| 1. |
- Ding Yuan, Chen, 1991, et al.
(författare)
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Impact of in situ NH3 pre-treatment of LPCVD SiN passivation on GaN HEMT performance
- 2022
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Ingår i: Semiconductor Science and Technology. - : IOP Publishing. - 1361-6641 .- 0268-1242. ; 37:3
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Tidskriftsartikel (refereegranskat)abstract
- The impact on the performance of GaN high electron mobility transistors (HEMTs) of in situ ammonia (NH3) pre-treatment prior to the deposition of silicon nitride (SiN) passivation with low-pressure chemical vapor deposition (LPCVD ) is investigated. Three different NH3 pre-treatment durations (0, 3, and 10 min) were compared in terms of interface properties and device performance. A reduction of oxygen (O) at the interface between SiN and epi-structure is detected by scanning transmission electron microscopy (STEM )-electron energy loss spectroscopy (EELS) measurements in the sample subjected to 10 min of pre-treatment. The samples subjected to NH3 pre-treatment show a reduced surface-related current dispersion of 9% (compared to 16% for the untreated sample), which is attributed to the reduction of O at the SiN/epi interface. Furthermore, NH3 pre-treatment for 10 min significantly improves the current dispersion uniformity from 14.5% to 1.9%. The reduced trapping effects result in a high output power of 3.4 W mm(-1) at 3 GHz (compared to 2.6 W mm(-1) for the untreated sample). These results demonstrate that the in situ NH3 pre-treatment before LPCVD of SiN passivation is critical and can effectively improves the large-signal microwave performance of GaN HEMTs.
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| 2. |
- Gerken, Jan, 1991, et al.
(författare)
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Equivariance versus augmentation for spherical images
- 2022
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Ingår i: Proceedings of Machine Learning Resaerch. ; , s. 7404-7421
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Konferensbidrag (refereegranskat)abstract
- We analyze the role of rotational equivariance in convolutional neural networks (CNNs) applied to spherical images. We compare the performance of the group equivariant networks known as S2CNNs and standard non-equivariant CNNs trained with an increasing amount of data augmentation. The chosen architectures can be considered baseline references for the respective design paradigms. Our models are trained and evaluated on single or multiple items from the MNIST- or FashionMNIST dataset projected onto the sphere. For the task of image classification, which is inherently rotationally invariant, we find that by considerably increasing the amount of data augmentation and the size of the networks, it is possible for the standard CNNs to reach at least the same performance as the equivariant network. In contrast, for the inherently equivariant task of semantic segmentation, the non-equivariant networks are consistently outperformed by the equivariant networks with significantly fewer parameters. We also analyze and compare the inference latency and training times of the different networks, enabling detailed tradeoff considerations between equivariant architectures and data augmentation for practical problems.
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| 3. |
- Gerken, Jan, 1991, et al.
(författare)
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Geometric deep learning and equivariant neural networks
- 2023
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Ingår i: Artificial Intelligence Review. - : Springer Nature. - 1573-7462 .- 0269-2821. ; 56:12, s. 14605-14662
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Tidskriftsartikel (refereegranskat)abstract
- We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds M using principal bundles with structure group K and equivariant maps between sections of associated vector bundles. We also discuss group equivariant neural networks for homogeneous spaces M= G/ K , which are instead equivariant with respect to the global symmetry G on M . Group equivariant layers can be interpreted as intertwiners between induced representations of G, and we show their relation to gauge equivariant convolutional layers. We analyze several applications of this formalism, including semantic segmentation and object detection networks. We also discuss the case of spherical networks in great detail, corresponding to the case M= S2= SO (3) / SO (2) . Here we emphasize the use of Fourier analysis involving Wigner matrices, spherical harmonics and Clebsch–Gordan coefficients for G= SO (3) , illustrating the power of representation theory for deep learning.
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| 4. |
- Gourevitch, D., et al.
(författare)
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A reduction principle for Fourier coefficients of automorphic forms
- 2022
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 300, s. 2679-2717
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Tidskriftsartikel (refereegranskat)abstract
- We consider a special class of unipotent periods for automorphic forms on a finite cover of a reductive adelic groupG(AK), which we refer to as Fourier coefficients associated to the data of a 'Whittaker pair'. We describe a quasi-order on Fourier coefficients, and an algorithm that gives an explicit formula for any coefficient in terms of integrals and sums involving higher coefficients. The maximal elements for the quasi-order are 'Levi-distinguished' Fourier coefficients, which correspond to taking the constant term along the unipotent radical of a parabolic subgroup, and then further taking a Fourier coefficient with respect to a K-distinguished nilpotent orbit in the Levi quotient. Thus one can express any Fourier coefficient, including the form itself, in terms of higher Levi-distinguished coefficients. In companion papers we use this result to determine explicit Fourier expansions of minimal and next-to-minimal automorphic forms on split simply-laced reductive groups, and to obtain Euler product decompositions of certain Fourier coefficients.
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| 5. |
- Prakash, Om, et al.
(författare)
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How Rigidity and Conjugation of Bidentate Ligands Affect the Geometry and Photophysics of Iron N-Heterocyclic Complexes : A Comparative Study
- 2024
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Ingår i: Inorganic Chemistry. - : American Chemical Society (ACS). - 0020-1669 .- 1520-510X. ; 63:10, s. 4461-4473
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Tidskriftsartikel (refereegranskat)abstract
- Two iron complexes featuring the bidentate, nonconjugated N-heterocyclic carbene (NHC) 1,1′-methylenebis(3-methylimidazol-2-ylidene) (mbmi) ligand, where the two NHC moieties are separated by a methylene bridge, have been synthesized to exploit the combined influence of geometric and electronic effects on the ground- and excited-state properties of homoleptic FeIII-hexa-NHC [Fe(mbmi)3](PF6)3 and heteroleptic FeII-tetra-NHC [Fe(mbmi)2(bpy)](PF6)2 (bpy = 2,2′-bipyridine) complexes. They are compared to the reported FeIII-hexa-NHC [Fe(btz)3](PF6)3 and FeII-tetra-NHC [Fe(btz)2(bpy)](PF6)2 complexes containing the conjugated, bidentate mesoionic NHC ligand 3,3′-dimethyl-1,1′-bis(p-tolyl)-4,4′-bis(1,2,3-triazol-5-ylidene) (btz). The observed geometries of [Fe(mbmi)3](PF6)3 and [Fe(mbmi)2(bpy)](PF6)2 are evaluated through L-Fe-L bond angles and ligand planarity and compared to those of [Fe(btz)3](PF6)3 and [Fe(btz)2(bpy)](PF6)2. The FeII/FeIII redox couples of [Fe(mbmi)3](PF6)3 (−0.38 V) and [Fe(mbmi)2(bpy)](PF6)2 (−0.057 V, both vs Fc+/0) are less reducing than [Fe(btz)3](PF6)3 and [Fe(btz)2(bpy)](PF6)2. The two complexes show intense absorption bands in the visible region: [Fe(mbmi)3](PF6)3 at 502 nm (ligand-to-metal charge transfer, 2LMCT) and [Fe(mbmi)2(bpy)](PF6)2 at 410 and 616 nm (metal-to-ligand charge transfer, 3MLCT). Lifetimes of 57.3 ps (2LMCT) for [Fe(mbmi)3](PF6)3 and 7.6 ps (3MLCT) for [Fe(mbmi)2(bpy)](PF6)2 were probed and are somewhat shorter than those for [Fe(btz)3](PF6)3 and [Fe(btz)2(bpy)](PF6)2. [Fe(mbmi)3](PF6)3 exhibits photoluminescence at 686 nm (2LMCT) in acetonitrile at room temperature with a quantum yield of (1.2 ± 0.1) × 10-4, compared to (3 ± 0.5)
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| 6. |
- Gourevitch, Dmitry, et al.
(författare)
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Fourier coefficients of minimal and next-to-minimal automorphic representations of simply-laced groups
- 2022
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Ingår i: Canadian Journal of Mathematics. - 1496-4279 .- 0008-414X. ; 74:1, s. 122-169
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we analyze Fourier coefficients of automorphic forms on a finite cover G of an adelic split simply-laced group. Let ππ be a minimal or next-to-minimal automorphic representation of G. We prove that any η∈πη∈π is completely determined by its Whittaker coefficients with respect to (possibly degenerate) characters of the unipotent radical of a fixed Borel subgroup, analogously to the Piatetski-Shapiro–Shalika formula for cusp forms on GLnGLn . We also derive explicit formulas expressing the form, as well as all its maximal parabolic Fourier coefficient, in terms of these Whittaker coefficients. A consequence of our results is the nonexistence of cusp forms in the minimal and next-to-minimal automorphic spectrum. We provide detailed examples for G of type D5D5 and E8E8 with a view toward applications to scattering amplitudes in string theory.
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| 7. |
- Berman, Robert, 1976, et al.
(författare)
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Emergent Sasaki-Einstein geometry and AdS/CFT
- 2022
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Ingår i: Nature Communications. - : Springer Science and Business Media LLC. - 2041-1723 .- 2041-1723. ; 13:1
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Tidskriftsartikel (refereegranskat)abstract
- A central problem in any quantum theory of gravity is to explain the emergence of the classical spacetime geometry in some limit of a more fundamental, microscopic description of nature. The gauge/gravity-correspondence provides a framework in which this problem can, in principle, be addressed. This is a holographic correspondence which relates a supergravity theory in five-dimensional Anti-deSitter space to a strongly coupled superconformal gauge theory on its 4-dimensional flat Minkowski boundary. In particular, the classical geometry should therefore emerge from some quantum state of the dual gauge theory. Here we confirm this by showing how the classical metric emerges from a canonical state in the dual gauge theory. In particular, we obtain approximations to the Sasaki-Einstein metric underlying the supergravity geometry, in terms of an explicit integral formula involving the canonical quantum state in question. In the special case of toric quiver gauge theories we show that our results can be computationally simplified through a process of tropicalization.
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| 8. |
- Carleo, Ilaria, et al.
(författare)
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The Multiplanet System TOI-421*
- 2020
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Ingår i: Astronomical Journal. - : American Astronomical Society. - 1538-3881 .- 0004-6256. ; 160:3
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Tidskriftsartikel (refereegranskat)abstract
- We report the discovery of a warm Neptune and a hot sub-Neptune transiting TOI-421 (BD-14 1137, TIC 94986319), a bright (V = 9.9) G9 dwarf star in a visual binary system observed by the Transiting Exoplanet Survey Satellite (TESS) space mission in Sectors 5 and 6. We performed ground-based follow-up observations-comprised of Las Cumbres Observatory Global Telescope transit photometry, NIRC2 adaptive optics imaging, and FIbre-fed Echelle Spectrograph, CORALIE, High Accuracy Radial velocity Planet Searcher, High Resolution echelle Spectrometer, and Planet Finder Spectrograph high-precision Doppler measurements-and confirmed the planetary nature of the 16 day transiting candidate announced by the TESS team. We discovered an additional radial velocity signal with a period of five days induced by the presence of a second planet in the system, which we also found to transit its host star. We found that the inner mini-Neptune, TOI-421 b, has an orbital period of P-b = 5.19672 +/- 0.00049 days, a mass of M-b = 7.17 +/- 0.66 M-circle plus, and a radius of R-b = R-circle plus, whereas the outer warm Neptune, TOI-421 c, has a period of P-c = 16.06819 +/- 0.00035 days, a mass of M-c = 16.42(-1.04)(+1.06)M(circle plus), a radius of R-c = 5.09(-0.15)(+0.16)R(circle plus), and a density of rho(c) = 0.685(-0.072)(+0.080) cm(-3). With its characteristics, the outer planet (rho(c) = 0.685(-0.0072)(+0.080) cm(-3)) is placed in the intriguing class of the super-puffy mini-Neptunes. TOI-421 b and TOI-421 c are found to be well-suited for atmospheric characterization. Our atmospheric simulations predict significant Ly alpha transit absorption, due to strong hydrogen escape in both planets, as well as the presence of detectable CH4 in the atmosphere of TOI-421 c if equilibrium chemistry is assumed.
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| 9. |
- Harrison, Sarah M., et al.
(författare)
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BPS Algebras in 2D String Theory
- 2022
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Ingår i: Annales Henri Poincare. - : Springer Science and Business Media LLC. - 1424-0637 .- 1424-0661. ; 23, s. 3667-3752
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Tidskriftsartikel (refereegranskat)abstract
- We discuss a set of heterotic and type II string theory compactifications to 1 + 1 dimensions that are characterized by factorized internal worldsheet CFTs of the form V1⊗ V¯ 2, where V1, V2 are self-dual (super) vertex operator algebras. In the cases with spacetime supersymmetry, we show that the BPS states form a module for a Borcherds–Kac–Moody (BKM) (super)algebra, and we prove that for each model the BKM (super)algebra is a symmetry of genus zero BPS string amplitudes. We compute the supersymmetric indices of these models using both Hamiltonian and path integral formalisms. The path integrals are manifestly automorphic forms closely related to the Borcherds–Weyl–Kac denominator. Along the way, we comment on various subtleties inherent to these low-dimensional string compactifications.
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| 10. |
- Harrison, Sarah M., et al.
(författare)
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Fun with F 24
- 2021
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Ingår i: Journal of High Energy Physics. - 1029-8479 .- 1126-6708. ; 2021:2
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Tidskriftsartikel (refereegranskat)abstract
- We study some special features of F24, the holomorphic c = 12 superconformal field theory (SCFT) given by 24 chiral free fermions. We construct eight different Lie superalgebras of “physical” states of a chiral superstring compactified on F24, and we prove that they all have the structure of Borcherds-Kac-Moody superalgebras. This produces a family of new examples of such superalgebras. The models depend on the choice of an N = 1 supercurrent on F24, with the admissible choices labeled by the semisimple Lie algebras of dimension 24. We also discuss how F24, with any such choice of supercurrent, can be obtained via orbifolding from another distinguished c = 12 holomorphic SCFT, the N = 1 supersymmetric version of the chiral CFT based on the E8 lattice.
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