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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. DEAD-box helicases (DDXs) function in an ATP-dependent, non-processive manner and the conserved helicase core is composed of two RecA-like domains D1 and D2. Here the authors present the crystal structure of the D1D2 core from human DDX3X bound to a 23-base pair dsRNA in the pre-unwound state and discuss the implications for helicase mechanism.

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.

A bstract In this paper, we compute holographic Euclidean thermal correlators of the stress tensor and U(1) current from the AdS planar black hole. To this end, we set up perturbative boundary value problems for Einstein’s gravity and Maxwell theory in the spirit of Gubser-Klebanov-Polyakov-Witten, with appropriate gauge fixing and regularity boundary conditions at the horizon of the black hole. The linearized Einstein equation and Maxwell equation in the black hole background are related to the Heun equation of degenerate local monodromy. Leveraging the connection relation of local solutions of the Heun equation, we partly solve the boundary value problem and obtain exact two-point thermal correlators for U(1) current and stress tensor in the scalar and shear channels.

A bstract Canonical forms of positive geometries play an important role in revealing hidden structures of scattering amplitudes, from amplituhedra to associahedra. In this paper, we introduce “stringy canonical forms”, which provide a natural definition and extension of canonical forms for general polytopes, deformed by a parameter α′ . They are defined by real or complex integrals regulated with polynomials with exponents, and are meromorphic functions of the exponents, sharing various properties of string amplitudes. As α′→ 0, they reduce to the usual canonical form of a polytope given by the Minkowski sum of the Newton polytopes of the regulating polynomials, or equivalently the volume of the dual of this polytope, naturally determined by tropical functions. At finite α′ , they have simple poles corresponding to the facets of the polytope, with the residue on the pole given by the stringy canonical form of the facet. There is the remarkable connection between the α′→ 0 limit of tree-level string amplitudes, and scattering equations that appear when studying the α′→ ∞ limit. We show that there is a simple conceptual understanding of this phenomenon for any stringy canonical form: the saddle-point equations provide a diffeomorphism from the integration domain to the interior of the polytope, and thus the canonical form can be obtained as a pushforward via summing over saddle points. When the stringy canonical form is applied to the ABHY associahedron in kinematic space, it produces the usual Koba-Nielsen string integral, giving a direct path from particle to string amplitudes without an a priori reference to the string worldsheet. We also discuss a number of other examples, including stringy canonical forms for finite-type cluster algebras (with type A corresponding to usual string amplitudes), and other natural integrals over the positive Grassmannian.

Background. Solid pseudopapillary tumor of the pancreas (SPTP) has been reported as a rare disease with low malignant potential. The aim of this study was to summarize experiences of the diagnosis and treatment for the patients reported in the Chinese population. Method. 2450 SPTP cases reported in English and Chinese literature before Jan 2020 were for our review and analysis retrospectively. Result. There are 389 male cases and 2061 female cases, and the ratio of male/female was 1 : 5.3. The average age was 29.3 years. The main clinical symptoms were upper abdominal pain and bloating discomfort in 51.6% of the cases and epigastric mass. 38.6% of the tumor was located at the head of the pancreas and 55.4% at the body and tail of the pancreas. The most frequent operative styles were tumor enucleation (38.4%). Pathology showed that the average diameter of the tumor was 8.2 cm and 12.3% of SPTP was malignant. 98.3% of cases had favorable survival. Conclusions. SPTP is a rare indolent tumor occurring mainly in young women, and the main clinical performances are abdominal mass and abdominal pain; most tumors are distributed at the head and the tail of the pancreas; the prognosis after complete resection is excellent.

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.

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.

A bstract We define and study infinite families of all-loop planar, dual conformal invariant (DCI) integrals, which contribute to four-point Coulomb-branch amplitudes and correlators in supersymmetric Yang-Mills theory, by solving “boxing” differential equations via HyperlogProcedures [ https://www.math.fau.de/person/oliver-schnetz/ ]; the resulting single-valued harmonic polylogarithmic functions (SVHPL) are nicely labeled by “binary” strings of 0 and 1 without consecutive 1’s. These functions are special cases of the so-called generalized ladders studied in [ JHEP 02 (2013) 092], where extended Steinmann relations (no consecutive 1’s) are imposed due to planarity. Our results can be viewed as “two-dimensional” extensions of the well-known ladder integrals to many more infinite families of DCI integrals: the ladders have strings with a single 1 followed by all 0’s, and the other extreme, which nicely evaluate to the “zigzag” SVHPL functions with alternating 1’s and 0’s, are nothing but the four-point DCI integrals from the very special family of anti-prism f -graphs (while all other binary DCI integrals lie in between these two extreme cases). We also study periods of these integrals: while their periods are in general complicated single-valued multiple zeta values (SVMZV), the “zigzag” DCI integrals from anti-prism gives exactly the famous “zigzag” periods proportional to ζ 2 L +1 , and empirically it provides a numerical lower-bound for L -loop periods of any binary string, with the upper-bound given by that of the ladder (also proportional to ζ 2 L +1 ). Based on f -graphs as a tool for studying these periods, we discuss several interesting facts and observations about these (motivic) SVMZV and relations among them to all loops, and enumerate a basis for them up to L = 10.

A bstract Recent years have seen the emergence of a new understanding of scattering amplitudes in the simplest theory of colored scalar particles — the Tr( ϕ 3 ) theory — based on combinatorial and geometric ideas in the kinematic space of scattering data. In this paper we report a surprise: far from the toy model it appears to be, the “stringy” Tr( ϕ 3 ) amplitudes secretly contains the scattering amplitudes for pions, as well as non-supersymmetric gluons, in any number of dimensions. The amplitudes for the different theories are given by one and the same function, related by a simple shift of the kinematics. This discovery was spurred by another fundamental observation: the tree-level Tr( ϕ 3 ) field theory amplitudes have a hidden pattern of zeros when a special set of non-planar Mandelstam invariants is set to zero. These zeros are not manifest in Feynman diagrams but are made obvious by the connection of these amplitudes to the new understanding of associahedra arising from “causal diamonds” in kinematic space. Furthermore, near these zeros, the amplitudes simplify, by factoring into a non-trivial product of smaller amplitudes. Remarkably the amplitudes for pions and gluons are observed to also vanish in the same kinematical locus. These properties for Tr( ϕ 3 ) amplitudes hold and further generalize to the “stringy” Tr( ϕ 3 ) amplitudes. The “kinematic causal diamond” picture suggests a unique shift of the kinematic data that preserves the zeros, and this shift is precisely the one that unifies colored scalars, pions, and gluons into a single object. We will focus in this paper on explaining the hidden zeros and factorization properties and the connection between all the colored theories, working for simplicity at tree level. Subsequent works will describe this new formulation for the Non-linear Sigma Model and non-supersymmetric Yang-Mills theory, at all loop orders.