Partition bound is quadratically tight for product distributions

Let $f : \{0,1\}^n \times \{0,1\}^n \rightarrow \{0,1\}$ be a 2-party function. For every product distribution $\mu$ on $\{0,1\}^n \times \{0,1\}^n$, we show that $$\mathsf{CC}^\mu_{0.49}(f) = O\left(\left(\log \mathsf{prt}_{1/8}(f) \cdot \log \log \mathsf{prt}_{1/8}(f)\right)^2\right),$$ where $\mathsf{CC}^\mu_\varepsilon(f)$ is the distributional communication complexity of $f$ with error at most $\varepsilon$ under the distribution $\mu$ and $\mathsf{prt}_{1/8}(f)$ is the {\em partition bound} of $f$, as defined by Jain and Klauck [{\em Proc. 25th CCC}, 2010]. We also prove a similar bound in terms of $\mathsf{IC}_{1/8}(f)$, the {\em information complexity} of $f$, namely, $$\mathsf{CC}^\mu_{0.49}(f) = O\left(\left(\mathsf{IC}_{1/8}(f) \cdot \log \mathsf{IC}_{1/8}(f)\right)^2\right).$$ The latter bound was recently and independently established by Kol [{\em Proc. 48th STOC}, 2016] using a different technique. We show a similar result for query complexity under product distributions. Let $g : \{0,1\}^n \rightarrow \{0,1\}$ be a function. For every bit-wise product distribution $\mu$ on $\{0,1\}^n$, we show that $$\mathsf{QC}^\mu_{0.49}(g) = O\left(\left( \log \mathsf{qprt}_{1/8}(g) \cdot \log \log\mathsf{qprt}_{1/8}(g) \right)^2 \right),$$ where $\mathsf{QC}^\mu_{\varepsilon}(g)$ is the distributional query complexity of $f$ with error at most $\varepsilon$ under the distribution $\mu$ and $\mathsf{qprt}_{1/8}(g))$ is the {\em query partition bound} of the function $g$. Partition bounds were introduced (in both communication complexity and query complexity models) to provide LP-based lower bounds for randomized communication complexity and randomized query complexity. Our results demonstrate that these lower bounds are polynomially tight for {\em product} distributions.Comment: The previous version of the paper erroneously stated the main result in terms of relaxed partition number instead of partition numbe

Motion correction for phase-resolved dynamic optical coherence tomography imaging of rodent cerebral cortex

Cardiac and respiratory motions in animals are the primary source of image quality degradation in dynamic imaging studies, especially when using phase-resolved imaging modalities such as spectral-domain optical coherence tomography (SD-OCT), whose phase signal is very sensitive to movements of the sample. This study demonstrates a method with which to compensate for motion artifacts in dynamic SD-OCT imaging of the rodent cerebral cortex. We observed that respiratory and cardiac motions mainly caused, respectively, bulk image shifts (BISs) and global phase fluctuations (GPFs). A cross-correlation maximization-based shift correction algorithm was effective in suppressing BISs, while GPFs were significantly reduced by removing axial and lateral global phase variations. In addition, a non-origin-centered GPF correction algorithm was examined. Several combinations of these algorithms were tested to find an optimized approach that improved image stability from 0.5 to 0.8 in terms of the cross-correlation over 4 s of dynamic imaging, and reduced phase noise by two orders of magnitude in ~8% voxels.K99 NS067050 - NINDS NIH HHS; R01EB000790 - NIBIB NIH HHS; R01 EB001954 - NIBIB NIH HHS; R01 EB001954-09 - NIBIB NIH HHS; P01NS055104 - NINDS NIH HHS; R01 NS057476 - NINDS NIH HHS; K99NS067050 - NINDS NIH HHS; R01 EB000790 - NIBIB NIH HHS; R01-EB001954 - NIBIB NIH HHS; R01NS057476 - NINDS NIH HHS; P01 NS055104 - NINDS NIH HHS; P41 EB015896 - NIBIB NIH HHSPublished versio

Multiparametric, Longitudinal Optical Coherence Tomography Imaging Reveals Acute Injury and Chronic Recovery in Experimental Ischemic Stroke

Progress in experimental stroke and translational medicine could be accelerated by high-resolution in vivo imaging of disease progression in the mouse cortex. Here, we introduce optical microscopic methods that monitor brain injury progression using intrinsic optical scattering properties of cortical tissue. A multi-parametric Optical Coherence Tomography (OCT) platform for longitudinal imaging of ischemic stroke in mice, through thinned-skull, reinforced cranial window surgical preparations, is described. In the acute stages, the spatiotemporal interplay between hemodynamics and cell viability, a key determinant of pathogenesis, was imaged. In acute stroke, microscopic biomarkers for eventual infarction, including capillary non-perfusion, cerebral blood flow deficiency, altered cellular scattering, and impaired autoregulation of cerebral blood flow, were quantified and correlated with histology. Additionally, longitudinal microscopy revealed remodeling and flow recovery after one week of chronic stroke. Intrinsic scattering properties serve as reporters of acute cellular and vascular injury and recovery in experimental stroke. Multi-parametric OCT represents a robust in vivo imaging platform to comprehensively investigate these properties

A Bioinformatics Resource for TWEAK-Fn14 Signaling Pathway

TNF-related weak inducer of apoptosis (TWEAK) is a new member of the TNF superfamily. It signals through TNFRSF12A, commonly known as Fn14. The TWEAK-Fn14 interaction regulates cellular activities including proliferation, migration, differentiation, apoptosis, angiogenesis, tissue remodeling and inflammation. Although TWEAK has been reported to be associated with autoimmune diseases, cancers, stroke, and kidney-related disorders, the downstream molecular events of TWEAK-Fn14 signaling are yet not available in any signaling pathway repository. In this paper, we manually compiled from the literature, in particular those reported in human systems, the downstream reactions stimulated by TWEAK-Fn14 interactions. Our manual amassment of the TWEAK-Fn14 pathway has resulted in cataloging of 46 proteins involved in various biochemical reactions and TWEAK-Fn14 induced expression of 28 genes. We have enabled the availability of data in various standard exchange formats from NetPath, a repository for signaling pathways. We believe that this composite molecular interaction pathway will enable identification of new signaling components in TWEAK signaling pathway. This in turn may lead to the identification of potential therapeutic targets in TWEAK-associated disorders

Integrating transcriptomic and proteomic data for accurate assembly and annotation of genomes

© 2017 Wong et al.; Published by Cold Spring Harbor Laboratory Press. Complementing genome sequence with deep transcriptome and proteome data could enable more accurate assembly and annotation of newly sequenced genomes. Here, we provide a proof-of-concept of an integrated approach for analysis of the genome and proteome of Anopheles stephensi, which is one of the most important vectors of the malaria parasite. To achieve broad coverage of genes, we carried out transcriptome sequencing and deep proteome profiling of multiple anatomically distinct sites. Based on transcriptomic data alone, we identified and corrected 535 events of incomplete genome assembly involving 1196 scaffolds and 868 protein-coding gene models. This proteogenomic approach enabled us to add 365 genes that were missed during genome annotation and identify 917 gene correction events through discovery of 151 novel exons, 297 protein extensions, 231 exon extensions, 192 novel protein start sites, 19 novel translational frames, 28 events of joining of exons, and 76 events of joining of adjacent genes as a single gene. Incorporation of proteomic evidence allowed us to change the designation of more than 87 predicted noncoding RNAs to conventional mRNAs coded by protein-coding genes. Importantly, extension of the newly corrected genome assemblies and gene models to 15 other newly assembled Anopheline genomes led to the discovery of a large number of apparent discrepancies in assembly and annotation of these genomes. Our data provide a framework for how future genome sequencing efforts should incorporate transcriptomic and proteomic analysis in combination with simultaneous manual curation to achieve near complete assembly and accurate annotation of genomes

Electronic Colloquium on Computational Complexity, Report No. 151 (2006) The Communication Complexity of Correlation

We examine the communication required for generating random variables remotely. One party Alice will be given a distribution D, and she has to send a message to Bob, who is then required to generate a value with distribution exactly D. Alice and Bob are allowed to share random bits generated without the knowledge of D. There are two settings based on how the distribution D provided to Alice is chosen. Average case: D is itself chosen randomly from some set (the set and distribution are known in advance) and we wish to minimize the expected communication in order for Alice to generate a value y, with distribution D. We characterize the communication required in this case based on the mutual information between the the input to Alice and the output Bob is required to generate. Worst case: D is chosen from a set of distributions D, and we wish to devise a protocol so that the expected communication (the randomness comes from the shared random string and Alice’s coin tosses) is small for each D ∈ D. We characterize the communication required in this case in terms of the channel capacity associated with the set D

The Communication complexity of correlation

10.1109/TIT.2009.2034824IEEE Transactions on Information Theory561438-449IETT