Directed acyclic graph

BlMa94 Daniel Bleichenbacher, Ueli M. Maurer Directed acyclic graphs, one-way functions and digital signatures Crypto 94, LNCS 839, Springer-Verlag, Berlin 1994, 75-82. 

A Bayesian network over a set of n species represents a joint probability distribution over all the species. The network is restricted to a directed acyclic graph there are no feedforward or feedback loops, and the word directed dictates that the flow from one species to another is in one direction only. These are limitations to which we shall return later. A further specification is a conditional probability distribution for each variable given its parents in the graph G. 

Networks such as the previous one are commonly called feed forward, because their graph is a directed acyclic graph. Networks with cycles are commonly called recurrent. Such networks are commonly depicted in the manner shown at the top of the figure, where / is shown as being dependent upon itself. However, an implied temporal dependence is not shown (Fig. 2). 

A key feature of Bayesian Belief Networks is that they discover and describe causality rather than merely identifying associations as is the case in standard Statistics and Database Technology. Such causal relationships are represented by means of DAGs (Directed Acyclic Graphs) that are also used to describe conditional independence assumptions. Such conditional independence occurs when two variables are independent, conditional on another variable. 

The extensive application of binary SVM classifier provoked several researchers to discover the efficient way of extending binary classifier to multi-class classifier [23-26], In the literature there are one-versus-rest (OVR), one-versus-one (OVO), directed acyclic graph (DAG), all at once, error correcting code etc. Among these we have used three most commonly used methods of multi-class SVM classifier in this application. A brief description of the OVR, OVO and DAG method is explained below. 

Like ROBDDs, MTBDDs may be represented by directed acyclic graphs where the leaf values contain elements of A. 

Binary Decision Diagrams (BDDs) are a canonical representation of Boolean functions /(xi, 2j 2 3,..., Xn) in the form of directed acyclic graphs. The reader should refer to [4] and [5] for a tutorial introduction to BDDs. 

A Multiway Decision Graph (Mdg) is a finite, directed acyclic graph (DAG) where the leaves are labeled by Thie (T), the internal nodes are labeled by terms, and the edges issuing from an internal node v are labeled by terms of the same sort as the label of v. Such graph is a canonical representation of a certain quantifier-free formula, called a Directed Formula (DF). Each term in a DF belongs to either a concrete sort or an abstract sort. Concrete sorts have enumerations, while abstract sorts do not. 

Up to now, we only model single-assignment basic blocks, which can be represented by directed acyclic graphs (DAGs). This is sufficient for the scenarios we are dealing with. Fig. 1 shows the DAG and the deflnitions of the concrete data flow model for an example. 

Bayesian Networks allowed the creation of a multilevel directed acyclic graph, where conditional proba-bihties come from the test data. 

A Bayesian network takes the strucmre of a direct acyclic graph (DAG), i.e., the arcs cannot make cycles. They must be unidirectional, i.e., it is impossible to return to the initial node. 

New methodology for exact reliability quantification of highly reliable systems with maintenance was introduced in (Bris 2008a). It assumes that the system structure is mathematically represented by the use of directed acyclic graph (AG), see more details in (Bris 2008b). Terminal nodes of the AG that represent system components are established by the definition of deterministic or stochastic process, to which they are subordinate. From them we can compute a time dependent unavailability function, of individual terminal nodes. Finally a correspondent time dependent imavailability function U(x,t) of the highest node (SS node or top event in classic PRA model) which represents rehabdity behaviour of the whole system may be found. It is clear that U(x,t) < Us(x). 

Bris, R. 2008b. Parallel simulation algorithm for maintenance optimization based on directed Acyclic Graph. Reliability Engineering <6 System Safety 93,974-884. 

Graphical component (or quaUtative component) is a directed acyclic graph (DAG) denoted by G = (N,A) where A is the set of arcs in the graph and N its node set. The node set N is partitioned into subsets C, D and V such that ... 

Probability techniques can help the system work in uncertain situations or scenarios. With respect to the proposed model, DL Reasoning can provide more than one possible solution, which can enable indecisive behavior of robots. In a nondeterministic world, the deterministic way of seeing the world is often not expressive enough to address real-world problems [16]. Mathematically, a Bayesian Network is a directed acyclic graph in which a set of random variables makes up the nodes in the network. A set of directed links connects pairs of nodes, and each node has a conditional probability table that quantifies the effects of parents on it. 

The data flow model represents operations, operation inputs, and data dependencies between operations using a bipartite directed acyclic graph. 

The control and timing model represents events and relations between events, also using a directed acyclic graph. 

Bayesian Behef Networks are directed acyclic graphs. The nodes represent nncertain variables, and the edges are the causal or influential links between the variables. Associated with each node is a set of conditional probabihty values that model the uncertain relationship between the node and its parents. 

The functional hierarchy is really a directed, acyclic graph, not a simple tree. This is because parts may implement multiple functions, and have multiple function units. Thus, there are nodes with in-degree greater than one, and the links do not have to observe strict hierarchy (i.e. a part may be linked to parts at various abstraction levels). For example, in Figure 5, a section of an actual functional hierarchy is shown. Notice that the part 6846 is linked to a read-only memory (G.ROM-0), a timer (68XX TIMER 0), and a parallel device(68XXJ>IO.O). 

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