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This paper is concerned with the problem of reconstructing an unknown rank-one matrix with prior structural information from noisy observations. While computing the Bayes optimal estimator is intractable in general due to the requirement of computing high-dimensional integrations/summations, Approximate Message Passing (AMP) emerges as an efficient first-order method to approximate the Bayes optimal estimator. However, the theoretical underpinnings of AMP remain largely unavailable when it starts from random initialization, a scheme of critical practical utility. Focusing on a prototypical model called Z 2 synchronization, we characterize the finite-sample dynamics of AMP from random initialization, uncovering its rapid global convergence. Our theory—which is nonasymptotic in nature—in this model unveils the non-necessity of a careful initialization for the success of AMP. 

Abstract Background Events of gene fusion have been reported in several organisms. However, the general role of gene fusion as part of new gene origination remains unknown. Results We conduct genome-wide interrogations of four Oryza genomes by designing and implementing novel pipelines to detect fusion genes. Based on the phylogeny of ten plant species, we detect 310 fusion genes across four Oryza species. The estimated rate of origination of fusion genes in the Oryza genus is as high as 63 fusion genes per species per million years, which is fixed at 16 fusion genes per species per million years and much higher than that in flies. By RNA sequencing analysis, we find more than 44% of the fusion genes are expressed and 90% of gene pairs show strong signals of purifying selection. Further analysis of CRISPR/Cas9 knockout lines indicates that newly formed fusion genes regulate phenotype traits including seed germination, shoot length and root length, suggesting the functional significance of these genes. Conclusions We detect new fusion genes that may drive phenotype evolution in Oryza. This study provides novel insights into the genome evolution of Oryza. 

A bstract In celestial holography, four-dimensional scattering amplitudes are considered as two-dimensional conformal correlators of a putative two-dimensional celestial conformal field theory (CCFT). The simplest way of converting momentum space amplitudes into CCFT correlators is by taking their Mellin transforms with respect to light-cone energies. For massless particles, like gluons, however, such a construction leads to three-point and four-point correlators that vanish everywhere except for a measure zero hypersurface of celestial coordinates. This is due to the four-dimensional momentum conservation law that constrains the insertion points of the operators associated with massless particles. These correlators are reminiscent of Coulomb gas correlators that, in the absence of background charges, vanish due to charge conservation. We supply the background momentum by coupling Yang-Mills theory to a background dilaton field, with the (complex) dilaton source localized on the celestial sphere. This picture emerges from the physical interpretation of the solutions of the system of differential equations discovered by Banerjee and Ghosh. We show that the solutions can be written as Mellin transforms of the amplitudes evaluated in such a dilaton background. The resultant three-gluon and four-gluon amplitudes are single-valued functions of celestial coordinates enjoying crossing symmetry and all other properties expected from standard CFT correlators. We use them to extract OPEs and compare them with the OPEs extracted from multi-gluon celestial amplitudes without a dilaton background. We perform the conformal block decomposition of the four-gluon single-valued correlator and determine the dimensions, spin and group representations of the entire primary field spectrum of the Yang-Mills sector of CCFT. 

A bstract In a recent paper, here referred to as part I, we considered the celestial four-gluon amplitude with one gluon represented by the shadow transform of the corresponding primary field operator. This correlator is ill-defined because it contains branch points related to the presence of conformal blocks with complex spin. In this work, we adopt a procedure similar to minimal models and construct a single-valued completion of the shadow correlator, in the limit when the shadow is “soft.” By following the approach of Dotsenko and Fateev, we obtain an integral representation of such a single-valued correlator. This allows inverting the shadow transform and constructing a single-valued celestial four-gluon amplitude. This amplitude is drastically different from the original Mellin amplitude. It is defined over the entire complex plane and has correct crossing symmetry, OPE and bootstrap properties. It agrees with all known OPEs of celestial gluon operators. The conformal block spectrum consists of primary fields with dimensions ∆ = m + iλ , with integer m ≥ 1 and various, but always integer spin, in all group representations contained in the product of two adjoint representations. 

A bstract In celestial conformal field theory, gluons are represented by primary fields with dimensions ∆ = 1 + iλ , λ ∈ ℝ and spin J = ±1, in the adjoint representation of the gauge group. All two- and three-point correlation functions of these fields are zero as a consequence of four-dimensional kinematic constraints. Four-point correlation functions contain delta-function singularities enforcing planarity of four-particle scattering events. We relax these constraints by taking a shadow transform of one field and perform conformal block decomposition of the corresponding correlators. We compute the conformal block coefficients. When decomposed in channels that are “compatible” in two and four dimensions, such four-point correlators contain conformal blocks of primary fields with dimensions ∆ = 2 + M + iλ , where M ≥ 0 is an integer, with integer spin J = −M, −M + 2 , … , M − 2 , M . They appear in all gauge group representations obtained from a tensor product of two adjoint representations. When decomposed in incompatible channels, they also contain primary fields with continuous complex spin, but with positive integer dimensions.