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(1) Social Networks: RDT-M5K, IMDB-B, IMDB-M from TU Dataset {{cite:c278079a7a24df2e91f6cae9bb3cdefb1befd422}}.
| m | 4c01905ed99b4900a21d79d39002da12 |
One of the interesting features of the compact objects is the
strange quark star (SQS) composed of the strange quark matter (SQM).
The composition of SQS was first proposed by Itoh {{cite:c72ab620863705691fe08faf0bb4dfbf532dc806}}; simultaneously
with formulation of Quantum chromo dynamics (QCD).
Later, Bodmer discussed the fate of an astronomical object collapsing
to such a state of matter {{cite:d618639925d6e6158b5ee2d8d85dd5abcd49e491}}. The perturbative computations of the equation of state of the SQM
was developed after the formation of QCD, but the region
of validity of these calculations was restricted to very high densities {{cite:a338ab0513ad4f2457c95c2d47e1295f02af4856}}.
The concept of SQS was also discussed by witten. He proposed that SQM composed of light quarks, and is more stable
than the nuclei {{cite:2a0f1b44f9f46982e17ddb7aa9a9cec455a4a73f}}. Therefore the SQM can be the ground state of matter.
With this point of view, other authors proposed the concept of SQS.
The SQM is composed of 3-flavors of quarks (up, down and strange)
and a small number of electrons to ensure the charge neutrality
{{cite:557d592e06994a6d82339338d2e43d9d96d193f2}}, {{cite:e8c2c7390a4ed81fdea3889a42f5d252cc4a3a53}}. A typical electron fraction
is less than {{formula:97c893ba-1016-499c-8916-07bb5783fae5}} {{formula:1542aa5f-7c54-45d7-bd92-02996fd651d6}} and it decreases from the surface to the center of SQS.
| i | d215e12244c14a64a07a538246f7f011 |
In this section, we present experimental results to validate the proposed sampling method for semantic segmentation.
We first describe experimental configurations in detail.
Then, we validate our SDSS on two public benchmark datasets, GTA5 {{cite:5e683ec1145c73ee70ceffafc8d43873cbb35ade}} and SYNTHIA {{cite:5125fd6d2c2d87e5f00b93d862b0fcc95aa7ba1c}}, and provide detailed analyses.
Then, we verify and analyse the performance of our method on our new dataset called, Ocean Ship.
Note that the Intersection-over-Union (IoU) metric was used for all the experiments.
{{table:7744eb8d-54b2-49d7-9a35-5a33617c0208}} | r | 4ca8ac34e10b08efe97e5b2dcdf36542 |
Crucially, Rényi divergences account for behavioural differences in a way that is formally distinct from a change in prior beliefs. This stems from the ability to disentangle different preference modes by varying the bound's {{formula:852c8c5b-3489-45ac-a65d-648e340f8c97}} parameter. Our simple multi-armed bandit setting illustrates this: e.g., large {{formula:f16e3097-8c12-4e0c-8e02-d0dd5219ef20}} values exhibit greater consistency in preferences. This contrasts with formal explanations based upon adjusting the precision or form of the prior under a variational bound based upon the KL divergence (i.e., {{formula:cb260d3d-691a-4396-bf0a-feafa03b46de}} ). Under active inference {{cite:c9d47ad4c2e5b92eefd65c5d3eb88cb0c0b940f2}}, {{cite:c6015409bf267ef8c577ba3f92a1607472a4beed}}, multiple behavioural deficits have been illustrated by manipulation of the precision over the priors ({{cite:0459603fc5f1bb71808af6c4242416a4888b89cc}}, {{cite:4440ccae58b634a4beca6f095f9f886d800ec382}}). Although there has been some focus upon priors and on the form of the variational posterior ({{cite:9932e36552c2bdf97593400dcec058d4a5df3249}}), relatively little attention has been paid to the nature of the bound itself in determining behaviour.
| d | 97d562c8b0f67e6709c49c502a0f177b |
Recall (i.e. {{cite:5383f078d4a9caa496a70eac17a524208a130f46}} or {{cite:384c38cdf793b89f73b95f75107ed3250dac308b}}) that there exist sets of orthogonal
polynomials forming a part of the so called 'AW scheme' that are orthogonal
with respect to measures with densities mentioned below. Although our main
interest is in providing simple proof of the so called AW integral we will
list related densities for better exposition and for indicating the ways of
possible generalization of AW integrals and polynomials.
| r | 9125a30c85c04762f675716dd4774808 |
A question fundamental to this topic is: what contributes to the strength of a tie between two people? Or, more specifically, what attributes of a relationship can we use to predict a tie strength value that properly represents the closeness of two individuals within a social network? This question has no singular answer, though there have been popular works delving into possible interpretations {{cite:7e8ac0e6028081d317c4170c4e0b378a46a32577}}, {{cite:7eed1c528c9db9b40d05cd42fdee5635150291d6}}, {{cite:5dbb0d33012d6dbc46d91a6704d6658080bfb7a9}}. Such works have pointed to both qualitative and quantitative attributes of relationships that seem to influence the strength of a the relationship between two individuals, and therefore would contribute to the evolution of tie weights within the involved social network.
| i | 532146b43aaed24ef20679d30257f80f |
The Lambda Cold Dark Matter ({{formula:034edbd8-dd63-4033-95db-a43c2b03397a}} CDM) paradigm has been successful at explaining many cosmological observations.
However, on smaller scales (galactic/sub-galactic), dark matter clustering depends on particulars of the dark matter model, so even if large-scale observations are consistent with a cold dark matter particle, probing small scales can reveal an exotic dark matter scenario.
For instance, in warm dark matter {{cite:3a42cf57cb9948f01048e9c0bedc5854b7ec386e}}, {{cite:e81aabd377f4b481b8ff3a4fb9083447265b5cb6}}, {{cite:370a0b00e7e0d35bed34a7d6673aecd250a85b13}}, self-interacting dark matter {{cite:cf3aecc7b6abcb9da16e7a5c0c8814b19294e77a}}, or ultra-light bosonic dark matter models {{cite:c59b3ed098371e14e5de6800dc51c0d0630d0132}}, {{cite:1e69e6f0603c265b715fe31c4dda6bb103183dec}}, overdensities below a certain threshold do not collapse to form bound structure, which creates a low-mass cutoff of the halo mass function.
For instance, warm dark matter with a mass of few keV can cutoff the halo mass function around {{formula:bbd5ed1b-46cf-4345-bc4b-8682e705487a}} with larger masses having lower cutoffs {{cite:ef276f865d82890fe05fe5356a6f89694bc44af0}}, {{cite:66c733b9d42b68901bd43bbb1606ffcfc6a6ce24}}, {{cite:62a24665c7cc2dfa55c512f3ba5f1d937311506a}}, {{cite:cfd97189119f307f340d618537f121e5891d7b63}}.
Therefore, searching for the low-mass dark matter halos serves as a test for the {{formula:9f725e78-e844-4e7d-a3f6-33ade03466c3}} CDM paradigm and can help reveal the nature of dark matter.
| i | d0af522d926e86339c3c150068fe83e0 |
Please note that for the scenario, where edge fluctuations happen in the first iteration, the estimators are trained offline for just finding {{formula:5b1a2417-19a3-474f-8c6b-3fdc7404222c}} . Then, the offline trained parameters are used for initialization. For the rest of iterations, the parameters of the estimators are updated online via (REF ). Finally, the proposed approach in this section can be used for also different types of graph filters such as FIR {{cite:6ac1e37ed39336b70a1daa41f41c67d780698588}} or edge-variant graph filters {{cite:070ba9d62c41bc02eee478b84e5001f8bb972379}}.
| m | 6ef0d51c83558e06cd4d5890ce6771fa |
To avoid the tensor matricization and maintain the intrinsic data structure, Kilmer et al. {{cite:c3eaeb5ed2fd0c5198a085dddc2048cb5739ea5a}} proposed tensor singular value decomposition (t-SVD) and this motivates the new tensor multi-rank and tubal rank. Another advantage of such method is that the resultant algebra and analysis are very close to those of matrix case. Zhang et al. {{cite:3f5427d87a8f24f914a9a7bd1aa3dd39053309f1}} give the definition of a new tensor nuclear norm (TNN) corresponding to tubal rank and t-SVD. Leveraging the conclusion of matrix case, they state that TNN is the tightest convex approximation of tensor average rank. Furthermore, they derived the exact recovery conditions for LRTC problems in {{cite:a91aaa9047fd817d3ee3037901070c481994b883}}.
| i | 2a187f2ff991cf5b82177bef54f56b4f |
We focus on incorporating differential privacy (DP) {{cite:23672d53de4900a1ddb3dd12b8884e4c2d6bd2b7}}, which (informally) requires an algorithm's output to be insensitive to the change of any single entity's data. For MTL, using task-level DP directly would require the entire set of predictive models across all tasks to be insensitive to changes in the private data of any single task. Such a requirement is too stringent for most applications, as it implies that the predictive model for task {{formula:3e31322b-3eb1-435b-a252-82db87d229a7}} must have little dependence on the training data for task {{formula:68583a2c-cd84-4c5f-a1f1-928d8de955f6}} , thus preventing the usefulness of the model (see Figure REF ).
| i | 88a3554670b9a74a7f19449be65f9cdd |
In order to analysis low performance of Co-Teaching+{{cite:2f05e56e762785ad1f4af6f9a6ef68d5b561467e}}, we conducted a series of experiments on CIFAR-10 with 40% noise level. Firstly, we used a similar architecture as the one used in their paper (pairflip 45% noise level) and reproduced their results (39%, 43% for Co-Teaching and Co-Teaching+ at 120 epochs). Next we conducted experiments with different settings to analysis sensitiveness of Co-Teaching+, and the results are shown in Table REF . When the pairflip noise and 2-layer CNN (one used in Co-Teaching+) is considered, Co-Teaching+ performs better than Co-Teaching, and it is opposite when the noise setting is changed. When the wide capacity model is considered, Co-Teaching+ is inferior in both noise settings. To understand this behaviour, we observed the pure ratio of the selected instances of both methods, and found that the pure ratio of selected instances decreases after few epochs of Co-Teaching+ loss (Co-Teaching+ uses a warm-up strategy with Co-Teaching method for 20 epochs). For example with CIFAR-10 at 40% noise, the pure ratio of selected instances is approximately around 57%, whereas in Co-Teaching it is around 70%. It is noted that in {{cite:2f05e56e762785ad1f4af6f9a6ef68d5b561467e}} considered a unrealistic noise simulation (Pairflip), which flips the class labels with respect to the successive classes without considering class similarities, where as in our paper we have considered a class dependent noise, which flips the label according to the class similar classes {{cite:9b97e16ba0e85d54d895f02cc156f5f93f459e6e}}.
{{table:59f799d6-3438-4c7b-8a8e-6e9e7a85d430}} | d | d56ad4aa93fa5c1c7c87d5d23f63e507 |
The results of the experiments conducted are shown in fig:experiments, where we compare the estimated graphs obtained with our algorithm in (REF ), denoted as “Joint-Hid” in the legend, with other popular graphical models.
The algorithms considered as baselines are: (i) the graphical Lasso algorithm, denoted as “GL” {{cite:a41b71332224f298799902f73204c0a5fde6c12a}}; (ii) group graphical Lasso, a variant of the graphical Lasso algorithm modified to jointly estimate several related graphs that is denoted as “GGL” {{cite:d6505e5b1a80157b2ce512894b8b20a245c644cb}}; and (iii) latent-variable graphical Lasso, a variant of graphical Lasso that accounts for the presence of hidden nodes that is denoted as “LVGL” {{cite:49cd8ca10dcbd8d118c1d99ec45a310c1d4df7c0}}.
Then, to prevent additional errors associated with the scale ambiguity that often appears in graph learning algorithms, we consider the following mean error metric
{{formula:8b55e806-40dc-4c2a-9c39-f2f1dd45f3d1}}
| r | ebc3e94e04445df9ba0405796ae6c815 |
In this section, we compare our qcmlb model to other recent approaches under
two schemes: with and without the attention mechanism. In particular, we compare our
approach to mlb {{cite:d258db54da38ba3929a45e37961abf2e4a3bd2c5}}, mutan {{cite:c554efaded139da94912dd1d7f87336a79bbab28}} and gmlb {{cite:e7f93a93defbd44a48c1fb626f153bd787f69f6c}}. The mlb and mutan
models were trained using the code available from the mutan Github pagehttps://github.com/Cadene/vqa.pytorch. The evaluation metrics were strict macro-accuracy, defined as the percentage of correct answers, macro-precision and macro-recall scores for all datasets mentioned in Section REF . For the sake of readability, we will denote macro-accuracy, macro-precision, and macro-recall by just accuracy, precision, and recall from here on.
| r | f8cdfa9559d5b4333d2469855fe607e9 |
In this paper, we have explored survival methodology built on neural networks for discrete-time data, and how it can be applied for continuous-time prediction.
We have compared two existing discrete-time survival methods that minimize the negative log-likelihood of right-censored event times, where the first method {{cite:1be98b2064b3bab9aa74db2590d0f5abfd59a1be}} parameterize the event-time probability mass function (PMF), while the second method {{cite:9d4857d34752a0ba732d6ce8bb1d628338819897}} parameterize the discrete hazard rate (Logistic-Hazard).
Furthermore, we showed that the multi-task logistic regression {{cite:98b1232201c26955201fdf24ac544a0308e219d0}}, {{cite:835e3038cb519e52f75b9b443410c143e766bba0}} is, in fact, a PMF parametrization.
Through empirical studies of simulated and real data sets, we found that the Logistic-Hazard method performed slightly better than the PMF parametrization.
| d | 710544c8455e34c8aefe6e6b53e16347 |
Case-Based Reasoning (CBR) {{cite:7f301e206d571105500a05e8f7db164e8b57cdd9}}, {{cite:2b8b90b4a17c0a4ae41ed8a8da0f9efa30f09a88}} is used widespread across different domains, e. g., modeling of cooking recipes {{cite:14947496bfd266b42b8b002b37ecb4499aebf92c}}, prediction of seawater temperatures {{cite:bcf1f5a98901e3909c71c812201d02c8595a052e}}, natural language processing of support tickets {{cite:d64b3408aa77a6c8000b1e9aefc9f32ac056d8d6}}, and assisted reuse of data mining workflows {{cite:4b265c00cfdaf8d2961b79745fe6bb2209daa42e}}. One of its strengths is the use of structured domain knowledge that is modeled, among others, for the case representation, for the definition of similarity measures, and for case adaptation methods {{cite:2b8b90b4a17c0a4ae41ed8a8da0f9efa30f09a88}}. An integral part of recent CBR research is the use of Deep Learning (DL) methods, which is indicated by workshops dedicated to this topic, e. g., the workshops on the International Conference on Case-Based Reasoning (ICCBR) in 2017 {{cite:81d4008f17ff6d945de6f3be89efd0f39025b00e}} and 2019 {{cite:eccc4b32346922f2727e7fee954b1a58d4569118}}, and a variety of published papers, e. g., {{cite:a3e32a678e9c239ab18bc41163b481b57725e7f3}}, {{cite:14947496bfd266b42b8b002b37ecb4499aebf92c}}, {{cite:d64b3408aa77a6c8000b1e9aefc9f32ac056d8d6}}, {{cite:da8d15835c074d7c4794ea2444fe074df4de72c4}}. Many of these works are hybrid approaches where DL components are integrated in the underlying CBR methodology {{cite:9aca60d09092b768dfb52ba2da3b7b1a53272794}} to solve certain core tasks such as similarity assessment or case adaptation. This is a reasonable choice due to the ability of DL to automatically learn patterns from available data, diminishing the need for time-consuming manual data analysis and extraction {{cite:63d4a62859293a43a569b632b9963a818e1d18cb}}, {{cite:aa6c3a21a9ccf9eba0ce0f5a7119a89ee1a25c25}}. However, most of these hybrid approaches lack a comprehensive integration of the CBR-provided knowledge into the DL methods, leading to possibly unused potential of improved quality and performance. A recent trend in artificial intelligence research explicitly deals with such an integration of symbolic knowledge into machine learning methods, i. e., Informed Machine Learning {{cite:4a7f4f759a20d355cf8a1058fc69efe147ad3e5a}}. The core ideas of informed machine learning can be directly used in our scenario of hybrid approaches by combining the strengths of CBR and DL: On the one hand, CBR offers a large amount of domain knowledge that is often of high quality. On the other hand, the DL components provide the flexibility and expressiveness to integrate and process this domain knowledge.
| i | 197781e57fd0ecc64d082b6c305eaaa2 |
Reference-less automatic evaluation methods, on the other hand, have been proposed recently.
napoles-etal-2016-theres evaluated a GEC system using the number of errors detected by the grammatical error detection system and showed that it performed as well as GLEU.
asano-etal-2017-reference proposed a method for evaluating correction sentences in terms of grammaticality, fluency, and meaning preservation, using logistic regression models for grammaticality, RNN language models for fluency, and METEOR {{cite:d09f8f9dfeb33e759de4642fa778af3e4d6a5443}} for meaning preservation.
yoshimura-etal-2020-reference proposed a method to optimize the three evaluation measures for manual evaluation as an extension of asano-etal-2017-reference.
The method builds a quality estimation model by finetuning a pre-trained sentence encoder (BERT) on the manual evaluation of each measure and shows better correlation with the manual evaluation than asano-etal-2017-reference.
| m | ca81523ec50ecac241f0a16447e9020d |
Eq. REF shows that the minimum planet mass required to sculpt a disc depends on the orbital radius of the outermost planet, which {{cite:b088677d3f6d557d07612762d23ed51cb1340aee}} argue is roughly the inner edge of the disc. Whilst such a planet would also clear debris beyond its orbit, and would actually be located interior to the disc edge as in Sect. REF , for this analysis we follow {{cite:b088677d3f6d557d07612762d23ed51cb1340aee}} and assume that the outermost planet resides at the inner edge of our disc. The effect of this is that clearing may occur slightly faster in reality than assumed here, but the discrepancy is expected to be small. In the few cases where the disc is asymmetric, we approximate the outermost planet orbit to be circular with radius equal to the pericentre of the disc inner edge, because this provides a lower-limit for the required planet mass; whilst the assumption of circular planet orbits may not hold for asymmetric discs, the low degrees of asymmetry in our discs make this a reasonable approximation. We therefore use {{formula:c4f40abd-af9f-40df-8686-6a2c2ebebb68}} .
| m | 9271bd1d64c25523d911eb49727649a5 |
Motivated by the articles {{cite:aa690e84132321bbb3682590a4015365757660c3}}, {{cite:c1799e0aef6afe33e0f47723d0aa48d526b998e7}}, {{cite:a883da5d389561ca4a5059d7390f75f76edae9ab}}, our primary goal in this paper is to present a version of the penalization technique that will enable us to obtain results on the existence and multiplicity of solutions for equation (REF ), depending on the decay of the potential at infinity, under versions of hypothesis (REF ) that allow the nonlinear term to have supercritical, critical, or subcritical behavior near the origin. Furthermore we contemplate the possibility of having {{formula:f5f73763-3648-42d4-b9dd-7aaf85dc27d5}} nonautonomous and assuming negative values. We also establish results on the existence of multiple and infinitely many solutions when {{formula:4fac5af9-3b76-4fdc-a37e-448eccf0348c}} is odd with respect to the second variable.
| i | 02c7d54df23fa5a36437187f8a0243a2 |
Following the setting in previous works {{cite:f89291a7d41e1e03b3b74d1cd058e45e314ebe88}}, {{cite:002c7a2f2b9d3b1db96cc27e38ef0b40529c1e79}}, {{cite:d9474197916441736c467cd9bce3963599af46fe}}, {{cite:002c7a2f2b9d3b1db96cc27e38ef0b40529c1e79}}, {{cite:d9474197916441736c467cd9bce3963599af46fe}}, {{cite:63bc7c3e706778d7ceac46e2ade0f6e21ac97294}}, {{cite:0eb475eab516251f5d044e358e0fc4f8d21c395d}}, {{cite:01654c90decfc82a26b6447e17e6b744dd3382d5}}, {{cite:7f02f9a30a2a4c3f67c2764fc10a23ceaac7ddb6}},
the models observe 3.2 seconds (8 frames) of every pedestrian and predict the future 4.8 seconds (12 frames) of the person trajectory.
We use the pixel values for the trajectory coordinates as it is done in {{cite:4d0f2d07f3daf4a76b46ec63fb493b8cc2b68401}}, {{cite:f89291a7d41e1e03b3b74d1cd058e45e314ebe88}}, {{cite:a9ec659af2208f28412b32e4b3d31051004761c7}}, {{cite:585c1bf5b55db5bda860eb9c14c6092df10ec2a0}}, {{cite:37aa20667792be7ed79fadac14d60980498846d1}}, {{cite:0eb475eab516251f5d044e358e0fc4f8d21c395d}}, {{cite:8bed4e1fb62211ad1b03dc020249eb3530cb657e}}, {{cite:abf740b35c870ddeea7c1731c1d5c5945af13489}}, {{cite:7f02f9a30a2a4c3f67c2764fc10a23ceaac7ddb6}}.
By default, we evaluate the top {{formula:2a7de4fb-5c28-4106-9894-b58a55c79b61}} future trajectory prediction of all models.
| r | 7aa49492fcdbeaf5092838238a7b3509 |
Our results suggest that while an efficient normalization is not sufficient in itself to achieve good performance on ImageNet, it is still a necessary condition, together with regularization. In our results, it is always with extra regularization that PN yields the most benefits. Importantly, the fact that PN consistently leads to large improvements in training accuracy [REF ] suggests that additional benefits would be obtained on larger datasets without the requirement of relying on regularization {{cite:223df6ad6b26b846cf7e280843b6f0c4ede6b2fd}}, {{cite:8139a265a03274eea07537f8b2c7677833130923}}.
| r | fc99591e07f5f23cfbb1066c5d2ec835 |
Unlike recent SSL based methods {{cite:71ca1f18456cb1eb40fcae1aff2f5609c204f035}}, {{cite:64a9e522931964710d6077a2ecf4b3f53c967ccd}}, {{cite:713b8b129c05906e1fcfc844ce73e25bce4b1b51}}, {{cite:69de16f9d1f8ece2377afb840e3ca4027f7b374e}}, {{cite:3336ea291da21a5dc3ddefe6cb0742770085394a}}, {{cite:d0e09d47299cb5087ddbbaa8a303d40ef59afa89}}, {{cite:3a1efffac86d43474d28cd29b9fe6c80ea66005d}}, {{cite:d325a5b646f24c2c5506a70c15112e6b6858d582}}, GMML does not rely on maximising similarity between different views of the image. Instead, GMML is motivated by a successful NLP pretext task masked language modelling (MLM) {{cite:ba24f8cddc3762a63f583f6f4d02c0d5133bd3e1}}.
There are several considerations when designing MLM alternative, masked image modelling (MIM), for image domain. These considerations are discussed in this section. The system diagram of GMML is shown is Figure REF .
| m | 22184d7bc50325c8ee972b4b7671544c |
We provide here (Table REF ) the full results of the state-of-the-art comparison (Table in paper). We report the additional CRPS metric. We observe that STRIPE S+T obtains the best results evaluated in CRPS on the Electricity dataset (equivalent to DeepAR {{cite:d86431cc5d09ff65b65ea4bae85d998e3cd9c966}}), and the second best results on the Traffic dataset (only behind DeepAR that is otherwise far worse in diversity and quality).
{{table:231611ac-36c9-4945-ad2e-2e92ffe4dc5d}} | r | 4f844472649c0d761fc370924c4da836 |
While intelligent systems must typically undergo at least some amount of training to function, it can be useful for certain computational features to be built in {{cite:17b37b92c3802111add0afe6d63de7eb0073d724}}. Flexible compositional coding is of particular relevance as it provides a substrate for computing with novel objects or events if they are made from familiar elements: an autonomous vehicle should be able to manipulate a representation of "child on scooter behind car in front of bus", even if previously it had only worked with the isolated scene elements. While many trained systems, e.g. translation networks {{cite:7e651aba51c39b12f50959e5e3c572af570c6a9c}}, {{cite:b918d8fc1502ef5f03512dab8e4b913010c2f433}}, {{cite:68410bcdfaf4b4394cb0a13bd809d99e11be570b}}, have some implicit capacity for compositional encoding (otherwise outputs would be disordered), it is unclear how they could handle complexity beyond their training data, and understanding their internal representations can be challenging {{cite:71569219fddd573cbdabb0658bfffdf5fefd53e1}}, although exciting progress is being made in interpretability {{cite:01009d4e48a05ae1da1f74085580285f0e03aa2d}}, {{cite:60744df6f04153556afb3e7d0df04d4b3d6d4369}}. Alternatively, one can design HDC algorithms with a priori flexibility, then attach or embed them in trainable systems. Basing training on convolutional binding, for instance, allowed an artificial network to efficiently and scalably learn knowledge graphs and out-perform state-of-the-art methods at link prediction {{cite:dc7bfbf23581dabf36f169d7ccc5473adc86f3c1}}. It stands to reason that identifying robust HDC codes could prove useful to improving artificial systems, and potentially guiding investigation of neural computation in biology.
| d | e2b8b898f3b6166b3a0ff7f806c5d82d |
This disk transition may be important for the evolution of misaligned, eccentric-binary+disk systems {{cite:b8fc17cc969ad6460771245553563596dd10f7b4}}, {{cite:e0f9c159f8f007f35dba4c89c8864aec1c961246}}, {{cite:ec64d11b71c1afeaeda0fe5e26af03460ace2c68}}, which could be investigated in future 3D studies. There may be implications for observed, misaligned stellar binary-disk systems {{cite:75dc4d2364975e719b6b8492c32fce0a2f6b0a3e}}, the spins of the binary components {{cite:32fdf7389edbc821a14b8dbb57fcd8ddd170ab49}}, and the Kozai-Lidov mechanism for accreting systems {{cite:c7a9aefdb76bb9ab9933187f017f8e2c71f59cd7}}.
| d | 7172bac116905a931f253f988916a841 |
The deep networks that are trained by the standard gradient descent algorithm are memorizing the training data, and use the memorized samples for prediction with a weighted similarity function{{cite:4f06da3e97d407f0e7c4088d02227f4ac8060fdf}}, {{cite:e28474cbb3abf55a70c4a7218d427f047af391c4}}, {{cite:d7c25e1feb7b61951f6a5e9b5c5f41c5ff095ba6}}, {{cite:6b6263e639fae8e8997496966ac510d2ea883760}}, {{cite:a60ed013c913eec5e7ba08d83863420fa34d563d}}, {{cite:d0a26575de5365d9961911d0d83f68903670a74b}}.
| m | e5edbf8dc54809f20591387c0a7f7471 |
The first method, referred to as I-VAE, is based on the regularization proposed by Adel et al. {{cite:fed41458abf4a02e55feade9259d2b676c20b18c}}. It uses a separate linear classifier attached to each regularized dimension to predict the attribute classes. Note that while Adel et al. use this regularization while learning a non-linear transformation of a latent space, we apply it during training of the latent space itself. This is a suitable choice for categorical attributes and is similar to the regularizer used in MIDI-VAE {{cite:b70dfb639550038989b8d1c0dc939001748da280}}.
The second method is the S2-VAE {{cite:2c12925bf332e5ef10623fcf53dba8684df9cb49}}. This regularization, designed for continuous attributes, uses a binary cross-entropy loss to match attribute values to the regularized dimension.
The third method is the AR-VAE {{cite:3f010f79e6e7a3201c4e7894aa7bdcbdcffc38d8}}, which uses a batch-dependent regularization loss to encode continuous-valued attributes along specific dimensions of the latent space. This method is effective at regularizing note density and rhythm-based musical attributes {{cite:eb065e6a3d678b2e1f3da6fb95311e4dd8723c20}}. For comparison, baseline results obtained using the unsupervised {{formula:386cf430-dbfa-4bba-a28a-5bafdaa3d0b0}} -VAE method {{cite:277311bc2031e82f1b04c3cee25f51ce6b31b0a1}} are also provided.
| m | 7b0114b9b58906b1f9f7815b6a542117 |
The solution curve of general differential-algebraic equations is not efficiently
followed on an infinite interval by the traditional ODE method
{{cite:e48b0a861e2e4db7323b451fcaac01996cd3855b}}, {{cite:12d1d34a32897463012a0d9615b12cab14b0549e}}, {{cite:8ad8129bee016ff865abb59c5b06d851392e96d6}}, {{cite:f4122f60bee116c04e6434fc41a9b0f60006c7ad}}, so one needs to construct the
particular method for this problem (REF )-(). We regard the
algebraic equation () as a degenerate differential equation
{{cite:12d1d34a32897463012a0d9615b12cab14b0549e}}, {{cite:d4ba08911f85a5b5dfdb376c1bec6e948e7313cb}}, {{cite:8e96a6f07ff32191aa8663b434f6a5709c142ce7}}, and apply the first-order implicit Euler
method to the system of differential-algebraic equations (REF )-(),
then we obtain
{{formula:5c3497f5-e15a-474c-9627-5101251799c1}}
| m | 2b20a72c6e6cdf4ca112b0bb854891c3 |
However, developing such resource scheduling algorithms for DNN training clusters is highly non-trivial.
In a computing cluster, DNN training jobs are submitted over time with various competing resource requirements (numbers of CPUs and GPUs, size of memory, etc.), and the training process is both resource-intensive and time-consuming.
For example, researchers showed that it could take 115 minutes to train a model with ResNet50 dataset {{cite:c36e2c61c56383df714a0eefeddbe8bc2af49d69}} on a DGX-1 machine with 8 V100 GPUs {{cite:63b20d8497ed311b45a1de758b84b6126d95b7dc}}, and even 3–5 days to train the DeepSpeech2 model {{cite:7b96cbf1a460fbcc4523e63600908393aab5e84a}} on the LibriSpeech dataset {{cite:20103d16d1d13ad5450532f87abb91e1e876ac57}} using 16 GPUs {{cite:7b96cbf1a460fbcc4523e63600908393aab5e84a}}.
Also, to date, there is a lack of a tractable and accurate analytical model that takes different mechanisms of communication-computation overlapping into consideration based on the layered structure of DNN.To speed up the training process, the idea of exploiting the special layered structure of DNNs to overlap communication and computation has been explored recently in{{cite:e5e0983d143bab41f89b096a19b2b06fe10024ea}}, {{cite:87b9c28beab488d40e639fcad23bac4c529ee032}}, {{cite:da12e20ef13199c07ccb63a640ff730e646a5aff}}, which showed that the training throughput of the MXNet framework could be improved by 25%–70%.
Furthermore, similar to the design of most scheduling algorithms for large-scale distributed computing clusters, the computing resource limitation for DNN computing jobs naturally leads to integer bin-packing-like constraints in the scheduling problem, which makes the problem NP-Hard.
Also, the objective function of the DNN resource scheduling problem has a sum-of-ratios structure due to the computational speed characterization in DNN training.
As a result, the scheduling problem is non-convex even with continuous relaxation, which introduces yet another layer of difficulty to the already-challenging problem.
| i | 0896ed52fe818d3e4eba073ba2dc931a |
Because our protocol is an MDI-type protocol, the density matrix of the single-photon pair component is always identical in the X and Z bases for each user, regardless of the asymmetric source parameters chosen. This makes it possible for a dynamic quantum network to add or delete new user nodes without considering the source parameters of existing users. In contrast, to guarantee that the density matrix of the two users' joint single-photon state in the X basis is the same as that in the Z basis for SNSQKD protocols, the transmission probability and intensity of the coherent state must follow strict mathematical constraint {{cite:8f767fb5a964aee82e24c16b668087df5293e2f5}}, {{cite:c85865a62e7b397d2786054dc12f3c426638e678}}. However, this constraint is difficult to realize in practice, especially in networks where users are added and deleted over time, which greatly degrades their performance. By exploiting the quantum coin concept {{cite:2dedcdc8a5db0de9f09ad47c0346fa5213318aab}}, {{cite:23bf5f1259947062b90c9f592ee3c1614ad44c5c}}, a recent study provided a security proof for the SNSQKD protocol when the constraint is not satisfied {{cite:d93b27ccc2f166e7809be38bce0df69dd99dad8c}}.
When comparing the key rates, we considered that the intensity of the coherent state in AOPP does not satisfy the mathematical constraint (which is often the case in practice) with a modulation deviation of decoy state {{formula:8fe4d504-dc0a-428d-8d2e-9e947319867e}} to {{formula:bac1e424-b065-4d9b-82d5-7ba059308dde}} , and the other parameters have no deviation. The key rates in symmetric channels are shown in Fig. REF . The simulation results show that the key rate of asynchronous-MDIQKD is always higher than that of PMQKD and AOPP. At 500 km, for {{formula:2455ace5-7502-446e-bc03-93ed8d2144b0}} , the secret key rate of our protocol is {{formula:11cc7f27-e4e0-4ca3-a878-07c1e2db139b}} higher than that of PMQKD, and the transmission distance is 240 km longer than that of AOPP. For {{formula:50df0eaf-54e2-491b-b07c-3f386bbf3d95}} , our protocol transmits over a distance of more than 500 km. Fig. REF shows the key rate in the asymmetric channels, where {{formula:846f119b-ac91-4da3-88a0-bdc2cac2f84c}} km. Notably, our protocol also performs well in asymmetric channels. At 500 km, for {{formula:690c87e5-77f7-44c2-85e9-30c9af64783d}} , the key rate of our protocol is {{formula:fd8ddc8b-8421-4e65-a4e5-3b5be8698b6f}} higher than that of PMQKD, and the transmission distance is 150 km longer than that of AOPP. Similarly, when {{formula:d7632e4e-ffe6-4dc9-92f8-358c549b2ca9}} , the transmission distance of the asynchronous-MDIQKD protocol is 50 km higher.
| d | 22475cb8f57a28fbfc48b66174b97a70 |
In order to evaluate the performance of the proposed algorithm, different
types of images as text, face, natural and low-light images are studied in this section.
Also Windows 10-64bit, Intel(R) Core(TM) i3-5005U CPU @2.00GHz, by matlab 2014b
have been used for the calculations.
The results of the algorithm are evaluated using different tests such as
Information content Weighted Structural Similarity Measure
(IW-SSIM){{cite:2daea7c8708b0f3507008aa0e265b60f2d59931b}}, Multi-scale Structural Similarity (M-SSIM) {{cite:88cf07b83202a9acefd086dbe2a0dc1f9913ecc7}}, Feature Structural Similarity(F-SSIM) {{cite:b28b449b44b1e4cfce4bf2dce2cb79e6d9c16281}}
and Peak Signal-to-Noise Ratio (PSNR).
| r | d5d5d36b9948e98fc27d87a483f65dc5 |
In general, the methods presented in this subsection all have the weakness that they are specific to the problem of instrumental variable regression, and do not necessarily generalize to other conditional moment problems. Conversely, our VMM approach not only enjoys strong theoretical properties for this problem, but it can easily be extended to other conditional moment problems. In addition, a simple version of our proposed neural VMM estimator (with {{formula:54f700c3-fb77-4043-aa14-8a778890dd59}} ) has previously demonstrated strong empirical performance for instrumental variable regression {{cite:1af7ecf474ccce39af5d92eb564887958ad4adf6}}.
| m | a673bef00928c4e12e4c38119f8e9f99 |
Concurrently, there have been solid advances in theory of SG-MCMC methods and their applications in practice. Sato and Nakagawa {{cite:77d3878a3d0b87042cd275c0dd9dbf19131d048d}}, for the first time, showed that the SGLD algorithm with constant step size weakly converges; Chen et al. {{cite:f0fac9bc0e00afed6c52735d4d3e7ac8e9f7acf4}} showed that faster convergence rates and more accurate invariant measures can be observed for SG-MCMCs with higher order integrators rather than a 1st order Euler integrator while Teh et al. {{cite:0a0ab3b18750ee7234a5f488067aac02a2985615}} studied the consistency and fluctuation properties of the SGLD. As a result, verifiable conditions obeying a central limit theorem for which the algorithm is consistent, and how its asymptotic bias-variance decomposition depends on step-size sequences have been discovered. A more detailed review of the SG-MCMC with a focus on supporting theoretical results can be found in Nemeth and Fearnhead {{cite:f849f9c383a6832371a4729788958339b8c7c90d}}. Practically, SG-MCMC techniques have been applied to shape classification and uncertainty quantification {{cite:994d3beccdb7d05293f60036d5fad43aca0eef05}}, empirically study and validate the effects of tempered posteriors (or called cold-posteriors) {{cite:19eb5a6b745462613deb6535056b8cde342952e4}} and train a deep neural network in order to generalize and avoid over-fitting {{cite:bcdb493ea6032ff3a65935a42c05159757d9b12d}}, {{cite:03a03b973b04f0840800ea0deefad28d936e698d}}.
| m | eeee8fe497c3f16caa4db931be5e0119 |
The fourth term of (REF ) is {{formula:f5a2b358-18e4-4604-ac54-b2dd207bab20}} . It is the smoothness loss, which encourages neighboring pixels in the in-plan direction to have similar transformation values {{cite:e165267a0a88f248612e48fa8d356f21ba2e365b}}. The loss function of {{formula:8451e884-9e37-424f-b583-9148596ac87a}} is defined as follows:
{{formula:b7edd114-9d6b-46be-83c5-7eb55a4f8d34}}
| m | 9098c03738b9b2417fac974d8c01360f |
The idea behind gravitational leptogenesis{{cite:fb38db8334e4cc53943119a04cf7d8da7f317f72}} is, a C and CP-violating operator {{formula:bc9a95ea-c4de-47fd-93cd-f2667fce1d14}} with {{formula:fa0b631c-a29b-44a9-b59a-b46d10e7598c}} as a real effective coupling, corresponds to a chemical potential {{formula:9d5eaf05-2ceb-4793-9d2a-6d3b140e3e4f}} for the lepton number in the theory. Therefore, the normalised (by photon density {{formula:a6132ec0-c811-4219-9a4e-f5864b5357b3}} ) equilibrium lepton asymmetry (using standard Fermi-Dirac statistics with energies {{formula:98902f7c-a39f-40bd-81b0-ee05e5477502}} ) is given by {{formula:c12aff1a-4c02-4d95-9ddc-86d7de3a7b98}} . Interestingly, {{formula:38eecb21-e2bb-4a0d-b078-aa03cc39e4b2}} can be generated in a UV framework using the seesaw Lagrangian even when it is minimally coupled to gravity (see e.g., Ref.{{cite:3f1be53d2cd38ce058d15bdca6c4d9e1ff06c207}} for an in-depth discussion, sec.II of Ref.{{cite:5168f9346575a8c12e990f2c1a352b6d38cf37d6}} for a brief summary). As a computational insight, one calculates an effective {{formula:fa06630c-e719-4ace-b2e0-7f6d61021730}} vertex corresponding to the operator {{formula:f8fa72b6-de7d-44e1-bfe9-2504441f4635}} using a conformally flat metric {{formula:e82fa8cf-4c8d-4002-b774-0b0a5dbca267}} with {{formula:710ba846-7122-4c10-926b-0e0362218566}} , capitalising the fact that the coupling `{{formula:19b398ed-0acc-4366-bb6f-9bed9774747f}} ' is independent of the choice of background. In seesaw model, a similar {{formula:706ef0e3-e207-4f28-9c3b-0200b65a8b5d}} vertex that manifests the {{formula:bfb00a65-7988-4ec3-b50f-a688942098bd}} operator, can be constructed at two-loop level, where the Higgs and the RH masses mediate the loops. Then simply comparing the coefficients of both the vertices up to linear order in {{formula:7ce3ea7f-91f7-4cbd-9d63-056d3e617478}} , the coupling {{formula:327fb760-9484-422b-9564-b7df4423ed55}} can be calculated in terms of the Yukawa coupling {{formula:b6544035-8250-4329-9ddb-70a568204163}} (where, {{formula:a252cf18-4b41-45ba-bbd1-3d3a95249f9e}} is the Yukawa interaction in seesaw, with {{formula:fd0b5bb3-ea22-41ee-8239-c1fabbde5939}} , {{formula:82f8645b-b5a1-42d8-99ac-badf115c12ea}} and {{formula:c242d3f1-e66a-4baf-be04-af333be0c46b}} being the lepton doublet, Higgs and RH fields respectively) and RH neutrino masses {{formula:7b265ffc-1c40-4766-bee6-c3d1c5708d83}} . The expression for the equilibrium asymmetry then reads
{{formula:241688c0-e00d-4284-aacd-8e59edc4ab2e}}
| r | af05622e7039cf26592300de06232483 |
Finally, regarding our proposed SGD we must note that similar results might be obtained with a MCMC method where information about the gradient is taken into account. For example, {{cite:2e3649e2af0a8f7ea279ff086879958482f2e4a0}} use a Metropolis-adjusted Langevin method which basically follows a gradient-descent and adds some noise to the step. However, the noise added to the gradient step in our approach is different—SGD noise has been shown to be approximately constant but anisotropic {{cite:0a935e6e64cbcad2a031f1ab2ed22e46bf6bc602}}. Another possible alternative to our method is to use Riemannian optimization, which is possible when the DGM approximate manifold is smooth. Although it is possible to compute the direction of the gradient by using the pullback Riemannian metric, which may be obtained as suggested by e.g. {{cite:41256a27df55303dfcb0fb350a95fc8fd1b58089}}, {{cite:2002f34ad57ac5d222280e9bdacee66f6ae84240}}, {{cite:810ac409d7cfd9c4590920c04e144f4c452fadf6}}, it is not straightforward to compute the step because it would have to be along a geodesic curve instead of a straight path and such geodesics are computationally demanding to compute.
| d | 3a434cb786b56246a22998caa49d64c1 |
We choose this family of models in order to be consistent with early works that analyzed training and generalization properties of neural networks in the NTK regime {{cite:2c8f514609cbd24f1fb3c3a4be4c58decfa54acf}}, {{cite:95316b25dc1aa454aa615e88eafabed58c5a2782}}. We perform experiments on image classification on MNIST and on a binary task extracted from CIFAR-10 (car vs airplane). We train the networks in a regression fashion, minimizing the {{formula:74f397c8-a34d-44b5-bd3b-eb0e825a4eeb}} loss between the predictions and one-hot vectors, using full-batch gradient descent on the entire dataset (full training data for MNIST and 5K images for each of car and airplane in binary CIFAR). We keep the learning rate fixed to {{formula:92d8454c-c859-4e56-9ba6-7152b212226f}} and vary the width of the network in {{formula:792872ad-0191-43d4-a20a-0a3e255385bd}} . We train 3 networks for each dataset until convergence ({{formula:6784b9f5-7c72-45b6-aa02-dd24cef9a50b}} epochs), each initialized with a different random seed. When we measure quantities from the neural net, we subtract the initial prediction {{formula:385a2d4e-7e10-4f96-a439-c4f2d8dd3628}} , since the NTK expression Eq. (REF ) does not take the initialization of the network into account. When attacking the models ({{formula:34522ae5-026e-4e11-8ba7-92709e533db4}} attacks), we use perturbation budget {{formula:c1f7782b-b3d8-4eb4-9f89-379a05c2ee8b}} for MNIST and {{formula:c8eb0190-f707-47a6-83a0-ee46638f0bd7}} for CIFAR-10. The experiments are performed with PyTorch {{cite:58ffaec059bc4d6ce4dbc3a1cc54913049ba9805}}.
| r | 5b5d14354ba2cd71f3886a4d5cac659d |
Content-based filtering, user-based collaborative filtering {{cite:f969efaa73925f16947d9116f30eb434f3f58687}}, item-based collaborative filtering {{cite:f969efaa73925f16947d9116f30eb434f3f58687}}, matrix factorization using alternated least-squares {{cite:279fce2b3c41e8a4700cc7dd5f4508a7938f17df}}, and matrix factorization using Bayesian personalized ranking {{cite:7990b0de6ec3e499d6e0c25716e332a9548b2141}} were also evaluated, performing worse. We do not report their results due to lack of space.
| m | 314f6c4ec98a0c0df877db216af0508b |
Table {{formula:2efab0d1-97cb-48b9-b413-774594caf731}} shows the prediction accuracy for phase shift of each element on RIS in the testing stage, where the prediction accuracy is defined as the probability that the prediction result is the same as the CEO algorithm. Here, the prediction accuracy shows the generalization capability of the trained parallel DNN system. As we have mentioned before, there are {{formula:c50bf5db-5c9d-40cc-afd2-565056010927}} elements on RIS, and each element is associated with one specific DNN in the parallel DNN system. Therefore, there are {{formula:784ff339-55cf-47e3-a64a-de8e6ccb1c8b}} prediction results as shown in Table {{formula:e63c9da6-8d3d-4431-aa8b-b85221a80302}} , where the average prediction accuracy is about 0.99 for all {{formula:4fcc03bb-a862-40af-a3ae-4e4e000cf527}} RIS elements. It should be noted that, due to certain randomness of mini-batch gradient descent {{cite:f4c3b6124aceffbe9a3b2096735eed545090cf51}} in the training stage, the prediction accuracy of each RIS element has a slight difference.
{{table:ef9d00a3-29a3-43ce-a757-73f31de0a36b}} | r | f703e25f8aac6847a67608e838e8c5b0 |
Ngiam et al. {{cite:312711813481a7c3fb569e00c71ec5dd54e62e8a}} were the first to address a multimodal deep learning approach in audio and video retrieval. They trained deep networks for a series of multimodal learning tasks to learn a shared representation between cross modalities and tested it on a single modality, for example, the system was trained with video data but tested with audio data and vice versa.
| m | 6bc353b504a90c4f3b80ced656e1bcfc |
The wide range of relevant time and length scales in polymeric systems makes them natural targets for multi-scale modelling.{{cite:f145425f51eddb960be51fd74eda45a2e52a94ca}}, {{cite:82347404939cd5ae38e6ef4ab9b318784d80e197}}, {{cite:49a562270f2a03d7ca9e7198577bdec45e8ff605}} In particle-based models, the resolution ranges from the atom scale to DPD-like descriptions, where entire chains are represented by one or two soft spheres or ellipsoids{{cite:186584b0ca36835accd954e35f04c91462236d97}}, {{cite:697df3e8d08e695044443828eb3a673d99ff4c7e}}. What is the natural place of KG-like models in this hierarchy? And how should they be parameterized?
{{figure:92c644cf-2b1b-4878-b0c3-a1830d88c7bb}} | d | 7bf58ff98bf7aa3b9859d9de3d9a4954 |
if the limit exists for each {{formula:16d05a98-f539-48d5-8c7f-759b8b146cfd}} - real number. The notion of asymptotic density allows define the asymptotic distribution function analogously as the distribution function of random variable in probability space. This leads to the possibility of application of results of Edmund Hlawka, {{cite:86a6a69257910f9c8fc916baae8211ebe1510439}}, and other authors which defined later the uniform distribution for compact metric space with Borel probability measure.
From the 70 ies the monographs {{cite:814193a7fdb2da62d867edcdac1b33e7b4e47bf2}}, {{cite:00c7ad82f4c7f9558b4ef88cfba9f576cb1a19ba}}, {{cite:a4ff87f32bd6de985f5bcf8adb1ed2ac0cc66f88}}, {{cite:8a7159441437da1daf4de87fc0857c079e47583a}} and {{cite:8a216af71a9f392bebf1ba8034508eaa9fc7c640}} were published. The aim of this paper is to apply such a probability measure for describe the distribution of sequences in some cases using asymptotic density. The properties of the compact ring of polyadic integers were utilized in {{cite:c8f2360bf5a8e7411ddc2a53126d89175dacad01}}. The additive compact group of polyadic integers provides the existence of Haar probability measure. This measure plays an important rule in the study of distribution of polyadic continuous sequences. Very useful is the fact that
the sequence {{formula:e351562b-126a-4c30-b7f5-aa7abeb61dcd}} is uniformly distributed in the probability space of polyadic integers in the sense of Hlawka.
In generally the completion of {{formula:b5b7fe6e-0ceb-4e57-8154-0b2dcd751678}} is not necessary an algebraic structure. The other name for asymptotic density is "natural density". Because of this we call the corresponding metric and measure "natural".
We define the "natural metric" as metric that the completion is a compact providing the existence of such probability measure that the mentioned sequence of natural numbers in natural order is uniformly distributed. Such measure is called "natural measure". By the application of Riesz representation theorem to the linear space of continuous functions we derive a necessary and sufficient condition providing that given metric is natural (REF and Theorem REF ).
| i | 6acc57e7710d0c7b2f6eea6762fdf7b1 |
Theorem 2.4 (Local minimax lower bound)
Let {{formula:24a25f77-be9e-4244-8fac-cdbce6d5146f}} . Then for any {{formula:67ebe629-0410-43bc-a3ca-4588c23923b1}} , as long as {{formula:35b80f8c-fbbe-4102-9d26-27dd3a2dde2d}} , it holds thatIndeed, the lower bound holds for blackboard interactive schemes {{cite:96a534b7e8a0e5387cd289bc02effc024c3f5f1c}}, a more general class of interactive schemes than {{formula:f7233a93-a7b5-46c9-bb4c-901475e58c5e}} . See {{cite:2c8c40ab07dec5f68393e8cac0d62a59c56c5e55}} for a discussion of blackboard schemes.
{{formula:2cec6bb9-4231-44c8-b7e4-aee078c17fe2}}
| r | 18f865cea4e4851607dd79358988f536 |
We have evolved a large number ({{formula:a9cfd899-e74f-4dde-8d31-8970b39e7f0e}} ) of binary systems in each model, by setting a grid of initial parameters
as follows. The primary masses {{formula:37bfda44-4105-4f2a-99f3-5b1442b022e9}} vary in the range of {{formula:ed33867c-148c-46af-ad23-411634023cd9}} , the secondary masses {{formula:51b638fe-6251-43e9-befb-5003d1b70da2}}
in the range of {{formula:b49e874e-7b15-49c0-b3e1-a01c97f0d786}} , and the orbital separations {{formula:cf141bc0-f9cb-4ef2-9fb9-068e7da72478}} in the range of {{formula:64a8ecb4-f13a-451b-8e3b-b63f90e740ac}} .
For the primary stars, less massive ({{formula:e36c0a25-ffc9-4de2-8872-f5f616450344}} ) ones can only develop degenerate He
cores {{cite:0a2fafc4495e73fa1560b2bb1d6f6241b0ad0075}}, and more massive ({{formula:a6c2b242-a099-4d76-8ef4-f17d6d9abe5e}} ) ones are extremely rare due to the initial mass function (IMF).
For the secondary stars, only the systems with {{formula:af81df44-1faa-456c-9c88-cc4eb226ead5}} are evolved.
Each parameter {{formula:4a62c787-b57f-433e-b34d-ebb072ed645a}} is logarithmically spaced with the {{formula:53658905-9333-4009-ab37-d2ed4cdcddee}} grid points, thus
{{formula:17f6dbb9-fb5a-4110-a15d-3eee145343b7}}
| m | 66bf355dee5ad4da4bb65571dff771f7 |
Method and Scoping.
We synthesize available literature that uses explainable ML for (offensive and defensive) cybersecurity tasks. To this aim, we collect relevant literature, construct a taxonomy based on common themes (i.e., application objectives), and classify the literature into those themes. Applying a reflexive thematic analysis {{cite:17d1e84db2514facb64fc1e7f0fb3bec2928db36}}, the literature was collected by seven researchers. Each paper was investigated by at least two researchers independently and discussed with all authors during weekly meetings. The code-books were updated as new categories emerged.
| m | f793e1ca566810a523e1b3d1b23e0927 |
Classical Neural Networks ignore the underlying physics.
In the most general form, constitutive equations in solid mechanics are tensor-valued tensor functions that define a second order stress tensor, in our case the Piola stress, as a function of a second order deformation or strain measure, in our case the deformation gradient {{cite:0af75a4f823a4a40f0071af045b4de0912ed29d4}}, {{cite:db4bd9e3fb6cb9a489e85744b522e2909720fd76}}. Classical Neural Networks are universal function approximators that learn these functions {{cite:d1bccedce1576d93b6f166a7dae214e509195765}}, in our case the stress, from training data, in our case experimentally measured stress-strain data, by minimizing a loss function, in our case the mean squared error between model and data stress. Neural Networks have advanced as a powerful technology to interpolate or describe big data; yet, they fail to extrapolate or predict scenarios beyond the training regime {{cite:795d886121e8a30f3c0216ed575ad10a7666b736}}. They are an excellent choice when we have no information about the underlying data, but in constitutive modeling, they entirely ignore our prior knowledge and thermodynamic considerations {{cite:422706683262fec2df6be1e486dc70bdb001519e}}.
| d | 59a6fe9f4aad31b4213249778e943cf8 |
In the article {{cite:8287f1c468c3665cd418193ff83348583cf5e904}} we have presented construction of {{formula:7caff93a-d71c-4188-9630-2294eb697c79}} -dimensional integrable bi-Hamiltonian systems associated with Novikov algebras. These systems are multicomponent generalizations of the Camassa–Holm equation {{cite:1b82f15490ffb355448c4506e4c9cf5ff086b005}} and can be interpreted as Euler equations on the respective centrally extended Lie algebras. On the other hand, the central extension procedure is one of the most effective methods allowing for the construction of {{formula:227fca4a-24fa-4709-a07c-663cb6df9b4a}} analogs of {{formula:de37c16a-fa4b-4d44-b803-eb2d265e6813}} -dimensional systems. However, such procedure is not always possible. All the more, there is very limited number of approaches allowing for the systematic construction of {{formula:1331485e-698e-40fd-aff6-3cb603b8ae5c}} - and higher-dimensional integrable systems, see the recent survey {{cite:dd3ede9831fd473474130e752a63711e66cc2cbb}} and references therein.
| i | 9b1dfda62f34a9d0fea70da8a8770fca |
Building on DirectPred {{cite:cc1ba31928c75ade75fb6a7ff5273342e824d20c}}, we presented a simple analysis formulated in the eigenspace of representations that illustrates how BYOL/SimSiam's asymmetric similarity loss avoids representational collapse.
Specifically, we showed that these architectures induce an implicit loss that regularizes representational variance and prevents dimensional collapse.
Further, we showed that this formulation allows easily crafting new types of “IsoLosses” that yield faster and more stable learning dynamics, thereby allowing to dispense with EMA target networks.
Finally, the eigenspace view laid out in this article builds a conceptual bridge to other SSL approaches that explicitly regularize representational variance through additional loss terms {{cite:e5fbb840f78e161afd70b0689205449f8c77078b}}, {{cite:95a5c875d5fce81e1d6c1320e7025cf26245d465}} and lays the foundation for
better understanding modular architecture choices in terms of their equivalent objective functions.
| d | 9c00605899e464902ae105c6bc4bca53 |
Both H{{formula:822e5376-e209-4bfb-a5c4-26b2857b871f}} CO and CH{{formula:4a7d35e5-d5e4-4690-8c30-b43b3f258c38}} OH lines are firmly detected. IRS 48 is the second known Herbig disk with a detection of CH{{formula:eaf9d9d8-3229-4d87-9952-01573cf02eda}} OH, following HD 100546 {{cite:02d4f1e9f33b54e46e7cd0c18c4ca471c1b57f98}}. It is immediately clear that both molecules follow the dust trap morphology (Figure REF ), in contrast with {{formula:549cac8d-1a53-4b9d-a0ab-7e51ae421ee8}} CO which shows a full disk ring, just like the small grains {{cite:e038f2b242530bb3fe64d303554d2f56281fc845}}. This confirms the findings of {{cite:b60732e5ed01cfe324062484e51428446a90a9f2}} of their suggested location of the H{{formula:f360ed8b-d753-444c-8479-000789140341}} CO emission.
| r | a0bcf04e1257ddbe37ec5848446a743d |
Statistical or machine learning approaches have been in existence for decades.
While machine-learning and statistical methods are sometimes classified separately{{cite:16193862921fc1be91b050160d144e6def7f1fc0}}, we group them together as “statistical”, as both terms encapsulate approaches that use patterns from past incidence in order to forecast future incidence.{{cite:d60ea51a095e0ae913906ac935746534a1cb1b06}}
These approaches can be used for `data mining', by which large amounts of data are extracted from various online sources for pattern-recognition tasks, or for modeling, using empirical methods such as random forests, neural networks, or or support vector machines that do not make any parametric model assumptions.
These techniques came about in the computer science and artificial intelligence communities (see, e.g. {{cite:f76774ce61bd62a96b6b586ea5c656eb90072bb3}}), but can also be expressed statistically {{cite:a1846b5eea0130e328d42f2d06d9ab514a136884}}.
| m | 3b65216fd83e820e8a15bfef9e3195b4 |
Search for and exploration of mesoscale quantum phase transitions in materials with non-magnetic order parameters. For instance, it is well-known since the early work of de Gennes{{cite:073fd219186558daad4530444bfe9f59f304da95}} nearly seven decades ago, that ferroelectrics are also model systems par excellence of the transverse field Ising physics. Accordingly, we expect similar behavior near ferroelectric quantum phase transitions,{{cite:a839e227a1c43e8e300f5537ddc35ed2060ddb27}}, {{cite:00276870130e99f10b2e35dfc47820384bbbdf58}}, {{cite:825b4b76318ac8db386ac8f4188f45285bd2d6da}} and, on a more general note, multiferroics and related compounds.{{cite:fc66586a69a74c3665c65dae729eef200222a299}}
Experimental techniques
Several single-crystal LiHoF{{formula:ddcc00ca-db29-44fd-b94e-600201223b93}} samples were purchased from AcalBfi/Altechna Germany. The optical appearance, characterization by x-ray and neutron Laue diffraction, as well as magnetic properties measured in a Quantum Design physical properties measurement system consistently confirmed excellent sample quality in agreement with the literature. For our measurements single-crystalline pieces were carefully ground and polished into spheres to reduce sample-shape related inhomogeneities of the demagnetizing fields.{{cite:673091c9466a2a0ce30f368815747e2e0bec857a}}, {{cite:c9529802e0eaa0d40527c6d7b0cccae0cfbcbb25}} In our study a sample with a diameter of {{formula:08ff0fd9-1e2c-42ce-a598-c241728bc2c6}} was investigated. After grinding and polishing the quality of the samples was remeasured and found to be unchanged excellent.
The use of spherical samples here proved to be decisive. Using instead cuboid-shaped samples, we observed strongly smeared out transitions for {{formula:327ac555-3911-4d37-858c-51f9c703ff2d}} and {{formula:ad855562-c889-45d6-8c6f-09b7949d2db3}} {{cite:9c1ac3a4d64704b3ebc8277cdf057752c348b550}} rendering a tractable interpretation essentially impossible.
In our study we measured the ac susceptibility along the easy magnetic axis of LiHoF{{formula:c682ae5d-1110-4483-b55b-19ff1c260192}} , probing the ferromagnetic order parameter by means of a bespoke miniature susceptometer comprising a primary coil with a balanced pair of secondaries {{cite:46e647d8874352f44f5929d2bdb6b9dd7566054f}} (cf. Extended Data Fig. REF ). Data were recorded at an excitation frequency {{formula:423410cd-402e-497f-879d-85b5e6a79c62}} and an excitation amplitude {{formula:67961dbb-a844-4f94-b27c-ca80b90bc847}} .
The susceptibility data were calibrated by means of measurements of the longitudinal susceptibility, i.e., {{formula:065b7faa-6d13-4009-af1a-238e2b46273e}} , using a Quantum Design physical properties measurement system down to 2.3 K {{cite:a20c82ebaa96ffce55ec5a2be7270c393997fa11}}. All susceptibility data are reported in SI units following convention.
A JT Oxford Instruments dilution refrigerator in combination with a two-axes American Magnetics vector magnet (9 T, 4.5 T) was used for the measurements under transverse fields down to mK temperatures. The sample temperature was tracked with calibrated RuO sensors purchased form Lakeshore.
The susceptometer was mounted such that its orientation was perpendicular to the vertical axis of the dilution refrigerator.
For the measurements of the susceptibility the sample was attached to the sapphire rod with GE varnish such that the easy magnetic axis was parallel to the susceptometer coils and thus perpendicular to the axis of the dilution refrigerator. The orientation of the sample with respect to the sapphire rod and susceptometer coils was confirmed to be better than a degree using x-ray Laue diffraction.
The precise orientation of the sample with respect to the susceptometer coils and the vector magnet was determined and adjusted by means of a two stage procedure. At first the critical field was mapped out at {{formula:22a3cca4-9048-4140-ba28-59d15871e1a5}} as a function of the magnets field angle for an orientation of the dilution refrigerator such that the easy axis was roughly perpendicular to the plane of the vector magnet. Following this the dilution refrigerator with the susceptometer attached was rotated by 90{{formula:cc610451-7672-484e-9dee-4a7687077d6e}} with respect to the vertical axis and thus the plane of the two-axes magnet. This effectively brought the easy axis close to the plane of the two-axes magnet. Next, the critical field was mapped out again as a function of the field orientation, analogous to Fig. REF . Based on the data recorded for the two magnetic field planes, the precise orientation of the dilution refrigerator with respect to the plane of the two-axes magnet was determined and the vertical axis adjusted such that the easy axis was accurately located in the plane of the two-axis magnet.
Small tilt angles of less than a few degrees of the easy axis with respect to the vertical axis of the dilution refrigerator were finally inferred from measurements through a wide range of angles. For the sake of clarity only the angle {{formula:add4cec3-794e-48aa-a5d2-0fa5fde65b91}} of the field orientation with respect to the easy crystallographic axis is reported in our manuscript as depicted in Fig. REF b.
Based on a careful estimate of the combination of systematic uncertainties in the alignment procedure and the statistical error of the vector field, a conservative estimate of the accuracy of the angle {{formula:bd92d94f-b35f-4b16-a45d-edca24a4632f}} of the field orientation is {{formula:4ed6e81d-f2cc-468d-b5e4-35b603fb4aab}} . The uncertainties of the magnitude of the applied magnetic field corresponded to the jitter of the power supply, well below the detection limit. The error of the temperature stability corresponded to better {{formula:19cb44c3-97d6-4730-bb53-2cef5dd73e66}} , whereas the absolute accuracy of the calibration of the thermometers corresponded to the values provided by the commercial supplier.
Theoretical modelling
Our theoretical model starts from a microscopic description of the full local Hilbert space of electronic and nuclear moments and a mean-field treatment of the interactions between the electronic moments, as in earlier work.{{cite:6876e1e5632b935bec254c538f1e789bcfff462a}}, {{cite:825d1da0b9129999174e568a753cb1351e885682}}, {{cite:32c93fe9e860bdfce14d19f7711c865b235675dd}} This is supplemented by the magnetostatics of a mesoscopic periodic arrangement of domains of variable size and magnetization. Importantly, the combined theory thus contains the interplay between microscopic and mesoscopic degrees of freedom. Full details of the theoretical framework beyond the summary presented in the main text and here may be found in Supplementary Information Notes through .
Microscopically LiHoF{{formula:f6d8ad07-1f38-486e-9970-61c5bfa32f42}} is described by a transverse-field exchange model augmented by crystal electric fields {{formula:d52b2fa6-a1de-4e6b-83a9-6a02b6cefc4f}} and hyperfine coupling {{formula:5e90906f-83f7-44c6-9986-723cf1580884}} to nuclear spins,
{{formula:150bd0e0-7121-48d3-805f-9da3234cf481}}
where {{formula:a5793410-6a26-4b60-83ac-c02b23f7b216}} ({{formula:ece0a6ae-1526-411d-9821-1398884c1451}} ) are the electronic (nuclear) Landé factors, and the external field {{formula:f2464b8c-ecef-4066-8e12-b3ae564ba703}} is varied in its strength {{formula:41b1f8ef-8611-4d9f-9695-400b2cf7ffb1}} and tilt angle {{formula:8490698e-2e1b-4cec-a2f6-a168586973d7}} . The electronic moments interact via dipole-dipole and exchange interactions; their combined effect is captured by the nearest-neighbor ferromagnetic coupling {{formula:cb28670a-9302-440a-8309-3d072a4ad770}} . The Ising anisotropy is exclusively contained in the single-ion crystal field {{formula:12d6c2f1-8cf5-4016-8bb3-0c4ed37e1580}} . The electronic and nuclear moments with {{formula:928f8b89-8b27-4712-84b5-440231382bfd}} and {{formula:69076f48-0fd1-47d1-9525-73c7655dea18}} , respectively, form a {{formula:74f8f27f-b5dd-499a-9b8c-cd41e9740746}} -dimensional Hilbert space on each site, which is kept in its entirety,{{cite:6876e1e5632b935bec254c538f1e789bcfff462a}}, {{cite:825d1da0b9129999174e568a753cb1351e885682}}, {{cite:32c93fe9e860bdfce14d19f7711c865b235675dd}} in contrast to some previous works which used a projection to an effective {{formula:cb299abe-8d6c-4786-a33d-2ca0360afc68}} dimensional model.{{cite:1af23524d0658be536d710c039f6ff0dc7531e6a}}, {{cite:709a579545f75369fa3db5324a8dba1f2716f71e}}
In order to solve {{formula:e70cabdc-ffe2-4735-bad3-796fbdc59f7c}} , the interaction is treated in a mean-field approximation, with site-independent mean fields {{formula:8fece0ea-5384-4eab-8640-1c56827d3aee}} .
Domain formation is incorporated by introducing two types of domains, 1 (up) and 2 (down), and by accounting for stray fields. The domains form an alternating pattern on mesoscopic scales and are assumed to be sheets stacked in the {{formula:573ef5d4-23e2-493a-95c3-f4d0865a8a23}} direction, as sketched in Extended Data Fig. REF a. Assuming a homogeneous magnetization in each domain, the sum of total stray-field and domain-wall energies can be expressed as a function of the domain magnetizations, where it takes the form of an effective antiferromagnetic interaction (Eq. ) between domains of type 1 and 2. In the spirit of the mean-field approximation, this interaction is decoupled in a fashion similar to the microscopic spin-spin coupling. Estimates for the domain-wall energy density {{cite:5ed8562accc1ea7909d7e7ff7bf5ea33548a9f55}} and the domain sizes {{cite:c3f87360e525d922806ec6b87b9fbd3b53f5eebd}}, {{cite:108e7f031efb5b391265967f46f5930f6fd49cdb}}, {{cite:1aef07d3a7f524b66514fb9f616fd385a1ddad2b}} are taken from the literature. Together, this results in a consistent mean-field treatment of the multi-domain ferromagnet, with a separate set of mean fields for each domain type. Importantly, it includes the volume ratio {{formula:e811bf6a-a32c-476f-8dbb-0c36947189af}} of the domain types 1 and 2, {{formula:09496293-acfa-4ec3-8646-050c9b428926}} , as variational parameter. The single-domain solution is obtained in the limit of either identical mean fields in domains of type 1 and 2 or vanishing volume of one domain type.
References
Acknowledgements
We wish to thank P. Böni, C. Castelnovo, T. Enns, M. Garst, P. Jorba Cabre, M. Knap, J. Knolle, M. Lampl, S. Legl, M. Meven, R. Moessner, H. Ronnow, J. Schmalian, S. Säubert, F. Pollmann, and W. Zwerger for support and discussions.
We acknowledge also support by S. Mayr and the mechanical workshop at the Physik-Department of the Technical University of Munich.
Financial support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the Munich Center for Quantum Science and Technology (EXC 2111, project-id 390814868), the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter – ct.qmat (EXC 2147, project-id 390858490), SFB 1143 (project-id 247310070), and TRR80 (project-id 107745057) is gratefully acknowledged.
This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 788031, ExQuiSid).
Author Contributions
A.W., F.R., C.D., M.K. and C.P. conducted the measurements.
A.W., F.R. and C.P. analyzed the data.
C.P. proposed this study.
H.E. and M.V. developed the theoretical model.
A.W., H.E., M.V, and C.P. conceived the interpretation and wrote the manuscript.
All authors discussed the data and commented on the manuscript.
Additional Information
In the supplementary notes we report detailed information on the theoretical model and the theoretical analysis, comprising the Landau theory of the transverse Ising transition under tilted magnetic fields, the microscopic Hamiltonian of LiHoF{{formula:ef157581-8f61-4e0f-8843-dca641934250}} and its mean-field approximation, the account of multi-domain energetics and the numerical evaluation of our combined model connecting the microscopic and mesocale phenomena.
Data availability
Materials and additional data related to this paper are available from the corresponding authors upon reasonable request.
Competing interests
The authors declare no competing interests.
Correspondence and requests for materials
Correspondence and requests for materials should be addressed to C.P. or M.V.
Extended Data
[figure]labelfont=bf,name=Extended Data Fig.,labelsep=space
{{figure:bd814211-527a-4482-a6f7-2649609eeae8}}
{{figure:cd391f3d-4049-4a36-9a47-611e8c8ae227}}
[figure]labelfont=bf,name=Extended Data Fig.,labelsep=space
{{figure:888bef23-b1ce-40e0-a37e-83512d72c653}}
{{figure:bb3ad001-2e74-4b38-a0cd-6125bf6fc5af}}
{{figure:53a17769-7236-471b-b4fc-ba099b7c840d}}
{{figure:fe75912f-8f5b-4b97-87a1-e2e4ea353f5e}}
{{figure:76070247-80ae-4ef0-ab2c-413469de3874}}
{{figure:d54ed592-b12c-4360-ba95-951824897ab3}}
{{figure:4bdfcf58-9be8-474a-95c0-5608cfd6f6b6}}
[figure]labelfont=bf,name=Extended Data Table,labelsep=space
{{figure:365c15dc-af7d-42da-9490-5d34540be735}}
Supplementary Information
In these Supplementary Notes we present additional information on the theoretical derivations and numerical evaluation of our model. The details reported are intended to be pedagogical. The Supplementary Notes are organized in eight sections.
We begin in Supplementary Note with comments on various aspects of the theoretical analysis, notably possible scenarios of the line of phase transitions under tilted fields, and a review of theoretical models of LiHoF{{formula:b4e86cda-a038-4419-a7c5-d99348bb97c8}} reported in the literature so far.
In Supplementary Note we introduce the phenomenological theoretical framework of the transverse field quantum phase transition under tilted magnetic fields.
This is followed in Supplementary Note by an account of the microscopic Hamiltonian for LiHoF{{formula:7f7867f1-2e1e-48be-a44d-ad3b53e8e070}} , notably the Ho{{formula:97634d08-b30f-46fd-8cb5-0d5d2dcc2885}} ions, taking into account the crystalline electric field (CEF) potential, Zeeman terms of the tilted field, hyperfine coupling to nuclear spins and interaction between electronic spins.
In Supplementary Note we present the mean-field approximation of the microscopic model, involving the diagonalization of the {{formula:8b556dc1-dc7e-4914-90e1-b07267b2709c}} matrix.
We then move on to review the literature on magnetic domains and domain patterns in Supplementary Note in order to motivate our choice of sheet-like domains considered in our model.
In Supplementary Note we deduce an exact expression for the stray-field energy for a given domain pattern and find that it can be rewritten in terms of effective interactions between average magnetization components in the different domains in the spirit of an antiferromagnetic coupling.
We then proceed to combine the microscopic interactions and the domain energy into a joint mean-field description described in Supplementary Note .
In a first assessment of the combined model, presented in Supplementary Note , we discuss the energy of the stray field and the domain walls as a function of domain number. This shows that our results are insensitive to the precise choice of domain shapes and validates the assumptions we make.
Supplementary Note , finally, describes how the full Hamiltonian is solved in a mean-field approximation where the domain pattern is optimized in the spirit of a variational ansatz.
Here we address in particular changes of the phase diagrams in the presence of domains, as well as the intricate interplay of the non-Kramers character of the Ho moments with the hyperfine coupling.
Aspects of the theoretical analysis
We report the experimental observation of a well-defined line of phase transitions that emanates under tilted magnetic fields from the text-book example of a transverse-field quantum critical point. The observation of the phase transition under tilted fields raises the question for the existence and nature of the underlying symmetry breaking. Close inspection of the well understood microscopic spin Hamiltonian of LiHoF{{formula:fbb97810-5c0e-44bf-8827-3f642fd1029e}} reveals that its spin symmetry is fully broken in the presence of an applied magnetic field tilted away from the hard plane. A subtlety concerns here that the atomic positions of the F{{formula:e9402e16-3ffd-4880-840c-4db6bdcc7271}} ions imply also a symmetry breaking within the hard plane. Thus, even under perfectly transverse fields the paramagnetic phase displays a tiny magnetization component perpendicular to the applied field as illustrated in Extended Data Fig. REF . Representing a small effect, this does not question the validity of the account of the TF-QCP as such.
Given that the spin symmetries of the microscopic Hamiltonian under magnetic field are fully broken, only a few putative mechanisms exist of the symmetry breaking. Appreciating that the formation of domains has long been known in LiHoF{{formula:70595807-b996-494b-9152-d6dd8e73c7e9}} , the simplest mechanism is a breaking of translation symmetry associated with the formation of magnetic domains.
Alternative causes of the symmetry breaking comprise some form of microscopic antiferromagnetic or polar order, a transition of the electronic structure (say a metal-insulator transition), or a transition of the crystal structure. These options are exceedingly unlikely. Namely, there is no evidence suggesting additional magnetic interactions that may cause a transition of the microscopic magnetic structure even under tiny tilted magnetic fields. Further, the crystal structure has full inversion symmetry and polar degrees of freedom are not expected to exist. Also, the electronic structure is very well understood with a large band gap far from any instabilities. Last but not least, the crystal structure is known to be very stable under substitutional doping as well as for the entire series of iso-structural Li-R-F{{formula:9c6343e3-0c23-46ed-ba3b-1748905926e2}} compounds, where R is a rare-earth.
Hence, the observation of a line of phase transitions that emerges continuously from the TF-QCP and evolves monotonically as a function of field direction appears to be very difficult to reconcile with the four mechanisms just mentioned. Moreover, the field and temperature dependence of the susceptibility evolves monotonically between the well-understood behavior at the TF-QCP under transverse fields to the characteristics of a conventional hysteresis loop for field along the easy axis. In turn, the formation of magnetic domains appears to represent the only plausible explanation of the line of phase transitions under tilted fields.
At this point it is instructive to summarize concepts and models from the literature used to describe transverse-field Ising systems in general and LiHoF{{formula:c7291e4f-e57e-4a29-b523-33e1f558b42b}} in particular. These set the stage for the account of ferromagnetic domains under tilted fields. In general, the models can be distinguished according to their local degrees of freedom, the interactions between them and the treatment thereof, and whether or not mesoscopic inhomegeneities are taken into account.
A first group of theoretical studies explored general aspects of Ising ferromagnetism. This includes the properties of branched domain structures for Ising ferromagnets.{{cite:9beee45dd4485f8a01096d8a82a72b7bfa019995}}, {{cite:b503bc57b0e8ca4aa19def0de56d6b3ea39f6226}}, {{cite:a06384cd52a608d3d46cccf9773fabb1aa09708f}} Using an effective spin 12 model without hyperfine interactions the thermodynamic signatures and domain structure at zero magnetic field was found to be in excellent agreement with experiment.{{cite:5ed8562accc1ea7909d7e7ff7bf5ea33548a9f55}} Focussing on the possible existence of domain wall roughening by means of the effective spin 12 a renormalization group analysis no domain wall roughening for long-range interactions at zero and high temperature was observed.{{cite:775bb8c42bbd978f17147abba980967240a7e988}} Even an accurate estimate of the demagnetization factors was reported recently, however, without discussion of the magnetic field dependence and quantum criticality.{{cite:c9529802e0eaa0d40527c6d7b0cccae0cfbcbb25}}
Turning to specific models for LiHoF{{formula:b4aef98d-5aa8-48ab-8752-b9fe72aab534}} , the seminal work of Bitko et al. {{cite:6876e1e5632b935bec254c538f1e789bcfff462a}} employed the complete Hamiltonian of the Ho{{formula:f84ba3a5-41fc-45b5-9ce1-ba6047051a0b}} with a {{formula:78c2f794-31cf-4743-b818-0a18e121ade7}} electronic spin and {{formula:c151f20c-9d2d-4bcb-be1a-0ea9930ca70e}} nuclear spin in the full CEF scheme resulting in a {{formula:513828be-aaea-449d-856a-5c1157c1ad49}} matrix. Bitko et al evaluated this model on a mean-field level, using an empirical demagnetization correction to correct for domains. A similar approach was pursued in studies of the collective excitations by Ronnow et al {{cite:825d1da0b9129999174e568a753cb1351e885682}}, {{cite:4266d7a49ee9b036402ca4c9d4fcd1eed6028f89}}, {{cite:629a10b6c198934e0fdb668a8d8f9b51951d2260}}, where the effects of fluctuations were included using a {{formula:81b3f8e3-db8f-4c68-831c-91745784a12b}} expansion in an effective medium approach as first introduced for HoF{{formula:c6486fe7-274b-472c-a12c-269d4c8e75da}} .{{cite:660de830e4dc9c0da0aa349948857a067b6fd9c5}}
To reduce computational complexity, the work by Chakraborty et al. {{cite:1af23524d0658be536d710c039f6ff0dc7531e6a}} developed an effective spin 12 model of the non-Kramers ground state, keeping the {{formula:2196182a-fa49-48d1-b652-a083d1735950}} nuclear spins. A Clausius-Mosotti equation was used to determine the effects of magnetic domains, incorporating the effects in terms of a renormalization of the couplings constants. Evaluating their model by means of quantum Monte Carlo simulations, the hyperfine coupling was taken into account a posteriori in terms of a renormalization of the applied field. Taking this model one step further, McKenzie and Stamp {{cite:709a579545f75369fa3db5324a8dba1f2716f71e}} recently solved the effective spin 12 model using mean-field theory and RPA. To interpret microwave spectroscopy of electronuclear modes near quantum criticality another variant of the effective spin 12 model was used, where the effects of ferromagnetic domains was included by means of an effective demagnetization factor while not considering the domain structure as such.{{cite:c815b37eb24d6466a83fd8e5901f0f5b1bd6ce3b}} Finally, several studies explored also the validity of the effective spin 12 model in doped systems, where random fields are dominant.{{cite:32c93fe9e860bdfce14d19f7711c865b235675dd}}, {{cite:e6404c5f429a7669916feee8636963fa62857005}}, {{cite:9425615d7adc4847248276f956c9fbbd9d9b2bb1}}
For the description of LiHoF{{formula:4d832346-bf1b-4975-b738-963f92c46454}} in tilted fields, it turns out to be crucial to include both microscopic and mesoscopic degrees of freedom {{cite:1886a8f4de75cd3c549d680ebfcf1882678bb528}}, with the latter referring to the sizes of magnetic domains. Aiming at a quantitatively accurate description, we include the complete a {{formula:0a9aa37e-a038-4386-916f-9c489a5d649d}} -dimensional local Hilbert space, as in earlier works,{{cite:6876e1e5632b935bec254c538f1e789bcfff462a}} and combine this with the magnetostatics of an arrangement of magnetic domains which is assumed to be periodic for simplicity. We treat the dominantly dipolar interaction in a mean-field approximation, but it is important to keep distinct mean fields for up and down domains to account for the explicit symmetry breaking by the field tilt. Hence, combining such a variable domain description with an accurate microscopic mean-field theory is the new aspect of our approach.
Landau theory
The simplest phenomenological description of a transverse-field Ising quantum phase transition in Landau theory is by means of a scalar order parameter {{formula:c6085ca2-3cd0-4019-8057-d9c16157c169}} with Ising symmetry. The (bare) order-parameter mass is given by {{formula:2903850f-2c35-4d4c-8d67-e0042ed566fa}} for perfectly transverse field {{formula:5fe2b11f-120c-4906-bd3c-4fddbbbf0b3c}} , such that an ordered phase is realized for {{formula:9acf1a65-c99f-4bcf-b8fe-e5d005eaf3f1}} . Accounting for tilting of the field by an angle {{formula:7f1fcad6-73e9-4156-bad8-cd0a9ea2a5a2}} yields a Landau functional of the form
{{formula:8defcf82-aac5-41ad-b392-d660b4ae6f04}}
where {{formula:da07a916-d25c-4fc5-ab1d-d5e5e26f7ef4}} represents a field conjugate to the order parameter. For {{formula:b64a99a8-073b-42eb-bf64-3b44e02921a9}} the transition at {{formula:34834291-27f4-42fb-8d95-f763c19da457}} displays mean-field exponents, i.e., {{formula:672d2037-178e-4cf4-b725-4f78e02575f9}} and {{formula:8e7edd51-ed6f-46e4-938a-47cd83573511}} .
The presence of a longitudinal field at finite {{formula:b8302eee-a8b4-4601-983b-06dbf2b624db}} renders {{formula:28ef5330-6ffb-4651-a789-df5f46268464}} non-zero for any order-parameter mass and hence destroys the field-driven phase transition. The transition turns into a crossover, whose location {{formula:6b5170cf-a904-4302-8d65-8c12d02eac97}} may be defined via the maximum of the susceptibility, {{formula:e3603ebe-5d9d-42cb-bf2c-aad7e13c90f0}} , as a function of {{formula:470dc20d-5948-4a63-a530-b5de0c3bfce0}} . A straightforward calculation for small {{formula:8a46322f-7a6b-4808-a00f-0e490c212530}} yields
{{formula:0619b2a3-726f-47d6-99fc-2ed34a971c2a}}
The general result is expected to be {{formula:80a9c4c0-894f-4efd-9e9c-dae32d6754b3}} deduced from the critical power laws.
Our explicit microscopic calculation for LiHoF{{formula:80232e4b-6d74-4f2d-b416-cc33a95ab30d}} , described in more detail below, indeed yields a crossover at {{formula:b953cfc8-80d2-4e6f-a99e-1f68c98826a2}} if domain effects are neglected, see Fig. REF d.
In stark contrast, the experiment measures qualitatively different behavior. Instead of a crossover, a sharp transition is observed, with the critical field approximately shifting proportional to {{formula:49036bda-e346-464b-9a6b-6aba2e4768da}} . The existence of a sharp thermodynamic transition at finite tilt angles is clearly beyond a single-component order-parameter description in the spirit of Landau theory.
Microscopic modelling
A single Ho{{formula:10cf167c-a1dc-4e5a-ab54-2697858d62e9}} ion in a magnetic field applied under an angle {{formula:b00a1a16-e59b-4c3e-9bd1-6ff992851a42}} with respect to the hard axis, {{formula:0c38dac0-5854-4bf5-8406-8811d99f45d3}} , and subject to a crystal field of {{formula:4a74cb19-0d13-49a1-b0ba-ebe7446e434f}} symmetry, which in LiHoF{{formula:1875a9ad-8ea0-4768-ac4c-0a6eb6b891d0}} is created by the neighboring {{formula:086f4d3b-857b-4666-a349-8a463bdba2ea}} ions {{cite:900a53caa1355186b181506fffcef797d8b478b1}}, can be described by the Hamiltonian
{{formula:3d23a8d0-4e7c-4c30-b28b-31a428c9c5fd}}
with {{formula:32630195-d082-4219-ad3e-c74b443fe4f4}} electronic moments and {{formula:df9ae3fe-90cf-48c9-9be5-0a53d38b4ecc}} nuclear moments. The hyperfine coupling to the nuclear spins is assumed to be of Heisenberg type {{cite:709a579545f75369fa3db5324a8dba1f2716f71e}}. The associated material-specific strength of the hyperfine coupling for LiHoF{{formula:0aac3d3f-189d-47a8-88dc-90ab437010b3}} is {{formula:ea539979-cc3d-41d4-957a-ea320cdd6d59}} mK. The CEF term is given by
{{formula:4faee190-08c4-4fc3-b56a-77637a3ef478}}
with the Stevens operators {{formula:810b052d-b8c4-4cf5-b880-c8288a9b3077}} and the coefficients {{formula:c4f6526f-0b83-4a6e-8b60-78ebe2ffae9e}} taken from Ref. 2004ChakrabortyPRB. The Stevens operators are polynomials in {{formula:598eaca0-fb9b-46a4-b0b0-625c182fc1b3}} that encode the angular dependence, while the radial component is included by fitting their coefficients {{formula:b49b0709-a9ce-4d6f-b82a-0c8de07e5974}} to experimental data. We note that {{formula:54e35f59-8b3c-4cbe-ba8f-ca856a866d5e}} may be either positive or negative depending on the crystallographic position of the F{{formula:e62912ff-ce57-4ef3-9e6c-e01649b8be07}} ions{{cite:4266d7a49ee9b036402ca4c9d4fcd1eed6028f89}}, see Extended Data Fig. REF .
The electronic Landé factor {{formula:7f94a08d-d0e2-476e-8ce1-d87723d1db75}} of a single Ho{{formula:0d75eb44-161d-4eb2-9816-36155d161b03}} ion can be derived from the Wigner-Eckardt theorem to be {{formula:456be609-d849-4392-a755-9c4ff3177147}} {{cite:1af23524d0658be536d710c039f6ff0dc7531e6a}}. Small deviations from this single-ion value are expected in the extended crystal {{cite:9e286406f8e863b7d94361cd28ab44dd40a20ffe}}, {{cite:ea18114f15fe803917f90c81da8d17ba78a55841}}. To achieve good agreement with experimental data we used {{formula:79af1292-b85e-442f-abf7-aa2b784e0986}} , i.e., {{formula:0a595f78-8aa1-411f-b09f-7d31a0d137a7}} lower than the single-ion value. Without this adjustment our results remain qualitatively unchanged, but there is a larger mismatch of {{formula:93e9866c-71cf-4584-a96b-dca96466987d}} compared to experiment. We note that the value of {{formula:65969bd8-44ef-46cf-9add-42957f95c686}} not only re-scales the magnetic field but also influences the stray-field energetics, see below.
For completeness we also include the nuclear Zeeman term with {{formula:61a53658-50d3-42bd-89ce-1e5c85cf1a6d}} , although its effect on observables is small because the behavior of the nuclear spins is dominated by the large hyperfine coupling.
Diagonalization of {{formula:ce0b6379-40ae-465c-90f0-e99630933e88}} in its 17-dimensional electronic Hilbert space gives a low-lying non-Kramers doublet which is separated from the next CEF level by an energy gap of 11 K, Fig.REF c. The ground-state doublet displays a large moment along the Ising axis, {{formula:f93dfd9c-5dca-4727-88f5-956c473047be}} , but zero moment along {{formula:32c1eb24-36a6-42dc-aba4-0d05aa7ef1d5}} and {{formula:ddea6457-e2f7-4212-a126-a96ba04f0814}} . As a result, the application of a magnetic field along {{formula:11fca35a-8d42-4278-add3-c4d6894994e1}} leads to the corresponding moment scaling as {{formula:a46227da-22ce-4a32-b284-7d460f84dc53}} , Fig.REF d, resulting from mixing with higher CEF levels.
In contrast to parts of the literature {{cite:6876e1e5632b935bec254c538f1e789bcfff462a}}, {{cite:825d1da0b9129999174e568a753cb1351e885682}}, {{cite:32c93fe9e860bdfce14d19f7711c865b235675dd}}, {{cite:1af23524d0658be536d710c039f6ff0dc7531e6a}}, {{cite:900a53caa1355186b181506fffcef797d8b478b1}}, {{cite:709a579545f75369fa3db5324a8dba1f2716f71e}} where the ground-state doublet was treated as a pseudospin {{formula:eaba28a2-bb85-4166-89d4-a1b6ba467216}} , we keep the full 17-dimensional Hilbert space. This way we account fully for the non-Kramers physics in our calculation. This proves to be essential when describing the effects of an applied magnetic field in both the {{formula:a509b5a0-8798-4b10-a5c0-06f2bd7ec763}} and the {{formula:43e31fc6-6fd5-4fb6-bebb-bb311bf0e24c}} direction.
Ferromagnetism in LiHoF{{formula:c2947d59-fc69-4bdd-ba50-66ab69f43fb6}} is driven by interactions between the electronic spins of different Ho{{formula:7c9b5def-f3db-404e-a266-6d4fd76c7666}} ions, which involve both long-range dipolar and nearest-neighbor exchange interactions. For simplicity, we model this combination by a nearest-neighbor Heisenberg interaction {{formula:dfa53483-c523-47c3-b340-c2d9309fff04}} {{cite:900a53caa1355186b181506fffcef797d8b478b1}}, recalling that the dominant source of magnetic anisotropy is the CEF term.
Taken together, this leads to a microscopic Hamiltonian of electronic spins {{formula:d8be6229-594e-427e-b908-dbc5f933955c}} and nuclear spins {{formula:f9884184-663f-469a-9fff-7ecce5010612}} of the form
{{formula:174d948f-5e18-4edd-ad46-c1f172612b38}}
where {{formula:9931e7a1-ebc0-49df-8ad3-d8f688e820c6}} runs over pairs of nearest neighbors. At this point the strength of the effective interaction reduces to a fit parameter. For good agreement with the experimental critical temperature {{formula:82b83f5a-7313-488f-820b-09be84feee2b}} we choose {{formula:e8eedf51-6687-45fa-9dfb-95e64dd68467}} mK, which is consistent with the order of magnitude of values estimated for the dipolar and exchange couplings in LiHoF{{formula:5c2ce07a-8798-4d76-8790-b722c552fad2}} . {{cite:709a579545f75369fa3db5324a8dba1f2716f71e}}
Mean-field approximation
Due to the long-ranged nature of the dipolar interaction in LiHoF{{formula:bd7710db-db1b-40bb-83a6-e2412840f94b}} , the effects of fluctuations are suppressed and a mean-field treatment appears justified. In particular, the upper critical dimension of the finite-temperature transition is {{formula:6e90e849-eeb0-45c6-9597-d79c0e1338f8}} – as opposed to 4 for short-ranged interactions – such that the phase transition is of mean-field type both at {{formula:4dca72ba-8c6b-4f84-b8f4-ef0d42069eae}} and finite {{formula:097732aa-fc40-41cf-9003-fd771b40ad35}} (the latter with logarithmic corrections).{{cite:81b5f7ffffc7ff2ef7ebb794f9aa17a3b8a0b863}}
Within mean-field approximation, the Hamiltonian in Eq. (REF ) reduces to a single-site problem
{{formula:33c50219-1026-4f4a-9929-cd71b92fd1ce}}
where {{formula:e78ca5d4-0775-4e1c-b5e2-6984ee965d15}} represents the number of nearest neighbors. Solving {{formula:a9c56c66-7df5-4045-a5ed-ca8bda098c9a}} amounts to the diagonalization of a {{formula:618b80a6-27cd-4c36-8b12-2a81e28b509d}} -dimensional matrix, supplemented by the self-consistency condition {{formula:8c0424b5-0aca-4c2c-a06b-3815ca766a60}} .{{cite:6876e1e5632b935bec254c538f1e789bcfff462a}}
The resulting zero temperature phase diagram of this purely microscopic (i.e. single-domain) scenario is displayed in Fig. REF d. It features a quantum phase transition as function of applied field at {{formula:0c22280c-46eb-4f96-96fa-715f35c3f5bf}} , i.e., for perfectly transverse field, and a crossover at a field {{formula:5ed1e896-24c9-4158-855a-671c248791d9}} under tilted fields {{formula:61095fe4-a9f6-4fe5-a465-2070ef7b0bab}} . The properties of this crossover are consistent with the results from Landau theory as outlined in Supplementary Information Note . Namely, the susceptibility {{formula:32ef1b39-1ad6-4d8f-b414-f7dea12d34ba}} displays a maximum as function of applied field at {{formula:b741eeda-7c18-4b57-bc57-4031b46fc0b5}} , the location of which is marked by arrows in Fig. REF d. At small angles, we find {{formula:fd6ddba6-7ba7-4246-9429-8d0b2f24fb1f}} as expected. However, the level of theoretical modelling is insufficient to explain the experimental observations. Instead the well-known fact that ferromagnets exhibit domains must be included.
Relevance of magnetic domains
The formation and shape of magnetic domains in uniaxial (Ising) ferromagnets has been studied extensively starting with the seminal papers of Landau/Lifshitz and Kittel.{{cite:bcc7099938af506ddf2635fbf3714c7f2c9f170a}}, {{cite:35a6e24d0248830acc9dfef7fce03332d151b4b1}}, {{cite:9a6076ef21311d54ba2c6f73b35c00e139120e6a}}, {{cite:cb031a7ccf592f779d0bc49287841fbe53604731}}, {{cite:9d3aa70245fcf35ad1e272bef0e792bfbeacdb03}} It has also long been appreciated that the shape of a given sample strongly influences the formation and shape of the domains.{{cite:3bcc4ba2981e7d1038cbf09711d5b08b5ee1b2b1}}, {{cite:7d6d8f34f806d7ea585fb5aaa877d8e681d43a7a}}, {{cite:9d3aa70245fcf35ad1e272bef0e792bfbeacdb03}} In platelets two remanent domain structures were observed subject to the thickness.{{cite:a483469bde32115457a457398aa83572f889b628}}, {{cite:a0ef7f924ac87ffecbb9fbf79b4789f87090e397}} First, the parallel-plate domain structure proposed by Landau and Lifshitz, where the easy-axis is normal to the platelets. Second, the honey-comb domain structure consisting of closely packed arrays of circular cylindrical domains. Detailed assessments revealed that the total free energy of the two domain structures differ by tenths of percent being essentially identical. Further studies revealed the presence of closure domains and branching at the surface of the samples that reduce the stray field energy.{{cite:c3f87360e525d922806ec6b87b9fbd3b53f5eebd}}, {{cite:108e7f031efb5b391265967f46f5930f6fd49cdb}}, {{cite:9beee45dd4485f8a01096d8a82a72b7bfa019995}}, {{cite:b503bc57b0e8ca4aa19def0de56d6b3ea39f6226}}, {{cite:50f3a6dabb3386c13dcb299cebac30c6a1d62efe}}, {{cite:1aef07d3a7f524b66514fb9f616fd385a1ddad2b}}, {{cite:a06384cd52a608d3d46cccf9773fabb1aa09708f}}
Extensive studies explored the dynamical properties of domain structures and domain walls in Ising ferromagnets where a logarithmic rather than an exponential time dependence of relaxation processes was attributed to a wide distribution of barriers arising from the domain branching.{{cite:a06384cd52a608d3d46cccf9773fabb1aa09708f}}, {{cite:8f02042b104fa1ca99adb4dcc97c0873c5b8ac5f}}
The domain structure of LiHoF{{formula:2cf7cd9a-9273-44b4-ab9c-2118dcf5a2b1}} was first studied experimentally by means of Faraday rotation, finding evidence for stripe-like domains along the magnetic easy axis with a thickness of order {{formula:0e4422ee-39b9-4f81-822b-6ba3ca599562}} . {{cite:ea18114f15fe803917f90c81da8d17ba78a55841}} Further studies analyzed the domain pattern in more detail for a slab-like geometry as a function of a longitudinal field at {{formula:d55aedfb-00c9-4717-8859-f8753f31a432}} K, where discontinuous transitions from a stripe pattern to a bubble pattern followed by the uniform state were reported. {{cite:c3f87360e525d922806ec6b87b9fbd3b53f5eebd}}, {{cite:108e7f031efb5b391265967f46f5930f6fd49cdb}} Moreover, branching near the surface was observed, in agreement with theoretical results in dipolar Ising magnets. {{cite:9beee45dd4485f8a01096d8a82a72b7bfa019995}}, {{cite:b503bc57b0e8ca4aa19def0de56d6b3ea39f6226}} This is consistent with more recent studies using scanning Hall microscopy, which reported also the observation of substructures within the domains. In addition, these studies reported changes of the domain size as a function of temperature and transverse field they attributed to surface branching. {{cite:1aef07d3a7f524b66514fb9f616fd385a1ddad2b}}, {{cite:ec1569c49f9f8e103135f227f8b4771d739b19c4}}
Theoretical studies of LiHoF{{formula:953b3261-04f2-4e1e-9a8d-9690dfac85c6}} addressing the long-ranged dipolar interaction employed an Ewald summation {{cite:357833e91c1cb5c05c123bb61bce68a3ba2784ec}} or the reaction-field method.{{cite:c23781f7e119bef3d919d4c015886243337df155}} The former naturally leads to domain formation in Monte Carlo simulations with a large enough unit cell and appropriate boundary conditions.{{cite:5ed8562accc1ea7909d7e7ff7bf5ea33548a9f55}} In Ref. 2009BiltmoEPL a domain pattern of parallel sheets was found to be favorable at {{formula:6093c91a-d828-4405-8d22-4a34ca1620e8}} and {{formula:8a571437-07a2-4ac5-a3f9-e9fc37c69b40}} , and the energy density of domain walls was estimated. The latter incorporates the presence of domains by considering an imaginary microscopic sphere in an effective field of surface charges.{{cite:1af23524d0658be536d710c039f6ff0dc7531e6a}} The structure of domain walls in transverse-field Ising models was investigated in Ref. Mias05 and long-ranged interactions were found to prevent domain-wall roughening.
In summary, due to the strong Ising anisotropy the domain patterns are comparatively simple in several important aspects. First, the two dominant domain patterns observed experimentally are energetically almost equivalent{{cite:a0ef7f924ac87ffecbb9fbf79b4789f87090e397}}, {{cite:cb031a7ccf592f779d0bc49287841fbe53604731}}, {{cite:ea18114f15fe803917f90c81da8d17ba78a55841}}, {{cite:c3f87360e525d922806ec6b87b9fbd3b53f5eebd}}, {{cite:108e7f031efb5b391265967f46f5930f6fd49cdb}}, {{cite:1aef07d3a7f524b66514fb9f616fd385a1ddad2b}}, {{cite:ec1569c49f9f8e103135f227f8b4771d739b19c4}} suggesting that the precise choice is not important at the level of our results. This is consistent with the numerical evaluation of our model presented in Supplementary Note which justifies to focus on a scenario that is mathematically amenable. Second, the observation of branching is confined to the surface of samples as reported in the literature.{{cite:50f3a6dabb3386c13dcb299cebac30c6a1d62efe}}, {{cite:c3f87360e525d922806ec6b87b9fbd3b53f5eebd}}, {{cite:108e7f031efb5b391265967f46f5930f6fd49cdb}}, {{cite:9beee45dd4485f8a01096d8a82a72b7bfa019995}}, {{cite:b503bc57b0e8ca4aa19def0de56d6b3ea39f6226}}, {{cite:a06384cd52a608d3d46cccf9773fabb1aa09708f}}, {{cite:8f02042b104fa1ca99adb4dcc97c0873c5b8ac5f}} It concerns a small volume fraction only that will not change the main conclusions of our study. Third, due to the strong Ising anisotropy roughening of the domain walls is not expected.{{cite:a06384cd52a608d3d46cccf9773fabb1aa09708f}}, {{cite:8f02042b104fa1ca99adb4dcc97c0873c5b8ac5f}}, {{cite:775bb8c42bbd978f17147abba980967240a7e988}} Taken together it appears therefore well-justified to account for the formation of domains by means of a simple antiferromagnetic arrangement on mesoscopic scales.
Effective interactions induced by domain formation
As argued above, and consistent with our mean-field approach, it proves to be sufficient to refrain from a detailed modelling of domain and sample shape.
We assume a cubic sample with base length {{formula:bc5a91c7-c20a-4af2-ba27-32845e3f9941}} , with {{formula:265b687f-c86c-49a7-8fc9-dc8ae025b19a}} m for the results shown, and a periodic arrangement of two types of sheetlike domains stacked along the {{formula:e18dbe33-7847-4ed5-995a-504eb1e18f3e}} direction, Extended Data Fig. REF a (cf. Fig.REF f and REF g).
We note that an alternative domain arrangement with sheet-like domains along the {{formula:2621d12f-616b-40c8-b9ff-cac3c6d21f19}} instead of the {{formula:ac22c60b-9c73-4c20-87a8-63e7d62e6f6b}} direction is energetically unfavorable due to induced charges on the domain walls. We assume, further, a homogeneous magnetization within each domain.
The domain thicknesses are denoted {{formula:7736aa60-5176-4d6d-b62d-c905e0787cb2}} and their magnetization densities {{formula:2e9627d5-e631-48ad-8ae4-7fd257bbcc35}} , where the indizes 1 and 2 refer to the majority (up) and minority (down) population, respectively. At zero field we expect {{formula:40daac09-04cd-452c-b0d7-9b0848d5bd1d}} and {{formula:124f8469-3016-4463-bb43-7139216576b4}} , reflecting the Ising symmetry. At finite field, the magnetizations will develop both {{formula:ab8ad37a-0706-43e0-9695-07facf57339c}} and {{formula:a9e47cad-b8cc-456b-876b-ae856e2fce19}} components, and the domain sizes can be different. Assuming {{formula:50d10f7b-6873-4414-bd64-3ebdab7a9dc9}} , we introduce the volume fraction of the minority domains as
{{formula:f81c8ba2-e9da-4c27-a6b4-dfc38b81766a}}
where {{formula:9c463666-3722-47ef-94c2-5ad092a7d0b3}} is the average domain thickness and {{formula:d8b2fbb5-c30b-4582-9a5f-1c928910852e}} the number of domains of each type. In what follows below, the fraction {{formula:f0c98383-077e-4099-b498-99afadc88839}} will be treated as a variational parameter.
In general, the total stray field energy of a sample without volume charges ({{formula:a84b1a53-33c0-45e1-aea7-ef1c362b74cb}} ) is given by
{{formula:9db22474-234b-4fbb-a733-4cd39bc85664}}
where the surface charge {{formula:23722ca0-9d57-4da5-a921-6ae9c9aa0057}} is given by {{formula:660a5d32-30f2-4198-a6c9-c78887751ffa}} with the surface normal vector {{formula:391cafc0-296d-4ae8-ac3e-d5d04ae9bd43}} {{cite:9d3aa70245fcf35ad1e272bef0e792bfbeacdb03}}.
This expression for the stray field energy can be applied to two parallel rectangular sheets of constant charge {{formula:97c62b8a-2edd-4f66-9c3d-c47abb3232f7}} and {{formula:2cf94a10-c9bf-4527-98a6-17b28bcecac8}} at coordinates {{formula:bea9a838-b5ff-4441-8236-a377bffb1a8c}} and {{formula:17f4946a-073c-4743-9b6a-7be21d46d497}} . For a constant surface charge, the integration amounts to integrating {{formula:0e2d6123-d587-42b0-90d9-b0da1b6e340d}} twice with respect to each {{formula:bb40d937-6cdc-42b6-a06a-29e5ac4a2e4d}} and {{formula:f3b303b4-b155-4367-b790-e31763717f2e}} . Using appropriate choices for the integration constants this leads to
{{formula:4f3af12b-11fa-4669-92b5-4ab62ef66792}}
with {{formula:064c07f1-efc5-46b4-8c16-944b157163a8}} {{cite:9d3aa70245fcf35ad1e272bef0e792bfbeacdb03}}.
Insertion of the appropriate boundaries gives the interaction energy of two parallel sheets as
{{formula:3430a673-e373-44ef-8e51-b08c9e808a70}}
The total stray-field energy can be decomposed in sums of pairwise interactions between such rectangular sheets of constant charge for the domain configuration in Extended Data Fig. REF a, since the surface charge is piecewise constant on rectangular patches on the sample surface. The domain walls are not charged because the magnetization along the {{formula:86d255de-139a-41b6-80c1-ecf9e1551920}} direction is small and neglected here. The energy contribution of sheets perpendicular to each other cancel due to symmetry, such that no mixed terms of the form {{formula:5480142d-fc83-405c-8ead-90b0be93e6d3}} arise.
In addition to the stray-field energy, the domain-wall energy must be taken into account. The total energy cost for domain walls in the sample is assumed to be
{{formula:ce456709-1a62-42da-9f7b-0de90b8f25b2}}
where {{formula:f0c471b6-5780-4359-8b4d-8d26f568b81d}} is the area of a domain wall and {{formula:a57c73d7-e933-4fac-8ecd-3f301d4bed2b}} the number of domain walls. {{cite:5ed8562accc1ea7909d7e7ff7bf5ea33548a9f55}} The denominator {{formula:bf005020-4c6c-4d2d-b3d8-8d0c92ff1f72}} compensates the units of the magnetization density, where {{formula:2f3f8568-4a9d-4406-a86a-fe323cf703bb}} is the number of lattice sites, {{formula:28e7f8e7-1016-415f-bcd8-7cb45e0fddad}} the sample volume and {{formula:d4ded4c6-1f96-4b81-be2a-1ae7daa72f81}} m{{formula:4951796e-70ea-4ff3-9f30-b8067a649696}} the unit cell volume, which contains 4 Ho{{formula:fd7399e9-a450-4f77-9ff1-09be3e68abaf}} ions {{cite:6876e1e5632b935bec254c538f1e789bcfff462a}}. The energy density of domain walls in LiHoF{{formula:4bc6590a-ae96-499b-bc4c-c99610b4ff53}} was estimated from a Monte Carlo study{{cite:5ed8562accc1ea7909d7e7ff7bf5ea33548a9f55}} as {{formula:1558ecee-6b8e-4076-b2e1-7d6cf3d5bc03}} J/m{{formula:f27250e9-6657-4b7c-8278-aa1cec8a6901}} .
The domain energy, i.e. the sum of {{formula:d272adac-cbb1-4b69-b8a9-78ce81f98bfd}} and {{formula:958b7308-494f-4761-98b1-7a237bbe963d}} , is bilinear in the magnetization components. It contains pieces {{formula:182325db-c8af-4433-a0c2-a23db40a1f05}} and {{formula:01de0f60-4f8e-4e3d-8807-559688b25c42}} which can be interpreted as interaction between the domain magnetizations which is antiferromagnetic in character, as neighboring domains favor antiparallel alignment to minimize the stray-field energy.
Combined Hamiltonian and mean-field approximation
We now proceed to combine the microscopic interactions and the domain energy into a joint mean-field description. To this end, we express the domain energy in terms of microscopic moments. Since the nuclear {{formula:0e17815e-0388-4acd-a5fa-a3a2ab45dcaa}} factor is tiny compared to the electronic {{formula:cf3d4585-573d-4e01-aef0-1cc93ca9353b}} factor, neglecting the contribution of nuclear spins to the magnetization within each domain is a reasonable approximation. Therefore we relate the magnetization density to the electronic moments as
{{formula:cb1b8520-b4d8-48ba-a0ec-8b2c26949184}}
With our assumption of a homogeneous magnetization within each domain, the total domain energy can be re-written in terms of the expectation values of electronic moments {{formula:487f3281-a721-4347-b49e-dbd3172ae693}} in the domains 1 and 2:
{{formula:d9887c9d-f86a-4fff-b17e-bff144b24066}}
with the parameters {{formula:68aa3ed3-05ea-41e5-82cc-a9fbf64cf5d5}} containing the potential-energy contributions of the surface charges caused by the magnetization component {{formula:571a09f1-03bf-47c2-b0b4-6f2c18fc1a80}} as well as the domain-wall energies. The symmetry of the domain configuration, Extended Data Fig. REF a, dictates {{formula:7f2753a7-d9b5-4e78-bac9-442e044a0261}} for {{formula:6b91b332-6e72-4616-8427-3081b817f450}} . Moreover, the parameters {{formula:88ab9bcf-4bb7-466e-af15-cb273a0f61cc}} are not needed since {{formula:f7f2a623-350e-472a-b39b-e30878ad990b}} is small and can be neglected.
Inserting the expressions derived above, we find the effective couplings as
{{formula:1623e06a-e232-462f-aea2-305103b189b5}}
for {{formula:29a00a51-7989-4a02-b992-ca45bda68603}} . For equal-sized domains, {{formula:2e9ff7c4-6d56-4043-9e3c-b6c93df7ce7f}} or equivalently {{formula:14dece64-dd45-47ce-917e-8705151aef18}} , we have {{formula:1655fc55-b455-4ee0-9633-0db5a0f3f4ca}} . Moreover, {{formula:039d9b08-1c5e-4308-a528-cf0c0202c752}} is symmetric under the exchange of {{formula:f30460b9-ad63-42b2-b57d-d7ca83785dd0}} with {{formula:512c7cc1-3eda-42ba-97aa-416a7fd4e6a4}} .
The sum of the coefficients {{formula:738869fe-96d6-483d-9426-806992de9686}} gives the domain energy of the single-domain state, {{formula:890fa83b-cd60-49e2-a22f-d97c0a9d68aa}} . It is therefore independent of the domain ratio {{formula:e60cc2d1-936c-4935-a58c-c51450affada}} .
Numerical evaluation for {{formula:2e2e04f7-c13a-4219-b61e-a7645b5a042a}} , {{formula:efe416f8-02ab-4986-a32d-0598464f7ece}} (and all other parameters as given above) yields {{formula:99ea197f-2c70-4e71-abb1-5f861676d0cd}} mK, {{formula:02c54f47-2695-4b21-95d6-0259f4f3ad20}} mK, resulting in {{formula:56d805ad-c7f0-4c59-927e-8ff09e4af82f}} mK. The coefficients vary smoothly and monotonically as a function of {{formula:db9bbc2a-6038-4abf-a52a-4333e6aaed5d}} . For instance, at {{formula:dc2197fd-ffb3-4fb2-ad7a-3dc32e7bf000}} we have {{formula:e61b433c-c866-49a6-a020-1e8dc4dc10cd}} mK, {{formula:03ba7a88-6b62-4443-813b-ec5ae384ad15}} mK and {{formula:4f4d1d27-a3e7-4d4e-8688-cc5ec2a151e4}} mK. In practice, we fit the dependence on {{formula:bc1cd163-357e-420b-a4a6-e5205cf8b658}} by a fifth-order polynomial in {{formula:2df84aad-0276-4520-bc84-5733cd5a16cc}} to save computation time when optimizing {{formula:397dc38e-1721-46d8-bce2-3a0c4619cef8}} .
The fact that {{formula:2242ac3a-dc12-4b41-bedd-4a8940d6115d}} reflects that the effective interaction between domains due to the minimization of the stray-field energy is antiferromagnetic. Similarly, {{formula:5d72ba52-1235-4ef3-96c3-6e43e595e0b3}} within each domain, implying that the stray field competes with the ferromagnetic interaction between the individual moments.
Further discussion on the choice of {{formula:6dc1f43b-e4db-4660-8968-0dd91c2e4dcf}} and its influence on the resulting energetics can be found in Section ; numerical results are shown for {{formula:39b738fe-9182-4286-9588-9ec385f42f92}} unless noted otherwise.
We are now in the position to combine the microscopic Hamiltonian Eq. (REF ) with the domain energy Eq. (REF ). Introducing domain-dependent mean fields, {{formula:71e1055c-18dd-470e-93d7-8c9adbc5de9c}} , and neglecting the weak microscopic interaction across domain walls, we obtain from {{formula:d39df058-c951-4602-b3b7-624aa206e7ee}} two independent mean-field problems of the form (REF ), one for each domain. These two problems get modified and coupled by the domain energy. The condition of minimizing the total free energy can then be cast into two coupled mean-field Hamiltonians
{{formula:421f346d-0bea-4f4c-8137-ef0e06ea073b}}
and
{{formula:245b8fb9-c3e3-440a-aa1c-fceb522ad135}}
with the self-consistency conditions
{{formula:faad1433-79af-4795-9b8e-9cb045413962}}
where the expectation value is taken with respect to {{formula:769b8c92-f95e-4755-9a9a-58594074a9c4}} . This is apparently equivalent to promoting {{formula:5f4e3316-a5d1-4973-b9e2-599d53d4cd73}} Eq. (REF ) to a bilinear Hamiltonian and decoupling its interaction terms in a mean-field fashion, resulting in the terms {{formula:53ad56d4-570b-4602-ac80-87e94d8f3356}} etc. The total energy then reads
{{formula:df10e1fc-fdd3-4dd8-a853-d6566bd40992}}
The self-consistency equations (REF ) are solved iteratively. In each step, the Hamiltonians {{formula:9dbfbaad-90cb-499a-80fb-f0007b2c5933}} are solved exactly via direct diagonalization in the {{formula:7225c774-2cf8-4dd2-bfca-7997e0ef18da}} -dimensional local Hilbert space. Depending on the initial conditions, in particular the relative sign of {{formula:4ac24cb2-690e-4266-93b7-4df55b2d59ed}} and {{formula:9a8519ec-b7fb-426e-b402-a6652347042f}} , one either obtains a single-domain or a multi-domain solution. Comparison of the total free energy {{formula:7f28b997-53d7-46a5-b065-8ed26b6cf81a}} yields the stable state.
For each set of parameters {{formula:5f89cdfc-279e-41bd-ba4f-0bd067a20d94}} the optimum domain ratio {{formula:cdb6862e-a502-4497-a5a0-5eccc14cd26b}} is obtained by minimizing the free energy {{formula:4ef23259-325a-411e-93e8-c2e479ac6c47}} with respect to {{formula:f8d57661-a498-4e25-9fb9-d60d8f52d880}} . Since {{formula:c9210f7a-374c-4040-97c3-505b11abf524}} is parabolic and smooth, Extended Data Fig. REF b, the optimum value {{formula:9aa03b50-19eb-454d-b2ec-77d6f0083359}} can be accurately found by means of a parabolic fit through a relatively small number of test points.
It is important to emphasize that Eqs. (REF -REF ) constitute a combined and consistent description of the microscopic interactions, the mesoscopic domain energy terms, and the backaction of the stray-field physics on the microscopic expectation values.
Importance of the domain shape and size
For a numerical assessment of our model we calculated at first the dependence of the domain energy {{formula:20a57411-6e46-4091-82d3-03d113dee1c7}} (REF ) on the number of domains. On the one hand this provided information on the relative importance of the stray fields as compared to the contributions by domain walls. On the other hand this served to optimize the computational effort and allowed to choose a suitable domain number and thus domain size for meaningful results.
Shown in Extended Data Fig. REF is the domain energy per site, {{formula:cc941f69-dc35-4c9e-8590-b907b5d108d0}} , as a function of the number of domains, {{formula:12aef878-205f-46a2-b2e6-046c60f8fc25}} , for {{formula:8b4f4477-dd2e-4d8e-9523-6d0941e12f36}} between 1 and {{formula:0de63507-02ef-456a-b70d-1a35aa9d9700}} . The calculation assumes a sample size of {{formula:f715f2e1-ee5a-4e12-b352-2bf5d3597114}} such that {{formula:cc514630-b207-4f46-a686-4e791b07036b}} translates into domain sizes between mm and several {{formula:a17fbd38-85e5-4d2f-83e9-8518e43edb54}} . At zero magnetic field, the latter correspond to typical domain sizes observed experimentally in LiHoF{{formula:e9efd447-b00d-4867-ba5f-b6235430a851}} {{cite:ea18114f15fe803917f90c81da8d17ba78a55841}}, {{cite:c3f87360e525d922806ec6b87b9fbd3b53f5eebd}}, {{cite:108e7f031efb5b391265967f46f5930f6fd49cdb}}, {{cite:ec1569c49f9f8e103135f227f8b4771d739b19c4}}, {{cite:1aef07d3a7f524b66514fb9f616fd385a1ddad2b}} as well as related compounds such as LiTbF{{formula:74b9b6bc-7a12-4b4d-967b-a50df2ef167a}} {{cite:8f02042b104fa1ca99adb4dcc97c0873c5b8ac5f}}.
As shown in Extended Data Fig. REF a at zero magnetic field the domain-wall energy is tiny in comparison to the stray-field energy and proportional to the number of domains {{formula:49f78b62-8e0a-4a4e-93ef-13184582d137}} , since the number of domain walls is proportional to {{formula:5c63ab40-652e-4333-a7a3-44d5604e72be}} . In comparison, the stray-field energy varies as {{formula:b9f0c224-7a7c-406b-a0a6-c8fc392d8e78}} . This can be understood as follows: The main contribution of the stray fields is from within each domain, since any contribution beyond the size of the domain is reduced by the staggered alignment of first-neighbor and second-neighbor domains. This contribution to the stray-field energy scales as {{formula:c5e4b362-2ad5-454b-81f1-3465f5723cb4}} , where {{formula:5b564c35-8a0d-4b04-9b3e-66344e1ce106}} represents the magnetic surface charge of each domain. Summing over all domains one finds that the energy of the stray fields scales as {{formula:8da947e7-b497-4e20-aa74-4dcb0996bc4a}} .
The competition between stray-field and domain-wall energies determines the optimal domain size, i.e. the optimal value of {{formula:8abcec00-a156-452f-8ff5-93f605cbb85b}} , as hinted in Extended Data Fig. REF b. The computational effort to determine the stray field energy of each domain scales as {{formula:b520f767-4962-4e91-9944-17ba882fa848}} , such that the minimal domain energy, located at {{formula:2411242f-0d97-47ac-89e0-812855f54714}} , is difficult to access.
In the presence of an applied magnetic field parallel to the {{formula:bc7fef22-65ac-4c72-979f-d3cc2e04f272}} -axis a substantial homogeneous magnetization is added. Because its additional contribution to the stray-field energy is independent of the staggered arrangement of the domains, it is independent of {{formula:e728ba68-7653-4010-87e7-fc01a43b0a08}} , in agreement with our results obtained numerically, see Extended Data Fig. REF a and REF b. At the same the energy of the domain walls reduces very weakly. Taken together, the results for the domain energy become less sensitive to the details of the domains with increasing field.
Our simulations were carried out for sheet-like domains (cf. Extended Data Fig. REF ). It is instructive to hypothetically assume that the domain-wall energy were larger by a factor of 100 than they are really. Then the optimal {{formula:8bc26975-b6c0-42f3-a9eb-c10d9f9e1e1b}} were around 200, see Extended Data Fig. REF c. It is clear that minimum gets shallower as the field increases, so especially near the critical field the results are not sensitive to the precise value of {{formula:eac72b37-3823-41de-b849-77ee2a91239a}} . We have therefore performed all simulations for {{formula:9c9d8916-a750-4206-a185-1b18098ca8fb}} .
Numerical results and discussion
Phases and phase diagram
In zero field, we find the standard mean-field behavior. At temperatures {{formula:a363c69c-d335-4b9d-b448-bf1a2a4c2532}} the mean fields vanish, corresponding to a paramagnet at finite temperature. For {{formula:b5d3d6ee-2f50-4a59-8366-1171e9272681}} solutions with finite mean fields are found, with a multi-domain state having lower free energy than a single-domain state – this simply reflects domain formation in the ferromagnet.
In contrast, with a large magnetic field applied, a field-polarized single-domain state is most favorable. This implies that there is a sharp field-driven multi-domain to single-domain transition for any temperature {{formula:d8c9e535-fbb2-42f5-841a-85f8ce1206b9}} and any field direction. For {{formula:0290b65e-3965-41a6-8c84-35a3faae24f6}} this domain transition at {{formula:51464f50-4d2b-4697-a4f6-f64299f14d8d}} coincides with the microscopic transition involving broken Ising symmetry. The multi-domain state for {{formula:177fde2e-43be-4b4f-8307-f31ebae20a90}} has {{formula:ab10cf38-1fb6-4c6a-84bc-050990178b14}} , while {{formula:4619f8ca-34ab-4052-a523-7ef437d08ad5}} for {{formula:d10b2739-54cd-495e-9d6e-b14b1a88d34f}} .
The resulting phase diagram is shown in Fig. REF h. The phase boundary corresponding to the domain transition follows {{formula:2b1c0c3c-af04-4865-b2b2-3be707635196}} at small {{formula:af3583a3-be15-4b9f-8fd8-b29afa24ec2c}} in agreement with experiment.
Our calculation, which correctly accounts for the stray fields, automatically incorporates demagnetization effects. For instance, the uniform susceptibility {{formula:857061af-1a29-4064-a70e-ee43f0fb6e57}} , which one would associate with the order-parameter susceptibility of the ferromagnet, does not diverge at the transverse-field transition. Moreover, the variability of the domain ratio {{formula:a6b5f30d-5de2-4743-b491-5bb2b5f25fe9}} implies that {{formula:80e73dc6-c6d0-4f50-92f0-50db86d3aa6a}} is large (and essentially constant) throughout the entire multi-domain phase, Fig. REF h, because the system responds to a change in {{formula:e67a550d-a4cd-472b-8584-52b2a08983bc}} by a change in {{formula:20288418-9e8d-49a2-a623-d179bfbf3c1c}} , i.e., by shifting domain walls{{cite:9e286406f8e863b7d94361cd28ab44dd40a20ffe}}, {{cite:f9e0edd25058bf99bc9fa225670683d8a6ddb7a2}}.
Numerical results for the domain ratio are shown in Fig. REF b and Extended Data Fig. REF c. For transverse field, {{formula:6754613a-15f0-4156-bb88-51f49efacfaa}} , the domain ratio is {{formula:70baa17c-9f25-4b57-8f77-13f956043cbd}} by symmetry, while for tilted fields {{formula:c52031ef-2c38-480e-84af-6997f2bc72c8}} is determined by a competition between the Zeeman and stray-field energies. When approaching the transition field from below for {{formula:ec7773d1-b9dc-48ba-84cd-66c1b55afc44}} , the minority domains, whose {{formula:453650de-eba3-47a5-82cc-755beb3f3df3}} component of the magnetization is antiparallel to the {{formula:b538e82d-3357-40af-bfc3-8d0965eccf80}} component of the field, are squeezed out, i.e., {{formula:f2cd784a-e6af-4a81-bb36-9c318fe053f8}} approaches zero continuously. The properties of the domain transition evolve continuously from small {{formula:f7188041-9b50-4b7c-b5a7-8b879da7176a}} to large {{formula:a3684f55-305b-4cb6-bce0-4ff94dd926fa}} . For {{formula:4c81701c-2dc4-439a-a316-356b58c1c20a}} {{formula:a15b0df3-f802-44ce-a7a6-40aba993d658}} can be identified with the coercive field.
The suppression of the minority domains when crossing {{formula:3c1ba48e-5303-41bc-b5e0-ed3e778312cc}} at finite {{formula:8e2afde9-2358-4e44-b36a-4fd70aa7134c}} implies that the magnetization along the field displays a sharp kink at {{formula:466e1ae4-621d-4c4e-acd5-3bb6d985c429}} , Fig. REF c, and that {{formula:39df2194-ad91-445e-9243-0ccd55f42c0f}} drops discontinuously, Fig. REF d, because the high-field state is devoid of moveable domain walls and displays the microscopic response. The field and angle dependence of {{formula:049e9ed0-3fa4-4c84-996b-977d19e900dd}} in Fig. REF d is in excellent agreement with the experimental data for {{formula:71c706e0-81d6-4d96-bea9-ba761bcea55f}} in Fig. REF , with the only difference that the observed domain-wall freezing (which may be subject to defect pinning) is absent in the theoretical calculation. Note that the calculation determines the static susceptibility, whereas the experiment probes the ac susceptibility at 511 Hz, but the frequency dependence of {{formula:d93ef198-aa87-439c-b32c-1b176b4290d3}} is vanishingly small for {{formula:e23deda2-08e1-4017-8b2a-c1e00cd6b39f}} and {{formula:36461ec3-3668-4f2e-abcc-c451a7dfe3cb}} , i.e., far from the regime dominated by magnetic domains, as shown in Extended Data Fig. REF .
Parenthetically, we mention that magnetic saturation may only be reached for fields much larger than the CEF energies, i.e., for {{formula:ef9683c1-c063-480d-8b8d-ff55d557ca20}} T.
It is interesting to note, that the microscopic properties of the model taking into account the effect of stray fields, exhibits a crossover akin that observed in the purely microscopic model at {{formula:009b48be-6114-4feb-93b4-04783c03e6bf}} (cf. Fig. REF d). However, the crossover may only be seen in the regime of the phase diagram not dominated by magnetic domains, i.e., for {{formula:7105b996-d05b-4366-ba6b-44795bab9e29}} and {{formula:2d7fe6a8-0b99-486a-acac-1049185884fe}} . For the sake of clarity we did not mark the location of this cross-over in the phase diagrams shown in Figs. REF h and REF e.
The {{formula:e6746075-637b-4505-b682-9bc21de86824}} -{{formula:003ec397-f5ae-4cb1-9511-4b2a353b37a7}} phase diagram calculated theoretically for different angles {{formula:d7b2d688-5776-49e4-97a2-da66e179903b}} is shown in Fig. REF e (recall also Fig. REF h for the zero temperature limit). The quantitative agreement between theory and experiment is remarkably good, in particular given the simplicity of our approximations.
We recall that we have ignored the dipolar character of the interaction and that we have made fairly crude assumptions concerning the domain shape and homogeneity. Concerning the latter we believe that the spherical form of the sample measured in this study is advantageous, because it leads to uniform internal fields. We note that the experimental transition at finite {{formula:547114cf-84d8-4fbe-904f-cde6acc28b28}} appears to be slightly broadened as shown Fig. REF ; this is likely due to tiny residual inhomogeneities in the magnetization and domain distribution across the sample.
Interplay of non-Kramers moments and hyperfine coupling
We finally discuss the surprising sensitivity of the transition field {{formula:866d3085-e2aa-4003-b38c-2dc0cd18df73}} to small tilt angles and the disappearance of the inflection point in the phase boundary as a function of temperature for {{formula:86a496ed-49b6-4c84-a6f8-e0a83b53f838}} (cf. Extended Data Fig. REF ). Both are related to a combination of non-Kramers physics and strong hyperfine coupling.
First, a key property of the CEF levels of the Ho ions concerns that a finite expectation value {{formula:0d1f1bde-1ff8-430e-83f4-ada5a2c2cb46}} cannot be realized by a superposition of the non-Kramers doublet states, but only via interaction with higher CEF states. As a consequence, the magnitude of the magnetic moment {{formula:e8527f62-7269-4dc1-be9e-fc80d242dac0}} is not constant as a function of {{formula:cdd84805-6b04-47de-88ec-8772720e16ad}} , but has a pronounced minimum near {{formula:8f0b9dc6-0c25-4d87-8b14-b892261eeadb}} because the field-induced {{formula:a0910aef-5bf7-411b-92e4-dc18d2e20878}} component grows quadratically only. In tilted fields this minimum of {{formula:84b36764-0ef7-435c-9485-3bda1f28ae6d}} is shallower because {{formula:7d4cfa51-7168-4740-9244-a204e1d51bf8}} decreases more slowly and remains finite due to the longitudinal field component, Extended Data Fig. REF b.
Second, the hyperfine coupling {{formula:14e7ce07-806f-400e-9193-04db31a52a2c}} energetically prefers large electronic moments {{formula:482122fa-8273-402d-9269-0744475089f4}} , i.e., more hyperfine energy can be gained by anti-alignment of nuclear spins if {{formula:dd6c119d-1616-436f-a442-74289da68679}} is larger. Hence, the hyperfine coupling stabilizes the ferromagnetic with respect to the paramagnetic phase for temperatures {{formula:41738e38-b776-4e71-b8ce-f6286d9e2e3c}} K. This leads to the low-temperature hump in the phase boundary {{cite:6876e1e5632b935bec254c538f1e789bcfff462a}}, see Fig. REF e and Fig. REF e and Extended Data Fig. REF a.
Third, with increasing tilt angle {{formula:c6f01af7-c4c6-47d8-b42d-c6989cc97f09}} , the variation of {{formula:aefdfd57-6439-47e0-b21e-77a7b590cbdc}} gets less pronounced, such that the relative energy gain of the ordered phase decreases and the critical field is only mildly enhanced by hyperfine effects. This explains both the absence of the hump of the phase-boundary for {{formula:3ea9cb59-70d8-4f66-8f77-8066c31bd589}} and the strong variation of {{formula:00c7183d-9bb1-4c10-83d7-5154d8b80ac1}} for {{formula:908a1348-bde9-4e7f-86dc-a770b1b7678b}} as shown in Figs. REF h, REF i, REF e, and Extended Data Fig. REF a. In short, tilted fields rapidly eliminate the non-Kramers variation of {{formula:305d1800-880d-4b39-8b85-c3ef7feb757b}} and hence the hyperfine-induced enhancement of {{formula:d60202e3-85e8-4fd2-9d95-3d9a81f2bf01}} .
For comparison, we repeated the same calculation without the CEF terms, where the ordered moments are standard {{formula:9be45d2a-ec69-4058-9df6-ede409260676}} spins, implementing the Ising anisotropy via a single-ion term of the form {{formula:53521404-39d2-434e-a368-4b851d8615f8}} with {{formula:6057d6fc-62f9-491b-a926-2ef29c72de30}} K. While all qualitative properties of the transitions remain unchanged, the critical field is now essentially independent of the hyperfine coupling, Extended Data Fig. REF c, because the magnetic moment {{formula:d12ac661-c1ef-4fa1-8510-8413a02bb1c7}} is nearly constant across the phase transition, with only tiny variations due to entanglement with the nuclear spins, see Fig. REF d.
We conclude that the non-Kramers physics magnifies the effects of hyperfine coupling, which proves to be very helpful for disentangling the microscopic from the mesoscale effects.
Supplementary References
| m | 16f04116da8bd8a2f9480be7d92519c4 |
This result extends the work of {{cite:74d2083a954c76d292d4c203104fab0b4cfd3dd3}}, who examined prompt emission only, to the temporal domain covered by XRFs and reinforces their main conclusion that
the two techniques, wavelets and pulse-fitting, can be used independently to extract a minimum time scale for physical processes of interest as long as close attention is
paid to time binning and the proper identification of distinct pulses.
| r | 0077f54a739ee4525cf319933f949369 |
Another issue that was only briefly touched upon in section 5, is
that of line emission. It is generally thought that the line
emission in AGN comes from clouds in pressure equilibrium with a hot
intercloud medium, the result of the X-ray heating thermal
instability {{cite:ea80d8232e59a153e141c5ad6e38d44ba6994640}}. Our simple estimates, even though they
have ignored this possibility, they nonetheless provide an account
for the observed correlation of the H{{formula:45719a13-f8d7-493a-a269-6cfdb28867b0}} (a transition with
minimal radiative transfer nuances) with the AGN bolometric
luminosity. However, one should bear in mind that our model winds do
allow for the formation of such clouds at sufficiently small
latitudes (below the Alfvén surface) where the flow is close to
hydrostatic equilibrium, i.e. under conditions of a given pressure.
We expect that past the Alfvén point, where the flows are under
conditions of given density, the formation of these clouds will be
less forthcoming. The issue of cloud or wind AGN line emission is an
issue that deserves more attention and study, given the smoothness
of the AGN lines profiles that implies a very large number clouds
involved in this process {{cite:5103e17835c8adb5431f4ba8a47bf45280da899b}}, but certainly beyond the
scope of the present paper.
| d | 26e547eb74a4d83bff2434e664091b49 |
From the perspective of objects, relationships, and messages, the above methods can also be divided into object contextualization methods, relationship representation methods, message-passing methods, and relationship context methods. In the scene graph parsing task, all objects and relationships are related; accordingly, the corresponding context information should be fully considered. Most of the bounding box-based SGG methods consider the context information of the object {{cite:0f956aedf3cf36cc0ffbb5f85d8c9c6f4bbdd91b}}, {{cite:7bf698d50b62b34108b8cc7abbcc1a6a736c5a0a}}, {{cite:7ea46a59531b95e3b1506f87af08cc03e887e9c3}}, {{cite:50f1345456b8c17303ebd185dc99ddcdebe1fc1c}}. Because objects in these methods can be adequately interacting in the process of contexualizaiton of Link {{formula:07bed8cc-d2aa-4de7-8670-0b489656faeb}} , Link {{formula:49a8f909-569b-4620-a4ee-5d96492f539d}} and subsequent {{formula:1d44ebf5-08ea-42de-b5df-f87cdb1a17a7}} . Furthermore, due to the good modeling ability of RNN/LSTM in a relational context, the related SGG method is also favored by many researchers (as discussed in Section.REF ). There is a large amount of related work contained herein, including RNN {{cite:01c52a1b12d871c9707b8d0f59b25e6c8ac2e323}}, {{cite:64013ba1ae3fee281ca887a5e2ca93783b6c4b20}}, GRU {{cite:f629652f63e45416f9b0faae035786b38e2d5832}}, LSTM {{cite:882d4e2dcbe44e8e31a6d0fe25ceee407d73b1f8}}, {{cite:2c03f900856f09f3430190856492c1847a8b80d3}}, TreeLSTM {{cite:459ed8faf7053d81b689dc562bea32e9afef8196}}. Specifically, for example, in feature extraction (Link {{formula:8f4d63c0-d25f-4cd2-a349-475a72d728b8}} ), in order to encode the visual context for each object, Motifs {{cite:882d4e2dcbe44e8e31a6d0fe25ceee407d73b1f8}} chooses to use Bi-LSTMs (bidirectional LSTMs). In PANet {{cite:01c52a1b12d871c9707b8d0f59b25e6c8ac2e323}}, it uses the combination of class embedding, spatial information, and object visual features as the input of RNN in the contextualization process to obtain instance-level and scene-level context information. The relationship representation method is also the main research direction at present because it directly affects the accuracy, completeness, and hierarchy of the relationship modeling. It mainly includes chains {{cite:882d4e2dcbe44e8e31a6d0fe25ceee407d73b1f8}}, fully connected graph {{cite:f629652f63e45416f9b0faae035786b38e2d5832}}, {{cite:9fa55b11116ab0d364e484a2f649288d153e915e}}, {{cite:541bae50f75bce43f527992d03b88fb817af1c6f}}, {{cite:582bc910917fd2ee6dd3507c8659642b8a045249}}, {{cite:7fc297857e444de2da6d541126dc4de02ed3972b}}, {{cite:7f479bf3bc3a8bd170d6271e4393a66a4ac97258}}, {{cite:7ea46a59531b95e3b1506f87af08cc03e887e9c3}}, subgraph {{cite:7fc297857e444de2da6d541126dc4de02ed3972b}}, and tree {{cite:459ed8faf7053d81b689dc562bea32e9afef8196}} structures (see Fig. REF ). The related research helps in establishing a better explanatory model. For example, MSDN (Multi-level Scene Description Network) {{cite:fc831bf4e22f5a8e9d3b78c50397a3c474f8d83d}} builds a dynamic graph from three different levels of object, phrase, and region features in the process of contexualizaiton of Link {{formula:b5e825ae-7094-4b16-a214-caa79c13874e}} , Link {{formula:9fd337b1-dbc8-4c37-a03c-50d0166730c1}} , and Link {{formula:5f248908-6763-4b66-be57-e7abd72b7039}} , in which the feature refining phase message can be passed on the edges of the graph. VCTree {{cite:459ed8faf7053d81b689dc562bea32e9afef8196}} uses Bi-TreeLSTMs (bidirectional TreeLSTMs) {{cite:724a3acd7c375c3bd6f6cf1d6d2c053fcb767069}} to encode visual context in feature extraction (Link {{formula:6cacbd8e-ed76-4191-9a99-9fba808fb8c8}} ). In addition, message passing {{cite:f629652f63e45416f9b0faae035786b38e2d5832}}, {{cite:6ef8dcc009cf3578e6ea489ac9b56a7eaee7244e}} is also an important research direction, as it directly affects the degree of information interaction between objects and relationship nodes (as discussed in Section.REF ). In the future, the mining of relevant contextual information will continue to be a highly promising research direction. In addition, it is also necessary to add reasoning capabilities to the model, as this will aid in solving the long-tail problem.
| d | 582d670c18f0ddc724482b7849b9c7c2 |
In fig:distortedconst, the GS-128 constellation, optimized as described in {{cite:4ebe67f0a58ac5f3afce5c3ef2bb542d28374d80}}, is shown.
fig:ngmiswing depicts the NGMI when transmitting this constellation using only linear precomp for different output swings of the DAC . Higher swings are associated with higher transmitter OSNR , but with more transmitter nonlinearities. As seen form fig:ngmiswing, the maximum NGMI occurs at SI 400, for which the received constellation points are given in fig:distortedconst. The points are shifted and compressed, resulting in worse maximum performance. This is simulated in fig:gssnrngmi, where AWGN is added to both the original GS-128 constellation and the distorted one. A penalty of 0.02 in NGMI can be observed between the original and the distorted constellation.
indicating that without predistortion, the tested GS constellation is not the same as the designed one.
| r | a2c1b0da6fd6fa837d8545574ee19c96 |
A powerful approach for training models without requiring a large amount of labels is semi-supervised learning (SSL).
SSL mitigates the requirement for labeled data by providing a means of leveraging unlabeled data. Since unlabeled data can often be obtained with low human labor, any performance boost conferred by SSL often comes with low cost. This has led to a
multitude of SSL methods, for example for image classification {{cite:8b529d278dfed870dd376b1d0debe6fc8178d9bf}}, {{cite:1beb9851795343fc7ab3fe81a48706025df85c53}}, object detection {{cite:2755f603b970412c30be732e9208cb404ec6feb7}} and keypoint localization {{cite:9ddbedeb58386e8d2a64ee250e60d11c99463052}}. However, only limited attention was devoted to SSL for 3D pose estimation.
{{figure:9b729bfc-f83c-4a5f-ace0-0b0f08915961}} | i | b5d1f51ec7ae3be0bbac560853047713 |
We compare AdaProp
with general KG reasoning methods
in both transductive and inductive reasoning.
In the transductive setting,
the training and test set share the same set of entities and relations,
i.e., all the entities and relations in the test set are visited during training.
In the inductive setting,
the training and test set share the same set of relations
but different entities,
namely
the entities in the test set are not seen during training.
We follow {{cite:619f2e8a5ceccb1315b9ce566148c189b496cab5}}, {{cite:7feaad883684f5f26ab82c9c4060c667b9f7eec7}}, {{cite:0d139099255dc84894add27fa4a87f318a20a380}}, {{cite:a84822d9ea275cc052a57f26e8a789849f1f93ca}}
to use the filtered ranking-based metrics,
i.e., mean reciprocal ranking (MRR)
and Hit@{{formula:bd12fa94-100f-4b50-a2b6-72380a3688fc}}
for evaluation.
For both metrics,
the larger value indicates the better performance.
For AdaProp,
we tune the number of
propagation steps {{formula:f0271d4f-6aca-4466-be06-dc2fb9267430}} from 5 to 8,
the number of sampled entities {{formula:bd85bb66-5f6b-4976-af78-2d77e6185f3a}} in {{formula:e0f02cf1-a329-4dd7-b02c-fe20dc292bc9}} ,
and
the
sampling temperature {{formula:f9d47d3e-b36b-4ceb-bba7-1b69c4e8b985}} in {{formula:be5ac633-1c65-42f3-923a-022fa3c6e181}} .
The details of other hyper-parameters are listed in Appendix REF .
| m | 9faf28f55f26e52e449ffa4faf2dd69e |
This is the main aim of this article where given the importance of the tensor
current in QCD for exploring beyond the Standard Model we will compute the
Green's function with that operator inserted at zero momentum at four loops.
This will extend the equivalent three loop exercise of 20 years ago,
{{cite:3d8a6cb64d469ea2580980dc19f5e6f44ce7d2a2}}, which has been used in various lattice analyses that are focused on
understanding the various SM extensions mentioned earlier such as {{formula:89657d03-9947-473b-9ccd-1f22ed162cac}} meson
decays, {{formula:e4c7de79-0201-45a7-8371-622df26413f3}} decay of nucleons, electic dipole moments of nucleons and the
{{formula:ab8a9c9f-cded-4be2-b48c-8be85fac4495}} decay constant. See, for example, {{cite:5535a290a84a3e70d4eb2358e4dfde6ef11fda18}}, {{cite:9cb352205e668c81aa08078b9f9af7d909097169}}, {{cite:d4cec52d07bfb129f9eaf7f697de982e0be1edf6}}, {{cite:3f049388280cf5e644804098fa3a742df7f03dc8}}, {{cite:e5584f1f4af52a374a7fa7bd9d191bcc04dc7cab}}, {{cite:26026e89e6b3f4991cb0763adb634daed718c7b2}}, {{cite:3e337a476ed9350ac202714bd6960f67c96dbaa5}} for
several instances including the recent results of {{cite:d509e1b166cca14c43c2f3b0a66cef4073c4635f}}, {{cite:1b4f8e2a8257dd538fe87083eef12b3957a3bcaa}}. Equally there
are also applications of the tensor current to effective field theory
formulations of the SM, {{cite:21eb6ee1bfb13935c14d85ad3bb12d329c0441dd}}. In particular we will compute the matrix
element in the modified minimal subtraction ({{formula:9e6a1198-ac47-46c2-a054-863a3ea47049}} ) scheme which is the
standard reference scheme for comparing to experiment. However, as lattice
measurements are carried out in a lattice motivated renormalization scheme
known as the modified Regularization Invariant ({{formula:684f6a0b-f3b7-42fa-9cb0-f6f8975b1e72}} ) scheme, {{cite:e22faa2fe323a2d54799674b26a0b21db23deb6a}}, {{cite:c5d7304dc95945b5043d075d4d9fe108a381dd30}}, we
will also produce the Green's function in that scheme. Equally we will
determine the anomalous dimension of the tensor operator to four loops in both
schemes. We qualify this by noting that the {{formula:de4e3d5a-363f-4338-b456-2fa53c2d36f9}} four loop tensor anomalous
dimension is already available but only for the {{formula:c2696dc8-c4d7-4a9d-a59d-f9c26bd34521}} colour group,
{{cite:83b5941c3fae825a85cac496d29f948d5d3ca6ab}}. We will provide the full four loop {{formula:ed0d87f4-be11-48b0-99ad-6fc4ad3a22b6}} result for an arbitrary
colour group. Although lattice computations of operator Green's functions are
invariably performed in the Landau gauge we will take a more general point of
view and carry out our calculations in an arbitrary linear covariant gauge.
| i | 8f57a24744b170a3c072318e3e28e0cb |
Contributions.
Interior point methods are a much used tool in convex optimization {{cite:9b53fcd561cb0dcac18f2db6f99dfa17dbf05d6d}}. We propose using the log-barrier function on the coupled inequality constraints as our inexact penalty function. The GNE problem is then converted into an NE problem whose costs go to infinity at the boundary of the constraint set. We consider GNE seeking using this new set of penalized cost functions for nonlinear agents with a class of equilibrium-independent passive (EIP) dynamics. The benefit of considering these agents is two-fold. First, we are able to capture versions of a variety of already known NE seeking algorithms. Secondly, we are able to consider certain types of dynamic agents. For the full-information case a gradient based feedback is used. In partial information setting, we instead use a Laplacian based feedback, {{cite:331b07674be821430643ef77c54d1dc366d4adaa}}, for the case where agents have full knowledge of the constraint information.
| i | 7725ea3a718d66fc2bbcb90fdeeaa509 |
where {{formula:884ed852-b90f-4807-9e6f-3610d9422743}} denotes the {{formula:0e7fd71e-0001-4da8-84e2-5776d7d63a73}} -th row of matrix {{formula:7d7f8a60-d489-45c9-b504-aaad39da8ec5}} .
Standard Gaussian concentration results {{cite:a25f36e3af92f5ddcee18972955432b98a6515d4}} reveal that {{formula:e3a22a2d-7243-46a3-9937-78c1f4d9def0}} falls within {{formula:8da60c9b-9ada-4730-94c8-db61b4e82111}}
with probability at least {{formula:8d3e8961-50f7-416c-b5fb-be2772c6c2ac}} , provided that {{formula:859fbaab-9bfa-49d1-96b1-77db42c8c7f7}} is large enough.
As a result, it is readily seen that
{{formula:908b9887-a2cf-442c-9c2c-1c07409b691d}}
| r | 1de0c99dc7798b8e20a6f73cb5980a87 |
Although direct sampling methods have been studied for many inverse scattering problems using far-field data there is little to no investigation for the case of near-field data.
The imaging functionals are also studied for both isotropic and anisotropic scatterers.
In order to construct our imaging functionals and analyze their behavior we will need to develop suitable factorizations for the data operator for the measured scattered field initiated by a point source (see for e.g. {{cite:e6ef4e435c8b0fdbad9acf827779da20603de6e2}}, {{cite:f536e3811d6f435950702205d1f7141b9ad08ee0}}, {{cite:a09b3670d4e866c6f5935e069c81bde2658bca26}}). The factorization method was initially introduced in {{cite:8854b8d724f77ccce317f6f371c855d3bd767934}} for far-field data but has been extended to many other models, see for e.g. {{cite:a2e66e85aab2c0226487cddfcc8087574dd2bd6c}}, {{cite:e6dfc05b97a5d5136d1a97cfcd2111ca2bf6d9d1}}, {{cite:da20d8f704f5a618e8f452169eb936e9d3b81735}}.
Also we derive explicit decay rates for our imaging functionals by two ways. The first is by applying a `far-field' transform to the measured scattered field and by appealing to the Funk-Hecke integral identity with the decay of the Bessel functions to prove the bounds. Another method for deriving the decay rate is to use the measured Cauchy data
and the second Green's identity
| i | f509eec6c2ba1cd6dcc054219ea34f43 |
a fixed `cross' trigger pattern at the top left corner of the inputs. When selected, the adversary updates the broadcasted global model using backdoor images for 6 local epochs with an initial learning rate of {{formula:84765595-238e-44e9-968a-6b989511e007}} that decreases by a factor of 10 after every 2 epochs and uploads the poisoned model for global aggregation. All these parameter values are chosen following the method discussed in {{cite:93cb7bbb7eda869712cd56d969abbd39186a07de}}. We consider two scenarios for the evaluation: (1) single-shot poisoning - adversary injects backdoor at stable point, same as PerDoor and (2) continuous poisoning - adversary injects backdoor continuously whenever it is selected during FL training from the beginning and stops uploading the poisoned updates after the stable point. Figure REF shows {{formula:7e8c795f-0a7c-4c46-9877-e9581c656dee}} over successive FL rounds after the backdoor injection for both scenarios along with PerDoor. We can observe that single-shot poisoning obtains very high {{formula:c0bf543d-6ee9-45a5-8c1b-17f0c79ec126}} immediately after that round. However, that decreases significantly as FL training continues. The continuous poisoning maintains high {{formula:a06dc4c9-8b57-4762-b6fe-a15072f9b381}} at initial rounds when selected. However, the backdoor impact diminishes whenever the adversary stops uploading poisoned updates. On contrary, PerDoor maintains high {{formula:2b2872ba-dce3-4538-842a-b72548bb19b2}} throughout the training rounds, demonstrating its efficacy in preserving {{formula:53fd0920-1ae6-442f-988a-42f97201a7ba}} . PerDoor, on average, achieves {{formula:bf8b9b9c-b2f6-4957-a0e3-c70ced139310}} more {{formula:e6d63bb3-09c9-468f-99c1-549bb6304506}} than single-shot poisoning over 5000 rounds and {{formula:08767fe7-dccc-4297-8e1f-863ce056e3c3}} considering continuous poisoning.
| r | 354f3c611747e967bb0d379fc9adeeb5 |
For that purpose, we consider the fermion loop correction to the effective action in a simplified Higgs-Yukawa model.
This toy model captures the essential features necessary to grasp what is going on in the realistic Higgs inflation model:
As in the real world, we neglect the Higgs mass term which is much smaller than the one from quartic coupling {{formula:602095bf-c300-42e3-a0f8-c6e08524e045}} at the large field values under consideration;
the renormalization group (RG) running of {{formula:6f7de730-4680-4299-8528-5f3598d8d2e9}} is governed by the loop of top-quark, which is represented by {{formula:323489cb-909b-4435-aca4-c2ebe3061dc3}} .In reality, the loop of gauge bosons also contributes to the running of {{formula:9ab47ebb-21ef-484a-996c-82997f17690c}} . However, the {{formula:24f00096-8908-4acc-96a8-e0dfd6314be4}} -dependent effective mass of the canonically normalized gauge boson, {{formula:71b803eb-5b92-484a-a299-aac80d15851f}} , has the same {{formula:f4260706-00f3-4aeb-8215-4af2c6b8d0b0}} dependence in the Einstein frame, {{formula:154908b7-5a78-41a2-825f-546c808e3932}} , as the effective mass of fermion {{formula:ccba9d27-2398-4083-a173-2f97368b61e1}} which becomes {{formula:11513b71-9a35-4490-a633-9bd74e32bbb1}} ; see e.g. Ref. {{cite:2f7b40922635fe98f363799af1303c16928c10b0}}.
Therefore the arguments for frame independence and for prescription dependence should apply without modification after we include gauge boson loops.
| i | 6f1a643ff1f1e224c58cf952c127dd3c |
RQMC methods are finding uses in simulation optimization problems
in machine learning, especially in
first order SGD algorithms.
We have looked at their use in a second order, L-BFGS
algorithm. RQMC is known theoretically and empirically
to improve the accuracy in integration problems
compared to both MC and QMC.
We have shown that improved estimation
of expected gradients translates directly into improved
optimization for quasi-Newton methods.
There is a small burden in reprogramming algorithms
to use RQMC instead of MC, but that is greatly mitigated
by the appearance of RQMC algorithms in
tools such as BoTorch {{cite:d9169ac82e60e59bc2b1ce9f2867138d63329980}}
and the forthcoming scipy 1.7 (scipy.stats.qmc.Sobol)
and QMCPy at https://pypi.org/project/qmcpy/.
| d | 15982662f8a38ae2be43103291628882 |
A method to contextualise knowledge graphs is to express the facts that they capture as projections of frames. Frames are cognitive structures that are used by humans for organising their knowledge, as well as for interpreting, processing or anticipating information (cf. {{cite:383dc8d066e3b6d3aaf3108e33876917f54f3734}} for a discussion encompassing both linguistic and knowledge-based approaches to frames). In linguistics, a reference model for frames is Fillmore's Frame Semantics {{cite:4cd6d7e72c336e1e6df4b32da56abbc89e58c80a}}, where a frame is introduced intuitively as “a kind of outline figure with not necessarily all of the details filled in”. More precisely, a frame is a structure that reifies an n-ary relation with multi-varied arguments, denotes a situation, event, state, or configuration, and is supposed to bear representational similarity to the knowledge encoded in cognitive systems. Any binary projection of a frame is called a semantic role. For example, in the sentence I bought a pair of shoes, the word “bought” identifies an occurrence of a commercial event, where “I” and “pair of shoes” are objects that play the roles of “buyer” and “`goods” respectively in the Commerce_buy frame.
Fillmore's Frame Semantics has been substantiated by FrameNet {{cite:3afe6b1bdfa48329bfefbae36f8b31c23eac2919}}: a long-standing, manually developed resource of (English) frames represented in a structured format by a group of linguists in Berkeley.
| i | 3ea38e3d6c8d40dd0ed2163dba9c208a |
In this paper, we chose MNIST {{cite:1b19c3f72cded66f1c7dbd5d533461742052f2f7}}, FMNIST {{cite:69f38e4979ff47b264e39db8a55c192794906b3f}} and UCSD {{cite:7a9b937d16e7c1ed4d6424beb8c8996bba0ff751}} for anomaly detection. These benchmark datasets are widely used in the anomaly detection literature. In the following, we provide descriptions of each dataset as well as the protocols for evaluation.
| r | 0e48edb9d2d1634a650f4ef1fb7cf0fc |
Scaling to larger TSPs: We note that works such as {{cite:a0e53a462d923b4965daff1b49c87c1ca4cec3a4}}, {{cite:079f8af99f4b8dc89dece1e16cfba9b97aeb52fb}} are able to predict on larger TSPs. However, a key difference between our work and these is that these works rely on a pre-trained supervised learning model in {{cite:f081b710f58474e018e261a888be21b4301a9231}}, whereas ours works solely on reinforcement learning. Since both our model and {{cite:f081b710f58474e018e261a888be21b4301a9231}} aim to produce edge probabilities, we plan to investigate if we are able to learn strong edge probabilities for larger instances since our approach is faster and less compute intensive than other reinforcement learning approaches.
| d | c44396a29f2b20954d2a078fe162092d |
All of the aforementioned algorithms are analyzed on three test cases of different dimensions and complexity.
The first test case is the 0D model proposed by {{cite:aef93e32fc2601efd4803289b00b638e098d31a1}} as the simplest dynamical system reproducing the frequency cross-talk encountered in many turbulent flows. The second test case is the control of nonlinear travelling waves described by the 1D Burgers' equation. This test case is representative of the challenges involved in the control of advection-diffusion problems. Moreover, recent works on Koopman analysis by {{cite:0d6fcf69f8247dd0f12994feddd7e703f25e0656}} and {{cite:36ec5a8b4ff815decb280e452739281baee590ae}} have provided a complete analytical linear decomposition of the Burgers' flow and might render this test case well suited to test the full arsenal of possible "white-box" control methods. Finally, the last selected test case is arguably the most well known benchmark in flow control: the drag attenuation in the flow past a cylinder. This problem has been tackled by nearly the full spectra of control methods in the literature, including reduced order models and linear control {{cite:d6eede39fc73e148dc8e76d09fdb3b22744a7c20}}, {{cite:fdceb881116788ec86bed93739c2490f1eb03cd4}}, {{cite:afd3aec62daee1f62c2b7f36a26023aa20ec100a}}, resolvent-based feedback control {{cite:66e2eedd52cf7729d6b7832284632606749504b3}}, reinforcement learning via stochastic {{cite:90ff558a097d38afddc18e8d3b7f42790ea9285c}} and deterministic algorithms {{cite:4f8320521519a95b88cbd771545cfbbaaf98296b}}, and reinforcement learning assisted by stability analysis {{cite:e856389aef86eca37d15b9c835efc71199b558f7}}.
| i | 2a0745e4990491c0ecd4a12dce764b67 |
where {{formula:42a57c60-ffe3-4097-be07-220be29fe475}} and {{formula:656b90f9-da0b-414d-b9bf-ed9537618fe3}} . If {{formula:60506162-551b-4023-be01-b4224f05ebd2}} is bounded from below and {{formula:71c07391-1d77-4886-af69-c40e23e86b54}} , one can obtain the rate {{formula:70a2b690-9dff-4617-8248-07d2718cb1d0}} and {{formula:65816924-8372-4523-b79b-73cc9ad22ef1}} ; see Example 7.4.6 in {{cite:9a1cf1a6cd539316233c52835cc7bdbfd866cbe5}}. Thus, {{formula:e162fda5-ab05-4eb9-b647-9b5d9370c782}} under the null, therefore the asymptotic null distribution would be valid.
On the other hand, when {{formula:bef74d9e-999a-4377-a390-983a15511e33}} , {{cite:18ace6c84a9f9e38a1c4437f71c6fc0028df213b}} showed that the rate of convergence of MLE in Hellinger distance is not better than {{formula:3ce3e14c-f6ac-46c9-a7d6-610917972a0a}} . In this case, Theorem REF does not apply because {{formula:9f6fef71-ec87-4eee-826c-8157bd1c6bdb}} becomes the dominating term under {{formula:b1916eb9-e06d-4bd9-a9d7-30f0a910ed22}} .
| d | ab48678231e652aceeaba10f46f2fa9c |
We introduce a new graph-theoretic concept, that is motivated by the problem of network monitoring, called monitoring edge-geodetic sets. In the area of network monitoring, one wishes to detect or repair faults in a network; in many applications, the monitoring process involves distance probes {{cite:e988561c8f9d84ec770a075cf2a4aa6d6064b283}}, {{cite:147a11c4a470490ef4afbf1335213db67526a2e6}}, {{cite:d7885bbc9f5954243d908bab213b0b5f409a2dbe}}, {{cite:d5b204a17d05ce71b840a06bfb0b1d9a9e00d402}}. Our networks are modeled by finite, undirected simple connected graphs, whose vertices represent systems and whose edges represent the connections between them. We wish to monitor a network such that when a connection (an edge) fails, we can detect the said failure by means of certain probes. To do this, we select a small subset of vertices (representing the probes) of the network such that all connections are covered by the shortest paths between pairs of vertices in the network. Moreover, any two probes are able to detect the current distance that separates them. The goal is that, when an edge of the network fails, some pair of probes detects a change in their distance value, and therefore the failure can be detected. Our inspiration comes from two areas: the concept of geodetic sets in graphs and its variants {{cite:c517bb5c2dc217272a83e8c60fc0e33a3cb490c4}}, and the concept of distance edge-monitoring sets {{cite:9cb0a39baca053862b19b7881f6e791eacede49d}}, {{cite:d5b204a17d05ce71b840a06bfb0b1d9a9e00d402}}.
| i | b61f4d017b24567ca00db783d0ba3bbe |
We also showcase the impact of JPR in downstream question answering which takes the retrieved passages as input and generates the answers. Improved reranking leads to improved answer accuracy because we can supply fewer, higher-quality passages to a larger answer generation model that can fit on the same hardware.
This practice leads to a new state-of-the-art on three multi-answer QA datasets and NQ {{cite:1addbbc40456d2d091390a362f839b5db7d52211}}.
| i | 247de33ab3d99c69949db58517c31b80 |
The past decade has witnessed rapid development and growing popularity of
blockchain technologies. This has been attracting tremendous interests and
enthusiasm from both research communities and industrial applications. The
blockchain technologies were originated from a digital financial sector as a
decentralized, immutable, auditable, accountability ledger system in order to
deal with daily transactional data. So far it has been envisioned as a
powerful backbone/framework for decentralized data processing and data-driven
autonomous organization in a peer-to-peer and open-access network. For
blockchain technologies, readers may refer to books by Narayanan et al.
{{cite:552278a885ea049682c4045c06b3930b9335c8e7}}, Bashir {{cite:5d40db5181544c35b4a6b5b492c4cafa838fb5a6}}, Raj {{cite:2937047e493117f67300715725b100d534407bd5}}, Maleh et al.
{{cite:ab5e7c3bcace787339c0396fa6d4760438f25a2f}}, Rehan and Rehmani {{cite:63ea9b4d4faa837c6c76d365c8381533b61a5971}} and Schar and Berentsen
{{cite:003a322de7f7212b807f87f98d7982580eb5b9ae}}; and survey papers by Fauziah et al. {{cite:7613505768734ccb81fa034861ef0d6d1cf97cf1}} for smart
contracts, Sharma et al. {{cite:124cf879a60cdbf18a006f4f2e50e5056fc4714d}} for cloud computing, Ekramifard et
al. {{cite:f8aa6555749f360bb853b29f2aba24a66263730f}} for AI, Dai et al. {{cite:cc0888128382997b10a230d11c867112fc8616df}} for IoT and Huang et
al. {{cite:eac1b32643ce44220d44f9b41c8a6d16c6853d39}}.
| i | 2438295dceb37ff040310cab4e5d4ec8 |
The standard way most detectors are evaluated in the literature is to stay in the same domain and use similar datasets. The error rates are based on a narrow binary classification and due to this there are much better error rates. You can see this throughout the literature where there is one domain, like TweepFake{{cite:a1842616ec6225b19ed03840361a47427160c27c}}, news oriented models {{cite:a042adb8f6aec3b3e24f9a7e2073b8ff279658ef}}, language based models {{cite:ce3052188f1872f3142cde17c791d05d043e83e9}}, and other niche categories sticking to their own evaluated domains.
| r | 819367f6878ff42cdcb7cb4520f04c19 |
The consistently strong performance of one-hot encoding suggests that position-wise information is crucial for function prediction. Averaging position-wise embeddings only captures the frequencies of each embedding dimension and destroys local sequence patterns which may be important for function prediction, consistent with the poor performance of averaged one-hot encodings in TAPE {{cite:e3ca4bfac5d64ae0a06ad7d6f42c68fc45ca59f3}}. Methods such as Soft Symmetric Alignment {{cite:197833ae26a469aff08abd670a8dc59245807e2d}}, concatenating all position-wise embeddings, learning a linear combination of position-wise embeddings, or using a single attention layer with one learnable key as the top model may improve embedding performance for protein function prediction.
| d | 517c8c6250c8a16ff4e4200c6e8bcc46 |
implies that {{formula:941a93b5-05ae-45dc-bf2b-5b324a9cacff}} and {{formula:5009e852-9aac-4ab7-9e5c-9ef36c48e825}} are {{formula:ab70d8ca-a819-488b-8cf3-7b883d34f641}} -linearly dependent. Hence, {{formula:3aaf8507-ebd1-4105-a390-d5091beb3874}} -polynomials satisfying this condition are called scattered by Sheekey in {{cite:0babf6aee8525ff10af287da68515ef2fc7833e9}}.
| i | bed3105655e5de5e66df2e6450f64031 |
In order to explore the effects of the different bacterial reproduction mechanisms, we have used a very similar methodology to that described in {{cite:42ef9dd06d98b6f5e7d3373db459615faf2ad756}}. Thus, the first stages of biofilm growth, when it can be considered two-dimensional, were modeled using an Individual Based Model (IbM) {{cite:02da8990c0b0e5a6d949e2e9055d36d6013c8d5e}}, {{cite:23ef5096390d3b0cd767397f62b6d6ae92bb7985}}, {{cite:a1ce622c4c1c286a6e3bc9541f275330084e7364}}. In our model, we have assumed that the bacteria lack the capability of active motion, being displaced only by the effect of the interaction with other bacteria as well as through passive diffusion. More specifically, a rod-like bacteria is modelled as a bidimensional spherocylinder. This shape consists of a cylinder of instantaneous elongation {{formula:49d2f2c8-b48d-4714-bbbf-34603f5f9b49}} capped by two hemispheres of diameter {{formula:7344893e-5b6a-4063-8e35-a44df46c8efd}} . During the simulation, the elongation of the cylinder will change over time, while the diameter is going to remain constant throughout the evolution of the system and for all bacteria. Accordingly, the instantaneous aspect ratio of the cell is {{formula:e67348fa-bf1c-4dd6-ad59-92c0429fa07d}} . As in {{cite:42ef9dd06d98b6f5e7d3373db459615faf2ad756}}, we have considered that bacteria interact with each other via the soft spherocylindrical potential {{cite:75dc6013d6342de5f243e2f23ecd56e24c426654}}, {{cite:b8003d2327dddfad71aae1c130402689d4ae7c55}}:
{{formula:b05836b5-02e2-45cd-bba5-4fcadd7152c3}}
| m | 55991b43d361dc2a6389a9b9f1e59882 |
The proposed method is evaluated based on 3D cardiovascular MR images from the HVSMR 2016 challenge {{cite:5a8bbb9a8ae73da9623c24e6f53a5c85eb752440}}. The set consists of ten axial, cropped volumes from ten different patients with ground truth annotations. The images are segmented according to three labels: background, ventricular myocardium, and blood pool. The baseline method is a fully supervised cGAN employing a U-Net with skip connections as the generator network and a PatchGAN as the discriminator {{cite:117968ad17252f0887ab67ed8e52e23c9eb65b5d}}.
{{figure:76b66d63-e6c1-4c71-9756-ed34a04f371f}} | r | 2fc8a6bf3c9dc4f8999b6b490190f981 |
The outburst's peak bolometric luminosity is roughly {{formula:e1c95ef4-46b6-4702-b4c7-6161eed3c300}} 30%{{formula:a66caa45-3057-4d2a-b79a-7bf5132707d0}}
under an upper limit of the distance 6.3 kpc.
Based on the normalization of the disk emission derived from spectral fitting, the estimated inner-disk radius is {{formula:edfc0360-6acd-4c5f-bed2-94020cdb8735}} 40 km, assuming an inclination angle of 0 (face-on scenario) and a distance of 6.3 kpc.
The inner-disk radius of AMXPs is widely used to derive the magnetic field of the NS, although there is a large systematic uncertainty.
Taking the Alfv́en radius as the magnetospheric radius {{cite:594a563561f57b8b5b7d22527342b4b47d109ac0}}, {{cite:1619512d36b270174e99affa75cbdd5e8c318420}}, {{cite:db7f264f17324475bcdd4783b1b8825b5b18d81c}}, the magnetic field is estimated as 7.1{{formula:6554d2fc-3bf7-4844-bb88-f62b4723092f}} Gauss ({{cite:a490a56dfa66110a126d608161f64b52b06e156a}} or equation (4) from {{cite:cfe00cc3e3f09e49705ae4d434aa9d8ce33c59c0}}).
The co-rotation radius at which the angular velocity of Keplerian motion matches that of the NS is estimated at 25.3 km for MAXI J1816–195.
Considering the inclination angle and distance uncertainties, the two radii above are consistent.
| d | 11eaf1977ce7d9b834081bf2495b39fb |
In order to train the network using gradient descent, we need a differentiable version of loss (REF ).
To do so, we use the re-parametrizable Gumbel-softmax relaxation {{cite:5ab754571fcc24fb1e2b63d2a9bbd46320e26de1}}, {{cite:e566e5359a7dbc909c675556f1daec7ba1e9197f}}.
The Gumbel-softmax relaxation replaces categorical samples {{formula:3b234751-3a73-4670-a0e2-bf665ede8ca9}} from the distribution {{formula:43a2ca68-93bd-43aa-86ac-d7ae499089e4}} with continuous samples {{formula:f94a27ac-2b9e-40eb-8e3e-e504343b803b}} from the distribution {{formula:0d32c58f-b878-41a4-8cf1-1429bd1ecc97}} .
We take {{formula:211db9e0-9304-4658-b46a-b37339d24888}} samples from this distribution to evaluate the expected negative log-likelihood, further reducing variance.
Then we simply replace {{formula:bd910647-0450-4c30-acdc-bbdfa2e5c498}} for {{formula:ba680381-0115-4eb7-a368-0f89ffe290de}} in e:nelbo, leading to differentiable quantities.
| m | 7828f4da6e1357474b61928bc3f2b376 |
Due to their close relation to rank-metric codes, {{formula:c787a207-ed5a-42e1-81d0-eaa5b9de627c}} -matroids have gained a lot of attention in recent years.
They were first introduced in {{cite:656d0373bd74be79e6f6fdd604550fbcf9bbf40b}}, and their generalization to {{formula:a260abff-6309-4f47-a619-b7cc51a08db1}} -polymatroids appeared first in
{{cite:a2bdb5cccebd2bed52c91907d8c5fb71b400496d}} and {{cite:78996e9fd2ffc4049ebdc3da8c1ba760d578a3f5}}.
While {{formula:54532879-36a7-4e8e-920a-90a42c12cc64}} -linear rank-metric codes induce {{formula:685b7585-f500-45d4-831f-ff17b344e7c2}} -matroids, {{formula:e5636a31-b547-4483-8d75-ad00eab26521}} -linear rank-metric codes give rise to the
more general {{formula:5d0075a8-96b7-440f-bcb5-39bed49d36bb}} -polymatroids.
| i | 239ebd05a4f84a8ac82498f6b73216de |
Even though autoencoders are designed to learn a lower-dimensional representation of the input while minimizing information loss, in this work, we used them to perform semantic interpolation and thereby recover spatial information in anisotropic medical images. Specifically, we used an over-complete autoencoder that can potentially retain all information contained in the input. Theoretically, such an approach could learn an identity to minimize the reconstruction loss. Nonetheless, in line with previous research ({{cite:24148a4e3e0b17f731c49ff90983f870278778fc}}), the results presented in this work seem to indicate that such a model can learn a useful representation of its input.
Furthermore, the experimental results revealed that interpolation between image representations is feasible to approximate information orthogonal to the input images. This suggests that the proposed approach learns to extract contextual and high level conceptual information from the input images. Moreover, the results demonstrate that the decoder learns to exploit this information to instantiate semantically meaningful intermediate slices. While previously developed shape-based interpolation approaches of {{cite:f15c9ea8b90898065f17b5d3e4f204a8ffe2fa3d}}, {{cite:3f212a1c71548f1b78cf3462b9e02101fcea773e}} exploit anatomical shape information to achieve high-order interpolation between cross sections of 3D anatomical structures, we argue that our approach performs semantic interpolation between two spatially adjacent slices.
| d | 1091cad3987dd9d78a02aefe9cfe59f4 |
we associate univariate B-spline basis functions {{formula:0742ee8c-347d-4ade-9ea9-4e6a3740d97a}} , where the integers {{formula:55df4157-1694-4362-8461-cd6f2a298a34}} and {{formula:d1c4a858-d8da-4f63-854c-881c86193ff9}} are the polynomial degree of the B-spline, and the number of basis functions and control points, respectively.
Starting from a knot vector (REF ), B-splines are built recursively starting from piecewise constant function when {{formula:b5618afc-2086-45fe-9890-46848735a7d5}} , obtaining B-splines with support {{formula:ba8b9cea-2dec-4d02-9cf6-3f947a4e4497}} , {{formula:fbf8e7d1-e6ad-47a0-ad65-d4045accedc1}} (see, e.g. {{cite:ce6a40b2035c3151e563c76df882a8f9cf037823}})
It is known that B-spline basis functions are {{formula:4e2c8e63-5a09-4b30-8b82-177657db4998}} -continuous if internal nodes are not repeated, whereas they are {{formula:b90adb80-6e68-4841-b543-d702e1c88059}} -continuous, {{formula:5f657de9-ed83-47df-a355-2caf67a1e062}} , {{formula:960bd992-4956-400f-a4ce-422c039abbf2}} being the multiplicity of the associated knot. Moreover, when a knot has multiplicity {{formula:570ad154-2572-43c1-88b7-95e230741e6e}} , the basis is {{formula:88a8de04-548d-43dd-963d-f536f27649d7}} -continuous, interpolating the control point at that location where the knot has multiplicity {{formula:6c180d93-a0ad-47e6-9807-2a518673fb1b}} . From now on, we will assume that the maximum knot
multiplicity is {{formula:1f383cc8-e177-4d2c-8cc4-c1a112ee7063}} ensuring at least the global continuity of all considered functions.
| m | 3524e0aea389d72f1ec1d99b1705676a |
As a measure of the resemblance between the experimentally measured correlations between each pair of modes {{formula:d2e5a63a-1ee3-49f8-b114-24f4b53784b2}} and the theoretical predictions {{formula:b8b49441-9c6f-4c11-ab0b-ebce64d00d39}} for each unitary transformation, we utilize the commonly used statistical fidelity defined as {{formula:e35ae4fc-255a-431f-baba-eb3be67eb552}}{{cite:83062ebb80206d0e343818b7796c135c4b776d03}}. A histogram of the 400 statistical fidelity values is presented in fig. REF a. The average statistical fidelity obtained in our experiment is {{formula:fc498bb5-e4e6-4751-9fc5-c086c4e96a50}} . The fidelity can be improved even further by increasing the number of planes in the MPLC. To show this, we simulate the performance of the MPLC for random transformations as a function of the number of planes (fig. REF b). Statistical fidelities of up to {{formula:3dfb9842-4a6f-4a1a-adb5-815009cebcbe}} can be obtained by as few as 10 planes. The high statistical fidelities we obtain between the MPLC generated transformations and the target Haar transformations, manifest the capability of MPLC to generate arbitrary unitary transformations, as by definition Haar matrices uniformly sample the space of all unitary transformations{{cite:d002eb78c6a9080a8d5872daa46199f000ed3d52}}.
{{figure:78e70513-c486-4bc5-9faa-1daa98155a0e}} | r | 62712899b6fccc79949871ceb6a8c7aa |
In the case with the SH0ES calibration, we obtain tight constraints {{formula:033e6df0-301d-4c1f-b7b2-d1cbeca6c3d2}} km s{{formula:bdd64e55-4e18-4606-8635-a8f15aea2a83}} Mpc{{formula:867d9424-29be-4e21-8940-f5956b03cc0f}} and {{formula:e081fceb-8c74-41d8-bce7-5d4a5322325b}} , which produces an evidence of DE at the {{formula:70f3509f-aecf-4427-849d-a7c992582dce}} confidence level, is completely consistent with the result from Ref.{{cite:0021d96c5a6e9e954c01aad4e85b2a1c2fdbdf84}}, and is well compatible with the Planck-2018 measurement at {{formula:e48ee4be-2d2f-4603-ae6d-8864e8bc39b3}} confidence level. The first three bins reduce the parameter space of background dynamics of the universe and give very strong constraints on {{formula:581c3906-f130-4f9a-be57-884b62a8f423}} and {{formula:d5e8d5e0-142a-4594-ac44-effb310d6286}} . Similar to the case without the calibration, the first bin still dominates the constraining power of the whole sample and higher redshift bins exhibit a weaker constraining power than lower ones. It is interesting that bin 3 can alleviate the {{formula:65f8ae6a-32fc-4888-bd8b-03a52329052c}} tension to {{formula:31ad984e-d7f5-454c-a76f-16d86fc173de}} . Although this may be due to the large data uncertainties from bin 3, it give a new clue towards the final solution of the {{formula:5c6675f6-3064-4b57-8ace-f95a7e2853b3}} tension, i.e., searching for the possible solution in {{formula:7bd7a764-fb2b-4a09-a33c-cbe1872d2eaf}} .
| d | 7102a91f504d3bab104a5ab52910ecfd |
Our goal is to build a generative model for vector graphics that does not
require vector supervision, i.e., that only requires raster images at training
time.
Our model follows an encoder–decoder architecture (Fig. REF ).
The encoder has a standard design {{cite:a0cb63b06d03ed14b894b6dbf20694fd8c1c555b}}; it maps a raster image
{{formula:26509e60-8588-4fc1-b22e-2e4ef02f4661}} to a latent variable {{formula:25d57b9e-facf-4733-9ef5-89e0c6c1a769}} ,
which is then decoded into a vector graphic structure.
Our decoder has been carefully designed so that it can generate complex
graphics, made of a variable number
{{formula:3b7562f0-d01e-4aa6-8d41-c88674d6c200}} of paths, with varying lengths and no predetermined
topology (§ REF ).
We also train an auxiliary model to predict the optimal number of control points
for each path (§ REF ).
Finally, each vector shape is rasterized using a differentiable
rasterizer {{cite:47201aa18cbc0a128fc06d33e00c8fe45cb56f5f}} and composited into a final rendering
{{cite:5ba10446a9a95ae9ed006b7747921661be371d04}}, which we compare to a raster
ground truth for training (§ REF ).
| m | 6a281135a184b21bc5dc7357a2af7287 |
Next we consider sampling algorithms for composite potentials of the form {{formula:5f3fe128-6b46-4e33-863e-2273e15a1a7a}} , where {{formula:b99ff3d7-ea94-4158-9318-8f3dbcd91fe6}} is convex and smooth, and {{formula:f917f2bb-6d75-45a4-a8e9-0332ba3dc60c}} is convex and non-smooth/semi-smooth.
In {{cite:14543dd7d7b33c5dcfb016ad791ed826268e573a}}, the authors developed an algorithm that needs an oracle to sample from the target potential regularized by a large isotropic quadratic term and to compute the corresponding partition function, akin to the RGO used in ASF {{cite:6093b3acd24d799e105adf7c3c220617e1ac1753}}.
In {{cite:5d9c0791f21ef8d75dcbd4005c8911160397c5cb}}, the authors introduced an algorithm by running LMC on the Moreau envelope of the potential.
In {{cite:955f441b89f038b215ad4997e54ac56279e9db64}}, the authors proposed an algorithm embedding the proximal map of {{formula:8c9c6ef9-95a5-46f9-9c40-5079b52dd6ba}} into LMC and analyzed the convergence of the average of distributions over iterates. In {{cite:c5ea477d7c3b8e3fcee64bdcdc213f1c4db787b1}}, the authors improved the results in {{cite:955f441b89f038b215ad4997e54ac56279e9db64}} for the cases where {{formula:3e1e9a9d-bb31-449f-a91a-ed849c1d6b7e}} is an isotropic quadratic term.
The paper {{cite:74c1f670df13f39c5fc2f38abff2d42889515476}} provided a primal-dual interpretation of the algorithm proposed in {{cite:955f441b89f038b215ad4997e54ac56279e9db64}}, and established a slightly improved complexity result when the smooth part {{formula:451c2800-1d4e-407f-be41-6cfe04f2b1c8}} is also strongly convex. In {{cite:043e50b6cc597c441b3b49c00587129bffbb96c8}}, the authors also examined the problem from an optimization perspective and established a complexity bound in the cases where {{formula:9ee9afe1-f864-4c5d-a83f-44b5aa80e597}} is strongly convex.
Another approach for sampling from the composite density {{formula:bffb378e-1d16-4ac3-8238-84b6c984c405}} is to apply LMC on the Gaussian smoothing of the potentials.
In {{cite:bd6c449b82541cc67eeafba330b71b8b9d9673a5}}, the authors proposed this algorithm for sampling from composite densities.
Following this paper, {{cite:60ff27db2b1b5250f0d324486fc9343de7007ec8}} further developed algorithms based on generalized Gaussian smoothing and obtained improved results when {{formula:10c4159e-e2c5-43f2-bfad-3408dd8b5703}} is strongly convex.
| i | 2390edf2637635101558b152ade3f9aa |
where the components of vectors {{formula:9eedf8bc-1e9c-4e1d-90ca-78463331b8e0}} and {{formula:baeeff40-a9a3-4ead-bfc2-ff4b0046bbee}} are
{{formula:7610dd5c-2b4b-42de-88f1-e2c0f1d8e06b}} and {{formula:0794b9f9-5bbc-4689-8edb-2dba5d578eaf}} , respectively.
The inequality follows from the Cauchy-Schwarz inequality. Then {{formula:1bb4aae2-e712-4118-b1df-b21b2d8f90b1}} ,
and the log-sum-exp function {{formula:97552306-7c0a-44a1-90a5-a66a4ab8ffa0}} is concave. Therefore,
{{formula:d02ac140-253a-459f-823e-4175c196c2c3}}
is an increasing and concave function w.r.t. {{formula:b207eeba-c0c1-46ad-be9c-a5afc3bd4f5f}} .
Recall that {{formula:4e858c1f-1ee6-4b1d-a8dd-58069a5dda58}}
is biconcave of {{formula:41bab438-2053-4efd-a206-ff7abb08a261}} and {{formula:91ac0c82-3e94-434d-a267-3dae4065cd48}} . Finally, according
to the composition principle {{cite:52e8be8bb2ebdbd09f1b34b55fc2e79a1eb901d4}}, {{formula:3b07b459-aeed-4b6f-a98d-f23d15d03924}}
is biconcave of {{formula:fee591c8-8226-4c12-96ab-a2107aa1681e}} and {{formula:8ad4f1b8-832b-4739-b255-0fb691c22154}} . The proof is complete.
{{formula:e9cbab9a-2641-40cd-9021-d4866f1adf3d}}
| m | 4af51d727cf7d217e7ebf0b1c66d2528 |
In our final submission, we chose RoBERTa as a sentence encoder and sampled {{formula:688de953-778f-473f-8331-13c8408a09de}} texts per user for Task 1 and {{formula:beb9f92f-1875-495f-a0e2-0673c3d88cef}} for Task 2. We used the standard formulation of the transformer network {{cite:4c2e100f2308ddf0858b2448a5cc0e98d107b162}}, with 4 encoder layers, 8 attention heads each and a dimensionality of 256. Both networks were trained for 120 epochs, with AdamW optimizer {{cite:2ee0a1e61ced9039a9e282e9d7268d20c35bdbbb}}, with a cyclical learning rate {{cite:ed398320c3ed96d4af3b8429f3f9dc16c712eb38}} ranging from 0.00001 to 0.0001 across 6 epochs and a batch size of 128. To account for class imbalance, we computed balanced class weights with respect to each dataset and adjusted the loss function accordingly. Finally, we opted for a very high threshold when predicting the final decision.
| m | ca4aa9bb58d8462ffc3bdd680c5f62d0 |
Last year on May 24 the SpaceX launched the first set of 60 Starlink satellites and up to now the total number is approximately 400 aiming to reach at least 12000 {{cite:967689ac2c467827ae46ade3a1d997d6df9d2403}} at the end of a decade program announced by Elon Musk. Such a huge number of satellites, distributed over almost the whole surface of the Earth might be considered as the first prototype of a possible megastructure around the Earth, which in principal, might be visible from the cosmos. Similarly, one may search for techno-signatures of alien civilizations.
| i | d0a612cb019942cf5b756b46be132889 |
The proof relies on the asymptotic behavior of {{formula:2f98ac96-ab26-40f4-8e7b-c630faaa5c1a}} and {{formula:6d2a5ce5-b479-4d5b-80f8-fc34b39c4300}} as
{{formula:72341275-cfe4-457b-9c0b-8ca7c4851d3c}} , which is an idea similar to Sakamoto and Yamamoto {{cite:3c21a3bd190796097a8a53e7fa719cd1a4590833}},
Yamamoto {{cite:a3af17b6ab922dc66fe2767de6b4b6c905ffad08}}, but by the non-symmetry of {{formula:3fcb3e24-f4c4-4aaf-93b1-b0ea638cdb79}} and {{formula:44e22d82-0d8e-4e96-81d6-45379f8da77c}} , we cannot
make use of the eigenfunction expansions of tne solutions {{formula:d5d2be52-e304-40b1-bb47-9771f8c14494}} and {{formula:a53079f6-b569-48a0-9e2d-f575cb615f36}}
themselves. Alternatively we derive asymptotic expansions of
eigenprojections of {{formula:f73462dc-8e75-4c18-8cac-cb0c47fbe924}} and {{formula:e89781ff-1c4a-4ea6-a86c-d3a09cf38b56}} in view of the completeness in
{{formula:e0d527fe-76e3-4c51-8079-cd13c603adee}} of generalized eigenfunctions for each of {{formula:4db3344f-1d54-48e0-bb4d-2aa27af93052}} and {{formula:fe51f9ab-7614-4bd2-ace4-8b2826fc990a}} .
| i | f248876eb7ba81d977fbeee07778e751 |
where {{formula:bfca47ca-8919-4db6-90c5-0f421f107791}} is the spectral quality factor, {{formula:0aa6b547-3521-4d97-81ce-2b2c2c9bd780}} is the resonant frequency of the vibrational mode, and {{formula:31217939-8a70-4f75-a492-8f79c9f43a3b}} . Figure REF b shows that {{formula:e51badec-eb83-450b-a481-9d381f561ccf}} is low and does not change within the range of {{formula:5fbd91a7-201f-46d0-9513-6d15d67639bd}} , while {{formula:b0908b8a-5959-428a-9a00-c1972785c11b}} increases with {{formula:787d8621-038c-4198-a191-ec702a63ffa7}} (Fig. REF c). In the absence of nondissipative spectral broadening processes, {{formula:0d9401fb-d3c5-41ba-a285-b22750858e94}} is inversely proportional to the rate at which energy stored in a resonator gets dissipated in a thermal bath. In low dimensional resonators based on 2-D materials and on nanotubes, {{formula:748831ec-7ac2-4558-91a9-44ecab7720cf}} at room temperature is always found to lie between 10 and {{formula:912a7e55-f868-4b61-a73d-1fb5a854fdc8}} {{cite:fb6dc08ce3164bb0b909e469ba1431324bae2746}}, {{cite:08d2917bf49dccde7b44220e74e5c2002357c6ee}}, which is surprisingly low given the high crystallinity of the resonators. Proposed mechanisms to explain such low {{formula:7615f6e9-4487-44db-a791-eac56d514afe}} 's include losses within the clamping area {{cite:94009037fa857a38d741175d881601a2ac3b61dd}} and spectral broadening due to nonlinear coupling between the mode of interest and a large number of thermally activated modes {{cite:982c8722638fa167dd3fa5e911722df09519f3b6}}, {{cite:d7336e98e0fa77b4116e9079301274e572a4bfa8}}. In turn, the increase of {{formula:42243292-abb8-4a4f-b940-48b64b08d5a6}} reveals a hardening of the spring constant of the resonator. The latter may be due to vibrations responding to photothermal forces with a delay {{cite:2c1494602d6d4646a56acdba375c0252e93fbe90}}, {{cite:22405b4c27b555ea3ad68a1db95f31cb0239d7b4}}, {{cite:b1923a5a65efd98cff995659ca52b7bba5f9b364}}, {{cite:47e6422e55ff6e746dd113b35f2437b5026a84cc}}. However, because {{formula:82f57f40-6a61-4ac5-85b3-583e31cbc960}} does not appreciably change with {{formula:ff3f41e0-e2fd-4a7e-bf48-841edeae77fd}} , the hardening of the spring constant is more likely to be caused by absorptive heating accompanied by a contraction of the membrane {{cite:8949cd12718370a43c7a6b3892f0e99b784c187b}}, {{cite:0eeb55a56fca115037c4b983ed7e33e691559e94}}. In this case, it is interesting to relate the change {{formula:aaa2214f-c422-4195-b205-c1e98a0423ad}} induced by a change {{formula:81363b89-8d10-476e-904c-d3bd62501b49}} to the thermal expansion coefficient {{formula:cf666c45-ca7a-4bc4-9a4f-0ec5c3cf69dd}} and to the thermal conductivity {{formula:eb10fa47-dcf4-427c-9ae5-2380da05d00d}} of the membrane. For this we borrow a result from Ref. {{cite:8985682f22c1ac4cb35fb81a68d991be7c9598d6}}, namely {{formula:6594f101-6d71-432c-8cef-6d40c74b4f97}} , with {{formula:1145408e-37ea-4c1d-abfc-3426ca3590fe}} the power absorbed by the membrane, {{formula:520f2ce3-80e0-4964-8e82-5523355fcffc}} the strain within the membrane, {{formula:fef6de09-95fb-4df5-9534-17319d81077b}} m the thickness of the membrane, and {{formula:4f9fe189-6d8c-4107-a8e1-98384794e9f3}} a factor that depends on the beam radius, on the membrane radius and on Poisson's ratio. We convert {{formula:2032aaf9-cbbf-4271-9f77-d2f9b09b5d84}} into {{formula:61683d69-0c7c-4b76-87a3-36a881e35b84}} using the absorbance {{formula:31d38cb1-bd0e-44e1-b4e6-a6a0b762c04d}} of our FLG suspended over the gate electrode. We measure {{formula:40748f2b-3c0a-4372-a477-c859f11702a7}} from the ratio of power reflected by the cavity covered by FLG to the power reflected by a nearby uncovered cavity (Supplementary Material, Section III). Further, we estimate {{formula:4de5fd00-7254-4cda-8f08-4afb0f23644f}} from {{formula:886f0fc0-ecbe-4ac4-9395-50fa499e157b}} by calculating the elastic energy of a disk-shaped membrane {{cite:2b3786b465b5c6651ec9e45eb100afa9184a7980}}, {{cite:110e49a16324df0fa7f01a422a7eea212a591b7c}} and deriving from it the spring constant of the fundamental mode (Supplementary Material, Section IV). We make the simplifying assumption that the electrostatic force is uniform over the membrane. We also assume a Young's modulus of {{formula:0967b13a-e90a-4842-a49f-6ccf3acb771b}} Pa and a Poisson's ratio of 0.165 {{cite:3f60a954e5938064d801e6f6841d8fe922c2fc26}}. Combining {{formula:b5999de5-7ff6-4dfb-ae9b-7e859a631106}} , {{formula:9fc064da-3ac7-4d8f-a36d-f7884b227fd3}} and {{formula:b2cbc82c-b8cd-40bb-afed-9f0d0d8ec6cd}} , we find {{formula:d4368eec-0e0b-4495-9e2a-65ef4df7621d}} m/W. This is a reasonable estimate, considering for example {{formula:ce7dec15-16af-44b0-8021-9672bcdad09f}} m/W with {{formula:a2b700cd-182b-40cb-a94b-3a2ed76b5b9d}} K{{formula:763e8665-dfda-482a-8265-943250323a1d}} from suspended singe layer graphene {{cite:0eeb55a56fca115037c4b983ed7e33e691559e94}} and {{formula:a42d6262-7dec-4c98-8b21-9ffc9a352cfb}} Wm{{formula:c739a0ac-1506-44d0-bc06-9418c9c71f83}} K{{formula:c1f3d5d7-ed93-4626-a1c1-0b6393ece251}} from pyrolytic graphite {{cite:918b556592130d83131ac05486793276335e80ae}}, both at room temperature.
| r | 71529d8595b0948ca972595d22361ad2 |
In recent work, H.Yakura and J. Sakuma {{cite:07803760aa0b68cb4c27712c50c43b76eb8f6d90}} put forth a method to generate a robust adversarial example that could attack DeepSpeech {{cite:9ef9f2300a5092069779371a179cf193dd41e69c}} under the over-the-air condition (e.g., the given adversarial example played by speaker and radio.) In our work, we employ both the gradient and gradient-free adversarial algorithms in our enhancement methods, and try to minimize physical threats of robust adversarial examples in the over the air setting {{cite:07803760aa0b68cb4c27712c50c43b76eb8f6d90}}.
| i | 6c5987f655198bc73692aa74810076e8 |
It is impossible to quantify the learning rates of kernel methods for time series without presenting any restrictions on the dependence among samples {{cite:62a05573567e8385081cfa5eebef629d4261de17}}, an extreme case of which is that all samples in the data set are identical. Therefore, some mixing properties {{cite:f8abc4dcb932d33dd44fe451453b8ec62dc53d30}} concerning the weak dependence among samples should be imposed on time series. {{formula:ee01e580-a25b-4f50-80dd-2a49e00550a3}} -mixing {{cite:f0141d607bee96da1180144a70dee0d83003ec18}}, {{formula:1aa031c7-ab63-49ee-b1cb-0babbabb214c}} -mixing {{cite:b4c9bb0d9e49cdb6f14441935d4e30006a8aa49d}} and {{formula:ca7511e6-f4f8-4add-860c-7541bde8264b}} -mixing {{cite:78ea26bc2f764d1ee79e0337d5728c1360ebf6a4}} are three most widely used conditions in learning theory.
| m | c8977aa6f7a9bb5b4bdc160c91272027 |
Numerical evaluations presented in {{cite:60bb69197bd987af721eaf1cef0ed59ccc28fe18}}, {{cite:d77f19f43a084941449ce20aac092ae652784e0a}}, {{cite:3dac1e0621c1c20ce765dadc624655ffe27e8b22}}, {{cite:e327fcd3bc0a8bf1aa18695dd9b228ac42943efb}}, {{cite:42181b50fc20f32ea0b5812a02caa68d9d914c22}}, {{cite:961d8094111646ac05c22fb0bb2b7419d34b3887}}, {{cite:b4a800d58de6e0eab93a9a85c350e76f05c1d711}} showed that Adam and its variants perform well when they use a small constant learning rate {{formula:9159d5c5-ee76-4916-bc69-c5e1cbc98c47}} and hyperparameters {{formula:4d2df135-d376-4d7f-a18b-160845c4dafa}} and {{formula:07e968a5-575b-4a36-a5ed-6f32161a63f5}} with values close to 1. Hence, we would like to show theoretical evidence that Adam performs well when we set a small {{formula:a99def54-f7dd-45d0-803b-6b6dee548c38}} and {{formula:13394daf-1100-43af-ab6e-14f3fdf1fad0}} and {{formula:a08de371-c7fa-4497-8898-8df96e6686a8}} close to 1. In particular, we will show that Adam (REF ) using {{formula:fbdedf26-13b5-4157-a30b-93128e6123cd}} , {{formula:6c3e7248-cd10-4812-adaa-071508c43b36}} , and {{formula:2411fdbc-a7f1-479b-a059-ba31b142d40f}} satisfies
{{formula:7a0e6155-9913-4424-bb28-5a53d614aa87}}
| r | e9a017c92654139dd396afa99cb2fbd7 |
The sensitivity of our TMC-1 data is better than
previously published line surveys of this source at the same frequencies {{cite:5ad8f3b4fb04c96eab60d3f9198a29ca17ca88a9}} by a factor 10-20.
In fact, it has been possible to detect many individual lines from molecules
that were reported previously only by stacking techniques {{cite:1b639eeaceea5665304e720bda84971b19e25886}}.
The recent discovery of some molecules
containing the ethynyl group (CCH), such as vinyl and allenyl acetylene {{cite:32c9aea4a8377c3d061b938d0b7a39aa0e86284a}}, {{cite:b56a81b153b36defc751221ab89ab5dd15edb259}},
and of the propargyl radical {{cite:33bbfee4cf4fe38103dd75d09988804a695d6362}},
prompted us to search for other chemically related hydrocarbons.
Line identification in this work was done using the catalogues
MADEX {{cite:191248d92e6e706352ecd8b2681904a3fc1c4072}}, CDMS {{cite:51fb9353b4ae84d7075dae6f77c02e48ffbcb319}}, and JPL {{cite:39be419d72378916d8cc2ecd31d9602952673ec0}}.
| r | 6e1f107b7fc00eaa02b09f7a18bc18f9 |
In the models under consideration, the asymmetry between the ascent
and decent phase of the sunspot cycle is inherent from the pattern
of the toroidal magnetic field activity. In particular, the 1D1 model
has the toroidal magnetic field butterfly diagram with maximum located
very close to equator. Therefore, applying the definition Eq.(REF )
for this type of the toroidal magnetic field evolutional pattern we
obtain the decent phase of the sunspot activity shorter than the
ascent phase. The opposite situation is in 2D models. There, we relate
the sunspot activity with the toroidal field in the subsurface layers.
The turbulent diffusivity in the model decrease outward this leads
to increases the decay time when the toroidal field gets closer to
the surface (see {{cite:ceac68fe3176a441ec22d35022dec2b0c0ac37be}}). We find that the effect of the magnetic
helicity on the {{formula:b0e74e9a-c952-4c1e-8da3-8ef4a0c747bc}} -effect can amplify or saturate the asymmetry
of the cycle shape depending on the mechanisms of the helicity loss
employed in the model.
| d | da6031b9a692088c9ecd8e2ac1b34b51 |
While the literature suggests that a second-price sealed-bid auction is optimal (in terms of revenue for the auctioneer) for our setting {{cite:66f294e260454a8d1a06a566e6034ab147490eeb}}, this type of auction is not widely used.
Two-stage auctions, however, are common.
The optimal two-stage auction design when the values might be correlated was explored in {{cite:8daeb91406c1242ce650bd4bb67f3aa2e3c1e923}}, that considered a model where the second stage is a second-price sealed-bid auction.
The optimal information to be released by the auctioneer in a two-stage auction where the second stage is a second-price sealed-bid auction was investigated by {{cite:daae1ea2b2704b115da43639a44f77f98d5ff1ac}}.
Our research is restricted to the more common auction structure, where the second stage is a first-price sealed-bid auction.
As far as we know, this model, particularly the question of the optimal information structure, has not previously been explored.
| i | f7cffed8325a0159e31b214081176ede |
DANN Component:
In ML-based NIDSs, as is the case in other application areas as well, it is difficult and time-consuming to label real-world data. Consequently, synthetic datasets are often used for training and evaluation of machine learning models.
However, these synthetic datasets usually do not adequately represent real-world networks and suffer from distribution shift, i.e. a significant difference in feature distributions {{cite:0eb984b41c8c81416e0de96789f9524251df215c}}.
Generally speaking, domain adaptation aims at as making the distributions of source and target domains similar, so that if a classifier or detector is trained on the source data, it can perform well on the target data. {{cite:6d904f920d206eef7109b588dfb9a7528e71702d}}.
| m | b8ed6ee7dbc11235db7ffac190b69adf |
The MCMC results in this study successfully capture the true
parameters and their uncertainties. The results contain natural biases arising from the use of prior distributions, internal variability of the climate, and use of a
single noisy sample as synthetic data. Despite the sampling variability and emulator constraints, our
MCMC samples were able to capture the true parameters within an estimated 99% confidence
interval in our examples, demonstrating the potential of
EKI-trained GP emulators for MCMC sampling. Validation of the emulator (Figure REF ) further supports the MCMC results,
as do our comparisons with MCMC using the benchmark emulator
(Table REF ). The GP emulator both smooths the objective function and allows us to quantify uncertainty by sampling from the posterior distribution. This contrasts with uncertainty quantification based on the EKI ensemble, which underestimates the true uncertainties in our experiments by an order of magnitude. As used here, EKI should be viewed as an optimization algorithm and not a sampling algorithm.
Adding additional spread to match the posterior
within EKI may be achieved for
Gaussian posteriors {{cite:94f14fedd2089bf7734f1da0f7763504f2ffd6ae}}, {{cite:813b9d66f9b7ef32e91597200817793d112ebf62}} or by means of EKS {{cite:9b99e7dd416229782d31da3d0be6f04f667bef69}}; however, these methods
are not justifiable beyond the Gaussian setting. The
MCMC algorithm within CES, on the other hand, samples from an
approximate posterior distribution and is justifiable
beyond the Gaussian posterior setting {{cite:7827b077afb45ffc6b6a42e5811a5fb964a50f5b}}.
| d | a038786e26237c605004ed5bc663bbc3 |
this choice leads to an interpretation of (REF ) as a simplified manifold MALA proposal (SM-MALA) in which the curvature of the target {{formula:5fe879dc-586c-4f60-a6ae-9031a155263e}} is assumed constant (but remains position-specific, {{cite:5b03abd586f460ecce196db406ea592ab292ce49}}). We make a connection between a modified SM-MALA update and the Gibbs sampler available when the latent process and all outcomes are Gaussian.
| m | aa75dc23381a7445854dae5d3f5eaee1 |
Remark For a general graph {{formula:b2e30cea-320d-4326-bb8a-f938195f7f19}} , the best-known mixing time bound is {{formula:afa2ce6e-d941-494a-9934-84eef71a763e}} due to Jerrum and Sinclair {{cite:2926ce42a87250a7560ac7b3c9a5cc7479164df0}}, refined in {{cite:5d6baa6265f296225c698f6e2238f387a94852b9}}. On the other hand, {{cite:ed7f4d3adba7aabb0c194c962bb01aaa47cd3903}} along with the improvement in {{cite:6a54757f5a8512be5c2605e80cdcdc7caccd3b03}} gives the optimal mixing time {{formula:17662db7-3c22-4ef7-9fed-e89593c253e7}} for graphs with maximum degree {{formula:42c7e7f9-0b24-49e4-a7b1-2a3089e33e3f}} . Note that this latter degree bound excludes the case of constant average-degree Erdős-Rényi graphs.
| r | 39b77ce72b8445fef8b24909a5021108 |
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