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In 2008, we published the first set of guidelines for standardizing research in autophagy. Since then, this topic has received increasing attention, and many scientists have entered the field. Our knowledge base and relevant new t...
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In 2008, we published the first set of guidelines for standardizing research in autophagy. Since then, this topic has received increasing attention, and many scientists have entered the field. Our knowledge base and relevant new technologies have also been expanding. Thus, it is important to formulate on a regular basis updated guidelines for monitoring autophagy in different organisms. Despite numerous reviews, there continues to be confusion regarding acceptable methods to evaluate autophagy, especially in multicellular eukaryotes. Here, we present a set of guidelines for investigators to select and interpret methods to examine autophagy and related processes, and for reviewers to provide realistic and reasonable critiques of reports that are focused on these processes. These guidelines are not meant to be a dogmatic set of rules, because the appropriateness of any assay largely depends on the question being asked and the system being used. Moreover, no individual assay is perfect for every situation, calling for the use of multiple techniques to properly monitor autophagy in each experimental setting. Finally, several core components of the autophagy machinery have been implicated in distinct autophagic processes (canonical and noncanonical autophagy), implying that genetic approaches to block autophagy should rely on targeting two or more autophagy-related genes that ideally participate in distinct steps of the pathway. Along similar lines, because multiple proteins involved in autophagy also regulate other cellular pathways including apoptosis, not all of them can be used as a specific marker for bona fide autophagic responses. Here, we critically discuss current methods of assessing autophagy and the information they can, or cannot, provide. Our ultimate goal is to encourage intellectual and technical innovation in the field.
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We study global fluctuations for singular values of M-fold products of several right-unitarily invariant N x N random matrix ensembles. As N -> infinity, we show the fluctuations of their height functions converge to an explicit G...
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We study global fluctuations for singular values of M-fold products of several right-unitarily invariant N x N random matrix ensembles. As N -> infinity, we show the fluctuations of their height functions converge to an explicit Gaussian field, which is log-correlated for M fixed and has a white noise component for M -> infinity jointly with N. Our technique centers on the study of the multivariate Bessel generating functions of these spectral measures, for which we prove a central limit theorem for global fluctuations via certain conditions on the generating functions. We apply our approach to a number of ensembles, including square roots of Wishart, Jacobi, and unitarily invariant positive definite matrices with fixed spectrum. using a detailed asymptotic analysis of multivariate Bessel functions to verify the necessary conditions.
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We study the nonconvex optimization landscape for maximum likelihood estimation in the discrete orbit recovery model with Gaussian noise. This is a statistical model motivated by applications in molecular microscopy and image proc...
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We study the nonconvex optimization landscape for maximum likelihood estimation in the discrete orbit recovery model with Gaussian noise. This is a statistical model motivated by applications in molecular microscopy and image processing, where each measurement of an unknown object is subject to an independent random rotation from a known rotational group. Equivalently, it is a Gaussian mixture model where the mixture centers belong to a group orbit. We show that fundamental properties of the likelihood landscape depend on the signal-to-noise ratio and the group structure. At low noise, this landscape is "benign" for any discrete group, possessing no spurious local optima and only strict saddle points. At high noise, this landscape may develop spurious local optima, depending on the specific group. We discuss several positive and negative examples, and provide a general condition that ensures a globally benign landscape at high noise. For cyclic permutations of coordinates on Double-struck capital Rd (multireference alignment), there may be spurious local optima when d >= 6, and we establish a correspondence between these local optima and those of a surrogate function of the phase variables in the Fourier domain. We show that the Fisher information matrix transitions from resembling that of a single Gaussian distribution in low noise to having a graded eigenvalue structure in high noise, which is determined by the graded algebra of invariant polynomials under the group action. In a local neighborhood of the true object, where the neighborhood size is independent of the signal-to-noise ratio, the landscape is strongly convex in a reparametrized system of variables given by a transcendence basis of this polynomial algebra. We discuss implications for optimization algorithms, including slow convergence of expectation-maximization, and possible advantages of momentum-based acceleration and variable reparametrization for first- and second-order descent methods. (c) 2021 Wiley Periodicals LLC.
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We show that the traces of -intertwiners of [ESV02] valued in the three-dimensional evaluation representation converge in a certain region of parameters and give a representation-theoretic construction of Felder-Varchenko's hyperg...
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We show that the traces of -intertwiners of [ESV02] valued in the three-dimensional evaluation representation converge in a certain region of parameters and give a representation-theoretic construction of Felder-Varchenko's hypergeometric solutions to the q-KZB heat equation given in [FV02]. This gives the first proof that such a trace function converges and resolves the first case of the Etingof-Varchenko conjecture of [EV00]. As applications, we prove a symmetry property for traces of intertwiners and prove Felder-Varchenko's conjecture in [FV04] that their elliptic Macdonald polynomials are related to the affine Macdonald polynomials defined as traces over irreducible integrable -modules in [EK95]. In the trigonometric and classical limits, we recover results of [EK94,EV00]. Our method relies on an interplay between the method of coherent states applied to the free field realization of the q-Wakimoto module of [Mat94], convergence properties given by the theta hypergeometric integrals of [FV02], and rationality properties originating from the representation-theoretic definition of the trace function.
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We modify and give complete proofs for the results of Etingof-Schiffmann-Varchenko in [ESV02] on traces of intertwiners of untwisted quantum affine algebras in the opposite coproduct and the standard grading. More precisely, we sh...
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We modify and give complete proofs for the results of Etingof-Schiffmann-Varchenko in [ESV02] on traces of intertwiners of untwisted quantum affine algebras in the opposite coproduct and the standard grading. More precisely, we show that certain normalized generalized traces solve four commuting systems of q-difference equations: the Macdonald-Ruijsenaars, dual Macdonald-Ruijsenaars, q-KZB, and dual q-KZB equations. In addition, we show a symmetry property for these renormalized trace functions. Our modifications are motivated by their appearance in the recent work [Sun16].
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We provide Harish-Chandra type formulas for the multivariate Bessel functions and Heckman Opdam hypergeometric functions as representation-valued integrals over dressing orbits. Our expression is the quasi-classical limit of the r...
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We provide Harish-Chandra type formulas for the multivariate Bessel functions and Heckman Opdam hypergeometric functions as representation-valued integrals over dressing orbits. Our expression is the quasi-classical limit of the realization of Macdonald polynomials as traces of intertwiners of quantum groups given by Etingof and Kirillov Jr. in [10]. Integration over the Liouville tori of the Gelfand-Tsetlin integrable system and adjunction for higher Calogero-Moser Hamiltonians recovers and gives a new proof of the integral realization over Gelfand-Tsetlin polytopes which appeared in the recent work [4] of Borodin and Gorin on the beta-Jacobi corners ensemble. (C) 2015 Elsevier Inc. All rights reserved.
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Bond relaxation from one equilibrium to another under perturbation matters uniquely the performance of a substance and thus it has enormous impact to materials science and engineering. However, the basic rules for the perturbation...
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Bond relaxation from one equilibrium to another under perturbation matters uniquely the performance of a substance and thus it has enormous impact to materials science and engineering. However, the basic rules for the perturbation-bond-property correlation and efficient probing strategies for high-resolution detection stay yet great challenge. This treatise features recent progress in this regard with focus on the multifield bond oscillation notion and the theory-enabled phonon spectrometrics. From the perspective of Fourier transformation and the Taylor series of the potentials, we correlate the phonon spectral signatures directly to the transition of the characteristic bonds in terms of stiffness (frequency shift), number fraction (integral of the differential spectral peak), structure fluctuation (linewidth), and the macroscopic properties of the substance. A systematic examination of the spectral feature evolution for group IV, III-V, II-VI crystals, layered graphene nanoribbons, black phosphor, (W, Mo)(S-2, Se-2) flakes, typical nanocrystals, and liquid water and aqueous solutions under perturbation has enabled the ever-unexpected information on the perturbation-bond-property regulations. Consistency between predictions and measurements of the crystal size-resolved phonon frequency shift clarifies that atomic dimer oscillation dictates the vibration modes showing blueshift while the collective vibration of oscillators formed between a certain atom and its nearest neighbors governs the modes of redshift when the sample size is reduced. Theoretical matching to the phonon frequency shift due to atomic undercoordination, mechanical and thermal activation, and aqueous charge injection by solvation has been realized. The reproduction of experimental measurements has turned out quantitative information of bond length, bond energy, single bond force constant, binding energy density, vibration mode activation energy, Debye temperature, elastic modulus, and the number and stiffness transition of bonds from the mode of references to the conditioned upon perturbation. Findings prove not only the essentiality of the multifield lattice oscillating dynamics but also the immense power of the phonon spectrometrics in revealing the bond-phonon-property correlation of solid and liquid substance.
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We refine the statement of the denominator and evaluation conjectures for affine Macdonald polynomials proposed by Etingof-Kirillov Jr. (Duke Math J 78(2):229-256, 1995) and prove the first non-trivial cases of these conjectures. ...
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We refine the statement of the denominator and evaluation conjectures for affine Macdonald polynomials proposed by Etingof-Kirillov Jr. (Duke Math J 78(2):229-256, 1995) and prove the first non-trivial cases of these conjectures. Our results provide a q-deformation of the computation of genus 1 conformal blocks via elliptic Selberg integrals by Felder-Stevens-Varchenko (Math Res Lett 10(5-6):671-684, 2003). They allow us to give precise formulations for the affine Macdonald conjectures in the general case which are consistent with computer computations. Our method applies recent work of the second named author to relate these conjectures in the case of to evaluations of certain theta hypergeometric integrals defined by Felder-Varchenko (Int Math Res Not 21:1037-1055, 2004). We then evaluate the resulting integrals, which may be of independent interest, by well-chosen applications of the elliptic beta integral introduced by Spiridonov (Uspekhi Mat Nauk 56(1(337)):181-182, 2001).
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We give a new representation-theoretic proof of the branching rule for Macdonald polynomials using the Etingof-Kirillov Jr. expression for Macdonald polynomials as traces of intertwiners of U-q(gl(n)) given in [11]. In the Gelfand...
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We give a new representation-theoretic proof of the branching rule for Macdonald polynomials using the Etingof-Kirillov Jr. expression for Macdonald polynomials as traces of intertwiners of U-q(gl(n)) given in [11]. In the Gelfand-Tsetlin basis, we show that diagonal matrix elements of such intertwiners are given by application of Macdonald's operators to a simple kernel. An essential ingredient in the proof is a map between spherical parts of double affine Hecke algebras of different ranks based upon the Dunkl-Kasatani conjecture of [8, 9, 13, 20].
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