83 research outputs found
Integral invariants in flat superspace
We are solving for the case of flat superspace some homological problems that
were formulated by Berkovits and Howe. (Our considerations can be applied also
to the case of supertorus.) These problems arise in the attempt to construct
integrals invariant with respect to supersymmetry. They appear also in other
situations, in particular, in the pure spinor formalism in supergravity.Comment: 15 page
Homology of Lie algebra of supersymmetries
We study the homology and cohomology groups of super Lie algebra of
supersymmetries and of super Poincare algebra. We discuss in detail the
calculation in dimensions D=10 and D=6. Our methods can be applied to extended
supersymmetry algebra and to other dimensions
Weierstrass cycles and tautological rings in various moduli spaces of algebraic curves
We analyze Weierstrass cycles and tautological rings in moduli space of
smooth algebraic curves and in moduli spaces of integral algebraic curves with
embedded disks with special attention to moduli spaces of curves having genus
. In particular, we show that our general formula gives a good estimate
for the dimension of Weierstrass cycles for lower genera.Comment: arXiv admin note: substantial text overlap with arXiv:1207.053
Homology of Lie algebra of supersymmetries and of super Poincare Lie algebra
We study the homology and cohomology groups of super Lie algebra of
supersymmetries and of super Poincare Lie algebra in various dimensions. We
give complete answers for (non-extended) supersymmetry in all dimensions . For dimensions we describe also the cohomology of reduction of
supersymmetry Lie algebra to lower dimensions. Our methods can be applied to
extended supersymmetry algebra.Comment: New version with some additions and correction
Cohomology ring of the BRST operator associated to the sum of two pure spinors
In the study of the Type II superstring, it is useful to consider the BRST
complex associated to the sum of two pure spinors. The cohomology of this
complex is an infinite-dimensional vector space. It is also a
finite-dimensional algebra over the algebra of functions of a single pure
spinor. In this paper we study the multiplicative structure.Comment: 5 page
Effects of Bentonite Activation Methods on Chitosan Loading Capacity
The adsorption capacity of bentonite clay for heavy metal removal from wastewater can be significantly enhanced by a high loading of chitosan on the surface. In order to enhance the chitosan loading, we tested activating bentonite clay by three methods prior to chitosan loading: sulfuric acid, calcination, and microwave treatments. Meanwhile, several parameters during chitosan loading, namely the initial chitosan concentration, stirring speed, reaction time, temperature, and pH value were investigated. Our results indicate that chitosan is attached to bentonite clay through intercalation and surface adsorption according to X-ray Diffraction (XRD), Scanning Eelectron Microscopy (SEM), and Fourier Transform Infrared Spectroscopy (FTIR) analyses. The maximum chitosan loading on 200-mesh raw bentonite clay (126.30 mg/L) was achieved under the following conditions: the initial chitosan concentration of 1000 mg/L, the stirring speed of 200 rpm, pH of 4.9, 60 min of reaction time, and temperature of 30 °C. The chitosan loading was further increased to 256.30, 233.70, and 208.83 mg/g, when using bentonite clay activated through 6 min of microwave irradiation (800 W), 10 % sulfuric acid treatment, and calcinations at 600 °C, respectively. When the chitosan loading was increased from 34.76 to 233.7 mg/g, the removal percentages of Cu(II), Cr(VI), and Pb(II) were improved, respectively from 78.90 to 95.5 %, from 82.22 to 98.74 %, from 60.09 to 86.18 %.
-Equivariant Vision Transformer
Vision Transformer (ViT) has achieved remarkable performance in computer
vision. However, positional encoding in ViT makes it substantially difficult to
learn the intrinsic equivariance in data. Initial attempts have been made on
designing equivariant ViT but are proved defective in some cases in this paper.
To address this issue, we design a Group Equivariant Vision Transformer
(GE-ViT) via a novel, effective positional encoding operator. We prove that
GE-ViT meets all the theoretical requirements of an equivariant neural network.
Comprehensive experiments are conducted on standard benchmark datasets,
demonstrating that GE-ViT significantly outperforms non-equivariant
self-attention networks. The code is available at
https://github.com/ZJUCDSYangKaifan/GEVit.Comment: Accept to UAI202
S2SNet: A Pretrained Neural Network for Superconductivity Discovery
Superconductivity allows electrical current to flow without any energy loss,
and thus making solids superconducting is a grand goal of physics, material
science, and electrical engineering. More than 16 Nobel Laureates have been
awarded for their contribution to superconductivity research. Superconductors
are valuable for sustainable development goals (SDGs), such as climate change
mitigation, affordable and clean energy, industry, innovation and
infrastructure, and so on. However, a unified physics theory explaining all
superconductivity mechanism is still unknown. It is believed that
superconductivity is microscopically due to not only molecular compositions but
also the geometric crystal structure. Hence a new dataset, S2S, containing both
crystal structures and superconducting critical temperature, is built upon
SuperCon and Material Project. Based on this new dataset, we propose a novel
model, S2SNet, which utilizes the attention mechanism for superconductivity
prediction. To overcome the shortage of data, S2SNet is pre-trained on the
whole Material Project dataset with Masked-Language Modeling (MLM). S2SNet
makes a new state-of-the-art, with out-of-sample accuracy of 92% and Area Under
Curve (AUC) of 0.92. To the best of our knowledge, S2SNet is the first work to
predict superconductivity with only information of crystal structures. This
work is beneficial to superconductivity discovery and further SDGs. Code and
datasets are available in https://github.com/zjuKeLiu/S2SNetComment: Accepted to IJCAI 202
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