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The Many Variables & The Spurious Waffles
Published in Richard McElreath, Statistical Rethinking, 2020
To understand this better, it is helpful to introduce a particular type of causal graph known as a DAG, short for directed acyclic graph. Graph means it is nodes and connections. Directed means the connections have arrows that indicate directions of causal influence. And acyclic means that causes do not eventually flow back on themselves. A DAG is a way of describing qualitative causal relationships among variables. It isn’t as detailed as a full model description, but it contains information that a purely statistical model does not. Unlike a statistical model, a DAG will tell you the consequences of intervening to change a variable. But only if the DAG is correct. There is no inference without assumption.
Evolution of Embedded Internet
Published in K. R. Rao, Zoran S. Bojkovic, Bojan M. Bakmaz, Wireless Multimedia Communication Systems, 2017
K. R. Rao, Zoran S. Bojkovic, Bojan M. Bakmaz
A directed acyclic graph (DAG) [29] is a directed graph having the property that all edges are oriented in such a way that no cycles exist. All edges are contained in paths oriented toward and terminating at one or more root nodes (traditionally called sinks in WSNs). RPL routes are optimized for traffic to or from one or more roots (sinks). As a result, RPL uses the DAG topology and is partitioned into one or more destination-oriented DAGs (DODAGs), one DODAG per sink. RPL specifies how to build the DODAG using an objective function. The objective function computes the optimal path according to certain routing metrics and constraints. In this way, DODAGs with different characteristics can be formed. For example, different DODAGs are constructed with the objective to (1) find the best path in terms of link throughput while avoiding battery-operated nodes, or (2) find the optimal path in terms of latency while avoiding nonencrypted links. There can be several objective functions operating at the same node depending on the different path requirements of a given traffic. In this way, it is possible to have multiple DODAGs active at the same time to carry traffic with different requirements. Example 9.1RPL specifies local and global repair mechanisms for recomputing routes when an inconsistency is detected or based on administrative decisions [30]. Local repair means detaching a node’s sub-DODAG by increasing its rank value. Once a root initiates a global repair event, all the nodes in the DODAG recompute their rank values and reconfigure their parent sets. An example topology of a RPL network together with nonstoring and storing modes is presented in Figure 9.5.Solid arrows represent each node’s preferred parent (determined from the node’s neighbors and their rank values) whereas dotted arrows point to the other nodes in the parent set. To support routing to various destinations within the DODAG, which is the root, RPL uses the destination advertisement object (DAO) message. RPL supports scenarios in which in-network nodes do not have enough memory to store routes to all possible destinations. In this case, the DAO messages, which contain information on the desired parent set of a destination node, are propagated up the DODAG until they reach the root. The root gathers DAOs from all nodes in the DODAG, and uses them to construct “down” routes to various destinations. Data to these advertised destinations is forwarded along a DODAG until it reaches the root, which then attaches a source routing header and sends it back down the DAG. Alternatively, nodes in the DODAG may store next-hops to downstream destinations. However, a key design simplification was not supporting “mixed-mode operation” in which storing and nonstoring nodes coexist because this was still considered a research issue; thus, all nodes in a DODAG must either store or not store routes.
A theoretical framework to accelerate scheduling improvement heuristics using a new longest path algorithm in perturbed DAGs
Published in International Journal of Production Research, 2023
Golshan Madraki, Seyedamirabbas Mousavian, Yasamin Salmani
In a DAG, no cycle is allowed, so, the reachability operator is defined over the set of nodes, i.e. for a given DAG, , implies that there exists a path from node to (Cheng et al. 2006). A topological sort of des for a DAG, , is defined as a sorted set of nodes such that for all , if , then which implies that each node in the set is reachable only from nodes that come before it in the sort. It is obvious that the topological sort of nodes is not unique (Madraki, Bahalkeh, and Judd 2015).
Fuzzy-based Security-Driven Optimistic Scheduling of Scientific Workflows in Cloud Computing
Published in IETE Journal of Research, 2020
J. Angela Jennifa Sujana, T. Revathi, S. Joshua Rajanayagam
The workflow application can be modeled as directed acyclic graph (DAG), to represent the features of a scientific application like the execution time of tasks, the size of data to communicate among tasks and task dependencies. The workflow is represented as, W = (T, E), where T denotes the task set T = {t1, t2, … , tn} and each individual task denotes workflow application task. Similarly, E denotes the set of communication edges among tasks and each edge e(i,j) ∈ E denotes that the task depends on the task , i.e. task can be executed only after the execution of the task . We have discussed about similar schedule primitives in our earlier work [1].
Efficient distributed algorithms for distance join queries in spark-based spatial analytics systems
Published in International Journal of General Systems, 2023
Francisco García-García, Antonio Corral, Luis Iribarne, Michael Vassilakopoulos
In the era of Big Spatial Data (Eldawy and Mokbel 2017), the research community is focusing on developing new distributed data management systems that can efficiently analyze and process large-scale spatial data. Nowadays, with the development of modern mobile applications, the increase of the volume of available spatial data, from smart-phones, sensors, cars, satellites, etc., is huge world-wide. Recent developments of big spatial data systems have motivated the emergence of novel technologies for processing large-scale spatial data on clusters of computers in a distributed environment. Parallel and distributed computing using shared-nothing clusters on large-scale datasets is becoming a dominant trend in the context of data processing and analysis. Apache Spark1 is a fast, reliable, and distributed in-memory large-scale data processing framework. It takes advantage of Resilient Distributed Datasets (RDDs), that allow data to be stored transparently in memory and persisted to disk only if it is needed. Hence, Spark can avoid a huge number of disk writes and reads, and it outperforms the Hadoop-MapReduce platform (Shi et al. 2015). Since Spark maintains the status of assigned resources until a job is completed, it reduces time consumption in resource preparation and collection. Spark programming model consists of an advanced Directed Acyclic Graph (DAG) engine. Spark builds its query computations as a DAG; its DAG scheduler and query optimizer construct an efficient computational graph that can usually be decomposed into tasks that are executed in parallel across workers on the cluster (Damji et al. 2020). Conceptually, a DAG is a directed graph that has a topological ordering, a sequence of the vertices (RDDs) such that every edge (data dependency) is directed from earlier to later in the sequence, i.e. a DAG is a graph that never goes back. Spark DAGs allows simple jobs to complete after just one stage, and more complex tasks to complete in a single run of many stages. Spark DAGs help to achieve fault tolerance, and thus we can recover the lost data.