Perturbation of the Eigenvectors of the Graph Laplacian: Application to Image Denoising

The original contributions of this paper are twofold: a new understanding of the influence of noise on the eigenvectors of the graph Laplacian of a set of image patches, and an algorithm to estimate a denoised set of patches from a noisy image. The algorithm relies on the following two observations: (1) the low-index eigenvectors of the diffusion, or graph Laplacian, operators are very robust to random perturbations of the weights and random changes in the connections of the patch-graph; and (2) patches extracted from smooth regions of the image are organized along smooth low-dimensional structures in the patch-set, and therefore can be reconstructed with few eigenvectors. Experiments demonstrate that our denoising algorithm outperforms the denoising gold-standards

A Multiplexed Single-Cell CRISPR Screening Platform Enables Systematic Dissection of the Unfolded Protein Response

Functional genomics efforts face tradeoffs between number of perturbations examined and complexity of phenotypes measured. We bridge this gap with Perturb-seq, which combines droplet-based single-cell RNA-seq with a strategy for barcoding CRISPR-mediated perturbations, allowing many perturbations to be profiled in pooled format. We applied Perturb-seq to dissect the mammalian unfolded protein response (UPR) using single and combinatorial CRISPR perturbations. Two genome-scale CRISPR interference (CRISPRi) screens identified genes whose repression perturbs ER homeostasis. Subjecting ∼100 hits to Perturb-seq enabled high-precision functional clustering of genes. Single-cell analyses decoupled the three UPR branches, revealed bifurcated UPR branch activation among cells subject to the same perturbation, and uncovered differential activation of the branches across hits, including an isolated feedback loop between the translocon and IRE1α. These studies provide insight into how the three sensors of ER homeostasis monitor distinct types of stress and highlight the ability of Perturb-seq to dissect complex cellular responses.National Human Genome Research Institute (U.S.) (Grant P50HG006193

Notes on the spheroidal harmonic multipole moments of gravitational radiation

The estimation of gravitational radiation's multipole moments is a central problem in gravitational wave theory, with essential applications in gravitational wave signal modeling and data analysis. This problem is complicated by most astrophysically relevant systems' not having angular modes that are analytically understood. A ubiquitous workaround is to use spin weighted spherical harmonics to estimate multipole moments; however, these are only related to the natural modes of non-spinning spacetimes, thus obscuring the behavior of radiative modes when the source has angular momentum. In such cases, radiative modes are spheroidal in nature. Here, common approaches to the estimation of spheroidal harmonic multipole moments are unified under a simple framework. This framework leads to a new class of spin weighted spheroidal harmonic functions. Adjoint-spheroidal harmonics are introduced and used to motivate the general estimation of spheroidal harmonic multipole moments via bi-orthogonal decomposition with overtone subsets. In turn, the adjoint-spheroidal harmonics are used to construct a single linear operator for which all spheroidal harmonics are eigenfunctions. Implications of these results on gravitational wave theory are discussed.Comment: 20 pages, 4 figure

Knowledge-based matrix factorization temporally resolves the cellular responses to IL-6 stimulation

<p>Abstract</p> <p>Background</p> <p>External stimulations of cells by hormones, cytokines or growth factors activate signal transduction pathways that subsequently induce a re-arrangement of cellular gene expression. The analysis of such changes is complicated, as they consist of multi-layered temporal responses. While classical analyses based on clustering or gene set enrichment only partly reveal this information, matrix factorization techniques are well suited for a detailed temporal analysis. In signal processing, factorization techniques incorporating data properties like spatial and temporal correlation structure have shown to be robust and computationally efficient. However, such correlation-based methods have so far not be applied in bioinformatics, because large scale biological data rarely imply a natural order that allows the definition of a delayed correlation function.</p> <p>Results</p> <p>We therefore develop the concept of graph-decorrelation. We encode prior knowledge like transcriptional regulation, protein interactions or metabolic pathways in a weighted directed graph. By linking features along this underlying graph, we introduce a partial ordering of the features (e.g. genes) and are thus able to define a graph-delayed correlation function. Using this framework as constraint to the matrix factorization task allows us to set up the fast and robust graph-decorrelation algorithm (GraDe). To analyze alterations in the gene response in <it>IL-6 </it>stimulated primary mouse hepatocytes, we performed a time-course microarray experiment and applied GraDe. In contrast to standard techniques, the extracted time-resolved gene expression profiles showed that <it>IL-6 </it>activates genes involved in cell cycle progression and cell division. Genes linked to metabolic and apoptotic processes are down-regulated indicating that <it>IL-6 </it>mediated priming renders hepatocytes more responsive towards cell proliferation and reduces expenditures for the energy metabolism.</p> <p>Conclusions</p> <p>GraDe provides a novel framework for the decomposition of large-scale 'omics' data. We were able to show that including prior knowledge into the separation task leads to a much more structured and detailed separation of the time-dependent responses upon <it>IL-6 </it>stimulation compared to standard methods. A Matlab implementation of the GraDe algorithm is freely available at <url>http://cmb.helmholtz-muenchen.de/grade</url>.</p

Hunting B modes in CMB polarization observations

In Chapter 1, I will introduce the current cosmological model and review the theoretical aspects of the CMB anisotropies and the present status of the observations. In Chapter 2, I will focus on the diffuse emissions of our Galaxy in the microwaves, expected to be a serious contamination for the CMB studies. The separation of these diffuse components and the CMB cleaning will be the main topic of Chapter 3, where I will describe a few algorithms I\u2019ve worked on during my Phd . Finally, in Chapter 4, I will present a couple of applications of these methods aimed at B mode recovery

Neural Connectivity with Hidden Gaussian Graphical State-Model

The noninvasive procedures for neural connectivity are under questioning. Theoretical models sustain that the electromagnetic field registered at external sensors is elicited by currents at neural space. Nevertheless, what we observe at the sensor space is a superposition of projected fields, from the whole gray-matter. This is the reason for a major pitfall of noninvasive Electrophysiology methods: distorted reconstruction of neural activity and its connectivity or leakage. It has been proven that current methods produce incorrect connectomes. Somewhat related to the incorrect connectivity modelling, they disregard either Systems Theory and Bayesian Information Theory. We introduce a new formalism that attains for it, Hidden Gaussian Graphical State-Model (HIGGS). A neural Gaussian Graphical Model (GGM) hidden by the observation equation of Magneto-encephalographic (MEEG) signals. HIGGS is equivalent to a frequency domain Linear State Space Model (LSSM) but with sparse connectivity prior. The mathematical contribution here is the theory for high-dimensional and frequency-domain HIGGS solvers. We demonstrate that HIGGS can attenuate the leakage effect in the most critical case: the distortion EEG signal due to head volume conduction heterogeneities. Its application in EEG is illustrated with retrieved connectivity patterns from human Steady State Visual Evoked Potentials (SSVEP). We provide for the first time confirmatory evidence for noninvasive procedures of neural connectivity: concurrent EEG and Electrocorticography (ECoG) recordings on monkey. Open source packages are freely available online, to reproduce the results presented in this paper and to analyze external MEEG databases

Inversion and Analysis of Remotely Sensed Atmospheric Water Vapor Measurements at 940nm

The understanding and acceptance of remotely sensed atmospheric data depends strongly on the steps taken to characterize experiment error and validate observations through comparisons to other independent measurements. A formal error analysis of the Stratospheric Aerosol and Gas Experiment II (SAGE II) water vapor operational inversion algorithm is performed and compared to previous results. Random measurement errors were characterized by segmented least-squares profile fitting of the slant path absorption which found the error to be uncorrelated in the stratosphere with estimated variances significantly smaller than expected from 18-30 km. Estimates of null space error were developed from radiosonde hygrometers in the troposphere and from SAGE II in the stratosphere. Systematic model bias errors are significant only in the troposphere where they reach 20% at the surface. Systematic errors associated with radiative transfer modeling are similar to previous analyses. A comparative error budget study between the operational inversion algorithm and several other algorithms was conducted with formal error analysis and by examining the error characteristics of two years\u27 data inverted with each algorithm. Four other algorithms were considered; onion peel, Mill-Drayson, Mill-Drayson with stratospheric profile smoothing, and a sparse grid non-linear least-squares fitting method. Stratospheric random errors were largest for the onion peel due to the lack of stratospheric profile smoothing while the Mill-Drayson with smoothing was identical to the operational. The Mill-Drayson algorithm exhibited random error reduction greater than expected from the form of the contribution function with stratospheric random errors approaching operational levels. The sparse grid contribution function was found to be relatively insensitive to grid point density and computationally intensive. SAGE II upper tropospheric observations are compared to radiosonde climatologies and in situ radiosonde reports. SAGE II clear sky climatologies are shown to be half the level of the clear/cloudy sky radiosonde climatologies while correlative comparisons display nearly the same amount of bias. Much of the bias is attributed to the least sensitive hygrometers with SAGE II agreeing quite well with the most accurate and responsive hygrometer. Incorporating isentropic trajectories into the pair matching process greatly increases the number of correlative points but does not materially affect the comparisons

Genome-wide inference of ancestral recombination graphs

The complex correlation structure of a collection of orthologous DNA sequences is uniquely captured by the "ancestral recombination graph" (ARG), a complete record of coalescence and recombination events in the history of the sample. However, existing methods for ARG inference are computationally intensive, highly approximate, or limited to small numbers of sequences, and, as a consequence, explicit ARG inference is rarely used in applied population genomics. Here, we introduce a new algorithm for ARG inference that is efficient enough to apply to dozens of complete mammalian genomes. The key idea of our approach is to sample an ARG of n chromosomes conditional on an ARG of n-1 chromosomes, an operation we call "threading." Using techniques based on hidden Markov models, we can perform this threading operation exactly, up to the assumptions of the sequentially Markov coalescent and a discretization of time. An extension allows for threading of subtrees instead of individual sequences. Repeated application of these threading operations results in highly efficient Markov chain Monte Carlo samplers for ARGs. We have implemented these methods in a computer program called ARGweaver. Experiments with simulated data indicate that ARGweaver converges rapidly to the true posterior distribution and is effective in recovering various features of the ARG for dozens of sequences generated under realistic parameters for human populations. In applications of ARGweaver to 54 human genome sequences from Complete Genomics, we find clear signatures of natural selection, including regions of unusually ancient ancestry associated with balancing selection and reductions in allele age in sites under directional selection. Preliminary results also indicate that our methods can be used to gain insight into complex features of human population structure, even with a noninformative prior distribution.Comment: 88 pages, 7 main figures, 22 supplementary figures. This version contains a substantially expanded genomic data analysi

Resiliency Assessment and Enhancement of Intrinsic Fingerprinting

Intrinsic fingerprinting is a class of digital forensic technology that can detect traces left in digital multimedia data in order to reveal data processing history and determine data integrity. Many existing intrinsic fingerprinting schemes have implicitly assumed favorable operating conditions whose validity may become uncertain in reality. In order to establish intrinsic fingerprinting as a credible approach to digital multimedia authentication, it is important to understand and enhance its resiliency under unfavorable scenarios. This dissertation addresses various resiliency aspects that can appear in a broad range of intrinsic fingerprints. The first aspect concerns intrinsic fingerprints that are designed to identify a particular component in the processing chain. Such fingerprints are potentially subject to changes due to input content variations and/or post-processing, and it is desirable to ensure their identifiability in such situations. Taking an image-based intrinsic fingerprinting technique for source camera model identification as a representative example, our investigations reveal that the fingerprints have a substantial dependency on image content. Such dependency limits the achievable identification accuracy, which is penalized by a mismatch between training and testing image content. To mitigate such a mismatch, we propose schemes to incorporate image content into training image selection and significantly improve the identification performance. We also consider the effect of post-processing against intrinsic fingerprinting, and study source camera identification based on imaging noise extracted from low-bit-rate compressed videos. While such compression reduces the fingerprint quality, we exploit different compression levels within the same video to achieve more efficient and accurate identification. The second aspect of resiliency addresses anti-forensics, namely, adversarial actions that intentionally manipulate intrinsic fingerprints. We investigate the cost-effectiveness of anti-forensic operations that counteract color interpolation identification. Our analysis pinpoints the inherent vulnerabilities of color interpolation identification, and motivates countermeasures and refined anti-forensic strategies. We also study the anti-forensics of an emerging space-time localization technique for digital recordings based on electrical network frequency analysis. Detection schemes against anti-forensic operations are devised under a mathematical framework. For both problems, game-theoretic approaches are employed to characterize the interplay between forensic analysts and adversaries and to derive optimal strategies. The third aspect regards the resilient and robust representation of intrinsic fingerprints for multiple forensic identification tasks. We propose to use the empirical frequency response as a generic type of intrinsic fingerprint that can facilitate the identification of various linear and shift-invariant (LSI) and non-LSI operations