The Rényi entanglement entropy (REE) of the states excited by local operators in two-dimensional irrational conformal field theories (CFTs), especially in Liouville field theory (LFT) and N = 1 ...super-Liouville field theory (SLFT), has been investigated. In particular, the excited states obtained by acting on the vacuum with primary operators were considered. We start from evaluating the second REE in a compact c = 1 free boson field theory at generic radius, which is an irrational CFT. Then we focus on the two special irrational CFTs, e.g., LFT and SLFT. In these theories, the second REE of such local excited states becomes divergent in early and late time limits. For simplicity, we study the memory effect of REE for the two classes of the local excited states in LFT and SLFT. In order to restore the quasiparticles picture, we define the difference of REE between target and reference states, which belong to the same class. The variation of the difference of REE between early and late time limits always coincides with the log of the ratio of the fusion matrix elements between target and reference states. Furthermore, the locally excited states by acting generic descendent operators on the vacuum have been also investigated. The variation of the difference of REE is the summation of the log of the ratio of the fusion matrix elements between the target and reference states and an additional normalization factor. Since the identity operator (or vacuum state) does not live in the Hilbert space of LFT and SLFT and no discrete terms contribute to REE in the intermediate channel, the variation of the difference of REE between target and reference states is no longer the log of the quantum dimension which is shown in the 1 + 1 -dimensional rational CFTs (RCFTs).
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DEAD-box helicases (DDXs) regulate RNA processing and metabolism by unwinding short double-stranded (ds) RNAs. Sharing a helicase core composed of two RecA-like domains (D1D2), DDXs function in an ...ATP-dependent, non-processive manner. As an attractive target for cancer and AIDS treatment, DDX3X and its orthologs are extensively studied, yielding a wealth of biochemical and biophysical data, including structures of apo-D1D2 and post-unwound D1D2:single-stranded RNA complex, and the structure of a D2:dsRNA complex that is thought to represent a pre-unwound state. However, the structure of a pre-unwound D1D2:dsRNA complex remains elusive, and thus, the mechanism of DDX action is not fully understood. Here, we describe the structure of a D1D2 core in complex with a 23-base pair dsRNA at pre-unwound state, revealing that two DDXs recognize a 2-turn dsRNA, each DDX mainly recognizes a single RNA strand, and conformational changes induced by ATP binding unwinds the RNA duplex in a cooperative manner.
We present a compact formula for the complete tree-level S-matrix of pure Yang-Mills and gravity theories in arbitrary spacetime dimensions. The new formula for the scattering of n particles is given ...by an integral over the positions of n points on a sphere restricted to satisfy a dimension-independent set of equations. The integrand is constructed using the reduced Pfaffian of a 2n×2n matrix, Ψ, that depends on momenta and polarization vectors. In its simplest form, the gravity integrand is a reduced determinant which is the square of the Pfaffian in the Yang-Mills integrand. Gauge invariance is completely manifest as it follows from a simple property of the Pfaffian.
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A
bstract
In a recent note we presented a compact formula for the complete tree-level S-matrix of pure Yang-Mills and gravity theories in arbitrary spacetime dimension. In this paper we show that a ...natural formulation also exists for a massless colored cubic scalar theory. In Yang-Mills, the formula is an integral over the space of
n
marked points on a sphere and has as integrand two factors. The first factor is a combination of Parke-Taylor-like terms dressed with U(
N
) color structures while the second is a Pfaffian. The S-matrix of a U(
N
) × U(
Ñ
) cubic scalar theory is obtained by simply replacing the Pfaffian with a U(
Ñ
) version of the previous U(
N
) factor. Given that gravity amplitudes are obtained by replacing the U(
N
) factor in Yang-Mills by a second Pfaffian, we are led to a natural color-kinematics correspondence. An expansion of the integrand of the scalar theory leads to sums over trivalent graphs and are directly related to the KLT matrix. Combining this and the Yang-Mills formula we find a connection to the BCJ color-kinematics duality as well as a new proof of the BCJ doubling property that gives rise to gravity amplitudes. We end by considering a special kinematic point where the partial amplitude simply counts the number of color-ordered planar trivalent trees, which equals a Catalan number. The scattering equations simplify dramatically and are equivalent to a special Y-system with solutions related to roots of Chebyshev polynomials. The sum of the integrand over the solutions gives rise to a representation of Catalan numbers in terms of eigenvectors and eigenvalues of the adjacency matrix of an
A
-type Dynkin diagram.
A
bstract
The search for a theory of the S-Matrix over the past five decades has revealed surprising geometric structures underlying scattering amplitudes ranging from the string worldsheet to the ...amplituhedron, but these are all geometries in auxiliary spaces as opposed to the kinematical space where amplitudes actually live. Motivated by recent advances providing a reformulation of the amplituhedron and planar
N
= 4 SYM amplitudes directly in kinematic space, we propose a novel geometric understanding of amplitudes in more general theories. The key idea is to think of amplitudes not as functions, but rather as differential forms on kinematic space. We explore the resulting picture for a wide range of massless theories in general spacetime dimensions. For the bi-adjoint
ϕ
3
scalar theory, we establish a direct connection between its “scattering form” and a classic polytope — the associahedron — known to mathematicians since the 1960’s. We find an associahedron living naturally in kinematic space, and the tree level amplitude is simply the “canonical form” associated with this “positive geometry”. Fundamental physical properties such as locality and unitarity, as well as novel “soft” limits, are fully determined by the combinatorial geometry of this polytope. Furthermore, the moduli space for the open string worldsheet has also long been recognized as an associahedron. We show that the scattering equations act as a diffeomorphism between the interior of this old “worldsheet associahedron” and the new “kinematic associahedron”, providing a geometric interpretation and simple conceptual derivation of the bi-adjoint CHY formula. We also find “scattering forms” on kinematic space for Yang-Mills theory and the Non-linear Sigma Model, which are dual to the fully color-dressed amplitudes despite having no explicit color factors. This is possible due to a remarkable fact—“Color is Kinematics”— whereby kinematic wedge products in the scattering forms satisfy the same Jacobi relations as color factors. Finally, all our scattering forms are well-defined on the projectivized kinematic space, a property which can be seen to provide a geometric origin for color-kinematics duality.
Assessment of groundwater quality and health risk was conducted in the Shenfu coal mine area in Ordos basin, northwestern China. Statistical analysis, Piper and Chadha diagrams were used to reveal ...the hydrogeochemical characteristics of groundwater via physicochemical analysis of 44 collected samples. The suitability of groundwater was assessed for domestic and irrigation purposes, and the fuzzy comprehensive method was adopted to assess the overall groundwater quality for further discussion on groundwater management. The model recommended by the USEPA was selected to estimate the non-carcinogenic risks caused by NO
3
−
, NO
2
−
, NH
4
+
, F
−
, Fe and Mn through oral ingestion and direct dermal contact. The results revealed that the predominant hydrochemical types of groundwater were SO
4
∙Cl–Ca∙Mg and HCO
3
–Ca∙Mg types and the major cations and anions followed the orders of Ca
2+
> Na
+
> Mg
2+
>K
+
and HCO
3
−
> SO
4
2−
> Cl
−
, respectively. Groundwater is generally acceptable for irrigation. However, for domestic purposes, 47.73% of the collected samples are of excellent and good quality and are suitable for direct consumption. Both adults and children face non-carcinogenic risks because of exposure to contaminants such as nitrate, nitrite and fluoride. The risk to children is higher than that to adults, which is consistent with other studies. Nitrite contributes most to the risks, followed by nitrate and fluoride. Home-use water quality improvement devices and rainwater harvesting are suggested to enhance the groundwater quality protection and management in this area. The research also indicates that health risk assessment should always accompany general water quality assessment to ensure the reliability of the water quality assessment.
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A
bstract
Inspired by the idea of viewing amplitudes in
N
=
4
SYM as differential forms on momentum twistor space, we introduce differential forms on the space of spinor variables, which combine ...helicity amplitudes in any four-dimensional gauge theory as a single object. In this note we focus on such differential forms in
N
=
4
SYM, which can also be thought of as “bosonizing” superamplitudes in non-chiral superspace. Remarkably all tree-level amplitudes in
N
=
4
SYM combine to a
d
log form in spinor variables, which is given by pushforward of canonical forms of Grassmannian cells. The tree forms can also be obtained using BCFW or inverse-soft construction, and we present all-multiplicity expression for MHV and NMHV forms to illustrate their simplicity. Similarly all-loop planar integrands can be naturally written as
d
log forms in the Grassmannian/on-shell-diagram picture, and we expect the same to hold beyond the planar limit. Just as the form in momentum twistor space reveals underlying positive geometry of the amplituhedron, the form in terms of spinor variables strongly suggests an “amplituhedron in momentum space”. We initiate the study of its geometry by connecting it to the moduli space of Witten’s twistor-string theory, which provides a pushforward formula for tree forms in
N
=
4
SYM.
Groundwater is critical for the sustainable development of the Loess Plateau, while groundwater quality is generally poor in this area due to natural factors and anthropogenic pollution. This study ...was carried out to investigate the suitability of groundwater for domestic and agricultural purposes in Yan’an City on the Chinese Loess Plateau and to assess its implications to sustainable groundwater management on the plateau. The index levels were compared with the threshold values established by the national and the WHO drinking water guidelines, and the suitability of groundwater for irrigation purposes was assessed using multiple agricultural water quality indicators. An entropy-weighted Technique for Order Preference by Similarity to an Ideal Solution (entropy-weighted TOPSIS) was adopted for overall groundwater quality assessment. The results indicate that the study area is characterized by saline, hard, and slightly alkaline groundwater, mainly of the HCO
3
–Ca·Mg type, accompanied by some minor SO
4
·Cl–Ca·Mg type. The dissolution of carbonates and gypsum and the leaching of soluble salts are important natural processes influencing the groundwater ion chemistry. The parameters TH, TDS, and SO
4
2−
are major indices, while Fe, Mn, F
−
, and NH
4
+
are minor contaminants affecting groundwater quality. The overall groundwater quality is generally acceptable for irrigation, and most of the water is suitable for drinking. Rainwater harvesting, water quality improvement programs, regular water quality monitoring, and multidisciplinary water research programs are suggested as measures for sustainable groundwater management on the Loess Plateau.
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A
bstract
Motivated by reformulating Yangian invariants in planar
N
= 4 SYM directly as
d
log forms on momentum-twistor space, we propose a purely algebraic problem of determining the arguments of ...the
d
log’s, which we call “letters”, for any Yangian invariant. These are functions of momentum twistors
Z
’s, given by the positive coordinates
α
’s of parametrizations of the matrix
C
(
α
), evaluated on the support of polynomial equations
C
(
α
) ·
Z
= 0. We provide evidence that the letters of Yangian invariants are related to the cluster algebra of Grassmannian
G
(4
, n
), which is relevant for the symbol alphabet of
n
-point scattering amplitudes. For
n
= 6
,
7, the collection of letters for all Yangian invariants contains the cluster
A
coordinates of
G
(4
, n
). We determine algebraic letters of Yangian invariant associated with any “four-mass” box, which for
n
= 8 reproduce the 18 multiplicative-independent, algebraic symbol letters discovered recently for two-loop amplitudes.
Enhancing soil organic carbon (SOC) through applying animal manure is of interest for both sustaining cereal production and mitigating greenhouse gas (GHG) emissions. Previous syntheses showed that ...manuring‐induced SOC changes varied substantially with agricultural managements and environmental conditions, while their significance and relative importance to such variability are still largely uncertain. Here, we presented a new synthesis using an updated and balanced database integrating the manuring‐induced SOC stock changes and their plausible explanatory factors in 250 observations at global 120 sites. Manure application increased SOC stock by 7.41 ± 1.14 (95% confidence interval, CI) and 8.96 ± 1.83 (95% CI) Mg C ha−1, respectively, compared to their mineral fertilized (REF‐min) and unfertilized (REF‐zero) references. Of which approx. 72% and 34% were directly contributed by manure‐C input, respectively. Following the IPCC (Intergovernmental Panel on Climate Change) approach, these changes corresponded to the manuring‐induced SOC change factors of 1.27 ± 0.04 (95% CI) and 1.40 ± 0.08 (95% CI), respectively. Basing on a balanced database, we identified the amount of manure‐C input as the most important factor to the global variations in the resultant SOC stock changes. More importantly, our integrative analysis distinguished the significance of soil properties (e.g., soil pH and initial SOC content) in regulating the efficiency of manure application in enhancing SOC stock. These results indicate that, at the similar rate, applying manure could sequestrate much more carbon in alkaline soils than in neutral and acidic soils. By integrating the impacts of agricultural managements and environmental conditions, our findings would help to develop region‐specific tailor‐made manure application measures in agriculture and to refine the SOC change factors for regional GHG inventories.
Baseding on an updated and more balanced database, we evaluated the significance and relative importance of agricultural managements and environmental conditions in determining the manuring‐induced SOC stock changes. The amount of manure‐C input is the most important factor, while soil properties (e.g., soil pH and initial SOC content) govern the efficiency of manure application in enhancing SOC stock. Our findings would help to develop region‐specific tailor‐made manure application measures in agriculture and to refine the SOC change factors for regional GHG inventories.
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