Abstract:We present the marmoteCore software project, an open environment for modeling with Markov chains. This platform aims at providing the general scientific user with tools for creating Markov models and accessing the many solution algorithms available for their analysis. We describe its objectoriented architecture, some of its presently available features, and we discuss through examples how existing software can be interfaced with it.
“…The solving of Markov chains (micro and macro) is done with a power method implemented in the marmoteCore framework [28] using a precision of 10 −8 . Indeed, the use of closed formulas suffers from numerical instability [23].…”
Section: Decomposition and Aggregation Methods For Calculation Of The...mentioning
confidence: 99%
“…They are respectively referred by VI, RVI, PI and PI Adapt. The algorithms are all described in [26] and are already implemented in the software [28].…”
Section: Unichain Algorithmsmentioning
confidence: 99%
“…This part is devoted to numerical experiments and the comparison between all previous algorithms. We have implemented all methods in C++, with the stand alone library [28].…”
Section: Numerical Experimentsmentioning
confidence: 99%
“…The heuristic in the (MC) model provides the following solution: C * = 9, 99375; and : [11,25,28,39,51,58,70,72,88,94,95,96,97,98,99]; , 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15].…”
Section: A Numerical Experiments Examplementioning
We consider a horizontal and dynamic auto-scaling technique in a cloud system where virtual machines hosted on a physical node are turned on and off in order to minimise energy consumption while meeting performance requirements. Finding cloud management policies that adapt the system to the load is not straightforward and we consider here that virtual machines are turned on and off depending on queue load thresholds. We want to compute the optimal threshold values that minimize consumption costs and penalty costs (when performance requirements are not met). To solve this problem, we propose several optimisation methods, based on two different mathematical approaches. The first one is based on queueing theory and uses local search heuristics coupled with the stationary distributions of Markov Chains. The second approach tackles the problem using Markov Decision Process (MDP) in which we assume that the policy is of a special multi-threshold type called hysteresis. We improve the heuristics of the former approach with the aggregation of Markov Chains and queues approximation techniques. We assess the benefit of threshold-aware algorithms for solving MDPs. Then, we carry out theoretical analyzes of the two approaches. We also compare them numerically and we show that all of the presented MDP algorithms strongly outperform the local search heuristics. Finally, we propose a cost model for a real scenario of a cloud system to apply our optimisation algorithms and to show their practical relevance. The major scientific contribution of the paper is a set of fast (almost in real time) load-based threshold computation methods that can be used by a cloud provider to optimize its financial costs.
“…The solving of Markov chains (micro and macro) is done with a power method implemented in the marmoteCore framework [28] using a precision of 10 −8 . Indeed, the use of closed formulas suffers from numerical instability [23].…”
Section: Decomposition and Aggregation Methods For Calculation Of The...mentioning
confidence: 99%
“…They are respectively referred by VI, RVI, PI and PI Adapt. The algorithms are all described in [26] and are already implemented in the software [28].…”
Section: Unichain Algorithmsmentioning
confidence: 99%
“…This part is devoted to numerical experiments and the comparison between all previous algorithms. We have implemented all methods in C++, with the stand alone library [28].…”
Section: Numerical Experimentsmentioning
confidence: 99%
“…The heuristic in the (MC) model provides the following solution: C * = 9, 99375; and : [11,25,28,39,51,58,70,72,88,94,95,96,97,98,99]; , 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15].…”
Section: A Numerical Experiments Examplementioning
We consider a horizontal and dynamic auto-scaling technique in a cloud system where virtual machines hosted on a physical node are turned on and off in order to minimise energy consumption while meeting performance requirements. Finding cloud management policies that adapt the system to the load is not straightforward and we consider here that virtual machines are turned on and off depending on queue load thresholds. We want to compute the optimal threshold values that minimize consumption costs and penalty costs (when performance requirements are not met). To solve this problem, we propose several optimisation methods, based on two different mathematical approaches. The first one is based on queueing theory and uses local search heuristics coupled with the stationary distributions of Markov Chains. The second approach tackles the problem using Markov Decision Process (MDP) in which we assume that the policy is of a special multi-threshold type called hysteresis. We improve the heuristics of the former approach with the aggregation of Markov Chains and queues approximation techniques. We assess the benefit of threshold-aware algorithms for solving MDPs. Then, we carry out theoretical analyzes of the two approaches. We also compare them numerically and we show that all of the presented MDP algorithms strongly outperform the local search heuristics. Finally, we propose a cost model for a real scenario of a cloud system to apply our optimisation algorithms and to show their practical relevance. The major scientific contribution of the paper is a set of fast (almost in real time) load-based threshold computation methods that can be used by a cloud provider to optimize its financial costs.
Motivation: Prioritizing genes for their role in drug sensitivity, is an important step in understanding drugs mechanisms of action and discovering new molecular targets for co-treatment. To formalize this problem, we consider two sets of genes X and P respectively composing the predictive gene signature of sensitivity to a drug and the genes involved in its mechanism of action, as well as a protein interaction network (PPIN) containing the products of X and P as nodes. We introduce GENetRank, a method to prioritize the genes in X for their likelihood to regulate the genes in P. Results: GENetRank uses asymmetric random walks with restarts and absorbing states to focus on certain nodes of the PPIN, as well as novel saturation indices providing insights on the visited regions of the PPIN. Using MINT as underlying network, we apply GENetRank to a predicitive gene signature of cancer cells sensitivity to tumor- necrosis-factor-related apoptosis-inducing ligand (TRAIL), performed in single-cells. Our ranking provides biological insights on drug sensitivity and a gene set considerably enriched in genes regulating TRAIL pharmacodynamics when compared to the most significant differentially expressed genes obtained from a statistical analysis framework alone. We also introduce gene expression radars, a visualization tool to assess all pairwise interactions at a glance. Availability and Implementation: GENetRank is made available in the Structural Bioinformatics Library (https://sbl.inria.fr/doc/Genetrank-user-manual.html). It should prove useful for mining gene sets in conjunction with a signaling pathway, whenever other approaches yield relatively large sets of genes.
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