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In this work, we propose to solve the challenge by adopting differential modulation at the devices and designing non-coherent multi-device data detection at the AP. Such design can bypass channel estimation. The implementation of the transmitters is very simple, where each device is assigned a spreading sequence and transmits information with differential modulation. The receiver needs to first identify active users without the assistance of any training signals, and then performs multi-device data detection for the active users. We assume that the channels remain constant over two consecutive symbol intervals. The active user detection and multi-device data detection are performed symbol by symbol, so that the devices are allowed to access and leave the channel freely without packet level synchronization and channel estimation, which are the key to achieve high flexibility and high efficiency. To this end, the design of efficient active user detector and multi-device data detector is crucial. We use the factor graph and message passing techniques to address the problem. With the sparsity of active users, the active device detection is formulated as common support estimation of sparse signals, and we develop a message passing based sparse Bayesian learning (SBL) algorithm to solve it, where belief propagation (BP) {{cite:c69f9b18de391110cadc471232423a59e701f5b3}} and mean field (MF) {{cite:bb3d090ccd24cd2ebe5ce195699a0d3c0367dfc9}}, {{cite:abdfdd607e26af0640d374148a9443c1732047cb}} are combined to implement the SBL. After active users are identified, non-coherent data detection needs to be performed. For this, we investigate the problem of non-coherent multi-device detection problem and design a BP-MF message passing based data detector, which treats the differential modulation as a constraint and encodes it into a probabilistic form as a local function in the factor graph representation. We show that exploiting the constraint can improve the detection performance remarkably, compared to the conventional detection scheme. Simulation results are provided to demonstrate the effectiveness of the proposed scheme and superior performance of the developed algorithms.
| i | 02edf65bd41e07efb48e4ed554b8c431 |
SIMPLEX uses the simplex method of Nelder and Mead {{cite:018d16796a21811783be961d38ff90ea71711d1b}}.
MINIMIZE minimises the user-defined function by calling MIGRAD, but reverts to SIMPLEX in case that MIGRAD fails to converge.
MIGRAD, undoubtedly the workhorse of the MINUIT software package, is a variable-metric method, based on the Davidon-Fletcher-Powell algorithm. The method checks for the positive-definiteness of the Hessian matrix.
MINOS performs a detailed error analysis, separately for each parameter, taking into account the non-linearities in the problem, as well as the correlations among the model parameters.
| m | d411d7a790044ea1a0d8e0c3403ee8da |
To apply the visualization tools described above to sparse functional data, we required an appropriate data fitting and depth for data ordering. On the basis of MFPCA ({{cite:4619bd3067f18076a1b382bba3c1f584f2e63cdf}} {{cite:4619bd3067f18076a1b382bba3c1f584f2e63cdf}}), we improved the fitting of data through the iterated expectation from bootstrap ({{cite:eb694b7d89148104e55419be64651fe4be320195}} {{cite:eb694b7d89148104e55419be64651fe4be320195}}). We took the multivariate functional halfspace depth (MFHD, {{cite:a31f669e8ddbe34ee44eff3e980f16c3360d1100}} {{cite:a31f669e8ddbe34ee44eff3e980f16c3360d1100}}) as a building block for proposing various revised depths for sparse multivariate functional data. We obtained the best depth via the Spearman rank coefficient simulated in various data settings and sparseness scenarios. In the univariate functional setting, MFPCA became UFPCA ({{cite:4d54e43faf7576c8cf5bdd0070dc05278403b9e3}} {{cite:4d54e43faf7576c8cf5bdd0070dc05278403b9e3}}), and we used the modified band depth (MBD, {{cite:b3c173a3675aa4e79fb4435e89010f8e834dc401}} {{cite:b3c173a3675aa4e79fb4435e89010f8e834dc401}}) to order the data before applying the functional tools.
| d | 6a2b4491fb3c36d526128be2e9e11238 |
The final critical exponents ({{formula:fe734ed6-e96b-4ce3-ad3c-4e87335723ae}} , {{formula:c814d47c-5483-4f2c-8a77-77ee0294dbc8}} , {{formula:9d045912-484d-475d-b6b2-6f0cea2461bf}} ) are in agreement with those recently reported by E. Clements {{formula:e61af911-5c08-4b86-84a9-4dc02c938365}} {{formula:fe508e7e-0cc7-447c-b071-7bd7f9f572b7}} {{cite:94e7adf03bfbc78cf018b4d2e19e92f6b1fda71d}} which confirm the reliability of these obtained exponents.
Both sets of exponents from these two works are very close to the theoretical prediction of 3D-Heisenberg model ({{formula:6eeea4cf-ca12-4fcf-8f2d-fca40023fc0d}} , {{formula:9485bc24-e0e1-45dc-adbb-365c3a37f627}} , {{formula:75bd4cb4-b637-4530-858e-5b72f5658e99}} ), which suggest a short-rang magnetic coupling of Cr-Cr {{cite:532a4c64c5b93f03f74a6ddab3457894f917eb80}}, {{cite:94e7adf03bfbc78cf018b4d2e19e92f6b1fda71d}}.
Although the structure of Cr{{formula:11d57ed2-a1e4-4b13-8d76-ce19b70edcbb}} NbS{{formula:12db0a8f-b911-46ac-9c99-8e39c78eb4ac}} is two-dimensional, its magnetic coupling is of a three-dimensional type.
This indicates that the magnetic interactions of Cr-Cr are coupled not only within the {{formula:bcd3f766-a787-4d52-bcba-45e53c77598e}} -plane but also between the inter-layers along the {{formula:ec4dcec4-f568-4f26-9592-f18ac5af3a34}} -axis.
As we know, the DM interaction plays an important role in the magnetic structure of Cr{{formula:a8560f6a-6d3b-4e72-bcf3-4aaa8e2a9229}} NbS{{formula:e943eb7e-32ac-4b18-b4ba-bcfc5d3a2ada}} , which makes the spins exhibit spiral ordering.
However, the DM interaction has rarely effect on the critical exponents due to two aspects.
The DM interaction is much weaker than the ferromagnetic exchange, which is only {{formula:93953bd4-b75c-49be-bf1b-11f33047370b}} orders of magnitude of the ferromagnetic exchange {{cite:e63dec9883cc8c20cb82211b27b9b7b87db509d3}}.
Thus, the critical exponents are mainly determined by the magnetic exchange interaction.
In fact, in the systems with DM interaction such as FeGe, MnSi, Cu{{formula:5191471f-d0f0-4187-aa6f-5ae208eee944}} OSeO{{formula:311d9096-8458-46a7-9896-b8048df194c2}} , Fe{{formula:4e1eac8d-c74c-4edf-9223-2da4d6c4fc00}} Co{{formula:99770667-ef6e-4687-a869-b7b06e384cde}} Si, their critical exponents are either rarely influenced by the DM interaction {{cite:e63dec9883cc8c20cb82211b27b9b7b87db509d3}}, {{cite:f4b7bdc999b0218bcd87e6d0d265f1073ffaf6d2}}, {{cite:ebefef184f443763caad6229a916330b1ba18baa}}, {{cite:ad7cd27075338dad735931af9e20e84bdd2d430a}}.
| r | be5b132252502cd9f9037e9ffec19d01 |
The Spitzer data show the presence of dust throughout the 2006-2009 period, even though the {{formula:9fc0dd79-8db8-41a9-aaa6-30d7066be64f}} m excess disappeared in 2007, only to reappear by mid-2008 {{cite:28edcc7a7a64674fd0f8881d0bf1e9602b893b20}}. This could be due to variations in {{formula:16cf62e6-1c7e-4aca-af68-a7008a6198c1}} and the amplitude of the Wein side of the dust SED. However, the dust continuum is not significantly lower in the 2007 Spitzer data. This suggests that the stellar continuum is higher at this time, dominating the dust emission below {{formula:e5681bb3-aa0d-4681-80fd-fe3070c8b911}} m. The infrared photometry shows that there are times when the {{formula:646aae1b-9609-4007-bf24-2363ecc0e8fe}} colour is stellar (about {{formula:553ccd12-2e59-480e-8bbd-1f65ca44d39b}} for an early M giant; {{cite:e0512332ef21c690b57b78a49db523348016fa43}}) as well as times when it shows the dust excess {{cite:854f540ccb7f21ad62d19f2cd58212f684c1cfb7}}.
| d | 870527ac8f86906ff7099740fca63ca3 |
HMM-crowd. This is an extension of HMMs {{cite:41202de09dda5400c586398c9587f83bd0884ce7}} and LSTMs {{cite:0d3e62cdc9b7e726a28dc582e64c97986907e5af}}
in which crowd component is introduced by including additional parameters for workers reliability.
| m | 8e7f5e90843c562532afd7d8420f2ba8 |
Assumption 1
The function {{formula:579c11aa-3a42-48ab-9704-50a09fd09544}} is {{formula:a861f037-d877-4758-8ffd-fe727795e673}} -strongly convex, i.e., {{formula:d05e8673-af46-4696-afce-514c2ff38cde}} , {{formula:2cb7d880-cdfb-4b49-8d26-2bd1c629c40d}} , and {{formula:58f06abf-26be-4be6-81aa-abedd7cfa76c}} , we have {{cite:b55d47efbcf3905c9bad9e3c25a9430807470374}}
{{formula:1ca23189-1fc3-45d9-9973-e99472f4e303}}
| m | 3a66815a597f96afe0e9053a6a633f7f |
where GRU is a gating mechanism function in recurrent neural networks, introduced by Kyunghyun Cho et al. {{cite:e23fec3b11d73c8da2210845d0868bafd76af523}}. Another related approach would be similar improvements based on the LSTM architecture {{cite:16e97ca895baaeb7a536492219bc127e8c4916d4}}.
| m | 6bc209a63bc5053b0f36791de67958ff |
where {{formula:1692e9d2-f504-4db7-bde3-7a6411ae4a77}} is the training example, {{formula:1e468440-612e-4ac2-accd-92adc78e16d0}} is stochastic augmentation function reevaluated for each term in the summation, {{formula:eb2e542a-e998-4546-b6b1-df086e579ad1}} is a temporal moving average of model weights used to generate pseudo-label targets, and inputs are pre-processed with standard random horizontal flip and crop. In practice, this consists of initializing a copy of the initial model and maintaining an exponential moving average as training progresses. Some methods directly average multiple label predictions together at each optimization step to form a single pseudo-label target {{cite:e1aa4a09729a9fcc671cc256b44ed76a90a2d898}}, {{cite:22da4a87622da32c5e168f4d5f9d898418da447b}} but we find pseudo-label target distributions generated by {{formula:59f067fe-3314-4ec4-bf14-4fa567d78055}} to be better suited for the learning with noise problem due to the intrinsic ensemble nature of the weight averaging process over many optimization steps {{cite:d922885fa7879ea739a879d79e21050e2e8bfc0e}}. In semi-supervised learning techniques, it is common to leverage a large batch-size of unlabeled data for consistency regularization. However, we found that modulating {{formula:773199f3-2a08-48b6-ab69-87e343c8caa5}} , rather than the batch size of the consistency term, yields a monotonic increase in model performance consistent with related works {{cite:efcd07b061e2ff1193322c42d4a73958da3165dd}}. Moreover, in semi-supervised learning, different batches are used for supervised and unsupervised loss terms but we find (see Section REF ) that for the case of learning with noise, batches synchronized with task loss term yields superior performance.
| m | 190e6450f87ee3fa7828229c9a6701b0 |
It is easy to see that for pure states, the LN reduces to {{formula:b1ddda87-5fe1-4716-9de9-23b5d5b40e45}} Rényi entropy{{cite:ada0de5945e80f1efa4975dbc088bff7e2bbf098}}. It is worth mentioning again that LN is expected to capture only quantum correlations and has been studied previously in several works{{cite:7f4cad399c80c04fbc57724691c59cd292a31e25}}, {{cite:998125cbbe9d43db4ceeff5aef2d2a2b7f8f648b}}, {{cite:f76d3bfe6c4d5ad5659f8c3a480ed2b3847de574}}, {{cite:c364e1abea42118d4699394e2623190d502cdaea}}, {{cite:663e50d602af6de8c136ac37fb0b89dce666c419}}, {{cite:8dda67b136bc74d562eb94c5e57f1f4a8defac87}}, {{cite:db02a420b03b908324df01adf94e193a09316a49}}, {{cite:5ee988b1af69bf6cb004e259f204838956c2d8e4}}, {{cite:0f9589664a8231220f4f61059cab0356c102e7c4}}, {{cite:92722838c41409ac5fd615e173bc9e97797c0cd6}}, {{cite:5188c6141c3a125591e5e6d993e617d9f9d38723}}, {{cite:93e75a8972c0ece1c222f2344d80dc016520de93}}, {{cite:afe8e684718c1661b8cdccfc30233da355bb24ea}}.
Interestingly, it is argued that in the limit of long times and
large subsystems with a fix ratio, the LN equals half of the Rényi mutual information
{{formula:177d1a8c-6fa9-4493-a5e9-79b2b19a7d2a}}
| i | 5bdc2edbee7cac21381177bcfd414e29 |
which leads to a {{formula:2c0f5c64-e739-42f6-b0bd-4d32c182abd6}} difference between the Planck result and the result arising from local observation. Since the Planck analysis is based on the {{formula:93294f4f-85fc-4222-af62-ed7a4fb173d4}} CDM model, the discrepancy
between the high {{formula:df10e936-8e2d-4fba-8d6d-6fa089144d5f}} and the low {{formula:c8c4b8bd-a613-4edb-a763-1ceacbc4e2de}} results
represents an indication of physics beyond the standard {{formula:9c0ed893-9ea0-49cb-9a0b-7c8baa65efc6}} CDM model.
There is a large number of theory models which attempt to explain this difference (for a review see ref. {{cite:a90120a24bae99fcc8da2c824b0817ae41e654bf}}).
One of the simplest avenues is the possibility of having extra relativistic degrees of freedom present during recombination,
which would cause an increase in {{formula:9126d50c-2bea-4408-a777-5437cca0c55f}} and bring it closer to its measured local value. Extensions of the SM with new particles in thermal equilibrium with the neutrinos, such as a majoron {{cite:5576dd3c587b75ddec79d98950fec6744d017c1e}}, {{cite:2a59f45dcc3dde2d93a03b7391200631037df188}}, or with an extra {{formula:ae5a5647-c2f2-4b28-81f2-fd74a20d8a13}} symmetry and {{formula:20d0cc2a-a339-43a9-bc9c-e9239a882f12}} bosons decaying to neutrinos or otherwise {{cite:561324578d83195684303a10d9e59a996a010cd5}}, {{cite:765700beae3684c7351dc5830c48f787aed6efa9}} can explain the tension. We note here that models that can successfully explain the
Hubble tension are those where the extra degrees of freedom would affect only the dynamics in the CMB era, but not impact BBN. This is so because the precise predictions of light element synthesis during BBN can be translated into strong constraints on the effective degrees of freedom such that
{{formula:1d17a485-2c6b-40c6-89f1-496bdce7e788}} at 68% C.L. {{cite:8b9bd01e5aa2d0e5d52a221c036661647898e440}}, {{cite:db045ead5e6bd51d8e88e1bee1fbafc0f73721d4}}. This appears to be consistent with the SM prediction of {{formula:d684a7a3-0b85-43e6-8e6f-3ef63707dae9}} {{cite:778180335037fd350e2389e49463691e0f93d7ee}}.
Since the effective degrees of freedom are tied to the energy density in the universe, which affects the Hubble parameter, any deviation from {{formula:32f91ec4-ea01-424c-8855-97e5f08c042d}} at BBN would have an impact on the expansion rate of the universe as well as on predictions of light element synthesis during this epoch. Thus any model looking to add extra relativistic degrees freedom at CMB time to resolve Hubble tension should not violate the BBN constraints on {{formula:2c5186e8-bea9-4a15-ab70-840f7d097f7b}} .
| i | e08a11b2801e45b258620c957b14e3a5 |
vd Bergh-Hagen 176: Originally reported as an open cluster
in {{cite:7aa94e53db98fe5eb90dc5e6fab0bed4402ee2b8}}, this is a very interesting object that has been
profusely studied over the past almost five decades. Much of the interest
comes from the fact that it is still not settled whether this is a metal-rich
globular cluster, an old open cluster, or a transition-type cluster in between
these two objects.
According to {{cite:f89acd43bfc54653062fc354636a3eb8d2c6257f}} this is an object in the border line
between globular and galactic clusters, located at a distance of 13.4 kpc
and as old as NGC 6791 (i.e., in the range 4-8 Gyr).
{{cite:88905dc9d3b65482d4d7cb6a17a05b395bc337e8}} claim that this is a either a massive old cluster or a
young globular cluster, in both cases metal-rich with [Fe/H]{{formula:19c20188-e530-4528-84ed-36dc362e3887}} .
The distance and age given in this work are 18{{formula:4ecb5c56-6648-42d9-a22d-61a421cece1c}} 1 kpc and 7.0{{formula:84e290bf-c1a9-4455-a587-6952bb8772aa}} 1.5 Gyr,
respectively.
{{cite:563024fa82343e4b27b27e26aebc5d19aa164134}} analyzed this cluster in relation to the Galactic
anticenter stellar structure (GASS), and obtained a distance of 15.8{{formula:5cbe2d41-c4a0-48a9-bf57-39ac74c8bfa6}} 0.5
kpc, an age of 6.3{{formula:0a108be0-e977-4f58-b61c-cffeb87c97c1}} 1 Gyr, and suggested a solar metal abundance in
coincidence with Phelps & Schick.
{{cite:bcd01d32108ffa4b7ca7d205e971f8b7709ecd78}} used 2MASS and FORS2 VLT photometry and labeled this an
old metal-rich open or transition-type cluster. The estimated distance is
15.1{{formula:8d931269-01a8-4449-bbfd-d595b469ac29}} 0.5 kpc with an age in the range 6-7 Gyr, and a metal content of
[Fe/H]{{formula:5f3a7711-ef79-46d7-9fcc-1c538ff024f9}} .
In {{cite:1d4b4f4395ac0446eeecd22d88a22791fe64e3cd}} the author lists this object as part of the known
Galactic globular clusters. The values are taken from
the {{cite:74f92f3f866512a668e4c3aec2bccd1e2d15aa2b}}, {{cite:b8b0311bc0f42ff3dc53700a41f6409ac641f809}} catalog of globular
clusters,https://physics.mcmaster.ca/~harris/mwgc.dat
where the distance is given as 18.9 kpc,
and the metallicity is solar ([Fe/H]=0.0) with no age value reported.
Using medium-resolution Gemini spectroscopy {{cite:fdd889324662ad01ecb9d420c47143e20c680c4c}} obtained
values of 15.2{{formula:f1a3b78b-e5fb-483a-b919-cee3c1e50824}} 0.2 kpc, 7{{formula:c38a0864-1758-46d0-b4f2-3373ab6f519c}} 0.5 Gyr, and [Fe/H]=-0.1{{formula:39cdecbd-f064-4c8c-934f-d36e25c06fc5}} 0.1, for the
distance, age, and metallicity, respectively. The authors conclude that this
is an old metal-rich open cluster that could belong to the thick disk.
Recently {{cite:9922d56988568a13531aa94087086879175e0645}} used Gaia EDR3 parallaxes of 90 selected
members of this cluster to derive a distance of 13.9{{formula:865538b8-25d1-42bd-ad28-300f0b1e452b}} 3.5 kpc
(0.072{{formula:982275d2-af6b-4f40-892e-8e09c1c95c00}} 0.018 mas). They state that this cluster is part of a group of
objects that may be old open clusters rather than globular clusters.
Although the position of the TO can not be established as it is not visible
in the CMD, the RC for this cluster is clearly defined which allowed
ASteCA to estimate a distance of 18.3 kpc and a cluster age of 5
Gyr. Our distance is thus far from the Vasiliev et al. value, but close to the
value reported in the Harris catalog. It is also very similar to the value
given by the MWSC catalog of {{formula:83b6e26d-afdf-4671-acc5-1557e24d4313}} kpc (with an age of 6.3 Gyr).
This large heliocentric distance means that, if confirmed as an open
cluster, vd Bergh-Hagen 176 could be the most remote open cluster found to
date. In agreement with previous studies ASteCA also classifies this
cluster as metal rich ([Fe/H]{{formula:0a773d1a-b8aa-403a-9a31-602355debe39}} 0.15) and massive (M{{formula:18cfc2cb-9bd5-45df-aad0-b5b825fb57c8}} ), the most massive object of our sample by far.
| d | 332333128d802a820d4232289a27a5e0 |
Fig. 4 shows the NMSE of the cascaded channel vs. the bandwidth. The curve Method {{cite:a7b113811125413ef0924ea33c3689bf622c5f97}} denotes the NMSE of the conventional compressive sensing based method proposed in {{cite:a7b113811125413ef0924ea33c3689bf622c5f97}}, which assumes that the range of equivalent angles is {{formula:44871f43-0641-45ff-8b31-7961e0f1369c}} and directly utilizes the OMP algorithm.
We observe that when the system bandwidth is small, the conventional method and the proposed method have similar NMSE performance. However, as the bandwidth grows, the effect of beam squint becomes severe, which degrades the performance of the traditional channel estimation method.
{{figure:1049eec7-3663-439e-a842-278e5e8ab94e}}{{figure:c724b833-058d-45b7-ba54-d92c83f642ea}} | r | 19ca4abeea52c12854348a64482067d2 |
Can the logit normalization improve existing scoring functions? In Table REF , we show that the LogitNorm loss not only outperforms, but also boosts competitive OOD scoring functions. Note that all the OOD scoring functions considered are originally developed based on models trained with cross-entropy loss, hence are natural choices of comparison. In particular, we consider: 1) MSP {{cite:aa17a917261dadb1d5510efe76141372a399152e}} uses the softmax confidence score to detect OOD samples. 2) ODIN {{cite:0d095b6f622035d9e1395acea50cec5bb53aabbc}} employs temperature scaling and input perturbation to improve OOD detection. Following the original setting, we use the temperature parameter {{formula:ac70c548-7a9d-4bd2-8487-d6c404cc63e4}} and {{formula:b20582e3-906b-4f15-bcbc-5c31939d1861}} .
3) Energy score {{cite:b9b9f280f0d20be7f8611bbb9b7b65a841d898eb}} utilizes the information in logits for OOD detection, which is the negative log of the denominator in softmax function. With LogitNorm loss, we set {{formula:ae4a3918-2172-4f81-a990-c6556738204b}} for CIFAR-10 and {{formula:9de29e57-006f-4eb3-a647-96b510e70ac2}} for CIFAR-100. 4) GradNorm {{cite:4ff40f469ed393e838e4c2c4ff4a23c9776f7a13}} detects OOD inputs by utilizing information extracted from the gradient space.
| r | 0bd585393ebc59451bd9ba98f8bf53e4 |
Another way to test the spin polarization, is to couple one of the
{{formula:4308d305-9d2f-416b-b295-9d3995e4707c}} -nodes (Fig. REF ) to a side quantum dot, that is in a Pauli
spin blockade region. {{cite:0095664c312207a77d229479b8d06bcbf2c9d07d}} After a while, the side dot will
capture one of the polarized electrons, and this will block the
current (which contains electrons with the same polarization).
Changing the parameters will then change the spin direction of the
propagating electrons, and allow some current until the next
blocking occurs.
| d | 513b32979bac6028a5d14aef1a7f03f7 |
Recovering “watermark" or “watermarked signatures"? Recent studies show that DNNs can “memorize” some training examples in various ways {{cite:d1f854a85f875768c5a946b7e25d93f8ce817e65}}, {{cite:275c4487ea30e0a162c5e1b4228bd5e3f0391e9e}}, {{cite:67263143f989e148fb4b51307da6c515d0cffe63}}, and one can recover certain meaningful low-resolution images from CNNs {{cite:67263143f989e148fb4b51307da6c515d0cffe63}}. Hence, it is tempting to conduct verification by recovering the user {{formula:fd584c39-1156-40dc-b693-a788d81a0d39}} 's images from the CNN {{formula:64af4204-881f-4e80-8788-74e023931232}} . However, there are many challenges with this approach. First of all, the CNN {{formula:8d6a424c-0dad-4b33-92f5-50f4b6cf6196}} may memorize some training images but not this user {{formula:55c61c63-8a7d-4f59-90b3-e914cf9786b4}} 's. Moreover, even if the model happens to memorize some of this user's images, the recovery success rate is low. Existing works {{cite:67263143f989e148fb4b51307da6c515d0cffe63}} can recover semantically meaningful images from some CNNs, but they do not resemble any training images, to the best of our knowledge. Finally but not the least, it incurs high computation cost, often by many iterations of gradient descent, and assumes that the CNN classifier {{formula:c2b260a7-00e0-41bf-98a6-540fc92c0825}} is a white box, disclosing its architecture and parameters.
{{figure:b3349a54-6f49-45d5-bac4-4d09dd893e1b}} | m | f18d6e79dc76fdb1561ad370f602b345 |
Our model-free approach directly exploits the nonlinear time-embedded dynamics of observational data, and implements autonomous detection of target information without any prior models or training. Starting with noisy observational data {{formula:7d228909-b19c-46d8-a8e8-2ed3ce3fd8b5}} (see Fig. 2-a), it involves four steps, i.e., (1) constructing an enriched observable space via appropriate basis functions (see Fig. 2-b), (2) obtaining a reduced representation of an orbit in phase-space (see Fig. 2-c), (3) reconstructing the low-rank linear dynamics (see Fig. 2-d), and (4) detecting information from the profile of an evolving trajectory (see Fig. 2-e and f). In particular, (2) and (3) combines to forward the measurement of the current state to the next, thereby providing an alternative realization of the Koopman operator {{cite:edabea62deca94eb5c4fcdc61bc3e252bd024416}}. The procedure is universally valid as demonstrated in the ensuing three models of different origins.
| r | aaa38584bcdc60edf251cf80f073cf32 |
We assess our method, denoted as VesRec-SSL, in two DR grading scenarios: unsupervised domain adaption (UDA) and conventional classification problems. In the first case, all UDA methods are trained using both supervised samples in the source domain and unlabeled samples in the target domain. The performance is then evaluated using the target domain's testing set. In the second case, we train and test in the same domain, i.e., the training set's labeled images are utilized in the training step, and trained networks are measured on the remaining data. For the latter case, our method may be viewed as a pre-training phase {{cite:4367bc3182ac8c1805652c05285977e17c3b63dd}}, {{cite:c66ae020c4a51501b72e6bbd02b04e5b34f3c8c0}}; thereby, obtained weights after training VesRec-SSL will be used in the fine-tuning step using partially or completely supervised training samples.
| m | 745bd19c9a4afdd9620b40f047a5b281 |
Causal convolution blocks are stacked with a nonlinear activation function and batch normalization, with a residual connection applied for gradient stability. These blocks are stacked in a layered architecture to form a deep, overparameterized neural network as in {{cite:c265d1472ff8938c48b24248f44c2ca706c0a206}} and {{cite:93c59a7e9110c213f949700ad43590c89ce6d8e2}} (see figure REF ). End2End-TCN was designed to output a full time series of predicted states at every forward pass, allowing for simultaneous multi-step prediction of quadrotor states.
| m | de29d620ed578f898e5845bbd4a02310 |
Further, our approach can adopt the three types of clustering analyses for time series data {{cite:1ee870c779f1e035951857ae5972bac6c29acd21}}, {{cite:2a0365537992758c49da61566b2b3c0c630e0bd1}}: Whole-time series clustering for clustering individual time series based on their similarity; subsequence clustering for clustering subsets of each time series, the subsets are extracted via a sliding window; and Timepoint clustering for clustering time points based on a combination of their temporal proximity of time points and the similarity of the corresponding values.
| d | 571502145489444238a8435a06c03ba3 |
Proposition 2.8 {{cite:1263a11c3c016f01434489381ec767cfa74e2345}}
Let {{formula:fb05d0a8-8cdc-4202-ab18-32d2086c9377}} be a group of order {{formula:e805e5b9-8962-415d-8e17-2abfff0da1e3}} such that {{formula:8198cabb-2418-4cd6-bd45-184aa57a192e}} is realizable. Then {{formula:f1866aa3-58ce-4c14-95f7-a9611bf25931}} is solvable and almost Sylow-cyclic.
| r | ed699bebf259cb3614237ad08243b73f |
of size linear in {{formula:c992178c-c9f5-4e60-ab66-e9498b79ed7b}} (for {{formula:a2b85d15-588c-4d37-9509-867efeb12dec}} ) and arbitrary metric space of dimension {{formula:1e33c8a2-f085-4ba8-9ec6-1f47d5bff04e}} . Current coresets that are subset of the input have size at least cubic in {{formula:a9285ccf-ed3f-4623-b220-594a32cafd8f}} {{cite:61278e9a65da84c4c522b0c94365135c09e0dd68}}. This is by reducing the total sensitivity to {{formula:6711d47d-a3e6-40b8-ba2f-6f431c377f2c}} without introducing negative weights that might be conditioned on the queries as in {{cite:d1feb532c217d949d7c53d727c1dc39fb4745123}}.
of size independent of {{formula:3e72dae6-b79c-452e-a107-480bf5bea260}} for the Euclidean case of {{formula:47bf10d3-f107-4c18-865d-00c233421e65}} -means (squared distances). This is particular useful for sparse input set of points where {{formula:cd4c8c4f-1d02-4a1a-8d7a-bcf1fbcc50e7}} , such as in adjacency matrices of graphs, document-term, or image-object matrices. Recent coreset for sparse {{formula:57d8ebb4-a85f-4de3-b435-9e1fe7dad24d}} -means of {{cite:6826839ba802ffa385a4fa84006d95243ebc7749}} is of size exponential in {{formula:3dc7f595-ed37-4d70-8a53-7df48af93fce}} and thus turn to {{formula:1f7df594-e978-4658-9b14-d48dac9e00c7}} when used when the merge-and-reduce tree (where {{formula:de50858e-7f94-4e3d-8ce8-0e4d6d9d2208}} is replaced by {{formula:9108a70d-ce7e-4ad1-89f7-bbde7a7c0faa}} . The result of {{cite:707dbf81c84d8f82deaab49e47944078b4fcb971}} for {{formula:0712f4e2-09ed-47b6-bd6e-f4873eaa35ef}} -means is exponential in {{formula:5b97bc2a-72a7-4d78-baa0-11edf9bf356c}} and fails with constant probability, so also cannot be used with streaming. Another result of {{cite:707dbf81c84d8f82deaab49e47944078b4fcb971}} suggests a coreset type set for {{formula:43a05c6b-2ba6-47d0-9896-4651842457c2}} -means of size {{formula:b204a0ca-f3c9-4db3-9251-0526ca71df6b}} but which is based on projections that loss the sparsity of the data. Similar sparsity loss occurs with other projection-type compression methods e.g. in {{cite:d53fbe80407f23ee91625aaecdaebc43055baa64}}. Nevertheless, we use the technique in {{cite:707dbf81c84d8f82deaab49e47944078b4fcb971}} to bound the dimension of the {{formula:6a1e5f3c-f11c-442d-a3d9-afe975007764}} -means problem by {{formula:0a145f97-e6bb-4766-b6f9-23cba8945d1a}} .
of size independent of {{formula:a7c8bd63-a8b8-4e9f-b94d-90fb7bfa3082}} for the Euclidean case, and non-squared distances, using weak coresets. These coresets can be used to approximates the optimal solution, but not every set of {{formula:bd16aa11-8d73-4696-acb9-0da0764572ea}} centers. Unlike the weak coresets in {{cite:d1feb532c217d949d7c53d727c1dc39fb4745123}}, {{cite:02e5a2bb03c9f2bdfd11a626c0dab4c90a5a33da}}, we can use any existing heuristic on these coresets, as explained in Section REF .
Robust to outliers. This is since the general pseudo-metric definition we used (inspired by {{cite:80a83b005c8c73ad559198ba7f8d1fdd29e9b1fe}}, support {{formula:778acb08-b860-4723-959b-797814ebc545}} -estimators which is a tool for handling outliers {{cite:2a4b17891a4e479e812f92dda84a5c94da3161cc}}. Unlike in {{cite:80a83b005c8c73ad559198ba7f8d1fdd29e9b1fe}} our coresets are linear (and not exponential) in {{formula:aa7de382-a72f-413e-b023-fb3bdace00f6}} , and also independent of {{formula:e1e739c2-2443-42da-855f-edc42d31ad27}} (and not logarithmic in {{formula:152aa3e9-c6c2-4c5b-9b1f-2f08ec79b951}} ).
| r | e31beae2cc32eeb6d49a27de8510897f |
Attenuation of wave energy over distance into the MIZ reduces the wave steepness ({{formula:1a5e9649-af56-4ae6-8791-57923ebb949e}} , where {{formula:860db560-baed-4b73-9ba6-96f3127abec4}} is the wavenumber associated to {{formula:13637aa5-e14d-4d25-a893-1fe9bd08579d}} ) from {{formula:c9161496-5a77-4c29-afac-bc2a523a710d}} at {{formula:447feda5-2a66-4703-90a3-8d6e73903ca8}} km to {{formula:bec4ce23-1863-4e8e-98f6-b3f2cc27cff7}} at {{formula:4afb25f0-38fc-4ec8-a274-c7a81997cb94}} –44 km.
Despite the large waves measured (Fig. REF a), the small steepness values in the MIZ indicate
wave probabilities should conform to linear wave predictions {{cite:2a9f0719c9696cc16c1f37513efed5795082ab8a}},
which is backed by the similarity between the probability density function and the linear wave theory benchmark (Fig. REF b).
The finding is in agreement with observations by Thomson et al. {{cite:6bfa0821ade8e2c39a682aad3ac467032c779abc}} in the Arctic MIZ for milder wave conditions.
Our measurements strengthens the argument that nonlinear wave mechanisms responsible for the generation of large waves (e.g. modulational instability) are weakened in the MIZ.
Note, however, there is no theoretical framework for wave nonlinearity in the MIZ at present, as it is defined only for waves in the open ocean {{cite:ecbef4743e20e03671efa7c3192a87b6e078b7ce}}.
| d | 098308bd2879c5a7e303b775d4528767 |
The focusing problem is more challenging. In one dimension, it was addressed in the earlier works {{cite:698e4034be29c2d376d55f19c91fbe608d018864}}, {{cite:96372950a206c9305e7a08711bd35b9fa3d888c9}}. The one-dimensional problem was revisited recently in {{cite:1965742e4b88f9264ae019b2148b389e504348dc}}, {{cite:886c9de991588b47e93aed71d3470cd1ed7cb478}}, {{cite:f0a67d2522be530a4576153672a9fcd0b029c8a1}}. For recent results on the fractional NLS, see {{cite:8686c3e970cf5446f6d28d8e410da82a1e86bed9}}.
| r | bc55a44a78e856093cd394da58252eb6 |
The expression (REF ) agrees with the basic constraints derived from the structure of Euler fluid equations, except the one of reversibility (which constrains smooth solutions but not singular ones). Irreversibility in the first term (REF ) is reflected by the fact that the product of absolute value of the vorticity by the strain tensor components makes the turbulent stress {{formula:fb7edaec-4824-4c37-929e-c8daf1bc3ec2}} change sign when changing the sign of {{formula:6128895b-2373-4ec4-8a87-464ec475d44d}} , whereas the inertial stress {{formula:13c25ea4-2832-4fc4-a386-02385898b4e4}} and {{formula:dc1a5884-926e-4442-8a1a-1c0fae2350ff}} do not change sign. In our picture of turbulence the irreversibility is due to the evolution toward finite time singularities of the Leray type {{cite:b6be948056a09a09981ee66dd7701abda5f34ba9}}, the solution disappearing close to the collapse time due to molecular dissipation at small scales, so that dissipation will ultimately yield the friction of Newton's drag law. This picture of dissipation at collapse time is analogous to Maxwell's theory of molecular viscosity of gases {{cite:1439172c575cd09d3d797e769015016881ee8fee}}, where the velocity difference between two colliding particles induced by a macroscopic shear flow reduces to zero when the particles collide, transforming the energy of this velocity difference into heat. As just written, {{formula:40ce82c9-3c61-4400-bd5a-b65fd11547e9}} does not change sign as {{formula:eb9d4ee8-fa80-4f60-bad1-0dad4723a572}} changes sign.
Therefore the addition of {{formula:31e1dce0-4894-4791-af9e-290bc9c781c5}} to turbulent stress will represent a contribution to this stress that does not participate to friction, that is possible a priori. In particular in the geometry of the mixing layer the {{formula:e7da8a1b-156f-4202-9446-3a09c8c0d644}} component of the stress cannot enter into the friction which, by symmetry, is a force directed along the {{formula:56b25bf4-3024-47fe-b8b5-6ce0a042214c}} axis and so depend on the components of {{formula:102232cb-61e6-40f1-8fe2-2089ad54cd19}} with at least one index {{formula:7cb1ef03-87c1-479a-8e20-93b803d1fcc0}} or {{formula:25b6c266-e81e-4ed3-abc9-6ae1d3a156d3}} equal to {{formula:20861508-4610-4681-a33a-154ab1243e33}} , which excludes {{formula:7afa8b3b-5a3a-4fe2-b3db-771641330a48}} .
| i | e56fc6fa2b36e2593b2e07c9c8fb080a |
Fig. REF shows the total processing time of each task when using different approaches. As illustrated in the figure, our proposed approach outperforms all other approaches for all tasks. Particularly, our proposed approach can achieve {{formula:caaca138-e7ea-489d-9a10-8f6fee96911a}} that is up to 90 and 10 times lower than those of the Myopic and OneNode approaches, respectively. For the static optimal code approach, although it applies the optimal code in {{cite:5923a9127ffbd1a6290690b5aaf7b594a7be0881}} and our proposed optimization to find the best nodes to perform, its performance is still not as good as that of our proposed framework. Specifically, for the largest-sized task, our proposed solution can reduce the total processing time up to 2.3 times compared with that of the static optimal code solution. The main reason is that, compared to our proposed approach, the static optimal code chooses a higher {{formula:828bb7b8-9bb2-4917-90e5-2f67f87869ab}} . Although this reduces the sub-task size, the server has to wait for more nodes to send their results, and thus it may suffer more from the straggling nodes and communication links.
{{figure:7f7bea34-3967-4f75-b1e5-61e62dce67d2}}{{figure:8b345e10-6464-4849-8631-202f356006e9}} | r | b8464f8ef31b548282545c419844821c |
Retinal Disease Identifier (RDI).
To identify retinal diseases, in our RDI sub-module, we provide two types of deep learning models based on {{cite:27c7f05ab71178376c49eabb6d8500657f80c525}}, {{cite:20e6dbf196315b63ca8a0b07e188793cb780abf6}}, pre-trained on ImageNet, and then trained on the proposed DEN dataset. From the lower level feature perspective, such as color, most of the medical images, e.g., radiology images of the chest, are mainly grey-scale {{cite:03c9fa07a61d01946818df0fa0e596217206b6f3}} but retinal images are mainly colorful in our dataset. Using the ImageNet pre-trained at least helps extract the better lower level features information. So, in this case, we expect that pre-training on ImageNet can improve model performance.
| m | 9082298bd140a1cb5ce66bb0715e06a5 |
A fundamental dogma in distributed computing is that a distributed algorithm
cannot be deployed in a real system unless it can cope with faults.
When it comes to recovering from transient faults, the agreed upon
concept for fault tolerance is self-stabilization.
Introduced in the seminal paper of Dijkstra {{cite:a922f4abe7a6a30b7406a981975f9652035f9651}}, an algorithm
is self-stabilizing if it is guaranteed to converge to a correct output from
any (possibly faulty) initial configuration
{{cite:6800908b57c8e492a91e423d9faa2041664522b2}}, {{cite:ec1343e3a08d2c26f772d2dc8ac16054909762f6}}.
| i | f0e7e5db10dd935d3dff6aafb81da048 |
In 2018, a study into explainability methods was conducted, which determined that most methods were acting as simple edge detectors {{cite:ceff25b19caf4202e1db2f86b123fe09c85eb508}}. The experiments showed that produced saliency maps were mostly independent of the model parameters and labels of the training data, except for notably the saliency maps created using Grad-CAM and DeConvNet. The Pointing Game was introduced as a way to measure the class-sensitivity and accuracy of class-guided explainability methods {{cite:e1ece29207a9e50ac0a39a8685e9af7320a3905d}}. Finally, ranking methods for pixel importance have been proposed via removal based methods {{cite:1cb511a5a7d1e637a99f8eac75f23052d1b9b712}}, {{cite:9555e870007b3a31d1602a6f0640faba0aa84124}}, {{cite:d4d04ca2cb59d4f4cc6811b633de2afd00abd1b5}}.
| m | 3444f277e1901949f3535a907021b512 |
The update (REF ) takes the same form compared to the typical weighted gradient method {{cite:257ce3bce15e1a62640b9b9f9b2dae33ae02804d}} which solves the same problem, but has a different weight matrix {{formula:d778b77f-1e5f-42c0-8786-fa47c7c2ad69}} .
| m | 7578906886d900114fd573a0f0e218cc |
Wireless power transfer (WPT) is one of the EH technologies that overcome above limitations, which can provide enduring charging for communication devices. The prospect of integrating WPT with communication networks creates a need for technology that can transfer both information and energy simultaneously to devices. Therefore, the concept of simultaneous wireless information and power transfer (SWIPT) is first introduced in {{cite:7a699a349fee12ab18af8dad331f5396c235ad59}}, and a capacity-energy function and a coding theorem are also defined. Developing green technologies and reducing the power consumption of devices are two of the eight major requirements for 5th generation mobile networks (5G) systems identified by industry and academia {{cite:cdf368b4a83d672d047c16ac8c4f613244371713}}. Thus, in the era of 5G, the SWIPT technology can be of fundamental importance for energy supply and information exchange among numerous devices {{cite:7e2fa45a64b5b0d4cc1b3a8ca9249f2cf08745d0}}, {{cite:957219bccb283ce4f2b0dbb6e5016f8411cdd541}}.
| i | 4290875ad054e78e345f54453c8791fd |
Included in this section are a number of qualitative examples for CenterNet {{cite:7c41440fe686239ad576e7bcdd728624661386a4}} and the proposed DeformCaps on the MS COCO test-dev dataset {{cite:867270e25a6a8bd36c23896078f4085144082b33}} using both flip and multi-scale augmentations. Results for CenterNet were obtained using the official code and trained models provided by the authors {{cite:7c41440fe686239ad576e7bcdd728624661386a4}}. While we do not make any sweeping claims, we wish to comment on a few general patterns that seemed to emerge in these examples. In Figure REF , we show a prototypical example of the general trend we are describing. In Figures REF – REF , we include more examples of this trend. In Figures REF – REF , we include a set of interesting examples of unusual object viewpoints or poses being better captured by DeformCaps than by CenterNet.
{{figure:3a47d237-97ce-4dfd-8f19-6c229b71d5f5}}{{figure:55eec6b9-7e34-436d-854c-f432830585f3}}{{figure:c3cfebee-4c41-4235-9956-b21c7f08ae40}}{{figure:fdb8bb95-a52b-48c0-b3fd-91d6cfcedf70}}{{figure:c501451d-e3a1-4771-a426-b2d551e4c1cd}} | r | 66b70eb965236011c5801146af4ad5ff |
As graph neural networks are more widely developed and used, their safety and trustworthiness also become of a bigger concern.
For instance, the adversary can steal the model through a model stealing attack.
Recent works have shown the high effectiveness of model stealing attacks on complex models even without knowledge of the victim's architecture or the training data distribution {{cite:8883015f60764444f931bc59bcfffd3afe3c64fb}}, {{cite:69b2ef6a7aa68080f89df1e43d21c87f0fb51863}}, {{cite:e9a030b706a427eeffa36a3e741738ecba72ced5}}. Such model copyright infringement may damage the intellectual property (IP) of model owners, and if the model is intended to be released for commercial purposes, it will lead to financial loss for the model owners. Therefore, it is crucial to verify the ownership of a GNN model to protect intellectual property and prevent the leakage of the deep graph models.
Additionally, similar to deep neural networks, GNNs are also vulnerable to backdoor attacks {{cite:3888c89797774dde1e063e909fc8c3aa1f51c029}}, {{cite:c02490cdcf0161c93774bdba1407129511cb9030}}.
For instance, in a Bitcoin transaction ego network, where the nodes are the transactions, and the edge between two nodes indicates the flow of Bitcoin from one transaction to another, the attacker can attack the GNNs to classify an illegal transaction as a legal one {{cite:86d80098b31c2b0b76fb7726a4e433f341b4fa69}}.
| i | dfaabebd858c9c85d0e04cda69f624be |
There are several advantages of using document NER models: (1) The models suggest a better way to bridge the gap between research and application fields.
Following previous studies, several researches have leveraged sentence NER models in biomedical domains {{cite:a6eef8c6efd4e85215a70e5b5a54ceafead312fe}}, {{cite:419e451f6383d8452f18f93b4d504656a1c796a4}}, {{cite:165907fe16779f9304af46b107db6a8d8e529d2c}}.
However, biomedical applications require an evaluation of the document rather than the sentence context {{cite:224261b2a4f18c3efefb804bf0b4027c3c17230f}}, {{cite:69dc6ac3f8760026fbba273b6e6b52a8e32f4280}}, {{cite:cf368ea99833b1b5ba969020a80b8c20c22adf7c}}, {{cite:88d189f5a0dcf194bf8b96b2bd8e1a6b296db353}}.
(2) Document NER models provide proper and consistent predictions owing to context completeness.
Recent works {{cite:7f87c19d735faf305ef784b0b7de621e444196fd}}, {{cite:0de748e156d54b42a0243b1f0d7a6a9dbbceaeed}}, {{cite:7be464bbdd11489d1d51ffff47dd9f040798995f}} have shown that using document contexts improves the accuracy of the models.
Although the authors of {{cite:7be464bbdd11489d1d51ffff47dd9f040798995f}} used powerful context representations such as BERT {{cite:16175c80873aa8ce3fbef954eb165cb2af8b2f11}} or ELMo {{cite:56fb36724d97c36624010fc870fdcd92a8dbfdbc}}, their inability to model document-level label consistency resulted in insufficient performance.
Therefore, it is challenging to understand which factors contribute to creating document NER models that produce a consistent prediction in the same manner.
| i | 5222ccee51b4ba2c080f6336f48bceb9 |
Research has been done to evaluate the idea of Lagrangian control of traffic with automated vehicles, demonstrating that vehicle automation can smooth traffic waves both in simulation {{cite:c94238d07a6e02d0fb4464754700a285bbf063d8}} and in full-scale experiments {{cite:5fd58f9460779a89adb9e7a58c6d7dbc0bd7da9d}}. These controllers dampen traffic waves through prescribed time-gap following, but they depend on advanced sensing and computation from the vehicles of tomorrow in order to close the loop with an accuracy and dependability that is on par with human-driven vehicles, with a requirement that 5% or more of the vehicles must be controlled vehicles.
| i | 02db3913832f6d583082dc0cb95881af |
In the low-energy gamma-ray band of 0.1–100 MeV,
we can observe various radiation processes in universe,
such as the line emission from the radioisotopes produced by the nucleosynthesis
in the supernovae or the neutron star mergers {{cite:3829981ff19d5aa326dc0daceeab83f8e403409b}}, {{cite:a2358f5cc83078989ca69bd2061b7cd46640c84c}},
the electron–positron annihilation line in the Galactic center region (GCR) {{cite:04544d361dff3391c0ed1b76d40b35253c074b89}},
the synchrotron emission and inverse Compton scattering with particle acceleration
in active galactic nuclei or gamma-ray bursts (GRBs) {{cite:bf5ba54e89f7929305a4c3c345162fec02b885e0}}, {{cite:bd1f0d61e5ce721d6ab4596c0fad8afb0f5e779e}},
the pion-decay radiation in the strong gravity field
around black holes {{cite:3d60ca18e981fe49dde1f2f0af96d598333cc7bf}}, {{cite:667e10cd0d9dd2b858e4f2c53c74a8cb97f7478d}},
the de-excitation lines from the excited nuclei by the interactions
between cosmic-rays and interstellar medium {{cite:585490fefb3df61e09468c2a411e53a0674bccdc}}, {{cite:ded86f999daa62499e262ce844445e9086bfc440}}.
Population III stars are expected to be detected
as long duration GRBs {{cite:60d16536b7164d9dd524660e99d936f6aadbac00}}, {{cite:97dc8cb35e6d7eb733bf4204fc812b1708c2a970}},
because the universe is very transparent in this energy band.
If primordial black holes (PBHs) having the mass of {{formula:14098d1a-447d-4c83-a411-a69df5ca5c40}} g exist,
the thermal emission may appear in the extragalactic diffuse emission
because such PBHs emit the thermal gamma-ray emissions in MeV band {{cite:b4e60a93a1fb1a03e692bf8ae39511399243f8a0}}.
| i | 3000b7fb5384ed08bf205d164e8ab5bc |
There are several options for the evaluating criteria on estimating layer importance, , weight magnitude {{cite:d70dbe58039386b4a185c7d4334d3077328d3e9d}}, reconstruction errors of layer activations {{cite:efcddfab4518025d7013b78d8697a47f75f8a866}}, BN statistics {{cite:7b7105f7ca9bb00879c4edd906077ca4b1068c34}}, and gradient of the cost function {{cite:bf3196d8ec87cd57989753da9fa509ffa85b4a27}}. We eventually choose the BN statistics, , absolute gamma value, as the criterion to reflect the importance of each layer to the final performance as it yields appealing results and requires little computation cost. Batch normalization {{cite:5d54948c356b9e301d2d5fc2f4b78218ec2da959}} has been a basic block in modern CNN architectures to address the internal covariate shift. Suppose {{formula:efbf15e1-d8ae-462a-8fcc-fe7e12634265}} and {{formula:9d0cb12f-349e-4cae-93b5-56bd800e9285}} are the input and output of the BN layer, respectively. BN layer performs the following transformation on the input:
{{formula:bdbca431-d713-4e86-8dac-a94308b76979}}
| m | d1401af7ce30ba7d1d46215b495f65dd |
We used 1D numerical simulations (described in Section ) to show that if a TNDW is able to propagate within the helium shell, then ignition within the CO core is guaranteed (Section ). We demonstrated this for {{formula:c8cc7fcb-efaf-4d23-9267-0a21d48b6985}} , where we were able to numerically resolve the ignition in a full-star simulation for the first time. Previous calculations of the DDM {{cite:4e9569a13f6833ca6d39f99fee7e7b2724baf43b}}, {{cite:30bdfae4ba221c556ea67afcba19b7c2627e79ed}}, {{cite:5d028d56e17b67cf2f589d8ca4f1eaf9891cb4e1}} used an unstable burning scheme (or implemented a stabilizing burning limiter, but relaxed it during ignition phases), in which the ignition is presumably a result of numerical instability. For example, a "scissors mechanism" was claimed for the CO core, opposite to helium detonation ignition spot {{cite:b3a767b8cc0ede4c7a71ee5b31a6f6ad185930a1}}, {{cite:e195de39c31ccda562a13f835b4e1fe0614648c5}}, {{cite:7a8dff163ae0c51e8d9e5be7245d5f2794247cd2}}. In these simulations, the ignition was obtained in a density of {{formula:73f920a4-ee23-4d41-ba1f-08dfd175fcc5}} and a temperature of {{formula:6742cf47-efca-4b1d-b2da-958b1af97557}} , where the burning time is {{formula:0338398f-a94b-4f1b-bc24-669abb81aec8}} (for the relevant composition of {{formula:57ede612-fcdf-4171-95ec-3a4ca0a6ee1d}} {{formula:f5b72cc4-47f1-40be-b5da-39c909d4eb24}} He, {{formula:bbd5818f-06b0-4d20-92c4-f271f462c5c3}} {{formula:32c79d0c-2a47-4398-8712-f58e93af53db}} C, and {{formula:adc463c7-6397-4b74-89e6-f5f21271ac7e}} {{formula:4959b3d2-f2e6-4515-83b7-c89718b15e74}} O by mass), which is much shorter than the sound-crossing time of the numerical cells, {{formula:5ae073cb-8903-4a8a-a938-ed153843c8a0}} (for the implemented {{formula:1ee4bb70-8a12-48fa-b25e-e8f5bf37dc3b}} resolution). Ignition under these conditions is obtained in the regime of numerical instability {{cite:46db2aaebaff6dd87fbc6156d6e7473bbab7e3a1}}.
| d | 8b49bfd330bccb0e6b2c708e3f61ada1 |
As shown by {{cite:1c4467e411939008385f002b41d24d1cb4185432}}, obtaining a motif clustering of the original graph can be done in two steps. First, we construct the motif graph, displayed in the bottom of Figure REF . This graph has the same vertex set as the original graph, but a different edge set: any instance of the motif in the original graph corresponds to an edge in the motif graph connecting the two anchor nodes of the motif instance in question. All edges of the motif graph have integer weights that correspond to the number of motif instances in the original graph that have the two edge endpoints as anchor nodes. In the second step we use {{formula:9d7b7ae9-9870-46ac-b9a6-5b33eb06a1c2}} -means spectral clustering on the motif graph to obtain the required motif clustering of the original graph.
{{figure:765cbde6-6319-4931-9169-95bace1d3152}} | i | 45432abda41c2c23990305368b5a2cbe |
First, I focus on the models with {{formula:34d12678-6757-4f2e-9bad-f63b3dd91155}} and 0.5 (the fifth and sixth lines in Fig. REF ; models AM3, AM5, AM10, AM20, BM3, BM5, BM10, BM20), which have a low mass accretion rate (Fig. REF ) and would form low mass stars.
Figure REF shows that both outflow and jets appear only in AM3 and BM3, which have the strongest magnetic fields ({{formula:4502c662-7573-4760-b7f5-7e2fd6fa9bfe}} ).
For these models, the outflow appears without resolving the jet driving region (Paper III).
The jet also appears as described in §.
Thus, it is considered that a high-velocity jet and low-velocity outflow are driven at different radii in the circumstellar disk, as expected from past core collapse simulations {{cite:8e40562ebb6ebaf96743d495f4dc191f0509184e}}, {{cite:56857c00529f6c2e68fcb7b5a0574a9eca0bb9fa}}.
On the other hand, when the magnetic field is not strong ({{formula:8c83f9ae-197a-4857-9148-1da2c33b6013}} ; AM5, AM10, AM20, BM5, BM10, BM20), jets do not appear.
In Figure REF , `Delayed Outflow' refers to the case where a (weak) outflow begins to grow only in the late accretion phase, just before the infalling envelope dissipates (Paper III).
Also, for BM10 and BM20, neither jets (this study) nor outflow (Paper III) appear.
Thus, for these models, the outflow and jet would not play a significant role by the end of the mass accretion phase.
Note that since the jet driving was calculated only for {{formula:bda7e79a-c212-41f9-a075-425ff7f12d40}} yr in the main accretion phase with a high spatial resolution, I cannot clearly state that the jet driving is completely suppressed by the end of the mass accretion phase.
However, since no jet appears, it cannot help to drive the low-velocity outflow, at least, in the early main accretion phase.
| d | fce202c095887c43d830703ff3215a87 |
We perform numerical simulations and apply radiative transfer post-processing to our data in order to analyze the influence of chemical inhomogeneities and optical depth effects on the {{formula:1c0f690b-b85b-4d92-8fdf-c97d25f48f90}} -variance analysis. Table REF gives an overview of our numerical models. Mass- and volume-weighted quantities are defined via {{formula:ecf06030-2059-41a1-8db4-8b47896fad4b}} and {{formula:9ac56e52-33b4-4c8c-94a9-80761fcac235}} , respectively. For more information about the H{{formula:75c27954-20bd-40b4-82e3-51a9beb009f7}} and CO distributions produced in this kind of turbulent simulation as well as integrated intensity and column density PDFs, we refer the reader to {{cite:db46f2c51e5ecd6703f30bf4335460f8c8633bef}} and {{cite:fb5aaafe592de6cd92a88e3724518ef6f36507b1}} (2011a).
| r | d2bd40fc9ee0830c0c755233e45d41f8 |
ID of classification layer does not predict the object detection performance in contradiction to (See 3.2 in {{cite:18c30ec1d65eeeb1262ef812d9c39e91bc6a9791}}) that corresponds to relationship between last hidden layer and accuracy of classification. In our case last hidden layers(fc layer) ID also have no relationship with AP (Table REF ). So, using TwoNN {{cite:a150d310531263a0de13de769d49ab923880a701}} algorithm, dependence of ID with AP over data sets cannot be confirmed but difference in ID is observed at feature extraction level that motivates us to investigate our hypothesis using a different approach later.
{{figure:f1ef7145-7437-4576-990b-90e945b8c549}} | r | fc4f3618a1a7fff1836a458571cbac05 |
(U3) There is an even unitary representation {{formula:4e342f43-d549-4cc6-b9aa-10bb96fa8ee8}} of {{formula:42e8d433-fb17-4e42-a6c3-862a76815499}} ,
the simply connected group defined by {{formula:61f8f6d6-5cef-4708-ad8c-a05a6fbf6941}} , on the completion
{{formula:c2b9e088-7c7b-406b-b2bd-696a3da1ef6b}} of {{formula:57c00eae-8726-442a-a32a-c99706c48696}} such that {{formula:75e85ddc-c0df-425c-af8f-b249a7ae96f7}} is defined on
{{formula:5cff11df-56d6-4239-834e-93cd5256845a}} for all {{formula:9cd7346e-142d-4752-acad-433a77ed22ed}} and coincides with {{formula:d85dbdc1-2621-47f6-a629-dd270f0d5d88}} on {{formula:a6cd0f2a-d50e-42b2-8a13-ae17b23cdc47}} ;
in the usual notation {{formula:a329f241-2e5a-4164-9ba3-9c8b223e6b75}} and
{{formula:990cd474-ee7d-41de-8344-e0556de0268d}} , {{formula:a0d6c2a5-14dd-45c0-8e04-7c84d7f25bcd}}
(see {{cite:740b6ca1258fc29c0dbe7b70d04513e4eac62430}} Ch. 8 for definitions and notation).
| i | 3cc6cf4e695575287f448872ba683f60 |
Quantitative Results. table:sotamr compares the performance of the state-of-the-art methods when trained with our proposed training framework on the Visual Genome dataset {{cite:4dfa9c1971c0b53c82b300047dbfc33e83c9f126}}. Our method consistently improves performance on all the three evaluation settings (PredCls, SGCls, SGDet) when trained with existing methods. With IMP {{cite:b705735f139ebf095ebd9e9f72949aa977ba10cd}} and Motif-TDE-Sum {{cite:0c54c31c484914b3b5a78fe6bda7c96fefb425a5}}, {{cite:b892f8a4c84e7f7cae49aebbe1e5a30574311f54}}, we obtain an absolute improvement of 3.4% and 1.7% in PredCls and SGCls, respectively. For the most challenging setting of SGDet, there is an improvement of 4.7% with the IMP model, showing the generalization ability of our approach on a visual-only model (no language/textual features). We also incorporate our training framework into other debiasing approaches, TDE {{cite:b892f8a4c84e7f7cae49aebbe1e5a30574311f54}} and EBM {{cite:464bc581a04e9b6853478cf640a46834c033bbc6}}, and obtain consistent improvements when trained with VCTree as the SGG backbone for these two methods. In both the cases, we gain significantly in all the settings and achieve a new state-of-the-art performance in scene graph generation by combining our proposed method with VCTree-TDE.
| r | c0b9669da471693490ae1df0be626748 |
Upper limits on {{formula:e5df4f93-b147-419b-96e8-0f45270f81f4}} for the 2HDM+S for each Type-I to -IV as a function of
and {{formula:aa307221-2136-4e54-9087-89d06cb6c90c}} are shown in Figs. REF and REF .
The assumed model branching fractions for pseudoscalar decays to {{formula:0fca998c-3e8f-410b-9cea-422f7af61040}}
and {{formula:a0cac7c5-41b6-4adc-8243-f6ce13120463}} are taken from Ref. {{cite:990397830875387710666b13a4bb5e12e1f11fba}},
and the branching fraction {{formula:a3f689fe-d451-442d-80e5-ae531f27d932}} depends strongly
on the 2HDM+S type {{cite:2954341b2fdb0b1d31b3095062a466d5f130bddb}}.
The branching fractions are calculated in increments of 0.5 above {{formula:d84df3de-9f46-476f-90ee-6b2780cb7d0d}}
and increments of 0.1 below, and
a linear interpolation is applied between the calculated points in Fig. REF .
For the Type-I and -II models, we primarily probe the {{formula:3df6173d-49b3-4a4d-a086-d9fe0668c367}} range,
with the Type-I upper limits approximately independent of .
In the Type-I model, the
most stringent limit of 5% is set for {{formula:c0f72d62-6e88-406d-b4a9-b5558347ee8b}} .
In the Type-III model, this analysis has exclusion power over the
full pseudoscalar mass range probed, especially at large .
For the
Type-II and -III models with {{formula:e389aaaa-3342-4c01-b00d-7896c96b6849}} below the
{{formula:7c441c54-3f8b-4d12-82c4-d6765f4d056a}} threshold, upper limits on {{formula:864ff611-19a3-4f8c-a90a-a8eedea78b6a}}
are stronger than the 0.47 inferred from combined measurements of SM
Higgs couplings {{cite:6dcd253da2dd522cc9c93686fec4da4935d035a4}} for {{formula:cc80d5c2-62ec-49ec-bc06-221dd9183d79}} -0.9, becoming as strong as 10% for
{{formula:007e9d06-b937-44d7-8d8c-15bcc816e613}} .
In the Type-III models, strong upper limits are set for all pseudoscalar boson masses tested when {{formula:9d8f7d17-cecf-44ca-9f39-6a0e54369eba}} .
The Type-IV model, however, can only be effectively probed
in the low-region. For a given {{formula:0f592c3a-35dd-4462-81f3-40dc7a5a71af}} , the ratio of decay rates to {{formula:56cb06b7-a58a-48bd-a323-b95ced9116be}} and {{formula:5cc255ff-fc5b-42c7-8b20-96d2f3a94d31}} ,
respectively {{formula:94cfb54f-2b0f-4762-bc15-0e1868622a7e}} and {{formula:2c2ee74c-f065-42d0-a274-d0a6b9d28e48}} ,
depends only on {{formula:dca8bb36-2f14-4795-9c79-582d5819eec0}} and {{formula:55125fdc-84e9-4bc0-98af-24ca79d8877b}} {{cite:2954341b2fdb0b1d31b3095062a466d5f130bddb}}, {{cite:990397830875387710666b13a4bb5e12e1f11fba}}.
Thus, these results can be converted into upper limits on {{formula:518ac06e-2747-4520-acc9-435d54218c7d}} .
Contours for different {{formula:9932ad60-7cc1-418c-b34f-d716e2414052}} values are overlaid.
Compared with an earlier result by CMS {{cite:2d21f60061d3fb77eb35710e4af527fc9c5228c1}}, these upper limits are more stringent (where they can be compared) and extend to lower values of {{formula:98a9ce19-3193-4697-a90c-c4ddb7e78419}} .
{{figure:380816e9-2c53-46ed-880f-3259719bdbba}}{{figure:79ce5295-f00d-487b-b00f-6b8217c31f3c}} | r | 0801c76224421670c447e77802de5cf6 |
A good introduction to the concept of networks can be found in {{cite:870e27bcb9b5a75e98e08e5a0cf8d31d12a07065}} and {{cite:c9f8408b56f4175818afb1ee25d6ffeb5de40808}}, whereas {{cite:4ad1a783f0284f41d48467c6648014986bee140b}} contains the same ideas described in the languange of graphs. Methods of weighted networks can be found in {{cite:82eefec5a0b96f62d35a79cc4242f6f5c85b6b29}}.
| r | c9429c0087a8cc837e8f99fe49357a18 |
A first glance on the figure reveals already how challenging an accurate description of the electronic-structure is: there is no method that performs well over the whole range of bond lengths. Clearly, there are more sophisticated functionals for DFT and RDMFT that perform much better than our chosen examples, but {{formula:953f5658-488a-4811-94e8-004038a3ed4e}} is also just a very simple problem. The accurate description of the ground-state PES over the whole range of bond lengths is for many systems simply not possible. Methods that are accurate enough are usually numerically too expensive and the most efficient methods can often only describe a small part of the full ground-state PES.
Close to the equilibrium position, single-reference methods are very accurate with HF providing a reasonable qualitative descriptionOne of the most precise electronic-structure methods for this regime is coupled cluster theory {{cite:bd9d5e02a15aae6f2481f14745271a00f2f86908}}, which systematically improves upon the HF ansatz and usually is significantly more accurate then typical DFT functionals. However, coupled cluster is also considerably more expensive than DFT. and KS-DFT leading the way in terms of efficiency. However, methods based on only one Slater determinant become usually inaccurate for large bond-lengths. We have discussed this in the last paragraph of Sec. REF considering the dissociation limit {{formula:9656943e-64f6-4e29-a42d-6a461a464b38}} , where we have to describe the two degenerate orbitals of the separate atoms. To describe this limit, we need two Slater determinants, which corresponds to a multi-reference wave function and makes the system strongly-correlated.
| m | 46bbebdbba52ee4a3ab1df2d0a8962bb |
Here we investigate the effect of using various saliency detection methods for our SaliencyMix data augmentation. We use four well-recognized saliency detection algorithm {{cite:2f26b5e9201bc4c7f1b48ae42f66d73380ffe444}}, {{cite:2adbb073a211aaad3d661f639c59085ff79ffd4b}}, {{cite:6ff52f63ee1c73148d026816504efd367e28a7f7}}, {{cite:e86bf43aaa3736db84bbb21de104d1438ae5ae0a}}, and perform experiments using ResNet-18 as a baseline model on CIFAR-10 dataset with traditional data augmentation techniques.
| m | 2b4323fcddbcece3fe766bb3e5a0e25d |
Human biases toward abstract knowledge might be linked to their ability to verbalize this knowledge through natural language {{cite:5deb5f00e1fe65070c663d6d18d503a24cedb165}}, {{cite:587baa068983411ed77f0be7e36ed6c0c1b04d6c}}. Human language descriptions can therefore act as a repository of this prior knowledge. Recent work in machine learning has shown that neural network representations can be shaped and structured through natural language supervision for various tasks {{cite:f3853105f0916f2082d7cd641a7e3ea30fcd73dd}}, {{cite:67c5d8e2a9d11d8222727a41c3461f76f62d0d63}}, {{cite:f33e94a00155da7426303e7492c87b0a6e1face7}}, {{cite:cbb010bf02821345f44060497fc4f3427791bf68}}, {{cite:4b06976a1d6bf6e3bcd67f285153b59a81f8b1e9}}, {{cite:4bbfe4ed143aa55a950b4474f205cdb5d9e04994}}, {{cite:00ddbd85e7cae515e8aa28d38a7d6b194684403b}}. Abstract knowledge in humans has also been modeled by program induction {{cite:8a2f0f62a9210d90460905d1143dca80ee0e72d8}}, {{cite:9b2eee940404ce2be939fec748bac891020b513c}}, {{cite:bc041554bc273da7b3c6c7d7fa4289f38f497258}}, {{cite:ffde69e17bf2715168d42dff1a044be838e4e77d}}, where a model directly infers a structured programmatic representation from data. These programmatic representations are constructed from primitive atoms using symbolic rules and procedures. Recent work has leveraged neural networks to make this otherwise expensive and brittle process more scalable {{cite:6759c53b3997c65c404081453e6a63b9d8db215e}}, {{cite:3b17518af72dd16b18061e1e65fbd967aa8ae1d3}}, {{cite:e63594c147432cf800b6ab0ae40d54a571afaae3}}.
In these approaches, abstract knowledge is built-in explicitly into the artificial agent using a pre-specified and built-in Domain Specific Language (DSL), which can be restrictive. In many situations, we would like artificial agents that are implicitly guided towards human-like abstract knowledge {{cite:6d324949783bdf4f391cc096efb3b66493f6eccc}}, {{cite:ec2479774ab930504dc843ceb7e61ddba69c0677}}, {{cite:b9653bf289cd5a89047a87f95741f6e7a2b538dc}}, {{cite:1f189af134d8a4d252238fb2f966d1e5d48af3d3}} rather than explicitly building it in, since it can be hard to determine what specific concepts to build into a DSL for any arbitrary environment. Therefore, in this work, we focus on how to use representations from program induction to guide artificial agents that don't have these built in concepts.
| i | 54a5bc7d85b53e48f215c99c310c0a99 |
There are some approaches to quantize time in quantum mechanics such as the multiple-time states formalism of Aharonov et al. {{cite:2a9d1eb61e6fb39566a6962143bd60d1059f130f}}, {{cite:1d6fa33199286a0bd060056cc70627dd85dfe35c}}, the entangled history formalism of Cotler and Wilczek {{cite:6b6a544636973ddfc0b8a5b171107f40f2e9d90a}}, and the conditional quantum time mechanism of Page and Wootters (PaW) {{cite:afb3e78e9d6356384866cc4d13fa18d9c7b1d484}}. For a review, see Ref. {{cite:8abc2d8cfd3740a72e648128ea6a711e88f9fba1}}. Interested readers can confer Ref. {{cite:d1ca92a9d36c76c40515f9cf0da0a9d7d6ecab09}} for a possible connection between the multiple-time state and the entangled history formalisms, and Refs. {{cite:91851fe529dfe4607a90f2414013bf9d4898f7e8}}, {{cite:6c255ac89aa6987dfd5d0d5aa93f9d2a94910aab}} for a revised version of the PaW mechanism. See also Refs. {{cite:c8b45eaa7f366e30514b3fdd692606cc2135d5a7}}, {{cite:8f55b0ac6512867882c27bb45ce409b298f504d3}}, {{cite:2019323c0069c4808aaa168dc39e17b6d0964a1c}} for the prospects of experimental realization of quantum time.
| i | ca38119ba5bdaafc29ff211a45f0af7e |
We compare our methods to various competitive baselines, including BitFit {{cite:e1fda4068338a6ce682bd27f963e5e5f2c4c9990}}, VPT-Shallow {{cite:cb88f30cafe2c3a5268ed60ac22555cd3de8312a}}, VPT-Deep {{cite:cb88f30cafe2c3a5268ed60ac22555cd3de8312a}}, Adapter {{cite:105732d28330f4224cd9a134e867a9d054a65d09}}, {{cite:537fa0887c2927c1b4fb94a462b11accbaacfab5}}, AdapterFormer {{cite:0ced3735fa35423ca1b6372ba471f58dac1b797d}}, LoRA {{cite:b802258c054d04581ec40feda82377e877a1a038}}, and current SOTA method NOAH {{cite:5b540bcb3e8f8beb5954bff74aedad08b32af209}}. Following {{cite:5b540bcb3e8f8beb5954bff74aedad08b32af209}}, the hidden dimension {{formula:633b2816-9a8b-4d5b-afd9-803539e181ef}} of Adapter and AdaptFormer and the rank {{formula:353f3ff5-a980-474d-b346-dde155fcd1de}} of LoRA are all set to 8. The prompt length {{formula:0ec6a2a2-ffb6-40ca-8453-314fed97fa1c}} of VPT follows the recipes in the original paper. We also report the results of two traditional transfer learning methods: Full fine-tuning, which updates all parameters on downstream tasks, and Linear probing, which learns a linear classification head on the pre-trained backbone.
| m | 6f722541435fe205714f5fcaf1b954dd |
In Section REF , we present a surprising result: finetuning converged BASIC checkpoints on more ImageNet labeled data leads to worse robustness results. The metric for robustness in Section REF is the average top-1 accuracy of the finetuned models on 5 robustness benchmarks derived from ImageNet {{cite:cf510bc681074ca25d6879150561f74b85211e27}}, {{cite:6c874c736adcb05c95c0ac74afce83d68da57aee}}, {{cite:b51c3996e0ba19e7f9a16358d32f4066afd92da2}}, {{cite:c0f1a1de22cb5a2606dfff6ae115aa29f5d065d7}}, {{cite:b4a71d76452a27e05aa66e6bdd8e8bf915ac3863}}. It turns out that each of these benchmarks can demonstrate slightly different results for the finetuned models. Here, we discuss such benchmarks.
| d | 444a36d80225da9ac4bd73f4a13824a2 |
The purpose of this study was to investigate the applicability and potential advantages of adversarially robust models in the field of medical imaging.
A limitation of deploying such models in clinics is a potential performance degradation as compared to conventionally trained models that has been found by other research groups {{cite:1760e522b97b308c6306d4859cc4fc21864b48e0}}.
In our experiments shown in Fig. REF , however, we found that this effect appears almost negligible when training the models on large image data sets (Table: luna,Table: knee,Table: chexpert) and when applying dual-batch norms, i.e., no significant difference in the AUC was found between the standard model and the adversarially trained model with dual batch norms.
Furthermore, we have validated that robust models can generalize well on external datasets by employing 22,433 X-rays from the ChestX-ray8 dataset, that had not been part of the training process and originated from a different institution.
Most likely, the reason that other groups had found significant differences between the performance of standard models and adversarially trained models is the use of a single batch norm in adversarial training:
we consistently found in all our experiments, that to achieve the best results in adversarial training, it was necessary to employ separate batch norms for real and adversarial examples.
By using dual batch norms, our adversarially trained model achieved state-of-the-art results on thoracic pathology detection {{cite:267d377cd9291c04f709d966a61da1238ac29d17}}.
| d | 3917dabaabe8da606895f07008b720cd |
We are primarily concerned with the problem of learning general nonlinear SSMs. The aim is to find
a model that can adaptively increase its complexity when more data is
available. To this effect, we employ a Bayesian nonparametric model for the
dynamics (REF ). This provides a flexible model that is not constrained by any limiting
assumptions caused by postulating a particular functional form. More specifically, we place a
Gaussian process (GP) prior {{cite:381606407a4be5ad6ea0606ec8e00b51e5392a4c}} over the unknown function {{formula:9dfc9b7c-d320-431a-964a-f4fe2e9200a7}} . The resulting model is a generalization of the standard parametric SSM.
The functional form of the observation model {{formula:ceb5f5d5-ee28-44a5-a650-0272ebfdbfc8}} is assumed
to be known, possibly parameterized by a finite dimensional parameter. This is often a natural assumption, for instance in engineering applications where {{formula:7f967f46-01af-4dc9-888d-82bc01b3e9e0}} corresponds to a sensor model
– we typically know what the sensors are measuring, at least up to some unknown parameters.
Furthermore, using too flexible models for both {{formula:a0cecdea-761b-4b53-b25b-9ac21949fa21}} and {{formula:050b7b61-b62a-48eb-9da1-34b32f102e2c}} can result in problems of non-identifiability.
| i | ab1186fee53cb39497cdec90872880c8 |
Lossy kernelization stems from parameterized complexity, a branch in theoretical computer science that studies complexity of problems as functions of multiple parameters of the input or output {{cite:b38d7ae8d23ee8d618305a2d73eb3ac543c2a3e7}}.
A central notion in parameterized complexity is kernelization, which is a generic technique for designing efficient algorithms availing a polynomial time preprocessing step that transforms a “large” instance of a problem into a smaller, equivalent instance. Naturally, the preprocessing step is called the kernelization algorithm and the smaller instance is called the kernel. One limitation of the classical kernelization technique is that kernels can only analyze “lossless” preprocessing, in the sense that a kernel must be equivalent to the original instance. This is why most of the interesting models of problems arising from machine learning, e.g., clustering, are intractable from the perspective of kernelization. Lossy or approximate kernelization is a successful attempt of combining kernelization with approximation algorithms. Informally, in lossy kernelization, given an instance of the problem and a parameter, we would like the kernelization algorithm to output a reduced instance of size polynomial in the parameter; however the notion of equivalence is relaxed in the following way. Given a {{formula:d4a5d8b9-3202-4e69-a7ab-377935763e54}} -approximate solution (i.e., one with the cost within {{formula:ea76606e-a091-46e5-9b57-d7b7ec55b5d0}} -factor of the optimal cost) to the reduced instance, it should be possible to produce in polynomial time an
{{formula:30e06bc7-c020-4480-835e-3a7f16ede430}} -approximate solution to the original instance. The factor {{formula:e2b34fc6-1396-490f-bbb3-e797143e8a3e}} is the loss incurred while going from reduced instance to the original instance.
The notion of lossy kernelization was introduced by Lokshtanov et al. in {{cite:dd9262169d3b889a25940a8d89c03fdbcf03d5a1}}.
However, most of the developments of lossy kernelization up to now are in graph algorithms
{{cite:a43733cdc5daffe342a9ead0c863d968197ae41c}}, {{cite:1497278df9192c86322f4e1cedd67289b7177df4}}, {{cite:79a4625dcdac065e293edd458ac2f2ae600f7c24}}, {{cite:a7d745beb56b514159e94a01d2a4c429162055e0}}, {{cite:f0e9223c6bc2d9406886bd8252ad91570d4a7f68}}, see also {{cite:271980417855055f1a9f2fc12a95a3d65c17b143}} for an overview.
| i | 677b14a9e6cf5e3d300f36adeb162d9f |
However, modeling conductor motion still has several challenges. First, the conductor motion is highly complicated because it conveys various types of information, including tempo, strength, and emotion. Meanwhile, the generated motion should be closely synchronized with music. Moreover, because of different conducting styles, mapping music to conductor motion is a one-to-many task, which is difficult to learn by standard mean squared error (MSE) regression.
In this demo, based on the constructed dataset, we propose the VirtualConductor system to tackle the above difficulties. We use a combination of MSE loss, pose perceptual loss, and adversarial loss to train the motion generator. In this way, the generated motion can be simultaneously diverse, plausible, and synchronized to music. Finally, by combining 3D animation rendering and pose transfer {{cite:57212952b9b72a5249e24629b120f0aa56ae7990}} module, the system can generate conducting video from given music and a single user's image. In the following sections, we will introduce our system in detail.
{{figure:b89cb7cc-4871-4f46-a2bf-a08d642a30c1}} | i | 425e8dbe9b1c60c2a84ab5f03fc57943 |
In this section we adapt Theorems REF and REF to two
different asymptotic regimes when the temperature becomes large.
In the first regime we fix the chemical potential {{formula:f7a0473d-d072-4e5f-9c3c-985dc94f9f5d}} ,
which is reasonable since we work in the grand-canonical formalism
{{cite:c105c395c892e4527280434eac21dbb3ea318b24}}, {{cite:1aad963d4655d76d367ff39153a157e11829916f}}. In the second regime we fix the particle density.
This is often the physically more relevant case
and this will be discussed in more detail after presenting the results.
As above, {{formula:dc5b1722-ced1-4ad1-bca0-cdc51a989268}} .
| r | e42083ce8138d12fba5e920a17c54bdd |
A key aim of next generation experiments is to reveal the nature of cosmological electroweak symmetry breaking. It is expected that future colliders could definitively rule out or confirm a strong first order electroweak phase transition {{cite:0b0bd56ffe779ab0686f642b101c38b29f1192c3}}, {{cite:24c0db622cb2774825e3d2fc48833b112b7edf1c}}, {{cite:2beddfc39faf326f5f6698289558acf25b60224c}}, {{cite:c571fa5e7923c9336e0a0f8f1c198f52b65909cb}}. This departure from thermal equilibrum could supply one of the necessary ingredients for baryogenesis, explaining why there is more matter than anti-matter {{cite:30b16f56817b74c5cad0124d873e166e372c9bf2}}, {{cite:b593369c3de17d9733bd3ece8c394ac622c6e105}}, {{cite:a6320e2105ae4b1c27ee71674372ca1d2a4ef4a8}}, {{cite:68094a73da020bef171732f94a974f7bd59d1a3b}}, {{cite:b6b9df5acadb83b552a353d89c9aa407b235ab3d}}, and produce a stochastic gravitational wave background {{cite:2beddfc39faf326f5f6698289558acf25b60224c}}, {{cite:a78816edbbf9f2e46788dccfcfb112f28acc8e36}}, {{cite:3a848673a700c239117f8a279e1824dcbfb1e0f1}}, {{cite:fa71902cc5b5e67e3b5d8d21d11dcfb921d5ead3}}, {{cite:52b3c8203b4d94aa99710c520ff3e3dd30d03317}}, {{cite:5606ef84807b867f537d58ac7ea676aba346dec4}}, {{cite:363f296a55dc2fb6f2fc818e7fdb0f23ab4c3f26}}, {{cite:e435d19961355dbb567a3a1357b35e61646069d4}}, {{cite:4f64e8daf2c767ce40520b9c6d3209dfa656ccf4}}, {{cite:b85443d04252fd684109578bf4b192c321415ae1}}, {{cite:5141f9b9f1ec4575e6b558456289fe61ce569fcf}}, {{cite:855ac09c25c194690ee11114a5afec1c861f16be}}, {{cite:d53ecaa619f4c8ca073c404640a708e301dd8b0f}}, {{cite:f6a5d5d0f401e79a414b315b8133b1f845912ebe}}, {{cite:2dafabce8ac470780c2be5942302913864d412d8}}, {{cite:4b9af1a0325582da7af397702ee1730f7adba106}}, {{cite:6734f63576525b6428f214ab802a361dff8741d4}}, {{cite:8f5c49ec255b706b5ba309636b6a6880280591cf}}, {{cite:cd96897b214dda54d47ee7e5bdf771d6797faeec}}, {{cite:3444e9bb0a1627c1d3722c137daddfa248d8fe89}}, {{cite:a25fea684f5b16a1e79d5bc839174a3d0a531386}}, {{cite:047708f137f02307d8349f80c74b5463b042d4a6}}, {{cite:dd365b0d3f484c7d6ac6288c4c9d2d768a6bd208}}, {{cite:5ca7d33606bdd819cf7256a6962a3c31a8953273}}, {{cite:a4f33e1f791d1346753aa422cea19db577d9c665}}, {{cite:ac2cda0af1f87c2c950b3b93477db1b4627ac9a8}}, {{cite:2f2eebc7e6ee4fa3000851296a92929702ea8ec1}} that can be measured by LISA {{cite:b84174ad96271971f45135e889ddee4a82358e22}} and other experiments in the mHz to kHz frequency range {{cite:fdfa1471260270bc216204513283ca1337ae7add}}, {{cite:6000547c507e871aa1308232346d6d7e1695edf0}}, {{cite:20743a5e6bc7bc6a92f3a4d45127c993b8ab5f23}}, {{cite:0a24dee3b23b94827bcfacf5cf26d7758941e912}}, {{cite:b573672711639d5f9214c23cc080b29e4fcb208d}}, {{cite:280e6bdd616e17b0decdda03c26ab2f24cdd7c74}}. Besides this, strong phase transitions can appear in hidden sectors {{cite:3b2ca5cfa5e9f8eb50fa77251fe4a262140d9b37}}, {{cite:9aac7053a52d3ca9e17666a9ff7511b042cdc96f}}, {{cite:b92bb9577553040d159145ba1dfaa26a9c601af8}}, {{cite:5b19256aefb89dcb4898ce02a849010f289c2416}}, {{cite:53a3c8cb64759cd221904f463e1fb448b6b6f504}}, {{cite:bf39156c70fda28f575c29c48709712cb60fc891}}, {{cite:517564a5d049a7e1b25b4605a643a5546f4e1eae}}, {{cite:73f35b464b427a29c69f6ef23045872ff722d281}}, {{cite:8b47945a698c5f988bfe2d7d85c96deaf5cc7990}}, {{cite:b88ff4303366520d8cc833a52f2bc31e6c71871f}}, {{cite:13d931b3bc4ea9a217802d4c1003717c6d489459}}, symmetry breaking chains in grand unified gauge theories {{cite:376db879af3a73c25acc5729145309b20b83e465}}, {{cite:b4f23035fe0b3207251995912d41d26207380665}}, {{cite:ab15456451ba29731aa181d376438f91d5a806cb}}, {{cite:a0b790eea0f57cafe1e7f17301a90e2ff2ea64f0}}, {{cite:6cd55a42d3619423bbfa6a386fcf9c8deaf22622}} and any number of other motivated scenarios {{cite:c5659192886884824c13ac9e7648466ef3dd22a2}}. In all cases, a proper treatment of perturbation theory is needed in order to make the theory predictive.
| i | 018cf26a64944cad12047a7d364d37ff |
We study three geometric operations for Legendrian surfaces in 5-dimensional contact manifolds. These are Legendrian isotopies {{cite:c7e7c17542ee37cf01a67e24e0958d30ab2c4025}}, {{cite:7b472395da313665f282148beee7cd16cb6a26a4}}, {{cite:a7eaf111509345d400e26b2b0a2cb12b33f3e767}}, exact Lagrangian cobordisms {{cite:0327ce4269e5b3f9c3909fd38acea550c2b33498}}, {{cite:9066c1ba3615c854ab8aae3f72431268169127eb}}, {{cite:7d29611bad893f60daaa8b81bd8e74d59317bba5}}, and Legendrian mutations, which we define in Section . Lagrangian cobordisms of indices 1 and 2 correspond to Legendrian 0- and 1-surgeries. We establish a correspondence between each of these three types of geometric operations and the combinatorics of {{formula:3678c0b4-efc0-4c80-a81a-8ebd3ea54a6d}} -graphs. In addition, we describe a combinatorial stabilization of an {{formula:4d98f406-d56c-4b5f-a0ab-bee11842506a}} -graph, which can be understood as a five-dimensional analogue of the Markov stabilization of a Legendrian braid {{cite:50be6012b5b5b05d37fcbd80d8a1f713c59d4a03}}, {{cite:b9bd8027631f952ea2d32b8117fa98c71a2e3c9a}}. Part of these results are summarized in the following two theorems (see Section for details), which are developed in the text:
| r | 0e70ddece41d6343d22b6b805eadf9b0 |
In order to obtain it, we need the quantitative version of the isoperimetric inequality proved in {{cite:cc3cb1a7cd2a30de64c953bcc5c3fb3a4e1607f4}}
{{formula:1e36e3f8-5605-4db1-a74c-9fe17163da52}}
| r | 7730a0fad7e8aab01ed706d4744fc8b4 |
Let us review {{cite:837e2d4d9d9131078d7e03719e8c81b2076b7563}}, which shows
{{formula:fdfd1ea5-0230-4954-b13d-8650605c9ace}}
| r | ffd3c6de1b53bb48e45d5ed4cd91e9cf |
Superpixels can be defined as groupings of perceptually similar pixels to create a meaningful image with fewer primitive elements for processing. The term coined by Ren and Malik in Learning a Classification Model for Segmentation set out to solve the problem that as pixels are not natural entities, they are meaningless as representations of images {{cite:e2fdadb9032d196cac4dd3f8dca8f8b0681ca2e5}}. Superpixels have been used to segment medical images as they capture similar subregions in images such as tumours {{cite:4c0d373b20b822f907c20728fe461faa5052e5b1}}, {{cite:d24a61e041917f112e517e0a45fd6f520d762817}}.
| i | f275f38347c95f2e066b8441c104e1d3 |
In addition, there is an evolving line of work on the early learning phenomenon and early stopping methods.
{{cite:871d1289118100aa01b328e1f325b3119a1e036c}} observe the dimensionality compression and expansion stages of training a deep neural network, and propose an adaptive loss function according to the subspace dimensionality during training.
{{cite:5116e2515cf7852defe96e3da6c513be4abc8253}} propose Co-teaching, where two networks select for each other the training instances to learn from. However, the selected instances typically have low losses, and these easy instances may not help the network generalize to unseen data.
{{cite:09d1d7404a1671a6b54396794cc6d70b1c845c13}} propose to train a network with early stopping, and then resume the training using only instances that are correctly classified. Their method suffers from the same drawbacks as {{cite:5116e2515cf7852defe96e3da6c513be4abc8253}}.
Theoretically, {{cite:94b98574e586dd50ca726f57750de0c6fe8d076a}} show that when training an over-parameterized network, first-order early stopping methods are provably robust to noisy labels. However, in practice, we observe that for a network trained with cross entropy loss, its best test accuracy is still inferior to that of other robust methods (for example, see Figure REF ). Simply using early stopping does not yield optimal performance.
{{cite:e5f16c03d704cc1a10008b772ca159ae46b525a6}} prove that early learning and memorization occur even in high-dimensional linear models, and design a regularization term that magnifies the gradients of clean instances and diminishes the gradients of noisy instances.
| i | 5114fbb21d215860c957dcec3caee7b7 |
LINE & GAE: LINE {{cite:e1ac09ce72089d431d620702c8c4fbb6985f5446}} and GAE {{cite:1369df7b479b2544aad35b1afac158f9674b6d32}} are two typical single-view clustering methods.
Baselines: RMSC {{cite:65cfa4adb61f9bb4c69cbe9fb88149195e2d7f32}}, PMNE {{cite:8c2f8bf606045a44dc26ead56c966470bf436db8}}, SwMC {{cite:60c679071bf49efa9576454a15ad59bdaa5e5a8e}} and MNE {{cite:b6e24ffc553bd75516a4415f9778f560e4440978}} are four classical multi-view clustering methods. All of them are graph embedding models, except RMSC is a robust spectral clustering model.
SOTAs: O2MAC {{cite:d912240b4b0b1a2317cdebe5922caa6a956df392}} and MAGCN {{cite:e080f9fb7d369eb11bbfd854b374d65fe022ede1}} are the methods that learn from both attribute features and structural information. In addition, graph filter-based MGC methods, like MvAGC {{cite:e1fc7475e2350fe4733215b622e7b994ee92f3a8}} and MCGC {{cite:bd545715cf204aeb817b108d0d433c9048827dea}}, are included. COMPLETER {{cite:a39ec6b2b1bbfb2b60b28d5dac9f353eef7577da}} and MVGRL {{cite:30961fed810d120f37aa0d285a412f7d23f612e8}} are contrastive learning methods to learn a common representation for clustering.
| m | 87fc54ac3d58509bda8cfe84dcbc0680 |
At {{formula:f77b1885-a229-41b4-8dba-2722276fd1c8}} nonperturbative magnetic screening effects arise {{cite:7a735033a92af96a9b81a3710da85c858961b195}}, {{cite:3354339b30601a3425f453a84d2e54f6cbda57cb}}, {{cite:216e15bc3dc161a463e2e945ec40dc6a9035dc94}}.
Kajantie et al {{cite:bad174b234be1e10b532f8340be9dbe8ecee49fc}} were able to calculate the {{formula:48bfce80-29d3-4d4d-b37d-ea14ce719582}} perturbative terms and found both {{formula:10d83813-e76c-41d3-995e-5f6af4515758}} and {{formula:f601b11a-6f3a-4684-badd-32b3e7ce9bdb}} . A convenient reference that discusses all the results is Sec. 8.4 of Kapusta and Gale {{cite:8e148ee70735e7fc6dd35144150f29086573f024}}.
| r | c795ba4a87c894be90e65f15c5420b46 |
He et al. 2019 {{cite:556ba596ee0c1fdfd42e50aac88744c35beaaef1}} CNN Epilepsy Five Classes: Healthy (A, B), Seizure Interictal (C, D), and Seizure Ictal (E) From Andrzejak et al. {{cite:679219f58a4afe9b829b1e90079bfe77e3a88236}}, 10 Participants (5 Healthy and 5 Epileptic Patients)
| d | 8d1086c4da25de36260a6b1c7f0a79af |
The study of shock waves is an important issue in the theory of both inviscid and viscous conservation laws, such as the compressible Euler equations and N-S equations in gas dynamics.
We first overview several remarkable works in one dimension.
The shock stability for hyperbolic conservation laws has been done by many articles such as {{cite:fdbe60a733764cc5647dea69db755fafba1623bf}}, {{cite:7eac19b0b29287c9339cc133bb273b801c81323c}}.
In the viscous case, based on a comparison principle, the study was initiated by {{cite:fdbe60a733764cc5647dea69db755fafba1623bf}} for the scalar conservation laws. Then {{cite:df5f656718d7f30b3922983c536b4835f07c1858}}, {{cite:848e7dbda04fc1b01e4221d4883739545b224a31}} extended the stability results of viscous shocks to the systems by using basic energy methods, provided that the initial perturbations satisfy a zero-mass condition.
Without this condition, the problems with generic perturbations were solved by introducing additional diffusion waves and coupled diffusion waves propagating along the transverse characteristics; see {{cite:8f65c6db4cb6e3e837236f49147a66b3a5d78c4f}}, {{cite:115b6695a0458e23691822a12cc96915a4e80367}} for the uniformly parabolic systems.
And {{cite:306f9cec2d2a9ab05ee36489e87d7cabc36314eb}}, {{cite:8ac87a735cf3685ae8866d0dae5ce2c59512ce99}} made more subtle analysis to study some physical models including the compressible N-S equations. We also refer to {{cite:27a1ac4028c29a8e8ab78446718fa5afc52ea003}}, {{cite:809a3ffa7f62282a63ef80200b78b6dc41911ddc}} and the references therein for the spectral stability of viscous shocks, where the shock-strength is allowed to be large, and to {{cite:c989650ffb1f0e9b5805d912ec11974e4e59d79e}}, {{cite:c4a84e7ceff1468a793e56ed6335c3121e931318}}, {{cite:3937bcdad4106d498b1ac22a47ff0791c0a73811}} for the nonlinear shock stability, which can be derived from the spectral stability in some appropriate senses.
| i | 7e9476f2fafda08183295cc14bef1795 |
We use the test set of MatterPort3D {{cite:9363f2e5fc7a0f331d23bfe2196b2d8bac7bbcaa}} to evaluate the effectiveness of our method in the high-resolution structure recovery. MatterPort3D images tested in this paper are consisted of 1,965 indoor images in 1280{{formula:ad64faf0-7615-4e7c-930a-934ce600ac81}} 1024. We resized them into 1024{{formula:39778bb6-d29a-4886-be13-94ea2c48a116}} 1024 as shown in Fig. REF . We provide some qualitative results of our method and LaMa compared on MatterPort3D in Fig. REF . For these structural images, our results enjoy better structures.
| r | f64e3210d64716cb308b8643714da8a1 |
This section defines our experimental setup, then proceeds to present the results. First, we test SKDCGN – as defined in the [sec:approach]Approach section – on both ImageNet-1k and MNIST (Section REF ), and based on the observed findings we make some changes to the proposed architecture to improve the quality of the results (Section REF ). Due to computational constraints we test these improvements on a smaller dataset, namely the double-colored variant of MNIST {{cite:85d5a41877e6eb12c754ccda20d4199a3c7b2ebf}}. Finally, as an additional contribution, we conduct a thorough study on the composition mechanism, to gain a better understanding of how each mechanism influences the classification accuracy of an invariant classifier. We present the results of such a study in Section REF .
| r | 5767311f821331cdc11185a900dc1ba1 |
Con-Reg: Con-Reg aims at regularizing the embedding space so that its layout becomes more similar to the feature space of the pre-trained feature {{formula:c6029fca-4bd5-427a-84c1-1d2533670142}} . To do so, we utilize the features extracted from the audio and add an extra loss term {{formula:8c9ac29b-4146-4a33-92f7-3c7ab6852099}} based on cosine distancePilot experiments using {{formula:9c7bdb35-300e-415f-9016-eda56d172be5}} as the distance function did not lead to competitive results. to minimize the distance between embeddings and pre-trained features:
{{formula:21505001-40ee-4d16-bbc7-0814921a6ea1}}
where {{formula:20e695ab-492d-4785-b99c-36c92dfcf959}} represents a 1D CNN with kernel size [1] {{cite:d41ce26b39b7c05010e3ff631a328d4321f22888}}
to transform the feature dimensionality {{formula:967d71df-ef59-43db-a1d9-988c910bd6df}} to match the embedding dimensionality, allowing us to compute the cosine distance between {{formula:2abb42bc-526b-40e0-aa9c-9f666356509e}} and {{formula:b0d971a7-c75a-4066-8605-204fbaf54132}} .
Dis-Reg: Dis-Reg is a distance-based regularization. Similar to Con-Reg, the embedding space is regularized with an additional loss. In this case, however, the additional loss term {{formula:15ccdf2b-e2a5-4659-9193-0e000167ffb7}} aims at forcing the distances between pairs of embedding vectors to be similar to the distance of corresponding pairs of pre-trained features:
{{formula:3bb0c96a-b108-4b66-868e-a7ecf6561b8d}}
where {{formula:df47790c-cbb8-46a7-86ca-77af615d5dd0}} represents the cosine distance between two embeddings from samples {{formula:573bf281-e5e2-41e3-acc0-f057e6797f50}} and {{formula:c6279073-ae3a-44ed-bd0a-69e8a02b6822}} ({{formula:d90a1353-1ef1-4a4d-8948-a6493023438f}} ) or the distance of two corresponding learned features, respectively.
| m | 6fd958a01daf4408dff25c94e82159e0 |
This view of metal-poor GCs being accreted and metal-rich GCs forming in-situ
presents a problem: the stars in the thin disc have higher metallicities than these GCs
{{cite:5c7d9eacf01f9b01223e6721b7f5edd33cc9edd7}}, {{cite:9383fc9fcecffe9499f8679583bfa605d1d88d9c}}, {{cite:482d21cf3c8859261004a1d2730a37faae07bced}}, {{cite:f588b2c58e643de9953704df14a5fa84aaa25df5}}, {{cite:146339a075d60390d7684af84e413c90498d02af}}. If the GCs were formed from
the same material, they should have similar metallicities. One possible solution is that the metal-rich
gas in the MW was mixed with another source, such as an accreting metal-poor dwarf galaxy, which the GCs
were then formed from. This scenario was studied by {{cite:6f538482722a30ae426bac0cff2b1d2974367d4c}}, who found that this process
would form clusters of approximately [Fe/H] = -0.58, and that GCs formed by the dwarf before the merger
would average [Fe/H] = -1.45. This is remarkably close to the -0.6 and -1.6 peaks of the MW clusters and
may indicate that the metal-rich and metal-poor GCs shared an origin in the same accreting dwarfs. The
gas would experience pressure where the clusters would not and be pulled into the rough plane of the disc,
explaining why most metal-rich GCs orbit with a non-zero inclination (Fig. REF ).
| d | a8bd109263d613c374b19964f4c4a168 |
The main contribution of this paper is to introduce a novel model-based deep reinforcement learning (RL) based algorithm for DSS between LTE and NR. The main scope of the proposed scheme is planning in the time domain whereby the controller distributes the communication resources dynamically over time and frequency between LTE and NR at a subframe level while accounting for future network states over a specific time horizon. To enable an efficient planning, we propose a deep RL technique based on Monte Carlo Tree Search (MCTS) {{cite:c8671b497dcfa7b6066fb135c952b32b111ebe47}}. When a model of the environment is available, algorithms like AlphaZero {{cite:84d3f5ac233f04921d04c833bd04efb994ab2c1c}} have been used with great success. However, in the case of DSS, the LTE and NR schedulers are part of the environment, and these are not easily modelled. Inspired by the MuZero work {{cite:b45d322cb59312d765138c8484d1bd1b0a9a3a8c}}, we use a learned model of the environment for planning in the time domain. When applied iteratively, the proposed solution predicts the quantities most directly relevant to planning, i.e., the reward, the action probabilities, and the value for each state. This in turn enables the controller to predict a sequence of future states of the wireless network by simulating hypothetical communication resource assignments over time starting from the current network state and evaluating a reward function for each hypothetical communication resource assignment over the time window. As such, the communication resources in the current subframe are assigned based on the simulated hypothetical BW split action associated with maximized reward over the time window. To our best knowledge, this is the first work that exploits the framework of deep RL for DSS between 4G and 5G systems. Simulation results show that the proposed approach improves quality of service in terms of latency. Results also show that the proposed algorithm results in gain in different scenarios by accounting for several features while planning in the time domain, such as multimedia broadcast single frequency network (MBSFN) subframes and diverse user service requirements.
| i | ff1ea5667324bbdf47c1f67c7ea0aef0 |
Without parametric assumptions, ITE estimation is not feasible {{cite:8f7227026496278e7bbdecce7440b09612726362}}. We focus on linear models in particular, since they are important in developing theory. E.g., in the literature on optimal designs in active learning, much of the foundational theory is built around linear models. Identifying estimators based on linearity assumptions is an active area of study in the causal inference literature {{cite:69dd2c3e55f60d4f0b5fa38367b76f5098c03e5d}}, {{cite:5fdef171ae0aadcdb8688ab2aa399ba18b300dcc}}.
| i | 1332a6307bf4d3b10c1eb0bf512ffe8c |
The SSIM, introduced in {{cite:8fdd56afcefacdd233ce0b9552482f79d7e9071b}}, enjoys widespread use across a number of disciplines. While some recent works cast doubt on the popular notion that the SSIM truly represents human visual perception (e.g., {{cite:52c6e4caaab065d214c29229ed8cd011bcb7bb80}}, {{cite:5dd447421c25ea627b677895530e115cefb6b5e2}}), it nevertheless remains very popular in practice (due in large part to its simplicity) {{cite:1aaaf64ae251a07a0770db9c980e73c8c303eaea}}
and is a useful statistical measure.
The SSIM is the product of three factors that are intended to represent luminance, contrast,
and structure.
Consider comparing two images {{formula:4e15280d-519d-4969-a701-1889a33aea2d}} and {{formula:18161fa6-4e0b-417c-ba19-8e3acaa77260}} , each with {{formula:bb08dcb7-8da1-4b5c-9b20-0b4027a48d79}} pixel values. The SSIM is computed by first calculating so-called per-pixel SSIM values comparing local patches (or windows) of the images. Let {{formula:f4565bd2-43d7-4c7f-ad0a-81a830d8360d}} and {{formula:a226a5f7-fed3-46ad-b487-d903e3631119}} be local image patches (i.e., vectors) taken from the same location in {{formula:662ef5c5-6b06-4b98-b669-e21e592a5e07}} and {{formula:5829a069-4019-47e8-8ee4-97b3e12f5f97}} , respectively. Subscript {{formula:fc4f0011-e396-459b-b949-66998440a934}} indicates the pixel index in {{formula:aa2a83ac-beda-4690-9f13-270ff1fab5a0}} and {{formula:211bf9cd-72ec-4173-85e6-e80ceaa240b8}} that is at the center of the local window ({{formula:51520942-83e8-472e-b9fa-e29149e4cf7b}} ). And, let {{formula:f0f74d65-5f16-4c29-9a0f-828d1269e52e}} be the number of pixels in the local window. Then, in the local window centered at pixel {{formula:7a3147a9-fa78-4b79-99ec-8631fbb99f6f}} with vectors {{formula:4dd0a684-6d9d-4d06-b5f9-633ff6fe7fa8}} and {{formula:1026fbba-40b1-4202-bdb0-616aff3236b0}} containing
{{formula:1736cbd2-0427-4fa7-9334-96e6106b25cd}} pixel values, the per-pixel SSIM value is
{{formula:200fa9a4-d93d-4983-bb66-6c90284a542b}}
| m | 7b1ae9d4ef21e5baf6941d50f13cb7ca |
Previous work on the development of online SNN learning algorithms includes the work of e-prop {{cite:6f5a95aff7015d58a3004c42101c48cae24e6e87}}, which is a plasticity rule that was mathematically derived from BPTT, where a learning signal defined by a given loss function over a task is projected to all neurons in the SNN using random feedback connections. This projected feedback interacts with an eligibility trace that accumulates the BPTT plasticity approximation to update synaptic weights. E-prop was demonstrated to be competitive with BPTT on several temporal learning benchmarks. In ref. {{cite:34b0713672deaa2230d024d6feaba7369b97d3bc}}, a method called natural e-prop is introduced, which uses the plasticity dynamics of e-prop and learns a neuromodulatory signal toward solving several one-shot learning challenges. Another online learning algorithms for SNNs is Surrogate-gradient Online Error triggered Learning (SOEL) {{cite:5fd314cfc77cd7a46ed4eafb04a5ba6b77ebe57b}}. SOEL calculates a global error signal and uses surrogate gradient descent to create a plasticity-like rule for updating the network synapses online. Works like e-prop and SOEL are not competing algorithms, but rather are complimentary with respect to this framework. The e.g. timing parameters, voltage parameters, and, the surrogate gradient parameters could be learned by gradient descent using these methods as the inner-loop optimization to produce an even more effective version of the existing algorithm. There have also been many previous contributions toward neuromodulated plasticity in non-spiking Artificial Neural Networks (ANNs) {{cite:3579fc32f51ffe0247203a87579cb2a5f3e10552}}, {{cite:b7280ed2115d388e217aad489296b3f7eeaf6ae5}}, {{cite:56aa05b2c4dfb2a2ad03f31c77ca58cea3ac495a}}, {{cite:21802916ba7171e99b467d9bb9f4d4cbf7074729}}, {{cite:092731709cc5d5a9ce0249227551de49b6203a2e}}. However, plastic ANNs have been demonstrated to struggle maintaining functional stability across time due to their continuous nature which causes synapses to be in a constant state of change {{cite:f6dff1e434baf15a438190f8a5d075301cac7d27}}. The effect of this instability was shown to not disturb the performance as significantly in plastic SNNs as it did on plastic ANNs.
| d | 0f3e0a0a53954bcc78ee6958798c7095 |
Let {{formula:9fbb9e20-1e6a-4371-9f96-f0e7254ceecd}} and {{formula:c262f9e6-b214-48f9-bda0-f435e5a26afa}} and let {{formula:9e97ca8d-b66f-411b-b023-f1097fad950c}} denote the fine moduli space of principally polarized complex abelian varieties of dimension {{formula:4b0e04f2-7bcc-42a7-8312-54de875efc69}} and level {{formula:475dad6a-539c-4a74-a88e-8f96acdb55ee}} .
Let {{formula:5ea22960-b669-4629-a6cd-162f86423232}} be the universal abelian variety,
and {{formula:230fc84d-738d-4495-9f7d-d5079f949be1}} and {{formula:fdec2d16-a2b8-41d3-8ef8-8d16982509b1}} be any projective smooth
toroidal compactifications of {{formula:39078a0a-b592-486f-955a-653c3b0cfc64}} and
{{formula:3a1013b7-ebb2-405e-9f38-52e61b5f86c0}} , respectively, together with a map
{{formula:2d86e0fb-5a09-43d9-8d7a-d5653fc23427}}
extending {{formula:8fac6b75-4c6c-48f9-98f5-062d747b1e3a}} , as discussed for example in
{{cite:d66e277c7976a4989f6af7ffd8cd42e0692e8903}}. Let {{formula:aee9aa3f-8523-43d0-9464-00662fcb3349}} and let {{formula:9f4584d6-2837-4908-ae21-0e0968d64794}}
denote the line bundle of Siegel-Jacobi forms on {{formula:03b45421-77bc-4157-8d33-e817c2e346f2}} of
weight {{formula:28edb21d-31b8-4c5b-8594-b2280ac5ad55}} and index {{formula:066fdf07-9e7d-4101-95d5-8d4778e3a578}} . It is endowed with a
canonical smooth invariant hermitian metric {{formula:49d9d5f3-1cde-4f46-96eb-ac257937592e}} . The first
Chern form {{formula:0623945c-f95f-428e-bf6b-86133ac9e0f7}} is a semipositive {{formula:5523a1b7-3e99-47bb-b868-0d901696cdcc}} -form
on {{formula:383ccc2f-5434-4145-8020-5545845119c3}} .
| r | ae78ffc93ec778231680bd42c82b6cc8 |
These computations are all done at the level of the classical, as opposed to quantum, sigma model. This is in contradistinction to the twistor-string or ambitwistor string which generate amplitudes via quantum correlators (and requires supersymmetry). Clearly the twistor-strings of {{cite:cbed76145e222cae7aa587f72910d457f65138af}}, {{cite:4f7bee04d8bf48d82d229d0f75643fa40dc3cfb3}}, {{cite:c716b2b5f9a8dc3b44f28546f0bf0066612f9a16}} and 4d ambitwistor strings of {{cite:134dd6a21d5f9718b0add4d0fb23cff7a3d89d85}} can be similarly formulated as open string models, as above, even in terms of their gravity vertex operators. unlike conventional string theory. Perhaps more interesting would be to formulate the higher-dimensional ambitwistor models of {{cite:3ae17ebb38fe0c372408263b26d8ae23774ac252}} in this way, and to understand the underpinning semi-classical geometry.
| d | 8991bfd5d182372626eec41503807982 |
The proof of Lemma REF follows from Appendix A in {{cite:3bc6edc3e54ab354c39cd4708fa64f4b5b97a504}} with some modulations.
| r | d716f6a2920f04049cdb05eafc2916e6 |
where {{formula:2e2df46d-9c54-4cac-93d9-6201ef4c8e04}} , quantum number {{formula:14032a53-bc86-44d2-aa7e-69d327e6fa96}} is defined as {{formula:6ce31eac-196c-4c41-bdf1-63fed456c3e4}} , and {{formula:dfc5cc78-72ea-4b21-8e60-2a329788a2b9}} is the spherical Bessel function of the first kind {{cite:74028ecd19dab662d85871975daac06d2da9da8b}}.
| m | 13c90208935d57dc7a8d0808f761705b |
where {{formula:2d47fd70-7891-4a7f-9500-0e8d04448c87}} is the distance of the binary system from the Sun.
Since the average extinction
of the Galactic disk is {{formula:ae0c2ce4-48cb-47c0-8365-0f263e3b9c14}} {{cite:4b4219da54d56e29dda13fcf9eb74658597f1682}}, we adopt {{formula:bf60b127-508f-4afb-82f9-9f071ab72144}} .
To estimate the radial velocity semi-amplitude {{formula:57481bc7-8ec1-4292-9558-1f3408356997}} , the orbital inclination
of Be{{formula:069a7b5c-31e5-4203-91ef-cafebf6e2d68}} He binaries is assumed to distribute uniformly between 0 and {{formula:385c03a0-20d1-4662-aee0-4371f37c66f8}} .
From the BPS outcomes, we select all Be{{formula:666dbe06-600c-4212-ace6-24b8d80b0b34}} He binaries and record relevant parameters at each of the
evolutionary steps. The corresponding number of a specific type of binary can be evaluated by multiplying its birthrate
with the timestep.
{{figure:3b5469d3-2fde-4174-b235-ca575c75cb3d}}{{figure:80c234b9-2952-48c3-983c-70210832ee90}} | m | efae95c8db3c14134ce8d7f20b4eec12 |
Our formulation of semi-supervised learning sheds light on the working of current SSL methods. For example, the reference prior can automatically enforce consistency regularization of predictions across augmentations {{cite:eecb3b0c55932e7ad5f5f4ef173c82eb0c0fc0cf}}, {{cite:098f001710c66d3028e5cb3a1bbe7ae73953d55f}}, as we discuss in s:impl. Similarly, minimizing the entropy of predictions on unlabeled data, either explicitly {{cite:30043f72389fc927d02ac5c8e06308d19c7f813e}}, {{cite:332d5aad03d908d843ac4e00fac7309c05cd6c3e}} or using pseudo-labeling methods {{cite:92063b5045768f3c4676ffde735912c872223981}}, {{cite:4dcede569eab0e853e64fbd2d5339556ba3a34e0}}, is another popular technique. This is automatically achieved by the objective in eq:refssl. Disagreement-based methods {{cite:8eae24fb45239c15e9af73e475d4bac1972c1f8a}} employ multiple models and use confident models to soft-annotate unlabeled samples for others. Disagreements in our formulation are encouraged by the entropy {{formula:04bf37f9-80a8-420c-9843-522b70e258b1}} in eq:refssl. If {{formula:dc67a354-e47c-460b-aa01-76b8127393cb}} is uniform, which is encouraged by the reference prior objective, particles disagree strongly with each other.
| d | bbbc07d3e46430bf4bdc77503673795e |
With the four galaxies at the lowest redshifts one obtains the effective redshift {{formula:d0acf9ec-f9aa-4cc9-acc3-4dde3e30723e}} corresponding to the Hubble parameter value at the lowest redshift. Determining {{formula:1b20d23b-0783-4c5e-ac99-ff8e079c3995}} requires the determination of the derivative {{formula:57a46a92-5080-459b-a533-6eadf8331267}} . By fitting a straight line to the data using {{formula:941734ed-1313-45e9-9f75-a1c7053f2283}} minimization we identify the slope as the reciprocal derivative {{formula:ebac4aac-80f2-4c98-896f-71bdeb3d903b}} . Combining this with equation (REF ) yields the same central value as in {{cite:12ee0a8dbb366ae1cfcdae7c5615dd5ea2aa1f65}}, namely {{formula:11d9827d-3708-4679-80c6-8360834b2a64}} km/s/Mpc. However, using 12% uncertainties in the galaxy ages results in {{formula:783d5176-2556-477f-98c4-edc9ac399c47}} uncertainty in the Hubble parameter. It is also obtained when computing a weighted average of the first and second galaxy, and the third and fourth galaxy, and then calculating {{formula:44b6aaa7-14cb-44de-b152-144cf335e349}} with {{formula:4423d94f-4b06-4721-9f2f-479ea6fded43}} using these two weighted averages and regular uncertainty propagation. To obtain 10% uncertainty in {{formula:b69f5832-5980-4682-bc8e-6d76de3f3e49}} , as in {{cite:12ee0a8dbb366ae1cfcdae7c5615dd5ea2aa1f65}}, the age uncertainties must be lowered to {{formula:afff2626-52a5-4e13-bc90-59d8c7949274}} , i.e. a factor of ten.
| r | ffe1ca262d5447f4da3b5efc8a1a249f |
We evaluated the emotion recognition model using weighted accuracy (WA) and F1 score on each emotion.
Weighted accuracy, as used in {{cite:b7189cebe26f621f47e0af7f545d5dd7af60b306}}, is equivalent to the macro-average recall value.
We also averaged the metrics across all emotions to obtain an average WA and F1 score.
| m | e506bef953f6e1f3f68f2c557aab046a |
Consider the output follows Gaussian distribution. The noise scalar {{formula:fa94fb78-13dd-4d44-bac6-f3de7f961f2d}} is often fixed as part of the weight decay of neural networks. To capture aleatoric uncertainty with dependent data, we would tune the observation noise parameter based on maximum likelihood inference. Due to the minimization objective, the negative log-likelihood of the model is written as{{cite:d42241849909b0897e1a630089cc35c4ebf8aaee}}:
{{formula:9c7124cc-4c1e-4401-bd52-b26cc72ad49d}}
| m | 54458920fba920173957316d612833f2 |
Sentiment analysis has been approached across many domains, including products,
movie reviews and newspaper articles as well as social media (see e.g
{{cite:057ce2eea69e91ac195e3f200eb23750555b873f}} for a comprehensive overview). Typically, the methods employed
depend either on existing language resources (e.g. sentiment dictionaries or
ontologies) or on machine learning from annotated datasets. The former can
provide deep insight, but are somewhat inflexible in the face of the
non-standard and rapidly changing language used on OSNs, for which few suitable
linguistic resources currently exist. The latter are more scalable and can be
trained on relevant data (e.g. {{cite:dd5c8e6a75311a0b8060c4d19d55f054710a88e5}}), but generally depend
on large amounts of manual annotation (expensive and often problematic in terms
of accuracy) and in some cases the existence of grammatical resources for the
language and text domain in question (e.g. {{cite:21ab0e669669fd7ae21bca537b2e0d088f5450de}}). However, some
approaches leverage the existence of implicit labelling in the datasets
available (distant supervision), to avoid the necessity for manual
annotation: for example, user ratings provided with movie or product
reviews {{cite:4d445f3a2646b5e55289e2cc7198eac6e6b25ae8}}, {{cite:38305fd682fa47b1d09948bd22ad9b204f65420e}}); or
author conventions such as emoticons and hashtags on
OSNs {{cite:a190c983ff5995b2d9ef48f225718580d29c53eb}}, {{cite:55f17a06bd5ccac8dfa1fb0260b78e394a9c9344}}, {{cite:bc14fc65ad4d64c52dacbfd923ed3ba25f7b4975}}). Hybrid approaches also
exist, e.g. the use of predefined sentiment dictionaries with weights learned
from data (e.g. {{cite:d1c1ec34d5727fd6307d7a4ca8b1b2bdf54e0879}}).
| m | 683472e6db9546abc915e35eb0e57120 |
The introduction of pre-trained language models, such as BERT {{cite:bfd32f9e68dad1fffadc89c0b5102687d4d9d07a}} and Open-GPT {{cite:7ed7754fde3ab16231708cd6208370d68577824f}}, among many others, has brought tremendous progress to the NLP research and industrial communities. The contribution of these models can be categorized into two aspects. First, pre-trained language models allow modelers to achieve reasonable accuracy without the need an excessive amount of manually labeled data. This strategy is in contrast with the classical deep learning methods, which requires a multitude more data to reach comparable results. Second, for many NLP tasks, including but not limited to, SQuAD {{cite:b237e2f0a1aa0d477c8adf688dff5932687c4f7f}}, CoQA {{cite:c1f739d01929ee2fccfc45f1f20a6d317923e987}}, named entity recognition {{cite:66342301d05902551a23fb946b8d561d43fbd09c}}, Glue {{cite:7dfece67e943c439107e6acf9d769bfe7b52780b}}, machine translation {{cite:77ead7c6076245e78bd24feb75d3f34a357afe61}}, pre-trained model allows the creation of new state-of-art, given a reasonable amount of labelled data.
| i | 00495b8d5f4ea5167d26685e3dbeb0ae |
Since the development of deep learning, several excellent backbones (such as SegNet and U-Net) have been widely applied for image segmentation and can obtain satisfactory results {{cite:52af3b6549e1c0468264f1bfdd920331c5182e2d}}, {{cite:862e93bb4d894fa25a5aa88578bb5eb4c352375b}}.
The first 13-layer convolutional networks of VGG16 are applied in SegNet as an encoder, and SoftMax is applied for classification after the decoder.
U-Net is an end-to-end net of image segmentation with an encoder and a decoder.
It was designed for medical image segmentation, which meets the similar requirements of biovolume measurement as both of them are microscopic images, and the datasets are limited.
SegNet and U-Net train the yeast dataset for 60 epochs with a batch size of 8.
The CNN-based models can be trained independently without relying on feature engineering, and the models can obtain the expected results, showing strong generalization abilities.
The most-used pre-processing approach in deep learning is data augmentation to avoid overfitting and to increase generalization capabilities, but a limited pre-processing technique is used for denoising {{cite:2e03af5e721f24eeac44c6129b82906f81d635ea}}.
Here, SegNet and U-Net are end-to-end models trained without any pre-processing or pre-training.
The segmentation results of SegNet and U-Net are shown in Fig. REF .
The results show that U-Net has better performance for biovolume measurement, which means that concatenated operation of encoder and decoder can improve the precision of segmentation.
{{figure:ab5badd1-d5cc-4504-85c4-08a4cdadfa45}} | m | 9b92fbc2399582993db8698b5c0fb6c1 |
Remark 4 Observe that the feasible region {{formula:43e265c2-82a8-4feb-b33f-05c6cf340dc2}} of (MICP) is a rational polyhedron. From Corollary 17.1d of {{cite:453cf8e0a4e35db7fd28f630ace71584839295e2}}, there exists a feasible {{formula:bc9f2826-06ae-44d2-a497-d7dc03c95687}} whose size is polynomially bounded by the size of {{formula:f998b517-0f0c-4285-85d9-9045ee4538e3}} , and {{formula:44d96b3a-0f7e-4840-ad0c-76edba271e60}}{{formula:0bfac14a-6920-4565-b924-8ac32423192f}}
| r | d4e749ef170a00b73fef2cf7bea2285c |
In addition, the non-differentiable quantization function leads to zero-gradient problem during training. Although STE {{cite:e97f7b3aa602675f9df3319af87be13963985f3f}} can be employed, the approximation error is large when the bitwidth is low. DSQ {{cite:a3502f4467855262aca59b0c7d38cab452cc8a0b}} uses a series of hyperbolic tangent functions to gradually approach the staircase function. Despite this, the aforementioned methods process quantization of weights independently. Our proposed FAT tackles quantization with an explicit transform. It enables joint quantization from a holistic view during feed-forward, and informative gradient during backpropagation.
| m | 937b9a358f3d13d81955bf9f5434d887 |
The work on StyleGAN {{cite:d4b4dbc0db905b18267e099f49db6258fc98d3b8}} revealed certain input conditions that contributed to the generation of super realistic images, improving upon the blurry or distorted images generated by previous works. These conditions are a) images in the dataset should be of similar zoom ratio; b) the input to the GAN should be simple; c) diversity of the data should be balanced.
In our initial experiments with DCGAN {{cite:1afc8050fb0c96d132e37008c3617e31d5b21578}}, ProgressiveGAN {{cite:431c71b6fa210560ab564398a9765cc9a50f1bfd}}, CycleGAN {{cite:a59b057fb01292a49d0772b394d51a6ffc245010}}, and StyleGAN, we observed that if we pass the whole body with the head attached, then the results are blurry and the GAN fails to generate properly. In our experiments we made sure that the dataset is clean enough to have similar zoom ratio on the subject, images are diverse, and we removed any complex distractions, such as the head, before passing to the Poly-GAN inputs.
| m | f131fc448dfe74ea598bbe6603eddfd6 |
In Table REF , we investigate whether the proposed layer-wise attention pooling of language models performs better in contrastive learning. The experiment compares performance by training on language models with three training objectives. All results evaluate sentence embeddings on all STS tasks. Equation REF is basic supervised learning proposed by {{cite:9f817198d2f5decd884bc202f3c150b0e42e693b}}. And, Equations REF and REF are unsupervised, supervised learning proposed by {{cite:79e3936f384140e5b20aacbe9b85112eda92f2b1}}. However, in this paper, we could not experiment with the same parameters due to hardware. Therefore, as specified in Table REF of the Appendix, there is a difference from the original performance because it learns by choosing a low mini-batch size. {{formula:af3ad619-06ec-4f58-a3a2-991ab7461127}} is the original performance, and {{formula:5e0029b9-7802-45e7-b6d3-4062bede81fa}} is our reimplementations. As a result, the proposed pooling strategy shows higher performance in different language models and in all domains.
{{table:62faf6ef-8840-4412-affa-1d9c78f646fa}} | r | a223f76323095a496266a4a2c3a6b9b9 |
Sections REF and REF are structured as follows. We begin by assessing the performance of our models trained on different sets of features inspired by prior work. These experiments not only give us an insight into features integral for the LDP and BEP tasks but also allows us to view our work and feature set, in the context of listener disengagement and backchanneling literature. Next, we experiment with different characteristics of time series as features for Random Forests. In order to use a set of time series {{formula:5a057c6e-2a25-4c81-bcaa-900338e7421a}} as features for supervised learning algorithms such as Random Forests, one must first map {{formula:82933ab4-9399-436f-9191-b0a915583d5e}} into a feature vector {{formula:cfa3fa45-b559-441d-a819-c4a377341477}} , where each feature {{formula:c09654f4-d003-448d-90e5-e90a7ab1177c}} is a scalar value and a characteristic of some time series {{formula:32dfe28a-959a-409a-8a1d-37d19cdf1d45}} . Time series can be effectively and efficiently characterised based on the distribution of their values, correlation properties, stationarity, entropy etc. {{cite:c7edb698408e3b036de20d193621c011d1ad7756}}, {{cite:adf4cbe3cb58b562e1efc18425f69232c6674ef9}}. In our prior work {{cite:401b3cfe90af4c1dba99873fce39b658f98953d4}}, we had used the arithmetic means of all time series features at the window-level to predict listener disengagement and the extent of backchanneling using Random forests. However, in the present work, we experimented with various different characteristics of time series. In particular, we used two different sets of time series characteristics (or aggregates) for our prediction tasks: Basic and Tsfresh. The Basic set included the arithmetic mean (M), standard deviation (SD), minimum (Min), maximum (Max), median (Md), first ({{formula:48fc1f1b-481c-498e-b3d7-474a613fc05a}}) and the third quartile ({{formula:f81ceb4b-0c48-4eb9-83b2-dd2d595d3a73}}) of each time series feature at the window-level.
| r | 416e00e702aa8c4bc5846f89fdf2b2e6 |
(ii) CLIP pre-train models dominate over ImageNet-21K pre-train ones. These results well match the shift of paradigm in current AI research {{cite:bc8a6ae7527891328c9c1a1c6e9dce49a4713094}}, where pre-training no longer needs limiting to curated data and annotations to deliver good performance on downstream tasks, but can take advantage of broader scale web raw data.
| r | 72b579f620e964c69a09d48fa1b793ab |
It has been over a century since Einstein, Sutherland, Smoluchowski and Langevin formulated the theory of Brownian motion
to describe the thermal motion of particles {{cite:af4e772ebec6a82c6c0cbb725ea8e3c70baa1005}}, {{cite:8153baaeb62606ee4c33591d134aa8adf9802499}}, {{cite:4d2dbbb9907ac195b2cf8aeb58939e5bb1c2d217}}, {{cite:e759b5339f7e3fbc219f329475272f70319358e1}}, first reported by Brown {{cite:6c1b7af69715f224b5b74760b286906b41f27a42}} with his observations of the jiggling motion of pollen grains in water.
The two hallmarks of Brownian motion are the
Gaussian form of the probability density function (PDF) to find a particle at a given position at fixed time {{formula:44554d75-4344-4747-9eeb-8fe6d2fa460e}} and the linear growth of its mean squared displacement (MSD), i.e. variance, with time. The strict mathematical formulation of ordinary Brownian motion, also known as Wiener process{{cite:25347801375eab32e524ffe0d17dc33728115411}}, {{cite:1a17d1e13e05646ec4bb0d1eacaf2324482a4fed}}, — a non-stationary, Gaussian, self-similar process with stationary and independent increments, — highlighted the ubiquity of this random motion in nature due to Central Limit Theorem {{cite:aeb1fa3e9dc891ec32684b7cd9858c3b308b920b}}, {{cite:aed7cc4053db3f3ed45e4e84a422b84c8e7d0c17}}.
However, many experiments carried out on different scales ranging from astrophysical to inter-cellular ones reported non-linear growth of the {{formula:84073189-87e0-4314-9672-684b449a1ec7}} , {{formula:03222d47-036c-465a-8d54-a8ba6fad5749}} , a phenomenon now known as anomalous diffusion, see e.g. {{cite:c928d2adc55019706d96df93ff2230104744ecdd}}, {{cite:90fd5656e023132e27dbfdcd6da59aadc2574c62}}, {{cite:7db223984eedbe70675a08b1e21c06a745f78e40}}, {{cite:84203b45ed10bd5be5b340b941e810a9648ce7e7}} and references therein.
One of the paradigmatic models of such anomalous diffusion was suggested by Kolmogorov in the context of statistical description of locally homogeneous isotropic turbulence. It comprises a class of Gaussian, self-similar processes possessing stationary power-law correlated increments {{cite:ed59999834b002a0310e1b48c6720e748e97d27a}}. This model was called fractional Brownian motion (FBM) in the seminal paper by Mandelbrot and van Ness {{cite:751fdd7c9794f3c24c01e72f82981e2b853485c1}} who presented its explicit integral representation and advertised its relevance to a broad scientific community. As motivations for such a generalization, Mandelbrot and van Ness cited examples from economic time series
which exhibited cycles having periods of duration comparable to the sample size (long-range), studies of
fluctuations in solids (flicker noise), and hydrological experiments where Hurst found “an infinite interdependence” between successive water flows (Hurst's law). In the last decades FBM attracted attention in many applied fields, e.g. hydrology, telecommunications, economics, engineering {{cite:7e9b2a01483ac479e77efba801cde70437b8c04b}}. This is mainly due to its Gaussianity and the power-law behaviour of autocovariance function of its increment process, which leads to the notion of long-range dependence (long memory) {{cite:3e60d111fde3b7a22cdfbf201562fc5eed0f7837}}.
| i | f41cde431f760aacc4bdafd71bf0d929 |
Yet another interesting property, which distinguishes (REF ) from certain other well-known integrable equations such as the Korteweg–de Vries
equation, is that even smooth initial data can lead to singularity formation, also known as wave breaking, in finite time, cf. {{cite:ca5139b86a0cb002fd57d47d836ae7835cd19591}}.
Here the singularity formation corresponds to the slope of {{formula:9e96f80c-a9e4-4165-b917-e422f2744938}} becoming unbounded, while {{formula:77af50ca-cd7e-4b4d-a037-ea2837013f91}} remains bounded,
and so we say that the wave breaks.
This introduces an ambiguity in how to extend the solutions past wave breaking,
which led to the concepts of conservative {{cite:7dec6bdcfe961bef5862beb2b15126e371aabdd5}}, {{cite:e5d747af41ba016bb2a9377c4213cf242812a73a}}, {{cite:d5ff7f67d07d54ac2f2e0f10ed06b8e7c97cba7b}} and dissipative {{cite:68947dcef442f9aa417f3f015d36348346493744}}, {{cite:d7cff1755dd45348ec06280985caeaa7c9fd2ba1}}, {{cite:2cccd4d8f72021d56e17afa70dce68ffc8a96e2f}} solutions. The key element in these works is to rewrite (REF ) in its nonlocal form, i.e.,
{{formula:21f5f393-947a-46b4-ad5d-e00c2d9a84f6}}
| i | 800bdce3b96525539b0c630ba40491cc |
To evaluate the quality of audio and video generated by MM-Diffusion, we compare it with SOTA unconditional video generation methods DIGAN {{cite:6cb09aac220a6a8e4408466db971a080835ad874}}, TATS {{cite:14feb810350608ee0e6ebf8067b3906e7a582636}}, and audio generation method Diffwave {{cite:06ea0cf1061aba24dc099cc5705a3c5377ce27fb}}. Note that we select these baselines as they are widely-used and have released official codebases for standard replacement on our datasets.
To further explore the effectiveness of joint-learning in MM-Diffusion and to make fair comparisons to single-modality generation with the same backbone, we decompose the coupled U-Nets into audio sub-network (Ours-a) and video sub-network (Ours-v) for modality-independent generation.
The results on Landscape and AIST++ are shown in Table REF and Table REF .
| m | 9e60ad5710d64b0304eb252668bde551 |
In practice, the average fitness of the population changes over the lifetime of individuals in the overlapping model. An empirical study by Kenneth De Jong showed how the use of overlapping generations introduced genetic drift (i.e., faster takeover times) which increased in severity with the decrease in size of the offspring population (i.e., {{formula:6fcded3a-a089-4f6c-b81c-fdf94999da42}} leads to the most severe genetic drift) {{cite:caa0ef20a46931e659ac66908831e89ecd2866f5}}. As a result, the generational model was preferred by researchers and became the standard as well as the backbone of the canonical genetic algorithm {{cite:6dab3c56e66465ac26eefd8521c2ca599f66347c}}. Since fitness proportional selection was applied to select parents, fitness-scaling functions had to be used to distinguish between individuals and avoid premature convergence once all the population had similar fitness values.
| d | f263043ecd5b53a8c722e35913e0731f |
Heterogeneous degree distributions suppress diversity.
In typical networks with a heterogeneous degree distribution, most vertices have small degrees, while there is still a significant probability of finding vertices with large degrees. In other words, heterogeneous degree distributions tend to be characterized by large, sometimes unbounded, variations in the degree of a vertex. Degree heterogeneity turns out to be ubiquitous in real-world population structures {{cite:174ee657f82ca0271f6d18aaa35b92d6758a5ea6}}: from the World Wide Web {{cite:269bfb160be01f515a76e650461e8bbbd352a85b}} to sexual relationship networks {{cite:cb0c85ef5b84ed1bade841c815bbeb2bc9909db3}}, a “hub-and-spoke structure” is characteristic for human social systems. It is, therefore, imperative to ask: how does this feature of social networks affect the opinion diversity of a population?
| r | 1f1f0f54c8c44d27ac0d302b7e820137 |
All methods under this category follows the philosophy of using one generator and one discriminator in their models, and the structures of the generator and the discriminator are straight-forward without branches. Many of the earliest GAN models fall into this category, like GAN {{cite:106dd2a97adac818fa4730f4afa874dbbaeb952b}}, DCGAN{{cite:cfd01ef5b03e3e3cfaac43f5a5054df9ac97aa5a}}, ImprovedGAN {{cite:6c234070183e82dfd0af72011e85e50c68de3aab}}, InfoGAN {{cite:3e0b4758480921f1f1b57f65671640f1ef739834}}, f-GAN {{cite:19f3d0af3b89ba9faa9e918e0b6d490c9e2aaeb9}} and GAN-INT-CLS {{cite:16a86a1f0548fc5834eca41ee62f53089d41bd94}}. Among them, DCGAN is one of the most classic ones whose structure is used by many later models such as {{cite:3e0b4758480921f1f1b57f65671640f1ef739834}} {{cite:16a86a1f0548fc5834eca41ee62f53089d41bd94}} {{cite:9dc448ddb298cb6170322d53c47b8ff780a75a96}} {{cite:67320b2d155430780c84373921b4c647036093f0}}. The general building blocks used in DCGAN are shown in Figure REF , where the generator uses transposed convolution, batch-normalization and ReLU activation, while the discriminator uses convolution, batch-normalization and LeakyReLU activation.
| m | ed0c3ef35cd22d4bbb2d3d5c6720e9e2 |
Theorem 2.3 (c.f. {{cite:fd9a9ed428d2b887ec24092ed403b985dd919585}}, {{cite:b9051d1c0b597735d947208152620bb49106c12b}}, {{cite:2ced6c44c1bc99d68cd7d74bab421e983789db1d}})
Suppose that {{formula:3b22d691-af89-4ebe-910a-812c4ff7706d}} is a square differentiable system with a given interval extension {{formula:a5891cc2-400a-4909-9eeb-f726c776197a}} on an interval {{formula:7228aa0a-6a0a-4a5c-bf30-a104a0ba3d53}} . For an {{formula:3c4cb799-fef0-4051-a821-a0af90394e52}} -invertible matrix {{formula:c02449de-e1b9-4c4e-9e8b-b978ca49a28d}} and a point {{formula:fda7eccf-ae73-4b2d-81d5-ca80d0a7c104}} ,
| m | d0804929852544299ab4f2ffb244ee66 |
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