Law of the iterated logarithm for stationary processes

There has been recent interest in the conditional central limit question for (strictly) stationary, ergodic processes $...,X_{-1},X_0,X_1,...$ whose partial sums $S_n=X_1+...+X_n$ are of the form $S_n=M_n+R_n$, where $M_n$ is a square integrable martingale with stationary increments and $R_n$ is a remainder term for which $E(R_n^2)=o(n)$. Here we explore the law of the iterated logarithm (LIL) for the same class of processes. Letting $\Vert\cdot\Vert$ denote the norm in $L^2(P)$, a sufficient condition for the partial sums of a stationary process to have the form $S_n=M_n+R_n$ is that $n^{-3/2}\Vert E(S_n|X_0,X_{-1},...)\Vert$ be summable. A sufficient condition for the LIL is only slightly stronger, requiring $n^{-3/2}\log^{3/2}(n)\Vert E(S_n|X_0,X_{-1},...)\Vert$ to be summable. As a by-product of our main result, we obtain an improved statement of the conditional central limit theorem. Invariance principles are obtained as well.Comment: Published in at http://dx.doi.org/10.1214/009117907000000079 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

On martingale approximations

Consider additive functionals of a Markov chain $W_k$, with stationary (marginal) distribution and transition function denoted by $\pi$ and $Q$, say $S_n=g(W_1)+...+g(W_n)$, where $g$ is square integrable and has mean 0 with respect to $\pi$. If $S_n$ has the form $S_n=M_n+R_n$, where $M_n$ is a square integrable martingale with stationary increments and $E(R_n^2)=o(n)$, then $g$ is said to admit a martingale approximation. Necessary and sufficient conditions for such an approximation are developed. Two obvious necessary conditions are $E[E(S_n|W_1)^2]=o(n)$ and $\lim_{n\to \infty}E(S_n^2)/n<\infty$. Assuming the first of these, let $\Vert g\Vert^2_+=\limsup_{n\to \infty}E(S_n^2)/n$; then $\Vert\cdot\Vert_+$ defines a pseudo norm on the subspace of $L^2(\pi)$ where it is finite. In one main result, a simple necessary and sufficient condition for a martingale approximation is developed in terms of $\Vert\cdot\Vert_+$. Let $Q^*$ denote the adjoint operator to $Q$, regarded as a linear operator from $L^2(\pi)$ into itself, and consider co-isometries ($QQ^*=I$), an important special case that includes shift processes. In another main result a convenient orthonormal basis for $L_0^2(\pi)$ is identified along with a simple necessary and sufficient condition for the existence of a martingale approximation in terms of the coefficients of the expansion of $g$ with respect to this basis.Comment: Published in at http://dx.doi.org/10.1214/07-AAP505 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Early selection of \u3cem\u3ebZIP73\u3c/em\u3e facilitated adaptation of \u3cem\u3ejaponica\u3c/em\u3e rice to cold climates

Cold stress is a major factor limiting production and geographic distribution of rice (Oryza sativa). Although the growth range of japonica subspecies has expanded northward compared to modern wild rice (O. rufipogon), the molecular basis of the adaptation remains unclear. Here we report bZIP73, a bZIP transcription factor-coding gene with only one functional polymorphism (+511 G\u3eA) between the two subspecies japonica and indica, may have facilitated japonica adaptation to cold climates. We show the japonica version of bZIP73 (bZIP73Jap) interacts with bZIP71 and modulates ABA levels and ROS homeostasis. Evolutionary and population genetic analyses suggest bZIP73 has undergone balancing selection; the bZIP73Jap allele has firstly selected from standing variations in wild rice and likely facilitated cold climate adaptation during initial japonica domestication, while the indica allele bZIP73Ind was subsequently selected for reasons that remain unclear. Our findings reveal early selection of bZIP73Jap may have facilitated climate adaptation of primitive rice germplasms

Low-frequency dynamic ocean response to barometric-pressure loading

Author Posting. © American Meteorological Society, 2022. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 52(11), (2022): 2627-2641, https://doi.org/10.1175/jpo-d-22-0090.1.Changes in dynamic manometric sea level ζm represent mass-related sea level changes associated with ocean circulation and climate. We use twin model experiments to quantify magnitudes and spatiotemporal scales of ζm variability caused by barometric pressure pa loading at long periods (≳1 month) and large scales (≳300km) relevant to Gravity Recovery and Climate Experiment (GRACE) ocean data. Loading by pa drives basin-scale monthly ζm variability with magnitudes as large as a few centimeters. Largest ζm signals occur over abyssal plains, on the shelf, and in marginal seas. Correlation patterns of modeled ζm are determined by continental coasts and H/f contours (H is ocean depth and f is Coriolis parameter). On average, ζm signals forced by pa represent departures of ≲10% and ≲1% from the inverted-barometer effect ζib on monthly and annual periods, respectively. Basic magnitudes, spatial patterns, and spectral behaviors of ζm from the model are consistent with scaling arguments from barotropic potential vorticity conservation. We also compare ζm from the model driven by pa to ζm from GRACE observations. Modeled and observed ζm are significantly correlated across parts of the tropical and extratropical oceans, on shelf and slope regions, and in marginal seas. Ratios of modeled to observed ζm magnitudes are as large as ∼0.2 (largest in the Arctic Ocean) and qualitatively agree with analytical theory for the gain of the transfer function between ζm forced by pa and wind stress. Results demonstrate that pa loading is a secondary but nevertheless important contributor to monthly mass variability from GRACE over the ocean.The authors acknowledge support from the National Aeronautics and Space Administration through the GRACE Follow-On Science Team (Grant 80NSSC20K0728) and the Sea Level Change Team (Grant 80NSSC20K1241). The contribution from I. F. and O. W. represents research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration (Grant 80NM0018D0004)

Reciprocal roles of DBC1 and SIRT1 in regulating estrogen receptor α activity and co-activator synergy

Estrogen receptor α (ERα) plays critical roles in development and progression of breast cancer. Because ERα activity is strictly dependent upon the interaction with coregulators, coregulators are also believed to contribute to breast tumorigenesis. Cell Cycle and Apoptosis Regulator 1 (CCAR1) is an important co-activator for estrogen-induced gene expression and estrogen-dependent growth of breast cancer cells. Here, we identified Deleted in Breast Cancer 1 (DBC1) as a CCAR1 binding protein. DBC1 was recently shown to function as a negative regulator of the NAD-dependent protein deacetylase SIRT1. DBC1 associates directly with ERα and cooperates synergistically with CCAR1 to enhance ERα function. DBC1 is required for estrogen-induced expression of a subset of ERα target genes as well as breast cancer cell proliferation and for estrogen-induced recruitment of ERα to the target promoters in a gene-specific manner. The mechanism of DBC1 action involves inhibition of SIRT1 interaction with ERα and of SIRT1-mediated deacetylation of ERα. SIRT1 also represses the co-activator synergy between DBC1 and CCAR1 by binding to DBC1 and disrupting its interaction with CCAR1. Our results indicate that DBC1 and SIRT1 play reciprocal roles as major regulators of ERα activity, by regulating DNA binding by ERα and by regulating co-activator synergy

Actin filament reorganisation controlled by the SCAR/WAVE complex mediates stomatal response to darkness.

This is the final version of the article. Available from the publisher via the DOI in this record.Stomata respond to darkness by closing to prevent excessive water loss during the night. Although the reorganisation of actin filaments during stomatal closure is documented, the underlying mechanisms responsible for dark-induced cytoskeletal arrangement remain largely unknown. We used genetic, physiological and cell biological approaches to show that reorganisation of the actin cytoskeleton is required for dark-induced stomatal closure. The opal5 mutant does not close in response to darkness but exhibits wild-type (WT) behaviour when exposed to abscisic acid (ABA) or CaCl2 . The mutation was mapped to At5g18410, encoding the PIR/SRA1/KLK subunit of the ArabidopsisSCAR/WAVE complex. Stomata of an independent allele of the PIR gene (Atpir-1) showed reduced sensitivity to darkness and F1 progenies of the cross between opal5 and Atpir-1 displayed distorted leaf trichomes, suggesting that the two mutants are allelic. Darkness induced changes in the extent of actin filament bundling in WT. These were abolished in opal5. Disruption of filamentous actin using latrunculin B or cytochalasin D restored wild-type stomatal sensitivity to darkness in opal5. Our findings suggest that the stomatal response to darkness is mediated by reorganisation of guard cell actin filaments, a process that is finely tuned by the conserved SCAR/WAVE-Arp2/3 actin regulatory module.This work was supported by grants from the BBSRC (BB/ N001168/1; BB/J002364/1; BBF001177/1), The Gatsby Charitable Foundation and the Leverhulme Trust to A.M.H. and grants from the National Natural Science Foundation of China (nos. 31300213 and 31670408 to K.J.). This work was also supported by the Centre National de la Recherche Scientifique and the Commissariat a l’Energie Atomique et aux Energies Alternatives (for the IR camera) and the European Union Marie Curie FP5 Research Training Network (program no. STRESSIMAGING HNRT-CT-2002-00254 to J.M.C. and B.G.). J.M.C. was in addition supported by a scholarship of the Fundac ~ao para a Ci^encia e Tecnologia, Portugal (grant no. SFRH/BPD/34429/2006)

Spatiotemporal transcriptomic atlas of mouse organogenesis using DNA nanoball-patterned arrays.

Spatially resolved transcriptomic technologies are promising tools to study complex biological processes such as mammalian embryogenesis. However, the imbalance between resolution, gene capture, and field of view of current methodologies precludes their systematic application to analyze relatively large and three-dimensional mid- and late-gestation embryos. Here, we combined DNA nanoball (DNB)-patterned arrays and in situ RNA capture to create spatial enhanced resolution omics-sequencing (Stereo-seq). We applied Stereo-seq to generate the mouse organogenesis spatiotemporal transcriptomic atlas (MOSTA), which maps with single-cell resolution and high sensitivity the kinetics and directionality of transcriptional variation during mouse organogenesis. We used this information to gain insight into the molecular basis of spatial cell heterogeneity and cell fate specification in developing tissues such as the dorsal midbrain. Our panoramic atlas will facilitate in-depth investigation of longstanding questions concerning normal and abnormal mammalian development.This work is part of the ‘‘SpatioTemporal Omics Consortium’’ (STOC) paper package. A list of STOC members is available at: http://sto-consortium.org. We would like to thank the MOTIC China Group, Rongqin Ke (Huaqiao University, Xiamen, China), Jiazuan Ni (Shenzhen University, Shenzhen, China), Wei Huang (Center for Excellence in Brain Science and Intelligence Technology, Chinese Academy of Sciences, Shanghai, China), and Jonathan S. Weissman (Whitehead Institute, Boston, USA) for their help. This work was supported by the grant of Top Ten Foundamental Research Institutes of Shenzhen, the Shenzhen Key Laboratory of Single-Cell Omics (ZDSYS20190902093613831), and the Guangdong Provincial Key Laboratory of Genome Read and Write (2017B030301011); Longqi Liu was supported by the National Natural Science Foundation of China (31900466) and Miguel A. Esteban’s laboratory at the Guangzhou Institutes of Biomedicine and Health by the Strategic Priority Research Program of the Chinese Academy of Sciences (XDA16030502), National Natural Science Foundation of China (92068106), and the Guangdong Basic and Applied Basic Research Foundation (2021B1515120075).S