Convergence speed of unsteady distributed consensus: decay estimate along the settling spanning-trees

Results for estimating the convergence rate of non-stationary distributed consensus algorithms are provided, on the basis of qualitative (mainly topological) as well as basic quantitative information (lower-bounds on the matrix entries). The results appear to be tight in a number of instances and are illustrated through simple as well as more sophisticated examples. The main idea is to follow propagation of information along certain spanning trees which arise in the communication graph.Comment: 27 pages, 5 figure

Tight estimates for non-stationary consensus with fixed underlying spanning tree

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A Caged Ret Kinase Inhibitor and its Effect on Motoneuron Development in Zebrafish Embryos

Proto-oncogene tyrosine-protein kinase receptor RET is implicated in the development and maintenance of neurons of the central and peripheral nervous systems. Attaching activity-compromising photocleavable groups (caging) to inhibitors could allow for external spatiotemporally controlled inhibition using light, potentially providing novel information on how these kinase receptors are involved in cellular processes. Here, caged RET inhibitors were obtained from 3-substituted pyrazolopyrimidine-based compounds by attaching photolabile groups to the exocyclic amino function. The most promising compound displayed excellent inhibitory effect in cell-free, as well as live-cell assays upon decaging. Furthermore, inhibition could be efficiently activated with light in vivo in zebrafish embryos and was shown to effect motoneuron development

Tight estimates for convergence of some non-stationary consensus algorithms

The present paper is devoted to estimating the speed of convergence towards consensus for a general class of discrete-time multi-agent systems. In the systems considered here, both the topology of the interconnection graph and the weight of the arcs are allowed to vary as a function of time. Under the hypothesis that some spanning tree structure is preserved along time, and that some nonzero minimal weight of the information transfer along this tree is guaranteed, an estimate of the contraction rate is given. The latter is expressed explicitly as the spectral radius of some matrix depending upon the tree depth and the lower bounds on the weights.Comment: 17 pages, 5 figure

Reduced-Order models for a LNT-SCR Diesel After-treatment Architecture with NO/NO2 Differentiation

International audienceLNT and SCR are two leading candidates for Diesel exhaust nitrogen oxide (NOx) after-treatment. This paper deals with the modeling of the architecture combining the two systems in series with NO/NO2 differentiation, induced directly by the widening and hardening of the future standards. Model reduction is performed to allow for real-time automotive applications. Based on simplified chemistry and slow-fast dynamics assumptions, a complete reduced model is proposed, suitable for on-board diagnosis and model-based control. Validation has been achieved through extensive experiments

8-Triazolylpurines: Towards Fluorescent Inhibitors of the MDM2/p53 Interaction

Small molecule nonpeptidic mimics of alpha-helices are widely recognised as protein-protein interaction (PPIs) inhibitors. Protein-protein interactions mediate virtually all important regulatory pathways in a cell, and the ability to control and modulate PPIs is therefore of great significance to basic biology, where controlled disruption of protein networks is key to understanding network connectivity and function. We have designed and synthesised two series of 2,6,9-substituted 8-triazolylpurines as alpha-helix mimetics. The first series was designed based on low energy conformations but did not display any biological activity in a biochemical fluorescence polarisation assay targeting MDM2/p53. Although solution NMR conformation studies demonstrated that such molecules could mimic the topography of an alpha-helix, docking studies indicated that the same compounds were not optimal as inhibitors for the MDM2/p53 interaction. A new series of 8-triazolylpurines was designed based on a combination of docking studies and analysis of recently published inhibitors. The best compound displayed low micromolar inhibitory activity towards MDM2/p53 in a biochemical fluorescence polarisation assay. In order to evaluate the applicability of these compounds as biologically active and intrinsically fluorescent probes, their absorption/emission properties were measured. The compounds display fluorescent properties with quantum yields up to 50%

Purine and Pyrazolopyrimidine Derivatives: Design and Synthesis of Chemical Tools for Biological Applications

Purines can be found in a multitude of naturally occurring compounds with a range of functions. This thesis describes the design and synthesis of purines and structurally related pyrazolopyrimidine derivatives intended for biological applications. Pyrazolopyrimidines are structurally related to purines and are used as scaffolds for ATP-competitive protein kinase inhibitors. A pyrazolopyrimidine based selective inhibitor of receptor tyrosine kinase REarranged during Transfection (RET), a protein kinase involved in cell development, was modified with a photolabile protecting group. The modification allowed for photocontrolled release of the inhibitor. Photodependent inhibition of RET was demonstrated in both a biochemical assay and in a cell based RET-assay. The utility of the caged inhibitor was demonstrated in transgenic zebrafish embryos by demonstrating the effect of photocontrolled RET-inhibition on motoneuron development. In addition, it was shown that the timing of irradiation was critical for motoneuron development. The purine structure is a key constituent of aminoacyl-adenosine monophosphate (aa-AMP), an intermediate in protein biosynthesis. Stable mimics of aa-AMP could have potential as inhibitors of protein biosynthesis, a mechanism identified as a target for antiinfectives. A series of 8-(triazolyl)purines was synthesized as aa-AMP mimics. In addition, their photophysical properties were studied to evaluate their potential as fluorescent probes. Unexpectedly, these compounds displayed very low quantum yields in contrast to previous data for similar structures. Protein-protein interactions (PPIs) are ubiquitously present in cells, have a central role in cell signaling and have been identified as interesting drug targets. The α-helix secondary structure has been identified as a central element in many PPIs. In this project, 2,6,9-substituted 8-(triazolyl)purines were evaluated as α-helix mimetics and inhibitors of the p53/MDM2 PPI. A series of compounds were synthesized and two of the compounds exhibited micromolar activity against MDM2. In addition, a bromination procedure for 8-bromination of purines was developed. Bromination with pyridinium tribromide at room temperature resulted in high yields for electron rich 2,6,9-substituted purines. The procedure is a convenient alternative to elemental bromine for this transformation. The fluorescent properties of the compounds were also measured. One of the compounds showed a high quantum yield of 51% and several compounds had quantum yields between 5-10%. The fluorescent properties could be useful for example to study intracellular localization of bioactive compounds

Stability of leaderless multi-agent systems. Extension of a result by Moreau

18 pages; 7 figuresThe paper presents a result which relates connectedness of the interaction graphs in a multi-agent systems with the capability for global convergence to a common equilibrium of the system. In particular we extend a previously known result by Moreau by including the possibility of arbitrary bounded time-delays in the communication channels and relaxing the convexity of the allowed regions for the state transition map of each agent