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We now discuss the implication of our theoretical results. As noted
in the introduction, in La{{formula:03a80b63-441e-4747-b46d-9aa9a9d54810}} Nd{{formula:56a7df75-431e-4a57-8066-4a8930e8f1d9}} Sr{{formula:927e2ac5-84f5-474e-a6a3-40b5e2167780}} CuO{{formula:87d80e1f-2c4e-4e0a-8dbb-a241ae02a7f4}}
system, ARPES experiment has found that there is little or no
low-energy spectral weight near the nodal region, {{cite:d917f51afd02689469623fda002c658775330018}} and
optical conductivity experiment has observed a finite frequency peak
with almost the disappearance of the Drude mode, indicating an
"insulating" stripe state. {{cite:8b13a884d0bd8116f453a3e4e7568687d3c01a07}}, {{cite:f78b63383d3114f09d850b6424858de826844743}} These spectroscopic
features can be reproduced here with a strong spin domain-derived
scattering potential {{formula:6586d9f7-fa2b-46ba-9234-cae2c4b14b35}} and a weak charge domain-derived
potential {{formula:eebb4535-25e3-4824-beaf-b3dc628add1d}} and {{formula:fe109b3a-9214-4e42-a9c1-08ee3979021d}} , as shown in Figs. 3(a), 3(c),
4(a) and 4(c). Interestingly, in this parameter regime for the spin
and charge domain-derived scattering, the SC order is destroyed as
can be seen from Fig. 2(b). This is in consistent with the
experimental fact that La{{formula:ea70eaee-79a7-4816-8fe9-a0037b75d955}} Nd{{formula:ed7af582-0b5b-472c-bf64-9f008ef95044}} Sr{{formula:710c15d7-7802-4834-8cdb-dcaf89c6c123}} CuO{{formula:6f1db0ab-1cea-4897-8ff7-1dc9588edb58}}
is nonsuperconducting. In another cuprate
La{{formula:9b83ac28-1b40-492b-be25-7d3634f07075}} Ba{{formula:0725b103-dc9f-462a-a505-633c2f0a1e84}} CuO{{formula:741b9e04-cf41-4498-b515-f9c6b44ace43}} , ARPES spectra have identified the
existence of high spectral intensity around the nodal
region, {{cite:e41e281cf621d4195cd9fd23c2bf225c4640a077}} and the optical conductivity measurement has
observed a residual Drude peak without the finite frequency
peak, {{cite:5d925d8614a4703f677dbde0d38beadeb92275d7}} pointing to a so-called nodal metal
state. {{cite:81c36bb02c6d29a977cb7f82ddb88dfddec9b1e7}}, {{cite:9b9df152e972be3637b6c918c5e44427e59553ba}}, {{cite:c408e1f4e324cc85f827cbbdd1e24c5289c79430}}, {{cite:c9aaac478803cfb930834250616c25722a275037}}, {{cite:910c22c41608432eef0da5312a3bd4f764cebdf9}}, {{cite:5d925d8614a4703f677dbde0d38beadeb92275d7}} When comparable
spin and charge domain-derived scattering potentials are assumed
such as {{formula:2a5a5e8b-d204-4250-9c9c-9ac1e5978749}} and {{formula:f73658e2-875a-4362-8569-f33c47dab700}} , we can reproduce these
features consistently, as shown in Figs. 3(d) and 4(d). On the other
hand, a weak superconductivity emerges in the otherwise
nonsuperconducting regime (when only spin scattering potential
{{formula:f07a5a69-0613-4dd7-8069-8e0c7c647301}} is considered) with the increase of the charge
domain-derived scattering potential[see Fig. 2(b)]. This suggests
that the weak superconductivity in La{{formula:9f0ba56b-fc3f-4b78-a52b-387963b0ec3b}} Ba{{formula:fe4fe2dd-430b-4a06-a08f-e06cf7a1d18c}} CuO{{formula:156ca780-f26b-449e-975c-5550327c25e4}}
is likely beneficial from the metallic behaviors of the stripe state
originated from a sufficient charge domain-derived scattering. The
above mentioned consistent accounting for both divergent
spectroscopic features observed in two families of high-{{formula:d5529f2f-e083-492b-afc6-422dcdf19071}}
cuprates indicates that the stripe state may be intrinsically
"insulating" or "metallic", depending on the relative strength of
the spin and charge domain-derived scattering potentials.
Specifically, a large spin domain-derived scattering potential
favors the "insulating" state, while a large charge domain-derived
scattering potential the "metallic" state.
| d | 477c895582d8f0a893a0783fea038cfe |
In this section, we detail our method, {{formula:18e818ed-27a5-41a6-b650-a53d47e3302a}} , which is summarised in Figure REF . It consists of two primary components: (1) inspired by RCAN {{cite:94992bc3c7a035ad21c467fb136b9e3a64aee1e0}}, we train a Sim2Seg model that translate randomized RGB images from simulation into a shared {{formula:161bbbc0-5e9d-4783-a384-52e508e1a7cc}} form, which we define as a semantic segmentation map. (2) We then train a goal-reaching policy within this canonical representation to navigate in off-terrain environments. During inference, we use a frozen pretrained Sim2Seg model to perform zero-shot transfer on real-world images.
| m | 5dc02040db1c3dfc4a0fb7aed9d7d3ab |
As an additional baseline, we implement a fixed-topology CPPN with two hidden layers and sinusoidal activation functions and optimize its weights. Fixed-topology networks with sinusoidal activations are capable of capturing fine-grained detail over continuous spaces {{cite:de6cc8910e29815dcb17dee703dbe6bb83c8ae7d}}. Having a fixed topology allows us to naturally make use of CMA-ME to train the CPPN's weights.
| m | 8fb2fb02c4e7b36901c6c243123194b5 |
3D multi-view consistency. Theoretically, our method is not 3D aware. Nonetheless, for the purposes of portrait reenactment this is not essential for achieving consistent results in various head poses. Given that training videos are captured by stationary cameras, they provide access to a single view of the scene. This makes 3D NeRF-based methods an over-parametrisation for such data, which end up violating 3D consistency for upper torso and producing severe shoulder trembling {{cite:fdfaeb457e936ad1a8fbd3d788a12c8850b32a53}}. We argue that 3D modeling would require a video portrait captured by a moving camera from multiple viewpoints, as demonstrated most recently by RingNeRF {{cite:d1d2d2e34565ac86a0b2091616fe68a8c368dcd2}}. For videos captured by stationary cameras, our 2D model is able to generate frames with consistent appearance in diverse head poses and surpass 3D NeRF-based methods {{cite:fdfaeb457e936ad1a8fbd3d788a12c8850b32a53}}, {{cite:2c13724b33270e2bbd99eed9fbc638114424d3a9}} in visual quality and inference speed.
| d | b7ef40a401851cb722ac559cd29383e6 |
From the opposite sign in the bracket of Eq. (REF ), it can be seen that these three equations are mutually restrained. We can directly get the adversarial properties:
Training {{formula:63919007-d556-4f5e-a605-23bd05868ae5}} to minimize {{formula:bfe54f9e-4bec-4d85-b632-a532bb77683d}} (the domain loss) means {{formula:aa8a28b5-8dd2-4271-b464-01d77a23d91e}} cannot identify which domain the data comes from;
In the same way, minimizing {{formula:991dec9e-ddde-402e-8a79-76704a0626aa}} by training {{formula:ecf423bb-c1c5-40f3-bbfb-7b016f977c19}} is to predict the labels with high accuracy.
But it should be reminded that both {{formula:60dfb17e-07f7-46fd-a9e0-73857bebddc5}} and {{formula:d2588a21-b4a5-4640-af27-cfba1c59c8f6}} depend on the parameters of the feature extractor {{formula:7d322043-b8a3-4afa-be33-09e1f8414218}} ,
and {{formula:e793d9bd-ce1a-4542-b3f5-63f87218572d}} is determined by optimizing (minimizing) {{formula:9b92b18e-f00e-4298-85ca-67232633c6c8}} as an adversarial process. For a detailed explanation, please refer to {{cite:5d8cc5fe62d83d1d9e1bb8397226be0577104bbd}}, {{cite:d95532e280ba8f05bc27809b3e52a6b7b99d0660}}, {{cite:376836ef452ba18f8f15d95a3384ff75032f2e4f}}.
| m | 28370744dbd5894a7b771dd2b42cf027 |
We now numerically assess the proposed algorithm on two different models, namely (i) a linear Gaussian state-space model (for which the filter and joint-smoothing distribution flows are available in a closed form) and (ii) a stochastic volatility model proposed in {{cite:2db6c73bda314c247ae670941f22b5a11cdc1d86}}.
| r | 0e5a3e8fa64939e28443f6ff39806e73 |
For the cosmological analysis we use the CMB temperature (TT), polarization (EE,TE) and lensing angular power spectra from Planck 2018 release {{cite:42ef1a2679bd4096b700689457394354434bf6ba}} and the likelihood codes corresponding to different multipole ranges {{cite:958a148ab76517712fe83693658a3c3f154553f3}}http://pla.esac.esa.int/pla/cosmology.
The Planck data currently provide the best characterisation of the primordial density perturbations {{cite:f91949d436111cfe307dcda798af1c2dfad0300b}}, constraining the cosmological parameters at the sub-percent level {{cite:42ef1a2679bd4096b700689457394354434bf6ba}}.
| m | 66c5b47c1ffbdfbc70086a7e940a9d2c |
Traditional conic optimization methods detect infeasibility by computing matrix inverse (or equivalently, solving linear equation systems), usually as a subroutine of the interior-point method {{cite:dc4f61609815922052af93c581ec7db4a560ebd5}} or the Douglas-Rachford-splitting method {{cite:e4c983196059fcf0910097e028634eb831f7b6e9}}, {{cite:ddbf3102c8d1002674748572a0d24b85328f6151}}, {{cite:dfb36fcd0db19a0704b321807a03e972b22cf73f}}, {{cite:531bdaf8465dd33d6839a97424269ead4379ae0b}}, {{cite:c8807f3ea9f2ab6b63e4d561330886f5a63c3546}}, {{cite:f7558d4e3517c8fce353efd68caed58e87e1fd71}}. Such computation is numerically expensive for large-scale problems.
| i | c645efacee20d24e751894952bafcea6 |
Without physical randomization, we believe it is best to refer to the
same test as a quasi-randomization test, as the statistical inference
will be inevitably based on some unverifiable modeling
assumptions.Philosophically, it may be argued that true
physical (“ontological”) randomization does not exist; perhaps
which ball is drawn from an urn is not random to a
superhuman. Still, it is better to base inference on the randomness (we
think) we introduce and understand well. After all, it is easy for
us statisticians to assume the data
are independent and identically distributed and forget that this is
only a theoretical model that requires justification in practice. On
this, {{cite:d102110cd775ad60ff58c0cf921d4635351698eb}} offered a sobering remark:
“The postulate of randomness thus resolves itself into the question,
`Of what population is this a random sample?' which must frequently be
asked by every practical statistician.”
| d | 41bdb9b4943b1291c1883ab4da47c987 |
respectively, see {{cite:3e980b170bbecfd84ac1d78aaa4d416427fdeb89}}. Denote by {{formula:2008e9f1-344b-455f-a074-fa62b59ef201}} ({{formula:56e81e30-9186-468d-b229-a6c61e2845e6}} ) in case {{formula:2d41ea8c-19a2-4839-aec7-3ab6e72d4eac}} ({{formula:88fa7e63-d36b-423a-8cc3-22576e46c42e}} ). A measure-dimension mapping is a real non-negative function
| r | 29789f0371b4d23c72a6b3cc65f468d4 |
Finally let us mention the connection with another common approach to differential forms on quantum spaces, due to Woronowicz {{cite:53aeb7d08a8351a82a390cd28451e581926fcec8}}.
In this approach, given an algebra with an action of a compact quantum group, we introduce the structure of a differential calculus on the given algebra, together with various requirements about the action of the compact quantum group.
In general we have many inequivalent choices of differential calculi, but the situation is much better for the quantum irreducible flag manifolds {{formula:e1f81cf9-51f9-43ad-8f6a-21a83263a528}} .
In this case it turns out that there is a unique analogue of the de Rham complex, which enjoys essentially all the classical properties, as shown by Heckenberger and Kolb in {{cite:5abcdebbf7de9221127a7403d39779b6122ac420}}.
Within this setting, there is also a notion of Kähler forms introduced in {{cite:73a444cc296dfbd408c6e28d2ed12b25953cb086}}.
Quantum irreducible flag manifolds were shown to admit Kähler forms in this sense in {{cite:7cd33517b1f785b8869d29065118ddb97fb11b1d}}.
Finally we will show that these can also be identified with the forms {{formula:3dea48c8-bdf5-46f7-9b99-a02a1b95ec8d}} in the classical limit.
| i | bb6806b99d3eefa62d755a82e5ca49a2 |
In this section, we describe the architectures we adopt for calorie estimation as well as our enhancement of these models with the multi-task paradigm.
We use end-to-end algorithms,
meaning:NTF . i.e catcode:NTF a i.e. i.e. the networks operate on the raw food image without intermediate processing steps.
Similar to other multi-task approaches in food image processing {{cite:8b757977b6b90e19349a0d9bf8826d12f57970d7}}, {{cite:8804c71bbff2a23be5ad58863e00bb7f0d7b0085}}, {{cite:75f0294d4baa7b21e059b693b27c5dad279a9943}}, we leverage pre-trained networks that are popular in the computer vision community.
For this, we adopt multiple variants of the prominent ResNet {{cite:510d28b550f6d164461f382915b069f5a43df74f}} and DenseNet {{cite:cafd661f8dd46b3884a0ff5ae25bc02d9cfa8e6c}} architectures as our backbone models, which were pre-trained on ImageNet {{cite:19c6852462647e627ec6374caf62703533af140e}}.
As the original models were developed for classification, while we aim for calorie regression, we replace the last fully-connected layer with a regression layer and keep the rest of the architecture unchanged.
| m | 4cdc0cb1463caca0a9efb85592d68e17 |
Figure 2a summarizes model results over a range of semimajor axes, and shows that the effect of GEC heating on planetary radius becomes important for {{formula:ac3315d9-d34b-43fd-a91b-304aaea633f9}} , and is capable of inflating planets to radii consistent with those observed. Note that variations in (a) stellar magnetic field, (b) planetary magnetic field, and c) planetary composition will have potentially significant impacts which are not explored in detail here (though see {{cite:cef4a4f2787f845122d635c571301552effb2720}} for limited discussion). Further improvements to the model are planned, and include examining the effects of variations in composition and magnetic field, as well as GEC model interactions with other heating mechanisms, such as Ohmic ({{cite:7cc3d00c1c1eef370e428de30ac7e9111c1994e0}}) and tidal heating.
| d | 7b597571f096f5fe775441e480376687 |
Using (REF ) and (REF ), one has, for {{formula:aa9424a8-e074-4db8-a456-22b70858b671}} ,
{{formula:aa3d91bf-d6c8-492d-a055-722af121a5ce}}
here {{formula:27311bbe-8af0-4249-a5de-e9de6be7136b}} is used to denote a generic positive constant throughout this proof. Define a functional {{formula:93cf72a9-4a61-4f23-943f-5a943f3a3d2d}} that is obviously equivalent to {{formula:e70ee1bf-0a98-42bf-856e-9e4774a375e1}} as follows
{{formula:c1ad8a01-0f83-41cb-9b1d-ce3ada0849a4}}
then based on (REF ), (REF ), (REF ), for some {{formula:23c14556-76a8-4267-bf6a-694d067a3b9f}} and for any {{formula:f5fa79c9-d233-4b14-96e3-2339f3dde8c2}} , we have
{{formula:2d674ec2-23c5-44c6-adc6-f3183bee775d}}
here we have chosen {{formula:fc787c32-fb9c-41b8-85bf-b538c8d89020}} so small that {{formula:3796c4f1-31d0-4028-a8be-c3db21e4ec6f}} .
In what follows, we will discuss in two cases.
Case 1: {{formula:6e5c9f23-f3ad-4fef-be56-c417f6dc3375}} is linear Multiplying (REF ) by {{formula:bbd2aa9b-36da-44a5-bbea-6e5060447936}} , using {{formula:e025bf95-0300-4122-9e13-00491c744986}} and (REF ), one gives
{{formula:d52bb285-fc09-4604-9af5-15a3849ce1a8}}
which implies
{{formula:96eb56b7-044f-478e-a914-695d8124aabd}}
Integrating the above inequality over {{formula:3cec2cae-f40f-4d09-bcdd-7a228e6e1735}} , and using the fact that {{formula:25ecc65d-79ca-4350-8843-b098e2a1da06}} is equivalent to {{formula:59c50255-0a27-49ee-bfc9-981790f9791d}} , one has
{{formula:19e624b2-0f1a-408e-ab85-dba8af491f72}}
here {{formula:2eebbc3a-b486-41dd-b9f8-0748e4d69f0a}} and {{formula:00fd0ed9-916c-4794-a97a-c074362c9108}} are constants.
Case 2: {{formula:6be3dd03-1f76-4ef1-9608-f17b91c02b93}} is nonlinear Define a functional
{{formula:7d739506-2ee3-45f4-8e3d-28e9ccc433d0}}
Taking the combination of Lemma REF and the non-negativity of {{formula:98204d36-79df-4aaf-8b6e-21e21b071da8}} obtained by Lemma REF with the definition of {{formula:ab0717f8-ca9e-4edb-ba41-ac1f51736189}} in (REF )
, it is not difficult to get the non-negativity of {{formula:60f59582-7849-4cac-9a0a-5fa63a75b1f9}} . It follows from (REF ) and (REF ) that for some {{formula:76d5199c-25d7-4551-b9c3-b02a3e59f0f2}} and {{formula:edb6599c-bb01-4593-8d1c-533a387edc79}} ,
{{formula:82ae2bab-dedc-410b-b4a1-6b2b9b639747}}
Integrating the above inequality over {{formula:26eb9b1e-e66c-4874-b3ec-ae9b362eff2e}} yields
{{formula:c2c9d03c-790d-4765-8530-d73aec35c51b}}
which implies
{{formula:024b1830-f10b-4d99-aad7-04eb2dd33849}}
Define
{{formula:bc71a616-ec48-4ec6-a497-17318c2f8a1a}}
by using (REF ), then we give
{{formula:48146341-c53c-4306-9066-8c14554e2169}}
Thus, we can choose {{formula:c50b9fbf-f5df-4bdc-b8e2-7793777c3e09}} so small that for {{formula:d2451c06-c375-43e3-836d-17cb22510489}} ,
{{formula:e134355c-64dd-45fc-acdd-911e8c39ef4b}}
It is direct that
{{formula:316a5dc6-f93b-43ce-be5d-ceb64056fa9a}}
since {{formula:dbc4a5dc-414f-4076-a613-b70c90e0dca9}} is strictly convex on {{formula:fde62b14-6397-48c2-9d38-1b72db098fea}} and {{formula:de15d649-fd0b-4c82-a503-98fbd0d68766}} . Based on (REF ), (REF ), (REF ) and Jensen's inequality, one gives
{{formula:9c9020a9-5d42-4739-b90d-ef2ad663ac2c}}
which yields
{{formula:809cf379-285d-45de-9e3e-d4180fcbdc67}}
where {{formula:fb5e2261-78ea-4038-95bb-31c3ce573cb9}} has an extension {{formula:ce1a06f1-e96b-4910-b32f-cf460df99b30}} which is a strictly increasing and strictly convex {{formula:ef272b3d-77ca-47f0-b550-e51bd098df36}} function on {{formula:f664cf1f-a80a-44da-b675-176ec6e3d7c4}} as in Remark 2.1 {{cite:d3441a4301af5534bb44f24368df787b84c943cc}}.
Therefore, (REF ) becomes
{{formula:ae0cd0bb-9ad4-4bdf-b040-79710d8420e3}}
Let us define the functional
{{formula:64ea271a-65c6-44ce-9855-680e32ba63dc}}
with {{formula:ac829ec2-48ed-4de6-8718-753bbd24c72a}} then {{formula:60083856-98bf-4d1b-bbd3-3b2e21c886d2}} is equivalent to {{formula:e3ce2b1b-c13d-4902-bc78-5e705b733723}} and
{{formula:90a3b9d8-d33a-42de-9951-3d5fef2e7b84}}
by using (REF ), (REF ), {{formula:87c62353-a3cb-4f8a-94c2-b7edac185e01}} and {{formula:2d96339d-c4cc-47c0-8dea-0ac155f1da22}} . Let {{formula:cfb9c994-8751-43b5-9230-ff50e205d03f}} be the convex conjugate of {{formula:c0338ee6-0725-44d7-8a99-21875f108034}} in the sense of Young in {{cite:a7c253fede227004eb18dee564fdb954b17346b2}}, which is given by
{{formula:70a5f789-9972-4250-aee8-0b7e08f54e1e}}
and it satisfies the following Young's inequality
{{formula:9679f101-ee79-4fed-bc7f-39cc2f7b9d3f}}
Choosing
{{formula:7ea0f3be-5739-4998-913b-795992fe7006}}
then using (REF ), (REF ) and the non-negativity of {{formula:1044526c-d4c0-4dc7-9967-5b7a3de79899}} (REF ) becomes
{{formula:6a5a6eeb-0d9a-49c6-a8fb-f09b06cff585}}
Note that {{formula:adfe3a39-d827-4064-a6eb-83a0db44e021}} implies
{{formula:c5f149fb-b71f-4bae-9f25-ae2331407920}}
then one has
{{formula:78d0afb3-4426-42c1-b93b-71807cfb9741}}
by multiplying (REF ) by {{formula:6cf72b45-ac34-408e-a699-1fcbb803c483}} and by using the fact
{{formula:0b1391f4-dfc2-447e-8d57-461d2636dde0}}
Define the functional {{formula:f3fb754e-40ad-4f8c-91bc-dd8768d05690}} which is equivalent to {{formula:2e27ad88-b161-4319-9177-01ccb29c4033}} , which means
{{formula:01e69569-9f77-481e-82ef-a4ff4526aa93}}
for some {{formula:6d7be14e-f762-402c-8d15-d11c91e1e477}} and {{formula:f8ac176f-9f7f-4c0c-a118-150a37d30c57}} . Under a suitable choice of {{formula:4d60ae2e-4d8c-48ea-9f2f-8f97a5d2ccc5}} and for a positive constant {{formula:2b10a9f9-6628-44da-9bed-5be68c856b87}} , we have
{{formula:026a01cd-7499-4ebc-a79f-a1ffbe7e5d84}}
with {{formula:a6ba9749-f497-4a40-b41e-ccc6d07d3f69}} . Obviously, {{formula:eb4c1dc7-2102-46bc-80bf-fe8e4c33b107}} and {{formula:438d2fc6-a0b7-4153-afaa-7800126cee7e}} are positive in {{formula:bb40293d-9061-4ad0-91f6-679ae3e55b40}} since
{{formula:7925a885-253d-4bee-a873-f9ea051d081b}}
and the convexity of {{formula:6f31da87-8f70-4e6d-8a11-651091f7d068}} in {{formula:f325d742-073d-4264-ab32-b775abad3b01}}
(REF ) and (REF ) imply
{{formula:fa6cd9dc-7540-4ed2-9abd-8c269e2f7098}}
with {{formula:f3bc7749-3742-40e5-91c0-d2409b20903f}} . Setting {{formula:4f341b1c-8a7e-4c55-a719-c1203859906d}} , and then integrating (REF ) over {{formula:0ffd5774-447a-4e41-a60d-6fd91042cf57}} , one has
{{formula:e9cfa1e5-447a-4b55-aa0e-b9ebd4aa66ca}}
Since {{formula:56acdac5-599a-40e1-9cf3-28345a70935e}} , we have
{{formula:ac9575da-94ec-4a53-bcc9-888959c1d924}}
It is noted that {{formula:94ab5858-ec3d-44a7-b797-314e0ca0479f}} is strictly decreasing function on {{formula:8e230fa8-87c7-4c39-a447-ca680976b58d}} and {{formula:885ec427-e6f3-43a6-99c5-adcbd62feb86}} in Theorem REF , then
{{formula:9e44baa6-7a37-47c9-b670-fe2e3c3b7878}}
Since {{formula:c0462eb3-5246-4c22-a748-c4c4d61a06c1}} is equivalent to {{formula:269889c7-268e-4ad5-bdf8-0b28f5267d7a}} , further one obtains
{{formula:2c83fa41-bfe8-4063-b43e-e4f692251ffe}}
with {{formula:4e900199-01be-4f1a-a90a-d6eaaa1a26c6}}
This completes the proof of this theorem.
| r | 081a5e45e60f9444cf9a6a2139c55c52 |
The Hausdorff distance is a distance metric for mathematical sets proposed by Felix Hausdorff in 1914 {{cite:0685e2a6c143e2339810c2928580a58d680c31e5}}. It can be used to express the distance between two non-empty compact sets. Many explanations of the Hausdorff distance and how it can be calculated can be found, both in the literature (e.g., {{cite:d0752b4ca21e3b80c376f98ee9c9847722cf21d4}}) and online. For example, Wikipedia {{cite:2e63de63146e207f106bff03462c6447a17d1055}} states:
| m | a7886288fe40979e23041ab9f1509cf5 |
The Riemannian metric formulation for null surfaces fail as they degenerate and one has to resort to Carrollian structures that arise on such surfaces. Carroll group is obtained by a contraction of Poincaré group where the speed of light {{formula:e8c60519-faa5-4d97-bef0-2b62832381c0}} , and the associated kinematical structures allow us to define locally Carroll manifolds {{cite:c3d611aaabd252d1c414f3e08e75821ea4054b49}}, {{cite:e34d357e03e78807020c1e3484689f771bdd59fc}}, {{cite:b60699f471966d6bbbe34bbd98fb4b8e5d0f3edc}}, {{cite:6640dcfe24f625400a9a6798b1007dd5327d19c4}}, {{cite:30bd86e0b69d09c7cee43911cf68947c3f4823ca}}. These manifolds are endowed with a fibre bundle structure that keeps space and time diffeomorphisms separate from each other. The theories defined on such Carrollian manifolds can also be seen as a {{formula:7db8a108-4acf-4058-b67b-42f4fbd18629}} (often called Ultra-Relativistic) limit of relativistic theories. It is important to note the resultant theories are different from the diametrically opposite Non-Relativistic ({{formula:c286a04e-6e73-44be-a920-5445a8009150}} ), or Galilean limits, which find interpretation as the ones defined on a Newton-Cartan manifold {{cite:b60699f471966d6bbbe34bbd98fb4b8e5d0f3edc}}. However, there are interesting similarities, which become most manifest in the two dimensional theories we would investigate in this paper.
| i | dcee6b20cb0db5d936d8a37a2868d47d |
In addition to comparing with the original models of the respective methods, we also compared PSNet with other learning-based sampling methods in literature: SampleNet{{cite:fd3ab7f60ba256f41f94736a1cc396460d4251a5}} and CP-Net{{cite:518f96eb0039126fccc6cb4ff40552a50f9825fb}}. The data structuring part of PointNet++ is replaced by a learning-based method. However, SampleNet and CP-Net can only perform sampling. They have to be paired with other grouping methods such as kNN to complete data structuring. To the best of our knowledge, there is yet not a method which can perform sampling and grouping at the same time like PSNet.
| m | 205e0b4d4301b587a7fc792ad6e3c744 |
Following the common practice {{cite:9e3ce6a56a9a2d914997eefe7c159049170fc71c}}, {{cite:1f0c1d86e4cca650a5917c64ad580d48a18c2042}}, we interpret the MTL task into a multi-objective optimization problem. The optimization objective and its constraints in our method are both based on the mutual information {{formula:126617d6-180c-4bdf-81d9-3ed5856f374d}} and {{formula:36060edf-7319-497f-85ed-97b987b6b889}} . By incorporating the VIB structure {{cite:2b45a3f47b35baba73a1efb9aa646f79a76e13f9}}, the shared latent representation {{formula:3f48a97e-ffb3-418b-9b39-edbb44070584}} can be maximally compressed from the input while also sufficiently represents the targets in the upstream task and the downstream task, respectively.
| d | b655539d99eac96cd22757455a666d25 |
In conclusion we hope that our theoretical investigation will stimulate
further experimental analysis of triangular, and more generally frustrated
magnetic systems by Raman scattering. Several novel materials with
triangular structure have been investigated thoroughly over the last few
years, among them the cobaltites, Na{{formula:fa5731ad-2cd7-470b-9973-c69c3a79f341}} CoO{{formula:ae96d52e-96a1-42dd-bd7b-bfb84ee058ee}} {{cite:70e4619ce9b66d2872850286d388d8c4f8c00713}}, and the
spatially anisotropic triangular antiferromagents Cs{{formula:841b2ddc-07cc-49f8-b888-82bf616905a3}} CuCl{{formula:a0c7b603-8cec-46b4-9ca4-db64539e8b32}} {{cite:146a5aec87b6d597b7e8cefdeba0f1d4b99dcd90}}
and {{formula:f156024c-dc05-489d-baa2-554e879e04db}} -(BEDT-TTF){{formula:dd76cbb3-bd61-4a74-9371-cb2aa109b8ea}} Cu{{formula:ca079b8d-872f-4191-8c42-ce4582dbe346}} (CN){{formula:646e015f-e2e7-4dd0-ba47-494673d50704}} {{cite:c70f387423e0488ec46a3201a6faa30da300077d}}.
To our knowledge however, magnetic Raman scattering on such systems remains
a rather open issue.
| d | 75fe5710ed51b3ac1863a30931329a6c |
LSTM {{cite:3d13f12c8400fbea2f823e40acd09e8a88242e6e}}: It is a variant of RNN whose name is Long Short-Term Memory (LSTM). LSTM updates user (session) embedding by inputting a sequence of historical interacted items of the user into the LSTM cell, which could capture the long-term dependence of the item sequence.
Time-LSTM {{cite:5af905645db3238adb92e6b792da5d116bc444d0}}: It uses time gates in LSTM to model time intervals in the interaction sequences.
RRN {{cite:f4713bcf9ea8edc0d63351ddf1cd96d8ad54154e}}: Recurrent Recommender Network (RRN) predicts future trajectories to learn user and item embeddings based on LSTM.
CTDNE {{cite:06499972eae2fd6d9ca9a3da55f5b741749aa3b6}}: It is a state-of-the-art model in generating embeddings from temporal networks, but it only produces static embeddings.
DeepCoevolve {{cite:94221fa96dc4b67ff51de3a153d7334cdfb31f34}}: It is based on co-evolutionary point process algorithms. We use 10 negative samples per interaction following the setting of {{cite:f3beb512aa96402f5f80a092789adb8ee35a64ab}}.
Jodie {{cite:f3beb512aa96402f5f80a092789adb8ee35a64ab}} : It is a state-of-the-art model in dynamic recommendation problem. It defines a projection operation to predict dynamic embedding trajectory.
| m | 48a308e4495d7b6b91c3b7539a8f37d9 |
COMPAS Dataset. In COMPAS dataset {{cite:229bcac38fea4816dd65bedb4917236446ad216b}}, we consider the same type of fairness criteria, which is Equalized TPR. In this dataset, we consider that the equity is desired among races, which are “Caucasian {{formula:90b091b4-415c-498a-b6c4-6e18d7dc1a39}} , African-American {{formula:cea84fdc-c3a4-4257-bb86-0de06da2ce44}} and Hispanic {{formula:6b40037e-b881-49ef-8250-0d894632b1e5}} ”, and follow the similar preprocessing procedure as that in Adult Census Dataset. In this dataset, the number of samples in the group “Hispanic” is much smaller than the other two groups. Thus, we only consider to inject poisoning samples to {{formula:60e44852-2bf8-41a1-8169-005c2faaddeb}} or {{formula:e33800d4-af6c-45c1-a7ea-3f0bc45369e2}} . In Table REF , we report the performance of our studied attacks and defense, and we use {{formula:77a2f465-3119-4287-9368-a631061bc852}} to measure the “goodness” of fairness, where {{formula:5bf39faf-814b-4416-8c35-9a3f7f1c1757}} is the averaged TPR in the whole dataset. During training, we set the desired fairness criteria to be {{formula:18e2a175-b743-41c3-86cc-1b41d321970a}} .
From the result in Table REF , we can see that RFC is the only method that can consistently preserve the model accuracy and fairness after there are poisoning samples injected into the dataset.
| r | 53b0607df5d5b93b614aff660d33d754 |
As an application, we establish the local invariant theorem, which is a piece in the Clemens-Schmid sequence {{cite:3c57f322970406c4b6d8890a06b537a12b08eb24}}, when {{formula:31699003-b0b5-4678-9ef9-4427872c02a5}} is non-reduced. The local invariant cycle theorem first was proved by Deligne in an algebraic setting when the base is a scheme {{cite:5e747b028a3c7d4c65ba603e0a129cb2ecdc57bf}} and later treated in{{cite:9672e5f917606091fed88aa407c3af92051be807}}, {{cite:3c57f322970406c4b6d8890a06b537a12b08eb24}} and {{cite:bacdee5a7dad31f259de0c45354cf1eef2cb8eb0}} for a semistable Kähler degeneration. It also generalized to mixed Hodge module theory by Saito {{cite:09c3f6d8eefe4a93ffe7c1d863000f72e60bedd7}}, {{cite:ee20f41bee78bd65133baf7921f7aee459d2db99}}.
| r | 516bf75ff1fb01487e0e70c903dcb059 |
Light nuclei production in high energy heavy-ion collisions have been extensively studied both experimentally and theoretically {{cite:eba254a1a0cdc6b80cabde7383dbf74f7a379bc0}}, {{cite:31a9b369afbf35bcb50652e928f0aa7e17da8e4b}}, {{cite:1e82e49f74b5d45388beac4fd135e2dff913a83b}}, {{cite:7195223c031506aaae9aa1f1310d7e7774b833a2}}, {{cite:586d02a590a184f96fe7c31b6932bce904019c9d}}, {{cite:e242428ba182cc15eca4dc6add5dadc9dd9a5fee}}, {{cite:faa10b531e9d9b06a0274823ffcb187622460c95}}, {{cite:98efe89797bebd2b4b34f07dd6ca62b0551d3ab3}}, {{cite:53fe62790c4bccd94173ed123b8f9e9740d49ef2}}, {{cite:2fc2b884deefb8c870974abbf7a8c2b87fd56221}}, {{cite:df4cf006e8f9ef74b66fd7ab1bb1b914f957c10f}}, {{cite:fcdbc8215ba5dd7e44f8544dd75f3a5d31e89996}}, {{cite:4ac401c7e6e81aa98bb035796dcc8488641ef073}}, {{cite:8934742614758e2411ce6e9c1486fd7ef0b5be4c}}, {{cite:35fcc3f934153e64d719fd56ce6f4d28644ee1de}}. Besides its intrinsic interest, studying light nuclei production provides the possibility to probe the local baryon density and the space-time structure of the emission source in relativistic heavy-ion collisions {{cite:497933f42338e1d3586a4e89deaa5c61861dca4e}}, {{cite:1e409ed991944f381cc49733170c05d4a1ef2401}}, {{cite:9ca65d668b7c477828b9ea77993d026b4869eb3a}}. However, the production mechanism for light nuclei in heavy-ion collisions is still under debate. On the one hand, the statistical model, which assumes that light nuclei, like hadrons, are produced from a thermally and chemically equilibrated source, provides a good description of measured yields of light (anti-)nuclei in central Pb+Pb collisions at Large Hadron Collider (LHC) {{cite:9dce8241821572198535b0016b0267e7233c3898}}, {{cite:d626b97fa74b83d57c03a1070a7cc6d2992cdd5e}}, {{cite:56a061529e2369043b090dc9faaf51183df98f34}}. On the other hand, the coalescence model, which assumes that light nuclei are formed from the recombination of kinetically freeze-out protons and neutrons {{cite:76c07591211cc8d16e1ae9628a7e157fcd31d5e8}}, {{cite:39704c46257334383f902ae7ffd1611a457a5a98}}, {{cite:d9de67a1d7b012bd865b56ee6a3d20c9fffb3481}}, {{cite:206d15c4a8dac28189d33ba8532f0771abb67289}}, can also successfully describe the transverse momentum spectra and the collective flow of light nuclei in heavy-ion collisions {{cite:43967406996e07d9923af0307b45d974ccec8e05}}, {{cite:79d1d9679a80b381499af16b28db7141348026b5}}, {{cite:0e820578a12c4a28f607ef2a48e6dafd71263db4}}, {{cite:246f75761d4cce2b98eec8f25adb59b979495b29}}, {{cite:5f317d0d402dbbfb064eb503260289cc91faf1be}}, {{cite:8c5fe3c2a3e7f12c9617eec6f6f9dd9f66c27182}}, {{cite:68d3c260b5fe0921c236ea15cb67d4b2eee2cbd8}}, {{cite:aae7c0f59acf1209badb9945165b48aa5126bec5}}. In between above two extreme scenarios for light nuclei production in heavy-ion collisions is the transport model, which aims to study how light nuclei evolve during the hadronic evolution by including their production and annihilation, such as the processes {{formula:95884a1a-0600-4629-9b5b-824021d492ad}} for the deuteron {{cite:6d2b1eaeb063d352a1e4c497aa5ddec780f14960}}, {{cite:d8b02c6eecb7e54e3d2954be2a1e2807b99b30a7}}. In the latter study, it is assumed that the deuteron can exist in hot dense hadronic matter, although its temperature of more than 100 MeV is significantly higher than the deuteron binding energy of 2.2 MeV.
| i | 0bea26efd0505fd8addd2f11b9138d29 |
The conductivity of graphene was computed within the local random phase approximation, which is a function of the frequency of incident light {{cite:b2a4fdd3031b3a199c31df969c4684d7f73f5355}}, {{cite:6efd39f36117fc03f69fafeb50c896053812b25f}}
{{formula:686a67dc-f1b5-473b-badf-4f0fae7d3e1c}}
| m | 0f1467820b772d772af96380638854f0 |
In the OpenAI Gym environment, experiments on 12 Atari games in total were performed with both Pixel Novelty and the fitness-based approach. The specific games to be included in the experiments were selected to represent equal subsets of games, half of which contains multiple obvious local minima (e.g. Montezuma's revenge) and is expected to show the advantages of our approach. The results of the experiments are presented in Table REF in comparison with the fitness-based approach and reinforcement learning algorithms like DQN {{cite:7335b42f12f07035d099ab02a173cf643408c96d}} and A3C algorithm {{cite:f2c5d8491f6c17d0290676645410afea122643e3}}.
{{table:b025cc69-49dd-462e-8aac-fb0c49a7d71d}} | r | 45d3abed31c925da63679c20f13bedcb |
PIRL is a global, in-model method used in place of DRL {{cite:45e205fd8cda318a951af903624ed52ab9abde57}}. In DRL, neural networks reflect the policies and are difficult to comprehend. On the other hand, PIRL policies are expressed using a high-level, human-readable programming language. However, unlike standard RL, they limit the number of target policies by using a (policy) sketch. They use a framework based on imitation learning called Neurally Directed Program Search to uncover these regulations (NDPS).
Hierarchical policies technique {{cite:5d20f41261e4007dfde5ce8d8e9503dcd76d0b13}} is another in-model XAI technique used to interpret the decision process of multi-task complex RL systems but locally. The core tenet of this approach is to decompose a complicated task into smaller subtasks. These smaller tasks will be accomplished with the already learned policies or learn a new skill. This model also takes the temporal connections and task priorities to improve efficiency and accuracy. The technique builds on multi-task RL with modular policy design and a two-layer hierarchical policy based on minimal assumptions and limits. In {{cite:5d20f41261e4007dfde5ce8d8e9503dcd76d0b13}} they assess this technique in object manipulation tasks in the Minecraft game.
LMUT {{cite:4e802014881ed66fe02a1383a52c395d1097246f}} is a post-hoc explanation method unlike the methods mentioned above. They are flexible to be used to generate both local and global approximations of an RL model’s Q-predictions {{cite:f856e7cac1ba921789992c5b6bde55c32ee3ad51}}. LMUTs are an extension of Continuous U-Trees with the contrast in using linear models at each leaf node instead of constants, making them more interpretable and comprehensible. Because of the inherent interpretable nature of the trees, it becomes easier to generate explanations from the LMUTs as they mimic the original Q-function.
| m | 9022785ce930e5ba08d19629f3ed9aab |
CommNet (Communication Neural Net) {{cite:76869c6ae666fac01e31cc51f36251a18a36510e}} uses continuous communication to coordinate multi-agent system. CommNet is the typical work to replace manually specified communication protocol with a deep feed-forward network.
| m | 073d472994baf3135658501485b60e77 |
Quantitative Results under In-Domain Testing.
We exhibit more results with two settings that under In-Domain Testing, as shown in Tab REF . Specifically, the first setting (denoted as {{formula:b502e527-c077-47bf-bfb4-097023c61d1e}} in Table REF ) is case-specific training but testing on unseen poses, where generalizable methods such as IBRNet {{cite:a0a4852199da1800173fabbd2255dc064316092a}} and ours are trained following same protocol as case-specific methods such as {{cite:6ee37d4ee953eb6557bbf3b9123b7ebfd2e59778}}, {{cite:543b64631afaa5bb55db7285e84b35cd7f241dbb}}, {{cite:351238ff0220ee4bc26eca14ec07e822ac25805c}}, {{cite:13184ff686175b69d840703a21680609bbd94a08}}. This setting demonstrates the effectiveness of GNR of modeling the human geometry and appearance under a rather fair protocol comparing to case-specific methods. The second setting (denoted as {{formula:486ebb08-b30e-446b-a3d6-ca50a63fc6cf}} in Tab. REF ) is in-domain finetuned but testing on unseen ID unseen poses, where both generalizable methods are finetuned on training set of GeneBody-1.0, and tested on the listed 10 test sequences. This setting examines the capability of generalization in the same domain. From Tab. REF , GNR performs better under both settings, and is proved to benefit more than {{cite:a0a4852199da1800173fabbd2255dc064316092a}} from in domain finetuning.
{{figure:b87d7cdb-3621-43fa-82de-420036e6222c}} | r | 01cf17ad02414aa56a1aaaefda64902d |
Datasets In a centralized paradigm for visual recognition tasks, there are mainly two types of dataset benchmarking for long-tailed study. The first type is the long-tailed version of image datasets modified with synthetic operation, such as exponential sampling (CIFAR10/100-LT {{cite:629edc0f452f2eedbc732bcd8376ffcfa28ad2c7}}) and Pareto sampling( ImageNet-LT {{cite:1bae508d4df87869a5e766e3e8c8fa19117afafc}}, Places-LT {{cite:1bae508d4df87869a5e766e3e8c8fa19117afafc}}). They are shaped/sampled from the existing balanced dataset and the degree of the long-tail could be controlled with an arbitrary imbalance factor IF{{formula:3f164975-63b4-417a-9969-4af4ea6e0576}} . Second type is the real-world large scale datasets with a highly imbalanced label distribution, like iNaturalist {{cite:919461dd6c6038f225617a43dd1e457a4f98cb11}} and Google Landmarks {{cite:971dfe80281b6309d9d989d03d49dc7d13360d41}}. More long-tailed datasets are used in some specific tasks, such as object detection Lvis {{cite:97c38e4d981a1448b7b745e2777c7ac26cf9c1b5}}, multi-label classification VOC-MLT {{cite:c59390508a946df5a0b7beee457277ab5adfad60}} and COCO-MLT {{cite:c59390508a946df5a0b7beee457277ab5adfad60}}.
| m | 1a8d4f1fffe01e22f744320d11972d4a |
Lemma 1 {{cite:5e70f139ed929708d861af9b7a71051eb4359773}} Given {{formula:13c2036e-c60c-4d75-b542-b1ca4b727142}} , with {{formula:13d1e66d-2d26-4fe8-910e-b8ba15b4d9dc}} , {{formula:845120af-1179-4ba2-bf5a-8379caa16a8d}} , and {{formula:264f3efa-f563-4adf-947a-ad400b015a42}} .
Assume that the data generating system is controllable and that {{formula:899320d9-5b3c-4262-9a98-c68964469816}} is persistently exciting of order {{formula:3aae9113-6912-4d0d-812b-9a6d321320a7}} . Partition Hankel matrices built using the data trajectory according to the indices {{formula:cdbc69ce-6ccb-4698-92f3-c747045a1d21}} (p) and {{formula:da1e3d94-d8bb-4646-bd52-748410ea1470}} (f) as follows
{{formula:cdff23bf-2e5f-4c2b-988f-aaa72814a358}}
| r | df4f9dd3f4e0a8bb517f973eff657b9e |
The simplest way to think about discrete dynamics on a network is in synchrony, where all nodes update their states at the same time. Crucial insight can be gleaned by modeling dynamics in this way, for example in Boolean networks {{cite:cb2f9a7cbeb7c07f02cefd07bf1680d0a902d4ed}}. On the other hand, such models can overlook interesting processes, such as the mutual exchange of information between nodes before an update {{cite:271e6b2b4575b2e6bd2ec5cbf0d3512cc18a0150}}. Thus, we present maxmin-{{formula:2c19d007-6404-4298-935e-3bf4af800329}} , a model of such information exchange that produces asynchronous dynamics on a network.
| i | 115b14a37fde5c1641aa5723ed6be190 |
Let us mention that assuming metric regularity vs. strong metric subregularity of the mapping {{formula:ad70812b-1591-466e-b295-517013483981}} from (REF ) ensures the solvability of subproblems in the basic SQP method; cf. {{cite:a2e581a0ba2f1f9ba5e5a2dfb2a7cbd2dcc5080b}}. However, the next theorem shows that in our framework the metric regularity yields the strong metric subregularity of the mapping {{formula:e8912766-2c30-4119-940b-29f1f570ae1e}} , which is equivalent to the isolated calmness of solution map {{formula:26ec8cce-9051-43c5-ac16-574f21d9ec08}} from (REF ). Recall to this end that the isolated calmness of {{formula:dfe2a16e-e694-48c1-aa8a-a7f0341bfceb}} alone does not ensure the existence of the SQP iterates as shown in Example REF .
| m | 2b914c69ad435bdb1ce3b8f6e4617006 |
We have shown that in the MNIST dataset a correlation exists between the self-influence score (measured using TracIn) and the memorisation score. Contrary to our expectations, we did not find a significant correlation in our experiments for Fashion-MNIST and CIFAR-10. We suspect that one reason is the influence of short-cut learning. For example, under the Principle of Least Effort, the network may find it easier to fit the unique feature, than to learn features for training examples from Fashion-MNIST or CIFAR-10 {{cite:1a4acf3c0bfcb0393917513fb0f7a7c043024caf}}. For MNIST the task of learning is significantly easier and the unique feature is only memorised on very high influence examples. Another possibility is that TracIn does not trace examples that are necessarily memorable in datasets with more complex features, and hence the unique features are not memorised either.
| d | 24be99361f122582b7eccb88478c3a62 |
By Exercise 2.12 b) of {{cite:c6bf4948f6d3f52680b23bd905cc1012f1e61637}}, we also have for {{formula:63a24aa0-49f9-4985-94d5-aa1a27dcc0db}} :
{{formula:0b062c14-28ea-425c-8b5b-dcac560ed4ba}}
| r | b11990c569859c7f6750bfb87cddbe35 |
In passing, we note that we do not detect the radio halo of A2065 in our current {{formula:676abb18-0c28-452a-b8bd-1764a2f66f25}} resolution 250–500 MHz band image. This is likely to be due to the fairly short duration of our observing run (just {{formula:8e55f15c-53dc-4c06-beda-3dd334430a79}} hr), which results in poor ({{formula:0789ba63-398c-4c7e-a4c5-ac4465cd4576}} )-coverage at the short spacings that are critical to detect {{formula:2f753025-2d7d-4e26-8dd5-74e2b73545ee}} -sized structures like the radio halo {{cite:cc23570b5d9bf0ec2cc00449a66857391a5b1f9b}}. However, the large fractional bandwidth at 250–500 MHz band implies that it has excellent ({{formula:665d9234-acd9-4647-8554-affca5ea7f5b}} )-coverage at the intermediate and long baselines that are needed to accurately map the arcminute-sized structures like our target, the remnant radio galaxy (angular size {{formula:d0374e9b-cb93-400c-bb53-ad0c525c3f02}} ).
In addition, we have performed deep clean, where we have used the multiscale multifrequency synthesis process of combining data from multiple spectral channels onto the same spatial-frequency grid during imaging to take advantage of the increased ({{formula:f0385047-5890-4572-8f96-f698597c7df4}} )-coverage and imaging sensitivity, and hence we do not foresee any loss of flux density that could be linked to the remnant radio galaxy in the data presented above.
Below we discuss the nature of this newly discovered remnant radio galaxy in A2065.
| d | d5baa85e75f80521df41bea99b409f51 |
The existence of the QCD axion is well motivated by the strong CP problem {{cite:a78b6e68d591a82fc29fd6927bed3f6034bcec25}}, {{cite:ae6c29f47fb870cb3bf6e8f81faa182c964e3572}}. The QCD axion also arises in string theory models, along with a potentially large number of axion-like particles (ALPs) that do not couple directly to gluons {{cite:93823f9a0d1dfbf0ad57691cd0f2cf64b3b654a4}}, {{cite:96778f8a24feaed72b7e3aece5fc5c5d92582ef3}}, {{cite:77e2be323054f3ed593c986519c3ea0919c5a708}}, {{cite:4ed6e89848ba947124bba60c819234b7437e4eca}}. Significant experimental and theoretical effort has been dedicated to detecting these ALPs via their coupling to photons, either through astrophysical observations or through ground based experiments {{cite:3ee6c6d74eb17743917044a26cdd1bccd94a242f}}. In particular, in the presence of a background magnetic field, ALPs and photons may interconvert, leading to striking and potentially detectable signatures {{cite:67b5e64c3c3a52fb78b4c64b9f0c6185d2c2fa6d}}.
| i | 161596f968b7e7c6b8c695285acf154b |
Communities can also be identified by running dynamical processes on the network, like diffusion {{cite:496248424da63cc51e3b70e83b9231482cb0ef89}}, {{cite:9e8bf6f5888bca0c6be1a590b07659a724c7a3e1}}, {{cite:bfa265020745ff2b24f8994ddd74c05434d507dd}}, {{cite:7bb8e19b85336eca3f1a262abc83b6c4168fe1ba}}, {{cite:e3edeff4a4ebbb9cb0a6a5745127534da043bd3a}}, {{cite:f1925bc5ec873a3bb8f910b7fbd6debec371c2d2}}, {{cite:b6e9319ee6b8a470362b4ad5706abe945fe42264}},
spin dynamics {{cite:9e7d353e7c6b32ba1d4c43b569dcaedb4a09cc6e}}, {{cite:c86504b3fc975569a2146aa63835cd0ae9585114}}, {{cite:59e7f9f62bd1243506fc95860243a6a2bf7091de}}, {{cite:55681afd57423fb24f890552fd889240b3616639}},
synchronisation {{cite:ea6fe7b337d7a1c177eac5af5c34e870341295ff}}, {{cite:612385d955427b2be80045d445c93ad1739dbd4d}}, etc.. In this section we focus on diffusion and spin dynamics, that inform most approaches.
| m | adfb9ac35dc6c686f1782f4c011fd7db |
In many applications, {{formula:5d45e566-e534-4f26-9055-8a135269bc74}} is a multivariate normal
distribution with mean {{formula:00def6eb-d2cb-496e-a318-4edc97e813cb}} and covariance matrix {{formula:9ad53c6c-f2f8-43bd-b32b-fe797d52645e}} ,
where {{formula:ab68196a-2298-4473-942e-a361dbb5af41}} is the identity matrix, in which case {{formula:60e40e02-9abe-47a2-ba58-ac8bb8a68116}} is the
Lebesgue measure and {{formula:220c6137-3af3-4fb4-bc7a-7496469503ab}} is the Random-Walk Metropolis (RWM)
Markov kernel. Despite its simplicity, the RWM algorithm is known
to perform very well for certain classes of target distributions,
and furthermore to be a robust algorithm {{cite:48864d2f441abc626bc83433a8a9a3dd95177ee9}}, {{cite:5333f06469687536674751d09413b329237c4021}}, {{cite:644bd705f0ff87fe4b5d578664f06af5e59df935}}, {{cite:47f87b0abd962829fe5c321f7a72d192a6bb24cd}}.
In this paper, quantitative analysis of the {{formula:f3208e90-ca0e-46c5-bb98-38ee2ff1a92b}} -mixing time and
spectral gap of the RWM Markov chain is the primary application, with
a particular emphasis on the dependence of these quantities on dimension.
This analysis relies on a more general theory applicable beyond the
specific scenarios considered here; see Section REF .
| r | ac65a3b627d91d6e263c4d74792dac71 |
Bayesian spatio-temporal modeling has been used previously to determine change points. {{cite:53ba17d3f5b55542bbd30049f23569f7fffccd0f}} sought to identify changes in temporal and spatial associations; however, the change points they investigated represented changes in the spatio-temporal dependence processes, not changes in mean or slope. Further work has been contributed by {{cite:76913e78fe6dc49ff81914d6d66a11d9b1766d83}} who included temporal and spatial coefficients in their model to investigate the changes in assault rate decline over time. They fit several models with different numbers of change points and different fixed times of each change point in parallel and compared models using the deviance information criteria {{cite:c0b0070ce19620195a4014860e0c36678d7e1467}}. We also use DIC, a measure of the likelihood of competing models, for model selection. However, we make use of an automatic selection process for the number of change points, rather than a comparison of predetermined models.
| i | c833710338bef1abbdcaee9b4cee99bd |
One of the simple but novel contributions of the paper is to link the RL policy to firm-specific attributes. To this purpose, the inspiration comes from earlier work on characteristics-based investing.See, e.g., {{cite:5f368699fb0f58becce60849fc41a01f2283f5d8}}, {{cite:1166dac54cd8a3e153c4a3a19169baa7c8abb10e}}, {{cite:555c1722ae0e3fcfecd4e0646fbb0142a9932f42}}, {{cite:278d2fc237870f6622e09849b704e1784106616a}} and {{cite:72b4b2a4b9652c5bcbf1f8af539be36240cafef8}}). Our approach is closer in spirit to the most recent of these references. The idea is to map a linear combination of the characteristics into portfolio weights. While the traditional models aim to optimize expected utility functions, our approach seeks to maximize expected gains. The simplest definition of gain is a portfolio return but it is possible to adjust it to risk via the sequential Sharpe ratio computations presented in {{cite:5f01286399ae9e5212e08b9ea00be0fd543ba050}}.
| i | 0726be5f048d05fc7d03b8979947060f |
Second, Federated Distillation has advantageous communication properties. As models are aggregated by means of distillation instead of parameter averaging it is no longer necessary to communicate the raw parameters. Instead it is sufficient for the clients to only send their soft-label predictions on the distillation data. Consequently, the communication in FD scales with the size of the distillation data set and not with the size of the jointly trained model as in the classical parameter averaging based FL. This leads to communication savings, especially if the local models are large and the distillation data set is small.
Jeong et. al and subsequent work {{cite:f0cb2ed00fbc7e5e46f774f027fec80420bad438}}, {{cite:65f17b526116e6ee464f6a10441481501b8076c7}}, {{cite:b6ce6cec1728aefa9299954527692181e908e66e}}, {{cite:b9ad29a6e8c408d4e00b242c24170b325e3af292}} focus on this aspect. These methods however are computationally more expensive for the resource constrained clients, as distillation needs to be performed locally and perform worse than parameter averaging based training after the same number of communication rounds. Our proposed approach relies on communication of full models and thus requires communication at the order of conventional parameter averaging based methods.
| d | 987b1fff2b6a81cebb0010364c8836ce |
As mentioned, in addition to the four unigram dataset, we created complementary n-gram datasets for the two book series and the two task types.
In correspondence with the n-gram detection method used {{cite:d0f1e9afa87b159da9f4921ed794d6f41345ff05}}, in the datasets n-grams are words connected by the underscore symbol.
Many of the terms are person or location names such as Forbidden_Forest or Maester_Aemon. For reasons of brevity, we will not
include result tables here (see GitHub for details). The general tendency is that n-gram results are below unigram results in the analogies task,
for word intrusion results are comparable with around 70% accuracy (depending on model settings).
In comparison with word2vec, FastText-based models perform better on n-gram than unigram tasks,
this can be explained by the capability of FastText to leverage subword-information within n-grams.
| r | 5e940e9e441d2a6eb234214cb0e85738 |
as {{formula:31e0e520-db34-4cec-95b8-144526bec8a1}} .
Define {{formula:d39434d7-f2d0-4396-b875-30f4593a5179}} as
{{formula:99706606-bd17-4e96-833e-78d3ac853941}} and {{formula:43fa6814-c158-4b27-a4bf-24bb8bbcefab}} .
Since {{formula:ebbd4f71-065c-4ab7-8bf4-2ce0c7447530}} is a continuous function and for every {{formula:1bb76610-8634-4dd4-bd26-ab78492ee4d3}} , {{formula:a7472955-495c-4e29-ae37-c426e2ae2b2c}} as {{formula:c2d43b51-11bd-441e-b1d4-2deb67039c27}} , from (REF ), Theorem 2.7 in {{cite:40901d49d85974fc931f5f7bd7f1d02f4a309028}} and an application of Slutsky's Theorem, we get
{{formula:4876ad28-4dfc-4600-abac-afd7fa6f4a80}}
| r | 5621be54a806e1627f46d3459c3d7ec9 |
We also believe that the feature representations can be utilized to recapture the quantum kernel method beyond the tool for solving the scalability issue. For example, as discussed at the end of Section REF , we can relate the data reuploading model with the quantum kernel method by embedding the parameters in DQF and RQF and optimizing them. As another example, we may derive the condition for obtaining a quantum advantage as a constraint for the feature vectors by reexamining the discussion in {{cite:b4847580493332e584ae2b92766a056cb8b24751}} in light of DQF and RQF. We believe those understandings using the feature representations will pave the way for realizing quantum machine learning algorithms with an advantage over their classical counterpart.
| d | 195dd1dcb02eee61eff165b52c39fd90 |
Given into consideration that a small number of simulations tend to dominate
the benchmarking process, the cumulative total for a performance metric over all simulations seem to be too uninformative and misleading.
For this reason, we used Dolan and Moré's {{cite:dd4abd5479a87b6bad9aecae01cc6334bc0c395d}} performance profiles, which removes the influence of such simulations on the benchmarking process
and provides us information such as probability of success, efficiency and robustness in compact form. In more detail, each profile plots the fraction {{formula:31428786-7b63-4c6f-aac5-c964d135a535}} of simulations for which any given model is within a factor {{formula:63898839-a894-4a35-bc44-ccbbe7abfec8}} of the best model.
Additionally, in order to examine and reject the hypothesis that both models perform equally and provide statistical evidence about the superiority of the proposed model,
we utilize the methodology presented in {{cite:ed7e05d29e7695a3a690e36c5360a87addaaa9b1}}. More specifically, we apply the non-parametric Friedman Aligned-Ranks (FAR) test {{cite:d07cc6b9b85d1dd4c050f6e042d0b82a43e61f27}} in order to rank the models and the post-hoc Finner test {{cite:f72b3b4c3b46a06d9b1f9dff3c5b9c59dca26099}} for examining the existence of significant differences.
Next, we evaluate the performance of:
| r | da997dff1729bb8b342fce3752f3609f |
Frameworks like Isabelle {{cite:862d829a2ee7cfcde7431eab42b794880e1ba7e8}} and Coq {{cite:90b735ac258f051824c6878537f492b6077824c9}}, incorporate development of formally verified software. There are different solvers and tools developed within these frameworks {{cite:93128166c5f815afb8ecc68dea8c72b391d45313}}, {{cite:e6c21f8673e6ae5cf6916748598cff1b2e886e40}}, {{cite:e94d1cb5d6ff492beab22a5ec59c4e1a0d01be94}}. However, such development is very expensive and time consuming. A step towards formally verified software is a formal correctness proof of the proposed procedure while correctness of the implementation is based on the standard software development techniques. There are several different approaches for deciding sparql query containment, and for some of them, correctness of their procedures is proved.
| i | 8ca2071045d767c857394e9401b7d74b |
Out of our models, ResNet-BB achieved the highest score for the hayride metrics. This suggests the beneficial effect of propagating the image low level features deeper in the network for the task of scanpath prediction. DenseNet-BB is another model which uses skip connections and has achieved the best results for the MultiMatch metric. This also reinforces the importance of using skip connections to propagate lower level features. Both the qualitative an quantitative results for Inception-BB network results, suggest that it is the most useful for visual attention tasks. This might be due to the effects of using multiple scales for convolution kernels in a parallel manner, similar to the use of multi-scale data in many visual attention models in the past like {{cite:fe0fa7476bbac5f86a348825b4b59c2a80208c5d}} and {{cite:f89e4445543a69e91558af0a8887e23601757511}}. These previous results highly accentuates the usefulness of multi-scale and multi-level dense data representations using local skip connections in improving the task of scanpath prediction. Our results also suggest that fine-tuning simple pre-trained models using uncomplicated and straight forward training procedures can yield competitive results that can surpass state-of-the-art models for certain criteria.
| d | 2e5f2189405266496ad2d652cfa2670c |
Let us suggest a few directions for future work. The current method works marker by marker and is ill equipped to perform model selection. Lasso penalized regression is available to handle model selection for case-control and random sample data {{cite:e3810ee495af16325f539664adb8bb84ea36e6e1}}, {{cite:514b71f19ca9386fa4cee49e5cdc1f7f13eb031a}}, {{cite:2e7a63a6c59d24230b7f758ead496b9466f1cfa2}}, {{cite:db18269cf0a1aa75a2198d0b33f31e380cfec252}} and can be generalized to variance component models. Although we have generalized the score test to distributions such as the multivariate {{formula:cf11d4da-939a-4ea6-8044-fab2cf7dc1da}} , extending it to discrete traits may be out of reach. For likelihood based methods, there simply are no discrete analogues of the Gaussian distribution that lend themselves to graceful evaluation of pedigree likelihoods. Treating case/control data as a 0/1 quantitative variable is a possibility that has been explored by {{cite:6a1c75e814208ebf3a713365985f246cf0cd3094}}. The GEE method is another fallback option because it does not depend on precise distributional assumptions.
| d | e4838185b299dddcdeb6bc7f392cea6c |
We next test on the artif and oscigrne nonlinear least-squares problems from the CUTEst collection {{cite:0072a66ee5e59a7c414a60a50645f3ebc8f625ab}} with dimension {{formula:37d852a6-39a4-4293-bf24-dae08987e38e}} and {{formula:f996c15e-1036-4ca9-bf64-f80b9045ef7f}} respectively in both {{formula:bd14b9d5-c6b4-4cab-9c44-e2502b212ab8}} and {{formula:bb683ae9-7bf2-4fd1-8fa9-22fdb06b7f49}} . As before we run R-SGN five times for each problem for 100 iterations from the given starting points for each problem, with block sizes of 1%, 5%, 10%, 50% and 100% of the original. As we can see from the results in fig:artif and fig:oscigrne, R-SGN does not perform as well as on the logistic regression problems, due possibly to the increased difficulty/nonlinearity of these problems. However, it is still able to reach low accuracy solutions reasonably well, achieving a reduction of several orders of magnitude in the objective after just one second for both problems at {{formula:6e32b276-9c1c-44fc-8229-1ade22e5b08d}} block size (plotted in red).
The CUTEst examples show that more sophisticated approaches may be needed to tackle general nonlinear least-squares problems; for example instead of keeping the block size fixed at {{formula:045d55b3-662e-4f96-9bca-5bc00fd4d3cd}} , we may consider increasing {{formula:679ebcbc-6367-49e2-b51b-000daa50149a}} over iterations, a topic of future investigation.
{{figure:3ba8413b-0714-4589-ac3e-9fc92fb44e71}}{{figure:16906b2e-d8d2-4899-bbd0-78de05ce42bc}} | r | ca27755244d6ef63ceae74aa2a51b3cb |
Figure REF shows a TSNE-visualization {{cite:8984f62d8ad80cb676103d203f049b183db17a20}} of the embedding features learned from the CNN-model using the Triplet Loss_3 (REF ) variant.
We use the minimum cost multicut approach to cluster CIFAR-10 test dataset.
In the particular experiment example, the total number of clusters are 44 with a cluster accuracy of 80.27%.
The different colors represent the found class labels while in the ground truth, there are only 10 classes on the CIFAR10 dataset (which is shown in the legend).
Any other found clusters are considered as false positives and thus lower the cluster accuracy.
However, there are in fact 34 small clusters that contain less than 10 images.
Three examples of such mini clusters are shown in bottom left and right as well as on the top left corner.
Even though there are false positives shown in the examples of the smaller clusters, the multicut approach explores meaningful sub-clusters within a class label, which may be desirable on real-world scenarios.
For instance, instead of finding the class horse (in cyan), a subclass white-horses is also found.
| r | 6ff45d3d8fe5a6af7a6ce92bf22c99b9 |
where {{formula:32fe4ab2-eb8c-43b5-924b-71ee1a85a62b}} is the formal (linear or nonlinear) adjoint operator of the generator {{formula:bd36d6b7-cfb1-489f-9512-742f56e03ef4}} of a Markov process on a state space {{formula:d226010e-3042-47d7-9156-fd175f470f05}} and the unknown {{formula:78f00e4f-6fdd-497b-bea0-31f379a66721}} is a time-dependent probability measure on {{formula:5226914f-a875-4097-81eb-aa17563f0f86}} , i.e. {{formula:e42ce326-82d5-4c67-b2cf-d564addbedf5}} . Thus Equation (REF ) can be viewed as the forward Kolmogorov equation associated to the Markov process describing the time-evolution of {{formula:9c5ced6a-d33d-48a0-9120-f6e6231547bf}} . Equation (REF ) arises naturally in statistical mechanics for which {{formula:f0930fc7-e9b9-46b2-b2c0-94049730645a}} often models the probability of finding a particle, evolving according to the Markov process, at state {{formula:9f8f2d90-a68a-416d-acbb-c732fa8afa74}} and time {{formula:25d556ff-71f7-4530-9dd6-ffec0ed89cc4}} {{cite:abee39ff59e195265c4ebcef88ccd920f34d6bb7}}. We focus on systems where the operator {{formula:50c31ee7-f6ad-41d6-b3e2-3f906c909f3b}} has a general nonlinear drift-diffusion form
{{formula:fa9ab3e6-312f-45e3-b29b-608123175556}}
| i | 393a167b92ae943e90e684a370fc62a9 |
As we see in section:discussion, {{formula:6c5f9d19-3209-4331-8a79-36110be210a7}} and {{formula:f625e890-f339-41a8-a50e-883c8138e94a}} are the same order in {{formula:c1c103e0-1b4f-4d48-8c5e-7828e06a353c}} under the uniform class prior assumption.
By applying either the high-probability bound {{cite:fa5e7a61f8955bf92ce62ef6bada2e1e7cf70fb8}} or PAC-Bayesian analysis {{cite:9961ce5306b758a3311f46eeb1c96b5c704b6f3f}}, theorem:curlupperbound (theorem:curllowerbound as well) can be naturally extended to the form {{formula:5a30fc11-7de9-4966-acfc-81d43b76ff70}} with a complexity term {{formula:1b1b856c-4d78-46b7-9755-511680da8ee0}} , where {{formula:e130fde1-70c4-4067-82ef-8d9a5c2b250c}} is the empirical minimizer of the contrastive loss.
Since this is a routine, we omit the high-probability bounds.
| r | ed38b3be6e76e0bea276e75ba246a95d |
Graph problems have historically been an area of interest because of their various applications, but as the size of these problems becomes very large it becomes essential to design algorithms suitable for models handling such graphs, such as the streaming model. In the streaming model, the input graphs are presented as a read-once tape of edges where a possibly adversarial ordering of observed edges must be accounted for and low space complexity must be maintained. Much work studying undirected graphs is already present in the streaming literature{{cite:df31f6533e6880b3824c75475c939d324c7a4457}}; we refer the reader to the survey by McGregor {{cite:1526fe9abee66fb6ac49e030bd563b6bdb6896ce}}. However, relatively little has been done in the streaming setting for problems involving directed graphs (digraphs), with the exception of the initial investigation conducted by Chakrabarti et al. {{cite:475c72d6035a82d4465a9c3ca14479328c2fcecc}}, who study the Minimum Feedback Arc Set problem on tournament graphs, among other problems.
| i | ee9d99f4d9966bf4d01bb56db55d5a06 |
In figure REF , we show the spectrum efficiency of our solutions and benchmarks.
The number of IRS elements is set to {{formula:88c06da7-a1ed-4670-ab11-f1b4bd149891}} , the distance {{formula:5112fd82-8f93-46d7-92e8-4ee00ca0e753}} is set to 200 and the transmit power ranges from 10dBm to 30dBm.
We consider the following three benchmarks for comparison:
1) ADMM-based solution {{cite:1a16311f9381a0e24e4c935ef710f527a826ceea}}.
2) Random Generalized: {{formula:602392a1-f430-4f6e-86b2-ad774e73ff79}} phase shifts {{formula:0064ba03-2f01-4ba1-bdca-512ad108e875}} are randomly selected from a uniform distribution {{formula:728e08fa-15da-4fa7-8c6d-92957bcd2bc9}} .
3) Without IRS: the conventional fully digital MIMO benchmark.
4) AO-based solution: the AO-based solution proposed in {{cite:8ace9134f879146f21f927f29e2c91603c3b9926}}.
We observe that our proposed iterative solution imposes much lower complexity whilst having higher spectrum efficiency compared with SDR-based solution.
This is because the SDR-based solution only extract the optimal phases and the modulus of IRS element are set to 1 compulsively.
By contrast, in the proposed iterative solution, the phase shift of each IRS element is obtained in a one-by-one manner by maximizing the OF (18a).
During the iteration, the phase shift of each IRS element is derived under the constant-modulus constraint.
The iterative solution does not need the process of phase extraction, which is used in the SDR-based solution and inevitably deteriorates the spectrum efficiency.
Therefore, the proposed iterative solution behaves better than the SDR-based solution.
Our proposed iterative solution shows a similar spectrum efficiency performance compared to AO-based solution, whilst having a lower computational complexity.
We can also observe that the iterative solution has a slightly higher spectrum efficiency than ADMM-based solution, and the computational complexity is lower when the number of IRS elements is large.
Compared to the traditional MIMO systems, the spectrum efficiency gain of random generalized solution is marginal.
However, the IRS-assisted MIMO systems have an increased spectrum efficiency after adopting the proposed low-complexity iterative solution.
| r | fe6997dabe431843235415281a82df3f |
GCN {{cite:a796c997c68e85974ecae42750a438b2b271d2d3}} is the first order approximation to spectral GNN model.
GraphSAGE {{cite:9dd9f428ee1b094f8f98a32a7029156cb2307244}} is the first type of GNN that introduces sampling technique, enabling a good model generalisation on unseen nodes.
GPS {{cite:ba0c0264f8f5c6422d68757080803e9daf633f3e}} introduces an adaptive sampling technique, reporting good results on graph representation learning.
GAT {{cite:9cd22e76c718b87eff94bec063178310d5d6b445}} is the first work that incorporates the attention mechanism in GNN, computing attention scores for all connected node pairs.
| m | 022d35eb59dbfa41462bff7d86d5fb51 |
We compare with the following baselines. The unsupervised methods include DB-SCAN {{cite:dfaba090531236dfe6edff1f590c2fcc818ae813}}, ARO {{cite:00e4641cb7cb4531cab1af5af5c5b62ebf3d9324}}, HAC {{cite:5eca603150af66dfeea71a90e1ba78d83d630a1a}}, H-DBSCAN {{cite:cd29840402cd5ffa8a9586897bad9af3c7cc20dc}}, Graclus {{cite:ff34a82507ac4e997dd05dda5c7ffed60694a9dd}} and FINCH {{cite:f0c8307093374902d9b41d3e73e80efd960a148a}}, where the latter four are hierarchical baselines.
The supervised baselines include L-GCN {{cite:dcff50dcf29f7727d26fc03eec433b73f42a5e5a}}, GCN-V {{cite:8840bc85f7eb4f77df7745342ef2aed2f1ba3051}} and GCN-E {{cite:8840bc85f7eb4f77df7745342ef2aed2f1ba3051}}. Hyperparameters for the baselines are tuned to report their best performances respectively. For example, we tune the optimal MinPts parameter for H-DBSCAN. Supervised GNN baselines have their best parameters tuned with the validation sets (part of the meta-training set), e.g., we tune the optimal {{formula:98f606cd-c70e-4f0c-b654-a46a3c4abeb6}} -NN {{formula:5f124eb0-b9f0-4bdb-9d61-ec7547acebad}} and {{formula:10e172e9-42c2-493b-a987-c16aa9a970ac}} parameters for GCN-V/E.
| r | e0266bedbc64efd7dbc7901d2e5eb6bb |
In Table REF are summarized the results of the baseline networks, Efficient-CapsNet and some capsule-based methodologies present in literature. As for the MNIST dataset, also for smallNORB is evident the gap between classical CNN and capsule-based networks. Moreover, again our methodology has comparable results with all other similar methodologies but with half of the parameters. It achieves a mean accuracy of 0.974 with a min value of 0.97 and a max one of 0.983. Finally, as before we exploit the 30 networks, trained for statistical evidence, to produce an ensemble prediction. We select only the two networks with the lowest test error, and we adopt for both a 40 patch prediction {{cite:0f8618f54d7b97befdc8f9094af9097a0888bf1e}} before averaging their results. We obtain a test accuracy of 1.23, setting a new state-of-the-art result for this dataset.
| r | 2781eeef6e4d60c617f62a53848a6253 |
Therefore, for a system driven by a stochastic flow map of order {{formula:e4054a94-3e8f-4b67-8ec7-e0962f663aa8}} , the maximum number of basis vectors to use in a simulation with FSC is bounded from above by {{formula:c2fcbaec-3b53-4d68-85da-de2d484a5f1c}} .
Hence, regardless of the dimensionality of the random space, the probability information of the system's state can be completely captured in {{formula:e403db73-6712-49ac-b613-e681e966fe54}} if {{formula:0d89ed18-47c6-4a98-8f18-6604df9f9e8d}} .
It is for this reason that our FSC scheme is superior in terms of efficiency in comparison to mTD-gPC which uses a combination of full and total-order tensor products to construct a suitable basis for {{formula:2a790dde-254c-42ff-9c98-dd2089f6507e}} around {{formula:4243e4f4-273d-4865-99a7-45ba9066bffc}} .
We emphasize, however, that the FSC scheme does not address by itself the curse of dimensionality at the random-space level, since we still have the issue that the bigger the random space is ({{formula:60018291-9efe-484f-8657-258520d5663e}} ), the more difficult it is to compute the inner products accurately in (REF ) and (REF ).
This is still an open area of research and there are several approaches available in the literature for dealing with this issue {{cite:bf2846814397218909a0be7434043c78ae9defb2}}, {{cite:5e281d7f85e716d7144c13726a04b509ed120f1d}}, {{cite:e6022ef08e5324878d9ab9c0b7b50a90dd9aabed}}, {{cite:11c14cbf5bd832b692df527f926df92da0435644}}, {{cite:ba0f802b86790b55fa57e634ba63ffdc37f87efe}}.
| m | c397b79e3d525d0286b1c2173bd71c44 |
According to {{cite:f7871732bef1c43565cfb2554cb94a74076fee96}}, any straight line system is Zykov-planar, see also {{cite:cb3d6a198339c9215b4e0b5ed5d91a319a70f023}}. Zykov proposed to represent the lines of a set system by a subset of the faces of a planar map on {{formula:1ad0e212-9a92-439a-a873-31d7439fe91e}} , i.e., a set system {{formula:3f94067e-93c3-4d15-a78d-016a88d0fb67}} is Zykov-planar if there exists a planar graph {{formula:354883db-fd88-45c0-8f33-9f6c41083b14}} (not necessarily a simple graph) such that {{formula:e855ee9c-b366-402b-8ac7-22ec92516953}} and {{formula:241f77e5-c81a-4f66-bfb8-8538104bcd70}} can be drawn in the plane with faces of {{formula:ef15d5b8-58aa-4ed1-900b-2736aac533bc}} two-colored (say red and blue) so that there exists a bijection between the red faces of {{formula:001cb995-2327-4ffe-8230-6dfeef01fc4a}} and the subsets of {{formula:c338ac10-1ffc-4848-98a2-24e5acd51327}} such that a point {{formula:b44b2aab-e66b-4681-af66-6397cb5db5f5}} is incident with a red face if and only if it is incident with the corresponding subset. Walsh in {{cite:a62bfdbce06d2569c7e9d96b0e1dfddbfda1c473}} shown the Zykov's definition is equivalent to the following: A set system {{formula:eaae342f-16d6-4551-a2af-a08af09b20f4}} is Zykov-planar if and only if the Levi graph {{formula:20a0ff64-9c78-465c-8726-cfc86c1e794f}} is planar. It is well known for any planar graph {{formula:07d8248f-d9c2-48ff-b33a-44db1b2fdb23}} the size of {{formula:d10e1f84-38e6-4162-91af-062f63536d75}} , {{formula:c32417b9-62ef-4c7c-a0ff-50d927a3474a}} , is upper bounded by {{formula:d85afbd0-2da2-402f-8ba8-0a91f1b2e51c}} (see for example {{cite:39500659415324bc3a492f23aa8625331090af3b}}), where {{formula:652b12e5-d114-4f1a-a2cf-39d93cf135b1}} is the girth of {{formula:7ed222ca-d75a-4424-844f-be35f124e975}} (the length of a shortest cycle contained in the graph {{formula:10ce0c09-c588-43ec-ad9f-803c5186404a}} ).
| r | 08b628a24d95122cb993d6c27b948694 |
Zhu et al. {{cite:f04f59f2a0c2242405ef998a0ff87ba6f1443054}} firstly propose to use deep learning for feature matching and deep reinforcement learning for policy prediction.
The proposed framework allows the agent to better generalize.
And they propose to train navigation model in a simulated environment for the sampling efficiency of data.
Sequentially, Successor Representation (SR) {{cite:7e2f1628a6d5f4e12cdebe35d249205e9e1c1b8e}} is proposed to enable the agent to interact with objects.
This framework takes the states of objects and a discrete description of the
scene into consideration.
It encodes these semantic information and concatenate with the visual representation as in {{cite:f04f59f2a0c2242405ef998a0ff87ba6f1443054}}.
Different from {{cite:f04f59f2a0c2242405ef998a0ff87ba6f1443054}} that uses reinforcement only to learn a policy predictor, Successor Representation model bootstraps reinforcement learning with imitation learning.
Wu et al. {{cite:18dff59f15da2d2386d32214708a08772d701ae7}} builds an agent that is able to generalize to unseen scenes.
Since the navigation agent receives a partial observation as the input, this work advocates to introduce an LSTM layer to encode historical information.
By ablating different RL algorithms, this work proves that A3C {{cite:06f7131ef31f064a32d563c8e623bbc6eafcb466}} outperforms DDPG {{cite:24951c1aada6781eb86f8c2ccc8e92f4449a753f}} in navigation task.
The model is built upon House3D simulator {{cite:18dff59f15da2d2386d32214708a08772d701ae7}} that provides 45,622 human designed scene with segmentation annotation.
The model learned from semantic mask outperforms which learned from RGB inputs.
It indicates that semantic information is much more important than pure visual inputs.
However, the visual images in House3D are rendered by computer graphic, which are largely different from the observations from the real-world environment.
Li et al. {{cite:52e521417cb56b47c5aa1e0785efd882d3232f89}} propose a end-to-end model based on Q-learning that learns viewpoint invariant and target invariant visual servoing for local mobile
robot navigation.
| m | a8677c93f609a0e67f8b6d602612c40f |
Our work focuses on the representation of single-relation graphs, which is a different research topic with multi-relational graph embeddings or knowledge graph embeddings, so it is hard to find an appropriate experimental setting to compare them. Nevertheless, to address the concerns of comparison with the trainable curvature method, here we evaluate AttH {{cite:aa41dc76cb82a48c6c73f8ff22008f466a56e762}} on the single-relation taxonomy link prediction task. We tune the hyperparameters on the validation set and report the mean results over 5 running executions.
{{table:699f72c1-2437-47d8-acf2-ed175ceec061}}{{table:77b0682e-6f90-4549-b112-63953a3035b8}} | m | a94594ed0288004daf44f1eeabf32868 |
In order to define complexity we have used a measure that was developed in particular for Gaussian states and that is related to the {{formula:0ab037ad-e526-4d26-bf98-1a45f2cfcaeb}} symmetry of the associated quantum mechanics {{cite:2172d333097334faff032890a64f2f596d50a865}}, {{cite:179cd624abf5f99de3e07995f3162d3a299a856d}}. This measure is conceptually appealing, as it provides a link with hyperbolic geometry — see Fig. REF for a useful visual illustration of the evolution of cosmological correlations (using the same numerical models as in Fig. REF ). Moreover, the hyperbolic measure has a structure that is sensitive to both amplification and squeezing, which are precisely the features that are important for early universe models. A comparison with another popular measure is provided in appendix . It will be important to see how the present study can be generalised to non-Gaussian corrections, which are bound to play a significant role in future observations.
| d | 85658018dc8ccbe5e8ded6c3d1748700 |
Finally, we remark that other activation functions can be handled in a similar manner by analyzing the mass matrix {{formula:dd54c9f5-56da-49ac-9e8a-79ff80aadf54}} . For instance, a sinusoidal activation function results in a singular matrix (since the set {{formula:6e515f8e-cbd8-4d0f-90e2-e08be71db262}} lies in a two-dimensional linear space) and we have also experimentally observed that such networks also exhibit a spectral bias (see the appendix). Thus, new ideas are required to explain the recent success of sinusoidal representation networks {{cite:ab75d5ad52e68c73e9a7e3c44b99c0303cd4e263}}.
| d | 71fa478af642cb714c11736128d1b267 |
The availability of radial velocities for many Hipparcos stars has allowed the membership of OB associations to be determined in 6-dimensional position and velocity space. This can be achieved using a model for the spatial and kinematic distribution of the group, such as a 6-dimensional Gaussian or a mixture of Gaussians if one or more subgroups are known. {{cite:2fe695090a202e3211d39a9c3b66fdb1d4435885}} applied such a method to re-establish the membership of Sco-Cen using linear models in various dimensions of 6-dimensional space and calculating membership probabilities for individual sources.
| m | e21243a4cf881a4bcf706624ecfcdb3e |
Our results provide a nice illustration of the efficiency of the
twistor double copy, but are of interest in their own right. It is
often the case that a single copy of a given gravity solution can be
found, but not easily interpreted. A canonical case of this is the
single copy of the Kerr black hole, first formally identified in
ref. {{cite:f24a0a2827eead610df8aabd030037479b50dbf0}}, and denoted as {{formula:4902bf1d-8fdc-49a2-9dcb-3ce0828ea94e}} in
subsequent literature (see
e.g. refs. {{cite:58ad52891b8dedd644aab384dd53dcd5002e6a5c}}, {{cite:19f0d7f987e8fb779578f3bcbe6356b42846b776}}, {{cite:f6dff811427c2dc72290d5cf90b9b7b95379bc62}}). It
is known that this solution occurs by replacing the source for the
Kerr black hole (a rotating disk of mass) with a similar gauge theory
source (a rotating disk of charge). However, the nature of the sources
is subtly different in the two theories {{cite:f24a0a2827eead610df8aabd030037479b50dbf0}}, such
that it is not clear what impact this has on the fields
themselves. Multipole moments, however, allow us to fully characterise
the structure of fields in a gauge-invariant way. Thus, the fact that
the multipole moments for the Kerr and {{formula:b28cdb08-1453-44b5-957e-a9aba7d8be41}} solutions are
essentially identical tells us a great deal of information about how
to physically interpret the single copy, by recycling our intuition
gathered from the Kerr black hole. Furthermore, the fact that our
results apply for any type D vacuum solution makes this a rather
powerful statement, that may well help in interpreting and extending
the double copy in future.
| d | 832456d9a39dd74adbcb81b00f5a0b29 |
Watermarking has been applied for digital media ownership verification by embedding digital watermarks into the cover media to be protected. The owner is able to prove media ownership by extracting the watermark from it. Inspired by this, some works have been proposed to protect the IPR of DNN models by means of watermarking {{cite:54e9457a14e45fef0d0ab44e0002876f30a22436}}, {{cite:6f0a92933a58979d1bbe3c21989d08847e33c1fb}}, {{cite:7950015d40f0c642f6ba06d41b9a18741d2466ea}}. Different from media watermarking, in DNN watermarking, the watermark is directly or indirectly embedded into the model parameters. Based on the information required for watermark extraction, DNN watermarking methods can be divided into two categories, generally referred to as white-box and black-box watermarking.
In white-box DNN watermarking, access to the internal parameters of the model is required for watermark extraction. The watermark is embedded into the weights or the activations of the network. Embedding is typically performed by defining a proper loss function for the optimization, that includes a watermark loss term {{cite:54e9457a14e45fef0d0ab44e0002876f30a22436}}, {{cite:54a3ced013db81b002a00519c157d90defb664ea}}, {{cite:ea2dd7ac5fdef64aa2b878d5b8d747da06af4158}}.
However, many DNN applications are provided according to the Machine Learning as a Service paradigm, whereby only an Application Programming Interface (API) is available.
In this case, one can not access the internal parameters of the model to extract the watermark.
This limits the practicability of white-box DNN watermarking.
In black-box DNN watermarking, the watermark is read by checking the output of the network in correspondence to specific triggering signals, thus avoiding the need to access the internal parameters of the model {{cite:7950015d40f0c642f6ba06d41b9a18741d2466ea}}.
| i | 8d9c744740f1dc6a33b7e646d4e8febc |
To capture motion information, typically point trajectories are either formed by tracked image features or dense optical flow.
Then trajectories sharing similar motion characteristics are grouped into coherent motion clusters describing the motion of a particular object {{cite:a4bf32785a1c0cdbc36c2fffbac26078e93c6b00}}, {{cite:b1d3a629d016c8989edaa601908792ec9dfde2db}}, {{cite:72f84e025f7a79a6eac8de84da1cafa907532eca}}, {{cite:d29697adc729b74d32a7eec4e3ac9ebd12e288fb}}, {{cite:611a65943fa403877eec440cf342f8ece2e08f56}}, {{cite:1803feb4258bc129bf95c7792066d8c18f9869cd}}, {{cite:cc02f7ab718ece4f780e548b134426e456ff5dfe}}, {{cite:fdcef91ed6694de64b455b6c15c08a53a26dd421}}.
| m | e05de440704a57e433a55809d9f98551 |
MOT16/17.
MOT16 and MOT17 {{cite:53b153f0d0a1895398308c48a81e853b4a1096c4}} contain the same 14 videos for pedestrians tracking.
MOT17 has more accurate ground truth annotations compared to MOT16 dataset.
MOT17 also evaluates the effect of object detection quality on trackers, by providing three pretrained object detectors using DPM {{cite:87b9484807ee135a68d07f58546b8f349fbf9fad}}, Faster-RCNN {{cite:7decf6495b7772e1d735efccf429c95cd709cbc4}} and SDP {{cite:2a90d155f8b3722ec448dab93a481950a8b6ba04}}.
We report the performance and comparisons with the state-of-the-art methods on the private detection track of MOT16 in Tab. REF .
Our approach outperforms all other published trackers using the private detector in both IDF1 and MOTA metrics.
| r | eb1ea626aa69754d981d0d7a042e6ee1 |
Thanks to the recursion shown in lemma:approx descent, we can follow a standard analysis (cf. {{cite:ebd6bd9ffe2f768faef2f45d3ada917ab412951d}}, {{cite:c37eb5b64baf816d569dcfc7828ad2199cbfe208}}) to establish weak convergence of algo:gm-shuff. Our results in Prop:convergence complement and extend the (mostly non-asymptotic) results derived in {{cite:9bd3206d14bfb82211bee82b4c2ae8bf8691e329}}, {{cite:aa9d54c6d1c24a5fa95dbea8aef894c9577b498c}}.
| r | a7c51029888797c2d6ec61b72312b4d1 |
Case 1: stochastic differential equation (SDE) {{cite:4ee1714a124fd2121a6cf8cd4ae1f921b0e59057}}, {{cite:08202e3ad7a26b807d24b9f36f13afefb67bb822}}, {{cite:7e4f33f3c37b63129ab9a91b8a35301bb8d947b4}};
Case 2: random elliptic equation {{cite:acd1295474e4c902cb3b7c2d3b19f6499b81c2f9}}, {{cite:983e6b23fd7e5d83e324d7f5f82b10e3e40c940f}};
Case 3: particle method for transport equations {{cite:b0e8843dbb34a803fc2f8d12ed5a773376345900}};
Case 4: scalar advection equation with random time dependent velocity {{formula:2c74af50-9d8f-4b83-8c2a-e85017446cfe}} , see § ,
4.1, {{formula:95190ee4-d6b7-4d9a-97f6-e2be8b7b396b}} is piecewise constant in finite number of time intervals,
4.2, {{formula:53705726-59b1-46f1-9235-12918d6cb8c1}} is uniform white noise in time;
Case 5: Euler equations with random time dependent adiabatic constant {{formula:49776faf-c269-4428-b261-2318830a5482}} , see § REF ,
5.1, {{formula:e913da2e-cf4d-4aca-a5d0-02e1f4642c01}} is piecewise constant in finite number of time intervals,
5.2, {{formula:32b57578-3af8-4b8c-971e-a5cdf1c377d0}} is uniform white noise in time;
Case 6: shallow water equation with random bottom topography {{formula:de0b0abd-8b41-467a-8d39-7f8a55bc39ae}} , see § REF ,
6.1, {{formula:72b1c41a-60f2-452b-9423-369f15ec7f43}} has a finite number of random parameters,
6.2, {{formula:07724830-15ac-4ce5-949a-8fbf4247a198}} has uniform white noise parameters;
Case 7: random choice method for deterministic Jin-Xin model, see § ,
7.1, semi-random case, only use random choice for the relaxation step,
7.2, fully-random case, use random choice for both the convection and the relaxation steps.
{{table:08135d6c-abcd-44b5-a8d2-60123666a8bd}} | i | a6170fd3c04d9c0168cd689dbfb9b35f |
where {{formula:430b1dcf-7552-4e6f-a35e-fd90fe88570d}} 's are independent random variables each of which is following the standard exponential distribution with the mean {{formula:eabbdd2a-5c3c-471e-a1a2-a210d9cdfd72}} ; see for example, Theorem 2.2 in {{cite:87dcd73fe4662fb6c0d672a8b85d8b44bdb5ab4c}}. Hence,
{{formula:24dd3f8d-4b26-4630-82bf-db80036ef60d}}
| r | b6121511908dbb036d65336c41d021c5 |
We believe this work on multi-agent communication is of importance to our society for two reasons. First, it extends a computational framework under which scientific inquiries concerning language acquisition, language evolution, and social learning can be made. Second, unlike works in which agents can only learn latent representations of other agents through passive observations {{cite:dbbea20861ab4bac56d0a11c8c58167fd5b43465}}, {{cite:2a4a8f19566b824acc7e2fc389660ca6639460c5}}, it opens up new ways for artificial learning agents to improve their coordination and cooperative skills, increasing their reliability and usability when deployed to real-world tasks and interacting with humans.
| d | cb5f40a1f74afee96dac5b574ea96999 |
Note that in order to improve the coverage of speech data, SSAST {{cite:e75df926a7d1f11a8077f6afcfb482518d98435b}} and MAE-AST {{cite:8b9725d4e5a0843c91eef92f07a5676ed507a0dc}} further used the Librispeech {{cite:c78cb0e7eee85a9945621f301537c6db5a6b6094}} dataset, which has around 1,000 hours of speech. Despite that we only pretrained ASiT on AudioSet-2M dataset, we outperform the aforementioned methods on the SC-V1 and SC-V2 speech tasks with a large margin as shown in Table REF and obtained on par performance on the SID dataset, showing the generalisability of the proposed self-supervised framework.
| r | da036c4a2a3e92eafd43d29a34f8528c |
Previous work shows that metric neural representations of environments form when an RNN is optimised to predict agent position from agent velocity {{cite:b32377a1974abc5bc47ec1f04b8512c55c0e53c7}}, {{cite:085a351caba3f3cda64f4a0612aff2364eaba21c}} and non-metric representations form when an RNN is trained to predict future sensory events given direction of movement {{cite:7c84d09f21dcf8cffe5e70a2b3cbf442e4afa411}}. When training our model we do not provide the LSTM network with any explicit information about location or direction, it only receives sensory information. This is similar to the purely contextual input received by the model pre-trained by {{cite:8de9f1253d9f66fe06b444bf73994aa7e62f395d}} where no velocity input is given, however, the network used by these authors is still trained on position and landmark prediction in a supervised way.
| d | 06fb45331fa31b419900f1286049f64e |
In the precipitation scenario {{cite:bc7aebcf0304214227a1845836dbbccff29ccc0e}} for AGN feeding and feedback, cool clouds condense and can form stars or fuel AGN feedback when the cooling time ({{formula:9bf137dd-b88e-438e-a3ef-eb90a8f6fcee}} ) is significantly shorter than the timescale for the cloud to fall to the center of the cluster potential ({{formula:7cb862b1-4b91-4028-9d74-bb57b34cb206}} ). The latter timescale is a proxy for the mixing time of the cooling gas. The threshold for thermal instability is usually taken to be {{formula:3dc12039-1ab0-4b45-82df-07054aa0ac54}} {{cite:bc7aebcf0304214227a1845836dbbccff29ccc0e}}, {{cite:a6a90ce34fe11b9bdbadae81c51e5d3cd5616102}}, but this depends on the medium's susceptibility to condensation, the slope of the entropy profile, the amount of turbulence, and the amplitude of entropy perturbation {{cite:283d49a1e14ae455900011cc5b8da5208df3f385}}, {{cite:1b4626ad0d08b5860c1738389f282cc41f8efb12}}.
If a dense, low-entropy core is perturbed from the center of the gravitational potential, the timescale for mixing is increased while the cooling time remains constant, leading to an enhancement in thermal instabilities. Further, the separation of the low-entropy gas from the direct influence of the central AGN could prevent t{{formula:dbf6454b-c729-49c7-9814-ed17679dbd76}} from increasing. This displacement of low-entropy gas from the central massive galaxy would happen naturally during a merger (i.e., in CHIPS1911+4455). The X-ray data in Fig. REF support this scenario, depicting a disturbed cool core elongated in the north-south direction. While the bulk of the cool, star-forming gas extends along a southern-pointing filament, there is a fainter blue filament that connects the central BCG to the more northern X-ray peak. This suggests that the northern X-ray peak might contain low-entropy gas that is dislodged from the location of the BCG.
The existence of this system – a dynamically active but rapidly cooling core – provides evidence that mergers may stimulate star formation and enhance cooling. This process would be especially relevant in the distant universe when mergers were more common compared to present time {{cite:b925df92c92a6f5a231c7fc4a114e91446de430d}}.
| d | b61d2934eb5ef4592985fc6445b74758 |
It is well-known {{cite:57cafd6577aae5a7e0bdaca712e55883b499b97e}}, {{cite:ac3231ea527dafa64f771489d816a3cc6e6b534d}}, {{cite:46bb32b8db402cd6e0fa04e6c5eecef516fffe5f}}, {{cite:d1478e6c7612262a044cd85b86060c5af1a35735}} that for a suitable time evolution of
the AKNS scattering data the potential {{formula:b7108a1a-6104-4f43-8b1f-eaac1b0f0a74}} satisfies the matrix NLS
equation
{{formula:dc1a0874-2561-44ab-b2ff-d6f49f0f5aaa}}
| i | e4711a5878b999b15f3f622ada0ca6bf |
We utilize the A3C as the fundamental algorithm combing with the multiagent system to develop our learning mechanism. The A3C algorithm, proposed by Google’s DeepMind team{{cite:f91089327cdbe412ce36657913fc2f6e54f9d6e2}}, uses an actor-critic neural network architecture. It is a multi-process method including multiagents to learn parallelly and then feedback to the primary process. It serves the specific agent as our learning purpose in the simulation multiagent system. Figure.REF shows the interaction structure and process mechanism.
| r | e66070fa3fdea5581091e07d19ec091e |
Connection with integrable systems is understood better by considering a discrete Fourier transform of the instanton partition function at {{formula:eaf7d3ff-880a-451e-96a0-3cfe47db936a}} {{cite:eb28e1122051464a4351788472746fb5f5079a69}} with regard to the filling fraction, which is the Coulomb moduliThe generating function of the {{formula:9d5b01d2-94be-45c5-8a28-5e0b348ca800}} -deformed matrix model has been considered in {{cite:593b804dcde8bb970f0b18c27055e1bb8a97bab1}}..
Connection between the tau function of Painlevé equations and the generating function of the instanton partition function of four dimensional {{formula:b7038dd4-1cca-45ac-9d0e-efa638bc815b}} {{formula:e7dc2109-1eba-44dc-9d6d-81772128da12}} gauge theory with {{formula:5852d7be-02e1-4873-abee-912a26cd8fff}} and that of Argyres-Douglas (AD) type theories {{cite:933966794f1d2af026d4c4c38f7361ad80acf040}} obtained in {{cite:c4cd21d1ed95d172b1073f48238c466f3fbb4135}}, {{cite:b8abce10c57594e75296967f2da9063014b26cec}} References in the higher rank case include {{cite:8df48f5bedb7a9aa8dedacf4f0418b8acd8036ee}}, {{cite:05796bffd299913b2a634c2aea8b03e6fa213234}}, {{cite:c9070ad0f73261282c18ca9f7e036deae1117b5a}}. has been pointed out in {{cite:6601f69f1db3b956eec263d5b8667629a869813a}}, {{cite:beabd044ed5c6f708e3586295288798d7884e9e8}}, {{cite:6dc2ec5b70e29f7cabd3015bef8c1a0ed6c219d1}}, {{cite:33cd1f4f36762b5ea4bdc64b6172de1d2147fffe}}, {{cite:1c26be5e4194558589eb2fa8084e808dc2c987dc}}.
Some of these cases can be derived by using matrix models {{cite:6b52502eb39f8e6d96440b18b65831aad5b64b9b}}, {{cite:26b305e6769ad9f37ae5cd991afd71df9a594b07}}, {{cite:4668aa2b01982b1edd5199aa6b394935aab9bf63}}.
In {{cite:6b52502eb39f8e6d96440b18b65831aad5b64b9b}}, {{cite:26b305e6769ad9f37ae5cd991afd71df9a594b07}}, {{cite:7df79cec131c89c8266490ff6f6cee92f40b0b67}}, it was shown that in the case of two flavors can be represented by the unitary matrix model of potential {{formula:bc47a6f9-15d5-4378-9280-ddc80bebcb40}} type.
This is a Gross-Witten-Wadia (GWW) model {{cite:136a60728dc3790dc899cfb133be14dbf4475427}}, {{cite:b4c50aa96432899cc1472e9cbd29c7cf9332ed6a}}, {{cite:78cf125c8f6322d78b966a03e374a6434b99bf7b}} with a logarithmic potential.
The string equations, which are a set of difference equations arising from the recursion relations among orthogonal polynomials, have been shown to be the alternate discrete Painlevé II equations (alt-dPII)It is also called the discrete Painlevé equation {{formula:d5a7db06-9c33-4db8-85cb-8da1a6a1b70f}} -{{formula:1d653fd3-5bb1-4b38-bd3a-61d82dcd8a92}} in {{cite:784d60f905c5ebb14b641824cb83ca9421b64a70}}..
We have also shown that the partition function of this model is the tau function of alt-dPII equation which is closely related to the Painlevé {{formula:2b193311-24ba-4dce-8d9a-a1429b25aba1}} equation.
Using the partition function of this model, we have constructed the tau function of Painlevé {{formula:c97085bc-f1a1-41d9-983e-2f22a20f135c}} equation.
By taking the double scaling limit, alt-dPII equation turns into Painlevé II equation with accessory parameterFor an alternative approach based on the genus expansion of two-cut Hermitian cubic model, see {{cite:f38294496c02f82a133867f7e053e512252f6528}}..
| i | d34c68cf7df316277023a8760bda6c21 |
Several definitions of intelligence have emerged in machine learning literature in recent years {{cite:5df0b2d6ceb22bf65156c2119c3b7a52560ba7ee}}, {{cite:aba170a22d97321666c180956dbb6617ccdddfc8}}. Although many of these differ in particularities, one consistent requirement is that an intelligent agent must have the capacity to accumulate and maintain task proficiency across experiences {{cite:82ad9d275a07e0ae8d348998874ee1bc70014eaf}}, {{cite:41eefedbb37c26c7763fd9bbd22b8e1a0adb5a21}}. In contrast to biological agents, existing neural network approaches have proved lacking in this regard, with sequential task learning often resulting in catastrophic forgetting of previously encountered tasks {{cite:5fc8b31c3c6da568562624c80c1d32d945b0e7bb}}, {{cite:f3a3c0c2befd6574bf9feb8a1235f4056a314aec}}, {{cite:368f921144a2a1cce5c4ea38422b9d2322b97ec2}}. A proliferation of research seeking to alleviate the catastrophic forgetting problem has emerged in recent years, motivated by the requirement for machine learning pipelines to accumulate and analyse vast data streams in real-time {{cite:43871235822fd7daaefc9e3dd2cf0cef06c89dc6}}, {{cite:ca2dd75882630f9945c1ff7fc3bc954a39ab07e9}}. Despite significant progress being made through such research, both in theory and application, the sub-field of continual learning research is vast, and therefore benefits from clarification and unifying critical appraisal. Simple categorisation of these approaches according to network architecture, regularisation, and training paradigm proves useful in structuring the literature of this increasingly important sub-field. Furthermore, many existing approaches to alleviating catastrophic forgetting in neural networks draw inspiration from neuroscience {{cite:41eefedbb37c26c7763fd9bbd22b8e1a0adb5a21}}. In this review, both of these issues will be addressed, providing a broad critical appraisal of current approaches to continual learning, while interrogating the extent to which insight might be provided by the rich literature of learning and memory in neuroscience.
| i | 305c72cfe4c73371962b227d1339f574 |
An interesting question is whether FL can achieve the same or similar prediction results as CL. If yes, what are the conditions (e.g., the the dataset's size)? Otherwise, what are the guidelines on when we can use FL in place of CL? As our study is limited to the Bosch dataset from the manufacturing industry, we have conducted a literature investigation to answer this question. According to existing studies {{cite:febd0da967fc60b46e78660d51e92e7ca34f9520}}, {{cite:e81c710cae8006e10734949075f9be0ab2c2f2b8}}, FL's effect is mainly related to the data distribution and data amount. Two important facts are summarized as follows.
| d | d5970efabff9846084168c458bbbd592 |
At step {{formula:eff549b1-01b9-40b7-aa42-506723f1ade6}} , the residual can be upper bounded by a constant times squared norm of the gradient at point {{formula:5f66f4d7-7aa1-4c0f-9e29-69ee53a2b98e}} . When using recursively this upper bound, if {{formula:69cd8382-dfe2-4e0e-a7b3-df4c8a1fe3cc}} , then these terms cancel out. This is equivalent to {{formula:7a1d690a-a53f-45ad-8b2b-c0d152900413}} . It is natural to chose {{formula:c416ca54-aacc-4f3b-be77-7c2e19bff4fa}} .
The variance is then upper bounded by {{formula:bbcb2c9d-d211-4ca3-add2-29f1eabcb752}} . This is similar to the limit variance in simple compression {{cite:d95330dcc79337e0d72d66e650ba59b88495607b}} and lower than the variance for previous algorithms using double compression for which the variance scales quadratically with the compression constants: for Dore, see Corollary 1 in {{cite:079265a2e1b9bb22b1a764ede361c6a93d875d9d}} (with {{formula:37915dfc-0c48-4016-99b5-aef87995f823}} , for Artemis see Table 2 and Th. 3 point 2 in {{cite:8259fdc61503ee8f5a8858ae29a3b36df567955d}}. Especially this last theorem shows that the limit variance for Dore and Artemis type algorithms is provably larger than {{formula:5efacc0d-1a8c-417d-917f-d347a7fbb323}} . Also note that the result cannot be compared to the analysis in {{cite:7abc592bd87d195a8c4c6d061300d0bb4498fb48}}, who assumes a bounded magnitude for the errors on the compression (Assumption 1.3).
The key difference is that the main iterate does not suffer from the downlink compression. As a result, the impact of {{formula:73f13e4d-aef1-4c35-9bde-4b0e9a8f9683}} is attenuated by a factor {{formula:d6f9dafd-7ade-4042-a1ee-0f28281e18f2}} and thus vanishes.
The bound is in fact proved conditionally to {{formula:46ec9969-2c77-4fb6-bb6b-502cff6c13f6}} , recursive conditioning is required to propagate the inequality. We carefully handle conditioning in the proofs.
| r | a29a2e1049fa4b0291233ea63e2347ca |
Later, Gualtieri {{cite:138c0289406363c4a737f24091da20a930b534a0}} gave a natural description of this geometry using the language of Hitchin's generalized complex structures {{cite:9a703f16496d7dc16f8b327a58bf95aad96f72e0}}, in particular in terms of a pair of generalized complex structures {{formula:39f7cf95-72da-4e20-b0d7-35e6e6d9be7a}} satisfying some natural conditions (cf. §REF ). A fundamental question is to understand the degrees of freedom, moduli, and topology of the space of generalized Kähler structures on a given smooth manifold.
| i | 9d025377ed497af8f8129e332cbc8950 |
Functional RG (renormalization group) equation {{cite:323c56bd63a518dead39c9fbb8d61c65d849307a}}, {{cite:15b8c2ffff237a8a64420bb28f1f0ed8c3f1858d}}, {{cite:ee4142136787ced0347ceabbb707a2c22fd66d0b}}, {{cite:6b36d1374d86a85a4e286610f8ba567c7b904fa7}}, {{cite:a84456a1cc48438c6d3a735db5469580658ef0b4}}, {{cite:3915d18d16644267f610fb9efb197841d7a824ee}} studies, first introduced by Wilson and Wegner many years ago {{cite:323c56bd63a518dead39c9fbb8d61c65d849307a}}, {{cite:15b8c2ffff237a8a64420bb28f1f0ed8c3f1858d}} (and called by them the “exact RG”), have flourished into a powerful approach for investigating this possibility.
These equations describe the flow of the Wilsonian effective action for some quantum field theory, under changes in an effective cutoff scale {{formula:29b54c33-721b-4712-8bd6-c387bb056a37}} .
The asymptotic safety literature uses almost exclusively the flow equation for {{formula:86184954-41cd-489f-8932-81c820bc31c8}} which is, modulo minor details, the Legendre effective action (the generator of one-particle irreducible diagrams) cut off in the infrared by {{formula:6db2974e-12e3-4519-8c20-8a24b1ea359d}} . It was also formulated long ago {{cite:6b36d1374d86a85a4e286610f8ba567c7b904fa7}} (in the sharp cutoff limit) and then rediscovered for smooth cutoffs much later in refs. {{cite:a84456a1cc48438c6d3a735db5469580658ef0b4}}, {{cite:3915d18d16644267f610fb9efb197841d7a824ee}}. Following ref. {{cite:a84456a1cc48438c6d3a735db5469580658ef0b4}}, {{formula:90142d95-f4dc-4190-9a11-91b46d972f69}} is sometimes called the “effective average action”, however in this chapter it will simply be called an effective action.
| i | 85f9564fe21575ae6faa230abe01a019 |
These higher derivative theories suffer from
the massive (negative metric) ghost problem in perturbative regime,
although
there have been many proposals for possible
ways out (See e.g.,
Ref.{{cite:e7c51a4fbecf0a30267f26b7a82e8b60a91f3a98}}
for the review).
This ghost problem is, however, out of the scope of this paper.
| i | 4f297c6380c2d9fd4dd4c027e66375bd |
The second comment is on the entropy excesses on group scales (the X-ray-emitting gas has higher entropies in groups than in clusters when all entropies are rescaled to the virial one; {{cite:3851691ba9238daa454025afbb21187df6a877c6}}, {{cite:65522b175c5445da7adcebb7b2fe7f54a2283235}}, {{cite:948f5e04ba2f79a59ae6f290cb5a188388fa1b4a}}, {{cite:673db1f630da9d787efae8aa6ee4416598a811c7}}, {{cite:bd2f66fa05253a3ae92f1b3f5ff0035e95e2367c}}, {{cite:dd61e54eafc347feca0df5b2e2b0f68bb5e9e5a7}}).
Already {{cite:65522b175c5445da7adcebb7b2fe7f54a2283235}} made an explicit argument that these excesses have no reason to be present if shock heating from gravitational collapse is the dominant mechanism driving the evolution of the hot gas, while quasar feedback provides a possible explanation for their existence.
Hence, their observation disfavours model {{formula:2acb842b-bf68-434d-9590-edd04b4c3cc4}} , in which gravitational shock heating quenches SF. It also disfavours any model in which the only BH feedback is maintenance feedback: if BHs provided just enough heat to maintain the X-ray-emitting gas in thermal equilibrium, then BHs would prevent the hot gas from dropping below the entropy at which it was shock-heated but would not raise its entropy above it either.
The entropy excesses on group scales are evidence of a past epoch during which the gas was heated violently. Violent heating implies rapid BH growth. Hence, it is reasonable to associate it with the quasar-mode feedback that quenched SF.
| d | b4ac340e673acb6aac8ab182a552e350 |
Most of the researches on analyzing experimental images of natural sciences are based on feature extraction and end-to-end mapping to obtain valuable experimental target parameters {{cite:eef0493e70ad7197c434d2c5990d39d1ef3ff76f}} {{cite:cb8ce18051ce7be60bd5e813c039e20c908c1a43}} {{cite:3d9f91b409760a712a31096a4188571c00534a0e}}, which can be called as image-to-data task. And most of these researches are based on convolutional neural networks(CNN) and semantic segmentation {{cite:a343df30c8f144445046e124df08967119495480}} {{cite:67faddc102798f3fb2e0d76453a7daf73a5e51e0}}. Although impressive results have been achieved, none of these researches have built a data-to-image model.
| i | 489f2d281956af0bc3e40876e81bf8a0 |
In this paper we described an Abelian gauge theory exhibiting a confining potential at large distance. This unexpected
result, at least in ordinary Maxwell electrodynamics, is achieved by coupling the vector field to a Kalb-Ramond field.
Furthermore, both fields acquire mass via the Higgs mechanism implemented through one complex and one neutral scalar field.
The Higgs fields are then frozen in their respective non-trivial vacua in which dynamical
fields propagate. Integrating out the Goldstone mode and the Kalb-Ramond field one obtains
a non-local effective theory for the vector gauge field.
The resulting model resembles Lee-Wick higher derivative electrodynamics
{{cite:7bc7ec98c104b8bf5ea92400f642c83c9abf3f66}}, {{cite:aab1d09aea61843134c4acbae05bc633a54e18a7}}, {{cite:ea0a8e0fbbe44deb4eaa0ed24b69d33645791d87}}, {{cite:1f9f801c59921ec524e927c1548c2f0cac0f749e}}, {{cite:9c2854f525950f15fe6bd13912ea0432a32fdb6f}}, but with an important difference: the
former model was originally introduced in order to regularize short distance behavior of {{formula:bd1cc98a-ffc1-43de-9909-a5840f86261f}} . In the static limit.
the interaction potential energy is finite and linearly dependent on the distance between charges. The Coulomb behavior
is recovered at large distances.
On the other hand, confinement is characterized by the linear behavior but at large distances.
| d | 9253a51db926cc827fe9e7de4d1c4e00 |
Similar results are also on the Total-Text dataset.
When the shorter side is 320 pixels, the inference speed of our method reaches 84.9 FPS, which is at least 6 times faster than previous methods, while the F-measure is still very competitive (80.0%).
The best F-measure of our method is 85.3%, surpassing current state-of-the-art methods over 1.7 points. Meanwhile, its speed is close to 40 FPS, which is still 3 times faster than the second-fastest TextSnake {{cite:50629812c34e8dba72f02bf4414f978f14f182a0}}.
| r | 0db9c1a1c8fbbb96bc8518c6e36c9d13 |
Benefits of grid-based methods, such as the level set methods {{cite:57e6cf1b106073c37ff18ed560988fc43a2aa2db}} and fast marching method {{cite:44426ef49054f563522e910ed494e192dd53ccd0}}, are that the global optimality is guaranteed, and a closed-loop control is provided.
In other words, the optimal control is provided for any state-time pair.
However, due to computational complexity, grid-based methods are typically implemented offline to precompute the value function, and then used online with feedback.
Offline computation of grid-based methods is intractable for systems with continuous state dimension higher than six or seven.
| d | 2f25b77273ebb324af997a118f6beb8f |
Fig.REF (g) is a schematic of our four probe measurement setup: a bias current is driven between the source and drain external contacts, whilst the voltage difference is read between the two inner probes. A back gate voltage is applied through the bottom (Tr-WS{{formula:65a2d394-7811-422e-b2d9-461f92dd53d2}} or WS{{formula:8ac74997-4fca-49a5-9c61-c8fb8bf68125}} )+SiO{{formula:11d108c0-2b59-4f14-8fd5-b431c2915ef9}} insulating layers. Fig.REF (h) shows the four probe resistance measurements performed on the treated and untreated heterostructures by sweeping the back gate voltage (V{{formula:0ada9a09-1797-44cc-8dc9-1e0961b81625}} ). In order to evaluate the hysteresis, we performed forward (red) and reverse (blue) sweeps of the untreated (solid line) and treated (line with circles) heterostructures. The untreated heterostructure exhibits a considerable shift in the CNP, {{formula:83547b39-d084-4212-9a2a-148d27ee1c71}} V{{formula:09cc7dee-8162-4f40-b520-61ea2409b0b1}} , of {{formula:2ade2f59-b0c5-478f-9b73-ce13a85f90aa}} 5V). This shift could be explained as follows: when we sweep the back gate voltage, depending on the polarity, electrons or holes transfer from the graphene to trap sites on the substrate and become trapped. On sweeping back the gate voltage, the trapped charges electrostatically dope graphene, which manifests in shifting its CNP{{cite:d668f0be0f1ec825b11e52b230270a5a2fdacfdf}}. In our heterostructure, hysteresis is caused by the charge trapping of carriers from graphene within the WS{{formula:78a9bf75-23df-40ed-a5e2-ee9fd300b727}} vacancy sites{{cite:4d4a1f17ae5e09982faa87e363a790a1ac37e93e}}, {{cite:63313dc87fc99871afe6ac818b5cf25e8fc2910b}} and also at the interface with the SiO{{formula:69b6f22b-1564-48e3-9728-fc71174ab402}} surface{{cite:d668f0be0f1ec825b11e52b230270a5a2fdacfdf}}, with the former being orders of magnitude more dominant with respect to the latter{{cite:99cb4bfbec6f62933323753759c4a7d808415f2d}}, {{cite:db40cf810939311c504547afc76bd3f5b20ee3de}}, {{cite:d668f0be0f1ec825b11e52b230270a5a2fdacfdf}}. The heterostructure sample shows less than an order of magnitude hysteresis compared with the untreated heterostructure, with a {{formula:778677ff-2810-44b6-a4ea-9335e4974719}} V{{formula:dd5b2791-5c6b-4092-b9f2-8a4cfb30aecf}} of {{formula:ca4325aa-ba47-47f4-8306-bc273f1ec8f6}} 0.2V. The charge trap density {{formula:1c2c2f67-ed91-44bb-9d8c-8feb1216b55b}} is then also a measure of the sample hysteresis and can be calculated from the {{formula:90f4db4b-be54-4bd8-8ad6-7f13ee35de48}} V{{formula:5737a0c4-3733-40e1-aca2-12624c5ddd53}} as{{cite:d668f0be0f1ec825b11e52b230270a5a2fdacfdf}}:
{{formula:85e91f65-0e43-4fbd-9dc7-5311a2c67568}}
{{figure:ee462bc7-92ee-4ba5-87ed-5abc5ea99563}} | r | 503b97e9bcd6cb81ea5d7ed588056da8 |
The participant behavior is modeled using Hidden Markov Models (HMM) {{cite:18e68051d37c47c69c0a9dc2e64cddaad0663d50}}, and its parameters are trained using hmmlearn{{cite:b6029919f198cd889c50d603522680ae2e140de6}} on the treatment data separated in behavioral clusters, while simultaneously trying to find the preferred minimal HMM structure (number of states and transition structure) to achieve this. The resulting HMM models are both simple and transparent, containing enough modeling power to represent subjects' strategies in the IPD while also being generative. The latter is of interest as the inferred strategies could be directly be used within the context of theoretical simulations assessing their performance, which is left for future work.
| i | 943cbd6cfd8f6ab37a7d072ff315a8d7 |
blackKuramoto-type models have been used in the literature to provide intuition on the blackbehaviour of power networks blackat slow blacktimescales, by providing analytical results that hold in general network topologies.
blackSuch models have commonly been used to describe oscillators interconnected via lossless couplings {{cite:6779b572537eed27650dba0f56339f61b64d426d}}, {{cite:dcbac436ecaa581ecc0b80df23e545fd3a476b84}}, {{cite:085bea31b03e9434cfb066bad82e1ea326b8b909}}, {{cite:cf734f0dbe051dc8e8c00d75a9c0221807500549}}, {{cite:525cb6a337f6c94d7a628ffa4571b6c50b419e07}}, and thus the analysis of these Kuramoto-type blackmodels has been predominantly performed via Lyapunov functions.
However, the line conductances (or resistances) in e.g. inverter-based grids are important as they can inhibit synchronization.
Also, these power networks are usually characterized by nonhomogeneous
coupling weights and noncomplete
coupling graphs.
blackHence, here we consider a more advanced Kuramoto model that includes coupling conductances
together with heterogeneous coupling weights and noncomplete coupling graphs, in contrast to those in e.g. {{cite:dcbac436ecaa581ecc0b80df23e545fd3a476b84}}, {{cite:6779b572537eed27650dba0f56339f61b64d426d}}, {{cite:f00813e29aa2b3278b7b289da90cdd0f1aa82529}}.
Lyapunov analysis once blacksuch conductances and aforementioned coupling properties are included blackbecomes nontrivial as more conventional energy-like Lyapunov functions are not applicable or are conservative, as reported in {{cite:831c5ca6707cb11d782da218962eb974dea26240}}.
Small-signal analysis for this case exists in the literature, e.g {{cite:5c0ed5c4cfb1498e328eef003ef6e58f53997853}}; however, since the system converges to a manifold
a small-signal analysis is on its own inconclusive for the nonlinear system {{cite:7b65d75101a706582c19d7b7c177d37a919df886}}.
| i | 6db9b4cd696e570e6319498153efd838 |
where {{formula:5667f652-fedf-404a-8875-124b2f80f45a}} is the regularization parameter.
The {{formula:191b9945-e6c5-40d4-ab52-fec574db178e}} -norm regularizer provides sparsity on the rows of {{formula:2ccd6755-1e67-40aa-985a-65c43d5b00de}} , inspired by the group lasso penalty {{cite:bf3f8d68d1ca900e644a26ccaa6e091303ec77e6}}. The rows are closer to zero, then the corresponding features are more likely regarded as uninformative features.
| m | 8092a1bc8d6a2cdd839864593aa95aeb |
Finally, the fit to the {{formula:7ad72584-6cf3-411f-b8f9-c82924488600}} capture cross sections for {{formula:11dcd62f-1be4-42cd-97de-868b375aa1f7}} Be reaction as a function of incident {{formula:02b25026-e360-4e02-9ba0-49e7758baa38}} -energy in the range of E{{formula:3c90136c-b200-4427-bbc1-f19092dcf6d1}} = 9.0 to 13.5 MeV around the 4{{formula:be99c376-d1a0-4243-9f2e-20dc050f2965}} resonance state in {{formula:6267fb41-ca22-4b03-b2e4-c3b3d544c497}} Be is shown in Fig.REF . While the cross section curve from the simultaneous R-matrix calculation describes the maximum value of the cross section data well, the lower energy rise of the cross section in the resonance region appears to under predict the data. The fall off of the model cross section in the higher energy region describes the data well. The shape of the excitation curve of R-matrix model cross section in the 4{{formula:f75626d8-c900-48b7-8acd-b58af363421b}} resonance region, with a particle width of {{formula:9f6fd64c-36d2-457a-98e8-aabd520ac411}} =2.669{{formula:b15c0698-d3d8-4e09-82e7-e24246b69595}} 0.036 MeV, is some what narrower than that predicted by the cluster model (see Fig. 4 of Ref.{{cite:b0ccbb2f1fd55ff92808cc58e76cf80766080030}}). The best fit value of the {{formula:bb0306ae-cef8-426a-b74e-8cbbca00a71d}} -partial width is {{formula:33979aab-cdee-44bb-b9fb-2cf7afa70048}} = 0.502{{formula:9a40976e-386d-4428-94d8-db4923df7c11}} 0.084 eV, which is closer to the experimentally estimated width of 0.48{{formula:e65f666e-e272-4b8e-98ce-d36e9d8b1aa3}} 0.05 eV, which is based on a simplistic Breit-Wigner resonance, and leads to a branching ratio {{formula:282390e6-577b-4d2d-a21b-ec3cd8e22477}} = 1.88{{formula:b1e6ddc0-86ee-4d79-8967-bbcfcc7d2222}} 0.32{{formula:248d8858-d599-4116-9458-87fd02556bd1}} 10{{formula:e37cb802-0d7d-4494-ad65-d01020c72c96}} . The value is slightly on the higher side compared to the estimate of 1.37 {{formula:e136bf66-01f3-4eb2-861d-968c4489e067}} 10{{formula:89d05eb3-a2ba-4547-bd48-2dbb83ee3967}} obtained from the data assuming a Breit Wigner shape for the 4{{formula:3d9ec94d-5082-4c20-b387-442485f0818e}} resonance {{cite:b0ccbb2f1fd55ff92808cc58e76cf80766080030}}. The reduced {{formula:8734289c-6217-4c57-b562-50c55ac16c21}} transition strength or B({{formula:aced07e3-82e1-476f-8839-194dec59368c}} ) value from the R-matrix analysis is 21.96{{formula:f7e3000f-0845-4156-909f-5a3ec05448f3}} 3.86 e{{formula:202e9bc2-d22f-4647-abc5-e336daeeb096}} fm{{formula:00324fd2-fda4-4ff2-9df6-45e47e9036b6}} , which is within the error bars of the experimental value of 21.0 {{formula:ed2cae3e-197e-4575-8368-fa5b2e4b7d4f}} 2.3 e{{formula:1349e160-b1ce-4510-8fe7-fe6ea6b475ed}} fm{{formula:09f4dcf9-2cd6-4b57-b9bb-32016815b589}} . But the B({{formula:5639a86b-cf18-41a0-ac84-8ad687054fbc}} ) value from the R-matrix analysis is relatively smaller than the value of 27.0 e{{formula:d997e6b9-f257-46c0-8055-7de9bccd0e26}} fm{{formula:efff68a3-136e-43b5-920d-0a34fa3e3d37}} predicted by the ab initio calculation presented in Ref.{{cite:b0ccbb2f1fd55ff92808cc58e76cf80766080030}}, while the value is comparable with the cluster model prediction {{cite:371b932c622041f149587b75beeab743423ee65e}}. The excitation energy curve is then extrapolated to the low energy region encompassing the energy region associated with the {{formula:e379a899-e997-457d-8971-cf6bb1e56691}} transition from the resonance state around the excitation of E{{formula:9af557de-4049-4f12-b149-ed3eafac18c4}} {{formula:51460cd4-fccc-436e-b0e0-a4ade30b8e35}} 3.0 MeV to the ground state of {{formula:b9509b94-3603-4a37-b0ef-44bb881f4a6a}} Be. The peak cross section for the {{formula:311e3dd7-8c79-478e-bafd-21a970bdf151}} resonance is found to be 10.3 nb, slightly lower than the value of 14 nb, estimated in Ref. {{cite:1e660b7a5a5faa08df99cf10bf7fcc6a83126be4}} near 2.7 MeV. Adding the two contributions of the {{formula:9c4db6f5-8a11-4672-a4c5-22c8df90a103}} transitions corresponding to 4{{formula:5b45e770-d8af-4b81-bfc9-838c39657fcf}} 2{{formula:65cef194-77d4-4678-95b7-a40f56419f2d}} and 2{{formula:b317bceb-d4db-4868-acb6-766c631b25cb}} 0{{formula:3d6c8873-b18a-4abc-a3b0-cfce089b4655}} using the parameters of Table REF , the total excitation curve for {{formula:7a613604-0af0-4704-aac6-0693791b67ec}} capture has been generated and shown in Fig. REF .
| r | ff3b93c97d353fd13956db56b2e25d11 |
The planted clique and related problems have important applications in a variety of areas, including community detection {{cite:1799ef30cb7ae0513dadfdf2532a96c37a689211}}, molecular biology {{cite:4d8889a9d5ece1270bf75de29ae53b76f4eacd80}}, motif discovery in biological networks {{cite:dfa9c33e9f289cad9117fef71b75f6cff5382efa}}, {{cite:b3ab58b1993e2ed9ddeb564f1677a8d38e372538}}, computing the Nash equilibrium {{cite:d2f728596495c28e042b0275f496279364689ebc}}, {{cite:df53fdff8f35ed5aeffd454371495c467e7ff79a}}, property testing {{cite:20de24bd444ba99db835ad0ce519e4434f6d3f19}}, sparse principal component analysis {{cite:3fa2a2e917d8a280a0b28e158e7114a99c3f2180}}, compressed sensing {{cite:3199e84b40e909f84f815472bd845eb96858506a}},
cryptography {{cite:a7d0b32b2b2cacb4cd47d131cc6a9770d29c6470}}, {{cite:fa381791f0a578f48b60e5d5dfd9b32b789803b4}}, and even mathematical finance {{cite:5cb447946fbeed2cde27f57ced8cc9d4571d4a85}}.
| i | fb240de704299de35c931fd392126cd1 |
Global dynamics allow the Adaptive Restore process to make large moves across the space, a property shared by Standard Restore. This feature is desirable for MCMC samplers (since it results in a Markov chain with smaller autocorrelation) and has motivated the development of algorithms such as Hamiltonian Monte Carlo (HMC) {{cite:96ab7002c5d0b7eb00829b3476c9a4c44016bffa}}, {{cite:a8ae188e813636e0e5feab90ba2bdb5ecf079f20}} or its special case, the No-U-Turns Sampler (NUTS) {{cite:16242c20be0897e52fcd8b4fc61db71989dd62d4}}. Crucially, as the dimension {{formula:56edf881-b9fb-4805-be5d-7468abc55b7c}} of {{formula:f1cb5f16-6681-46e8-b1e0-e75ddfb972fe}} increases, {{formula:b669202c-3f59-46c6-8af0-6bc0c708b0e1}} remains close to {{formula:234f93df-1e36-4fc9-acf4-d658f6500bd9}} . Indeed, it is shown in {{cite:5bf92c576d218e97e5f2d1f2e624ac605a84b282}} for several examples that {{formula:f8654cf0-0241-4c69-adba-6c46e94b7df7}} has a stable behaviour in the high-dimensional {{formula:2fe35461-235c-47c1-8a24-333b051724a9}} limit. This means that, unlike other methods making use of global regenerative moves via the independence sampler and Nummelin splitting {{cite:d1212809cc150b92646f5157bfc94b958e1a298e}}, {{cite:9e2c101f4c659c9c40044b13d503d7e42b142cf4}}, global moves are more likely to be to areas of the space where {{formula:a2130efb-9122-4fab-9f08-ad0fdcdbfd96}} has significant mass.
| d | c5f7a51bfd8d7e4506f3f208334140ce |
First note that we bring all the vectors to isotropic position by rotating so that {{formula:e73671c1-9d89-407a-883c-bbacd16eb3aa}} . Now by definition for any fixed {{formula:61690dbf-c1c3-488f-8ba9-1d9bda704c11}} , each {{formula:4511e7b2-f7dd-4023-9187-46c7e55b077a}} is {{formula:f40deb86-a732-4762-a2e4-20c35c37023b}} and hence {{formula:9c7a3fbb-2696-47f6-843f-36414aff4ec1}} is {{formula:d2276214-cfcc-471c-b87b-af0d35e7a145}} by lem:prodsg. For the latter quantity {{cite:c67b3a1b8b32fae23dfc17e324aa2eba8b40ecf9}} proves the result when {{formula:e03df4a5-4eac-4a69-9835-681e48b10494}} using a standard covering argument along with a sub-exponential tail bound. A close inspection of the proof of {{cite:c67b3a1b8b32fae23dfc17e324aa2eba8b40ecf9}} shows that the aforementioned analogous statement holds when the sequence of random vectors is scaled by {{formula:868f6f52-85fe-41e3-bdbf-f2ead4727091}} .
| r | a234e133e6dc19d68d57a5ec90319b59 |
Although the simulation study has focused on estimators for binary endpoints, the approach can be used for all kind of endpoints (e.g., continous, ordinal, time-to-event, ...) and estimands as long as the considered estimators are consistent RAL estimators. In particular, our method can be applied to targeted maximum likelihood estimators {{cite:38e6a99411059bea6006cd41e6cde4d77c6b913d}}.
Moreover, all of the theoretical results in this paper can be extended to handle combined use of stratified randomization (which is commonly done in practice) and covariate adjustment by using the general technique from {{cite:f27aec3133d890c55ba3c49a7bf5b69dfd9bb904}}.
In addition, our approach can be expanded to handle missing data due to drop-out under the missing at random assumption (conditional on the covariates and treatment assignment) by using doubly robust methods {{cite:acece486bd772e4cb0cfece37e2a3a47695aca77}}.
| d | 9b62e6b6bfe757114f0e41b00662f8d8 |
According to Fig. REF , for any isolated system it is, in principle, simple to compute the microcanonical caloric curve just by considering the definition
of {{formula:a14f8e48-3099-4680-8c3e-989df75fbbdb}} , this agrees with the analytical solution of the one-dimensional Ising model in the canonical ensemble {{cite:9fb6ea8ff8a028003900218b0247f44415ad2659}},
where the partition function is given by
{{formula:d494a550-d013-4f5b-ae2e-d48c2fa1eddd}}
| d | 958b874968b5127418ee3d7b36f7d533 |
Specifying guarantees on privacy protection is of increasing importance for medical research.
National laws and regulations such as the US HIPAA Privacy rulewww.hhs.gov/hipaa/for-professionals/privacy/ (accessed 07/06/2022) require measures to protect the privacy of health information.
On the hospital level, protecting a patient's privacy is crucial especially when information is shared across institutions. Our method demonstrates the benefit of output sharing where hospitals keep their in-house model in a secured area and only share the output with other institutions, thus avoiding the challenges and difficulties of model sharing techniques such as federated learning {{cite:1f66255271cc02fb00b86874f0c9a1c1ebb911db}}.
On the patient level, a recent survey has shown that more than 30% of the participants are comfortable with sharing their electronic health data for personalized healthcare, while less than 5% are very uncomfortable with sharing {{cite:ea42ff2da87c6a861a4dfb08d790e667247e1f29}}. This means more than 60% do not have a strong opinion on this topic, thus we hope that an increasing number of people will share their data if stronger privacy guarantees can be given.
| i | df51df52bf0e60caedcdc8a02be22e4a |
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