Computable lower bounds for deterministic parameter estimation

This paper is primarily tutorial in nature and presents a simple approach(norm minimization under linear constraints) for deriving computable lower bounds on the MSE of deterministic parameter estimators with a clear interpretation of the bounds. We also address the issue of lower bounds tightness in comparison with the MSE of ML estimators and their ability to predict the SNR threshold region. Last, as many practical estimation problems must be regarded as joint detection-estimation problems, we remind that the estimation performance must be conditional on detection performance, leading to the open problem of the fundamental limits of the joint detectionestimation performance

On the influence of detection tests on deterministic parameters estimation

In non-linear estimation problems three distinct regions of operation can be observed. In the asymptotic region, the Mean Square Error (MSE) of Maximum Likelihood Estimators (MLE) is small and, in many cases,close to the Cramer-Rao bound (CRB). In the a priory performance region where the number of independent snapshots and/or the SNR are very low, the MSE is close to that obtained from the prior knowledge about the problem. Between these two extremes, there is an additional transition region where MSE of estimators deteriorates with respect to CRB. The present paper provides exemples of improvement of MSE prediction by CRB, not only in the transition region but also in the a priori region, resulting from introduction of a detection step, which proves that this renement in MSE lower bounds derivation is worth investigating

MSE lower bounds for deterministic parameter estimation

This paper presents a simple approach for deriving computable lower bounds on the MSE of deterministic parameter estimators with a clear interpretation of the bounds. We also address the issue of lower bounds tightness in comparison with the MSE of ML estimators and their ability to predict the SNR threshold region. Last, as many practical estimation problems must be regarded as joint detection-estimation problems, we remind that the estimation performance must be conditional on detection performance

On Lower Bounds for Non Standard Deterministic Estimation

We consider deterministic parameter estimation and the situation where the probability density function (p.d.f.) parameterized by unknown deterministic parameters results from the marginalization of a joint p.d.f. depending on random variables as well. Unfortunately, in the general case, this marginalization is mathematically intractable, which prevents from using the known standard deterministic lower bounds (LBs) on the mean squared error (MSE). Actually the general case can be tackled by embedding the initial observation space in a hybrid one where any standard LB can be transformed into a modified one fitted to nonstandard deterministic estimation, at the expense of tightness however. Furthermore, these modified LBs (MLBs) appears to include the submatrix of hybrid LBs which is an LB for the deterministic parameters. Moreover, since in the nonstandard estimation, maximum likelihood estimators (MLEs) can be no longer derived, suboptimal nonstandard MLEs (NSMLEs) are proposed as being a substitute. We show that any standard LB on the MSE of MLEs has a nonstandard version lower bounding the MSE of NSMLEs. We provide an analysis of the relative performance of the NSMLEs, as well as a comparison with the MLBs for a large class of estimation problems. Last, the general approach introduced is exemplified, among other things, with a new look at the well-known Gaussian complex observation models

A generic classification-based method for segmentation of nuclei in 3D images of early embryos

BACKGROUND: Studying how individual cells spatially and temporally organize within the embryo is a fundamental issue in modern developmental biology to better understand the first stages of embryogenesis. In order to perform high-throughput analyses in three-dimensional microscopic images, it is essential to be able to automatically segment, classify and track cell nuclei. Many 3D/4D segmentation and tracking algorithms have been reported in the literature. Most of them are specific to particular models or acquisition systems and often require the fine tuning of parameters. RESULTS: We present a new automatic algorithm to segment and simultaneously classify cell nuclei in 3D/4D images. Segmentation relies on training samples that are interactively provided by the user and on an iterative thresholding process. This algorithm can correctly segment nuclei even when they are touching, and remains effective under temporal and spatial intensity variations. The segmentation is coupled to a classification of nuclei according to cell cycle phases, allowing biologists to quantify the effect of genetic perturbations and drug treatments. Robust 3D geometrical shape descriptors are used as training features for classification. Segmentation and classification results of three complete datasets are presented. In our working dataset of the Caenorhabditis elegans embryo, only 21 nuclei out of 3,585 were not detected, the overall F-score for segmentation reached 0.99, and more than 95% of the nuclei were classified in the correct cell cycle phase. No merging of nuclei was found. CONCLUSION: We developed a novel generic algorithm for segmentation and classification in 3D images. The method, referred to as Adaptive Generic Iterative Thresholding Algorithm (AGITA), is freely available as an ImageJ plug-in

Recursive hybrid CRB for Markovian systems with time-variant measurement parameters

In statistical signal processing, hybrid parameter estimation refers to the case where the parameters vector to estimate contains both deterministic and random parameters. Lately computationally tractable hybrid Cramér-Rao lower bounds for discrete-time Markovian dynamic systems depending on unknown time invariant deterministic parameters has been released. However in many applications (radar, sonar, telecoms, ...) the unknown deterministic parameters of the measurement model are time variant which prevents from using the aforementioned bounds. It is therefore the aim of this communication to tackle this issue by introducing new computationally tractable hybrid Cramér-Rao lower bounds

Recursive Hybrid Cramér–Rao Bound for Discrete-Time Markovian Dynamic Systems

Abstract—In statistical signal processing, hybrid parameter estimation refers to the case where the parameters vector to estimate contains both non-random and random parameters. As a contribution to the hybrid estimation framework, we introduce a recursive hybrid Cramér–Rao lower bound for discrete-time Markovian dynamic systems depending on unknown deterministic parameters. Additionally, the regularity conditions required for its existence and its use are clarified

The Conserved Nup107-160 Complex Is Critical for Nuclear Pore Complex Assembly

AbstractNuclear pore complexes (NPCs) are large multiprotein assemblies that allow traffic between the cytoplasm and the nucleus. During mitosis in higher eukaryotes, the Nuclear Envelope (NE) breaks down and NPCs disassemble. How NPCs reassemble and incorporate into the NE upon mitotic exit is poorly understood. We demonstrate a function for the conserved Nup107-160 complex in this process. Partial in vivo depletion of Nup133 or Nup107 via RNAi in HeLa cells resulted in reduced levels of multiple nucleoporins and decreased NPC density in the NE. Immunodepletion of the entire Nup107-160 complex from in vitro nuclear assembly reactions produced nuclei with a continuous NE but no NPCs. This phenotype was reversible only if Nup107-160 complex was readded before closed NE formation. Depletion also prevented association of FG-repeat nucleoporins with chromatin. We propose a stepwise model in which postmitotic NPC assembly initiates on chromatin via early recruitment of the Nup107-160 complex

A BBP–Mud2p heterodimer mediates branchpoint recognition and influences splicing substrate abundance in budding yeast

The 3′ end of mammalian introns is marked by the branchpoint binding protein, SF1, and the U2AF65-U2AF35 heterodimer bound at an adjacent sequence. Baker's yeast has equivalent proteins, branchpoint binding protein (BBP) (SF1) and Mud2p (U2AF65), but lacks an obvious U2AF35 homolog, leaving open the question of whether another protein substitutes during spliceosome assembly. Gel filtration, affinity selection and mass spectrometry were used to show that rather than a U2AF65/U2AF35-like heterodimer, Mud2p forms a complex with BBP without a third (U2AF35-like) factor. Using mutants of MUD2 and BBP, we show that the BBP–Mud2p complex bridges partner-specific Prp39p, Mer1p, Clf1p and Smy2p two-hybrid interactions. In addition to inhibiting Mud2p association, the bbpΔ56 mutation impairs splicing, enhances pre-mRNA release from the nucleus, and similar to a mud2::KAN knockout, suppresses a lethal sub2::KAN mutation. Unexpectedly, rather than exacerbating bbpΔ56, the mud2::KAN mutation partially suppresses a pre-mRNA accumulation defect observed with bbpΔ56. We propose that a BBP–Mud2p heterodimer binds as a unit to the branchpoint in vivo and serves as a target for the Sub2p-DExD/H-box ATPase and for other splicing factors during spliceosome assembly. In addition, our results suggest the possibility that the Mud2p may enhance the turnover of pre-mRNA with impaired BBP-branchpoint association

Enabling planetary science across light-years. Ariel Definition Study Report

Ariel, the Atmospheric Remote-sensing Infrared Exoplanet Large-survey, was adopted as the fourth medium-class mission in ESA's Cosmic Vision programme to be launched in 2029. During its 4-year mission, Ariel will study what exoplanets are made of, how they formed and how they evolve, by surveying a diverse sample of about 1000 extrasolar planets, simultaneously in visible and infrared wavelengths. It is the first mission dedicated to measuring the chemical composition and thermal structures of hundreds of transiting exoplanets, enabling planetary science far beyond the boundaries of the Solar System. The payload consists of an off-axis Cassegrain telescope (primary mirror 1100 mm x 730 mm ellipse) and two separate instruments (FGS and AIRS) covering simultaneously 0.5-7.8 micron spectral range. The satellite is best placed into an L2 orbit to maximise the thermal stability and the field of regard. The payload module is passively cooled via a series of V-Groove radiators; the detectors for the AIRS are the only items that require active cooling via an active Ne JT cooler. The Ariel payload is developed by a consortium of more than 50 institutes from 16 ESA countries, which include the UK, France, Italy, Belgium, Poland, Spain, Austria, Denmark, Ireland, Portugal, Czech Republic, Hungary, the Netherlands, Sweden, Norway, Estonia, and a NASA contribution