplet loss: (1) there is a combinatorial explosion in the number of face triplets especially for large-scale datasets, leading to a significant increase in the number of iteration steps; (2) semi-hard sample mining is a quite difficult problem for effective model training.
| i | f250c045f2278540d35fd605f837517d |
To further investigate the effectiveness of LD3, we performed the “Friedman test with Nemenyi post-hoc analysis" in which we evaluate the statistical significance of our results, which is presented in Figure REF . We applied the two-tailed Nemenyi test to find our critical distance for Nemenyi Significance. Our critical distance is {{formula:cb74158d-c4e6-48dc-9188-7f7ebc6f4f90}} , which is calculated using Equation REF , where {{formula:6a3b8bbe-8d4d-443b-9541-de24b16155ad}} is the critical value acquired from the Critical Values Table from {{cite:5066d6da7f85aa0ebfcbdc569676da9d832ac3d8}} with {{formula:3f9952e2-5643-4bac-9a2b-b03668da4566}} and {{formula:9176c0c5-b665-451e-abe8-6423604a5674}} is the number of algorithms (16) and {{formula:34ff2cd2-3d28-424f-bc64-dd1f8734ef97}} is the number of datasets (12).
{{formula:e95fd0d3-3f85-4719-8b04-cc93fa7be630}}
| r | 1f359e2e424e72378598c22ff35efb1b |
To the best of our knowledge, the presented approach is the first to address stereo-endoscopic scene transformation for minimally-invasive surgical training. In this paper, we propose a novel cross domain conditioning GAN, which is superior in synthesizing consistent and more realistic stereo data in comparison to the unpaired CycleGAN approach {{cite:3dc622f498fa84a019dced4e146f9ec1f9218d87}}. Due to conditioning on a second image, which is drawn from the target domain (real or generated content), the network is also able to generate images with less artifacts and with more realistic color, heterogeneous textures, specularities and blood.
The reliability of the generated samples was indirectly assessed by asking clinically relevant end points considering visible pathology, surgical instrument and surgical phase. We want to especially emphasize that almost all of the questions could be correctly answered with high confidence.
In general, we decided against the conduction of a Visual Turing Test, as some shape-related features in the scene (e.g. a personalized ring shape instead of a standard commercial ring) would have been easily identified by an expert surgeon.
| d | 8b8be62004058e98a21b01781bdda136 |
In this section, we provide additional results on KITTI {{cite:b67ecaa9d15a037e90926385564d0c09ea851290}} and iBims-1 {{cite:34e4423fe4ac1c5741626956ab599774b9954575}} datasets. KITTI is an outdoor depth estimation dataset and iBims-1 is an indoor dataset.
| r | c8b3f00f46035ad14eb92c196d1d70ab |
In this section we obtain some auxiliary results concerning Banach lattices
which will be used in the sequel. Let {{formula:9f1859ce-beec-42f5-96e1-9044974ad23f}} be a (real) Banach lattice with dual Banach lattice {{formula:78e811a2-c514-4f73-a745-dbb735ecab3f}} . For the
general theory of Banach lattices, we refer to the books {{cite:d0f79881b50f3b2afa8a53d7daaae1c5ab6b0e56}} and {{cite:4f438c805d95353dc4ae8271404fd2fece203d36}}. First we recall some terminology and notation.
| r | dbfd0c434e0bb9a355bc652e6fd4cb9d |
The second issue is that there is a need to use the inverse observation error covariance matrix ({{formula:d09e8ac0-a52b-4fdb-8001-fe98dcbd2bb0}} ) in the computations. The most commonly used observation uncertainty diagnosis techniques provide an estimate of the observation error covariance matrix itself rather than its inverse {{cite:c230c454dce3fcea0debe0c08ced4bd61068137e}}. Since the observation distribution changes each assimilation cycle (due to quality control etc.) there is a different inverse matrix each cycle. {{cite:4e256f1ba74ef6bc801243b4f646e4407a81feda}} deal with this by using a Cholesky decomposition method {{cite:8b85d2d1edc5e4d680ca091d31c846345350752f}} which avoids the need to compute the inverse covariance matrix directly and is applicable to any form of error covariance matrix. {{cite:7ae99feff214ba9c67705f94566568c9d529292e}} model the inverse of a spatially correlated observation error covariance matrix directly using a diffusion operator and fast unstructured meshing techniques. However, this method only deals with spatial error correlations and it is unclear if this approach is also suitable when spatial error correlations and inter-channel error correlations are combined.
| i | c77f3fb57554d9abf48b24cee753b0ba |
R package Mclust {{cite:6c07f9914df61eeef2231316e0d976a49877cca1}} from R{{cite:6b556217675de6dff91a72b5619a4d0715185b7f}} has been used for the model-based clustering, which allows modelling of data as a Gaussian finite mixture with different covariance structures as well as different numbers of mixture components. Each component of a finite mixture density is associated with a group or cluster. The Gaussian mixture model assumes a multivariate distribution for each component and these components are assumed to have ellipsoidal distributions in parameter coordinates {{cite:2c6798f5226406f17645f6a2089852cfd7bd3f5b}}, {{cite:24dfec199957b6cec87e524daf87fa07da6ed58f}}. The number of mixing components and the covariance parameterization are usually selected using the Bayesian Information Criterion (BIC) {{cite:7dc90c2827ba5f38788fda1e8cd949b11740341a}}, {{cite:90dce6c088f0d5ae836cc88e09c3b42f19d8e96f}}, which puts its first priority on approximating the density rather than the number of groups. To solve this problem, {{cite:d129838efe64fbb61d39226c8b8b1dacc3cf81e7}} put forward the integrated complete-data likelihood (ICL) criterion, which penalises the BIC through an entropy term by measuring overlapping area to obtain good performance in selecting the number of clusters. When we apply the Gaussian mixture model method to our sample, both BIC criterion and ICL criterion suggest nine mixing components (groups). Figure REF shows BIC and ICL values distribute with numbers of components. The BIC criterion suggests nine groups, while it represents a local maximum for ICL criterion. The real maximum of ICL criterion is at four, and the four components are the canonical thin disk, the thick disc, the in-situ born halo and the accreted halo. We choose nine groups because we attempt to study components of the galactic halo rather than main components of the galaxy.
{{figure:4cb5233e-00b7-4d9f-8b68-e1e23317987d}} | m | 93ff5bd9a042d7ff8fa42e872e0206b5 |
These findings mean that the micron-sized domain of CrNb{{formula:6fe07327-2ee1-4809-b9dc-2e6906b9f157}} S{{formula:07e1f2ea-f86c-4122-9a74-43db5fa321b6}} , in which the DB lattice is excited, is a system where areas of stored energy are linked to regions of transverse spin accumulation. As such, there arises a strictly 1D periodic array of resonators whose stored energy can take only discrete values and is controlled by two degrees of freedom, namely, the kink/antikink number {{formula:2e4e80ab-4b77-4d2d-9843-98a8e5deb05f}} (or equivalently, by the BL period) and the BL frequency {{formula:d232d916-6785-4a32-8b50-ed8822a4805c}} (or equivalently, by the BL amplitude). According to our order-of-magnitude estimate, {{formula:7983ce13-84dc-4892-b13d-8d4a5d36ba91}} lies in the THz range. Because of nonlinearity, an amount of stored energy in these "breather capacitors" will be far beyond the capacity of standing spin waves. This functionality may be used to design spintronic resonators on the base of chiral helimagnets. Care should be taken to exclude resonances with linear spin waves, since frequencies of the dark breather modes lie inside the SW band. Whilst discreteness of the system ensures that these resonances may be avoided if the breather mode frequency is appropriately chosen, this issue requires more detailed examination in the framework of the special theory {{cite:511f780abb9fe69704b53cd9246ed1667927ba46}}, {{cite:345aef77c0fdaab143b8c5b427621ac393aedbe9}}. Another open issue relates to a way to excite in controllable manner these breather modes by external sources. The creation of special microfabricated microwave antennae, like those used in a noncentrosymmetrical ferromagnet LiFe{{formula:f1968081-d07f-4db3-a5ca-315436c041c8}} O{{formula:554704c3-583d-4a5f-81a7-fccda1c98d21}} to induce magnons with large momentum, appears to be a promising way {{cite:8f56130f1a1b7a7a789453b8ec0cfa6afcd8a336}}. In this case, microwave wavelength emitted by the antenna must be matched with a period of the excited BL mode. These challenges posed by the practical application together with the basic problem of finding similar discrete breather modes in the another ordered phases of the monoaxial chiral helimagnet, i.e. conical and soliton lattice ones, should be addressed in future works.
| r | 1d6be5aff84a072ab923bbc361404809 |
Section provides the simple derivation of expressions
[see Eq. (REF ) for the case {{formula:37ab6e08-8cfa-42fe-88fa-54a549347c88}} and
Eq. (REF ) for the case {{formula:3c6891c2-9628-4055-b88c-872d43ba396f}} ] for the Středa-like term
{{formula:ca85c58e-dc98-463a-935f-c10a46a46a41}} (REF ) of the anomalous Hall conductance
in terms of the averaged one-particle GFs in the momentum representation. These
expressions are valid both in absence of an external magnetic field and in
its presence and describe the dependence of {{formula:e4ba91c2-c33e-4763-ba43-6fd94bedbfe7}} on the
location of the Fermi level {{formula:77ce8169-0ae9-4138-978c-d7e3719504a3}} both inside the gap of the
one-electron spectrum and outside it. In the first case ({{formula:b9d6fa60-b5b3-42b9-a338-dfcaa8e0796b}} ), {{formula:148ec703-4250-4039-aa96-4194b5b4cdcb}} is proportional to the Chern number (in the case {{formula:225a9826-27a8-4e49-b096-ac188cb11324}} ),
which takes on quantized values regardless of the presence or absence of
disorder and/or an external magnetic field. The half-integer ({{formula:8a022d97-f3bb-4925-943e-df5a9b7e505f}} )
quantization of the anomalous Hall conductance of massive Dirac
electrons{{cite:982ccdfadddc0faa8e82001f2061d6af1fec468a}}, {{cite:50309121e00e0ec8535faab6a24e8544c4c68c85}}, {{cite:01f47ef502ebd5ca66f6152356f12ba61cee532b}}, {{cite:f192fcf0ce64a14b5d31a2f58016c5ad1745d61b}} is
a consequence of the fermionic numbers fractionalization{{cite:113119191dcf9f09ce40ee8164ab6f5c644d2ff6}}, {{cite:90a232cf3d4bd8957b15da479b8092889223a9ea}}, {{cite:d1589bed1f7f1b29fbc1370852411af41e5f7256}}. It should be emphasized that the bare bubble
part of {{formula:cfb358c1-c71a-435d-bd87-14eb9dbb0bf0}} , as well as the contributions to {{formula:13035dc1-556a-4ef2-8877-c3c072d6aa09}}
due to extrinsic mechanisms, vanish under these conditions. Thus, the survival
of the gap in the electronic spectrum of the Chern insulator is the only
condition for quantizing its anomalous Hall conductance in the presence of
disorder, external magnetic field, and other perturbations.
| r | f1ebcf4546ed591c7120d35be0d8174a |
The three-dimensional time dependent GPE modeling the dynamics of a BEC is represented by {{cite:24e9ad63644a01af8bc172d351d53f1413387605}}, {{cite:836948836b9e7dae4501da1a307fb0bfb8d04ac2}}, {{cite:ef8d95ce1261be95b08a90c5a6115270c5496c73}}, {{cite:41d23f5718578bb2e2f113a89b969441a9c31237}}
{{formula:2fecf390-365c-44df-976c-cb9572725bbc}}
| m | 14d3f9b283d25f63f5753af900070ef8 |
Recall that two matrices are cospectral if they have the same spectra.
We conclude this section by proving that a symmetric doubly stochastic matrix that is DS in {{formula:72295c39-202a-466e-a2eb-d674a06dd0cd}} may be cospectral to another element of {{formula:5da46d0b-30f8-453c-98ea-f0c9eaabde69}} But first, we need the following result for which the proof can be found in {{cite:2a075b7f5084be99746371760f1aae57105de3b4}}.
| r | 7197cd22bb44d37308bcb713ca712dfd |
In this section, we first introduce our proposed pre-trained grapheme model GBERT in Section REF . Then, we show the details of fine-tuning GBERT for G2P in Section REF and the details of fusing GBERT into the Transformer-based G2P model {{cite:ff4d3d52ed98dca1e0a91d5a9ef4d7933abe6740}} in Section REF .
| m | 56912d10f8613e5612cf417b5d7d70a7 |
Since a star {{formula:4e413b37-e9a5-4abe-ac4b-ca21416b2dca}} is a tree {{formula:82e895e4-f14b-4e45-90a5-6e93c8043309}} with {{formula:d1ed5bba-5d58-4e72-8430-85c58b96f5f8}} and any odd-ballooning of {{formula:53a10ba6-9325-4f27-9af3-32ac75cb4dd2}} is good, one can see
Theorem REF generalizes the results obtained in {{cite:f0774671eafccdf4ec10be491de50e05d2336187}}, {{cite:db2c80f32060feb9d0dbe8729d8099b751732b01}}, {{cite:c38428b9ee35a795a5740e7f1ae58a49746c5dae}}, {{cite:dda5f02572d5433b3f0a08c0e625976b29039c17}}.
Moreover, let {{formula:f9aca851-f6ee-4757-82d1-e364ee829083}} denote the maximum number of edges not in any monochromatic copy of {{formula:2529ca06-35a3-40a6-a0d6-e0a4c9b448cc}} in a 2-edge-coloring of {{formula:04498e6f-46bc-4bdd-a1d1-303516d1b2fb}} . As a by-product, Theorem REF also provides some counterexamples with chromatic number 3 to the following conjecture:
| i | fd7b7aecb516e3a881b6e6e90b6c6c37 |
We first check prior defenses that examine model traits, such as the model's test accuracy and l2-norm.
Note, due to the non-i.i.d.-ness of data, federated learning is designed to accept updates that appear slightly different (i.e., updates under a threshold). For test accuracy, we assume a threshold of 10%, the same as {{cite:f2aac1e50a0758eb140496f9e01f017db970216b}}. Most malicious updates fall in the range, nullifying the defense. Norm bounding defense is effective against all baseline attacks. Yet, as we point out below, an advanced attacker can conceal itself from the norm detection.
| m | a86bec54c6bb8352495894a34a34596d |
Bootstrapping necessarily involves producing repeated observations
of the effect variable {{formula:c75bb983-3272-4374-a323-4c1b20520346}} . In some applications this
is problematic. For example, given an observational sample, we may
want to test the performance of a causal predictor by bootstrapping
multiple interventional samples from that original data. However,
these multiple samples will share individual observations with the
original data, this will introduce an optimistic bias into the performance
estimates, which is particularly problematic for modern complex predictors
such as deep learning that can memorize individual observations {{cite:dc0445582bade21607aaf5b7268e89553d6a8cdd}}.
One solution to this is to use bootstrap bias correction methods {{cite:6cfbd0627a2b1de05bb2e591547b2f510ba84213}}.
An alternative is to use split-sample approaches for example, mimicking
cross-validation, whereby the original observational sample is bootstrapped
once and the bootstrap is split into multiple subsamples. The predictor
is trained and tested on non-overlapping subsamples of the bootstrap
such that no observations are shared between train and test.
| d | ef182b01615e9faf14c40e78bf077541 |
The idea that the central nervous system may operate in (or near) a critical condition has been suggested in the past, and may have computational advantages {{cite:24bab07684afe650279ea575df8b6b695751f4c8}}, {{cite:c154a7d9c5c9b7e34a14176f845e735ccdb3172c}}, {{cite:e5d3653c1582745ab7e3400e0bbc05bb030f8ded}}. However, this latter scenario also has shortcomings. The most obvious is that it can only be used to ensure and stabilize critical behavior. In addition, it cannot be used when one of the phases near the critical line is lethal.
| d | 3bd5d6832ed34abba6806df522bac4b2 |
We work in the {{formula:d86b27f2-f1e9-4774-86e7-457b59616e13}} -electron tight binding approximation. Intra-layer and inter-layer hopping parameters {{formula:ee1876fc-9e34-4634-a934-27297f9584a4}} eV and {{formula:08a54b7f-0f18-45c7-ad4e-1f358e52b7f2}} eV are used, respectively {{cite:6d88322c9c401595be13375fd5da940d0e459e8c}}, {{cite:eccbb5e3a8869b1b4d74d2c39ab5ddffc7d67851}}. Voltages {{formula:fe7f469c-1506-4ddc-8959-a6a62e78e86a}} and {{formula:28027233-e002-4288-84b2-09ccaf350559}} are applied to the top and bottom layers, respectively.
This keeps the Fermi level at zero energy. We consider two values of {{formula:dec23f59-415b-4495-80cd-02a63ef4502a}} ,
0.1 eV and 0.5 eV, because the layer localization of gapless states in multilayers with stacking domain walls depends on the value of {{formula:101440d5-4ecb-4d37-9f28-4a860c491280}} vs {{formula:bdbd1570-079b-4baa-b489-c2f4d0a32913}} {{cite:01f999e2f5d530e27c5056192edb602c9168a534}}, {{cite:829a74c35a9d48a7602647b22c875da0ac236d1b}}. Surface Green function matching technique (SGFM) for three-terminal device (TLG/SLG/TLG) is used to calculate the local density of states (LDOS) {{cite:0783c5c7f68210defad69c7567720c5c99966bf7}}.
| m | 7a05714479c6dc3affed3825f8569f1b |
Throughout this paper, we have established a set of theories that
generalise self-dual Yang-Mills and gravity. The momentum space
equation for each theory contains a manifest product of structure
constants associated with colour and / or kinematic algebras, thus
allowing theories within the set to be related via the double copy. We summarise the complete set in table REF ,
where the first column (consisting of choosing two potentially
distinct colour algebras) corresponds to biadjoint scalar theory. The
second column contains the the usual SDYM and SDGR theories (for a
hyper-Kähler manifold), whose double copy was discussed in detail in
ref. {{cite:bcad6397723c446838fcbece923b33e0f09e3ee3}}. The third column corresponds to our first
generalisation of the double copy procedure (section ),
in which one of the structure constants is taken to be a Moyal deformation of the kinematic
structure constant. This leads to single Moyal
deformations of SDYM and SDGR, and also a doubly deformed gravity
theory, whose equation of motion contains a product of two Moyal
kinematic factors. We should point out the (non-integrable) Moyal-deformed SDYM case considered in the table, which is the one that straightforwardly matches the double copy structure, is not the same as the more conventional Moyal deformation of SDYM commonly considered in the literature, as discussed in section REF .
The second generalisation considers the kinematic
algebra diff, where the area preserving condition has been relaxed. A
product with sdiff results in a Hyper-Hermitian manifold. In section
, we have studied this as well as its Moyal deformation,
a Diff-gauge theory, and a double-Diff gravity, as recapped in the
fourth column of Table REF .
| r | 04d3b3142d7c71c3ff719557a8bdc5ad |
We have considered here only linear RNN and LDS models. Non-linear low-rank RNNs without noise can be directly reduced to non-linear latent dynamics with linear observations following the same mapping as in Section 4 {{cite:394403a991ff580d6f3ad0902c3969052d68d3a8}}, {{cite:ea01940ed746b61721b0e5089907a5c549f49d18}}, {{cite:b790f61334e539160a0f431dd73c9cf6f0211c6c}}, {{cite:550bf984f99d27e62a959ca669d8310dc209ec14}}, and therefore define a natural class of non-linear LDS models. A variety of other non-linear generalizations of LDS models have been considered in the litterature. One line of work has examined linear latent dynamics with a non-linear observation model {{cite:deb3702c9d9ce5009eaf80b879813376c6f1cef4}} or non-linear latent dynamics {{cite:deb3702c9d9ce5009eaf80b879813376c6f1cef4}}, {{cite:199ed8701777b3e0b41f2222608f4686d35d022d}}, {{cite:fd20d8d4e386942e6380498981aa68328e5bb2d4}}, {{cite:ec7afba4f314c81117d1feb25a579c019e4fc15a}}, {{cite:7136d49b02e99082929db2545955fed6109c4acc}}. Another line of work has focused on switching LDS models {{cite:c4f0ffa0d7ca077827794ff9f6d55f71146beb7f}}, {{cite:9bafc4220433e090cb427cbe08a21afa45ade2da}} for which the system undergoes different linear dynamics depending on a hidden discrete state, thus combining elements of latent LDS and hidden Markov models. Both non-linear low-rank RNNs and switching LDS models are universal approximators of low-dimensional dynamical systems {{cite:402da5cdf8bd5c92c82f4df49d1f0956a58ac365}}, {{cite:17f4c74d4ae959a62a237b76d9566f74786a28d0}}, {{cite:b790f61334e539160a0f431dd73c9cf6f0211c6c}}. Relating switching LDS models to local linear approximations of non-linear low-rank RNNs {{cite:b790f61334e539160a0f431dd73c9cf6f0211c6c}}, {{cite:550bf984f99d27e62a959ca669d8310dc209ec14}} is therefore an interesting avenue for future investigations.
| d | f5864ca6629a8d97d02f6df7ed602c49 |
Finally, we propose a double-backward propagation mechanism to implement our framework in an end-to-end manner. Most WSSS methods require multiple stages, involving multiple models with different pipelines and tweaks, making them hard to train and implement.
Although the existing end-to-end approaches
{{cite:bed587b0b7cdd5f8461aded6564ec6b9415b6ee4}}, {{cite:66d8f5a3661f630f8e722a1afc7bb233da708a8c}}, {{cite:a8878ae18bc888d8649a5f304010338d817afafe}}, {{cite:e3ccccfff77797b8996e72e3cf9de4e6e31fc83e}}, {{cite:c92f40a188fe690cdabd6d5230bb62b6d78f43e9}}
are elegant, they
show substantially inferior performance to multi-stage methods.
Our method is easy to implement and extensive experiments on the PASCAL VOC {{cite:f65ccacb5b9b10aa3b2ad3b390e353cc70ff3c05}}
and COCO {{cite:1dd7868b9a8c64966c68e91996c6ababdecfcd94}} datasets verify it's effectiveness.
| i | 512d03db780a9ee24b3c77b3af1389e8 |
The primary difficulty is deriving the gradient estimate.
It is pretty hard to prove the gradient bound for general fully non-linear elliptic equations
on curved complex manifolds.
The blow-up argument is an alternative approach to deriving gradient estimate, as shown
by Chen {{cite:adbd6fd6043f2c5537e556657b6c50c9715903ed}} for Dirichlet problem of complex Monge-Ampère equation on {{formula:0ba1df24-60ce-45ef-8e8a-2ec837b123f6}}
where {{formula:81b2e816-9aca-461f-b7e4-76fbdcbeba99}} and {{formula:7449c573-c40f-4426-a48f-dbfb8a1a359f}} is a closed Kähler manifold, and by Dinew-Kołodziej {{cite:28f0f1a1c1be693ac57792151edd4cec8938538f}}
for complex {{formula:288a93fd-7a85-4255-8c5a-56dc83a61cbb}} -Hessian equation on closed Kähler manifolds using Hou-Ma-Wu's
{{cite:8b9ef2de9d5a76600983e04bf85d976d579e797b}} second order estimate of the form
{{formula:2fde7ffb-b1cf-4f01-a780-85e408b1abff}}
| r | 28ac72bd89a8ff17d523e66505b5ed5c |
In the following, we present numerical results for both BP and SMP decoding. The results, provided in terms of block error rates for {{formula:ee5125dd-2ca9-40f5-9968-a676b1d46e23}} regular nonbinary LDPC codes of length 256 and 2048 symbols, are obtained via Monte Carlo simulations. The codes parity-check matrices have been designed via the PEG algorithm {{cite:a833825066d93fa98723ac1306c64f635f129a40}}, with the nonzero coefficients drawn independently and uniformly in {{formula:8c0f0360-0476-4fcf-a177-5714843df95f}} .
For the constant-weight Lee channel, the error vectors are drawn uniformly at random from the set of vectors with a given weight. For the case of the (memory-less) Lee channel, we computed a finite-length performance benchmark via the normal approximation of {{cite:0d27978e89005a8ec17ef05bd74484fd5c86eca4}}.
| r | eb726a99f4a4f49ae40e049d0756a238 |
In addition to phenomenological expansions of the quark model to exotics, current non-relativistic effective field theories and lattice QCD calculations are also included in theoretical methodologies {{cite:6cae35a9e3565a3e3c9bab279f311823fa9deba6}}, {{cite:058e8d3234173d84bf3e3e5a18f35a6069ee5c6c}}, {{cite:1f438213e5da24467c0a4158febc68a6d87157c7}}, {{cite:b14a6f2bfb830fdf7d918a9baea8626dc15a18b2}}.
The decay behaviour of the state Y(4626) provides the most intuitive information: the major component is most likely a tetraquark system {{formula:a87f60b9-9895-48db-9a4f-f93fbc1dc154}} . In the same way that the deuteron is held together by the exchange of pion and other light mesons {{cite:7a7159b5763ada6fc60d03bb6708a97a668e0663}}, Karliner and Rosner predicted the masses of tetraquark state {{formula:c480c5fd-bc02-43aa-a0fd-e304333416b4}} based on the proximity of {{formula:9d73da6b-4003-4595-8b11-052d2eac6c3a}} pairs to thresholds {{cite:427d0d2764c49aacb3324d58915b1e593b2e1210}}.Albuquerque and Nielsen said that the state Y(4660) was the state [cs][{{formula:f2450f39-f713-4f2b-a544-26764c882c06}} ] with QCD sum rules {{cite:19ec5a4ec1278a19f5cb8125531206ea187b422f}}. Inspired by the states X(4140), X(4274), X(4500), X(4700), and Y(4140), the tetraquark state {{formula:43d00b42-3183-464f-8b0e-7b6608e4cdc2}} was also studied in different theoretical frameworks, such as simple color-magnetic interaction models {{cite:763e9898f2653b1b7b9769dd004f2c5ca7d04592}}, {{cite:e1cd2e788db4225d5b5d9b0430d4968958051739}}, the QCD sum rule {{cite:48fb8970f62114ee73ed6eb5e7fe6de11c785374}}, {{cite:19bffb5b3e9ea5ce1b0a1708fd19fb614410bb31}}, {{cite:ce2635eabd6df378150843b640f23499237652a1}}, nonrelativistic and relativistic quark models {{cite:c4408b213c6905cf668a5e972d0a254a3e2dc0cc}}, {{cite:69b2cc930f155d26e83841f6995f57725e9be65d}}, {{cite:2ae9709aa212fa00265d99d6cc25dd8ef0412c1b}}, the diquark model {{cite:7902a5a71bd26db255008342f25d08ff66acac23}} and lattice QCD {{cite:56d1fa42f3470ec77a8be08e2ccf424322bdf335}}.
| i | 6220336ba3827364e19c6d923f51abd8 |
We introduce an extension of SpotTune {{cite:38031c8c10c5f6fecad4a15ad5dba9a171ec264c}} on the supervised DA for medical image segmentation called SpotTUnet. SpotTUnet consists of two copies of the main (segmentation) network and a policy network (see Fig. REF ). The main network is pretrained on the Source domain and then duplicated: the first copy has frozen weights (Fig. REF , blue blocks), while the second copy is fine-tuned on the Target domain (Fig. REF , orange blocks). The policy network predicts {{formula:13ff1981-c931-4ee7-bf21-bc651f39fef0}} pairs of logits for each of {{formula:92933082-d835-4e44-9cbf-644153a336e9}} segmentation network blocks (residual blocks or separate convolutions). For each pair of logits, we apply softmax and interpret the result as probabilities in a 2-class classification task: class 0 corresponds to the choice of a frozen block, while class 1 means choosing to fine-tune the unfrozen copy. Then, for the {{formula:b175fded-53d3-4bee-b47d-890e1ad808d4}} -th level of the network (frozen block is denoted {{formula:edb118c4-18d3-4585-9ceb-13a7179f830d}} and fine-tuned block {{formula:5e26f129-d100-4936-b8e3-0b51d2ab3a68}} ) we define its output as {{formula:982c056b-c47e-4272-9fc6-eeacf299b792}} , where {{formula:d571aaa1-6dd8-45f7-bb28-7135df474a5a}} is the indicator of choosing the frozen block (i.e. class 0 probability {{formula:7ddb9c64-a0f7-4669-885f-b073b1c7d205}} ). Here, we use Gumbel-Softmax to propagate the gradients through the binary indicator {{formula:dae30eb7-58cd-40ce-a4a9-dc021a1642fc}} exactly reproducing the methodology of SpotTune {{cite:38031c8c10c5f6fecad4a15ad5dba9a171ec264c}}. Thus, we simultaneously train the policy network and fine-tune the duplicated layers.
{{figure:2c9fe541-2ef3-4b14-bd3f-8537fb8e3cd0}} | m | 6678be92318179df6990a17a62aafd6b |
Computing the fourth RV moment did require to recourse to the Weingarten calculus, whose apparatus, arguably demanding for the neophyte, turned out decisive for the pursuit of our objective. One may reasonably hope that future developments along that line will enrich the present results, replacing in particular the mechanical computation of Tables REF and REF by true mathematical arguments. However, determining the analytical, exact null distribution of {{formula:e47225ac-81e8-4ce2-8b6e-f67369290a1a}} , may reveal itself out of reach: as a matter of fact, the moment generating function (REF ) is an orthogonal analog of the celebrated Harish-Chandra trace integral for the unitary group, whose analytical expression has been determined ever since the fifties {{cite:6d4f3972d363d9949bd53eed52fe01aa20803be9}} (see also e.g. {{cite:de2ed02bea5b7da94607af2fbd1d2956f8dc6fee}} and {{cite:a1d632fbde9868577256c58818f0cfa5a57e0787}}). Yet, discovering a corresponding expression for the orthogonal case, precisely, has not been achieved so far.
| d | 722b16898d0803d9fddcb28ab404c1dc |
In contrast, the fact that the unobservable factors under scrutiny, like personality, economic preferences, family background, political orientation are not robust predictors of link formation in the students' networks contradict others studies (e.g. {{cite:575e194385ebc22998eccd09e1dcf140a5017058}}, {{cite:e0d2d15bbb8499af0be9e433b9f0273f4dcfb488}}, {{cite:c261d7ac5eafac9d0e94b9b8a25d6e42fbee83e0}}, {{cite:30541e50e17040569fdf53728841243534a99a08}}, {{cite:0acc2015ede3c114263c4669b44a3e93deb45403}}). We do not argue that none of them is correlated with friendship. Rather, we argue that whether they can predict friendship depends on other covariates in the link formation model, suggesting that the unobservable, imperceptible attributes are not the primary reason for how people become friends.
| d | 1587a887c168c8a79181a0302d0e9a52 |
For {{formula:1ac30913-d741-4204-943c-5d63356627cb}} , define
{{formula:37ce927c-3303-4aa0-9cf0-5669e955f5be}}
where
{{formula:1280440a-862e-4c25-a19c-a87428b3e7f3}}
denotes the gradient operator.
Obviously,
{{formula:8bf975ab-bea9-4a57-a548-64ddf058100d}}
Then, from the Stokes' theorem, we get
{{formula:169af89b-9b33-4351-84e3-e9927a02ecd6}}
i.e.
{{formula:3ccc2984-5036-4a98-953d-9bce8e211555}}
From the Stokes' theorem, we have
{{formula:3303543a-2730-4501-895e-f2dfa34cc200}}
By the definition of {{formula:78fa3bd9-801c-41fb-91b5-677add7ed3a5}} , {{formula:892e1932-374d-4c60-a687-13d3778247ce}} and (REF ), we obtain
{{formula:0587d1c7-f24b-4679-a32d-e4aca1e6a749}}
Similarly, from the Stokes' theorem,
(REF )
and
(REF ), we have
{{formula:b00ff186-23f5-427b-bf1e-16840f47636c}}
From the Rayleigh-Ritz inequality (cf. {{cite:78e2d86863123713f3520baaef11152e1a44a4cd}}) and
(REF ), we have
{{formula:1ed607c9-87fe-4779-92e3-117b26df11db}}
i.e.
{{formula:040f7b56-116d-441f-b790-608e0d8c1e86}}
From the Cauchy-Schwarz inequality, we have
{{formula:43f887ee-c6f5-4ac6-9dc3-b3cdb83fe234}}
i.e.
{{formula:0aa90dad-c992-42c6-8910-0ad3ac81dfc5}}
Define
{{formula:d4a14ba1-f513-46f5-8947-ada46a9aafb9}}
Next, we will deduce the maxima of {{formula:f81eca3a-19bd-4165-a244-f74a80d570ce}} by using the Lagrange method of multipliers (cf.{{cite:190c34ea3bd3d675ad7bb8dbc74f84236d2d1340}}).
For any sequence {{formula:7be365d6-83b2-43ad-9590-da1a38fb8b4b}} satisfying
{{formula:cfb457c9-7d48-4c23-9baf-5ff795f87de6}}
we define the function,
{{formula:ec24ae23-b307-4eb2-8407-1bd3b3c76df3}}
where {{formula:a325a1ff-8a6e-427e-9b6a-567da6e533a2}} are two real parameters.
Assume {{formula:59029d81-8abd-4d08-b834-1e3bc19d2e02}} is the extreme point of {{formula:5bdc39b1-594a-4e2d-a388-265c9c6d4c2b}} . Then for any {{formula:4aed4092-f9f5-431a-8fcb-5d977c69ea7c}}
satisfying {{formula:ecb31800-bec4-497d-bb5a-eb1d0d67287c}} , from
{{formula:c53e019d-860e-4797-a9e3-37f8a4d28615}}
we have
{{formula:6389446c-f526-4013-88c3-fe492fadfba7}}
Taking
{{formula:f715ef0d-1c6d-4f0c-b368-146ec9e7e4fb}}
in (REF ), we have
{{formula:e0358f6a-1953-49c4-9b45-3deea593eee1}}
From
{{formula:7129388c-3dcd-4eb6-be88-6ae550a5f2a4}}
we have the two constraint conditions
{{formula:e19e3928-39d1-4f5d-a068-76ab6431eb53}}
Since there are two Lagrange multipliers and
{{formula:29e89a9d-c996-4562-a7c0-8e81418cfc9e}}
from (REF ) and (REF ), there exist
{{formula:77d856aa-19f6-4daa-83bb-5037f32a4060}}
such that
{{formula:1ea436bd-4904-402c-99c9-4298bb744922}}
and
{{formula:3bf3a417-bb2e-45a6-bd16-9eab399d09ef}}
Hence, we have
{{formula:fcc3016e-659b-499a-bb67-f170a0962f10}}
where {{formula:b851b0bf-1f46-40f0-925e-3b17c72eae2c}} are the multiplicity of the eigenvalues {{formula:dbf6c075-0c5d-4236-b2ad-f6b506bfdaa0}}
respectively.
From
(REF ),
we have
{{formula:b191f924-ad05-4278-aa30-7904018651f4}}
From
(REF ),
we have
{{formula:249419a8-035a-419a-aa4d-c51dde1b900e}}
By the definition of
{{formula:350ae81c-2286-4072-9ed0-69d73419c4a0}}
and
{{formula:01896295-88d5-43fe-a3f4-b9e3703383d8}}
we have
{{formula:006d1132-d426-4557-a3a9-5d14da6027c2}}
From the range of the function
{{formula:3e4deb50-2245-4c51-8118-0cc82a727dd9}}
(REF ),
we have {{formula:2851da1d-9eb8-4e0c-81e3-8099b1191907}}
From
(REF ),
we have
{{formula:01b25893-a9a7-4c00-bcde-99433104effc}}
Therefore, we obtain
{{formula:849c8010-7499-4f66-8fb1-5a771885375a}}
From
(REF ),
and the definition of
{{formula:6bacf55c-d1ee-4a25-ab1c-81245390e4dd}} and {{formula:133be1c5-ab12-48c3-b05d-336b767147b4}}
we have
{{formula:e89be31b-3a81-4dcd-aacf-753733e990cd}}
which finishes the proof of Lemma REF .
| r | 7aa7620178aed7899fe0a140eed00e80 |
From this, we see that the dynamics of the RG flow, in each of the directions of K-space defined by the Koopman modes, is determined by the magnitude its corresponding {{formula:519ed6a2-1010-48cf-af72-08b2c1a3d6be}} {{cite:1a4a67172acf0d6b74eeae72feda9481ded0db42}}. While the accurate computation of the Koopman modes and eigenfunctions is difficult (although doable {{cite:e25172db0331650fde8fb2c34a5ae79f4b11d0d1}}, {{cite:46597e9212dcf7c0fba7d2719d717d1958d7f973}}, {{cite:1a4a67172acf0d6b74eeae72feda9481ded0db42}}), this representation, in principle, allows us to find the fixed points, and their relevant and irrelevant directions, of the RG flow all from measuring a single observable. Because these are not known for many systems, and because recent work has shown that even relatively simple models can have non-trivial fixed points with exotic features {{cite:ee28c8fe9d5768bbf024b671d4e7211c387081e7}}, we believe this is an area the Koopman RG can play an important role in.
| d | d4295f864afd3b1d4cb75caa3e01ae15 |
Interestingly enough, the mass of {{formula:6c75e210-73f2-402e-9f51-72398b8a0188}} possibly falls in the {{formula:2d7fcaa5-2cbb-4582-896e-10835a54806a}} GeV range. A mild excess in the {{formula:291a3856-c925-4230-ae13-f115915c3f98}} channel in this mass range was observed at LEP {{cite:507759d6e343d82f9340b1555ef5bb093198a825}}, {{cite:b82ad226af7f33d92c43c68ede2ba71f544a3bc7}}, corresponding to a signal strength of {{formula:7acee7c8-2846-4981-b354-1582ad384a08}} in units of the signal strength of a SM Higgs in the same channel. Moreover, the CMS collaboration has observed a mild excess in the {{formula:30fa6982-6b2a-44c8-bb38-31657cc604f4}} channel in this mass range both at 8 and 13 TeV {{cite:3a08e38666b7029a9ac47c3056169b451cfc71b6}}. Locally, the excess corresponds to a signal strength of {{formula:3bb98635-6029-465f-bd10-e8c78f9f349c}} in units of the signal strength of a SM-like Higgs boson in the same channel. Within the NMSSM, the excess at LEP was first discussed in {{cite:f99bd6b3168081779b6089b8db65ec4ec3fa2c83}}. A possible description of the excess at CMS within the NMSSM was proposed in {{cite:a3431e18af36b2acae8534119b5707358ad39e80}}, {{cite:6e96af960c6c89eb1b4930860ec58be9dcb28b69}}, {{cite:fbf2746dfdc6a4bc9d6cde1e5c48be743e5494d1}}, {{cite:85a9b0b2c154cc7909d2f6f8c253f784aa576656}}, {{cite:af8e54290268b8ae3c46418ef1447cb83be8f30e}}, {{cite:04c0e246c93e5b1befdb05f47e220fcd33bf5a72}}. Clearly, the production of a mostly singlet-like {{formula:8d56f625-340d-4bfb-ac50-2a923d758d0f}} at LEP or the LHC requires some singlet-doublet mixing. Such a mixing involving the SM-like Higgs boson at 125 GeV reduces its couplings {{formula:c27c5fd5-f492-4f70-9364-f9dfd039c9ec}} to the electroweak gauge bosons. Such a reduction is severely constrained by the recent measurements of properties of the SM Higgs boson by ATLAS {{cite:d8714f852e59bd52fe326ee6de040a453e7a57af}} and CMS {{cite:04fb4dd3a81563f99b0f06d2e545e2c42ba75e99}} which, taken together, imply {{formula:de0464f3-fcd4-46db-a336-dc5897d20cd0}} at the {{formula:defbc790-f648-4c11-9554-30acbd9aedee}} level. Applying this constraint, we find that {{formula:3768d4d9-8ba2-4385-a12a-aae43bac64a1}} in the {{formula:7887fd2b-bb22-4017-b407-38e96370acb6}} GeV range can have a reduced signal strength of {{formula:79d4911e-dd13-408c-80dd-e3587f4aafc8}} in the {{formula:5646ace4-d6ca-43e8-88a8-6b4a50d0a913}} channel at LEP and, simultaneously, a reduced signal strength of {{formula:09f93518-a847-4a7a-9871-044689dd7d96}} in the {{formula:00d9d6aa-6bd8-4644-a8d1-082a8e794a54}} channel at the LHC. (The constraint on the {{formula:cabb1d38-06ef-4680-a037-2ea982338bcd}} mixing angle also explains why {{formula:527cbbe4-17b4-4db4-9e67-58588bd6111d}} is bounded from below by {{formula:c4fe9763-2155-466f-a5a8-f5edceebe6ea}} in Fig. 4.) On the other hand, we could not discover points leading to a sizable signal in the {{formula:e97be900-c6d4-455d-b5bf-9f1030907cea}} channel, as motivated in the same mass range by the searches from CMS {{cite:1eaa98d5f4a4aa87720d42739235a50ac9458898}}.
| r | 11fb72cf8d51934b3a8bb0753b6f9dd9 |
with {{formula:9e6b6416-f6d1-4d68-a8eb-6f470790d48a}} . The equations (REF )-(), with the requirement that {{formula:8c783733-df8c-4141-8192-c5503d68c0a1}} and {{formula:71346230-c629-400f-ba0a-897513dd0d0f}} , are equivalent to the statement that {{formula:66d0af9f-2e70-40b7-9b86-e2ab6e5f3051}} is a transmission eigenvalue, with corresponding eigenvector {{formula:2c2e6717-e0fc-4fca-9b03-42e851288de9}} . {{formula:e4917999-c58a-410a-9b69-57f1c268fab2}} being a transmission eigenvalue is therefore a necessary condition for {{formula:d17913ba-e935-4261-827d-39d026a0fdbe}} being a non-scattering wave number, corresponding to the incident wave {{formula:b8a76c77-91f5-484d-bf33-12bd6d2c698b}} (defined on all of {{formula:5a971e0c-65dd-49ea-860e-be4407182035}} ). Whereas transmission eigenvalues exist for quite general (non-smooth) domains, the results we establish in this paper show that the existence of non-scattering wave numbers (for regular {{formula:c85a7194-7bfc-42f8-8d39-7447ad5ff9b5}} ) imply some degree of regularity of the boundary {{formula:6c56da18-6aa8-43b1-a3f5-aff66ae513d8}} (for quite general incident waves). In terms of the transmission eigenvalue problem (REF )-(), formulated only on {{formula:22729003-0e2a-4307-b9e5-71a430c8dc0c}} , similar regularity results would follow if we were to insist that {{formula:ab200633-146c-4633-941d-94ebc123cf97}} be appropriately regular up to the boundary (on top of being in {{formula:449c61cf-8fae-4ac3-870f-3df837061781}} ). This may also be seen as a reflection of the fact that a transmission eigenvalue only is a non-scattering wave number if the corresponding {{formula:d4352dd1-24b5-499e-992c-a270fccd44ce}} can be extended to a solution of the Helmholtz equation in the exterior of {{formula:c0eb1927-67dd-44cd-bf31-325c9dcfd01c}} . We recall that, if {{formula:fb882995-384b-4338-a665-7e3aad82647f}} is of one sign in a neighborhood of the boundary {{formula:f49c3524-6a48-4005-be5b-bd8557aaab0c}} , then the set of transmission eigenvalues (possibly complex) is at most discrete with infinity as the only possible accumulation point. Furthermore if {{formula:5d6dcf84-a951-413e-baea-1b55d43d34eb}} is of one sign in the entire {{formula:9a068e9a-5bdd-4fbb-b041-bba730be2804}} , then there exists an infinite sequence of real transmission eigenvalues (see {{cite:3b87ba9e64bdfa222ddf65bb6b439038610feafc}} and also {{cite:dd553cfb7f99d439795c22ebc634c7a7442874d2}}). However, this paper concerns the existence of non-scattering wave numbers, and our approach does not require any knowledge about the spectrum of the transmission eigenvalue problem.
| i | fbf4f5269ad2f74d57042c2b5649a551 |
Although subject to variability, its faintness could also be related to the young age of the radio jet. Indeed the steep radio spectrum of the source and the presence of a turnover at a few GHz in the rest frame are typical features of compact radio jets in their first expanding phases {{cite:e442f3276b839840026e5f81673503cf5bfe4687}}, {{cite:a482c465e6f34a3e6d5614cbd02c802ccbb7e1b0}}.
The linear size derived for VIK J2318{{formula:3a930b72-54c2-4618-9015-cf9d651f292d}} 3113 from the {{cite:117f829b4a41f22af8473c1d04d4d47cb8201b82}} relation for PS radio sources ({{formula:11387e0c-835b-4a45-a5a5-327a758df986}} 30 pc) is larger than the limits we found through variability arguments in the previous section. This could mean that the majority of the emission is concentrated in the innermost regions of the source, even if the jets extend up to tens of parsecs, as observed in other radio jets {{cite:4e3d4e286b491207da08f3a3827297f9f88e59be}}. Moreover, the orientation of the jet might play an important role on the observed size and therefore the derived values are only indicative. From the highest-resolution image we can only set an upper limit on the source's size of about 8.3 kpc (from the major axis of the ATCA follow-up at 5.5 GHz and eq. 14.5 in {{cite:6be94223071ffa145515804ed834ab9d7ad4bba2}}). Hence, Very Long Baseline Interferometry (VLBI) is needed to firmly constrain the dimensions of the source.
| d | 5f2744be51308206e1bee0366cab9ae4 |
In this paper, we present a novel self-supervised deep-learning-based algorithm to predict the depth map from a single 360° image. Our work is inspired by SfMLearner {{cite:299c2eedac060b49e8ee3c5c497b01d5989ab94b}} and its 360° extension {{cite:8cf785749ec9f2a12a1b76a0fd45d290dd5f6608}}, however we don't decompose the spherical image into multiple normal FoV images but instead directly applying CNN to an ERP image to maximally benefit from the entire scene context. Since directly applying CNN to ERP images is known to have an issue of incorrect prediction near the poles due to the distortion caused by the sphere-to-plane projection {{cite:c1245aac92cef6eeeba74d51cfad50a9eb872c35}}, {{cite:8f3a5df8a228520b1597368f631b9482a97b549d}}, we propose Distortion-aware Upsampling Module that weights the feature map of different layers based on the amount of the distortion calculated analytically. Not only does it make the network robust against the sphere-to-plane distortion, but it also prevents the network from overfitting to observations around high-latitude areas with relatively little texture, resulting in sharper depth maps. Since self-supervised learning is more effective in scenarios where it is difficult to acquire annotated training data. Therefore, our work focuses more on the challenging outdoor scenes rather than indoor scenes where synthetic datasets are often available. To this end, we train our model on large-scale outdoor walk-around videos {{cite:8a3f8509a51b7d6ae2c088200d52b2be60be20d2}} with no depth annotations and evaluate it on our own outdoor 360° image dataset where ground truth depth maps are provided using the multi-view stereo (MVS) algorithm since there is no publicly available outdoor 360° RGB-D image dataset. We compare our method directly against Wang {{cite:8cf785749ec9f2a12a1b76a0fd45d290dd5f6608}} and the extension of it where the backbone was upgraded to a more modern network architecture for the fair comparison.
| i | 2f6196f7dcb9b8e059a36476fdd0c3bd |
It is well established by neutrino oscillation data (NOD) that the neutrinos have a non-zero mass while in the SM they are massless. A mechanism is therefore needed to generate the masses {{cite:bf0613bf2f6114b29a54e150b54b5046406b8f8f}}, {{cite:24af1ba679b40a3cdb85f2b9c3e521ec0238b61c}}. The neutrinos are not only massive, but their masses are also much lighter than the other matter particles. The mass splitting between the first and the second eigenstates is {{formula:5a0de16a-c42d-4ea0-8860-77084c2f4f2e}} , and the mass gap between the second and the third is {{formula:cd4b0a21-8495-41d5-8a91-cf5b8f349e58}} {{cite:c1ed427b2a05c00765f789520b132814d83d9597}}. Also, from cosmological data, the sum of the neutrino masses is bounded by {{formula:12069588-a45c-4d52-8909-e7219d045ecb}} {{cite:3eccb076dfe0d5ecb5ab2590afc0aa78fe8a1c8a}}, {{cite:d30d3df5508066d381d10d8831f3e86143e6553f}}. These observations are calling for a new mechanism. Arguably the easiest and first proposed mechanism is the so-called type-I seesaw {{cite:d0e99b4915a6495985e6c091c83483d8d48e718c}}, {{cite:b8a604826fd0d60efe3f4cb7eb62d11cf0ac2827}}, where heavy singlet leptons are introduced: The mixing between the heavy singlet leptons and the light neutrinos can generate a small mass since the light neutrino masses are suppressed by the heavy mass scale, resulting in {{formula:7a25d386-a4e6-4384-a0b6-9d0b1e7ae51d}} where {{formula:54fe7d07-072c-49b3-84de-947591fb9cd1}} is of the order of the heavy lepton mass, {{formula:c94ddcd3-97e2-4352-9e8d-332c087d3266}} is the SM Higgs vacuum expectation value (VEV), and {{formula:4d0867f1-73aa-4950-9a6c-0b413fe9e234}} is the light neutrino Yukawa coupling.
| i | 9698290f04724068dba240e316b81741 |
{{cite:15c5ca8a9cdec2db853316aaaaa2eb22750f96d0}} provided theoretical proof for hard debias {{cite:775d42ab0c289f95e683b50828d539eca5ca8817}} and discussed the theoretical flaws in WEAT by showing that it systematically overestimates gender bias in word embeddings. The authors presented an alternate gender bias measure, called RIPA (Relational Inner Product Association), that quantifies gender bias using gender direction. Further, they illustrated that vocabulary selection for gender debiasing is as crucial as the debiasing procedure.
| m | 5190fa279f027a6a5ffd540aa19e54a8 |
According to the principle of maximum entropy, {{cite:090943f061f94fc8fc22391300d6d212cb36410a}}
the distribution with maximal entropy best represents the current
state of knowledge (i.e., {{formula:47c1d5df-d71a-47e8-b856-9fec756a948c}} ) when equations
REF , REF and the normalization constraint
{{formula:fb3e85c2-f852-4203-8741-40c4e975432c}} are satisfied. To find the maximally unbiased probability
distribution, we define the following Lagrangian
{{formula:5e1e542b-6606-45e2-99a7-fb2fe329f2ff}}
| m | 38e2de4d6e05237b52e98a1081048cf0 |
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