Recursive link

A network that contains a recursive (backward) link. 

One layer of input nodes and another of output nodes form the bookends to one or more layers of hidden nodes Signals flow from the input layer to the hidden nodes, where they are processed, and then on to the output nodes, which feed the response of the network out to the user. There are no recursive links in the network that could feed signals from a "later" node to an "earlier" one or return the output from a node to itself. Because the messages in this type of layered network move only in the forward direction when input data are processed, this is known as a feedforward network. 

Evaluation of protein sequence analysis methods based on the use of PSSMs in benchmarking experiments and in a number of test cases shows that these methods are capable of systematically detecting relationships between proteins that previously have been deemed tractable only at the structure-comparison level. Clearly, however, there is still a lot of room for improvement, as many automated procedures missed subtle connections that subsequendy have been revealed on a case-by-case basis, in part thanks to a careful choice of starting points for the PSSM construction. An exhaustive exploration of the sequence space by recursive iterative searching is likely to yield additional, on many occasions unexpected, links between proteins and, in particular, is expected to increase the rate of structure prediction. 

Since this recursion relation links every other coefficient, we can choose to solve for the even and odd functions separately. Choosing ao and then determining all of the even % in terms of this ao, followed by rescaling all of these a to make the function normalized generates an even solution. Choosing aj and determining all of the odd a in like manner, generates an odd solution. 

The P-polynomial is defined recursively. This means that we compute the P-polynomial of an oriented link in terms of the polynomials of simpler oriented links, which in turn are computed in terms of the polynomials of oriented links which are simpler still, and so on until we get a collection of unknots each of whose polynomial is known to equal 1. 

Note that according to the above definition, claims can be recursively supported by other claims (their sub-claims) to the depth that is arbitrarily chosen by the trust case designer. We also assume that evidence can be linked to references (documents, reports, data, models and so on) that are maintained within the trust case. 

When a stochastic model is described by a continuous polystochastic process, the numerical transposition can be derived by the classical procedure that change the derivates to their discrete numerical expressions related with a space discretisation of the variables. An indirect method can be used with the recursion equations, which give the links between the elementary states of the process. 

The recursive method of Macosko and Miller [27] has been described earlier for calculating molecular weight averages up to the gel point in nonlinear polymerization. A similar recursive method [34] can also be used beyond the gel point, particularly for calculating weight-fraction solubles (so/) and cross-link density. To illustrate the principles, we consider first the simple homopolymerization, that is, reaction between similar /-functional monomers Ay and then a more common stepwise copolymerization, such as reaction of A/ with B2. 

Problem 5.37 Consider the polyether network formation by the stepwise polymerization of pentaerythritol. Using the recursive method of direct computation, determine the following network properties as a function of the extent of reaction (a) weight-average molecular weight, (b) weight fraction of solubles, and (c) cross-link densities. Neglect the effect of condensation products on these properties. 

Although the relations for probability of a finite chain and cross-link probability derived by the recursive approach remain unchanged on taking into account the formation of condensation by-products, the latter do affect the calculated value of sol fraction. Modify Eq. (5.231) for sol fraction w in homopolymerization of Af (f = 3), taking into account the formation of condensation by-product which is removed from the reaction mixture. 

General aspects of the recursion method. The recursive residue generation method provides a computationally efficient way to compute spectra and survival probabilities in large multistate systems. Before presenting any details, we will first review some of the basic features of the method. In order to make a link between the lineshape function and the term residue, we will rewrite Eq. (6) in Section I.B as... 

Figure 4 The ball and spring representation of the first three steps in the Lanczos recursion. At the start, M = 0, we compute the self-energy of the initial state. This is represented by the first ball in the chain. In step M = 1, we then compute the first off-diagonal element and the second diagonal element these are shown as the spring and ball connected to the first ball. Then for M = 2, we compute the next spring and ball. Each successive step adds a ball and spring to the chain. The chain is thus built a link at a time.

On substituting this into Equation (4) and simplifying with the aid of identities linking polynomials of different /, we obtsiin a three-term recursion relation for the coefficients ... 

The position coordinates in the local coordinate system Ci of each link of a robot is related to its previous link in the chain from Ci to C by a link transformation Tj i. This link transformation must have one variable parameter, either an angle for a rotational joint or a linear distance for a sliding joint. Thus one can find the total transformation matrix for a robot arm from the following recursive expression ... 

Descriptions of the simplest data structure entities and explanations of their nature follow in succeeding sections. Basic data structures are stack, queue, and other linear lists multiple-dimension arrays (recursive) lists and trees (including forests and binary trees). Pointer or link simply means computer data constituting a memory location. Level indicates position in a structure that is hierarchical. Link, level, and the elementary structures are almost intuitive concepts. They are fairly easily understood by reference to their names or to real-life situations to which they relate. Evolving computer practice has had two effects. First, the impact of the World Wide Web and Internet browsers has acquainted many computer users with two basic ideas link (pointer) and level. Second, computer specialists have increased their use of advanced data structures. These may be understandable from their names or descriptive properties. Some of these terms are tries, quad-trees (quadtrees, quaternary trees), leftist-trees, 2-3 trees, binary search trees, and heap. While they are less common data structures and unlikely to be part of a first course in the field, they enable algorithmic procedures in applications such as image transmission, geographic data, and library search. 

---