Human activity modeling and Barabasi's queueing systems

It has been shown by A.-L. Barabasi that the priority based scheduling rules in single stage queuing systems (QS) generates fat tail behavior for the tasks waiting time distributions (WTD). Such fat tails are due to the waiting times of very low priority tasks which stay unserved almost forever as the task priority indices (PI) are "frozen in time" (i.e. a task priority is assigned once for all to each incoming task). Relaxing the "frozen in time" assumption, this paper studies the new dynamic behavior expected when the priority of each incoming tasks is time-dependent (i.e. "aging mechanisms" are allowed). For two class of models, namely 1) a population type model with an age structure and 2) a QS with deadlines assigned to the incoming tasks which is operated under the "earliest-deadline-first" policy, we are able to analytically extract some relevant characteristics of the the tasks waiting time distribution. As the aging mechanism ultimately assign high priority to any long waiting tasks, fat tails in the WTD cannot find their origin in the scheduling rule alone thus showing a fundamental difference between the present and the A.-L. Barabasi's class of models.Comment: 16 pages, 2 figure

GTPase Activity and Neuronal Toxicity of Parkinson's Disease–Associated LRRK2 Is Regulated by ArfGAP1

Mutations in the leucine-rich repeat kinase 2 (LRRK2) gene are the most common cause of autosomal dominant familial Parkinson's disease (PD) and also contribute to idiopathic PD. LRRK2 encodes a large multi-domain protein with GTPase and kinase activity. Initial data indicates that an intact functional GTPase domain is critically required for LRRK2 kinase activity. PD–associated mutations in LRRK2, including the most common G2019S variant, have variable effects on enzymatic activity but commonly alter neuronal process morphology. The mechanisms underlying the intrinsic and extrinsic regulation of LRRK2 GTPase and kinase activity, and the pathogenic effects of familial mutations, are incompletely understood. Here, we identify a novel functional interaction between LRRK2 and ADP-ribosylation factor GTPase-activating protein 1 (ArfGAP1). LRRK2 and ArfGAP1 interact in vitro in mammalian cells and in vivo in brain, and co-localize in the cytoplasm and at Golgi membranes. PD–associated and functional mutations that alter the GTPase activity of LRRK2 modulate the interaction with ArfGAP1. The GTP hydrolysis activity of LRRK2 is markedly enhanced by ArfGAP1 supporting a role for ArfGAP1 as a GTPase-activating protein for LRRK2. Unexpectedly, ArfGAP1 promotes the kinase activity of LRRK2 suggesting a potential role for GTP hydrolysis in kinase activation. Furthermore, LRRK2 robustly and directly phosphorylates ArfGAP1 in vitro. Silencing of ArfGAP1 expression in primary cortical neurons rescues the neurite shortening phenotype induced by G2019S LRRK2 overexpression, whereas the co-expression of ArfGAP1 and LRRK2 synergistically promotes neurite shortening in a manner dependent upon LRRK2 GTPase activity. Neurite shortening induced by ArfGAP1 overexpression is also attenuated by silencing of LRRK2. Our data reveal a novel role for ArfGAP1 in regulating the GTPase activity and neuronal toxicity of LRRK2; reciprocally, LRRK2 phosphorylates ArfGAP1 and is required for ArfGAP1 neuronal toxicity. ArfGAP1 may represent a promising target for interfering with LRRK2-dependent neurodegeneration in familial and sporadic PD

LRRK2 Biology from structure to dysfunction: research progresses, but the themes remain the same

Since the discovery of leucine-rich repeat kinase 2 (LRRK2) as a protein that is likely central to the aetiology of Parkinson's disease, a considerable amount of work has gone into uncovering its basic cellular function. This effort has led to the implication of LRRK2 in a bewildering range of cell biological processes and pathways, and probable roles in a number of seemingly unrelated medical conditions. In this review we summarise current knowledge of the basic biochemistry and cellular function of LRRK2. Topics covered include the identification of phosphorylation substrates of LRRK2 kinase activity, in particular Rab proteins, and advances in understanding the activation of LRRK2 kinase activity via dimerisation and association with membranes, especially via interaction with Rab29. We also discuss biochemical studies that shed light on the complex LRRK2 GTPase activity, evidence of roles for LRRK2 in a range of cell signalling pathways that are likely cell type specific, and studies linking LRRK2 to the cell biology of organelles. The latter includes the involvement of LRRK2 in autophagy, endocytosis, and processes at the trans-Golgi network, the endoplasmic reticulum and also key microtubule-based cellular structures. We further propose a mechanism linking LRRK2 dimerisation, GTPase function and membrane recruitment with LRRK2 kinase activation by Rab29. Together these data paint a picture of a research field that in many ways is moving forward with great momentum, but in other ways has not changed fundamentally. Many key advances have been made, but very often they seem to lead back to the same places

Ordonnancement dynamique d'une machine flexible Formulation en processus de Bandits-manchots

We explore the scheduling rules and the hedging levels that can be obtained by using a Restless Bandit Problem formulation of a make-to-stock production. The underlying dynamics are markov chain in continuous lime and the associate reward are piecewise linear. We observe that, the use of priority indices to sub-optimally solve the Restless Bandit problem yields, on a particular example, results close to the optimal

Dynamic scheduling of a multi-items production operating on a make-to-stock basis

The concept of priority indices defined to discuss the Restless Bandit Problem (RBP) furnish a relevant approximative framework to approach the optimal scheduling of a multi-products make-to-stock production when no setup cost and/or time are incurred. The resulting policy involves switching curves and hedging stocks. At each time, the index policy selects the item to be produced for any global state of the net inventories. Moreover, the optimal hedging level is also reproduced for a single item problem