BCJ numerators from reduced Pfaffian Du, Yi-Jian; Teng, Fei
The journal of high energy physics,
04/2017, Letnik:
2017, Številka:
4
Journal Article
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A
bstract
By expanding the reduced Pfaffian in the tree level Cachazo-He-Yuan (CHY) integrands for Yang-Mills (YM) and nonlinear sigma model (NLSM), we can get the Bern-Carrasco-Johansson (BCJ) ...numerators in Del Duca-Dixon-Maltoni (DDM) form for arbitrary number of particles in any spacetime dimensions. In this work, we give a set of very straightforward graphic rules based on spanning trees for a direct evaluation of the BCJ numerators for YM and NLSM. Such rules can be derived from the Laplace expansion of the corresponding reduced Pfaffian. For YM, the each one of the (
n
− 2)! DDM form BCJ numerators contains exactly (
n
− 1)! terms, corresponding to the increasing trees with respect to the color order. For NLSM, the number of nonzero numerators is at most (
n
− 2)! − (
n
− 3)!, less than those of several previous constructions.
A
bstract
In this paper, we investigate the expansion of tree level multitrace Einstein-Yang-Mills (EYM) amplitudes. First, we propose two types of recursive expansions of tree level EYM amplitudes ...with an arbitrary number of gluons, gravitons and traces by those amplitudes with fewer traces or/and gravitons. Then we give many support evidence, including proofs using the Cachazo-He-Yuan (CHY) formula and Britto-Cachazo-Feng-Witten (BCFW) recursive relation. As a byproduct, two types of generalized BCJ relations for multitrace EYM are further proposed, which will be useful in the BCFW proof. After one applies the recursive expansions repeatedly, any multitrace EYM amplitudes can be given in the Kleiss-Kuijf (KK) basis of tree level color ordered Yang-Mills (YM) amplitudes. Thus the Bern-Carrasco-Johansson (BCJ) numerators, as the expansion coefficients, for all multitrace EYM amplitudes are naturally constructed.
Hardware implementation of artificial synaptic devices that emulate the functions of biological synapses is inspired by the biological neuromorphic system and has drawn considerable interest. Here, a ...three‐terminal ferrite synaptic device based on a topotactic phase transition between crystalline phases is presented. The electrolyte‐gating‐controlled topotactic phase transformation between brownmillerite SrFeO2.5 and perovskite SrFeO3−δ is confirmed from the examination of the crystal and electronic structure. A synaptic transistor with electrolyte‐gated ferrite films by harnessing gate‐controllable multilevel conduction states, which originate from many distinct oxygen‐deficient perovskite structures of SrFeOx induced by topotactic phase transformation, is successfully constructed. This three‐terminal artificial synapse can mimic important synaptic functions, such as synaptic plasticity and spike‐timing‐dependent plasticity. Simulations of a neural network consisting of ferrite synaptic transistors indicate that the system offers high classification accuracy. These results provide insight into the potential application of advanced topotactic phase transformation materials for designing artificial synapses with high performance.
A ferrite synaptic transistor with topotactic transformation is presented. The electrolyte‐gating‐controlled topotactic phase transformation between the brownmillerite SrFeO2.5 and perovskite SrFeO3−δ is confirmed by the crystal and electronic structure measurements. This ferrite synaptic transistor can mimic important synaptic functions such as synaptic plasticity and spike‐timing‐dependent plasticity.
Artificial synaptic devices are the essential hardware of neuromorphic computing systems, which can simultaneously perform signal processing and information storage between two neighboring artificial ...neurons. Emerging electrolyte‐gated transistors have attracted much attention for efficient synaptic emulation by using an addition gate terminal. Here, an electrolyte‐gated synaptic device based on the SrCoOx (SCO) films is proposed. It is demonstrated that the reversible modulation of SCO phase transforms the brownmillerite SrCoO2.5 and perovskite SrCoO3−δ
, through controlling the insertion and extraction of oxygen ions with electrolyte gating. Nonvolatile multilevel conduction states can be realized in the SCO films following this route. The synaptic functions such as the long‐term potentiation and depression of synaptic weight, spike‐timing‐dependent plasticity, as well as spiking logic operations in the device are successfully mimicked. These results provide an alternative avenue for future neuromorphic devices via electrolyte‐gated transistors with oxygen ions.
An electrolyte‐gated synaptic transistor with oxygen ions is presented. Nonvolatile multilevel conduction states can be realized in the SrCoOx
epitaxial films, through controlling the insertion and extraction of oxygen ions with electrolyte gating. Important synaptic functions such as the long‐term potentiation and depression of synaptic weight, spike‐timing‐dependent plasticity, as well as spiking logic operations are successfully emulated.
Considering that the human brain uses ≈1015 synapses to operate, the development of effective artificial synapses is essential to build brain‐inspired computing systems. In biological synapses, the ...voltage‐gated ion channels are very important for regulating the action‐potential firing. Here, an electrolyte‐gated transistor using WO3 with a unique tunnel structure, which can emulate the ionic modulation process of biological synapses, is proposed. The transistor successfully realizes synaptic functions of both short‐term and long‐term plasticity. Short‐term plasticity is mimicked with the help of electrolyte ion dynamics under low electrical bias, whereas the long‐term plasticity is realized using proton insertion in WO3 under high electrical bias. This is a new working approach to control the transition from short‐term memory to long‐term memory using different gate voltage amplitude for artificial synapses. Other essential synaptic behaviors, such as paired pulse facilitation, the depression and potentiation of synaptic weight, as well as spike‐timing‐dependent plasticity are also implemented in this artificial synapse. These results provide a new recipe for designing synaptic electrolyte‐gated transistors through the electrostatic and electrochemical effects.
An electrolyte‐gated transistor using WO3 with a unique tunnel structure to successfully emulate the synaptic functions of both short‐term and long‐term plasticity is proposed. Short‐term plasticity is mimicked with the help of electrolyte ion dynamics under low gate bias, and the long‐term plasticity is realized via proton insertion in WO3 under high gate bias.
ObjectiveDiabetes mellitus (DM) is associated with an increased fracture risk; however, the impact of DM and subsequent fracture at different sites and the associations according to patient ...characteristics remain unknown.DesignMeta-analysisData sourcesThe PubMed, EMBASE and Cochrane Library databases were searched from inception to March 2018.Eligibility criteriaWe included prospective and retrospective cohort studies on the associations of DM and subsequent fracture risk at different sites.Data extraction and synthesisTwo authors independently extracted data and assessed the study quality. Relative risks (RRs) with 95% CIs were calculated using a random-effects model, and the heterogeneity across the included studies was evaluated using I2 and Q statistics.ResultsOverall, DM was associated with an increased risk of total (RR: 1.32; 95% CI 1.17 to 1.48; p<0.001), hip (RR: 1.77; 95% CI 1.56 to 2.02; p<0.001), upper arm (RR: 1.47; 95% CI 1.02 to 2.10; p=0.037) and ankle fractures (RR: 1.24; 95% CI 1.10 to 1.40; p<0.001), whereas DM had no significant impact on the incidence of distal forearm (RR: 1.02; 95% CI 0.88 to 1.19; p=0.809) and vertebral fractures (RR: 1.56; 95% CI 0.78 to 3.12; p=0.209). RR ratios suggested that compared with patients with type 2 DM (T2DM), patients with type 1 DM (T1DM) had greater risk of total (RR: 1.24; 95% CI 1.08 to 1.41; p=0.002), hip (RR: 3.43; 95% CI 2.27 to 5.17; p<0.001) and ankle fractures (RR: 1.71; 95% CI 1.06 to 2.78; p=0.029). Although no other significant differences were observed between subgroups, the association of DM with upper arm or ankle, vertebrae and total fracture differed according to sex, study design and country, respectively.ConclusionsPatients with DM had greater risks of total, hip, upper arm and ankle fractures, with T1DM having a more harmful effect than T2DM.
A
bstract
Tree-level color-ordered Yang-Mills (YM) amplitudes can be decomposed in terms of (
n −
2)! bi-scalar (BS) amplitudes, whose expansion coefficients form a basis of Bern-Carrasco-Johansson ...(BCJ) numerators. By the help of the recursive expansion of Einstein-Yang-Mills (EYM) amplitudes, the BCJ numerators are given by polynomial functions of Lorentz contractions which are conveniently described by graphic rule. In this work, we extend the expansion of YM amplitudes to off-shell level. We define different types of off-shell extended numerators that can be generated by graphs. By the use of these extended numerators, we propose a general decomposition formula of off-shell Berends-Giele currents in YM. This formula consists of three terms: (i). an effective current which is expanded as a combination of the Berends-Giele currents in BS theory (The expansion coefficients are one type of off-shell extended numerators) (ii). a term proportional to the total momentum of on-shell lines and (iii). a term expressed by the sum of lower point Berends-Giele currents in which some polarizations and momenta are replaced by vectors proportional to off-shell momenta appropriately. In the on-shell limit, the last two terms vanish while the decomposition of effective current precisely reproduces the decomposition of on-shell YM amplitudes with the expected coefficients (BCJ numerators in DDM basis). We further symmetrize these coefficients such that the Lie symmetries are satisfied. These symmetric BCJ numerators simultaneously satisfy the relabeling property of external lines and the algebraic properties (antisymmetry and Jacobi identity).
A
bstract
All tree-level amplitudes in Einstein-Yang-Mills (EYM) theory and gravity (GR) can be expanded in terms of color ordered Yang-Mills (YM) ones whose coefficients are polynomial functions of ...Lorentz inner products and are constructed by a graphic rule. Once the gauge invariance condition of any graviton is imposed, the expansion of a tree level EYM or gravity amplitude induces a nontrivial identity between color ordered YM amplitudes. Being different from traditional Kleiss-Kuijf (KK) and Bern-Carrasco-Johansson (BCJ) relations, the gauge invariance induced identity involves polarizations in the coefficients. In this paper, we investigate the relationship between the gauge invariance induced identity and traditional BCJ relations. By proposing a refined graphic rule, we prove that all the gauge invariance induced identities for single trace tree-level EYM amplitudes can be precisely expanded in terms of traditional BCJ relations, without referring any property of polarizations. When further considering the transversality of polarizations and momentum conservation, we prove that the gauge invariance induced identity for tree-level GR (or pure YM) amplitudes can also be expanded in terms of traditional BCJ relations for YM (or bi-scalar) amplitudes. As a byproduct, a graph-based BCJ relation is proposed and proved.
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