Data Assimilation and Inverse Methods in Terms of a Probabilistic Formulation

The weak-constraint inverse for nonlinear dynamical models is discussed and derived in terms of a probabilistic formulation. The well-known result that for Gaussian error statistics the minimum of the weak-constraint inverse is equal to the maximum-likelihood estimate is rederived. Then several methods based on ensemble statistics that can be used to find the smoother (as opposed to the filter) solution are introduced and compared to traditional methods. A strong point of the new methods is that they avoid the integration of adjoint equations, which is a complex task for real oceanographic or atmospheric applications. they also avoid iterative searches in a Hilbert space, and error estimates can be obtained without much additional computational effort. the feasibility of the new methods is illustrated in a two-layer quasigeostrophic model.

Platelet signaling: a complex interplay between inhibitory and activatory networks

The role of platelets in hemostasis and thrombosis is dependent on a complex balance of activatory and inhibitory signaling pathways. Inhibitory signals released from the healthy vasculature suppress platelet activation in the absence of platelet receptor agonists. Activatory signals present at a site of injury initiate platelet activation and thrombus formation; subsequently, endogenous negative signaling regulators dampen activatory signals to control thrombus growth. Understanding the complex interplay between activatory and inhibitory signaling networks is an emerging challenge in the study of platelet biology and necessitates a systematic approach to utilize experimental data effectively. In this review, we will explore the key points of platelet regulation and signaling that maintain platelets in a resting state, mediate activation to elicit thrombus formation or provide negative feedback. Platelet signaling will be described in terms of key signaling molecules that are common to the pathways activated by platelet agonists and can be described as regulatory nodes for both positive and negative regulators. This article is protected by copyright. All rights reserved.