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On more technical level, Maiolino introduces the transmission
spectroscopy as a main exoplanet characterization tool – in
the real world this is a commonly used technique that brought
up the first direct detections of exoatmospheres
{{cite:3cc4e4d48e71a5070e73615d25dfef4a1a17c1bb}}, {{cite:165f17192b97b4e492131a7c6984907169c2305b}}.
This method can be traced further back to the Russian scientist
Mikhail Lomonosov (1711-1765) who discovered the atmosphere of
Venus during a transit of that planet across the Sun in 1761.
{{cite:a10749bf37f403f0528236730c23c4ce2d3a882a}} summarizes the present-day status of
the transmission spectroscopy.
| m | 9341c72523c1c65fd0722be4e399dbd4 |
Further, we will call a snapshot {{formula:5ad70644-71e1-4644-b02f-d99e78e41367}} reconstructible from observations via {{formula:f567e8fe-e1a0-4739-b7ad-3ce7b6194484}} if it satisfies a particular type of source condition
which is sufficient to reconstruct {{formula:7ce788c3-b50a-44bb-b1e4-b5df3661a847}} exactly from the observation {{formula:2716d508-9286-4998-b21f-397c4bc8bd14}} via (REF ).
This source condition involves the existence of two dual variables {{formula:7bd713d5-7e14-4965-b88f-a5887f39d18a}} and three constants {{formula:c2aa93eb-ab9a-4bdf-9a6f-03251a48626c}} ,
and it will be stated in detail in def:reconstructible.
The main result of Candès and Fernandez-Granda in {{cite:a0166092cf329b18597b55137b1c9c637fd5b9a9}}, {{cite:6e2bd65ea6959d0f2ec222656363071f04dfe8ff}} essentially concerns this source condition:
if the forward operator {{formula:1893683a-79d1-4958-a207-29d6d1cccc8b}} represents a truncated Fourier series,
then {{formula:e7299036-1dee-4cdd-bcd4-971721f2bc78}} is reconstructible as soon as the minimum distance between its particles is (up to an explicit constant) no smaller than the inverse truncation frequency.
To obtain exact reconstruction or a bound on the reconstruction error, the following assumption will be relevant.
| r | 73896a85cc4dc06696b587e52ffce106 |
(i) PGG
In the most well-known and widely accepted version of PGG a cooperator contributes a {{formula:33d3746d-5c95-4865-936f-f4ebbdfc8043}} amount to the common pool, while a defector player does not. The sum of contributions is enlarged and distributed among all group members. The corresponding payoff values of the focal player playing either {{formula:0ba0263a-9535-474e-83fe-8accd9d244c7}} or {{formula:fe7078da-a0f7-43ab-9e63-f7487a5bc32c}} in the group are
{{formula:948e570a-d81f-400c-b779-4fd8827dba2d}}
(ii) Alternative PGG
In an alternative form, all players have an initial endowment {{formula:a030e610-fd7e-4344-b442-f185508532c4}} {{cite:e9dfe9b88b7b093a58a607cd12522b569508dc45}}. A cooperator player invests this whole amount to the common pool, while a defector player keeps it. As previously, the contributions are summed, enhanced and distributed among all competitors. The resulting payoff values are
{{formula:6a21bb01-2f8d-4779-a91f-ff6c6c13b30c}}
(iii) R-PGG
According to our proposal, in an R-PGG a defector requires {{formula:89dd1147-ac0a-4d9f-9918-5897fd6a733f}} from a common resource, while a cooperator player does not. The sum of required goods is wasted at a certain rate, which means an enlarged, and equally shared cost to everyone in the group, yielding the payoff values
{{formula:c490f1e7-3a55-46fd-b210-ce65857e08ed}}
(iv) Alternative R-PGG
In the alternative version, each player has an initial {{formula:9c164700-c7a7-4fc4-b179-ccb4398e3031}} deposit. Additionally, a defector requires {{formula:f1d3fa50-694e-4d81-bdec-4c21bd453650}} from a common resource, and related (enlarged) cost is shared among everyone in the group. Therefore, the payoff values are
{{formula:1d78432f-c66c-42ea-8abc-082e8e15063c}}
| d | 4228ad589e52fa02c2b40b725974a5f7 |
Both our methods use the same {{formula:0a1b3be3-e55c-479d-968d-4b05aeabf5ad}} backbone in order to obtain the localization map. This backbone is a ResNet 18 {{cite:ee9bbfec943652357f7f5836763b86dd0ce6b272}} with four blocks with a receptive field is of size {{formula:40b29815-77e3-4fe8-bfc4-4350e3153cbd}} . The Resnet output vector's dimension is 512, as obtained from global average pooling operator on the last feature map. This backbone is initialed with pre-trained imagenet parameters. In method I, a single Fully connected layer is used in order to obtain a prediction vector for classification. For the Siamese network, the 512 dim representation is projected linearly to a vector of 200 neurons that is used in the two triplet losses (Eq. REF ,REF ).
| m | 48189779e7e63370b1a97c8f53d73db8 |
Malcev Yang-Baxter equation and {{formula:7657d149-7a59-469c-824d-e6f054efc92b}} -operators.
The notion of Malcev bialgebra was introduced by Vershinin in {{cite:9b1c1022af66bd3593d2ce5c8fac254763a31709}} as an analogue of a Lie bialgebra
(also see {{cite:942e7612977ecc648f66e5b571a8538941620e3f}}). A class of Malcev bialgebras (coboundary
cases) are obtained from the solutions of an algebraic equation in a Malcev
algebra, which is an analogue of the classical Yang-Baxter equation (CYBE)
in a Lie algebra ({{cite:942e7612977ecc648f66e5b571a8538941620e3f}}). It is called Malcev Yang-Baxter equation (MYBE)
for convenience. The CYBE arose from the study of inverse scattering theory in 1980s. Later it was recognized as the "semi-classical
limit" of the quantum Yang-Baxter equation which was encountered by C. N. Yang in the
computation of the eigenfunctions of a one-dimensional fermion gas with delta function
interactions {{cite:fd3bd4ed1ec52d0bbaaf1e20e9d64fe29f3dd3fe}} and by R. J. Baxter in the solution of the eight vertex model in statistical
mechanics {{cite:38a1de2d835bb85fe78aba0294dbde87a660e655}}. The study of the CYBE is also related to classical integrable systems and
quantum groups (see {{cite:35b711dda1106a66c7e6b35dbf59bc5aa58914f4}} and the references therein).
An important approach in the study of the CYBE was through the interpretation of its
tensor form in various operator forms which proved to be effective in providing solutions of
the CYBE, in addition to the well-known work of Belavin and Drinfeld {{cite:ec81956594ab07f883f1d8cdfa0e9b57f0f99fef}}.
| i | b092e1b00f87b7ca5598eac664306bf8 |
Another sequence that arises in this way is the regular paperfolding sequence {{formula:607b0191-05af-4b02-910e-7044cf853132}} defined by {{formula:b6ce4bba-3464-41a0-8c9d-fec010dbdd0c}} and {{formula:eb72afc7-888b-4d6c-a781-e1e363f07245}} (see for example {{cite:4e68f5c2537b0e21c614f248e9e08c15dbf956f1}}). If we let {{formula:ecae6bc2-f197-4326-af9d-57be6075b59a}} , then through manipulation of power series, for {{formula:b8b27ee1-5e99-4cb4-9086-1007ba5ce940}} even one can obtain the congruence relation
{{formula:78df4b4d-c458-45a7-9a6a-d4efb83ab2ca}}
| r | 9e5e956f7dee3adb77837984a79d702b |
Next, our achievable scheme based on rate-splitting and superposition coding is combined with binning. This more general scheme requires for its analysis a generalization of the mutual covering lemma of {{cite:b6117960ebbec78e8f7cf029e8144aa737656647}} (see also {{cite:cfd7078c68781a1d57d5ffeefbb4ba64a8b9737f}}) which we prove here and call the recursive mutual covering lemma. This lemma helps succinctly characterize the conditions under which the probability of encoding errors due to unavailability of jointly typical codewords at the encoder can be made vanishingly small. Here too, we provide a connection to polyhedral combinatorics.
| i | 3849f299cd3d4179055534fcd813f35b |
Table REF shows the results for the three models we compare (IR, seq2seq, and Transformer) when using word overlap measures such as BLEU@2, which uses unigrams and bigrams only, and ROUGE-L {{cite:b450887a80f860296a3e9736a86def9678c06909}}, which uses Longest Common Subsequence (LCS).
{{table:ea435586-0aa0-4109-a1b1-37d4a470b99b}} | r | 61b38a5574f6445f1054350dfecfaaeb |
The uniform structure of the high-friction flow state in the form of spanwise rollers in figure REF resembles an instability of Kelvin-Helmholtz type. Such instabilities have a profound effect on wall-bounded flows that allow wall transpiration, for example, channels with porous walls or riblets {{cite:bfc5de55efdbad6f709edf54894d36601319fb0e}}, {{cite:f2ba2a97b6579204c28268e91ebf9ffb5bdda3e3}}. As in the case of Kelvin-Helmholtz instability, the advection of vorticity with {{formula:b0c45b08-5768-4c55-8a6e-0d0879089c23}} in (REF ) ({{formula:7889da79-b7a2-4dc3-99de-6408e4ea61ea}} ) is the necessary ingredient for the instability observed here, and if it is removed from equations, the positive growth rates are no longer observed. However, the control instability has two important differences. First, a Kelvin-Helmholtz instability requires two interacting eigenvalues to form a complex conjugate pair, as illustrated by a simple example of the piecewise linear mixing layer {{cite:8e826d1dea3d4ff784fb13acb57331584dcc09b9}}. In our case, each of the two control eigenvalues is associated with control at one of the channel walls. The control eigenvalues do not interact, and only one of them appears if the control is applied only to one wall. At the same time, when the eigenvalues go through a hyperbolic infinity in (REF ), they become essentially independent from the only velocity scale of the flow, {{formula:ab09bfc0-8d5b-4829-a4b5-2e9f9fe64826}} . The simplest interpretation is that the instability observed here is the instability of the control, in the sense of an unstable feedback loop. This is supported by the observation that the growth rates become larger as {{formula:75b3c735-fc3e-4f41-9fbf-c5be2591eca9}} , which represents reinforcement instead of opposition, since the control at the wall is in phase with the detection plane.
| d | ff14b47410a2a0ec35ccd703d48a2316 |
The Electron-Ion Collider at Brookhaven National Laboratory {{cite:0d015d8ea26852a55ce874b23648780a9360c7bb}}, {{cite:b73162f022d69426bb89c9ceaeba924ad4d30ac9}} will open an entirely new window on hadron structure through the use of high-intensity, high-energy electron and ion collisions. A recent proposal for later upgrading the EIC to a Muon-Ion Collider (MuIC) has been presented {{cite:01de38ee9e26385205eceececaba4e7a21a5b0f4}} and a case is being built within the community for such an upgrade path beyond the nominal EIC program {{cite:90486e59a450a77502e176dcf539f5915ccdd720}}. A MuIC would not only provide a useful step forward toward the eventual idea of a dedicated muon collider, but itself would facilitate a novel physics program that complements the High-Luminosity Large Hadron Collider (HL-LHC) and other future accelerator complexes (c.f. Ref. {{cite:898ba65cb2abd2977d14c73338ebae0b7df7ee8b}}). In particular, the center-of-mass energy possible in such a machine would facilitate a program that includes Higgs physics.
| i | 7a06b7e503fc2ab0041fa87fd5dde7ae |
A special case of constant modular weights is that all {{formula:e6812b1b-6dc6-452b-ae59-7f4b5ca026a1}} are the same,
i.e., a constant. In this special case, the signal sequence {{formula:9cff30ae-7fe2-4c8d-b25c-f82ddfafa11e}} to transmit
is the delta sequence, i.e., {{formula:95cff076-ed48-4b22-a992-53a0c77ba012}} , and {{formula:74f491e3-c6ce-4eea-aeee-4f2a73e66c2f}} if {{formula:6c46abfc-b266-447d-b9d2-7d798171907c}} ,
which is equivalent to the case of short rectangular pulse of pulse length
{{formula:f8a6866a-22f4-447b-aed5-0ac6b46c572b}} . When a high range resolution is required, a
large bandwidth {{formula:92019c3f-5b0a-4d8a-a4fd-de1dae0cc424}} is needed and then there will be a large number {{formula:57e40a40-24a9-4859-8708-57ebbb68f218}} of
range cells in a swath. This will require a large {{formula:f29302d9-86e8-46dd-8637-6207fe50d1e4}} . In this case, such a
short pulse with length {{formula:7edd1c3b-fa91-4d79-b0f3-22e4393c9fe3}} and power {{formula:a577876e-ba7c-43bb-8f43-559f25f56e61}} may not be
easily implemented {{cite:6db2fc9c581f5a545dea9219477fb94cc0b0dd85}}. This implies that constant
weights {{formula:3a17360a-c5ec-42e2-b71d-a4ce06db89f5}} may not be a good choice for the proposed OFDM signals.
| d | 84db778168710e23575de5f67bd5c224 |
In recent years, the single HSI super-resolution technologies have attracted increasing attention in remotely sensed data enhancement {{cite:6609379f1baafa9e972cb2e8a79f778111aae387}}. Particularly, Deep Learning (DL)-based single image super-resolution (SISR) methods have achieved significant performance improvement {{cite:4318da9ba7bf763fcc58bcc8c70bc4565f7c36b5}}. The first DL-based method for single image super-resolution was proposed by Dong et al. {{cite:e2b25c2c8d4559696f82fa69b9da4bbf528b3532}}, named as the super-resolution convolutional neural network (SRCNN). To recover the finer texture details from low-resolution HSIs with large upscaling factors, Ledig et al. {{cite:cd38742098aea8585a6ddfd1b16b710edb1977f3}} proposed a super-resolution generative adversarial network (SRGAN) by introducing a generative adversarial network (GAN). After that, various GAN-based deep learning models have been developed and proven to be effective in improving the quality of image super-resolution {{cite:c0ede2fb71a0e2a3637a37be4069d305366d5c0f}}, {{cite:ce3f5339f2fde7ec55e0291e38348f55595da84f}}, {{cite:691a7abaa3370f3c1491e19ab93d547fa7bd0fc1}}, {{cite:671e13f524637867d55360fa9ebe73b9b6c4ee1f}}.
| i | 5a30b87aa377a78f6f410288cc1507fb |
Rapid developments in quantum computing hardware {{cite:19e208f217eb5e1923729b752c174794c7a6a8e7}}, {{cite:6940b82206564d2d9e874a33c7953c7e47b32d46}}, {{cite:5b3ad4ca852d86cfab72d6a9307677cb7daba2cd}} have led to an explosion of interest in near-term applications {{cite:2529915e41da374627295c39bc6888aeb939db61}}, {{cite:20b6cf9e2696fe523fb45d3c73a7d8562a18c98e}}, {{cite:b581f8ebff88e4c905f81c4be9f01aa0fe5bdd51}}, {{cite:dc76eef30726441aa0fbffe8725c20fac635916c}}, {{cite:daff64978473b4005d6ebb89776c828897028987}}. Though current devices are remarkable feats of engineering, their current coherence times and gate fidelities exclude running general quantum algorithms such as Shor's factorisation, Grover search or quantum phase estimation. Nevertheless, it is hoped that Variational Quantum Algorithms (VQA's) will be able to demonstrate a quantum advantage on Noisy Intermediate Scale Quantum (NISQ) devices {{cite:4aeb8cb5d47dd66e0d6106f6f744332dacc75d41}}.
| i | 18648b66794bb84e3d9feb71f4674580 |
As described by, for instance, {{cite:9101d104f016f247884b903d3ab9f838a849c01e}}, {{cite:87a129f7fed1865990a7a999e3649bb91ef05968}} and {{cite:ebe455115132f9e7da7b159acb29708ec80d2fd3}}, if {{formula:21b77d6d-ccd1-4375-8393-d95dcdcbd330}} is a
majorizer of the convex function {{formula:b56d7c58-d922-4b05-a6c3-74aa36cd6b48}} , then the sequence {{formula:1e08fb5d-c4cb-421d-b420-1f592e895a46}} , defined through the recursion formula
{{formula:4b96222a-d141-424b-89ff-6325b26e943c}} , converges to the global minimum of {{formula:61052994-b9ee-43be-9c35-5b8030dac9e9}} .
Unfortunately, in our case, the optimization step of the surrogate function {{formula:582cb412-83e4-4cad-a18b-d33bd928f5cf}} in equation (REF ) does not admit a closed form expression, therefore, we must revert to the MM gradient algorithm. The Newton-Raphson's update for a fixed length {{formula:c489acae-04b8-477d-b704-d62d4384b5c4}} is
{{formula:41bfaee0-b4ed-441f-9bdb-6e2e08fa2db7}}
| m | 39ca412292152270f83c64aee05dbbdc |
This subsection will provide detailed discussion about the main difference among the proposed GSRC method, the BM3D mehod{{cite:7ee78bcca2846e3917c373d728de447853a5e31f}}, the NCSR method {{cite:5759df62abec4948dc20337e91e4614bc48787f1}} and most existing NSS prior-based denoising methods.
| d | 66d6da2e276a9e29215c550e8afe90fc |
Moreover, we investigated how the evolution of clouds depends on the parameters {{formula:bb292d2b-6e3e-4a10-8221-a331840f5dc5}} .
We found that for a large {{formula:472076f1-4bbd-4a14-b4fc-f6b93f05de69}} , clouds evolve into a quasi-stationary state as we obtained in {{formula:e64662b3-985f-4d3d-b107-8b1daf9786e4}} case.
As we decrease the value {{formula:8a16f0dc-512b-48a1-b6c2-420e2065afba}} , there appears a critical value at which the cloud becomes unstable. From our calculation, the instability occurs when {{formula:b1616006-e725-4e11-b6a4-a16face6460d}} Here, we assumed that the energy at the onset of the instability scales on gravitational coupling as {{formula:e60c6705-97b3-458e-8f12-8636da617c3b}} , which is motivated by the estimation of the energy when the bosenova happens using the non-relativistic approximation {{cite:6af8070ba2825bfc7df16b622212f35b9e39a648}}, {{cite:942fccc6dbabdb3fb7f0a44f91b0cdd32e445ad1}}.
Also, we found that the BH spin does not have any significant influence
on whether or not the instability occurs.
The main role of the BH spin is to control the existence of the superradiance and the superradiant instability time scale.
| d | 5a166bc4dc924d710cba87aa11fc740d |
On the other hand, although some magnetar theories predict the possible existence of QPOs of tens of Hz in SGRB precursor (e.g. {{cite:c0af9f67db04b648895b51cb088848af4f46b9e6}}, {{cite:c8f3c6d4a6c358dd9126df672a37381781d45a93}}, {{cite:27e24cd9d0618cc967466a54b0c535642bfa0c04}}), the duration of the precursors of SGRBs is just about {{formula:b0ef969e-19e8-4adc-9459-7aa8b451ebea}} 0.1 s (see Table.REF ), which means that only a few cycles of oscillations could possibly exist in a precursor, making the QPO search even more difficult. A definitive answer may come from sufficient statistics observed by more advanced detectors and higher detection signal to noise ratios, or a joined analysis using the light curves obtained by multiple GRB detectors, such as Fermi/GBM {{cite:4b9da641d9a0a785732ff74291db0189c143c425}}, Insight-HXMT/HE {{cite:20f8a8358970f8fc61d852592bbc3235e3a1f323}}, {{cite:04c664b0c751af4ac86ceaea73405eb835e1ed61}}, Swift/BAT {{cite:1684294059d709b222cef53f9944a8174ee09abb}}, and GECAM ({{cite:33282ff733bae8c2394a3376b0ecf84082482cd5}}, {{cite:b44eccc132e2743e16e1b02e1cfd13da492395c8}}). Especially for detectors with similar energy response will be more advantageous, such as GECAM and GBM {{cite:9eeff7989170ad0b8a252d2c8caec132b8a05336}}.
Also can by combining with the information from theoretical models and the QPO evolution with time as a template in searching for QPOs {{cite:60662bd4bbf8adaa44f5127759f1da4eb1ae22e1}}.
| d | 9c0f239112db9e69e383f1c2eb6eaaff |
Stockmeyer L.J. and Meyer A.R. have employed the highly ingenious technique
for the implementation of this simulation (see the proof of Theorem 4.3 in
{{cite:4997b092d99dadf20567db173719381fe6a663bf}}). Their approach permits writing down a polynomially bounded formula
for the modeling of the exponential quantity of the Turing machine steps
provided that one step is described by the formula, the length of which is
polynomially bounded. One running step of machine is described in {{cite:4997b092d99dadf20567db173719381fe6a663bf}} by
the Cook's method formula; this is a formula of the propositional calculus, and
one can construct it just as the sentences, which were applied for the modeling
of the polynomial quantity of steps of the nondeterministic Turing machine in
the proof of {{formula:8dd721f8-c849-4004-9de4-0ec730a8d171}} -completeness of the problem SAT {{cite:6027a715cbe41c1419bbce120bf341d5fda2fb29}}, (see also
the proof of Theorem 10.3 in {{cite:5c1498b78871756b07f4ca23a992ce84a651156b}}). There exists a Boolean
{{formula:9492ef51-cd8c-42b5-bc95-a069959f6fe5}} -formula, which corresponds to the Cook's method formula. We will
also name this {{formula:6ef121f9-56b3-4b05-b393-da98b6afb627}} -formula as Cook's formula.
| m | 473e10b2033bce60fa80a0a912f7245f |
Remark 1.9 The statement of Theorem REF is true for all non-elementary, finitely generated Fuchsian groups {{formula:1281d8e0-8442-4757-b4ad-3970babaaae6}} . For the modular group {{formula:df6e2216-64d6-4f10-b290-60bf16905c3d}} (in which case we have {{formula:9db85ccd-8fc1-474d-adbe-0962d866a9ff}} ) Selberg's famous {{formula:f91d217f-6c8c-4274-8790-0612575e3b8b}} -theorem {{cite:0dfb20d6033f66dffbd49d519b5f4a2b361c28ea}} gives a more precise statement with the explicit spectral gap {{formula:baaffce5-9d98-4de4-b12c-f9aab6d4460b}} . For {{formula:a6f5b48a-ab98-48d9-8d0f-c55b976f88fa}} , Theorem REF follows from Gamburd's thesis {{cite:2d543b9d3f073f47c7a7f5a7b9a844333c726fc2}} with {{formula:88268bc7-947f-4350-8052-94da68afd741}} . For {{formula:94a45e5e-12a5-491d-8b72-2130510c0adf}} , the statement was proven by Bourgain–Gamburd–Sarnak {{cite:a0eeb1ac50442a20e38883f736a1f621afae8034}}. The more difficult case {{formula:3ee348dc-36a7-4c04-9721-084dd1a2082f}} is covered by Theorem REF , since {{formula:ce6e7e3e-3d07-40ca-95fb-57766215c553}} implies that {{formula:9b5dc3b6-19ab-4912-be6a-db3dec554352}} has at least one cusp by {{cite:47b2e70b3f15abf9cdf9b606296752c54b29dc32}}, {{cite:de38aeecdf44156e7dd6b4c35b215f2a9e6cc875}} (see also Remark REF above). Similarly to {{cite:b753a9f5961a2818c0f667314534a4100a1d7132}}, {{cite:2ddce0318f3e6f5346d5c24fc0e9b940859fccfe}}, our method does not yield explicit bounds on {{formula:52ea80ca-e60e-45e7-9366-de1b6e469451}} , due to its reliance on the expander theory developed among others by Bourgain–Gamburd {{cite:4c7a3658f222796deea7a3fbbddaed8f3b184e3f}} and Bourgain–Varjú {{cite:93c266d46c9d747a45e1921d13f6d5e497ca11d5}}.
| r | 99d7a8223468054c72b0b35368c483de |
The solution theory of (REF ) is standard and was accomplished by Ito's calculus or martingale problem.
The existence and uniqueness of the solution of (REF ) under those initial conditions follow from {{cite:d4b9a751bcf2a9b1bacf76c5b1010c38acd518d7}} (see also {{cite:99c9cf091aa767cacb092bcc692a178789bbc5c6}}).
Thanks to {{cite:611f7968f8551cb87f5cd33c260c21be2ef5af99}}, the solution of (REF ) is strictly positive for all {{formula:d1b11175-1849-402a-9a4a-543569fe8c56}} when {{formula:06ebc212-57de-49ff-b95e-70a6ac2fdfd3}} is a positive initial data.
Logarithm of the solution of (REF ) formally solves the Kardar-Parisi-Zhang (KPZ) equation which is written as follows
{{formula:c3aa46a8-e328-43fa-b236-30cdeecbaeeb}}
| i | 2da3a8bd86699966ab7d7c16b85eb144 |
The most commonly used metrics {{cite:4114bfecf8c626eba6e6b64cc7321e4ff271b9b6}}, {{cite:387064fd32fa42cb63994ceab6eaa1abab8d0817}}, {{cite:c22734455b11ef598a36f06163c8debd4125ee49}} in continual learning literature to evaluate forgetting are the average accuracy
{{formula:f4d4eb9f-104e-44eb-a78e-2c0f692efcc2}}
| d | 2e7025327646e4a46785b9bd89c5f830 |
We show in Fig. REF the amplitude of {{formula:1e59ae87-d9b8-414f-9333-7c9493e7d697}} and its right-ascension phase as a function of the energy, as expected for the JF12 (left panel) and the JF+Planck (right panel) models and considering only the regular component, the regular plus the striated components or the complete field with also the random isotropic component.
We also included in the plot the results of the measurements from the Pierre Auger Observatory {{cite:7fb34f9f18234c19e1fb00d87fbf169febe53470}}.
| d | 96429b3957bd43577326ddebf248a9b8 |
As mentioned before we use joint predictive log-likelihood as a statistical measure of out-of-sample forecasting performance. It gives an indication of how likely the realisation of the modelled variable was conditional on the model parameters. The logarithmic scoring rule is strictly proper but it severely penalises low probability events and hence it is sensitive to tail or extreme cases, see {{cite:60f7302dfb0e4d591fe80ac0a863fcd6b4d80c8d}}. A different proper scoring rule could be used if deemed appropriate for a specific use case.
| d | 8c3574d3df71f7c4d4fa24d634a0f4fd |
As a conclusion, limited samples sizes and the selection/estimation of any specific model is still an issue in neuroimaging, further when the model and the interaction between model parameters become too complex for an accurate posterior probability estimation, or a feasible numerical computation of the Bayes rule. Given the connection between the two observation models, i.e. GLM and LRM, in this paper we propose the use of an agnostic theory about the estimation of dependencies and established in the pattern classification problem with limited amounts of data, to achieve statistical inference {{cite:6bda2c220a8129e04b059be6100d7c558c1289ec}}, {{cite:015999f1cc0d88e2787104fa6346caf940cdb312}}.
| d | 5845542452919efdf78f7715b92b491b |
Sun et al. proposed FuseSeg {{cite:6e0a0beef54bac1211520f4e88e2dd823c6c4103}} employing encoder-decoder structure and two-stage fusion strategy to achieve segmentation in urban scenes. There are two encoders taking three-channel RGB and one-channel thermal images as inputs, and DenseNet-161 {{cite:633c94a1a7b1800a244cc7d1837464e5ee4a4c90}} is employed as the backbone of the encoders. Moreover, FuseSeg introduces a decoder including three modules: a feature extractor with two convolutional layers, an upsampler, and an out block. The upsampler and the out block each have a transposed convolutional layer. The feature extractor is responsible for extracting features from the fused feature maps while keeping the resolution of the feature maps unchanged. The upsampler and the out block increase the resolution by 2. The out block outputs the final segmentation result. Sun et al. also proposed a two-stage fusion strategy to effectively use the multi-spectral inputs and reduce the loss of spatial information due to downsampling. In the first stage of the fusion, feature maps extracted from the inputs in the encoder are fused with element-wise summation in the RGB encoder. The summations are again fused with the corresponding feature maps in the decoder through concatenation.
| m | 4c8860bbc79badaf80e61feb2bd7bb1c |
Color: To compare with our method, we first set up a baseline representing manually bias identification method. In previous studies {{cite:be395af055653cb054aedb7db5d3564747fdf8d0}}, {{cite:d9dc3870ca69f4fd56db3767ac2a9aea6ca0a06d}}, researchers have found that normalizing unwanted color variations aids model performance in computational pathology, thus we use average RGB values of each image as the baseline attributes to compare with our framework.
ImageNet-C(IC): {{cite:4c40af9c351c163a8d61581f94dca6cce0300cee}} is a common robustness evaluation dataset, which has been used for debiased method evaluation in previous studies{{cite:0c5ad6182aafd479343b2729fc73b8559d158e96}}, {{cite:dc744af488f7610b126a12069d28d309253404d1}}.
In this paper, we apply the generation method from {{cite:4c40af9c351c163a8d61581f94dca6cce0300cee}} on medical image datasets to compare with our framework. Three possible corruptions in medical images are selected for experiments: brightness(B), contrast(C), and jpeg compression(J).
| m | b4058ff75c42664ad6e2a344e06ea81d |
which is incredibly convenient because the two terms in the expectation are disentangled. We refer to Section 13.3 in {{cite:1582eb8ffe3c4c7ab05a483474e0b71cfdbaefef}} for a proof of this result. It is thus imperative to derive analytical expressions for {{formula:cf6981f2-e805-4388-a910-e94bee7628b5}} as per the following Proposition.
| m | a7a794487feb759e15aa7dfe475d941c |
It is also interesting to investigate the effects of an external
magnetic field on the holographic superconductors. One of the
major properties of ordinary superconductors is that they exhibit
perfect diamagnetism as the temperature is lowered below {{formula:e7ec407f-2b19-400e-8acd-b04c8163790e}} in
the presence of an external magnetic field. In other words, at low
temperature, superconductors expel magnetic field line and the
phenomenon is known as Meissner effect. It is worthy to explore
whether or not such an effect can be seen in the holographic
superconductors when the magnetic field is turned on. Some efforts
have been done to disclose the properties of the holographic
superconductors in the presence of an external magnetic field
using both numerical approaches as well as analytical analysis
{{cite:b0e3bd05312b9efc70c9e93f86fa21c075680a19}}, {{cite:5d63dc11da6653489123e0cf5230ce97a60377d3}}, {{cite:661d114363dfe86ee5629de6b8d281a4e975ac67}}, {{cite:d0a0ba6f89e233330f9abde197fc36fd091e1391}}. As an analytical approach for deriving the
upper critical magnetic field, an expression was found in the
probe limit by extending the matching method first proposed in
{{cite:d4feecd2fd2d741974e876ddac5291372b743e91}} to the magnetic case {{cite:4bed008cba05e5753020f48e4e5076852ff56713}}, which is shown to be
consistent with the Ginzburg-Landau theory.
| i | 5a4a980060b8cd19986161321b9e339d |
Prompt-to-Prompt. Similar to UniTune, Prompt-to-Prompt {{cite:b39684d589b0c481cd784c8177cb8f47f890abfb}} also explores the problem of editing an image via text manipulation. Prompt-to-Prompt works best on images created by the diffusion model, and shows mixed results with arbitrary images. Also, as the Prompt-to-Prompt technique requires fixing the attention weights, it is restricted to localized edits, and supports only a limited set of edit operations (adding or changing a word). Our method is inspired by Prompt-to-Prompt, and relaxes those restrictions. While we did not perform a thorough comparison, for many cases where both methods are applicable, UniTune is able to generate equally pleasing results (see figure REF ).
{{figure:88f7b8af-73f9-4787-953d-7da1e4e0255f}} | m | 8e92776f36f48fc9cdfd8602e39bc7f0 |
However, the number of parameters needed in traditional convolution often makes deep learning models too large to apply on devices with low computational capacity.
Also, a model with too many parameters probably has a very long training process.
For example, VGG has more than 130 million parameters and has been trained for {{formula:3edcfdaa-df95-49d8-8e50-04912b05bf29}} weeks {{cite:1b3f0512d04b65c816ef01ea6fd406ab8428ff18}}.
It is not suitable for such a huge model to run on common devices.
| m | 3492170cf08686781414d1f6aecca085 |
Reinforcement learning (RL) has recently shown many remarkable successes, e.g., in playing Atari and Go at a superhuman level {{cite:24421a27efac59645a878b5185a8765f7ce01c99}}, {{cite:611ae45d3d86f502907687025d786455727570f4}}. Recently, there have been wide research interest and significant advances in robotics learning using RL techniques {{cite:e54dcc3177cc3a0e82856a8ef476c8ad3665c7fb}}, {{cite:2c2f383a4479f18c9d581849bc243c70511f76f0}}. The topics of RL and classical control theory are closely related: both aim to find an optimal policy that optimizes an objective function, given a system represented by states and transition dynamics. Therefore, RL algorithms have the potential of enabling robots to learn in complex real-world tasks such as locomotion, manipulation and navigation.
Unlike classical RL tasks, which have discrete action spaces and underlying state spaces (e.g. Atari and Go), problems in robotics often have high-dimensional continuous states and actions, and are often limited by real-world sample budgets {{cite:988bf784d82c8034fc557faa8448b05fc4096d85}}. To this end, prior research in robotic learning have developed RL algorithms capable of performing continuous control {{cite:6a86b6977f20203f20e8ccfb7eb025be2437967a}}, {{cite:0fbef1a271945e20aad737a62b71fde15614e91b}}, {{cite:2348e97d22e4d81c2afc51911a24d75ba083896b}}, {{cite:4f218df8fe5336a3bdbfaaea8e3866b9338269a4}}, and sample-efficient learning methods, e.g., {{cite:2c282d9befea827057352144937c44a15fbf6c4b}}, {{cite:e01ef82cb6e6d73b11b604f9c8cc3521d3c1924e}}, {{cite:0c6e4a89dbc956cec36dccdd97325e3a42c38e44}}.
| i | 4e6e61704cb5bf35bfd7bf0f811e8613 |
To obtain the full one-loop amplitude we must combine the unitarity
cuts. One possibility is to carry this out prior to integration by
finding a single integrand with the correct unitarity cuts in all
channels {{cite:10f8054a693b00f9f6be3ff5235e999c67a9f6b9}}. Some non-trivial examples where this
approach was implemented are high-loop computations in
super-Yang-Mills and supergravity (see
e.g. Refs. {{cite:df4b77d3b3ea3b48d3afc39dc3490f9509976ba5}}). On the other hand, in
high-multiplicity QCD calculations (see e.g. Ref. {{cite:83565b6314a4c8a0c6b709f03ea1f501a5ec1c0b}}) the
cuts are usually combined after reducing to a basis of integrals. We
apply the latter approach here. We do so by promoting each cut
propagator to a Feynman propagator, and each cut to a Feynman
integral. We then use FIRE6 {{cite:e17efbebdb8430bc9125b39b6930d40741792f64}} to reduce each
Feynman integral to the scalar integrals appearing in
Eq. (REF ). In each cut channel we only determine
coefficients of basis integrals with cuts in that channel. By
systematically evaluating each cut we determine all coefficients
except for those of integrals without kinematic dependence,
i.e. {{formula:30ad08b2-93c4-4a99-9fee-e45fbd97150d}} and {{formula:ea544f7c-cb9d-489f-9d6b-eb7799fc88cf}} . In the case of gauge theory, the
corresponding coefficients are determined by imposing the known
ultraviolet behavior of the amplitudes {{cite:6bd717776c89aa02327ad03aee47508fd45fa468}}. Below, we
describe an analogous procedure for the case of gravitational
amplitudes.
| m | 5d38ef7f9e0fef724dc1f60c5a04827b |
The very high EM3 honeycomb code threshold stems from three factors. First, two-local codes benefit greatly from a two-body measurement circuit architecture. Because of their two-locality, we can measure the data qubits directly without decomposing the effective measurement into a product of noisy gates. The result is a circuit with significantly less overall noise. Second, the particular error model we adopted from {{cite:2b6d566661dfe6a7f61d4d05488171bc7d2fa463}} is somewhat atypical. The collective failure rate of the two-body measurement includes both the noise it introduces to data qubits as well as the accuracy of its measurement - a demanding metric. While this does induce a richer correlated error model, it introduces less overall noise than two error channels applied independently to the qubit support and measurement outcome (see [fig:detectionfraction]Figure fig:detectionfraction in the appendix). However, we can still infer the excellent performance of the honeycomb code by comparing it to the surface code - we make such comparisons to avoid differences in absolute performance that depend on error model details {{cite:14eb9363792d3e1daf86a0a9ac3d7d0414967c29}}. Third, the honeycomb code is simply an excellent two-local code. While many other two-local codes involve high-weight parity checks {{cite:86cfb73e6ffcc1f782daf737ee0160078c631880}}, {{cite:bcf480d95d75e36c2f84d6cd00d64bd0fde3b6a7}}, the honeycomb supports parity checks of weight six. As a result, these checks are less noisy and the resulting code is more robust.
{{figure:d878cd92-9233-40ce-82d2-cfc956cddfdb}} | r | 8aa1b03af56152fbe90d013ce1687bd8 |
From Eq.(REF ), it is readily shown that piezoelectric materials presenting large (small) {{formula:6f4916ca-3d05-4dbe-9003-694d59280c56}} coefficients
[Eq.(REF )] will offer great (poor) band-alignment tunability as driven by uniaxial strain. Consequently, piezoelectric
materials possessing energy band gaps in the range of {{formula:80b1e1ad-fc28-470e-b725-d9419b54cd3f}} eV (to absorb the sunlight visible
radiation), small dielectric constants and large piezoelectric stress coefficients (the last two conditions as for maximizing
{{formula:1367287f-b858-42f2-ae4e-880aefa77280}} ), a priori should be regarded as promising piezo-photocatalysts. It is noted that large piezoelectric
stress constants typically are accompanied by also large dielectric constants {{cite:6961c4009442d8b37d80b4117e17b6c43b1e9823}}, {{cite:3e163b22fd9009e2256a29ca48c9300ef931c531}}, thus the natural difficulty
in finding materials with large band-alignment piezo tunability (i.e., large {{formula:5a2cf60b-1e42-42a1-8fb4-ad160767cf2d}} values). This small set of conditions
are not only physically insightful but also computationally convenient: the relevant quantities {{formula:4c858f5f-8a1f-4cf3-9ea7-89fede92ab95}} , {{formula:a77e523d-5fd1-4dd9-8a6c-3fc788f626d6}} and {{formula:3fb1a5ba-ea4f-448d-b633-94f629a621cc}}
can be efficiently estimated via bulk first-principles DFT calculations {{cite:d976e1fa7ac549232a12e719adc8b67d7a6b2dc1}}, {{cite:ee20271143d96e2f6d26cf5abd634f7a5afb5b4e}}, {{cite:ac0c027b2f9cff313dcdeb9690267314dfd0c8dd}}. As we will show in
the next section, this circumstance can be exploited to conduct high-throughput computational searches of piezo-photocatalysts
within large databases of piezoelectric materials that are publicly available {{cite:6cd7c470034069d322315afbe116c737c58d9956}}.
| r | 8a7df4377acb95fa53f87a57f61a7283 |
The idea of modulating a prediction error appears elsewhere in machine learning literature, and modulating the error in different ways or by different signals produces different effects. Here we have shown that modulating reward prediction error by action probability creates a human-like adaptation-to-change effect, including improved performance in simple but dynamic tasks, as well as a paradox-of-choice effect. Conversely, the Inverse Propensity Score Estimation (IPSE) approach used in counterfactual learning uses the inverse of the probability as a modulating factor {{cite:237609d21c703a2dc2652d12c186905d36a77db2}}, {{cite:8f34c4a8d6fea11db78f82ee500bccf280563647}}. This can have the effect of de-biasing learning from data collected in a population that differs from a target population. However, during online learning of dynamic tasks it would result in slower adaptation; opposite to our rule. We could also consider REINFORCE-style reinforcement learning algorithms, which modulate a prediction error by a “characteristic eligibility” term that expresses the gradient of the action probability with respect to the parameter being updated {{cite:d2d0faf6aa9a8d7b0e246de7c4c8b2d48960481c}}. This quickly makes rewarding actions more likely - in static environments where the gradient has consistent meaning. Our rule, on the other hand, demonstrates a similar learning effect in dynamic tasks. Making predictions is a central operation of the brain, and it is likely that neural circuits modulate prediction errors in many ways to get the right effect at the right time, creating what we know as human-like learning.
| d | d0beb90e337490f77dd3614fa8fd81dd |
Counterfactual queries aim at inferring the impact of a treatment conditioned on another observed treatment outcome.Typically, given an individual, a treatment assignment, and a treatment outcome, the counterfactual question asks what would have happened to that individual, had it been given another treatment, everything else being equal. An illustrative and motivating example is the case of clinical time series. Based on the observation of the outcome of treatment {{formula:e649be23-d9d0-4c2b-9a1d-602d9ebfdd91}} on a particular patient, counterfactual queries ask what would have been the outcome for this patient, had it been given treatment {{formula:d8e568a0-fe81-47e5-9592-18c04987c4ac}} instead. Notably, counterfactual prediction differs from interventional prediction, which is also referred to as counterfactual potential outcomes {{cite:51ce39cac078a13746694cfad7384c5c6751d43a}} and constitutes the second rung of the causation ladder {{cite:353bd7b0876e3a979c5687827d61ca00deed8d86}}. Counterfactual predictions are retrospective, as they condition on an observed treatment outcome. In contrast, interventional predictions are prospective as they only condition on observations obtained before treatment assignment.
| i | fece946adc1ce670fe000dd54e2fd3d0 |
Here we suppose that the coefficients of (REF ) are rational functions. As in the proof of theorem REF , we multiply {{formula:acfaabd3-317e-4119-800d-cec004247322}} on both sides of (REF ) with {{formula:46c3d03b-2e7a-4e00-ab96-747308e97f55}} and integrate the resulting equation to define an auxiliary function {{formula:e9b60b8f-beae-4944-ab51-ac8cd71c0119}} in (REF ) such that:
{{formula:c65e3602-06f2-401c-bb5d-dbd7931735a5}}
where {{formula:0742f0a5-a19c-4cd5-9770-f9427f5ae545}} are differentiable functions to be determined later and {{formula:495ca720-e09a-45e4-88c0-f7b8d4040fd4}} . In particular, for {{formula:04e2cd9f-0cc9-4cbd-9b7b-6d07bd40c7a5}} , we need to solve the following system of equations:
{{formula:71777395-649b-4c0f-9be6-1a3d9ee06192}}
Now, for {{formula:1cafb675-7fc6-435e-b0c0-505f9b7877e0}} in (), we use the relations in (REF ) to find that {{formula:6fb70ef7-3c98-477f-a3ac-3a986409de73}} and {{formula:b74dd575-546b-4fc6-a478-4cf3e2c8a798}} and the function {{formula:f1503361-e54c-4cbc-a227-256c25312f80}} in (REF ) satisfies:
{{formula:9a197f09-070f-4b2e-8381-e9a8e956083a}}
where {{formula:3f9555c2-ecc0-464d-b4e9-0d9f9c753d4f}} and {{formula:640348f1-7d3b-4438-ae34-d38c6db2f80a}} are integration constants. We may choose {{formula:fc107643-1154-48e2-846c-91058681efcb}} so that {{formula:926300a5-3088-4ee5-af87-3bf17c73cc5e}} or {{formula:1d82844b-aca0-4ba8-bd2f-bab23fcb1df7}} . Then by looking at the proof in {{cite:ba1a8cc094b10cf3a4672fb4538a7f55b5938f89}}, we easily obtain that all meromorphic solutions of {{formula:403ef30c-0341-424f-9340-8eb7a159ca79}} satisfy {{formula:11dbfc7a-610b-4349-a6a5-697b349a4e9f}} .
Thus the assertion of theorem REF follow.
| d | 5c442999df275af761439c84e75d9dc8 |
We find the lensing of fractional excitations to be a convenient picture for understanding the photon echo in the Luttinger spin liquid. A crucial feature of the lensing is the refocusing of the wave packets world lines, reminiscent of the refocusing of quantum phase accumulation in the NMR spin echo or photon echo in few-body systems. However, the lensing is unique to many-body system in that it entails the propagation of wave packets. It could be viewed as a conceptual extension of the more familiar interference picture {{cite:94d5b6db0afeddb86535443c98e34b642f191ffe}}, {{cite:15567ca12ea225f2d4d2c4145d911cbfb46173d4}} commonly used in the study of photon echo in few-body systems from the time domain to the spacetime domain.
| d | 223538b359335c8a55f269c9bed2cb4f |
In this work, we build independent emulators at each redshift ({{formula:144e4efe-5922-42ab-a82a-a8e583bfeed9}} ). Note that Ref. {{cite:ee98fafd9a9255691643f31ba11874111bcc84ae}} took a different approach by adding {{formula:c9b96b11-dc99-4d54-ba16-1b77abf6faea}} as an additional emulation parameter. We follow the strategy of multiple emulators at different redshifts for two main reasons: First, this approach allows us to implement different models for the redshift evolution of individual parameters after the emulators are constructed. Indeed, any redhsift evolution of individual parameters can be trivially retracted from the emulators at different redshifts as long as the parameter values (that are now evolved with redshift) remain in the range of the emulator. Second, not emulating redshift allows us to reduce the dimension of the regression model. Due to the curse of dimensionality, the required size of the training set increases substantially due to increase in the dimension {{cite:4d0b3c7e069ff56a0cde3b26152ced8492055cda}}, {{cite:a5db689a68dffcdc5c2b92db16da4d0c0734f914}}.
| m | 86d40c4d5355123c3d9efecb227e806a |
Fig. REF shows the qualitative result. Orange and blue bounding boxes represent ground truth and predictions respectively. As shown in Fig. REF , both PETR {{cite:c0531726c2f4ed25664b7ad366dc941f6777606b}} with ResNet50 backbone {{cite:799fe261c3a869a70c59a4c516c6ef68164bad5e}} and PETR {{cite:c0531726c2f4ed25664b7ad366dc941f6777606b}} with depth-pretrained VoVNetV2 {{cite:c1857146109a1ecc9e0d36889689bd07aa263e92}}, {{cite:5dbafd5f26da723e668e0a52e846113250840159}}, {{cite:a3ebbfbc0f1d19112b139ba307e62085ab35b277}}, {{cite:04758fd85a6a7d6a8e58ead34b4f2744fdff2449}} still predict a row of false positive predictions along the direction of depth for small objects. Since depth-pretrained backbones are generally pretrained on the external dataset and contain different settings on camera matrices, we suggest that those backbones can narrowly deal with the false positive problem due to weak depth estimation. Nevertheless, our method can predominately alleviate this problem due to referred depth information from the internal dataset {{cite:6e37a86ac5a38858081812e63c7e6cc24fb2d6a5}}.
{{figure:eb359a0c-3c6e-42d7-b5d7-dfd415019d5c}} | r | 8c8dc88cbe26e2390a21df2d381c6cef |
We review the various concepts of tangent and normal cones below (see, e.g., {{cite:7a81592b38c9f1910a0aaff689e216ee5981545e}}, {{cite:db05f9e66be15f9ad6f31f0a78b9c9446ea5602a}}, {{cite:803ff79442d655c20d500f377e9429ddb1f58afe}}, {{cite:fd495d2b2cb58f55c157cb972d60b8c5306028e0}} and {{cite:df846b807b613337f1995b6e1d4f94880747caea}}).
| r | 9d7a4320197a02b112edc93fd8db5d4f |
Because each cell can have a different structure in proxyless setting, we demonstrate only two typical types of cell structure among all of them in Figure REF a and Figure REF b. The first type is a chain-like structure where only one path exists in the cell connecting the input of the cell to its output. The second type is an inception structure where divergence and convergence both exist in the cell. Our further observation reveals that some cells are dispensable with respect to the entire network. After the architecture is determined, the network is trained from scratch with the batch size of 64, learning rate as 0.1 and cosine annealing learning rate decay schedule {{cite:a7060782dae3f2592436c2100e365d7f3c474900}}. The validation accuracy is also presented in Table REF . Although test error increases slightly compared to {{cite:62752f7c2b48b409957f1b763807e29a70d0dfff}}, there is a significant drop in the number of model parameters to be learned which is beneficial for both training and inference.
| r | 35640ae0c63315ef10f6ca328425b293 |
Actually, our method can be modified to take external labels into account.
To achieve this, we replace the predicted action classes in Eq. (REF ) with the external action labels. Specifically, given an input video, we use UntrimmedNet to predict the top-2 video-level classes and assign these classes to all the proposals in this video. Thus, each proposal has two predicted action classes.
To compute mAP, we follow {{cite:e340c8476fb436190f9801f8dccaefabcd1c6567}} to obtain the score of each proposal by calculating {{formula:29e91146-40a3-45e0-ad06-12ff6de16506}} ,
where {{formula:7d188c8c-5f14-4cb4-8299-1bac88b98fc8}} is the proposal score predicted by our model (, SSN+GCM),
{{formula:8841de33-d63e-4602-815f-235d2b0db396}} is the confidence score produced by BSN (or BMN)
and {{formula:ab6b3113-2b97-46aa-9b2c-1b6f46a633b6}} denotes the action score predicted by UntrimmedNet.
As summarized in Table REF , our enhanced version (, SSN*+GCM) consistently outperforms BSN and BMN when using the same proposals. Moreover, SSN*+GCM outperforms GTAD {{cite:e93189c35a8bd57c5a22d8f3fb3751679d01b1ec}} even though GTAD uses additional video classification scores from {{cite:68367dbaf19dc4fb2f73a112747bb72eba98c92c}}. These results further demonstrate the effectiveness of our method.
{{table:b5789ba9-9d86-4e4e-b05d-58a06736852e}}{{table:8b2de7b6-f830-491d-aa3a-dbb9ba637a0f}}{{figure:f0eb51a8-ce9f-418f-8da0-91f697ba89c6}} | r | fde50f3afc08403cee165156fd2e338a |
To evaluate the performance of the proposed algorithm, we consider {{formula:9e0f9d54-5ce6-4d8f-b063-21a0198d5aa7}} DRL agents in two different classic control environments: Cartpole-v0 and Acrobot-v1 of Open-AI Gyms {{cite:28beca5fa271e5a4b7e5dafc179cadbd9890bffc}}. The Cartpole-v0 consists of a cart that can be moved to the left or right and a pole positioned vertically above it. The goal is to keep the pole straight. The state-space of the Cartpole-v0 is a 1-dimensional array consisting of four floating values, representing the horizontal position of the cart, velocity, angle of the pole, and angular velocity of the cart. The action space is discrete, whereby potential actions are 0 and 1 to push the cart, respectively, to the left and right.
The second environment is Acrobot-v1 which is a two-link pendulum that only activates at the second joint. The two links initially point downward, and the aim is to swing the end-effector at least one link over the base. The state space consists of the {{formula:422e3dc8-7d90-4c14-ba10-895237841800}} and {{formula:c7803d08-0089-4e3d-acf8-2ffa2d072b83}} of the two rotational joint angles along with the joint angular velocities. The action space is to deliver +1, 0, or -1 torque to the joint between the two pendulum links.
{{table:6e6a20a2-8049-42cb-a014-ceaf47fe28ff}} | r | 2a2e4a0d0924620b6375fc5c5c9e3e19 |
In this section, we present our tentative results on future LHC reach at {{formula:2b3ebd99-cb31-41b4-ae8b-df254f23c47f}} for the non-minimal UED scenarios with/without {{formula:00027483-ab55-4ad7-98d4-71f7efc966dc}} coupling enhancement.
We work with four benchmark points of the universal BLKTs for 5D quarks and leptons {{formula:b8dd3199-2f76-4f5b-8761-b456e8b76cae}} with {{formula:fc2647b8-0fc1-45d4-b840-e7e475a46921}} and {{formula:18905075-fb61-4658-a965-7c6fae2c5fd2}} .
Here, we assume two things: (i) the Weinberg angle between the two states are exactly zero, which would be realized after considering one-loop corrections {{cite:f9d9003e8cf3cc339812ec20407b4f72f403d929}}; (ii) there is a {{formula:b1ff3572-bb2c-4505-8ce1-13ab02f6a09b}} mass-split between the two massive gauge bosons {{formula:ab1d9fff-6c8c-49f2-9d74-0743769f2218}} and {{formula:3573c536-eb5a-4ca8-95bd-079bcf1cd44f}} like in the corresponding minimal UED case, consequently the masses of the two level-2 states are
{{formula:14b1c48b-7461-4ef6-8130-3b43e986a74d}}
| r | 61881439056ee55c38c132f30af840bf |
where the “singular value” {{formula:97ed83fe-80cc-4e1b-96e7-eb879037fbfa}} is a scalar, and “singular vectors” {{formula:92f1e535-32f5-49a2-9a3b-2a66cbaaf9df}} s are unit length vectors in {{formula:9a6e1fb6-f262-4bfc-8f96-0a2422c114dd}} , and {{formula:16a6d862-f50a-4805-8996-0fcbe7eefbde}} is a noise tensor whose entries are independent and identically distributed random variables with zero mean and unit variance. The goal is to estimate the singular vectors after observing {{formula:70a37e25-8e68-47c8-9e86-c78262a429d1}} in a high dimensional setting where {{formula:e55d3d10-5b23-49bf-91ee-fcf9cb527b29}} is large. In particular, the special case when the noise tensor {{formula:5c4d7fe6-e3cc-4dd8-97ff-b7653d101b6b}} consists of independent standard normal entries has attracted much attention in recent years, and an intriguing gap in statistical efficiencies with or without computational constraints is observed. It can be shown that tensor SVD that seeks the best rank-one approximation to {{formula:c36d0e74-6df5-48de-9f99-02150b328a74}} yields a consistent estimate of the singular vectors whenever {{formula:3f0a4c1f-e5a3-43ae-98bf-289919a86d56}} . Hereafter, we say an estimate {{formula:bea46581-1baf-4e9f-8218-9ad0943f2aa9}} of {{formula:9446bcb9-c219-4a5f-8e12-8049c3ce9474}} is consistent iff {{formula:37810fe7-60e9-4a03-a3b6-d5bbb5eded15}} as {{formula:d28cd3e4-fdbc-44f3-af7e-3968a0a6d5ea}} where {{formula:c761e791-2c20-4eb6-8cc1-9de0ece16182}} is the angle between two vectors {{formula:979d2bf0-cad6-470c-83ca-16455b75b58c}} and {{formula:ca860b13-2560-4717-ab0e-016dfcab1e59}} taking value in {{formula:67a8e22c-039b-4960-956d-c5d9dfef2c40}} . However, computing the best rank-one approximation is known to be NP hard in general {{cite:0a3298006e25362adbd863528011f7aa0f68255c}}, {{cite:3cdeb116c6e6431c97029086f128b1ca2e0dddc4}}. On the other hand, consistent yet computationally tractable estimates are only known when {{formula:2024ba0c-b915-48e0-8aec-9f5a57d4443c}} . Hereafter {{formula:42431de9-a065-4c91-b60f-be3b2be5763d}} means that there is a constant {{formula:41fd1963-5ee3-4f13-b2da-fd67be4b28e6}} independent of {{formula:73eb4d32-0da2-4a61-9938-1d7a669c2178}} such that {{formula:a78aebcc-a006-4b40-a33f-bbfc4b1f1d4a}} . More specifically, it can be achieved by power iteration initialized with higher order SVD {{cite:0291728dea3160e22d28d1e81cc9697908443338}}, {{cite:68b388850d7a27f95d4625893aa2b9fdff2c0d01}}. While a rigorous argument remains elusive, it is widely conjectured that {{formula:9f8a9098-3fc4-4e0b-b8b7-a51ab583a295}} is the tight algorithmic threshold below which no consistent estimates can be computed in polynomial time. It is instructive to consider the case when there are independent Gaussian errors, and the signal strength {{formula:c02af05e-dc2c-4cfc-b0b5-d7e0668b1f89}} . These results can then be summarized by the following diagram. When {{formula:da709552-9444-4283-a2a8-397bd4e5a475}} , the tensor SVD estimate {{formula:3d688bfb-1e8e-4a4d-9add-225acac9be99}} is consistent, and indeed can be shown to be minimax rate optimal. Meanwhile, we only know of polynomial time computable estimators that are consistent if {{formula:c7e74cb9-1435-461f-920c-124b5dca535d}} . The shaded region between {{formula:ea393254-45d4-4e7c-8195-5cc123fae71e}} and {{formula:7fd11d5e-7add-44d3-a9a6-adf2fdf6463e}} in Figure REF therefore signifies the tradeoff between statistical and computational efficiencies.
{{figure:62c31c6f-c62f-4760-8b21-56a4f28f6617}} | i | cee7af12dd56afb0de3e58ee89fb9c87 |
We comprehensively evaluate our model on widely used eight benchmark FGVC datasets: Aircraft {{cite:e3a4fad85c92e34ad1e4e0258e1f32a5b94f612d}}, Food-101 {{cite:8a9f1eee27484f2e784860d14419206b7791fc13}}, Stanford Cars {{cite:7b37a1150b0cf745ee298add0c8ad44dddae8456}}, Stanford Dogs {{cite:e755041e90ad76b7a19b70b2aa8ae1d4900a52ef}}, Caltech Birds (CUB-200) {{cite:9040389a3636f5ebc91ae1e9a9cedea0459d5e57}}, Oxford Flower {{cite:40abd36b4831d6b69638e2fd3dbdcb1ee01a280b}}, Oxford-IIIT Pets {{cite:d102f01ce210ca74aa2c5bcd8f0f1c462877003e}}, and NABirds {{cite:25a0b6ac33432e8705dad50f36b21a9c83bb57b6}}. We do not use any bounding box/part annotation. Thus, we do not compare with methods which rely on these. Statistics of datasets and their train/test splits are shown in Table REF . We use the top-1 accuracy (%) for evaluation.
| d | 096a18014278e707034fd507f9b153a7 |
For quantitative evaluation, we manually generated holes with random size and positions on normal slices of the testing subjects. Therefore, the ground truth is known. The inpainted images were expected to have sharp and realistic looking textures, be coherent with {{formula:0612501c-f759-47ba-ad90-d74379c2646e}} , and look similar to its corresponding ground truth. Our results are illustrated in Fig. REF . The proposed method generated visually satisfying results. Table REF lists numerical comparisons between the proposed approach, Patch-match {{cite:869702b0087cb4896d5d4faae1e2b7d2ad0e5b47}}, GLC {{cite:d5fd1058307d65aa1e9eae52c4066c86a52320f2}}, and Partial Conv {{cite:21bf660e4a07ff582946a8d8e8c598fe5759da31}}. We note that the compared inpainting baselines {{cite:d5fd1058307d65aa1e9eae52c4066c86a52320f2}}, {{cite:21bf660e4a07ff582946a8d8e8c598fe5759da31}} are based on the 1-step framework. We used four quality measurements to assess the performance: mean L1 error, structural similarity index (SSIM), peak signal-to-noise ratio (PSNR), and inception score {{cite:84a99e6b459bf5792e2805d31a433aeebcf634b9}}. We directly computed the mean L1 error and SSIM over the holes, while the incepetion score is measured on the completed {{formula:528aa48a-799c-4a67-8063-146bc3eee0dc}} .
| r | f4a43f7e199c3aa4db08ac41854ac7ff |
The cause of the high electron density values associated with the shock excitation region
in interacting galaxies is essential to understand how the flux gas works in them.
High-velocity gas motions can destroy molecular clouds and quench star
formation {{cite:921af0adea4cf97baa9dc3643bd8d27358555cfb}}. To investigate if the high electron density values found in our sample are
associated with the presence of excitation by gas shock,
we plotted in Fig. REF the {{formula:00887b99-609a-4834-80e2-b50c7aa4084b}} versus the logarithm of
the observed [O i]{{formula:2305515f-9f53-4ada-8c2e-0c8462637a00}} 6300/H{{formula:d7952427-30fd-4564-bb38-635a3208beb9}} emission line
ratio. Objects with distinct gas excitation source, in according to Fig. REF , are indicated by different symbols.
No correlation is obtained between the presence of shocks and electron densities. The highest electron density values found in our sample do not belong to objects with gas shock excitation. Therefore,
the high electron density values found in the H ii regions of our sample do not seem to be caused
by the presence of gas shock excitation. However, a deeper analysis such as investigating the presence of correlation between the velocity dispersion of some emission line and its intensity (e.g. {{cite:2722ad4d92d0d25ca0ea037cb907fa342aa416d1}}) or the implications of multiple kinematical components in the emission line profiles on the derived properties {{cite:488394be089a04b4a35a2213719530cb2ad6d880}}, {{cite:b49e89e73939dc0abcdab4537ab766b528c0fb2a}}, {{cite:97b0220a61dad2c1c6efb1c3840dd4a59b363adc}} is necessary to confirm our result.
Interestingly, the objects with the highest electron density values present the smallest
[O i]{{formula:0b0851ef-b3ee-4718-b493-53fafdd88942}} 6300/H{{formula:f947b81c-7729-4d23-9c32-c92942326b46}} line intensity ratios.
{{figure:4e7186fd-6d1a-4c5e-856f-5b7037578e96}} | d | fe9ad6ca9cc0a3ccaafb1f67c8fa131b |
Regression problems correspond to the setting where the outcome {{formula:432002d2-bf02-4de7-90ba-943ad252b0bc}} is real valued, the predicted value for {{formula:f98ed587-3914-49ef-96bc-8bfba4ffc545}} is {{formula:423215c3-0bf9-4554-bc5c-6f013d397564}} . The linear regression or least squares
problem corresponds to the loss function {{formula:4c5d2ef6-6974-4152-846a-28a61cbd622a}} , a least squares model thus minimizes the average squared
prediction error over the dataset. The {{formula:5c70c135-22f4-4bdd-b40d-a822c9ad04c4}} -regularized least squares or ridge regression problem
and the {{formula:16bf7e67-95a6-4485-b5d1-4ac8d2ad54d7}} -regularized least squares or Lasso regression use the regularization term {{formula:f8a6f786-7694-4559-9c81-13776bfae4e4}}
to be {{formula:5ac55332-b55d-47cd-90d6-0bd749b718eb}} and {{formula:b02c2c8f-26b8-4971-a78c-0fe4570494d8}} respectively and are of considerable importance
in machine learning, see for example {{cite:840874a0ba8826f3f2e013dba24db12d06259175}}.
| m | d02e6beac6c6cf8c5b36b4b492571006 |
In the present work we have investigated the innermost regions of the OJ 287 jet, where the VHE {{formula:cb2e2188-ad4f-453f-bbae-6cd5d4e49f94}} rays are thought to be produced, by means of high-resolution millimeter-VLBI observations with the GMVA. One of the main findings is that during the MJD 57158 (March 31, 2017) 86 GHz GMVA epoch we detected a new model-fit component (K), in the region between the quasi-stationary components S1 and S2, that dominates the source total intensity emission. This is the closest-in-time GMVA epoch to the VHE event detection, separated by about two months (58 days). During the same period, an enhanced overall activity is detected at different radio frequencies (shaded red area in Fig. REF ).
These two findings, a high radio emission state and the detection of a new model-fit component, could be related to the VHE event and the passage (ejection) of K through (from) the S1 quasi-stationary jet component. We note that S1, as investigated and suggested in several works {{cite:f6131ae85f7b2a37f2b95e7a93970e43044c3f34}}, {{cite:04663c4ea9ff7209154d16bbb449c571429ec0a3}}, {{cite:7fd13fbca81675ffed759bad8ac66f0009472d25}}, is considered a recollimation shock.
The passage of a new component through a recollimation shock associated with an enhanced activity at high energies is a quite common event that has been observed in several AGNs {{cite:af009672ebbcc6075a84c853e8dddbd3098df4b8}}, {{cite:06d91304a7348134b8472e6a03417e22276417a6}}, {{cite:2052c075d05bf9ec6767ae13860ed6e27afbc55f}}.
| d | cb74ac241c4fce898cf7291630b84e4d |
Note, an advantage of dynamic pruning methods is that the pruning is performed during the training itself, although we have seen in Table REF , better results are obtained when pruning is performed post-training. Current dynamic pruning methods like DPF {{cite:d58da47a67a1e9965cc2de216a9085e8517b568f}} prune via global magnitude, and a possible future work would be to use WoodTaylor instead.
| m | 64e683911abc40f8e28bca81bb91de33 |
For large enough {{formula:b9005775-ef15-4fe8-af4f-875759052f8f}} , the fact that rank- and tree-width are vertex-Lipschitz functions imply that these parameters are tightly concentrated about their mean, for example using the Azuma-Hoeffding inequality, see e.g., {{cite:f5bb598d092a07b40c92dd1e0460d6ea52c3e035}}.
However, for smaller {{formula:1415b27a-9064-4f53-b587-c1b2cda71ae1}} is it not clear if these parameters are concentrated in a range of values of size {{formula:437027a0-ddf2-4d2c-bcdb-b3b1c244d2c4}} . It would also be interesting to know, if the parameters are tightly concentrated, what the correct leading constant should be.
| d | 253a089b6681ed6f80f0fe02b347419c |
Let us consider the behavior of the current density in the asymptotic
regions of the coordinate {{formula:3c687bd4-8ca4-49ed-bd4e-a7e7ca6ed142}} . For points near the Rindler horizon one
has {{formula:2db186d5-7bfc-40d4-965b-cc5ba912b437}} . In this limit it is convenient to use the
representation (REF ). Directly putting {{formula:0bc15d64-a5ae-446b-bc67-cac44d102f04}} , the integral over {{formula:9b7828b3-ad59-4f6e-a50b-c53748718ce0}}
gives 1 and we can see that the leading term in the expansion over {{formula:518299ff-cd12-410c-9192-7551d52fc34a}} of
the last term in (REF ) coincides with the current density {{formula:ff8ac1c4-0d55-41e0-ac2a-799c6d00eab7}} . From here we conclude that the current density {{formula:17be7034-2b6e-4b4f-a07b-7fa796460c9c}} vanishes on the Rindler horizon. In the opposite
limit {{formula:1987fb45-4c18-4852-8717-3f46e81e4e8d}} it is more convenient to use the representation (REF ). By using the asymptotic expression for the modified Bessel function
for large arguments {{cite:7d26da68227b51f0c435fb6b27548c28c93452f4}}, we see that the dominant contribution to
the series over {{formula:1c43531c-c498-4327-b92d-985717311605}} comes from the term with the smallest value
of {{formula:9000bd76-f108-4d70-806a-b36e3a7ffaed}} that will be denoted here by {{formula:e65145f3-cd86-47c8-9472-afbf9b40679a}} .
Assuming that {{formula:26296cf5-1cca-4ff0-a398-84aa36bb14c6}} , one has
{{formula:ef8f2e8c-4d05-492f-98d1-35c4249c1b30}}
| r | cea6a19636d542af641e11197892a0ef |
One may be interested in combining the proposed method RoLT with other loss functions. In particular, we attempt to optimize LDAM loss {{cite:a211d747724bda880064551a22a55ad5827e835a}} during training and the results are reported in the supplementary material. Indeed, LDAM encourages the model to yield balanced classification boundaries. However, it slightly distort these boundaries when applied together with soft pseudo-labeling because too much focus has been put on tail classes. Our experimental finding suggests using the ERM predictions as pseudo-labels leading to more significant improvements.
| d | 4b9641b9517a8725e59256e573874b2e |
One major issue with the application of FL is the performance degradation that occurs with heterogeneous data. This refers to settings in which data is not independent and identically distributed (non-IID) across clients. The drop in performance is seen to be caused by a disagreement in local optima. That is, because different clients train its copy of the neural network according to its individual local data, the resulting average can stray from the true optimum. Unfortunately, it is realistic to expect non-IID data in many real-world applications {{cite:750af6a9a582f229c5d088671b8a1708bad4850a}}, {{cite:45a56dfe860e7988f7b53a6e3496b41d250f29fe}}. In light of this, many works have attempted to address this problem by regularizing the entire model during the training process {{cite:b1ab73d99416aec24d78da884d1cbda4ce53165c}}, {{cite:dce31cf323bd677828aab7a72ed623d18e101dec}}, {{cite:ca56e3513c8a7f203014a5af4dff44f349173761}}. However, we argue that these works are based on a limited understanding of neural networks.
| i | 6d05232aa21128f7bcb0928ebe39e77b |
Consider the same setup as in ssec:elbofeedback. Let {{formula:3f1b3cce-7870-4fb2-9816-f47ae625046f}} ({{formula:fc69731a-8dc9-4df5-8d3d-12ad774409af}} ) be feature maps (before any nonlinear activation function) of the last convolutional layer (forward direction) obtained by forward passing {{formula:1cf476af-257c-41e3-8f1d-b1e472db91d1}} . The last convolutional layer is used since it contains the highest abstraction level of features {{cite:50050044c3a1ad80d49e7ad2878d2513e3347a78}}, {{cite:3a986670c248edb8e5113e89cce69dce9e63be24}}, {{cite:f66650dd9aa4bec9609379eed9283b95ec9395e5}}.
| m | 25b2a47e961cb29e58a8c8e4e5e0b4fa |
Remark. If Finiteness of Central Configurations is true {{cite:3aff09cb5e0e2f79e9fc7610b35c54e41a90d0e9}}, {{cite:e59f42898fb885da7738fc6007fe8e3d1c1a5d11}}, {{cite:00d5e945ff72ed8c780586d83f0bbbf6be598350}}, the proposition is obvious. But we don't need this hypothesis here.
| i | d33a3469db8cfd8dd3dd1406c73fe575 |
Finally, it is interesting to remark the presence of an additional high-velocity ejection almost orthogonal to the main one.
While astonishing, this is not uncommon among PNe, with examples of collimated outflows almost orthogonal {{cite:ed10e8b42c1d43a1981db1da19b666f0d3c90d22}} or along very different directions {{cite:d600a4f7d5e136c546fd2177a032c85dc4a00ab6}}, with the record case of NGC 6210 with five different symmetry axes {{cite:7bf99e71be883c539ca1d196601a67dfed89bb19}}.
It has been noted that jets misaligned with the main nebular axis might be characteristic of PNe with a post-CE binary {{cite:b18b238fbb61c3fab844dbd1408adbd62c2b2418}}, {{cite:d9df0c4a2f3eb079566bdf67e05c1bfddd811bf7}}.
There is not an obvious interpretation for these phenomena {{cite:8197c86225fea42b0e5e547002d486f5aca5367a}}, but, if associated with a CE phase, it is clearly suggestive of dramatic changes in the preferential ejection direction of the stellar system.
| d | cf04c1863c44ee8b56fc7c844b029610 |
Consistency with the Existing Experimental Results. Our results stand with existing experimental observations. Specifically, {{cite:7652d99476039367efc43f36636fe23ddc9aa5ef}} conduct experiments using GD and GDM on the same linear separable data (c.f., Figure 1 in {{cite:7652d99476039367efc43f36636fe23ddc9aa5ef}}), and it is observed that the training behaviors of GD and GDM are quite similar in terms of the direction {{formula:63fd575f-dd87-4cef-9e74-bf31852c3937}} , the training loss, and the margin, which supports our Theorem REF . {{cite:7fedf2e440131cd29eeb340a976b95e99acfb1ef}} extend the experiment to the stochastic setting (c.f. Figure 2 in {{cite:7fedf2e440131cd29eeb340a976b95e99acfb1ef}}), and observe the same similarity between SGD and SGDM, which agrees with our Theorem REF . {{cite:80d664fd1a5bc2f2743d802725136620616c67db}} conduct the experiments of SGD, SGDM, Adam (without momentum) and Adam on MNIST using homogeneous neural networks (c.f. Appendix F.1.2 in {{cite:80d664fd1a5bc2f2743d802725136620616c67db}}), and observe such similarity for deep neural networks. Our theorems apply to linear models, which is a special case of homogeneous neural network, and meet their observation.
| d | 36345f66d51d7567ef8c8812411a840a |
By Theorem 12.2 in {{cite:11efc2e3581d2c68287741b2e7c5c178be454735}},
we have the inverse Legendre-Fenchel transform of (REF ):
{{formula:5312034c-7015-49b5-a4b5-e903e9dc82df}}
| m | ad8adcd2b2295cd52519362ce7dad48b |
Discussion: Reproducibility. While the neural recommendation models have dominated in the recommendation field and claimed substantial improvements over previous models, recent efforts raise questions about their reproducibility and published claims {{cite:9c2c6daff9a4b8937c18472149d795d197035000}}, {{cite:fada17ca6fd21c3b15284902603797bc7e4db2c3}}, {{cite:a56457f98f4e8e5c16bfadb8e3360ebeb9255c22}}, {{cite:02f5b273f96c72eda5726f842fb5000f26b21183}}, {{cite:c9855a1f6585a9c343a7401ca0b547ede74d385e}}.
This can be attributed to two aspects. First, neural recommendation models are based on neural networks, which are hard to tune in practice. Thus, we should carefully choose the initialization, tune hyperparameters, avoid model collapse, and so on. Besides, due to the various application scenarios of recommendation, different models vary in the selection of datasets and setting of experiments. Specifically, it is well known that recommender models are sensitive to the dataset size, the dataset sparsity, the data preprocessing and splitting techniques, the strategy of negative sampling, the choice of loss function and optimization manner, and the evaluation metrics of performance.
Thus, it is very challenging to conduct a fair performance comparison.
In order to advance the recommendation community, some researchers make efforts on the data level, such as industry-relevant recommendation benchmark {{cite:564d99a3f06e068ccd6ac366007dcf16d363d12c}}, MIcrosoft News Dataset (MIND) {{cite:1a4dfd651a116fae21a1afe00fa5fcd9a8271cff}}, and Yelp datasethttps://www.yelp.com/dataset.
Others concentrate on the unified evaluation framework {{cite:f5034ed6a2f8b70a3f86923233949d163801ffab}}, {{cite:cef40daf43112216eca7ff292bcf1cb455603282}}.
For example, researchers argue that previously default choice of evaluating recommender models with sampled metrics (e.g., rather than using the full set, only sampling a small set of negative items during testing) would be inconsistent to the true trend {{cite:5c620d0902efe2ca86ac3e11c4372b6e8e486f74}}.
Towards fair and reproducible comparisons, it is of crucial importance to make the experimental settings transparent (e.g., release the codes, datasets, and experimental settings, and set up a leaderboard if possible).
Furthermore, beyond network architecture engineering and hunting for the “best” performance, research studies on theoretical considerations and reproducibility analysis should be encouraged.
| d | fee6c8bfa2fff49dbf205dc659125671 |
Shape-Invariant Representation. To translate between objects of different shapes and texture, we use JOKR as a bottleneck. As manual keypoint annotation is not always available (see Section ), we use an unsupervised keypoint extractor {{formula:1fa4998f-a475-4502-a015-e2842376311b}} , similar to previous work {{cite:84dfa336cd94f7b5629e4ac6949435fc165546ca}}, {{cite:50aa55c28bb3427635714dc76eb527ce066857a5}}, {{cite:3fbaa592b6ce8dbdc66a8c97d8b591b8725e4843}}, to extract {{formula:bee303da-334b-47a7-ae3d-8cef82b01994}} keypoints, denoted {{formula:9f7c0be6-947d-4e9e-84f2-0554a60552ab}} . To leverage the convolutional network's ability to utilize spatial information, we project the extracted keypoints to spatial maps by fitting a Gaussian for each keypoint, obtaining {{formula:cd6ffea0-2cd4-4c4b-9800-436af8f01659}} confidence maps {{formula:cb4b345c-1688-4884-b1fb-9110dcb20a4b}}
(see Appendix for more details).
| m | d5a496c092f49acc4b2efa27195468f5 |
For future use, we record here that the proof of the lower bounds in (REF ) is based on a key lemma from {{cite:bd96e543053b278c7e9dc5c8047cbd412999aef0}} showing Lusin-Lipschitz regularity of the flow of a Sobolev velocity field, in the form of a quantitative bound:
| i | a597b4cf798651c686ddf6d87611fb52 |
Adversarial Attacks and Defenses. {{cite:f831d7b6cf1975f3edc42630fcf43fc9e507ad42}}, {{cite:cded5d79291f1ff1fdd09f7b776f2b687c09fc3f}} pointed out the vulnerability of DNNs to adversarial examples, and proposed an efficient attack, the FGSM, to generate such examples. Since then, as increasingly strong adversaries {{cite:63be09cc823bb384c6b5317742f390b6fbeb7b3c}} are proposed, AT {{cite:19cf9a764f2f37a7cf8e7d25dd7965ef6e5cc2f6}} is considered as the most effective defense remaining. More recently, {{cite:94c84b8ba162af4d9b490bacc3d6bed53300fbe7}} proposes TRADES, extending AT and showing better robustness than {{cite:19cf9a764f2f37a7cf8e7d25dd7965ef6e5cc2f6}}. We refer readers to {{cite:301a19d8444e7f9c8459b9de843e449cb6357c18}}, {{cite:2014d591255e1b589ae90c4ce4e9210e2023bbba}} for more comprehensive surveys on adversarial attacks and defenses.
| d | cdf6cc42ed83ed77e4e0951116933fd7 |
We evaluate the impact of changing the required rates at the users ({{formula:5e633bf0-c779-4103-b150-17b6e095e9ba}} ), the number of users, and the location of both the relay and the RIS on the required total power of the system. In all figures, we compare the proposed system and the baselines discussed in Sec. REF . We assume that the channels between BS-relay, BS-RIS, and relay-RIS are all modelled as a Rician fading channel model, where the LoS is available. Whereas, the channels between any point to the any user is assumed to be Rayleigh fading channel, where the LoS is not available. The channel attenuation coefficient between any two points is given by {{formula:24cce223-ede3-4365-91bf-09c226e723f6}} , where {{formula:c1c297ab-4b36-419c-8889-b06e7d357a56}} , {{formula:89b316c7-1f33-4ab7-bf29-8ee181940e8b}} if the LoS is available, and {{formula:5bd8238b-c53d-4d71-abfe-dc874e470e60}} , {{formula:5084d9ab-3755-4f65-870d-9afce4d99dff}} if the LoS is not available, where {{formula:0032cb2d-a79a-48a4-8366-29e10d364e64}} dBi and {{formula:e4ab2cc8-e946-427e-83cc-dfd7f674db4a}} dBi are the antenna gains in dBi at the transmitter and the receiver {{cite:31c6be6eb58388dc62fa740c325ecf068afb6933}}.
{{figure:58d7c9b6-71e4-4449-b9d8-77cd748024d9}} | r | c47914180c68c80ecafee2c0c9e7603e |
Of course, many situations involve both types of neurons. Nevertheless, there are some situations only involving a single type. For example, theta-wave neuronal oscillations in the hippocampus are thought to play a considerable role in memory formation and spatial navigation {{cite:fbe7f8b0b62ed8126381a49e6dc685b66bb7447f}}, {{cite:033c4d7ee3b3f974f4a16ed32ed8aeb82c21f303}}. The currents driving these oscillations are believed to be primarily generated by recurrent excitatory-excitatory connections within the CA3 region of the hippocampus, whereby these neurons robustly synchronize using a “relaxation” mechanism akin to our model's predictions {{cite:fbe7f8b0b62ed8126381a49e6dc685b66bb7447f}}, {{cite:e23bbdf06eb9605d818fa203984d096ca1067fad}}. The present model suggests how these neurons can so easily toggle between and store the large number of complex oscillatory patterns required for their proper function {{cite:e23bbdf06eb9605d818fa203984d096ca1067fad}}, {{cite:8328caa37b4d18d86362f38ce563a54a8fa9c57f}}, {{cite:982171b303f124e3d75498dfdd8501e8dc2612c4}}.
| d | 8a06891c4103dcf04d83583bb1a23eb2 |
In order to measure the performance of proposed method on different PSNR targets, we plugged our method on the pre-trained model in {{cite:bf1a0307957a419e834ff37288c070dec902a105}} for the factorized entropy and the best neural compressing model cheng2020-anchor {{cite:7a02cfdbe6b406b91f72ab4b8a9d6fcbd9173c8b}} provided in {{cite:788f5e4164c1f8906e1d8e42fe58ad950aa5e94e}} for the hyperprior entropy.The performances are measured with Kodak and Clic-2021 Challenge's Professional test set. According to results in Fig REF , the amortization gap of factorized entropy varies from 8.5% to 9.5% in Kodak dataset where the proposed method gains from 5.3% to 6.8% in file size. In Click-2021 dataset, the gap (9.5%-12.5%) and our gain (8%-11.5%) are even bigger. Fig. REF reports the results of the hyperprior entropy, our method saves more than 1% of original file size in lower bit-rate and save around 0.5% in highest bit-rate. The simplest approach that parameterizes the new probability by the difference between center bin's probability in Eq.REF gives competitive result even better in higher psnr with zero-mean Gaussian parameterization.
| r | 789a6b87ca77b91a0cc879e55a89cc94 |
Lemma 3.3 ({{cite:3d0c242bce05a378659d6724470143f58ae0673e}})
There exist constants {{formula:aceff6ca-e7eb-41da-9cac-de3c05976a78}} such that for all {{formula:a4200df2-5e9b-43a5-be63-918711ec75d6}} we have the following vector inequalities for {{formula:9c121b31-03e0-438e-bb34-83eef1d60957}}
{{formula:48ca31f2-12fa-462b-8271-f4620e07b053}}
| r | c4e97558473275d9daa464981010faac |
In this experiment we performed target area segmentation with Fast-SCNN, a Fully Convolution Network and our model. Input images were down-sampled four times to 320 by 240 for efficiency. All training was performed on a single NVIDIA RTX 1060 and the inference time analyses were done on the same GPU. The experiment was implemented using the Pytorch 1.7.1 {{cite:54073d4df9e385e38fd57632149bc1614e8087a3}}.
| r | acd5aed1f20e4dfa9e35fc983cf01e80 |
Another key result emerging from our study is a very clear picture of the differences between the stellar
populations of the nuclei and the galactic main
bodies of the dEs. To our knowledge, no spectroscopic study has yet performed
such a comparison with a similar sample size.
Studies based on color differences ({{cite:9dfabb1cb08ab220586f87e2654d68cafc1f649d}}, {{cite:945b75927f60c924d6c22a4055e480da8c356564}}, and
particularly {{cite:15c2c277645376c5809601c82c989dde10d29efb}}) find slightly bluer nuclei. It is, however,
not straightforward to interpret these color differences in the
sense of stellar population properties, as we know that a
degeneracy in the age and metallicity exists with color (see also Appendix ). In
contrast to the explanation of {{cite:15c2c277645376c5809601c82c989dde10d29efb}} of having more metal rich
populations in the surrounding galactic main bodies, we find a metal poorer and older
population in the galactic part on average. In addition to this, as
{{cite:945b75927f60c924d6c22a4055e480da8c356564}} note, there exists a color-luminosity relation
for the nuclei. We also find that the metallicity of dE nuclei correlates
with the total luminosity of dEs.
| d | 0f11889cebf5e4cc95a903248ef5feb9 |
In Equations 1 and 2 in the main paper, we define bias as the absolute difference between the verification TPRs of two groups at a given FPR. However, it possible that a sensitive attribute consists of more than two categories. For instance, the skintone attribute consists of three categories: Light, medium, dark. In the main paper, we chose to define bias as the difference between the verification TPRs of light-light and dark-dark pairs at a given FPR. However, as shown in {{cite:8da54c5ef9aaafe5d28b4b0f9877ee4f844273b5}}, we can also define bias as the standard deviation (STD) among the verification TPRs of light-light pairs, medium-medium pairs and dark-dark pairs. In Table REF , we report these STD values for our PASS-s and MultiPASS systems (and the corresponding baselines) trained on Crystalface descriptors, along with the average of the TPRs obtained for the three skintone categories. We find that our proposed PASS-s/MultiPASS systems obtain considerably lower STD than existing baselines, thus mitigating skintone bias. We also provide the skintone-wise verification plots for all three skintones (light, medium and dark) on IJB-C dataset in Figure REF
{{figure:41e212e9-8621-4218-8ba1-8d4176b735fb}} | r | 9782fd2d10979817b61f13d6b68dfa5f |
The presentation of the ensemble
Kalman filter as a smart optimization tool
is also developed in {{cite:847cf9a1b03f11b523de2967fd35d7c461d4ac63}}, but the derivation of
the update equations in a space whose dimension is that of
the ensemble is not described there.
The analysis of ensemble methods
is difficult and theory is only just starting to emerge.
In the linear case the method converges in the large ensemble
limit to the Kalman filter {{cite:3a84a9d41e8879975465338011bec18b8e32b0a4}},
but in the nonlinear case the
limit does not reproduce the filtering distribution
{{cite:4990af44b5f664f7e7b5242161a16dae59c826bf}}.
In any case the primary advantage of ensemble methods is that
they can provide good state estimation when the number of
particles is not large; this subject
is discussed in {{cite:814b2759b02dca2267e6825fc9d208226c852e65}}, {{cite:9889096f92b5ad9b8b12ef4e392de0d9ab34a3bf}}, {{cite:5eaa3654be8ba8a6b4eed85e94e2850fa7e7ebb7}}, {{cite:02d238be27ab3a83aff1d4bfab3b1bce3f693362}}.
| d | f27e23c9ce9fa34e4446019773c10f2d |
Recently, considerable research has been devoted to Multi-Task Learning (MTL), a problem of improving the
generalization performance of multiple tasks by utilizing the shared
information among them. MTL has been widely-used in various
applications, such as natural language processing {{cite:8bc7332bb6e0055bc3d57abec2298843287c93ba}},
handwritten character recognition {{cite:955c39fedd7254b4461718f9bf383103a584f37a}}, {{cite:eee0031e12b8ab6285a507876f6cc8ddea67994b}}, scene recognition {{cite:487ee3882ca9d05650849593b02df3408afcaea6}} and
medical diagnosis {{cite:fe906a38f18bd5c74b9d6fb679a509665808aee8}}. Many MTL methods have been proposed in the literature {{cite:d5bef5c58921fe9aecba84556fbb1dcb0560782c}}, {{cite:0d43f290939a48529b130834fa61d852fc1c6ed3}}, {{cite:322e403808c4b50c5efc4ca7d01d8aafbf32edb8}}, {{cite:6d58230c1c73fe0342da074009491fe8f247053a}}, {{cite:008f0408eb40489553c1a8aeb587f2d0e0262397}}, {{cite:830dec98f94331f3176cf72e1646421dccff4604}}, {{cite:7f50aa7bf64878687b3a867764f54f2062df7dde}}, {{cite:955c39fedd7254b4461718f9bf383103a584f37a}}, {{cite:fa1e6ef0d220ecdf38385ec3202f266c6a47d9d9}}, {{cite:8bc7332bb6e0055bc3d57abec2298843287c93ba}}, {{cite:8bb05272df1d16e159735412b035560f0e93224a}}, {{cite:6faab8ad51c5455d74dd1bb0101beeed8b3c90c0}}, {{cite:59d035a2f72c755586cacab5a4bd379d8bbff28f}}, {{cite:487ee3882ca9d05650849593b02df3408afcaea6}}, {{cite:f48b3c12ab1345aff52cf5413c6d781328b8f0bc}}, {{cite:d7b4639f876a9419d6e7600fd348ebf035d03e35}}, {{cite:42a59caaac0761b9b5b0e2908df290d0823b6028}}, {{cite:822271b9983c05615f4a8cd8e6c16594fc55a06e}}, {{cite:d89b52f1e651a459fd59039b5f86b9ff9c5b1f20}}.
| i | 4d897fa3db665aaf12aabc0ab7e9b864 |
This theorem, which is established in {{cite:c9e7bd1ac942107c65da0104a1ccd570fed7109b}}, may be generalized to the case in which {{formula:d41fd286-a1ce-4e62-b125-bf0007702746}} has a boundary of nonpositive mean curvature, where the mean curvature is computed with respect to the normal pointing towards the asymptotic end in question. These surfaces, as below, are referred to as `trapped' and are connected with gravitational collapse {{cite:150844839603f6e8f249610bc0f0a131d9e4e8e6}}. When such surfaces are present, and the scalar curvature is nonnegative, the proof of (REF ) produces a strict inequality {{formula:878f50f9-0c9b-4bb7-b5f3-838c23c973c3}} . We mention also that an expression for the mass, related to Theorem REF , was obtained by Miao in {{cite:81118f7540362daddd53263b35900888f690025b}}. Furthermore, a version of this result for manifolds with corners is given by Hirsch, Miao, and Tsang {{cite:0a5966c7c0c3277f452250b3a5b93baebbbf4dd0}}.
| r | 20fb1b7a582f290f5875ea2bdf4928e5 |
The numerical results in Figure REF ,REF and REF tantalizingly remind one of the Farey seriesThe definition of Farey series of order {{formula:ed9c262f-38d3-406e-9e27-2099d75648bd}} , denoted by {{formula:ecb9c292-e111-471f-ba27-f62fa3d43300}} , is the set of reduced fractions in the closed interval {{formula:70e50f83-45ed-4781-9fa7-2b04e06dd6a8}} with denominators {{formula:c885f994-6d0a-47b5-a5bc-8187ae719406}} , listed in
increasing order of magnitude. For instance, {{formula:092d423a-3602-4e2b-9714-24bc7bb54c0d}} , {{formula:5bfadfad-c76b-4165-bb9b-4398e7cb0e20}} , {{formula:138f065c-b8bd-4a43-a48c-5ec1a7ded805}} and so on. (See {{cite:656ffc1759c112513da5e62cf1c421ecb2f9093e}} for details). One of the important properties of Farey series is that each fraction in {{formula:0c0e5c2d-0b5f-4098-a396-ee9eb9b8a484}} which is not in {{formula:a9d902b5-70ff-4c1a-aac6-0e232dd2c340}} is the mediant of a pair of consecutive fractions in {{formula:14521dea-81ce-4995-9d5b-e0cfa7c4fa55}} . For example, {{formula:f16f6713-f275-4726-8281-f6fc9b65f572}} in {{formula:6384f98f-ca09-415b-b903-3f7f482b3260}} is made by {{formula:59d00369-3b6d-479c-9404-4f300dca6961}} and {{formula:948599f6-08b2-428a-afeb-653d2d29c4ed}} in {{formula:5121a5a7-2134-4df2-8e28-900627b5fc0d}} , that is, {{formula:71a61f2d-26a1-43c2-a4cd-101a94754eeb}} . The operation {{formula:cee4725f-53a8-4480-937c-56c6a8f59d74}} is called the Farey sum..
In dynamical systems, periodic structures based on the Farey series sometimes appear, for instance in circle map models of cardiac arrhythmias {{cite:8e7030f2fdb69ef6a4bcc2e7b90ff242c822b1b9}}, {{cite:b953c65fdb86f9a2c44727ddedcaf42417e8da3b}}, {{cite:bfc73a3ed2572efcff73831bc0b741394844c862}}.
The fraction {{formula:707269b4-0819-47b7-8b71-5720bf75ae64}} corresponds to a rotation number of the system, that is, every periodic orbit has period {{formula:4d0eee70-c313-40c3-92b5-8a4ba45fa392}} . Nakamura {{cite:15e0ee4a2c3bc5647685d7ce698c3a9a8d62e349}} proved that the Markov operator corresponding to the perturbed piecewise linear map (REF ) exhibits asymptotically periodicity, and clarified the relationship of the periods associated with the Farey series for various parameters.
| d | 526514beb5586f009dfe37a851769587 |
Notation. By using {{formula:52e3bfcc-9650-493a-87a7-65546a707d28}} and {{formula:7ffad9b8-e2ab-499f-b25c-43ce8b1d31db}} , we will denote positive integers such that {{formula:cfac1941-af26-45f9-a76d-492e6fb6f505}} is the power of a prime number. For integers {{formula:34e3159f-1b14-4fb3-88e8-c000645cb58e}} and {{formula:da61ad60-807e-42f9-8848-5facd9615380}} , with {{formula:d6512f6b-94f0-4767-a66b-81852acf9759}} , {{formula:65ecc749-0387-4e7f-b08f-5dde6548b4e6}} will denote the multiplicative order of {{formula:7b8c7b76-04e4-4bc1-b768-0ee764ff2c21}} modulo {{formula:77c948e4-e39e-45c4-b77d-a300200b2bef}} . “{{formula:93f1edc2-8dd9-4435-b2bc-7e7b2c25c5e2}} " will denote the trace mapping from {{formula:9d308fc1-6d62-486c-95a0-a405e4a1e282}} to {{formula:a4741a85-0255-44fc-acf3-0a93e8a79443}} . By using {{formula:ff00a33e-802d-49c4-93fb-2a1b4e613a2f}} , we will denote a fixed primitive element of {{formula:d7467721-6d23-4886-83d2-c2755690c301}} , and for any integer {{formula:3694924d-aea6-493f-8898-924a33f9eb38}} , the polynomial {{formula:8666320b-c59b-479e-8c13-2ce9eac31148}} will denote the minimal polynomial of {{formula:b0616416-2484-44b0-8037-52f5e49c5b8e}} (see, for example, {{cite:df5088b06711ac8e37d56cb53de2cd2232d55b88}}). In addition, {{formula:25c9b1a2-5c4f-472c-932e-c2b1e777351a}} will denote the irreducible cyclic code of length {{formula:3e28271e-6e77-4eed-9ff4-4d20155774c1}} , whose parity-check polynomial is {{formula:8a8b10f4-a84b-4143-b697-411df77ef3e0}} . Note that {{formula:c2c42f0f-fac9-4cdd-9863-a106d31e5fea}} is an {{formula:c778d3f9-d0d5-401d-938e-293b87316135}} linear code, where its dimension {{formula:62821bf3-9625-4c44-9714-7235539028a4}} is a divisor of {{formula:1f508052-2f59-4e66-99d0-1f423899c3ec}} . Note also that {{formula:e4b6310b-e028-459d-a165-8aeb54854f2d}} is not several repetitions of an irreducible cyclic code of smaller block length.
| r | 810ecf410e6b81ccbcbf504917ffa91c |
In Fig. REF we show the evolutionary path of the
star and its wind, that we use in the simulations. The stellar mass
(panel a, in {{formula:45131fce-dea8-4036-ac27-fe535a3c5ae2}} ), the mass-loss rate (panel b, in
{{formula:a1e1eedc-8b68-4251-a3af-d42890b672d2}} ), and the terminal wind velocity
(panel c, in {{formula:2ac8b7b7-ecea-40ce-b545-0559a9423422}} ) are displayed beginning at the age {{formula:3c0d86e4-d55f-4785-be36-cbd38db685ea}} .
The wind properties of this zero-age-main-sequence, non-rotating
35-{{formula:f849cdea-858c-4fdf-8d69-4fbf03207d3e}} star at Galactic metallicity has been interpolated from
the Geneva library of stellar models calculated with the genec
code {{cite:c7a0647ee9472a1cbd1f26f16af10f6e2872bc69}} by means of the online interface
syclisthttps://www.unige.ch/sciences/astro/evolution/en/database/syclist/.
The terminal speed, {{formula:ac61e83e-5bba-4173-a82b-f995f4e72efc}} , is modified for high effective temperatures and massive stars using
the approximation of {{cite:c16e0cd45536fe5ac819b72faf07a683cb70bada}},
{{formula:3f8b0140-e255-4dc7-8c96-0f9a6d0b163b}}
| m | 79640eba1f41a7a62db7e6553b3b583c |
The proposed method is based on the following three insights: First, to tackle the large variation of drones and background scenes, data augmentation which maintains the video information in a short clip creates challenging scenarios; Second, due to real time applications and tiny object sizes, a fast and multi-scale, multi-level features extractor should be used for accurate detections; Third, temporal (video) information should be exploited while attending the important regions in the videos. To accomplish these goals, our framework consists of three components: (1) Temporally consistent preprocessing, (2) Spatial feature extractor module
(3) Spatio-temporal SwinTransformer {{cite:da4bce3ebeb32a0f6247ff7b2369ff605661ab83}} module. A schematic diagram of our framework is shown in Fig. REF .
| m | 3660351f4ab297ac14c21f85369422c1 |
The formulation of the coupled Burgers equation is taken from the work of {{cite:97d3d97363cae3f2aeb045e58ed3786169bd6a01}}. The training data used was obtained from a FEM Fenics solver. Each simulation progresses for 100-time steps, with 3600 simulations used as data. The length sequence {{formula:7a7cfc78-ef7d-496a-a6f6-9f7cd3dec7e5}} used for training is ten, i.e., we predict ten sequences of output with ten inputs. The back-propagation interval {{formula:abd84963-5f79-4dd8-b4d9-61c956ef987b}} described in section REF is kept as 5. i.e., after predicting 50-time steps in training and accumulating loss, the neural network will back-propagate to update weights by calculating gradients. The optimizer used is Adam's, with an initial learning rate of {{formula:0ff55097-6495-406f-935b-4dc7fa6498d4}} . The learning rate decreases by half if the valid loss does not decrease for two consecutive epochs and the training is done for 100 epochs. The validation is done with 200 simulations. {{formula:970c99cc-8c85-4704-b298-c67402a1dd61}} parameters were used in the network with configuration shown in table REF . Figure REF showcase's the accuracy of the test prediction done. The model was able to accurately predict the flow features and shock discontinuities across the domain for the whole period of 100-time steps.
{{table:6eb95d85-87c9-43c3-bd5c-c6579893d631}}{{figure:7a1b4667-73ce-419f-a93c-1868e428c614}} | m | 49d9bae9695ec532bc88634729b1e1e4 |
where {{formula:ee9166a4-cf4e-450b-aa32-d87bf3f86c20}} is the risk factor, {{formula:4ead50f9-f43b-4e69-8e7d-3403f2dde6eb}} are the genetic variants, {{formula:ad946f17-cad2-41cd-89ed-90706bf82767}} is the outcome, {{formula:7211fc9a-7c62-47ec-83a5-6d8ba5460b59}} is an unmeasured confounder, {{formula:15a4e9dc-d26d-4f96-80d3-e23a0cc065e0}} is the do-operator of Pearl meaning that the value of the risk factor is set to {{formula:75056a95-be52-4722-bff4-59679d6a1884}} by intervention {{cite:d7a33c9134f6cb62d9504625f040efa812117f0f}}, and the causal effect parameter {{formula:4e895da8-2623-4e11-99bb-17b63f1259de}} for all {{formula:6ff384b2-25a8-4f1d-9ba6-4d172e62da77}} . We also assume that the effects of the genetic variants on the risk factor are the same in all individuals. Although these assumptions are not necessary to identify a causal parameter (weaker assumptions have been proposed {{cite:c0cf9ec98b2b17c82d1c029a303bc82610e51379}}), alternative assumptions mean that the causal parameters identified by different instrumental variables are likely to be different. While these assumptions are restrictive, a causal estimate has an interpretation as a test statistic for the null hypothesis that the risk factor is not causal for the outcome without requiring the assumptions of linearity and homogeneity of the genetic effects on the risk factor {{cite:3477ff8f3f36ca3c6d6db409dabda3938d606d98}}.
| m | 0996c9c454ea11fc1d578ed4f17dfcd1 |
fig:summary shows summary statistics for the {{formula:15a8240f-8d3a-4f3b-a7d5-edc4263f230d}} instance of the (REF ) game for three different exploration profiles. The panels in the leftmost column show the equilibria (top) and utilities (bottom) of the 7 agents in 100 runs when {{formula:e311c707-fea8-4216-83f9-2e4e7f398c66}} for all {{formula:15bad682-b67d-4100-8c0d-793c0df68c6d}} (no exploration). In this case, the dynamics converge in all runs to the pure action for the odd agents and to some arbitrary (and different every time) mixed action for the even agents. This behavior of the learning dynamics is in line with previous results in adversarial learning when equilibria lie on one face (relative boundary) of the high-dimensional simplex (cf. {{cite:706f3cddc1c4da0dd12c546e8e2505035d9223f6}}).
| r | 7e53e53dd6cecdde3ecb931c72eecde9 |
In Fig. REF , we give comparison results under one roof for a blurred image corresponding to steering rate of 60 deg/sec. It is amply evident that the results of our method (shown in b and c) yield best performance consistently across Wiener filter, RL as well as {{cite:63753dc2c2a0d86ebe94a7195291258125ebb052}}. From the figure, it can be seen that the deblurred quality of non-blind methods using the estimated kernels from our approach is better than using the blur kernel returned from the blind deblurring method of {{cite:172c2900ebcf863c9d7423cec96b6518c121eff6}}. Estimation of kernel using {{cite:172c2900ebcf863c9d7423cec96b6518c121eff6}} is not only computationally expensive but also does not offer any advantage in getting good deblurring quality. Our PSF estimation methods are less computationally expensive and deliver good results. Visually, motion deblurring quality is better by using Krishnan et al. {{cite:63753dc2c2a0d86ebe94a7195291258125ebb052}} and Wiener filter.
| r | 2fa53f3bd4b1e9b60febc078550f077c |
First, in order to solve Problem REF ,
we seek a fixed point of map {{formula:18a66a34-4f28-4bc4-a506-f8b13d75d5cf}} .
We use the Schauder fixed point
theorem (cf. Gilbarg-Trudinger {{cite:cf47af3d98eda5b8b353818cbaa922b5aac088fb}})
in the following setting:
| m | 629ef567a2b3ff225cf28b496d065445 |
The conceptual foundation of our model is the basic fact that human diseases are rarely the consequence of a single defective gene, but the result of complex interactions within the cellular-molecular network {{cite:227f7fb4edfd6eeeca88279bf8a9a22d3f6a545d}}. The disease phenotype is hence a result of different and mutually dependent interactions.
| d | e47a16ac97f0ed9ddb02aae7f86e66f4 |
In this subsection, we discuss how to approximate {{formula:44cc8b41-3c82-4fc2-b09c-6af022576276}} based on Hutchinson's estimation {{cite:8a8119336363c4b2c0ad239430ab25721d1d5cc3}}, {{cite:898c3827ca900d023a10f622f42f0e12dbbcf29d}}, a technique from randomized numerical linear algebra. Assume that {{formula:ab6aa85f-266f-4cb4-b8a0-84af7f00d28d}} is a random vector with i.i.d. random coordinates with mean 0 and variance 1. Such random vectors serve as a random basis; that is,
{{formula:c6aef5f6-daed-49f8-9333-56b8e3d60bd0}}
| m | 09df4c72ac70b1af5aa0bb853039e501 |
Another doubly-robust method originally intended for generalizing experimental data is an augmented estimator which combines a treatment, sampling, and outcome model, similar to the clever covariates found in TMLE {{cite:15959be061cff107cea8afddfc3c5507c6722c60}}. We present the augmented approach with slight alterations to the estimator presented by {{cite:15959be061cff107cea8afddfc3c5507c6722c60}} so as to be relevant for the transportability setting. The setup to the problem solved by {{cite:15959be061cff107cea8afddfc3c5507c6722c60}} assumes that each unit in the target sample is prescribed a vector of known sampling weights. This in turn facilitates inference on the combined population containing samples {{formula:c416d0f7-04a9-4e16-82d6-0d3f004ad220}} and {{formula:f72e4904-271e-4b79-a60e-6452d682d2c1}} (i.e. the target population). Our setup to the problem, on the other hand, assumes that the target sample, i.e. sample {{formula:04d52dff-2887-4b13-b82c-5cc923055c37}} , is drawn uniformly from a target population. The distinction can be drawn from the implication that the target population may differ from the superpopulation. The problem they describe is more akin to generalizability {{cite:a697784e00de0b3bd0c085c3452f43c9bab5f5dd}} over a finite population whereas our focus is on transportability within a superpopulation framework.
| m | b987b2bcbebae35f457e006973a8f29a |
Tidal deformations of self-gravitating compact objects stand as key gravitational-wave observables to test General Relativity (GR) in the strong field regime. In a coalescing binary system, the deformability properties of the compact objects affect the gravitational wave signal at sub-leading post-Newtonian order through finite size effects in the pre-merger phase. These deformability properties are encoded in the so-called tidal Love numbers (TLNs) which reflect the rigidity of the system. Their measurements through gravitational wave astronomy provide rich informations, in particular to constrain the equation of state of neutron stars and the properties of compact objects beyond GR {{cite:dc2b0fbc0dbd8bc50b3f465468ef14e9bfdd2c64}}, {{cite:9a0f6c4764bfcd356e1d1704e6d3b763ed3149aa}}.
| i | f05bb50d5447a79f9db2b7c7004249dd |
The difficulty in simulating and training snn originates from multiple
factors.
First, time is an indispensable component of the functional form
of a snn, as even individual stimuli and their associated
outputs are spatiotemporal spike patterns, rather than simple spatial
activation vectors. This fundamental difference necessitates the use of different cost functions
from the ones commonly encountered in deep learning.
Second, most spiking neuron models are inherently non-differentiable at
spike time and the derivative of their output with respect to synaptic weights is zero at all
other times.
Third, the intrinsic self-memory of most spiking neurons introduced by the
spike reset is difficult to treat analytically.
Finally, credit assignment in hidden layers is problematic for two reasons:
(i) it is technically challenging because
efficient auto-differentiation tools are not available for most event-based
spiking neural network frameworks, and (ii) the method of weight updates implemented by
the standard backprop is thought to be biologically implausible
{{cite:7449ebe6307e4aa190dbf1c6afa79a0f19f8c652}}, {{cite:b4157747fc3794d2933e28dc4206b2ee5e4d47ac}}.
| i | 4f35f11e43f403183b61269f8951b7ca |
During the past two decades, an impressive experimental and theoretical effort has been invested in generating and exploring a new form of matter called Quark-Gluon Plasma (QGP) {{cite:358aa639d927241e24a0d7a1b9903068c2306c06}}, {{cite:a9910470a76ca706dabe501231f67f4a6fe2f0c6}}, {{cite:3b152ba7da5f6a80ab03f3693c4b05f056313a32}}, {{cite:cdd2b7adae6f955094a9b1fd0727358f1dffd89c}}. This form of matter consists of interacting and no longer confined quarks, antiquarks, and gluons {{cite:5be8ed58000e48245f9dd360398a40e81e7530fa}}, {{cite:04cec96b27a2404dd6de7f1f2db23b646713dd7e}} and is created at extremely high energy densities achieved in ultra-relativistic heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider
(LHC) experiments. An unprecedented amount of data for different collision systems (large and small), collision energies, types of particles, momentum regions, centralities, etc., are generated in these experiments, and one of the major current goals is to optimally use these data to investigate the properties of this exciting form of matter.
| i | f7df6ed3e0da6ff2d82f3678b1443d7e |
It remains to be seen whether a more sparse version of IQP sampling can be devised while retaining its classical hardness. Standard tensor network contraction techniques would allow any output probability of the above circuits on a square lattice to be classically computed in time {{formula:02ba0f7e-2d2b-4d98-a6b8-757c06b40d04}} , so achieving a similar hardness result for {{formula:77be44c8-d30e-4a0a-8e9e-3a9c884c61b5}} would violate the counting exponential time hypothesis {{cite:c24be1467d17d014b60c4749734b0bf2a65fe9f3}}, {{cite:ed9e444c0dbb30e785e222b115cafe4c665da4d7}}. The challenge remains to remove a factor of {{formula:9319651a-9868-4cba-ac6c-cc383515a702}} from the depth while maintaining the anticoncentration requirements of {{cite:0e110b1dae09b244dc53b89dd2f7c53c2d0d340e}}, {{cite:300bd8d36e4117d07754aef78df99ccb7b03913c}}.
| r | 624bb4629c9d88b454d5e732c70b50c8 |
The {{formula:e9648d35-6447-4fce-997d-f64db17995ce}} mesons with charm quark and the {{formula:8c373943-4663-421b-9d2e-5400fc91ab53}} mesons with bottom quark are typical heavy-light mesons, which is structurally analogous to a the
hydrogen-like atoms( the singly light antiquark and the heavy quark resemble the extranuclear electron and the proton, respectively). In recent decades, more and more singly heavy (SH) mesons states {{formula:c18c2167-b783-4daa-b1df-60479b93042a}} {{formula:34098c6a-5425-45df-8b13-2ed2be31bef8}} have been discovered by BaBar, Belleale, CLEO, and the LHCb experiment {{cite:42c920b6b1524e73d8ea2dd0baf39cfd1286ed27}}, so the study of heavy-light mesons system has been attracting great attention. It can be seen from PDG {{cite:1b774ef45f5e2fe6108a52ff48c48ef3b202b316}} that the experimental values of some low energy {{formula:09a38fa3-cbd9-4781-8ebc-01b439972aa7}} , {{formula:efd08b64-9fc3-4e44-a7a9-0d45695a71c5}} mesons {{cite:b5dbcb46f948e4eaf74797b428d7ca08c46b9ea5}} have been basically determined. Since the experimental observation of the singly charm mesons states {{formula:ba91b376-eb9d-486b-aae0-a78119471be8}} , {{formula:de66ce81-230a-423f-84f2-b2456e18de0c}} , {{formula:152e5506-e5e2-41fb-aadf-b2f708e62684}} and {{formula:fd615642-10ba-443c-b08c-325377e7326f}} , there have been different research methods {{cite:acfc895363bde208e4dea4c305b0a689660d40c6}}, {{cite:429378f6a972d868280b78dc36b5e231362d797c}}, {{cite:4a5c2f5adcc0afaf7d4bf714e8efd19a766aec7f}}, {{cite:d3ed559ce5fb4c2413d448ae2b4fdaf3fe5dcf57}}, {{cite:1a3f46338c347d47594223aee932cf37fad7b5a4}}, {{cite:f8e2ffee2141d3d8dfa15c637bca8b3f87ded7a9}}, {{cite:87d745c24a1ceca22c04c88fc193080d1a131f93}} for the calculation and analysis of these charm mesons states. For example, {{formula:5ced2ac5-da44-47c6-bf3f-7590d0867360}} model {{cite:25dd50ca32735b3903523a36f096eef8d40d3f94}}, {{cite:401454f7f0850f6f17da4aaae89be8006d11e67c}}, {{cite:209b62da9b3a6b35623be33ff0f2d06696c7cd14}}, Chiral quark model {{cite:50afc2f469540eea0094963c89d5950a51d37183}}, lattice QCD model {{cite:acfc895363bde208e4dea4c305b0a689660d40c6}}, {{cite:429378f6a972d868280b78dc36b5e231362d797c}}, {{cite:7f77d677230d1a81c83003acbbb617a753b3b2bd}}, other models {{cite:a6a9312f6eb81c02d8abdbef847828bec2c5c99b}}, {{cite:3a5725cec06acf646e53d976f9dfa82c99cb5e45}}, {{cite:7b0c60402ab5f187ccd8b9b23ff7c8850361a7c5}}, {{cite:c4018227e19ff7b4519335c3ed96bfe0c23044c8}}, {{cite:3a5725cec06acf646e53d976f9dfa82c99cb5e45}}, etc. In addition, the high energy {{formula:e7c04dcf-8795-47bd-9dfc-134d869bcc37}} , {{formula:d2644bc3-acdd-4654-8b1e-0b474a7be525}} mesons {{cite:dc7d0b0832b65bcff728080e3f57cbce41de10a1}}, {{cite:adabd63adccba7463473f2a92b1af80f4f938dfd}}, {{cite:26f57f928d9fb2d41b2a0ba85ceb7e7cce7e8dbd}}, {{cite:878fb5e2f8ced94869fd5ba1df18906c1286d2a6}}, {{cite:135194dcc0d62a1a5057251db18927d698b34e04}} have been extensively studied, there are different interpretations for the bottom meson states, such as {{formula:6d48773c-2fa7-40b1-8757-5da01534a088}} , {{formula:8e6c42e8-5bcf-410f-984d-1832320864ed}} {{cite:c977227aa3d68b33c6db75ebbd51f2b67e367663}}, {{cite:ede8339b0f523a5d240bc0eccb763a05ccf89912}}, {{cite:4b939288a4372f5b32963d90f3d22ce47330c005}}, {{cite:f2070ab9661297851d38373a5b6559a495cedfc4}}, {{cite:b1d867bab7022b4f7d0fa3bdde1f2c81291bb0f7}}, {{cite:ee84726805689c215f48b27ac0eda1dd1ba0d836}}. So far, these quantum states are still controversial and need to be further confirmed by experiments.
| i | 1fdb61021f7e29936625746d936efab2 |
The stability analysis of rotating equilibria shows similar
behavior to straight periodic sheets {{cite:40580da58db377c40e222bd5b6f6eb67adb0d1cb}} and circular
sheets {{cite:cd8240de8dedaf26399eda9ca5cbd37c051de6a1}}. More specifically, there is a
countably infinite family of unstable modes with growth rates
increasing with the wavenumber {{formula:6a3433e6-c8c2-4666-a554-a6566891dcb9}} , as shown in (). Away
from the endpoints and in the limit of large wavenumbers the
corresponding unstable eigenmodes resemble the unstable eigenmodes of
a straight periodic sheet which have the form {{formula:ce71e593-d023-4b13-93ad-163659ae1b02}} ,
{{formula:dd70f047-e3a9-4190-8bd5-f534f38da071}} . More precisely, near the centre of the sheet the
unstable eigenmodes have the form of slanted sine and cosine waves.
The reason for this analogy can be understood by examining the
structure of the eigenvalue problem () and the
hypersingular integral operator (REF ). We see that when the
eigenvalues {{formula:6933eb31-d4eb-4336-9b46-a2880a9bfb9c}} have large magnitude, the terms due to the
background rotation in () are dominated by the other
terms. Moreover, when the integral operator {{formula:8bedb06b-4340-42f6-bcf7-b5912d37bcbe}} acts on
high-wavenumber perturbations {{formula:57ac04bc-2b1a-4136-bda4-8934a7bde30c}} , the circulation
density {{formula:0b422e7b-b9a7-4b5b-b6b3-6daf11fe02c1}} in (REF ) can be locally
approximated by a constant for {{formula:da87b14f-6e2f-406d-bde5-e04cd915774a}} away from the endpoints. Thus, in
this limit, the structure of the eigenvalue problem ()
becomes similar to the structure of the eigenvalue problem
characterizing the stability of straight periodic vortex sheets
{{cite:40580da58db377c40e222bd5b6f6eb67adb0d1cb}}. Therefore, we can conclude that rotating finite
sheets are subject to the same Kelvin–Helmholtz instability as
straight sheets, which becomes more severe at higher wavenumbers and
rendering this problem similarly ill-posed.
| d | 7d3c7fd29aa4dc89b667e3b1ae98c689 |
The variance structures considered throughout this article by no means exclusively encompass all the possibilities, merely a few which exhibit well-studied conjugacy. Other structures, such as AR(1) with stationarity, and compound symmetry as required by the assumptions of repeated-measures ANOVA, do not (knowingly) associate with conjugate priors. Instead, priors for these structures must be manufactured; see, e.g., {{cite:c3148a477b012edf9341497484f45f4d8953b0c9}} for the compound symmetric case and {{cite:92339cd92db37f16eaf1f5943d27182e15cc1933}} for the AR(1) case. As such the prior and posterior normalizing constants may not possess a convenient closed form, but the intense development of Monte Carlo methods and the general increase in computational power available for practical use mitigates this issue as discussed by {{cite:6214f281800c5e18a3e626edf3d75add6b8d344a}}. Even so, one can show that the space of compound symmetric matrices forms a linear subspace of that of positive definite matrices; hence, one might expect the methods in Section REF to lead to a closed-form conjugate prior for that submodel. We also hope that researchers implement the evidence-flexibility paradigm elsewhere. For instance, we suspect the proffered link between Bayesian and frequentist model selection may lead to further justification and thus wider adoption of model selection criteria related to the evidence for missing data problems, such as the integrated classification likelihood {{cite:3d3dada42810d131cb1181baf7cf3ac47a057883}} or adjusted weight of evidence {{cite:cb4308040d79a08108005b26813fbed2527449bd}} used to select the number of components in a Gaussian mixture model. We plan to explore these particular examples in future articles.
| d | 9557b3bd0918a73e68ed57ce4265d993 |
NSEdit has achieved a new state-of-the-art performance on the code repair task of the CodeXGLUE benchmark {{cite:e48a4c0e5416a4b58b623059543ea810fbdb5d47}}, {{cite:0377e1424eb02001eba4fe0a3959aaabe45c5d5e}}. For code repair, it is more effective to predict editing sequences than fixed code.
| d | f8843557f7e8366f950fc8945a4833aa |
The presented method relies on computing the displacements of dots of a pattern via a cross-correlation method. In the present study, the configuration of the interrogation windows of size decreasing down to {{formula:13497212-00c2-4e71-b53d-515e2ac8ff7e}} pixel{{formula:bede029d-561f-4941-9cf4-8cef3cb6d6b3}} with {{formula:38fd30ce-88b1-4b62-a65e-799cd0a2e06f}} overlap (a suggested setting in Lavision Davis), and a sub-pixel Gaussian interpolation was used {{cite:584eee707f132ea30976e05d6f536be916036be5}}. The uncertainty is expected to be around {{formula:3e486c37-411b-449f-86d4-547fb51343a2}} pixel and smaller, because the random dot pattern was generated to satisfy an optimal PIV condition {{cite:1719698995a567d63dc9f003f7d07e3b32084367}}. In our problem, the uncertainty on each component of displacements of an instantaneous sample is up to about {{formula:19c656bd-d7fd-49e9-9394-f7712a7d158a}} pixel (from Lavision Davis{{formula:d403f167-84b3-4aee-8663-d4d5b041e57c}} , see {{cite:2315afb5475356f1a5b41d91bda4ea243079a5cd}}).
| m | 83b566bb47e8bf16f2e594f2d498ac06 |
The sample stars are selected from the APOGEE DR16 dataset {{cite:149c13fdefec6d8aa798ccc87db884248ad5e25c}} with parallaxes and proper motions taken from Gaia DR2 {{cite:3397e8f05af2f628301fb2bb22dedba8d6689d9f}}. We have removed stars with ASCAPFLAG or STARFLAG warnings and stars with {{formula:d993197a-f9b2-43c0-a082-b4ebe29c7cef}} values of {{formula:0e5a63a0-aeae-44f9-b654-b55421c87d1a}} , {{formula:943b8a71-40a6-4507-99ce-2c7cb0528132}} , [Fe/H] and [Mg/Fe]. We chose to use the Bailer-Jones distance GAIA_R_EST {{cite:c638af1e5c450c58a1a4a413bd3e187fec7f60cf}} and removed stars with {{formula:56e6a79c-ed6a-47ab-b710-bf6c96a6125c}} . After these cuts, there are 165 332 stars left. Then, we calculated three dimensional velocity components in galactocentric cylindrical coordinate with radial velocities from APOGEE DR16. Python package astropy has been used to transform observed quantities in ICRS coordinate into galactocentric cylindrical coordinate. The Sun is placed at height {{formula:33ba1886-69c9-44ec-a8f8-8f55966c904f}} kpc, galactic radius {{formula:a9083962-f0fc-4f06-a5f5-35ad33f41efc}} kpc with circular speed {{formula:ec9c4332-71d5-4bd6-b14d-2301ae47fa9d}} km s{{formula:5d46049c-8086-45d3-b6f6-7bf1661c37f4}} {{cite:41b0113ccbb7fda55fc41606d82a6f8d2cbcd81d}}. The peculiar velocity of the Sun relative to the local standard of rest is taken as {{formula:01d5f268-0bb2-4354-86d4-71981b48ddd4}} (11.1, 12.24, 7.25) km s{{formula:ff69e095-2a03-4c1f-9ed4-f3bb229610c6}} from {{cite:9d19475b58e6dba5e2f39009e22f6495dd19eb58}}. Since we want to analyse main components of the halo in the field, we removed those stars with PROGRAMNAMEs in the APOGEE DR16 catalogue associated with globular clusters, bulge, young stellar object, RR Lyrae stars, exoplanets, the Magellanic cloud or open clusters. Moreover, stars with PROGRAMNAME related to stellar streams and apparently clumped as a small group in the velocity coordinate have been removed. After those observationally clumped stars removed, there are 77 549 stars left. Stars with [Fe/H] {{formula:8a270794-392c-4669-be2f-231e466f5c02}} dex mainly belong to disk {{cite:392dfbab283daa114c183513a9fd1a6992d71406}}, {{cite:e7c3f5b2150bcd64fbc069ec9cbbff795ae7db50}}, {{cite:b146bc21f893a42ae3b2a50852dbee43cfd4a92e}}, {{cite:4191ea4d542ad031f341fa6e364c8e9f81933cbb}},
and we think it is not suitable for our method to decompose halo from those stars. There are still some stars with [Fe/H] {{formula:bf22ad9f-3ce1-4102-8e4c-2874e632cce6}} dex belong to the disk, but it is acceptable and we will keep in mind in later analysis. Finally, with metallicity cut, there are 3067 stars left in our sample. GalPot {{cite:8b5393ec7211b8c28097cb5c51daaa3aec3c23fe}} has been used to calculate orbital parameters such as energy E, angular momentum L, maximum height Z of orbit Zmax, guiding radius {{formula:fc610d3d-f004-43e7-b74f-ac38d4ad2816}} and eccentricity ecc. Eccentricities are computed as {{formula:a72cbef0-7820-47e4-b269-e967667f8bb5}} in which {{formula:31b9417a-188b-4460-810d-008255f478ce}} and {{formula:0b8c82d9-9d00-4c49-894a-a6c465bd6566}} are respectively the orbital apocenter and pericenter. The Galaxy potential chosen to calculate these values is the default potential called "PJM17_best.Tpot" supplied by GalPot.
| m | c9f73727b06c29f16c6fb7386d68072f |
In this section we introduce the basic definitions and some identities that we use throughout this paper. The definitions of terms we do not define, but appear in this paper can be found in {{cite:630ada057fe710998a2a8f9349c9db98b2416b6b}} or {{cite:8a55235c7fa0a2baa21959afa49c272188793732}}. For a positive integer {{formula:8be9dd42-a5a6-4368-a9b8-45cc89d2af7f}} , if {{formula:dc7d39de-3ec6-4c3b-8a39-c170c5050ff2}} is a Dirichlet character modulo {{formula:a21fa87f-68ac-45f8-80ac-07d0940f4fb6}} , then {{formula:16e298e6-a895-42d9-addb-543472bb6b85}} for some natural number {{formula:3650b534-ef55-4548-a807-a57064b7ce2d}} . The parity of {{formula:a61b2fac-5920-4643-8ac1-05415af55cff}} is the parity of this {{formula:ed633ce1-b5fb-40f7-b32d-167db4831279}} . Hence {{formula:beb2cae8-8ac3-42a5-aece-cce79ce99cad}} is odd if {{formula:6e4a8a8e-493e-4901-ba30-7b2d19b975ab}} is odd and even otherwise.
| r | b754d9e9b63803f5a29f9890cc229084 |
For our empirical analysis, 10 sets of randomly sampled initial parameters for each of the six model types, blackbox, constr. blackbox , {{formula:74253312-2616-4aed-8274-8d52aa4aa37d}} , {{formula:b907afe7-329e-4c90-add8-949e105947c3}} , {{formula:17f52631-ee27-473e-96fd-4469bea024bb}} , and graybox, were fit to the training dataset using the ADAM-W {{cite:42442dab8a304d50f498c240d45ba0f5de212081}} variant of stochastic gradient descent.
After training these 10 models instances per model type, they were evaluated on a held out test set. The test set was developed by randomly initializing five initial conditions from {{formula:6fbf39f1-cb2d-48cc-87e0-a189a423bd88}} each for five randomly generated input trajectories, which yields a total of 25 trajectories. The input trajectories were developed in the same manner as the training set with {{formula:0512dc6b-9fd6-466f-b686-f3f8772502d1}} . We note that the test set is the same for all model types.
| r | cb448be0fec9ac91b00e4dbb734a92ee |
Since {{formula:5f8a0a2b-0888-46bf-a05f-2e508f43aea9}} and {{formula:92464a71-bd1d-4974-83fa-7124fb3db38c}}
are strongly semismooth by Appendix A and the composition of
strongly semismooth mappings is strongly semismooth by {{cite:6cf307c9062cd79f824297c53a74a5b232c2cbc5}},
the mapping {{formula:f874cb5f-d9b0-41f0-aee4-1297a2831163}} is strongly semismooth. Inspired by this,
we use the semismooth Newton method to seek a root to system
(REF ), which by {{cite:509985f236535007a51a66a1e9c2d7d3964f0af9}} is expected to have
a superlinear even quadratic convergence rate.
By Proposition 2.3.3 and Theorem 2.6.6 of {{cite:2a1a57e650dbcfc2abaebbb426afa8546765e9b5}},
the Clarke Jacobian {{formula:7ba75820-af9f-4513-8252-791b87bf3836}} of {{formula:58a47f47-f2ef-4dcb-827a-35ce00b9e049}} at {{formula:a6b3ba44-5dcf-407d-836b-c212928b7bd4}} is included in
{{formula:ebad53f2-9a68-4dad-b169-bcf091046917}}
| m | 76a4fc983adb0e12b12278d579d598d4 |
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