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Learning to manipulate objects is a fundamental problem in RL and robotics.
An end-to-end learning approach can explore the reach range of future intelligent robotics.
Recently, researchers have shown an increased interest in visual affordance {{cite:c14c6c0515e46c803bf4ed1f54ba7cebb0f4d8e8}}, {{cite:92fe3510cecfbc29eda6af86356f637a67b87a16}}, {{cite:d1978babaece153fe3786cfa0345b095dde41a09}}, {{cite:181c5b74a39f942a3b77a5ac7f75e4acf1cf85f0}}, {{cite:033ec968c244de1f9a23092733f42480ae7177a3}}, i.e., a task-specific prior representation of objects. Such representations provide the agents with semantic information of objects, allowing better performance of manipulation.
{{figure:c9e92c1f-e343-4ec8-8b4e-fa5cd09c0026}} | i | 8371b8f8a0d6cd74cc0f27b36e25c030 |
Human perceive the world through a variety of senses, such as hearing, vision, smelling, and touching. Since the sound and vision are two dominant components, audio visual joint learning has attracted increasing attention in recent years. Audio visual event localization requires a machine to detect the event segment in an untrimmed video and recognize the category of the event. When an event occurs in both auditory and visual modes, it is regarded as an audio-visual event (as shown in Figure 1). Different from video action recognition{{cite:eab20250b2fa591250b7c587fe9aea81030fdef8}}, which directly recognizes the category from an untrimmed video, audio-visual event localization task{{cite:c1d01e962421d65e1ec98043402fb13acf856ba3}}, {{cite:401f4cf8ac20ec2ba1a1960c31ab8a23a3ebf781}}, {{cite:787790442cda6ad8256dfd510489dbeb9ecba063}}, {{cite:131a8f29f2e237c5e91cf4b1417ad403ff955929}}, {{cite:58f67005214373fe154d7ad05318de73c06f27a9}}, {{cite:c0e49a3e2a9c63a66023461924764b69258b8db5}}, {{cite:3fde16c30220adc10bdc00073d9d8498d8a7935b}}, {{cite:395c8e8ea65a80805beee3cb9d407baa4f15d4c3}}, {{cite:3ce2058282644c3a6d85252750d3b06c235b13c5}}, {{cite:ddfaae6eb2c32027a222cf41024149f8d1269526}}, {{cite:84d377fe55432cffca03e585c5a6f01bbcdc220f}}, {{cite:8b7a3a7eca739a6da738fc68dbf64673c3109859}} requires the computer to divide the video into some fixed length segments, recognize the category of each segment, and combine the adjacent segments with the same category as the detection result of localization.
{{figure:dcb85008-f006-44c9-b5c5-90322d115573}} | i | b603fbc2a2a6b20bac135f047c6ce9c6 |
The course, in addition to the Java language (version 8), provides an
introduction to UML {{cite:379b582df86ecd9e3b084329f27242341afb5d84}}, design patterns {{cite:3b7e37c6a0eba3ec5aaa096958b3b27bdfb0c3da}} and basic software engineering
practices. It basically follows the indications provided in {{cite:431a6c2b713206ea7a645f9cf9a3bd8df1e57fe1}}.
The three key practices that we integrated in the course are:
| i | 876c0a06ad058000fb6ec6cecb642998 |
where {{formula:2cfe2976-2827-4da4-b10d-a4ea78a47df4}} is the affinity matrix, and {{formula:ff041795-aeea-4f71-ac09-c56c96944548}} is the implicit regularization on {{formula:9331bd63-a26d-4b37-9a61-ef604a2bff0c}} to promote a unique and meaningful solution under the assumption of self-expressiveness. According to the imposed regularization on {{formula:a193a738-592f-4552-9a69-6215f9ccd49c}} , the existing approaches can be mainly divided into two categories: the sparse subspace clustering (SSC) based methods {{cite:cca2d3f5290214bdc305660f6ff22d32cc1511b5}}, {{cite:57575cd130a24910813f100a7cf79fd269cfa682}}, {{cite:05b38bc74129149d90be9f7769c80778776a8810}}, {{cite:847a1cec5691c8b3b8a22a07f47a4799f3a188c7}}, {{cite:b179a98e66fd94973f59b38919e7884b56adf758}} and the low-rank representation (LRR) based methods {{cite:8dde65a77f8869df2671ca5603c1f02667b70f1a}}, {{cite:d570d04d7604910077a4be900220429d64db1fd9}}, {{cite:571d482d479491938811084bbd8f11e6af5d2864}}, {{cite:93da047f9529f4b4a0ba66b41923401436e8ea5d}}, {{cite:237e57c6430a1452a3af35582341cb30260bb8d4}}. To be specific, SSC {{cite:cca2d3f5290214bdc305660f6ff22d32cc1511b5}} was proposed to find the nontrivial sparse representation, of which the {{formula:43ee072a-8212-4fff-a2ac-b1e1c05be4c4}} norm minimization (i.e., the tightest convex relaxation of the {{formula:df42a165-ef40-498a-8802-12dc2689a4a1}} norm) is employed. In addition, Wang et al. {{cite:05b38bc74129149d90be9f7769c80778776a8810}} explored the relations between data by integrating SSC and the least squares regression to improve the segmentation performance. Chen et al. {{cite:847a1cec5691c8b3b8a22a07f47a4799f3a188c7}} coupled the self-representation matrix and the segmentation matrix to encourage the within-cluster grouping. Since SSC based methods can only capture the linearly-relationship among samples, Kernel Sparse Subspace Clustering (KSSC) {{cite:57575cd130a24910813f100a7cf79fd269cfa682}} was proposed to exploit the nonlinear structure information in input space. However, in KSSC, the kernel function and the associated hyper-parameters are challenging to determine {{cite:8dbd35d6e9004f6420cc13c4f800ebda1c0762b3}}. LRR {{cite:8dde65a77f8869df2671ca5603c1f02667b70f1a}} and Robust Kernel Low-Rank Representation (RKLRR) {{cite:d570d04d7604910077a4be900220429d64db1fd9}} are the other two popular clustering methods that capture the global structure of samples with a low-rank constraint for coping with the linear and nonlinear data, respectively. Like SSC and KSSC, LRR and RKLRR also suffer from the above-mentioned issues.
| m | 5c119efe26f826ec4aceb338932f7064 |
Lemma 1 [Lemma 8 in {{cite:ad2a2234f0a1395d2283a88ef838c6ca38a7f9ad}}]
For almost all linearly separable dataset {{formula:d98bc6b1-31ee-4fb2-93ab-9661019b2d51}} , consider any sequence {{formula:95a81d9b-2650-45de-acc7-715d79f4218b}} that minimizes the empirical objective in eq. (REF ), i.e., {{formula:1e29fddc-cd5c-4fe7-8570-87a471fab658}} . If [(a)]
| d | 92d281da7154b0eb4030c8776d82ea67 |
Patched patterns we have discovered bear certain resemblance to coherence-incoherence patterns observed so far in coupled oscillators or coupled excitable systems, but also display considerable differences. In particular, patched patterns are different than bumps {{cite:11c090465f02efeeb313272179079afc747a6073}}, {{cite:cffc4cdd12fccabba8fd980739efde2da7722b52}}, {{cite:6d7dad725d860ec099b7203e9480c05a98298e19}}, {{cite:74717711006f4ba3f2cc3f93e5627bcf7f060829}} because there extensive chaos is spatially localized and the bulk units are stationary (inactive). Also, our patched patterns with interfaces are distinct from classical solitary states because the interface units are not isolated and randomly distributed, but rather form a spatially continuous profile. Distinct from classical chimeras {{cite:a745ef801d230f1ac38e728252546f0d2869f9da}}, maximal Lyapunov exponent for the patched patterns converges to a finite value instead of decaying with the system size. Still, we note a certain similarity to some of the less conspicuous types of patterns observed in coupled oscillators. First, we recall the so-called chimera Ising walls in non-locally coupled Ginzburg-Landau oscillators with a parametric forcing {{cite:5a172fa96ce505fa7c00144861253134eea75ffb}}. There, the incoherent units also form interfaces connecting frequency-locked domains, but in contrast to our patched patterns, the domains at two sides of an interface are 1:1 frequency locked. Second, our class of solutions may be compared to oscillons {{cite:d22ca558cbd7835786e25fa8e274fc465d8a9520}}, which also involve a temporally modulated localized spiking activity, as in our minority patches, but such an activity is embedded on an inactive rather than a spiking background. The emergence of spatially incoherent interfaces has also been observed for the so-called mosaic or skeleton patterns in coupled maps {{cite:4b624dce4fea20d5c40dd8fed22fe019875869c7}}, {{cite:9d3a624c0f0425c95c7a6e6a5f957b429371cd3a}}, but the onset of spatial incoherence there is not associated with temporal chaos in local dynamics. We note that the onset of an alternating activity similar to our interface units has been found for the so-called itinerant chimeras {{cite:eb5356f79ed77c48f6ac470b2e9ba125d4eaa245}}. While this is also not a finite-size effect, it involves all the units within an array, rather than remaining spatially localized. Finally, a recent paper on theta-neuron oscillators mentions non-stationary patterns with the frequency profile similar to ours {{cite:3fa6e414b9e7bde7e4291ea53b3f8c56fb957c4f}}, but instead of spiking, the majority units there are in the state of oscillation death.
| d | 59cfbeabb717ffe44d9bf3214ea52a4a |
The initial codebook {{formula:448cd269-f7a0-4825-8003-83b9f43a135c}} for methods {{cite:128ba63a0fbcb31ae29605137c46aaeab44a5510}}, {{cite:bb4943f0d4083b68638c7b859d558d2d82c65360}} are computed by
the fuzzy C-means method {{cite:3bf6b59481173e0f1a60611932775cac826d2df6}} with 100 iteration steps, and the thresholds chosen
in the thresholding technique of method {{cite:54a41ea15a52226d20b60b1925d1b848867345cd}} is using the automatic strategy therein.
The tolerance {{formula:09bb075d-88b8-42b6-8b03-124154727992}} and the step size {{formula:3c01b69c-870f-4f4e-a7e3-8988e8a6e6c6}} respectively in Algorithm 1 and
(REF ) are fixed to be {{formula:573028aa-0d0b-4ef3-bb27-f444aad271e3}} and 2. The parameters {{formula:124e56f1-c66c-4f7d-ab1b-ff8ab3d36851}} and
{{formula:bc2c20d4-d992-4ec0-930f-3473f8c10618}} in model (REF ) are chosen empirically.
| r | 60b132650bfbe5ff27ce17a7612c599e |
Explainability and biomarker discovery.
In order to determine the regions of interest in the brain that influence the prediction most, we extracted for each of the four tasks the learned weights of the RegGNN using the best-performing sample selection method.
In Fig. REF , we show the regions of interest with the 3 highest weights averaged over {{formula:c8ff03f6-cffe-4b7b-a3a5-cb19b9051145}} ; underlying is the AAL parcellation atlas {{cite:5e29c2e52fb3384378517648d1680aab89793bf9}}.The brain networks were visualized with the BrainNet Viewer {{cite:630521d233d3ea7ad1c5eb54ad4fa96543781e8e}}.
For the FIQ prediction task in the NT cohort, we see that the left superior dorsal frontal gyrus (SFGdor.L), right superior frontal medial gyrus (SFGmed.R), and right cerebellum 6 (CRBL6.R) have the highest weights. For the VIQ prediction task in the same cohort, left hippocampus (HIP.L), left heschl gyrus (HES.L), and left cuneus (CUN.L) possess the highest weights.
In the ASD cohort, the highest weights for FIQ prediction are left insula (INS.L), left calcarine cortex (CAL.L), and right pallidum (PAL.R), while the highest weights for VIQ prediction have the left superior frontal medial gyrus (SFGmed.L) left middle occipital gyrus (MOG.L), and left cuneus (CUN.L).
| r | 5f4a6d67bc1998d59e1156257201efd2 |
Given a gradient flow, which is a path {{formula:7f943628-c279-4bce-b99d-8dccec2b40d8}} satisfying the gradient flow equation, {{formula:eaf2e2a4-a0d8-4dd8-94da-6bc7424b4f17}} are critical points. Moreover, critical points carry important effect to the rate of the gradient flow. Namely, when the flow {{formula:2b9a1aac-b6bd-406b-8f18-74f2ba2b3140}} gets close to a critical point with index being {{formula:b0842809-ad22-41f9-93a2-2d1c3b2cceb6}} , {{formula:abbf3c28-bce4-41b0-9c08-0fe928ade313}} becomes small. In other words the flow slows down when it passes through a neighborhood of a critical point. Such a slowing-down effect of saddle points was studied in machine learning in {{cite:607b2630b3943a8245df9ab6e5995857d9046a51}}, {{cite:438ddafe5f1fc45daa385f48c9bccdb75da1abd9}}.
| d | 505a896751f28ec72690cd2e1c4c5a6a |
[leftmargin=*,topsep=0pt,itemsep=5pt,parsep=0pt]
Uncertainty: select closest example to current hyperplane estimate (i.e. {{formula:fb89e3fc-b033-4e1a-a460-23e1514be0e5}} ) at cost {{formula:26e548d9-6e4f-4448-8044-b9d78228d1a8}} . The action of Uncertainty sampling is comparable to that of the first term in (REF ).
Random: each example is selected uniformly at random from {{formula:78bd1100-d545-491a-937b-eb7d17da2c80}} , at {{formula:f8f68bf9-a5ee-4f74-8fac-460f24db4b96}} cost.
MaxVar: to isolate the effect of the second term in (REF ), we evaluate a control strategy that selects the example that induces the largest channel input variance (i.e. {{formula:3072c603-5d35-476b-9d6b-497ed2b4c0eb}} ), at cost {{formula:217cd81c-1f47-407f-ac7d-dbe4f1af8aeb}} .
InfoGain: selects the example with the largest information gain {{formula:b2947c66-ddaa-4712-bb2c-64028b3716db}} , estimated by sampling {{formula:156baa7d-c09d-4f7e-aa9a-2755bd535faf}} times from the normally approximated hyperplane posterior (here we set {{formula:4ccbe830-4acd-4782-83a0-549579cf1e83}} ) and for each candidate example evaluating a Monte Carlo approximation of information gain, at {{formula:dffb7f76-c77e-4c63-b470-a129b9f9bea1}} cost.
BALD: we approximate the logistic function {{formula:34dd2cb9-2b20-4c20-bf09-d60d65be24ce}} with a probit function and apply the probit regression active learning method of {{cite:d14e745a234206545de4edca042c8bd920579f15}}, at cost {{formula:ae57fdb1-d7e7-4a77-8caf-e5d1bbe1e6ef}} . Like APM-LR, BALD approximates the action of InfoGain and only requires the mean and covariance of the normally approximated hyperplane posterior.
| m | 6277f7a8176160119f9dc0e636328b99 |
+ ShaekDrop + PBA {{cite:2354de1c84473cb3784fbd98c6629a81cbf273a3}} {{formula:9b354b7f-917b-4cb5-b9bd-719380d365a5}} {{formula:52bf9291-6289-41a4-861d-9fa40ae0ef6c}} - {{formula:14ddc6cd-0593-4b06-928e-4a8e0b73e52e}}
| r | 52084d46209f8e2561cdbbf7df9ce3b4 |
All training was done using the hyperparameters: {{formula:d067db59-71f7-4845-bf3a-4a365fbab00c}} , {{formula:71f82d38-ad3b-4c22-95ab-103f74f9979f}} , {{formula:c0c1f4f5-d67a-4e8f-b974-9c92e0545ab8}} , {{formula:0df29663-f4d3-487f-8cb4-f88c610c0ef3}} , {{formula:bb5b85a1-51a9-4a43-a537-f05899522764}} , {{formula:b0f2db2d-fd04-4f49-bfea-8924bd0b9774}} and {{formula:7d89ca60-0520-4023-9208-5abe98fd703e}} . The hyperparameters {{formula:4ab487ee-ca60-4102-82ff-73c2a4f14419}} and {{formula:51f99b15-71c5-4eca-839f-cdbd5bf68966}} were determined using the Hyperopt python package {{cite:539828926d1a1e89bf703081d79d2d4662c8576a}} with a maximum evaluation number of 100. We trained the model on two NVIDIA TESLA V100 with a five fold cross-validation, in which one of the five sets was used for validation, while the other four were used for training and report the average F1-score of the trained models in Table REF . Due to the semi-supervised learning our model has three distinct outputs, the audio only output, the face only output and the combined modality output. we report the average F1-score of the cross-validation for both the single modality models and the combined model, to asses the classification quality of the different models. Comparing the single modality models with the full model shows an increase in F1-score for all four classes when the multimodal approach is used, indicating that the combined model can incorporate the input data from both single modality models successfully.
It can be seen that the audio-only model has the lowest F1-score in all classes and exhibits a higher standard deviation compared to the other models which is expected, as audio data contains more voice variance, due to different voice profiles, and general noise than the face data. In addition, the variance of the model can be a byproduct of the high compression performed by the VQ-VAE. Although the VQ-VAE can reconstruct clearly understandable voice samples, some features could have been lost as the latent output of the model is comparatively small, with only two percent of the input data.
In terms of individual classes, agreement shows the largest increase over the average score for each individual modality at 17.3%, while disagreement and confusion exhibit marginally smaller increases at 14.80% and 17.15%, respectively.
It is noteworthy that the F1-score of the disagree and neutral classes for the multimodal approach show only a small increase in their respective F1-score of 0.4% and 1.4% compared to the face-only model, whereas the agree and confusion classes show a considerably higher increase with 10.5% and 9.5%, respectively. While it was expected that agreement would benefit strongly from the multi model approach, due to the high correlation of features {{cite:7698975adf8efe7ea582e45fb6f18e2721de2da6}}, the comparatively low increase of the F1-score for disagreement was unexpected.
| r | 60f98eb4a40c9a436f887104f0ceab7d |
There are two benefits of unguided methods. First,
unguided methods are more robust to environments with light or weather changes since they only take sparse depth maps as inputs. Moreover, for the same reason, they are more computationally efficient.
However, unguided methods show inferior performance due to the lack of semantic cues and the irregular distribution of captured depth points.
As seen in Table REF , the best unguided method {{cite:d0047a074ffabd077bf84fcc6523dde16fd99fed}} yields RMSE of 901.43 millimeters on the KITTI dataset. Note that {{cite:d0047a074ffabd077bf84fcc6523dde16fd99fed}} also uses RGB images to guide model training. The best result obtained using an RGB-free method in both the training and inference stage is demonstrated in {{cite:10f66fbbbda829a7c032b4814b5462fd0156cbb6}} with RMSE of 937.48.
On the other hand, as seen in Table REF , the best RGB guided method, i.e., DySPN, demonstrates a significantly better result with RMSE of 709.12. Moreover, many RGB guided methods can easily beat the best unguided approach. Specifically, except for 3coef {{cite:2d8697c99f3c61be4cb42e62f4832eb786c7dbeb}}, EncDec-Net[EF] {{cite:90680ed54ce5934b25a2e4250e957190ba1e60e9}}, Morph-Net {{cite:ad14d0f49c25091cf012a75e15fe9f044eff3314}} and CSPN {{cite:19108131843e01f0ffa7b8d7c9f0dcda6867fcc4}}, all other RGB guided methods with supervised learning outperform HMS-Net, showing the advance of leveraging RGB information.
Another difference is that unguided methods cannot utilize additional unsupervised losses derived from images, e.g., photometric loss.
{{table:fad63b10-166d-4e3d-acf8-e8459d9f5416}} | m | e56ee888edd492c51b24b27e59c6e9d4 |
To extract such information from the measured GW signals, one requires template waveforms
that have to be compared with the observational data using a Bayesian framework {{cite:a077ba70a2037928e89c788d0b31d693f8444847}}
to estimate the intrinsic binary properties such as masses, spins, or deformability, and
extrinsic parameters such as the sky location or distance.
Various techniques have been applied to construct such template waveforms,
including Post-Newtonian theory (Ref. {{cite:de6274c18f6ec7d39325de3ffcb3f5e44eb2fb99}} and references therein),
the effective-one-body framework, e.g., {{cite:52068e6279808b6266a37fdba3f69df059b91e98}}, {{cite:16c053ca2044554dc04fbfb54467c86309438c27}},
numerical-relativity simulations, e.g., {{cite:3ced2467c8d3414f65a3987c5a919669cb7e3f6d}}, {{cite:ac029365aab001a7a6366e877cf887dea69fb452}}, {{cite:8fa123a2f4f47b532daabd9e11bd33f8597546b7}},
or simply phenomenological descriptions {{cite:d5fab0e7a060bdf3bcb131ca7a46e1673106ffa6}}, {{cite:36e3b5fad57fa2ae3d8839571881b888061de519}}, {{cite:c735c856c2ad3ee87fa48af82041309ac09eaebe}}, {{cite:24c5071aa2ef73945b3523a3a4da90957347f400}}.
| i | 5ed781d5008919467a32b4f1ebb79036 |
Incongruous Meta-learning.
When fine-tuning the task-specific optimizee variable {{formula:49cc5492-4cff-4a49-8ffb-3c3383eaeaf3}} by {{formula:b4cc8883-df9d-46d1-8945-5de72868d736}} (Algorithm REF , Step 6), we can use an invariant RNN architecture
to tolerate the task-specific variations in the dimensions of optimizee variables {{formula:d725c774-f0ec-41da-8add-e8c40371c0c4}} . Recall from (REF ) that {{formula:b63df7ca-966a-44f2-b4ad-db1fd95b7478}} uses the gradient or gradient estimate {{formula:f74306df-9a2d-4b99-b771-56a9b72ab2a3}} as an input, which has the same dimension as {{formula:0fe19adf-8164-436a-866c-fd2147372853}} . At first glance, a single {{formula:4d24efdf-d34f-40dc-9c3e-b17b0aa96065}} seems incapable of handling incongruous {{formula:4461d9d3-a678-4d7e-92a6-d13ed6bff17d}} defined over optimizee variables of different dimensionalities. However, a
{{formula:348f38ba-2598-44dc-b536-5ffacda48f7e}} configured as a coordinate-wise Long Short Term Memory
(LSTM) network (proposed by {{cite:48d6cd1e43aa6ba9455708dc57026d537dc51c3b}}),
is invariant to the dimensionality of optimizee variables {{formula:07fb4cd6-5f22-4cd8-aaf4-e75552207054}} . That is because
it independently operates on each coordinate of {{formula:346b1b92-37fe-48a1-8aa8-f8f6d01866d1}} regardless of its dimensionality.
In contrast to MAML,
the invariant {{formula:7a480371-8ae2-4f39-a260-cd0991f55e17}} expands the application domain of LFT beyond model weights/parameters over congruous tasks to incongruous ones such as designing universal adversarial perturbations across incongruous attack tasks.
| m | ec385c74cb89dfca8d11aa8b6349f7fc |
There are some basic laws to characterize the quantum world in compliance with quantum mechanics, of which the most well-known is the uncertainty
relation. The fundamental uncertainty relation is called the Heisenberg uncertainty principle with regard to the position {{formula:7a785690-c36e-405d-8c7e-b67913b94052}} and the momentum {{formula:a8a90db7-46a0-4299-a0da-af35363a8504}} in a given system {{formula:d4b6ef30-4d97-4c31-9b82-761edc8c5158}} {{cite:157c4aeb296c4dcd57b284887d8ed9b95976cf97}}; it is expressed in the form of {{formula:76ba4ee7-3957-4553-9845-4f19cc298037}} , where the variance {{formula:3deee3da-614e-4f86-b576-1b5ed5ff8695}} and {{formula:d6cba414-bd94-497e-a2cd-6a05e613e21f}} is the expectation value of {{formula:1960b6f8-22fc-459f-8c66-e59ed0ba3af8}} . Subsequently, a more general formula
was derived by Kennard {{cite:1ec6247e8ef32047575b01bc3d83da6c77da3107}} and Robertson {{cite:730750d0f1cdb878d07b168f0e8a0aaf828fc736}} for two arbitrary incompatible observables (say {{formula:7ade40c2-728f-455d-bf25-2ab8f3ed69bb}} and {{formula:78b772b3-ce12-4cef-870c-8d1ce2f77bee}} ), whose lower bound is undesirably dependent on the systemic state. In the area of
information theory, entropy is considered a useful property to depict the state of a system. To eliminate Robertson's inequality weakness, Deutsch {{cite:52379cd2bdfb7156649579e58ff353f9d8582769}} introduced Shannon entropy and proposed the entropic uncertainty relation, viz.
{{formula:1670fea9-6fce-4181-98c6-2c06fe5cde57}}
| i | 5301972a14af78ee1893542583565b30 |
(see {{cite:e8541d79ed8afab441af1a28ef3f9216075e5565}}).
| r | bc89b3792759585a254a9b6170237b59 |
The optimal/suboptimal solution: for the SINR balancing problem, the solution is obtained by using the iterative algorithm proposed in {{cite:1dad981bd09d22a27879cf73f6f69b8737882ff4}}; for the sum rate maximization problem, we consider the WMMSE solution in {{cite:23b24d7aa022e7b011e5a2d7e591bc524a1c44b2}}, which is obtained by using an iterative algorithm. It serves as a performance upper bound for all other schemes.
The MAML solution: this solution shows the adaptation result of the existing MAML algorithm {{cite:9f963d43b7b2b0f05d5db04f0b06d5b933622350}} described in Section II-B and Section IV-A for the offline and online scenarios, respectively.
The transfer learning solution: this solution shows the adaptation result of the existing transfer learning algorithm {{cite:9f963d43b7b2b0f05d5db04f0b06d5b933622350}} that fine tunes the last layer of the neural network to achieve the adaptation.
The non-adaptive solution: this solution shows the result of using a pre-trained model to predict the beamforming results directly in a different testing environment without any adaptation.
| r | 0cbeeb353c691734c1234412a90aab2b |
To solve the bubble wall velocity,
we firstly need to know the bubble dynamics which is quantified by the equation of motion (EOM) of the background field.
Based on WKB approximation we can derive the EOM of the background field{{cite:e8536e9d7e8b3614d4a3d1bacf2b9828cdc6c9ce}}, {{cite:d45501eaecc2ed76edbf3f3280e007b22f488f50}}, {{cite:de22b8846c39bdd374a0c34eae03c181a995fbb4}}, {{cite:dd6d6d051d28996d74a98707c9d7d3455dfc6b3f}},
{{formula:a58ca177-6c76-43f8-9044-261b5ed8685f}}
| m | a8fd3f68f39c68e0ca6213220a48730c |
The final goal of this paper is to show that the evaluation procedure must be adapted from how it is currently performed.
First, many evaluation protocols require to provide separate results for each protocol, and we have done the same mistake in our previous evaluation {{cite:bec66c9eb8516995e40c0a82d24be457832a1758}}, {{cite:b957e05e307f1ba0c14215d34087fff7cdb4ba49}}.
For example, the Celebrities in Frontal-Profile (CFP) dataset {{cite:0f0ead39b9e172b056d0b777f4a7acae37f59ee4}} provides two protocols, a frontal-frontal and a frontal-profile protocol, and more than 94 % accuracy is reported in {{cite:e3e397e2bae91cc9150c0941f623e2c7b092396f}}.
When evaluating both protocols separately, a different score threshold is selected for both protocols.
This is, however, not how face recognition works in practice where a single threshold is used independently of the type of image (frontal or profile) at hand.
To highlight the difference, we repeat the evaluation of the different poses from Fig. fig:poses by selecting a separate threshold per sub-protocol (one threshold for each face pose) on the dev set and plotting the FNRM on the eval set in Fig. fig:thresholds:optimal.
Clearly, the error rates drop drastically when a separate threshold is computed.
Second, in most datasets and evaluation protocols, ROC curves are plotted that show the performance of the evaluated system only on the eval set (aka. the test set).
How well a threshold selected on this test set translates to previously unseen subjects is not clear, but from comparing Fig. fig:thresholds:eval with Fig. fig:thresholds:optimal we can see that there is a trend to reduce error rates when selecting the threshold on the eval set directly.
We believe, splitting the protocols into dev and eval is critical to evaluate the algorithm on data that has not been seen at any stage of the process.
| d | b9a7d9a7dbc54837658e68200a42e6af |
We have also presented a specific superspace term that can induce Majorana
gaugini masses on a quintessence background and studied few of its properties.
We have seen that in the new-minimal formulation such term takes a very simple form
and we have argued that it does not lead to higher derivatives
(or higher order auxiliary field equations).
It would be even more surprising if such a completely new term also exists in old-minimal supergravity
in a way that does not give rise to higher derivatives.
Instead, our strategy here was to identify this term in the rigid limit
and then we used it as a perturbation in old-minimal supergravity.
However,
since the new-minimal formulation of supergravity can consistently accommodate such term,
one important future direction is to either perform the duality from new-minimal to old-minimal,
or otherwise study quintessence directly within new-minimal supergravity.
Massive vector multiplets may offer an interesting framework to construct such models
and mediate the quintessence supersymmetry breaking {{cite:d99c167cfdbe14acd061b69300aa60db31d15d8e}}, {{cite:ca9b2ce37c3fd0f88cf9edd3fe1ff3645c781004}}, {{cite:6dd62cfab6f99710a13a0f401bdddf17896e577d}}, {{cite:015e9df3c52fa67e0f6e2d652bfe83cd11de8141}}.
| d | c8ab2858d9ff2e78356141fa30f60161 |
In Fig. REF , we study the impact of the IRS location on the BER of the IRS symbols for {{formula:f3e2a8f1-93c0-46ff-84db-c95782565d04}} . Specifically, we study the BERs obtained with the considered schemes versus the IRS's horizontal location ({{formula:94ab99db-ed81-4a59-9dc3-5a71432b4e39}} -coordinate), ranging from {{formula:dbc83969-6685-4c75-a8f6-09f9618b399a}} to {{formula:d4ff63ae-1231-4a6b-8dea-a36e69423d39}} . Note that for {{formula:52633f78-430d-48db-86e8-ea3d34687929}} , the IRS is closest to the BS, while for {{formula:526dd34c-f012-40a5-825b-21553fd6a308}} , the IRS is closest to the IR.
As can be observed, if the IRS is deployed close to the BS or IR, the BER decreases. This is because for a short distance between IRS and BS or IR, the signal attenuation in the BS-IRS-IR link is reduced due to the smaller double path loss {{cite:2058f085c88de5dd56c0d92dfc19bfa310c7d826}}. Additionally, for CSR, the proposed scheme still outperforms Baseline Schemes 1 and 2. Similar results are also obtained for PSR. This further demonstrates the benefits of the proposed joint IRS phase shift and BS beamforming optimization.
{{figure:256533e9-09c2-481f-a4f6-3185a7fd0472}} | r | d943e1b98cd161a8444600ebc5bb986c |
We note that our work does not determine whether internal deformation {{cite:ca377757c9d53f931d1871dbaeba3650b33f5719}}, {{cite:7c3346dff99d3dadf868225f1fc73db12965ed51}}, {{cite:009cdd55e1c3d2bd1926d9557673f81ffbbf50e9}}, {{cite:f2cba6199ea35f1b31d3a0f8ba60d9eeade93a2a}} or surface mass movement without internal deformation , , is the primary cause of the considered asymmetric deformation process. If the internal structure is strong, Ryugu may have surface mass movement. On the other hand, if the interior is uniform, this asteroid may have internal deformation. We, however, rule out large density inhomogeneity between the western bulge and other regions because the center of mass of Ryugu derived by Hayabusa2 corresponds to numerical prediction based on the mission derived shape model with constant density within error {{cite:9031c93373bdac0199c412217dbc55fccfa42025}}. It is also possible that Ryugu may have complex deformation processes if its rubble pile structure possesses internal discontinuities that formed during the reaccumulation process after catastrophic disruption of its parent body.
| d | 3d0509c7646485d3b4b199f955a3ceba |
First, we observe that the fully unsupervised vecmap model, despite being the most robust fully unsupervised method at present, fails to produce a meaningful cross-lingual word vector space for a large number of language pairs (see the bottom triangle of Table REF ): many correlation scores are in fact no-correlation results, accentuating the problem of fully unsupervised cross-lingual learning for typologically diverse languages and with fewer amounts of monolingual data {{cite:c63217f99be4cc50ba6de2f637e1be941d012d6e}}. The scores are particularly low across the board for lower-resource languages such as Welsh and Kiswahili. It also seems that the lack of monolingual data is a larger problem than typological dissimilarity between language pairs, as we do observe reasonably high correlation scores with vecmap for language pairs such as cmn-spa, heb-est, and rus-fin. However, typological differences (e.g., morphological richness) still play an important role as we observe very low scores when pairing cmn with morphologically rich languages such fin, est, pol, and rus. Similar to prior work of Vulic:2019we and doval2019onthe, given the fact that unsupervised vecmap is the most robust unsupervised CLWE method at present {{cite:00d8ddcf50ab8a9be5fae82e0004de8f54b1ea7b}}, our results again question the usefulness of fully unsupervised approaches for a large number of languages, and call for further developments in the area of unsupervised and weakly supervised cross-lingual representation learning.
| r | 7cf891d8ebcc5d4899adf2948912bd6a |
In particular, BNN {{cite:b15c1d61eae5fc6f1af04dfa263dd99c395e17d1}} directly unitize the Straight-Through-Estimator in training stage to calculate the gradient of weights and activations as
{{formula:c63c7021-e80c-445a-83fe-53e1148dd1fb}}
| d | ef9af2ecf3feb69f8178cb8e22e04afc |
Per literature, a system of differential equations for Susceptible-Infected-Removed (SIR) sequences is a typical mathematical epidemiological model for COVID-19 forecasting.{{cite:8f3a68c2e774a1289d773ecc5bbc014b9035cad3}}, {{cite:737919bc263796873033486e151e2c066a06d598}}, {{cite:847589df97cbebeb5d2a0832e2930880a4f1a337}}, {{cite:00b4c4bdfe5ed41465366108aac47239f950176a}}, {{cite:a65db8b4e9264279185fbaed36ae2e5cf100ba85}}, {{cite:cac71c5482e5ec7e414d3a46e2278378ffbcb70a}}, {{cite:c1c9b6af7a4b5022de04ded742ab07b45e5ed674}} Joining SIR models,
Khan et al. proposed the SQUIDER compartmental model to predict the coronavirus 2019 spread {{cite:1caa65e0203cfe7f53ffe967e07234897c1c97c2}}, and Xu et al. applied the generalized fractional-order SEIR model.{{cite:11213202c3a4632a96db6404ecb08c6172aca52e}} The SIR model has a good fitting for the simulation and data of the outbreak in the early stage of the disease. However, the obvious limitations are not limited to that the overall model system has a small external control power, and the number of patients presents a typical exponential growth, which is due to the absence of external drugs and preventive measures.
| i | 856e91bf2c8183ec18b0f1b501125711 |
IGMs can create multiple views of images via their latent transformations {{cite:e08caa0b1ee82fd7e7692146ec613e9dd7397e67}}, making them useful for contrastive multi-view learning. In this section, we study the effectiveness of contrastive methods for learning representations from IGMs.
| m | efe679433bf7cad91473adf944524abd |
In this manuscript, for the QAH effect, we consider another method of creating
quasi-periodicity, by coupling two QAH layers with arbitrary ratios of
lattice constants. Experimentally, this can be realized by using state-of-the-art
fabrication technologies of topological hetero-structures{{cite:cc1af37f5720f7652c5187eb72aaf7141601d25c}}, {{cite:8b6b2dcf57f5b78d7e92a2609b2921333693a139}}, {{cite:ac9c323c22add8c1f9542e8bdf27284c86ca2b9b}},
ultracold atomic{{cite:b31af46fa4c1f1a2ef68046e830ee0a315256518}}, {{cite:0f85125340345df4fc7646cdaca290de2a4041a0}}, {{cite:0871e793ceb8f17f658307034bfc663709734d64}}
or photonic systems{{cite:def7f3fb00c9497d8cb549bcde0c13273f4e0f51}}.
Firstly, by comparing the numerical and analytical results
in the simple case of commensurate bilayer, we confirm that the fundamental physics
underlying this system is governed by two coupled 1D Dirac equations, if no bulk states have been considered.
Then, the quantum transports are investigated for different lattice constant ratios, by using a tight-binding model that naturally includes both bulk and edge states. The central plateau of the quantized conductance is not affected since the coupling has not been able to close and re-open the bulk gap. On the other hand, the phase boundary of this quantized conductance plateau consists of a fractal transitional region, with small and fractured
islands of quantized and unquantized conductances penetrating into each other.
This picture is distinct from that of the commensurate system, where the boundaries of
the topological region are clear. Moreover, we find that these unquantized states
in the transitional region are extending across the sample. This is also distinct
from that of the disordered topological systems (topological Anderson insulators)
where they are localized. As a result, the details of this transitional region is sensitive to disorder, shape of the sample, and even the configuration of leads connected to it. The effects from nonzero disorder and varying coupling strength are also discussed.
| i | 436401efeb4928e03b5bdc8a8d05e30f |
The window method has been presented for the first time in Ref. {{cite:e8f019e75657e80df24f3e575accb011a1cd8c0a}} as a tool to improve the accuracy of the HVP by supplanting the dispersive results based on R-ratio measurements {{cite:c6d1c894adf7d56d19eec50f8a9526adb9251d18}}, {{cite:89c0fe5f3014f7d4c500af891f34f61e4a3f4c1b}}, {{cite:e9478fa1d8e96d978de962dcfc0304ba16b9363a}} by lattice inputs in a time-region where the lattice data turn out to be more precise. The idea is that the lattice calculation is much easier if one discards very short Euclidean times ({{formula:e285f7a2-8d9f-4b03-8555-8813767d7764}} ), which are affected by large discretization effects, and the long distance contribution ({{formula:36c01b68-00db-439d-8352-d06dd82b8d36}} ), which is noisy and requires significant finite-size corrections. An additional feature of this method is that the chiral extrapolation is much smoother due to the suppression of the tail of the integrand.
| m | b9b0b6def99ce1ca117eb5a0e8cf652e |
Avoiding annotations of training images has a potential to further overcome the difficulty and high cost of acquiring a large annotated training set. As an attempt towards this goal, unsupervised cross-modality adaptation methods {{cite:bf9abeebd880d9ca508df7c6c4ed4c467fbdeade}}, {{cite:549fbe85467c25d8f18048d55df304dec5cf0ebf}} are proposed to remove the need of annotations in one modality (i.e., target domain) given annotated images in another modality (i.e.,
source domain), but they still require annotations in the source domain. Some traditional unsupervised methods that do not require human annotations for training such as the Iterative Randomized Hough Transform (IRHT) {{cite:7e340c3b4391ff4c54be44e064b57aa0e909669a}} and texture-based ellipse detection {{cite:3d188ed694b88ee22b85a7724dff93fd050bb487}} were proposed to detect ellipse-like fetal head from ultrasound images, and they have a low robustness when dealing with images with weak boundary information. Currently, there have only been few works on learning a segmentation model without the use of annotations of training images. For example, in {{cite:c783a096a7c4ffdc3165b85d1cb0dae20cca684a}}, {{cite:c1c0bce20a7c8bb2107b3adf0a3bdc9806f749f5}}, deep representation learning is proposed for unsupervised 3D medical image segmentation. However, the performance of such a method is still much lower than learning from human annotations.
| i | 300b26484fb705fce8f67595dd32be53 |
L-DAMP {{cite:fca8d8c162408cfcca2677b9361eb43233dca2f2}}, {{cite:845aa6be3a0dcad610ed95d7f17c291fd66b4c17}}: This represents a powerful deep learning algorithm that performs model unrolling. We use a denoising convolutional neural network (DnCNN) {{cite:2cb932ae5aeb614afbf311d4ab59930aa4327f48}} backbone, which is interleaved with gradient descent steps, for a number of 3 million total parameters and ten unrolled steps. We train a separate L-DAMP model for each value of {{formula:4eac239f-0d71-4343-afcf-ffb564fc72d0}} to further boost performance. We compare with this method as it is a representative and highly competitive supervised approach for MIMO channel estimation using deep learning.
WGAN {{cite:739698463beee23dd2b5b936991c8017a63fb521}}: This represents a framework for using generative adversarial networks in channel estimation. This is achieved with a two-stage setting similar to our proposed approach:
In the first stage, a generative model {{formula:b0ef734d-43a9-4998-a235-fdabba073365}} is trained to map low-dimensional vectors {{formula:473f4fa3-467e-496c-b52e-334829c4e17a}} to channel matrices {{formula:388008a1-35c5-4cc6-8d77-de77d49bb6d8}} , using an adversarial loss and regularization {{cite:ad5588b29dd61a072923822a70c83858077aec6e}}. We use the same deep convolutional GAN as in {{cite:739698463beee23dd2b5b936991c8017a63fb521}}, and validate correct training by sampling from the distribution of channels.
In the second stage, given a pretrained generative model {{formula:9a88be8a-86a6-48c1-b95b-2c53b1a14d61}} , channel estimation is solved by first recovering the solution to the optimization problem:
{{formula:d34cc7cb-e5dc-4473-ac80-cac52fad2a15}}
Given a solution {{formula:8aca2e15-a5a1-44db-854f-62a76e56b22e}} to the above, the final channel estimate is output as {{formula:9c705b2e-8a37-442d-83bc-f260e8b4f12e}} . In practice, we use the Adam algorithm to solve (REF ), with a learning rate and number of steps determined using a validation set of 100 samples from the same channel distribution as the training data. Additionally, we search for the optimal value of {{formula:491f281a-0f0e-49af-b73b-19ee02b959e4}} using the same validation set.
Lasso {{cite:e514cf112378843997b6963889432cd899ffed24}}, {{cite:7450a91a70c4c0d48b7617c48610b6a1a4fd149f}}: This is a compressed sensing-based approach that uses {{formula:fb15c8cf-cde8-42cf-9b1b-79ffc19ad4c7}} -norm element-wise regularization in the two-dimensional Fourier (beamspace) domain. That is, channel estimation is formulated as the solution to the following optimization problem:
{{formula:4acf30b2-b7d4-46ff-8b5a-20392f26269e}}
where {{formula:d8c4e77a-4ce2-4452-bdf5-770d504b0a76}} and {{formula:66c99dd5-6dd6-460d-b3f7-3afd7ba21fda}} are square, discrete Fourier matrices of size {{formula:c8fd8f7b-8920-4dcd-8ffb-815b821fe0e5}} and {{formula:74c4402f-4efe-4bc9-87a3-029f74ade89d}} , respectively. In practice, we use gradient descent with momentum to solve the above optimization problem, and we tune the step size, number of optimization steps, and the value of {{formula:07622731-2622-42a1-81c0-4a6476986212}} chosen via grid-search on set of 100 samples from a specific channel distribution. As different environments have different statistics of their scattering structure, different values of {{formula:d487f1e4-3c31-4efb-8f35-952569196c91}} may be optimal.
Fast, approximate atomic norm decomposition (fsAD) {{cite:05fb8a216827d9c35941871c8104950e81c86ea2}}, {{cite:b147a3877f258f28431fc454aa61e71050b48dfd}}: This represents a provably optimal, compressed sensing-based approach for recovering channel matrices that are exactly sparse in the continuum of spatial frequencies. Channel estimation is formulated as the solution to the optimization problem:
{{formula:929ffc93-310b-4295-b59b-672e11679615}}
where {{formula:76db4beb-b45e-490c-aaaa-d92462abac30}} represents the atomic norm of {{formula:effa1bef-1f9f-4f28-8491-b9e2e57af845}} with respect to the basis set {{formula:1c557cea-577f-4181-b4de-c8893352d47e}} . While this is an optimal approach, evaluating {{formula:8ba28b0b-788e-4082-b5a3-a90c076bb236}} itself involves an optimization problem {{cite:05fb8a216827d9c35941871c8104950e81c86ea2}}, which can quickly become computationally prohibitive in high-dimensional settings. In practice, in scenarios with uniform linear arrays (ULA) at both the receiver and transmitter, we use the following approximation to (REF ):
{{formula:c69e16ff-8a92-463a-bb36-b1b9e95c5889}}
where {{formula:7aa85328-4d2c-434f-bca0-5a12a6799601}} and {{formula:7f876ba3-11c2-4d63-b6e0-457fe5bf427c}} represent over-sampled Fourier matrices, with a lifting factor {{formula:d321b0c8-8a53-40db-9f73-c009d09f1f9a}} . In other words, this method leverages knowledge about the antenna array shape and imposes sparsity in the over-sampled beamspace representation of the channel, which approximates the continuum of frequencies as {{formula:0dc10381-31e8-4238-a457-cebc5e62912e}} , with the cost of increased computational complexity. In our experiments, we use {{formula:bfbd72cd-d5ad-4a16-9d85-c8ca9906514b}} , and tune the parameter {{formula:38a095ce-5dae-423a-9729-d3e3991d3cd7}} , step size and number of steps using 100 validation samples from the training distribution. We discuss the practical limitations of this method in detail in Section REF .
| r | 62c7005de70b885fed9787a684cd2e62 |
Before 2015, researchers usually model a specific texture model to represent a style. Because this modeling method is non-parametric, it requires professional researchers to work manually, which is time-consuming and low-efficient. Moreover, each style model is independent of each other, restricting it from practical applications. Gatys et al. {{cite:26cb38e66a5a6553735ba08ae8c82f8ff5d986c7}} began to perform image style transfer by leveraging deep learning networks. In recent years, researchers improved this method and proposed more image style transfers networks to achieve efficient, flexible, and high-quality style results. This book summarized recent progress in image style transfer from the above three aspects. A video style transfer method transforms a style image (e.g., a van Gogh's painting) of a source image to a whole target video sequence. This is a painstaking task if one performs this process by manual. Instead, researchers regard video style transfer as an optimization minimization problem or a learning problem. Therefore, some optimization minimization frameworks and deep learning based frameworks emerged to achieve high definition video style transfer effects over the past few years.
| i | 4f01b55cfb60b0e7de995642636d45cb |
where {{formula:c2ae95d9-1943-46b2-8700-241b39c66355}} denotes the regular representation from {{cite:f8d843e14c51201f8c2ea14e6c59ccf7aa829e1d}} (in that definition, this map is called {{formula:7fee38ee-9f78-4106-a4ab-641502b5b073}} , but we have changed its name to avoid confusion with the {{formula:896fe919-75a2-4a18-b036-cc2001083bd6}} -graph {{formula:f1d59dfc-c9a8-4df7-93e9-6896e4bcaf1a}} ).
| r | fbad272b98b1a2f051a67478ee5508df |
Approximating an Ising Hamiltonian's ground states can be achieved by applying simulated annealing based on a Markov chain Monte Carlo spin-flip dynamics. The most usual example consists of considering a time-inhomogeneous Markov chain based on a single spin-flip dynamics (such as the Glauber or Metropolis dynamics {{cite:8c950da2912c7e183f8732a1e1724540de8a31a0}}) while slowly decreasing its temperature towards zero. Some theoretical results (e.g., {{cite:4762672061beff090dfcc489b00bf6cfbf0de333}}, {{cite:d93d0a1551c4415b7f7a746efe6b1df2557058cf}}) show that if the temperature is decreased in time {{formula:effc0829-d021-47b0-9126-aff08b2e4675}} at a certain speed rate, such a procedure yields an approximation to the minimum value of {{formula:f89d4693-4d69-46ab-84f8-1973bd8a2f54}} . In {{cite:95ab6afb0c19a330fc3b0cd4f95b9764a3c51f31}}, {{cite:021588676c98fa211dec7a4007de5ccd88f052b5}}, the authors considered simulated annealing based on parallel spin-flip dynamics that, differently from the usual method, allows the system to update multiple spins independently, and simulations showed that it manages to converge to the ground states significantly faster compared to the single spin-flip methods.
In addition to these observations, in {{cite:bafb00eb1c09722e5c6d699b0dd3293b0859180a}} the authors investigated from the mathematical point of view a specific kind of stochastic cellular automata (SCA) which was derived from {{cite:23faa55662b5024bdcd188a1bd172b47f5db155d}}, {{cite:289aa7fadb89fec564cf7e34c427f94cc042ebd7}}, in order to determine sufficient conditions under which the convergence to the ground states is guaranteed.
| i | aa61c949462168d809a5ceda7594ac39 |
So far as we know, rare research work explores the conflict between the literal and deep sentiment.
Existing methods for sarcasm recognition focus on the sentiment contradiction reflected in word pairs or phrase pairs that appear in the sentence explicitly.
{{cite:a73da0a9d232968bd371a928fe925d83bfb19f01}} propose a feature-based machine learning method to classify sarcastic texts by different situational disparity. The disparity comes from the co-occurrence of positive sentiment phrases and negative situational phrases. Phrase pairs with opposite sentiments are used as features for SVM or other classifiers.
Whether word pairs or phrase pairs express opposite sentiment, they appear in the sentence explicitly. The pairs depicted implicit sentiment are not required to contain sentiment words. Along with Riloff's study, {{cite:a80e0edabc883fd39ef55b2339644dcc4d1d31f5}} follow that word pairs in a sarcastic sentence tend to be contradictory. To utilize this, they adopt attention mechanism to model sentiment conflict of word pairs.
{{figure:68c1bfef-69d2-424f-8646-b441dbb60d50}} | i | 551393c1de5256f01057597f08b864d8 |
Although GS98M was chosen as the best SSM with high metal abundances, the value of {{formula:fee7207e-2fc4-469b-9b95-135632b713af}} of GS98M
is slightly larger than the detected value of {{formula:959ee21c-0afd-48a9-be88-1e6f7190f111}} cm{{formula:ed3e2518-c8f3-47cf-a736-bd31ced48e62}} s{{formula:599152ca-60ca-4774-af09-d6c9b1e611ec}} {{cite:b7433a2b744a4aed226867657e2798ce1d12b02b}}.
That of GS98opr is in agreement with the detected one, but its {{formula:24f77fe4-0456-40cf-a245-a9d869e5848e}} B neutrino flux is lower
than that updated by {{cite:ef17ca3b87627212c18ee7308d04f6e2a39dbda0}}. Thus the updated neutrino fluxes do not favour the high-Z models.
Moreover, the values of {{formula:63205d41-762c-489f-bbad-e50ed15e33b3}} calculated from the models with the heavy-element abundance determined by
{{cite:275c9c92538c08260505e0e2baf1786a02799877}} are consistent with the detected value, but the {{formula:9b402f18-3dee-435f-993c-c9067395ec01}} Be and {{formula:630c5c98-bb37-4850-9619-24038064402b}} B neutrino fluxes
predicted by the models are much lower than those determined by {{cite:f37a14c3f9718a7c5a98ee9be5e1af7941e9cff3}} and ones
detected by {{cite:ef17ca3b87627212c18ee7308d04f6e2a39dbda0}}. Therefore, the updated neutrino fluxes also do not prefer the models with
the heavy-element abundance determined by {{cite:275c9c92538c08260505e0e2baf1786a02799877}}. For the same input physics, the fluxes of {{formula:8a69e16f-551b-427c-9760-58a783365745}} Be,
{{formula:819dfc9e-4524-4a8b-bf89-a5f3eb4a2b33}} B, {{formula:34064272-1ede-43f8-bcb0-4ff451ab386f}} N, {{formula:369b147f-1f73-4929-85be-f6a974995c57}} O, and {{formula:95cf3bde-b3dc-48a7-881e-2ab138435297}} F neutrinos predicted by models increase with an increase in metallicity.
These imply that the updated neutrino fluxes prefer a heavy-element abundance between that determined by GS98
and one advocated by {{cite:275c9c92538c08260505e0e2baf1786a02799877}}.
| d | 07724a1e0b3d0fdf90460e5fe437363a |
The implementation is done using an Ubuntu 20.04.4 LTS operating system with an Intel(R) Core (TM) i7-8700 CPU @ 3.20GHZ X 12 cores and 16 GB of RAM. The language used is Python and is executed on a jupyter notebook. Scikit-learn's {{cite:ef9a2406534b1a42fca18dcbefa35f98ce4fe6c8}} Bayesian Gaussian Mixture Model and Gensim's Word2Vec libraries are used. 100% of the data is used for training and detection in an unsupervised way. The proposed method doesn't require data balancing or to be trained only on normal instances.
| r | 0a901d513268f2444e0ad0986c60220e |
The current architecture uses non-linear functions as in the conventional neural networks, which is potentially a universal approximator and the property is supported by the non-linear functions and stacking of many layers as in other deep learning architectures
{{cite:47081da6bb60e51cc91cfb00af48480613824e92}}, {{cite:167e3b2dfdde34a48ebec06d1fe48721a4805363}}, {{cite:cbf94a19a39dc81f3cfefeb78e236caeb055fe81}}, {{cite:c226864e7d488bb3afa0a55b3e95eec568f14173}}.
It is important to proof, the covariant neural network is a universal approximator for gauge covariant local functions but this is out of scope of this work and we leave this for future work.
| d | c2fe9b7b31c10fec0488b709da3e571d |
While in small systems achieving the maximum {{formula:e18db193-989b-4a9a-8b6b-f4e5588a2326}} requires fine-tuning of {{formula:960e304f-e372-4028-a7bf-e57a88799d89}} to locate a resonance, for larger {{formula:d2a1c80c-3cdb-4956-b0e3-090b7c1f3b38}} this constraint is rapidly removed due to the exponentially increasing number of eigenstates crossed within the bulk of the spectrum. As a result the rectification is broadened over the many-body bandwidth of the chain. Moreover, the favourable scaling with {{formula:c58580e7-e325-42ff-82e5-0fcfbe602def}} means that giant rectification can be achieved with a reduced interaction strength. To evidence these effects, using the insulating Ansatz and tensor network simulations (see Methods) we calculated reverse and forward currents for {{formula:435cc9dd-df1b-4300-8e2c-d243ff544041}} and systems of {{formula:de8d9802-9dcf-4de7-a99e-c16113bb287b}} , shown in Figs. REF d and REF e respectively. From these we find {{formula:09c59bea-b286-463e-9252-0c353f22f5d2}} over a range of {{formula:a1d875cf-0a20-4934-8222-d501f3a460c5}} , as seen in Fig. REF f. This establishes larger rectification coefficients than those previously obtained for different types of non-homogeneous lattices {{cite:71eb20acea38b2fcbee86395556b16fe0c7fb0ab}}, {{cite:f854ef5e97be6e2917a97940086ef8e7ccf55cbb}}, {{cite:1610d78d0a4d7d4f9d7735b416c6d2a5e71e0d81}}, {{cite:6afde12880cb02cf18bd07009d390daf4d0dd893}}, {{cite:4d69ecf05357b548b8b5ac137b14afb1b863ca0e}}, with a more intuitive and easily implementable setup {{cite:eb2f59ad8c04699ea799a0aebbc3665abbc91de6}}, {{cite:a2ba823db6b87c96ea4ca6c9ccf605c76c8f9e19}}, {{cite:5de6542a8914133c607c2a9df5f7b5f662ba737f}}, {{cite:26c474f0746c53e0e5e77c09d719fea67ef93237}}.
| r | 42a6cd400165578308db53f7d9e26cd7 |
Orthonormal Directions: While constraining the directions to be orthonormal still leads to the same subset of interpretable directions being discovered, their quality suffers. This aligns with the observations of Voynov and Babenko {{cite:ad2858310f85b85812d425626d50f70f2c2739b5}}. However, their results show that some datasets benefit from orthonormal directions, leading to more interesting directions. We do not observe this on our data, and the lack of disentanglement is also clear from the lower RCA of the methods using orthonormal directions. Thus, it seems likely that directions offering semantic meaning are not necessarily orthonormal, strengthening our reasoning for choosing this method over Härkönen et al; Shen et al. {{cite:b7d14bacd1b278351ebb45bd02d483dadc17c8e0}}, {{cite:3caa1e7811c3eae607102f40aae3c4b10994f60b}}.
| d | 5c8406b19efd0a27cc00823df0afa3ec |
Table REF
reports the results of semantic segmentation on ADE20K.
The segmentation results
are from the corresponding paper.
We also report the
results
of object detection
and instance segmentation
for MAE
under
the Cascaded Mask R-CNN framework {{cite:75b3a1780080f5d2440eb591fd6534ed056667d6}}.
This is different from
Table REF
that is based on Mask R-CNN.
| m | f017d7b1d6cc33767efe25c18d512d8d |
As we shall see in Section , nearly all variance reduction approaches in RL employing the general framework of Algorithm REF , use an importance sampling technique. This could significantly degrade the performance of the approach as the gradient estimates depend heavily on these weights {{cite:97fc2a5e5205bf71efb3fb3efefc5733ff81050e}}. Besides, these variance reduction methods often need giant batch sizes at checkpoints which is not practical in RL setting. Finally,
the hyper-parameters of these approaches must be selected carefully as they often use non-adaptive learning rates. To resolve these issues, in the context of stochastic optimization, a recent variance reduction method called STORM {{cite:e31855ec2b02718db6c0a5e93dc0b4e3ca802604}} was proposed with the following update rule:
{{formula:c63e6fb3-861b-4485-8ff6-8bd467be26ad}}
| m | ec0a5f05ae02c8008d38163f0bd96728 |
In this section, we show the numerical results using the annealing schedules of transverse and longitudinal fields as defined in Sec..
First, we consider the annealing schedules as {{formula:7c3a31ae-fd66-4ba2-a16f-9a8c2d53ebfc}} and {{formula:dc0a98e6-399e-4ee5-8ec7-481edc936958}} where the value of {{formula:a17fbc0a-b696-4b7c-9937-5f31c19485c7}} may be positive or negative. Depending on the sign of {{formula:ccb5232e-1cd1-4dc9-85f5-ebc74842c9d7}} the system will
attain a ground state out of different degenerate ground states of spin glass.
Here, we have considered {{formula:0ec28102-223a-41b9-9e9f-605418c2ca6c}} and the system converges to a (final) state
(which of course changes with the sign of {{formula:49b6ebf9-d5a6-49cb-9053-8a73be317a2e}} ) at large time, and study its overlap ({{formula:b860a178-fcf0-4cf7-ab72-f20f1a107821}} ) with the ground state of classical system with Hamiltonian {{formula:200686e4-7e64-4016-82f5-e3659e3ac4b1}}
(with that particular configuration of {{formula:011597f7-9dd3-46b4-9608-18dff409e2b1}} ).
The exchange interactions ({{formula:9d5c3f9f-bb2e-4f13-825b-9d2566d0780d}} ) are taken from a Gaussian distribution (Eq.(REF )) with
zero-mean (approximately) and standard deviation {{formula:306842d6-e8b8-4be1-9d13-13d7580e88c9}} . Fig. REF {{formula:7aba10c9-7c0a-4508-9b64-e1db5a8f3ce3}} shows the time variation of the probability ({{formula:0d81d727-a70e-466a-a152-3917a1fca040}} ) with annealing of {{formula:7c40f124-c55f-48dc-973b-21764d0a41a1}} .
For comparisons, we also study the same with constant longitudinal field {{formula:e22162aa-dac0-4603-8317-a86a0ea1a278}} (as in {{cite:7b9748f8e1564d962f6c5d27c612631cbdfe1334}}).
The results shown here are
for a typical set of exchange interactions. Some gain in the overlap is clearly seen for annealed {{formula:a10ee8a9-4f79-4d31-a16e-ee1010e4ce77}} case.
In some isolated cases (with different set of exchange interactions), we have found little better results with annealing of {{formula:ac742bd8-a29f-4626-994b-74998220dbcc}} than in the case of applying a small constant longitudinal field.
| r | d31ba50152763327551bba1c646e933e |
Markov chain Monte Carlo (MCMC) methods are widely used algorithms for
drawing samples from complicated multidimensional probability
distributions. For example, in Bayesian analysis
{{cite:a78ef273d294f08ce2f224e9ecbf1fe31b66e076}}, we are often interested in
computing the posterior expectation of a function
{{formula:b96545a0-374f-4d1c-a908-03d7b80fdae0}} given the measurements
{{formula:f4563d53-c4a4-4c39-989f-422d60178504}} :
{{formula:80a807dc-3603-4a7d-b150-95e5dc06b07b}}
| m | f5e778708780a4f76d6a9cfe7f59a8f1 |
However, the work presented here does suggest that the late-time deviations from the conventionally considered
Hawking radiation thermal state do contain information that can be used to partially reconstruct the initial state of the BH (see additionally {{cite:4c2d747e54ab73e69c1050f5793ea4e1d5ef5261}}).
Qualitative evidence for this suggested in Fig.(REF ) of the numerical simulations of Eq.(REF ) for the
probability distributions {{formula:65222b91-4eab-438b-ac59-fed5c7c5cdab}} of the BH `pump' state, and {{formula:e7db595b-f73f-47fc-9910-41b076cae83e}} the outgoing Hawking radiation,
in the computational basis (Fock states) presented in Section .
The gray-dashed curve in Fig.(REF ) is the initial
coherent state probability distribution of the BH `pump' mode {{formula:0465a622-a990-42de-9b57-8fae177cb165}} with {{formula:63b86e22-7442-404f-9f0f-897cb32c904b}}
(the initial distribution {{formula:19734630-d4b1-4d4a-902c-30010becefa9}} of the Hawking radiation is a delta function at {{formula:4f6540c9-6063-4613-a1dd-f019ab4ccb38}} ).
The black-solid curve is the probability distribution {{formula:cb247256-2855-4d02-8636-8df17ed2141f}} of the outgoing Hawking radiation mode {{formula:e4733c9b-5939-4fe3-a5b9-8980572d0363}} at time {{formula:da516058-d583-49f9-9d78-a41dd9c2658f}} when {{formula:fd1814dd-828a-45c9-9547-0912bbedcd24}} . Is is qualitatively similar to {{formula:3ef9fccf-4bbe-4b06-85a2-461b0a2a01e2}} .
The black-dashed curve is probability distribution {{formula:d5f6b6a3-c0fb-44c4-874e-2313ee12a1cb}} of the BH `pump' mode at {{formula:3465d4dd-3733-4092-aaac-8febda4a141e}} .
The zeros (and near zeros) in {{formula:5fbeb178-34ac-4260-ab22-aac0b1bc25a2}} indicate that the BH `pump' is approximately
in a single-mode squeezed state {{cite:7be81a13e682519ce82859cd8be3efc7690a1dd1}} characterized by the
pure state vector {{formula:52fb28d4-7555-459a-a216-97bfd64ea361}}
(with odd {{formula:beec3e44-e234-4c10-97eb-3de3c8868363}} ).
The implication of these results is that, at the limits of the validity of our model, when {{formula:374b7f64-804c-47c3-85d1-8f6071aa1c5e}} ,
the two-mode squeezed nature of the short-time Hawking radiation is impressed upon the BH `pump', while the initial coherent state probability distribution of the BH `pump` is effectively impressed upon the late-time Hawking radiation.
If this were the approximate endpoint of the BH evaporation, the initial information of the BH (mode {{formula:c394e865-b2f4-4be8-a123-ebb88188e31e}} ) has (at least partially) been transferred to the outgoing Hawking radiation (mode {{formula:bfa2b9f3-03b5-47d2-9d9d-d5889f212f11}} ).
The results lends credence to negation of the assertion quoted in the Introduction to this work (from Lloyd and Preskill {{cite:4a2af41dec82483d41b438d6c7958c5b14d4ced3}}), that the infalling quantum state is cloned (by some supposedly unitary mechanism) in the outgoing radiation, which would violate the linearity of quantum mechanics.
| d | 401874648c0b78931fbf1addf5659d79 |
(the reader is referred to section 4.3.4 of {{cite:04df636e6fca6863db46ac8a12eab0ccec415e84}} for
more details). Griffiths & Tenenbaum's bridge to Kolmogorov
complexity is only established through this last theoretical result:
replacing {{formula:17de51f8-fad6-43a5-ac80-f3878324eac8}} by {{formula:294e3648-a605-4daa-89d4-3a1b23fc41eb}} in Eq. (REF )
should automatically give us some Kolmogorov complexity {{formula:74c3087c-4d56-40b8-bb10-0157f037f1a5}}
with respect to some underlying Turing machine {{formula:edbc864b-8036-467c-aa7b-9a88f5037e4e}} .
| d | 6b5f79ae1663422ebd798b62c02477f4 |
During the exchange of training experience, the parameters are usually updated along the direction of negative gradient. Without loss of generality, for each positive sample in the base model {{formula:2af0f71e-f9ec-4c65-90dc-a5f425697e58}} , the gradient of cross-entroy {{cite:78fd8cbc23e8850a4d5548da7bfc3f52befbb7ac}} in Equation (REF ) with respect to base model's logits {{formula:7f8f736c-8586-418a-9e88-f1d7ef1cd06b}} in Equation (REF ) can be derived as:
{{formula:54071f22-c715-44a8-9edf-b2c5b0ce7ed5}}
| d | 0bbc1520b295be27fbd940c5c089baea |
Compared with the state-of-the-art textually supervised method GroupViT, our initialized SegCLIP achieves 1.4%, 2.4%, and 5.6% gains on the VOC, Context, and COCO, respectively. We also conduct experiments for GroupViT on CC and COCO datasets for a fair comparison. Our SegCLIP trained from scratch achieves 5.2%, 4.3%, and 2.3% improvements compared with the GroupViT{{formula:a47e29e4-8fa5-44e4-81b4-9ae4c4299941}} . Note that the GroupViT{{formula:1f7b9db4-6fd8-4c52-93be-4bb516bde433}} achieves superior accuracy than GroupViT{{formula:5e8543bf-a994-4c6a-a556-f364564752bb}} in our settings. We suppose the CC and COCO, which are smaller than the CC12M {{cite:63ba52f7902b6e53993575875dea987961cf8cf7}} and YFCC {{cite:2ac4c93e7e19c17011f3af20a0bd56f462bcbf12}}, may lead the unstable and insufficient training for the 2-stage GroupViT. When initialized with the pre-trained CLIP, the SegCLIP improves the mIoU by 19.3%, 5.6%, and 11.3% on the VOC, Context, and COCO compared with training from scratch, respectively. It implies that our model could benefit from the pre-trained CLIP, which also proves the flexibility of the semantic ground module.
{{figure:af4995c8-a05c-4570-b8ec-ab4c2d7921c0}}{{figure:13e6a13b-9e3f-48e5-af11-d140296639b2}} | m | 43e49e5445de9710bba74fc36de6dadb |
Recently, {{cite:dcfc6cbc2d3b7ce6f7b787f695444bf0a2c3c851}} have shown that there is a strong connection between the low-diversity problem and what they call model over-confidence following {{cite:278b6391f9c92fe0455bd5b5c7a5057790d001f4}}, the phenomenon that a model incorrectly assigns most probability to only a few tokens.
However, the cause of this phenomenon remains unknown.
In §, we investigate and conclude that the model over-confidence problem is caused by an imbalanced training of tokens with variable frequencies, which favors frequent tokens and results in low-diversity.
To correct for this, we propose a FACE loss function that improves the traditional CE loss function by taking token frequency into consideration.
More specifically, we first analyze the influence of the commonly used CE loss function, and find that it prefers high-frequency tokens, which results in model over-confidence and low-diversity responses.
Then we propose a FACE loss function that improves over the CE loss function by incorporating a weighting mechanism conditioned on token frequency.
| i | 77af2a52173220d12fd17c71b1568c2d |
In this section, we evaluate our proposed calibration methods for the tasks of object detection, instance segmentation and semantic segmentation using pretrained neural networks. For calibration evaluation, we use the MS COCO validation dataset {{cite:5d54b93b05a101d0651632126a286f0e73275688}} consisting of 5,000 images with 80 different object classes for object detection and instance segmentation. For semantic segmentation, we use the panoptic segmentation annotations consisting of 171 different object and stuff categories in total. Our investigations are limited to the validation dataset since the training set has already been used for network training and no ground truth annotations are available for the respective test dataset. Thus, we use a 50%/50% random split and use the first set for calibration training, while the second set is used for the evaluation of the calibration methods. Furthermore, we also utilize the Cityscapes validation dataset {{cite:e834d5652264cbc05ba1bcaf5f28a9016e21f179}} consisting of 500 images with 19 different classes that are used for model training. The Munster & Lindau images are used for calibration training, whereas the Frankfurt images are held back for calibration evaluation.
| d | d5dfc10cdaff9153010d11dc17bca654 |
Tree based algorithm is a common choice in decision making studies{{cite:8645927d830de7447761ead83f2e1c7fe7a45233}}, {{cite:96e520e4ac9255dfa6f17d4e95c2ff45cd32401f}}, {{cite:6e8bd4b99161f87625138145e345277e9172ff46}}, {{cite:d73dd4ff4a26dbd862d9a266d617cd0a025d5b7b}}. A decision tree{{cite:0377a5d6f9bda5d6950d8d12c83f19a7847611b8}} is built using greedy algorithms in which the best split-point at each node is chosen by searching through all available features to minimize misclassification error. Also, its hierarchical structure naturally takes into account the interaction terms between predictors{{cite:8cb3885fc8f8d287b322e350fe17ca1822af151f}}. Since a tree algorithm puts more emphasis on subjects with larger treatment effects on NMB, individuals with small incremental NMB are more likely to be misclassified when the tree size is small, yet, fully grown trees may suffer from overfitting. Pruning is a technique in machine learning that searches algorithms to balance the complexity and the predictive accuracy of a tree. In our implementation using the R package rpart, we prune off any split that does not reduce the overall lack-of-fit by a certain amount, which is quantified using the complexity parameter (cp). We choose the cp that produces the smallest 10-fold cross-validation error. Decision trees are favored for properties such as interpretability, transparency, and straightforward implementation. The major drawbacks are overfitting and instability{{cite:70a99ed886e2b482a033bad2f76d0e2a851bdbf3}}, which may result in estimators with low-bias and high-variances (“weak-learners").
| m | b87fa39fcfcc4ecdbd2e7bf935a2f94a |
where {{formula:631fd33b-c4e4-462f-ba5b-ae2634e5c9a6}} follows from {{cite:7f9bab7983f48286778d8a4390ffadb398d4d8f9}}, {{formula:35403eac-1f50-4a99-b54c-6962977cb670}} follows from the log sum inequality {{cite:ebee5d0111ac11b1a5f036f57a00564e668cc5ec}} and {{formula:6eb6fe5c-0f12-44e6-b579-fdcffc7d22d0}} follows from the fact that {{formula:7ef0cece-9029-43ae-90fe-6f0efd4a48c2}} .
| r | 0f1adb07a8a96f01989f256eef29c5b2 |
The causal diamond method is discussed in Ref. {{cite:963fffa6bfe2b7ed9f97ae09a2ee979e93e908c5}} as the basis to obtain the field equation of Serrano-Liska gravity theory, whose entropy formula is given by
{{formula:d37b06e3-daf7-43d6-a25a-c2a08c34b711}}
| r | a291a659849f769f5089e2931d46b465 |
To the best of our knowledge, there is no report yet on the online training of spiking RNN with e-prop learning rule based on realistic PCM synapse models.
Our work compares several previously developed methods that are designed to cope with memristor non-idealities and demonstrates that accumulating gradients allows more reliable programming of PCM devices, reduces the number of programming devices and outperforms other synaptic weight-update mechanisms.
Future work will need to evaluate the impacts of the implemented weight update schemes using more extensive datasets for a more interpretable benchmarking, further incorporate the PCM devices for emulating temporal dynamics such as eligibility traces {{cite:db5de6ab572c3b4c77005af8e94991d97e3550a4}}, as well as exploring other learning rules such as OSTL or RTRL {{cite:1f746c66dcd9433a98765001869b962e40b087ba}}.
| d | 6903158f3aaacae071d3fab61f53bff1 |
In our findings we have exhibited that the M-SGD error is approximately Gaussian irrespective of the distribution of the weights used in the problem as long as the number of samples and the number of minibatch is large. This helps practitioners comprehend that the dynamics of the M-SGD algorithm is very similar to that of the SGD algorithm with a scaled Gaussian error. This is similar to the works by Dalalyan {{cite:48d2aa3894dccd666c603ecc1d58a672248ad070}}; Dalalyan {{cite:281608ab2dc8dbdf64924fec2d678a0a0bd3c812}}. Our results exhibit that the M-SGD algorithm is close in distribution to the SGD diffusion. The dynamics of the latter has been extensively studied and particularly exhibits the interesting phenomenon of escaping low potential regions (Hu et al. {{cite:e1a23b77b564cc5ba7867af7e46789089a19bf72}}). Our work has been the first step in establishing that the M-SGD algorithm also escapes low potential regions. The final result exhibits that the M-SGD algorithm is a valid optimization algorithm as we can exhibit convergence on average for strongly convex problems. This is in the spirit of Bottou et al. {{cite:a484cf3c6e9b824e4609030541f9cd3546d08116}} where the authors display similar results in different setting for the SGD algorithm.
| d | 3824a65ad2487c9add517d69e7bb145b |
Both studies show that the presence of embedded clumps is expected in clusters born from massive molecular clouds, and that they can easily survive until the stars explode as supernovae.
We also need to estimate the rate of cloud evaporation required to refill the gas and reproduce the masses in the observed shell. From the masses and ages of the remnants we require an injection rate of about 25 M{{formula:d7658343-71cb-496b-96a8-91789e3279d0}} per 10 kyr. {{cite:70f22be3378ef3b8513d4fe6032ce372b7ae68d8}} find that except at the onset of star formation, winds hardly affect the disruption of the molecular cloud; with photoevaporation dominating this process, so here we need consider only cloud destruction by photoevaporation.
| d | 74eaf96b1f2eb8db375718ec7159ff54 |
In this section we provide an overview of the population-based policy gradient method described in Section 6 of William's REINFORCE {{cite:cb61698e7e5575ff9f55bcb48e1f4ee25d3d4f56}} paper for learning a parameter vector {{formula:c656fbfe-4af5-4da5-a5f5-da5222d3a13b}} in a reinforcement learning environment. In this approach, {{formula:1c763c4e-d4c1-4044-a6d3-df45932d056b}} is sampled from a probability distribution {{formula:ed58033a-c1b7-430f-b6ca-c9ea822841e3}} parameterized by {{formula:b68c79f9-d07d-4cb0-904b-d64a804e3d5e}} . We define the expected cumulative reward {{formula:c4c94d91-1dbb-42ce-831b-b86141f48fd5}} as:
| m | 6f8c182773ba56e1d656db5f976bdfad |
We use RelaySum in the RelaySGD learning algorithm.
We theoretically show that this algorithm is not affected by differences in workers' data distributions.
Compared to other algorithms that have this property {{cite:03bb6dd6998c839bdf3fd8be1905900cab4f7776}}, {{cite:a78c99a702a18a1e3392ffa621e6fb1ed38e966c}}, RelaySGD does not require the selection of averaging weights, and its convergence does not depend on the spectral gap of the averaging matrix, but instead on the network diameter.
| i | 2b2c7a01805fa201ec3cbf8df2309361 |
Most of the notations, functions and identities we use in this paper are standard and their definitions can be found in {{cite:5d0b77729ddbd5d18d7e014b5b93dd764387d691}}. We give below the definitions of some other less popular terms and functions which we use in this paper.
| r | e0a4e55622ccfa3bbe44c91387a44b74 |
The LHC has just restarted for its third run in the spring of 2022, and the need for accurate fast simulation at the LHC is ever more urgent. Simulation of calorimeter showers with Geant4{{cite:305b288372a30bc3b8d1b53542b05d98818cc80c}}, {{cite:de983e0e9bb4f3511a419a4c88b00ba0450ae7cd}}, {{cite:77973148287a15d503b1153b2318eee7e5557002}} is already a major computational bottleneck at the LHC, and this is expected to further intensify as the detectors are upgraded and the luminosity is increased{{cite:f0fa235bf96e3e83d5ac9e5f747aa922397b6574}}.
| i | 6e685bcac052869b9bc3a565285d134d |
We find that high-mass Drell-Yan LHC searches into a di-muon final state
provide the most constraining bound
at large values of {{formula:7735a20f-a46b-46d6-ae1b-9233bc944ca8}} , irrespective of the model. The dominant
partonic {{formula:65aa937f-7991-4020-976a-0d4aec1d39ad}}
production processes are shown in Fig. REF ,
where it is
emphasised that one requires a {{formula:357f9832-a8ab-4141-9e54-7f56b1dec75c}} partonic initial state from the LHC
proton pairs {{formula:fff254d0-c837-4746-a6e8-ed8fb57f7e38}} .
The calculated {{formula:12c648e8-2254-4dcc-9a07-bec920011748}} production cross-section is thus dependent upon which
parton distribution function (PDF) set is used, since the {{formula:e977649d-c2bf-4efd-89e0-f15e8c42dcfd}} content of the
proton differs from PDF-set to PDF-set at relatively high values of the ratio of
partonic centre of mass energy to {{formula:2b71c0c0-f419-4be9-b9fc-86b2d5b2dd6a}} centre of mass energyWe observed
some 20{{formula:ba63e32f-7a8d-43ac-b851-cd973e71425e}} differences in the calculated production cross-section when
changing the PDF set used. For the results discussed below, the default
7.2.2 choice of CT14 {{cite:7646e366f1fd874a8d9643ba4ec385bac03d647a}} was used.
| r | f866ba33c2cc4e1531941bc74af8210d |
In AdS spacetime, there exist the Hawking-Page phase transition between AdS-Schwarzschild black holes at high temperature and thermal AdS gas at low temperature {{cite:c25fa91f80e265b39dc84bc188709c7f4cc4427d}}. This phase transition is first order, which can be considered as liquid/solid phase transition. This transition is also possible for non-rotating BTZ black holes {{cite:fca3f4f3898cd8efc85f31d58abf0b0aaad5f20f}}, {{cite:0bcae719d9738d3b4eb4e9783b79a8d6a2a78f10}}. We can analyse this phase transition from our approach. For non-rotating BTZ black holes, the central charge is {{formula:3497dd70-d9b2-41b4-ae42-1899d283305f}} . On the other hand, it is well known that the central charge at infinity is {{formula:a72d6079-15d7-45ae-a078-cf5a4101b203}} {{cite:6324f21211daf6108e65f108aa8fa738eaf5975c}}. Due to the red-shift, we consider the near horizon region as ultra-violet (UV) region and infinity as the infra-red (IR) region. Due to the {{formula:7e6990c9-176e-4944-bfe8-cbe862fda249}} theorem {{cite:70e8bdecf2f867319c6fd5cdf45c197332deb474}}, one should have
{{formula:4c676861-2aab-4bb8-a4a7-3a128ddd5e3e}}
| d | 06d6d4163682de10903e7651deda7d70 |
This paper has experimented with the use of a sequential importance resampling (SIR) particle filter (PF) as a means of dynamically incorporating data into a simple agent-based model of a pedestrian system. The results demonstrate that it is possible to use a particle filter to perform dynamic adjustment of the model. However, they also show that (as expected {{cite:33c95af900b199db95eca0af65be7d6b91e0c864}}, {{cite:23e6f24b7093583bf12dcba0cdf27b6a47889328}}) as the dimensionality of the system increases, the number of particles required to maintain an acceptable approximation error grows exponentially. The reason for this is because, as the dimensionality increases, it becomes less likely that an individual particle will have the `correct combination' of values {{cite:dfd4cbbf13e500f4d08914d2749f55240defdf2f}}. In this work, the dimensionality is proportional to the number of agents. At most 10,000 particles were used, which was sufficient for a simulation with 30-40 agents. However, for a more complex and realistic model containing hundreds or thousands of agents, the number of particles required would most likely number in the millions. The particle filter used in this study was provided with more information than would normally be available. For example, information was supplied as fixed parameters on when each agent entered the simulation, their maximum speeds, and their chosen destinations. Therefore the only information that the particle filter was lacking was the actual locations of the agents and whether they would chose to move left or right to prevents a collision with another agent. It is entirely possible to include these agent-level parameters in the state vector, but this would further increase the size of the state space and hence the number of particles required. This is an important caveat as in a real-world situation it is very unlikely that such detail would be available. Future work should begin to experiment with the number of particles that would be required when observational data that are more akin to those available in the real world are used.
| d | 92f67c5bd1a0f96492a7afb6393e2c23 |
We think that the reason for the imbalanced performance of the supervised learning model could be the training metric and network architecture.
Since the pre-training metric is large-dataset classification accuracy, the late layers are considered specialized to the pre-trained dataset domain{{cite:e96ea87fa414af9bf376e182c199d64c652fd30e}}.
In addition, many of the models based on the image domain network{{cite:06a952a09ceee6cd5f61c0bf57427160b27b32d7}}{{cite:bfbf5589d39075ff46bd1234411b70e2b0bbcfe8}} are not designed to process time-frequency (TF) audio input effectively for audio downstream use.
| i | 7fc221773d1e17e1c7136d35b28e0122 |
In this paper, to address this challenge, we propose a novel, robust maximum entropy algorithm, stable for a large number of moments, surpassing the limit of previous maximum entropy algorithms {{cite:e1e5ec79c70730aaf8c18fb1b64071d980fe1710}}, {{cite:0130782f6eddd7713a09a50a03caa16c24d5caf6}}, {{cite:59d364d660a8e3070968eddd682505abf3146bfb}}. We show that the ability to handle more moment information, which can be calculated cheaply either analytically or with the use of stochastic trace estimation, leads to significantly enhanced performance. We showcase the effectiveness of the proposed algorithm by applying it to log determinant estimation {{cite:4f0e7182d10facf61027fa4d92d26dd0768258a6}}, {{cite:882c9cd75e8765856f0ae5aa2dc33cfc85ee8452}}, {{cite:1fd143338b24e5f3659a93c10480c594a824b301}} and entropy term approximation in the information-theoretic Bayesian optimisation {{cite:007ccce138b796a03b9a485d14f3e4d6a8772538}}, {{cite:9574ee18ee7f8d015bfe8287a0fd61d2a395023a}}, {{cite:9e2901aff5d9430db4f79bff936497bca91cfc05}}. Specifically, we reformulate the log determinant estimation into an eigenvalue spectral estimation problem so that we can estimate the log determinant of a symmetric positive definite matrix via computing the maximum entropy spectral density of its eigenvalues. Similarly, we learn the maximum entropy spectral density for the Gaussian mixture and then approximate the entropy of the Gaussian mixture via the entropy of the maximum entropy spectral density, which provides an analytic upper bound. Furthermore, in developing our algorithm, we establish equivalence between maximum entropy methods and constrained Bayesian variational inference {{cite:715b1a736038f0817dcfa12be7017c472b636441}}.
| i | 565c13d88431ff4eb67b981252d275a7 |
Generating Assistive Information
Additionally, we show {{formula:bf3ce893-2ccf-4d07-8556-31ee50464886}} can be encoded and then used as input for local critics {{formula:d844b3d1-afa5-434b-999a-321b96cec69d}} , as assistive information aiding value factorization. As previous works suggests {{cite:ddc8fbb99b488cd8857ddf4297a916d3155e468b}}, {{cite:28f0a330c7ae6437c36b236f1335574c83b6ab39}}, we consider the information bottleneck method {{cite:36ea96828701bd08dc9f992d8d3c896c5d6eafcb}}, with the Markov chain o-m-{{formula:7d125e55-3f2f-44c2-8795-3875bb26eac6}} during encoding. To be specific, we regard the internal representation of intermediate layer as stochastic encoding {{formula:14f6bc26-daf5-4b76-b603-0b9ad058ab05}} of input source {{formula:738f4213-6eb0-48ea-82ba-7953c982ab7d}} , with the goal to learn an encoding that is maximally informative about the result {{formula:80cfe19f-671c-4740-b894-88d058a7a633}} .
Formally, the objective for each agent {{formula:3f538689-6bde-463c-930a-a39c3207d38a}} can be written as:
{{formula:9ac00c70-a82e-4d43-b781-b0f7ac1fcc83}}
| m | 7b9f44336b9a320d548e369b0c4ce2c6 |
In the second part of this work, we have used this structure to revisit the static response of the Schwarzschild black hole from a symmetry-based perspective. Following Refs. {{cite:e5c85331fcb185535e8e221edf9e7e1e8a5786f7}}, {{cite:e4b43cdfab39e8f70c07db5885f9158d9669f5dc}}, {{cite:571df1b414dff025f09f6d1dd18ad61ec3ea3859}}, we have adopted the test field approximation and consider for simplicity the case of a massless static scalar field on the Schwarzschild black hole. We have derived the infinitesimal generators of the Schrödinger symmetry for this system and shown that one of the {{formula:9c631515-aded-4662-8a11-9a7f115c016c}} transformation, i.e. (REF ), reproduces the horizontal HJPSS symmetry recently presented in Ref. {{cite:adf437d0112a3a9e0b8aea3aa2c12df0fdc19b8d}}. For each multipole, this symmetry leaves the growing branch of the solution invariant. This result clarifies the origin of this HJPSS symmetry and in particular the associated explicit finite transformation at the level of the action (REF ). Moreover, the generality of our set-up shows that this symmetry also holds for more general spherically symmetric backgrounds as well as for massive test fields. Let us point that in the free field representation, this HJPSS symmetry takes an even simpler form as it amounts at the invariance of the field under translation along the trivializing coordinate (REF ).
| d | d9f9e3ce19c4d0ddcf5ad223324b0aa3 |
A noteworthy aspect of conditional gradient algorithms is that they produce solutions which are sparse: each iteration {{formula:5eb630fa-ecb9-4978-a0df-80d32f2a36e9}} of the procedure yields a convex combination of at most {{formula:b3da90c9-41a2-47ac-8530-f206c3760094}} atoms.
This is true of all related algorithms known to the authors.
Sparsity has made conditional gradient algorithms particularly useful in problems such as statistical estimation, signal recovery, and the construction of coresets {{cite:8351da0a2bcf62468ffafc4a32a0d15af46c000f}}, {{cite:8710f8c76804f3c711d9645ff593af742d5a3c79}}, {{cite:d9ec28a814125b3b6aeca0f3c59181b296dba126}}, {{cite:16f7122a204eeec21b7d0d79c758aeba67fefdfc}}, {{cite:a611b8d19d3f9d93c183228d652e628be96d674d}}.
| i | 1abc86ed1ad16d57a3531f1b910f0efe |
The regular method to classify the holistic ECG signal with deep learning is to design a very deep neural network, like {{cite:b14d82ac4cf0ca39a538b7be0927488dda460d78}}. But the length of ECG signal is set using this method because the dimension of input is constant. And the depth of the neural network should increase with the length of ECG signal, which means that this method cannot achieve the classification of the long ECG signals. Thus, the typical recurrent neural network, LSTM, is chosen as the temporal stream to classify the holistic ECG signal. As the result shown in Table REF , the temporal stream can classify micro heartbeat classes. The result is not satisfactory as the stream is designed mainly to extract temporal correlations between heartbeats. And it will have a better performance when more tricks are utilized. Before the late fusion of two streams, the identified stream is pre-trained with the purpose of identification on the MIT-BIH database. Because the global structure remains, the stream also retains the ability to classify individual heartbeats, and the ability to extract identity features is given through pre-training. As the result shown in Table REF , the accuracy is improved when the two streams are fused. It illustrates that the architecture of the two-stream has a good effect on improving ECG classification by comprehensively considering the two influencing factors of ECG signals. And there is no doubt that our architecture has a large room for improvement, as there are several limitations in our model. First is the network chosen in the temporal stream, although LSTM is designed for sequences, it is not suitable when the period of ECG signals is too large (such as 24h). Second, our method is based on single-lead ECG recordings, and it is necessary to introduce a method for multiple-lead ECG recordings.
| d | 32b39ae49cd8bf55ec075387b942f9c2 |
The results on ImageCLEF-DA dataset are reported in Table REF . The CDEM method substantially outperforms the comparison methods on most transfer tasks, and with more rooms for improvement. An interpretation is that the three domains in ImageCLEF-DA are visually dissimilar with each other, and are difficult in each domain with much lower in-domain classification accuracy {{cite:0e1d13ba529caf56be28ded565f8d795c56212ac}}. MEDA and SPL are the representative shallow domain adaptation methods, which both focus on learning domain-invariant features. Moreover, SPL also uses selective target samples for adaptation. Consequently, the better performance of CDEM implies that minimizing cross-domain errors can further reduce the discrepancy across domains and achieve better adaptation.
| r | cc2e4af48a4eb3ae032dcf146d568c34 |
is
called the
transferred population between the first and last sites of the
chain, and we assume that {{formula:6bb07ba1-5a7a-4044-b89f-9c95dbc50859}} , where
{{formula:ac73cd18-d46f-45fa-90d5-e41a6530f021}} , as in Ref. {{cite:a61e62971081a509e1b9acbe6e8e5e9dab81ec85}}. The
pretty good transfer occurs when
{{formula:10ce97fb-e585-417b-b5b2-5a1a4454c3cd}}
| m | cb59fcd0ca68fa5ad1db4551e6f135ca |
Develop a chromatic variant of Forman's discrete Morse theory {{cite:b3d4b7023ca7809b22d9a64b42fd723cf6f2779d}}.
Two concrete questions are the extension of the collapsibility of the Čech complex to the Alpha complex proved in the uncolored case {{cite:fb98aa3efa562b8084fe7b83b6951ac40451bba6}} and the further collapse of {{formula:5167939b-49dc-46b2-b782-3f3974de907c}} to {{formula:891be972-78fa-441e-ad74-47da4642fa61}} .
In many biological questions, the mingling between different populations of cells changes over time; see e.g. the study of cell segregation in early development {{cite:af135ca5ca0c188947c8e24008cb5cd285a9b56f}} and an early topological approach in {{cite:c97a569fdc92f63feaeba46c2c4cac0dd8852e45}}.
It is thus useful extending the vineyard algorithm {{cite:2d5fcfe71bf57291268456016e3029f732cdc4b5}} to the chromatic setting introduced in this paper.
| d | dfca7e26f349213976a97fbb0be2d26d |
One should contrast the above with the Parikh and Wilczek tunnelling method (in standard general relativity) {{cite:ace049ae1776affb07348cfc613f4d4ec132d894}}, which cannot apply for particle production whenever the OMOTS surface is spacelike, because the whole concept of tunnelling only makes sense for a timelike surface, where `inside' and `outside' are well defined concepts (see {{cite:ace049ae1776affb07348cfc613f4d4ec132d894}}: paragraphs just after eqn. (8)). Therefore, the tunnelling picture is only applicable from the moment that the instantaneous Hawking radiation flux is greater than the matter flux and the black hole apparent horizon becomes a timelike surface.
| d | 10915f2bd90eddd3fd9cc31d30cdcfb0 |
Sampling the fine-tuned policy {{formula:10a849b8-6ad6-4e7c-a43c-3ca1d80b096a}} from the Gumbel Softmax distribution allows us to backpropagate from the discrete binary decision samples to the policy network, as the Gumbel Softmax distribution is smooth for {{formula:511cc1ed-2861-49f7-8b1f-f5912985ab90}} and has well-defined gradients with respect to the parameters {{formula:18cec841-7728-432f-a493-22bb494881ec}} . Similar to {{cite:e30512e18ca12643ee26117b25a072a48037a9ec}}, {{cite:24f86a7ad258c5e7c1ad320d9992889c88573351}}, we generate all freezing/fine-tuning policies for all residual blocks at once for the trade-off of efficiency and accuracy. During the forward pass, we sample the fine-tuning policy {{formula:782563a9-b66e-4d6c-8cc8-559fc071b559}} using Eq. (REF ) for the {{formula:dd3dc1ba-c1ca-4724-b3d5-3cb9594aea9d}} -th residual block. As for the backward pass, we approximate the gradients of the discrete samples by computing the gradients of the continuous softmax relaxation in Eq. (REF ).
| m | b5ea8509fcd3ea19824a101532a44283 |
Most recent improvements in imitation learning are based on improving the asymptotic performance of algorithms. In this work we showed a different direction that tackles the problem by directly addressing the mismatch between training and inference without requiring an extra human oracle or adding extra complexity during training. Our method is as simple as upsampling scenes by leveraging any existing simulator and training two models, yet it showed that there is still room for significant improvements without having to deal with human-in-the-loop, training rollouts or impacting the policy inference latency. We also described an important potential connection of our method with density ratio estimation for covariate shift correction {{cite:a331d844ee5b08ed773c72e00f8d1b422aa9fe95}}, which we believe is an exciting future research direction that could provide better theoretical understanding of the improvements seen in our experiments.
| d | d3812ec8556c8064c101c9c3ddee252c |
In the book by Samek et al.{{cite:0cd88b999aacbd8fd28c3cd13cc20fbe9d3b917a}}, the authors present recent trends in the research in explainable AI and some of the directions for future explorations. They have presented a topology for the various explanations methods like meta-explainers, surrogate/sampling-based, occlusion based and propagation-based to name a few. However, with the addition of newer methods and their adaptations to different types of neural networks and datasets, we propose to update the topology based on the domain to which the methods are applied and their inherent design. Comparing recent studies, two major types of explanation methods exist i) Black-box methods and ii) White Box methods. In this review, for both cases, we mainly focus on the explanations of decisions of trained Deep Neural Network (DNN) classifiers. This means that for each sample of the data the methods we review explain the decision of the network. This is why they are called "sample-based" methods{{cite:b7dba980374ecd73db01f9c702728f1412f1a92d}}. In the following, we will briefly explain the "Black box" methods and focus on "White box" methods in image classification tasks.
| m | a5610ed52756624d8e8cc7011a6d49a2 |
In our previous work {{cite:62172815fdee1d19033ac388f1bbd88c514640c0}},
the free parameters {{formula:e78abea7-0ca8-47ab-80fc-5a43a4bf4e10}} in Eq. REF were obtained by a global fitting of the total and differential cross section data of {{formula:76309be3-c783-43a1-9086-ad0d6c04eace}} meson {{cite:f276cbb3e832fc5294501dc41f0505b573a9f51b}}, {{cite:c1e99283b3f1ed63124206b13381be6ff1407db9}}, {{cite:ac98a9b485b8748447a20f2aff1fc4ff29243a79}}, {{cite:baaa2787c5e4dd9d9572db7ce7307a2a93c7e07e}}, {{cite:5a8f536b73a688740d4a0cfe12609986fa8526ab}}, {{cite:71f32c6ae447c81844dfea7dd6b1ff5e05326960}}, {{cite:d303728caf8d627f888b51808372d97f4ffeb496}}, {{cite:507b37e9778759d3640c3b97f4bf312441ea7f7e}}, as shown in Table REF . Meanwhile, the JPAC collaboration gave the free parameters {{formula:a530a802-cdd0-461a-b4db-7f37d5c009e9}} in the effective Pomeron model by fitting the total cross section {{formula:4ea8f222-15ff-40cb-8743-986746dd07de}} data {{cite:f276cbb3e832fc5294501dc41f0505b573a9f51b}}, {{cite:ac98a9b485b8748447a20f2aff1fc4ff29243a79}}, as listed in Table REF . The two models not only explain the {{formula:61a9072b-0716-4bff-ae70-034555667713}} photoproduction process well, but also show good consistency compared with the recent experiment data {{cite:743f1de1bd6e33bf9ed9a252777bf29ecd6d63d6}}, {{cite:f276cbb3e832fc5294501dc41f0505b573a9f51b}}, {{cite:c1e99283b3f1ed63124206b13381be6ff1407db9}}, {{cite:ac98a9b485b8748447a20f2aff1fc4ff29243a79}}, {{cite:baaa2787c5e4dd9d9572db7ce7307a2a93c7e07e}}, {{cite:5a8f536b73a688740d4a0cfe12609986fa8526ab}}, {{cite:71f32c6ae447c81844dfea7dd6b1ff5e05326960}}, {{cite:d303728caf8d627f888b51808372d97f4ffeb496}}, {{cite:507b37e9778759d3640c3b97f4bf312441ea7f7e}}, {{cite:3a764e3107c5e67ff882e11722cdb8c4db4ec8cf}}, which are shown in Figs. REF and REF .
One find that the theoretical results of the predicted {{formula:c977e763-0db1-4df0-a538-29eb69badcde}} photoproduction cross section by the effective Pomeron model are in better agreement with the Hall C data.
{{figure:6c071085-e0f7-4f59-94d6-7fb7c54c712d}}{{figure:0cf6898e-0259-48d1-a7ca-adcea7c79aeb}}{{table:622d866b-a7f7-48c5-b051-ab2c56c591b3}}{{table:f73f5125-cbfd-4c12-a791-05745539ec52}} | d | d1555b452dcb9876b7d081a1dfc2fff0 |
Probably the most interesting outcome of our analysis is the existences of structures mixing complex and paracomplex structures. As we have demonstrated, these mixed structures arise very naturally from (a pair of) pure spinors of a given real index. Such more general structures are only possible when the signature of the metric is not definite, and so it may seem that they are not of interest in Riemannian geometry. However, metrics of split signature {{formula:f0aa80dc-b824-41ba-b7a6-f4b81146e43c}} do appear in the context of generalised geometry {{cite:7c69ae32e53a58ac16cf53ce1d744b49d9402ab9}}. Thus, a generalised complex structure on a manifold {{formula:d9516a87-0aa5-47ee-b1f4-9bf6eac24e19}} of dimension {{formula:40d980ad-6273-4fd4-8131-af05436125f0}} is a complex pure spinor {{formula:9fea2caa-9831-41e9-a69d-55bbf3c407d2}} of {{formula:3180a5d3-62d1-4f0e-89b6-e4a326c9e797}} (which is a complex polyform on {{formula:9ea8f3db-4a77-4559-88c1-be46078e79cf}} ) that has the property {{formula:13f21d84-be7f-4219-bc04-326da2970ffb}} (and thus defines an almost complex structure on {{formula:292b63e6-b59c-432f-9ad1-499dd4c44052}} ), and which has the integrability property that the null eigenspaces of the complex structure defined by {{formula:b714e277-a82b-4d89-b810-5c2f8a1d8753}} are closed under the Courant bracket. The integrability condition can be shown to be equivalent to the condition that the polyform {{formula:e5d81a8b-45e7-4bd5-8dfb-27109ad59746}} is closed on {{formula:f7fb664a-7b13-4e37-be92-7a65c22fe0b1}} , see {{cite:7c69ae32e53a58ac16cf53ce1d744b49d9402ab9}}. Given that there are several different types of pure spinors of {{formula:6bb85947-6765-4865-abd7-7833e7ccad05}} (with different real index), with a pair of complementary pure spinors {{formula:40c705d5-cad8-4846-9ce3-deea71f2895d}} defining in general a structure of a mixed type on {{formula:5443d019-27e4-465b-a071-c084d58f42e2}} , it would be interesting to study the arising more general types of geometric structures on {{formula:436b1594-b713-4961-b89e-6bda79a984a5}} , thus further generalising the generalised geometry of {{cite:7c69ae32e53a58ac16cf53ce1d744b49d9402ab9}}.
| d | 0a48692464a7613a128acbaf1bef594c |
Another area for future research is the inclusion of positional information in the GAN models. Currently, our models treat the generation task in a `bag-of-patches' fashion, i.e. ignoring the potentially important spatial context for each patch. By including positional information such as in {{cite:3486eed0eb521cc48aef706d6664165ab62b5fb4}}, {{cite:71cd287c746537c2ca2a17b480c2fda8eac113e4}}, the models could be trained to learn the distribution of healthy tissue appearance at each position within the lung, utilising the prior information to help training. However, these methods would need a greater amount of training data, and would take longer to train.
| d | dcc8ada913685b93eb958da7ea8adf81 |
In this work, we have considered the complete scattering amplitude of all the channels instead of only logarithmic terms of the {{formula:106af128-46f3-4c49-8916-ec75e59e4dce}} -channel.
And all the thermal masses are included in our numerical calculations.
The contribution of massive Higgs boson is also taken into account.
Using Monte-Carlo algorithm, we have numerically calculated more precise collision term and
hence obtained more reliable bubble wall velocity in the representative effective model.
After considering more rigorous scattering processes and the corresponding collision terms,
our bubble wall velocity is smaller than the previous result under the leading-log approximation.
It could help us to improve the prediction on the baryogenesis and the gravitational wave spectra.
Based on the recent studies {{cite:203c86c6952acca5aaa98d57041581d04ee89cfd}}, {{cite:1fa162a505547799167df97f0f596e86144e0c06}}, {{cite:8a627c8e2e87f77cb3edf52b7d31cb300f9a5ab6}}, {{cite:73e655a1491f140ec6f75092dd6eb4fc2a07709c}}, more precise calculations
including the resummation over the large logarithmic terms {{cite:09f7a1c1efdacacda7eb929b499a00809679f8c3}}
are left for our future study.
| d | 84048406598f0118075a1bc7ee9d2ead |
The data we presented seem to support the claim {{cite:bb9fc5c110112d2460ef8d2551227b68e41df78b}} that the mass ejection in this object occurs
in two different ways: a somewhat ubiquitous and steady mass ejection,
with chemical properties of O-rich objects (SiO, SO, SO{{formula:6390332d-3e0c-426c-ac55-7170e279eb6f}} ) and
fast collimated outflows taking place at random directions in which
the sulfur is mainly constrained into H{{formula:7f7dc8dc-c432-45d3-86d2-9c66599f5b6f}} S. The SO and SO{{formula:a632c74c-f7fd-47db-9927-b1ae7b6c86c4}} emission would
trace swept-up material with high density.
The former ejections are likely due to convective cells, which
would generate an irregular and extended atmosphere of circumstellar
gas where most of the sulfur would be in the form of SO and SO{{formula:cb545da9-ba9f-454c-a3f6-e1f011024b9b}} ,
while another process, probably of magnetic origin, would generate
fast outflows of gas and dust, which, when colliding with the
surrounding material, would form H{{formula:060a4a9f-480a-42a1-a6c1-a0bf656ff98c}} S by shocks or evaporate
H{{formula:9e49e717-d6d7-4860-9272-18e809e76f9a}} S from dust {{cite:6a0dacd73b32507669c1b499f2bd593ed6425947}}.
| d | d9293567487b2e03a05c399e9cbd7994 |
For this ePFA workflow development, we use an unsupervised ML algorithm called NMF{{formula:ba6a6afb-2f59-43a1-a511-2c12b96a62a4}} {{cite:7c6419d3af8aeb2379aa981c5086a82280810106}}, {{cite:15207c4758e1e4607a5da5fd0c99b81a10683f76}} to discover hidden patterns in geothermal datasets.
The NMF{{formula:a99b8ea7-44cc-40c4-a313-49f440bfdebe}} is a machine learning method that combines non-negative matrix factorization (NMF) with customized {{formula:4488e4a8-78d4-4e7b-852a-5804722fb76f}} -means clustering.
NMF learns a parts-based representation {{cite:b33a5293acf76b85fcbfe0533b720bbc74c59f9f}}, {{cite:16cf3f02eee205b63d680d0896412baf1e1b5c4b}} of the analyzed geothermal data matrix.
The {{formula:2279f127-b1bf-4caf-8ad9-dbf553828d71}} -means clustering groups similar NMF learned pieces together and discovers unique underlying patterns {{cite:ebbe3bfdd06eecf4ab2a6530f0363793f8fa43ff}}.
Customization of the {{formula:fa2a196e-2534-4b5d-800d-05601768727f}} -means clustering provides insights on the similarity of learned parts within a given cluster compared to other identified groups {{cite:e648c4e1a53cc26f813210e4e6948eb42668b32e}}, {{cite:deaa6287d2d57d464dc3ace98fb9c920c154157e}}.
This study builds a data matrix, {{formula:b5372b04-a490-45bd-aefa-0f5d712144f3}} of size ({{formula:31859fd4-d3dc-44da-8f08-e12fcdf91906}} , {{formula:e12a0352-1e5a-4e39-b1f2-ee16ae2528df}} ), after curating the raw geothermal datasets.
This geothermal data matrix is developed by combining geophysical, geological, hydrological, and thermal data sources.
For instance, the DOE's Geothermal Data Repository (https://gdr.openei.org/) provides a venue to download such datasets for ML analysis.
The preprocessor normalizes the raw data such that the elements of {{formula:349c3fb8-0341-49f7-99bd-08f3d39d1fec}} are non-negative.
If needed, it also log transforms individual attributes to reduce the effects of outliers and nonnormal distributions.
Here, {{formula:1b505414-cef7-427b-9b9d-1d2529b68ad0}} is the number of geothermal data attributes, and {{formula:a8f3054b-4311-4241-b629-6c97f3937986}} is the number of spatial locations of geothermal measurements.
The NMF{{formula:8d158b85-bb5e-4a8a-bb57-222a53b00e7a}} is part of SmartTensors AI Platform and can be found at https://github.com/SmartTensors.
| m | 00c555b2d5d6b02fff25ebc1c01a5a35 |
Table 1 shows a comparison of performance between our work against CP-VTON {{cite:26284f4346e416d72c6e13527526490232dae0b6}}, SwapNet {{cite:176a1bb9ca50c7a7164e64ebffce510a2b8e6173}} and SieveNet {{cite:6433d6850a3d2e6609e87b4403f0deca1ae16beb}} on image quality metrics benchmark, IS {{cite:aeef5ec81a25c98d79215b345a37341ca9db4998}} for image quality, SSIM {{cite:9f2871c3ef642aef52f1ba5a47988e86945d14bb}} and MS-SSIM {{cite:eda3c6d85faf434591af9f7a89d1d23283aff1c7}} for pair-wise structural similarity. Although whether those benchmarks could define the quality of an image generated remains in debates, and some previous works like {{cite:32155a22ca2b56feab0a3512f73a21204019c175}}and{{cite:f86f9f8c3157d7ef13b02bd194c6dd37913ffd93}} are based on cloth image warpping, we show improvements on those benchmarks, and for the inception score (IS) our results are closer to the dataset. Also, our framework takes an amortised time of 6 seconds to process 100 different cloth transfer requests, which features low latency for large scale industry use.
| r | 9e7107d1aa373ee0f114288ed2262e4e |
The results of this paper indicate the way to observe the Aharonov-Bohm effect for the system confined by the external
potential in phosphorene. For circular quantum rings the Aharonov-Bohm oscillations
can only be observed in the excited part of the spectrum since in the degenerate ground state the electron density forms separated islands
and the persistent current circulation is interrupted. For an elliptical deformation of the confinement potential,
the oscillations of the ground-state parity appear with the Aharonov-Bohm periodicity.
The amplitude of these oscillations has been determined (see {{formula:0a51a1b2-6699-45ba-bf4a-0949139e3d6a}} in Table II).
Based on results of Ref. {{cite:fbc8b31807afb1dbfe190d05e647028b52bf3821}} one can expect that for {{formula:ca7c3900-d214-4b6a-9020-0949ad013a0d}} the ground-state oscillation should enter the experimental resolution.
| d | c042d7e7792e15ac2d2f23e2f0ff6264 |
Let {{formula:ca2b1b5b-5588-483d-b6d6-4ea6840705c9}} be a numerical semigroup. Since {{formula:dac05655-3cde-46fc-8fb1-1f355a4e5d81}} is finite, there exists the greatest integer not in {{formula:591ce05d-acf0-4119-a097-232b5c4ad4db}} which is called the Frobenius number of {{formula:db75873d-2c4d-4846-9ce5-1a7a203b94fb}} , denoted {{formula:3072c758-a036-47dd-8c3d-59e65d47c72d}} . The so-called Frobenius problem deals with finding a closed formula for {{formula:0a8b2e38-e0fd-4226-8bef-6416b5ad28a0}} in terms of the minimal systems of generators of {{formula:4a6819e1-8b2e-4b83-83c3-afb13e5c4cbe}} , if possible (see, e.g. {{cite:d368b64cba70395abb3a15fb65b86410ddaf0e6e}}).
| i | d61de8a3faf13781e27c309705ec3269 |
The classical mirror symmetry summarized in Section applies to the so-called (families of) lattice polarized K3 surfaces replacing the Kähler cone with the ample cones {{cite:390fbdc020f7e838c4b182fe56e048f48af68c6c}}. In our case here, we consider a primitive lattice embedding {{formula:f8cfa69c-ce8c-4c18-a1cd-d8282a4493a6}} with a fixed decomposition {{formula:2d6f5f9a-c7b7-4898-af51-2a433cbc2251}} . Then {{formula:926a3f69-783f-4eeb-945a-c2e27f17975a}} is a member of the {{formula:54a4001b-011d-4749-915c-c844d6d801a0}} -polarized K3 surfaces, while the mirror {{formula:09a37d27-64c6-4049-83b7-c6fc6d040ac4}} is a member of {{formula:90930984-93dd-4d53-9afe-701b63d95813}} -polarized K3 surfaces (whose transcendental lattice is {{formula:4d34b4ec-ff6d-432e-a734-ea95d1307ced}} ). The classical mirror symmetry in this case may be summarized in the following isomorphism:
{{formula:32d3f026-c6c3-46b8-b56b-f26b630ab604}}
| d | fead537a2f93cb2736b2998bfd3c4be4 |
The PhaseCut method {{cite:9d42da6e3fda6a567fb1def847939d68ca067846}} is based on the following minimization formulation for the the input modulus {{formula:d74e31d0-1bf9-4800-b77e-6b3e8ff064b1}} , unknown image {{formula:3c716542-ad31-4de2-acb7-a02b89e62b37}} with unknown phase {{formula:4e68d8e7-6c27-4ada-b7f2-d63273eb14ae}}
{{formula:d056fcba-5095-433b-a00b-86a7847fe2f2}}
| m | 7d35bea189950e52563e6956a204a7c3 |
Proposed-full-CSI: The channels are estimated using the proposed DFT-OMP-based
algorithm in Algorithm REF in the first coherence
block.
Proposed-gains: When the angle information estimated in the first
coherence block is fixed, the channels are determined by only estimating
the cascaded channel gains via the LS method in (REF ).
Oracle-LS: The angle information is perfectly known at the BS, and
the cascaded channel gains are estimated by (REF ). This
algorithm can be regarded as the performance upper bound.
LS {{cite:bd6589b0c8b5f955d5da90235524faa375c803d0}}: The channels are estimated using the LS estimator
(REF ) with the optimal training phase shift matrix drawn from
a DFT matrix.
Conventional-OMP {{cite:e9ae26dea6844ca881e6464485bd1b304de7bbc7}}: After approximating the cascaded
channel using the VAD representations in (REF ), a sparse signal
reconstruction problem is constructed by vectorizing the measurement
matrix. Then, the cascaded channels are estimated directly using OMP.
DS-OMP {{cite:f2fd3770fd409d8a52ba024266a8025ff30feab6}}: The double-sparse structure of the angular
domain sparse cascaded channel matrix {{formula:b8fcdc9a-fa8b-4d36-bb74-8f983034d501}} in (REF )
is exploited. The cascaded channels are estimated using OMP for each
non-zero row of {{formula:8166e5d4-7e09-48d2-8d18-a1c792eecd96}} .
| r | f93c8cd160f607d43a5cc3ccb02cdae8 |
{{cite:eefc1323ca054b314d5672b36c22195d16a4f998}} proposed a new recipe for quickly using crowdsourcing
to generate new compositional semantic parsing datasets
consisting of question-logical form pairs.
Using this recipe,
they created eight new datasets in small domains consisting of 12602 total
question-answer pairs,
and achieved an average accuracy on across datasets of 58.8%
| r | ea6223da318f57f020dc31b92b267271 |
We then used the generalized Lomb-Scargle
Peridogram {{cite:091a0bef78c560e4a0307fcead7b2d9b40303b2d}}, {{cite:b7743ba8245c67bd704fe00186bcd5bb4216e3cc}}, {{cite:6fc816cbae958444c5f3022c07bd35da0be0cfad}}
as an independent check for the result from the WWZ method.
The LSP method is a common tool in time series analysis for unequally
spaced
data, and can provide accurate frequencies and power spectral
intensities {{cite:6fc816cbae958444c5f3022c07bd35da0be0cfad}}. Only the light curve in Segment I was
analyzed. The resulting power spectrum is shown as the red histogram in
Figure REF . A sharp peak around 176 days, nearly the same as that
from the WWZ method, was revealed. The results confirm the signal detection
from the WWZ method.
| r | 17aae0167fec108d8e92639cf713f1e2 |
DeepGlobe Land Use Classification Dataset: Table REF shows a quantitative comparison of our method with the baseline for the DeepGlobe Land Cover Classification Dataset {{cite:6408150b45b7a2041eb9975a66db6356154e23c7}}. We report significant performance improvements over the baseline using both entropy and margin sampling strategies. We report a maximum mIoU improvement of close to 27% with as little as 2% labeled data, a maximum improvement of about 6% over the baseline when training with 5% labeled data, and an improvement of approximately 8% with 12.5% labeled data across the two active learning strategies. Figure REF shows some visualizations from the DeepGlobe Dataset where it is seen that our method results in fewer false positives than the baseline.
{{table:9082c418-8ed9-4887-a89d-8318f44c39d5}} | r | e30bb58d8a1056f28199f3cff54a29a7 |
Recent work has shown that policy gradient methods and Q-learning methods are
connected via maximum entropy RL
{{cite:67557aebd8e3430a2f21298387686a6032b89a29}}, {{cite:3b79229a70e9db8c27f1dc9547ca8b84939679f1}}, {{cite:fdef0e1b27ef47cc019f41d03f6aba52e1777bfa}}, {{cite:14351822bc56c6b5a50427b2c08035cf83033c71}}.
One such perspective is from
the soft policy iteration framework for batch-mode reinforcement learning
{{cite:17f519d9e39bc1d32436e24709c691f45a35b1fd}},
where at the {{formula:ece72a42-4757-43b4-ae40-ef3ec600a3f4}} -th batch iteration
the updated policy is obtained by minimizing the average KL-divergence
between the parametric policy class {{formula:4aa1164e-75e6-4240-822f-04af9f7910aa}} and a target policy {{formula:41a958ab-b85f-419c-8a74-4482f4cd530b}} .
Below is the soft policy iteration update,
where the subscript {{formula:9d8cb3e4-94d5-4f88-b371-1084bb5da7fc}} refers to the batch iteration:
{{formula:89d46d0b-7019-44c9-8a4d-64674b2decbf}}
| m | 0e2339cfb6add1db5e2657a89bdaa7c8 |
Then for any {{formula:79fb7c67-8442-4f79-86ae-4afd2f980e00}} , the following classical result holds (Theorem 1.5.3 in {{cite:64714a3ec49cd75aa8fb34789c6a6b2be36c1ef9}})
{{formula:f3f5b969-cedc-4ab6-9e1f-9a2d680c75bc}}
| i | 2eb820410a0e9a7142f9b26e4566cf3a |
(i)
Empirical test spaces are closely related to {{formula:5c69f489-e698-4827-9536-f2d0502ca31b}} -embeddings, which have been recently proposed for MOR applications by Balabanov and Nouy in {{cite:3096db8d0032f99f5527db91946479e5d36f8f54}}. In section REF ,
we formally link empirical test spaces for dual norm calculations to {{formula:fa890aa7-1a48-41aa-ba44-c2595311080b}} -embeddings, and we discuss the differences in their practical constructions.
Furthermore, in section REF , we present an a priori error bound that motivates our construction.
(ii)
The problem of sparse representation — or equivalently best subset selection —
has been widely studied in the optimization, statistics and signal processing literature, and several solution strategies are available,
including {{formula:c5a306f3-6577-44b8-9569-5a25021e660d}} relaxation {{cite:e5efc65a37d907e78727c76b218e76854646b6d4}},
Greedy algorithms {{cite:e16e3d71d757d1c6d1380214ef64f3d1be5356c2}},
and more recently mixed integer optimization procedures {{cite:5077ea8700e3d95c20bc930430316784a7f12d8e}}.
In this work, we show that the problem of EQ can be recast as a sparse representation problem, and we consider three different approaches based on {{formula:bd187e87-316f-4035-bd68-d163124af964}} minimization (here referred to as {{formula:1b8789b0-859e-4a26-9e88-89fd4587f368}} -EQ), on the EIM greedy algorithm (EIM-EQ), and
on Mixed Integer Optimization (MIO-EQ), respectively.
We remark that {{formula:4bdca2bc-e4cb-423d-85a8-94fe132baf6e}} -EQ has been first proposed in {{cite:1bd488fe11dd8531ae3a613234eb68927d7e5d40}} for empirical quadrature, while EIM-EQ has been first proposed in {{cite:8c1001afe522108dc8b6d31933a5c2d56d470d02}}; on the other hand,
MIO-EQ is new in this context.
In order to reduce the cost associated with the construction of the quadrature rule, we further propose a divide-and-conquer strategy to reduce the dimension of the optimization problem to be solved offline.
(iii)
To our knowledge, a detailed comparison of ATI approaches and EQ approaches for hyper-reduction is currently missing in the literature. In sections and
we
present numerical and also theoretical
results that offer insights about the potential benefits and drawbacks of ATI and EQ techniques, in the context of dual norm prediction.
| i | 7022a535c3b9a3f531cf6f30d3c6ae02 |
in agreement with the standard result {{cite:89a40be35405b882ddf5495008b9ae25b00d9cc0}}, {{cite:6bbff6b6b8d4a595422fdc517f70bb44d3f9ea36}}, {{cite:235343349931ad80205fcf0ef8e11de257cf219f}}. The radius {{formula:192c4b4f-a044-48ca-b83b-dbd6628c2179}} (REF ) is given by
{{formula:d3ec0f54-057d-4269-9126-2ce5fcc8a3c3}}
| d | 2498de2456d67834e31493f430b25da8 |
Downstream Evaluation. We pretrain our model with Mid fusion using MEP and CPP tasks (with CANS-Similar), and employ Part weight sharing. We use either Kinetics-700 or AudioSet for fair comparisons with prior work. Table REF (a)/(b) shows short-video/audio classification results on UCF-101/ESC-50. For fair comparisons to the baselines, we use only the visual/audio CNN (no Transformers); we finetune a linear classifier on top of the visual CNN end-to-end for UCF-101, and train a multi-class one-vs-all linear SVM on top of the fixed audio CNN for ESC-50. Although our model is pretrained on long video clips with no direct supervision to the CNN layers (gradients must flow through Transformers), it outperforms most of the baselines (except for AVTS on UCF-101) that received direct supervision from short video clips. We note that, similar to ours, CBT {{cite:6acdd56036f7c1a5f58b4bb06eeee600f10ed337}} is a multimodal Transformer pretrained on long video clips and thus is the most meaningful comparison to ours; ours outperform CBT on UCF-101 by 5.7%. For sound classification, our approach outperform all existing published results.
| r | 9415a703ff5b0978d63234561c03522a |
In the previous sections, we have shown the advantages of our proposal in quantum communication applications. In this section, we demonstrate that the proposed scheme can also be adopted for quantum computing applications. In quantum computing applications, the quantum information is usually protected with the aid of noise-free auxiliary qubits, which may also take form of pre-shared entanglement {{cite:99de6c4f1d30dd768763157dba8ea6abe919f8a0}}, {{cite:67bf8c5b7b4f8b978b0e4bb29419f578ab09c49f}}, {{cite:8d186ad866e16748e95adfee74e6a2fc1435660a}}, {{cite:58467433fff55d324d813ea4cb1228ad4a1f8ccd}}, {{cite:6b2c8c4559b19b89a269c4f5b91fff20cc04bc87}}, {{cite:0609d5447c9468e17d11341a2a60f58a967ff954}}. A prime example is constituted by the family of entanglement-assisted quantum stabilizer codes (EA-QSCs). Compared to the conventional QSCs, which are unassisted by noise-free pre-shared entanglement, EA-QSCs offer an error-correction capability improvement. This is reminiscent of having an additional error-free side channel between the transmitter and the receiver in the classical domain. The argument that we can always have noise-free pre-shared entanglement relies on the assumption that EPR pairs can be created abundantly and quantum entanglement distillation can be applied to them. The concept of EA-QSCs is favourable in the realms of quantum computation, since the EA-QSCs can be readily amalgamated both with transversal implementation of quantum gates {{cite:13824aba38fc462a21c0f13fec078b545896e542}}, {{cite:5b265d6e73b71e986e214cb0001530e0add2891d}} as well as with magic state distillation {{cite:27f19d3605659da4e9d954ecb7b9c45e740f3919}} for creating a universal set of fault-tolerant quantum gates. In the following, we propose an error-correction scheme that outperforms the state-of-the-art EA-QSC.
| d | 5125fefc13ced273c492373883f8baa4 |
One primary challenge faced by multi-aperture microscope designs is data management. In this work, we utilized a single FPGA to aggregate Mobile Industry Processor Interface (MIPI) data directly from all sensors, which led to several key benefits. First, the single FPGA allowed us to directly synchronize video capture across all 54 cameras within the array, leading to the ability to record gigapixel-scale video data without motion artifacts. Second, we were able to achieve a maximum data transmission rate of approximately 5 GB/sec, which corresponds to approximately 7 frames per second video (8 bits/pixel) with our 54-camera arrangement. It is possible to crop the sensors or reduce the camera count to increase the frame rate; for example, a 3072{{formula:ea0b7e2d-f0d2-4d79-831c-2b04cf4437c4}} 3072 square crop yields {{formula:96832619-1070-4f63-adf0-75013f96568b}} 10 frames per second. Transfer at such high data rates must account for limitations both in transmission links and in drive write speeds. In our prototype, we utilized a PCIe connection between the computer and the MCAM and stored data on pre-allocated RAM space before moving to a solid-state drive, which enabled approximately 249 seconds of video capture at full resolution. As solid-state storage volumes and write speeds continue to improve, we anticipate the ability to increase data transmission rates, and thus imaging frame rates, using the current array. We also anticipate that improved data transmission will open the door to novel MCAM designs that offer even larger full-frame sizes. Compression methods are likewise available to dramatically reduce video sizes in a lossless manner, for example {{cite:ede736213f464b4c737c47f2015dd947defd30ae}}, {{cite:4e1658c34daf08d62b1bcb95e6c10aa42324b1fa}}, {{cite:22e5502a3b72ad57090018a7004d5aa41a5c05e8}}, and we see the FPGA as a key means to pre-process image data for additional future speed-up.
| d | 34c606898601b145669b9a8cc8efa9b9 |
This result has significant implications for the ground state properties of {{formula:c3d0d4a2-dddb-4b63-a8c0-e25957de1041}} . For positive {{formula:a905dc61-46d4-4a42-a336-f6f675b633c4}} , in balanced bi-partite lattices where {{formula:7ee12ec3-3354-4414-ba36-f49486ba15f4}} (examples include any hypercubic lattice) the electron spins on sites in identical sublattices tend to align whilst those in separate sublattices misalign, creating an antiferromagnetic state with {{formula:701b3220-e35a-4f57-a190-69ab3f216eb7}} . The distance dependence of these correlations varies with the lattice dimension; along any spin-axis the correlations in a 1D chain are known to decay algebraically with distance {{cite:e31ce5437d6425759334f80c487a19a612ffb7b7}}, {{cite:6f47cd4c9cf93e60773fca56edc62cda597e124b}} whilst in a 2D square lattice the correlations along the {{formula:84c9c955-d41e-4bf3-bcb6-25d77602ee53}} spin-axis are oscillatory and long-range {{cite:4c179d8bff09a05cf3ffa154aa13d1f6bd3cd520}}, {{cite:bc1c5d35253dd8c07aa87a1b06eb4a68dc8abb90}}.
| r | 85490aaa498616cf3e8765964ff92c2e |
We also examined the case where moiré exciton condensates with two spin species coexist.
The condensate mixture with two spin species can be described by a spinor GPE,
with the inter-species exciton-exciton interaction weaker than intra-species one {{cite:0faab0e24658c9b14ec1caa5e0c804f3a341841c}}. We numerically find that the nonlinear dispersion is further
splitted, and the detailed structure is much more complicated.
Nevertheless, we have
checked that those splitted states due to inter-species interaction has similar
feature in terms of wave function symmetry. In addition,
when spin-up exciton condensate is dragged in momentum space from {{formula:2b6dc168-c7e2-44c7-b447-16017bc57420}} to {{formula:77b7c18c-c6fa-4e9b-8193-7b8bcfa7139a}} , spin-down exciton condensate will be dragged from
{{formula:4245cd23-abe4-410c-8554-a71b8c2186ba}} to {{formula:deec6b9f-0a81-423b-a9a2-241a20fcbd5b}} accordingly, which remains dark during the whole process.
So our prediction above on optical selection rules and
path dependent light polarization remains largely intact.
| d | c7405f125b08dd64fd67f104ca910710 |
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