Concatenated states

Conveniently, MMOs are characterized by a symbolic notation where L denotes the number of large and S the number of small oscillations during one period. Thus, the MMOs depicted in Fig. 27 are designated as F , P, and 1 P states. In the notation of the latter state, it is indicated that one period is built up from concatenated principal states. In fact, in the simulations, many such concatenated states were found for example, between the P and the P state, P(P) states with n going from 1 to 10 were observed. These sequences are called Farey sequences because a one-to-one correspondence of successive MMO states and the ordering of the rational numbers, which is conveniently represented in a Farey tree (see Fig. 31), can be established. In general, at low values of the resistance, the sequences of MMOs obey an incomplete Farey arithmetic. 

IF (expr) THEN statement ELSE state ment [f, then, else statement (on one line a V may be used to concatenate lines)... 

Complex mappings Complex mappings map a set of attributes in the source to a set of attributes in the target. For example, we can map the attribute address to the concatenation of street, city, and state. 

In Chapter 2 we looked at concatenative (wavetable) synthesis of music and speech. The idea there was to store pieces of waveforms and join them together in the time domain to make sound. The idea of a loop for periodic sounds (steady state of a trumpet, vowels of speech, etc.) was introduced. One way to... 

The generalized solid-state NEB (GSSNEB) [148] was developed recently to overcome these problems. This method uses the NEB formalism to optimize simultaneously the atomic coordinates and the simulation cell to the MEP. In the GSSNEB method the strains and stresses associated with the simulations cell are used as analogues of atomic positions and forces. These quantities are incorporated into the calculation by concatenating the strain associated with the cell of a particular image to the changes in atomic positions ... 

Contractions are not abbreviations. Abbreviations are words which have a shortened written form only, such as (Dr doctor). By contrast, contractions have shortened forms in both the written and spoken form, so they 11, formed from the contraction of THEY and will is pronounced /dh ey 1/ and not /dh ey w ih 1/. We can state more properly that contractions are shorted spoken combinations of words, whose properties are reflected in writing conventions. The question wilh contractions is whether we should regard the contraction as one word or two. First note that the contraction isn t always simply a case of concatenating a first written form to a shortened second written form. While they 11 is created this way, won t meaning will not is not formed this way, and similarly with aint. While don t can be formed fi om the concatenation of do and not followed by the replacement of o with, phonetically the process is different in that file vowel of DO, /uw/ changes to /ow/ in don t. Furthermore, sometimes the apostrophe occurs at the place where we would break the forms (eg. they 11) but sometimes not e.g. don t would break into do and n t, not don and t). 

E q)erience has shown that with a suitably recorded and analysed diphone set, it is usually possible to concatenate the diphones without any interpolation or smoothing at the concatenation point This is to be expected if the steady-state/transition model is correct (see Section 13.2.6). As we shall see in Chapter 16 however, this assumption is really only possible because the diphones have been well articulated, come from neutral contexts and have been recorded well. It is not safe to assume that other units can always be successfully concatenated in phone middles. 

To use these equations for recognition, we need to connect state sequences with what we wish eventually to find, that is, word sequences. We do this by using the lexicon, so that, if the word hello has a lexicon pronunciation /h eh 1 ou/, then a model for the whole word is created by simply concatenating the individual HMMs for the phones /h/, /eh/, /y and /ou/. Since the phone model is made of states, a sequence of concatenated phone models simply generates a new word model with more states there is no qualitative difference between the two. We can then also join words by concatenation the result of this is a sentence model, which again is simply made from a sequence of states. Hence the Markov properties of the states and the language model (explained below) provide a nice way of moving from states to sentences. 

Figure 8.11 Several states in the Farey tree for a sequence of states observed as the residence time decreases in the Mn-catalyzed BZ reaction. Each state consists of a concatenation of the basic 1 and patterns. Firing numbers are given in brackets. The 4/3 and 17/23 states in Table 8.1 are not shown here. (Reprinted with permission from Maselko, J. Swinney, H.L. 1986. Complex Periodic Oscillations and Farey Arithmetic in the Belousov-Zhabotinskii Reaction, J. Chem. Phys., 85, 6430-6441. 1986 American Institute of Physics.)...

In PrODHyS, the model of material is slightly coupled with the device (association relationship). Indeed, material is a ReactivePhaseSystem-type token (figure 4). When this token marks a hybrid place of the associated device, the resulting continuous model is built by the concatenation of DAE system of the actual material state with the DAE system of the actual device state. 

The evolution of a p-automaton is the following if the system is in the state x, the transition e to the state Xj is done with the probability P(x,.,e,x ). The probability transition function can be extended to the paths it c X(ZX) in the p-automaton Ap (a path is obtaining by concatenating the transitions, where the end state and the initial state of two consecutive transitions coincide). The probability of the paths is defined by the next equation ... 

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