The reconstruction model

In order to build a mathematical model of embryonic develoment, it is necessary to ignore a multitude of secondary features and to 

As we can see, the problem can be given a precise formulation, but what really counts is that it can also be given a solution. I have demonstrated that structures can indeed be reconstructed by using only 10% of the minimum number of projections (Barbieri, 1974a, 1974b, 1987), and an iterative algorithm which exploits memory matrices. More precisely, a reconstruction from incomplete projections is possible if two conditions are met (1) if the reconstruction method employs memory matrices where new information appears, and (2) if the reconstruction method employs codes, or conventions, which transfer information from the memory space to the real space. 

The reconstruction of structures, in conclusion, gives us a model that translates epigenesis into a workable problem, and tells us that 

The reconstruction of individual structures can be a model for the development of individual cells, but not for multicellular systems such as embryos. In this case, a model must be capable of performing in parallel a plurality of reconstructions, while taking into account a variety of interactions between individual structures. What must be simulated is an increase of information between initial and final structures, and on this point the reconstruction model is crystal clear. The difference between initial and final information, and therefore the overall increase of complexity in the system, is entirely dependent on the memories which are used in a reconstruction, because it is only in the memory space that new information appears. 

In the first case, a structure is reconstructed with the same strategy from beginning to end, and we can say that the reconstruction is continuous, or one-phased. In the other case, the reconstruction is discontinuous, or two-phased, because after an initial period where the collective memory does not yet exist, comes a second phase where cells can also use the information of the newly-formed collective memory. A discontinuous reconstruction produces a greater increase of complexity than a continuous one (because the collective memory adds additional information), but needs of course a more complex 

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They found a whole bunch of soft phonons, which are primarily horizontally polarized, near the zone boundaries between M and X. The most unstable mode they observed is the Mj phonon, the displacement pattern of which is shown in Fig. 40 note the similarity between this pattern and the reconstruction model in Fig. 39. According to Wang and Weber, these soft phonons are caused by electron-phonon coupling between the surface phonon modes and the electronic 3 surface states at the Fermi surface. They attributed the predominant Ms phonon instability to an additional coupling between d(x — y ) and d(xy) orbitals of the Zj states. 

These examples show that the two strategies proposed by the reconstruction model do indeed correspond to two developmental strategies that have both been exploited by nature. The model is capable therefore of simulating some important characteristics of... 

We have already seen that the reconstruction model makes a sharp distinction between real-space matrices and memory-space matrices, and suggests that embryos too have equivalent types of three-dimensional structures the real structures of the phenotypic body, and the memory structures of the body plan. According to the reconstruction model, therefore, during embryonic development there is not only a development of phenotypic structures, but also a parallel development of memory structures. It should be noticed, however, that these two processes are sharply asymmetrical. 

The phenotypic development of a body is practically a continuous process, while the development of contextual information is divided into two very different phases by the discontinuity of the body plan. In the first period, when the body plan does not exist, there is contextual information only at the cell level, and memory structures are confined to the cell. In the second phase, in contrast, the body plan becomes a source of contextual information above the cell level, and the embryo s development takes place in a totally new reference system. From this moment on, the body plan becomes a new intermediary between genotype and phenotype, and since it is shared by all members of a phylum, we can call it the phylotype, or the phylotypic body. The reconstruction model, in short, allows us to conclude that a multicellular organism consists of three fundamental categories - genotype, phylotype and phenotype - and that embryonic development consists of two different developments which come one after the other, i.e. in series. The first is the development of the phylotypic body the second is the development of the individualko y. 

The formulation (6.70) and (6.71) permits the application of the state quantity-related approach described in Sect. 6.9.4 for the reconstruction of the mechanical quantities s and F. In this case the reconstruction model of the self-sensing actuator results in... 

Fig. 15. Skeleton bifurcation diagram of the reconstruction model of CO oxidation on Pt(l 10) Equations (4) and of the reduced model Equations (5). Regions A and C are excitable, B oscillatory and D bistable. The latter is subdivided depending on whether one (Di) or two front solutions (Di) exist.

Fig. 3.21 R4O cluster bonding (reprinted with permission from [137, 140]) and the reconstruction models for the O-Rh(lll) [118, 133] and the 0-Ru(0001) surfaces of C3V symmetry [119, 120]. a At o < 1/4 ML coverage, 0 locates in the center of one of the four tetrahedral sites to form one bond with the atom labeled 1. The 0 induees and pushes the dipoles labeled 2 radially away and the C3V symmetry remains, producing the clusters of STM jrotrusion. b At o S 1/2 ML, O evolves into by forming another bond with a surface R atom labeled 1. The lone pairs sustain the dipoles (labeled 2). The dipole and ionic row move closer toward the sites without adsorbates, which generates the pairing-STM protrasion-depression patterns, c At o <1-0 ML, H-Uke bonds dominate at the surface. Two lone pairs polarize each surface R atom (1/2) which donates meanwhile one electron to other adsorbate. Formation of the H-like bonds restores the reduced work function and lowers the STM protrusions. The entire surface network is stabilized and becomes unreconstructed and restores the 3 crystallographic symmetry (reprinted with permission from [1])...

Chemical and bond-creating reconstructions that go beyond the range accessible by different terminations of the bulk stmcture have been found on SiC(OOOl) and SiC(lll) surfaces. They are induced by deposition of Si on the SiC surface and subsequent annealing. On the Si-rich side, the surface phase diagram begins with a (3 X 3) reconstruction, which is characterized by a Si adlayer terminated by an adatom tetrahedrally supported by three extra Si atoms [123, 124]. The reconstruction model is shown in the top and side views in Figure 4.44a,b. Chemically the reconstruction involves 13/9 monolayers of Si on top of an already Si-terminated bulk. Geometrically, the Si adlayer compensates the lattice mismatch of about 20% between SiC and Si, with the result that instead of a bilayer one... 

To search for the forms of potentials we are considering here simple mechanical models. Two of them, namely cluster support algorithm (CSA) and plane support algorithm (PSA), were described in details in [6]. Providing the experiments with simulated and experimental data, it was shown that the iteration procedure yields the sweeping of the structures which are not volumetric-like or surface-like, correspondingly. While the number of required projections for the reconstruction is reduced by 10 -100 times, the quality of reconstruction estimated quantitatively remained quite comparative (sometimes even with less artefacts) with that result obtained by classic Computer Tomography (CT). 

Forward modelling is the first step for inverting data for the reconstruction of the defect. For this purpose, the specialised code is better adapted because it is faster than the general code. 

This paper is structured as follows in section 2, we recall the statement of the forward problem. We remind the numerical model which relates the contrast function with the observed data. Then, we compare the measurements performed with the experimental probe with predictive data which come from the model. This comparison is used, firstly, to validate the forward problem. In section 4, the solution of the associated inverse problem is described through a Bayesian approach. We derive, in particular, an appropriate criteria which must be optimized in order to reconstruct simulated flaws. Some results of flaw reconstructions from simulated data are presented. These results confirm the capability of the inversion method. The section 5 ends with giving some tasks we have already thought of. 

The model is intrinsically irreversible. It is assumed that both dissociation of the dimer and reaction between a pair of adjacent species of different type are instantaneous. The ZGB model basically retains the adsorption-desorption selectivity rules of the Langmuir-Hinshelwood mechanism, it has no energy parameters, and the only independent parameter is Fa. Obviously, these crude assumptions imply that, for example, diffusion of adsorbed species is neglected, desorption of the reactants is not considered, lateral interactions are ignored, adsorbate-induced reconstructions of the surface are not considered, etc. Efforts to overcome these shortcomings will be briefly discussed below. 

Fig. 10 shows the phase diagram of the ZGB model with global reconstructions. For the standard ZGB model a narrow reactive regime within the range Fi. < < F2A is observed, as discussed above in the description of... 

FIG. 10 Phase diagram of the ZGB model with adsorbate induced global reconstructions of the surface. The plots show the dependence of the rate of AB production (7 ab) and the surface coverages with A and B species and 9q, respectively) with the adsorption probabihty of A species given by Fa-... 

FIG. 13 Snapshot configuration of the catalyst surface obtained for the ZGB model with local reconstructions using lattices and patches of side L = 129 and Lp = 3, respectively, and taking 7 = 0.331 and = 0. B species , A species. Empty sites are left white. Notice the formation of clusters of both species surrounded by empty sites. 

In the standard lattice gas model of adsorption we assume that the surface of the solid remains inert, providing adsorption sites. This implies that the state of the surface before adsorption and after desorption is the same. This is not the case if the surface reconstructs or lifts the reconstruction upon adsorption. Such a situation we want to describe. We introduce occupation numbers for the surface = 0 or 1, depending on whether the surface... 

Figure 5.8. Left STM picture of the so-called clock reconstruction that occurs when 0.5 ML of carbon is adsorbed on Ni(lOO). Right Hard sphere model of the reconstruction. Dotted rings indicate the unreconstructed positions of...

Figure 6. Structure model of the reconstructed 1x2 jAiase formed with Ni(110) at coverages > 1 monolayer. Small circles H aioms dark circles Additionally provided adsorption sites for H. Shaded atoms belong to the second Ni layer.

The term G T, a,, A/, ) is the Gibbs free energy of the full electrochemical system x < x < X2 in Fig. 5.4). It includes the electrode surface, which is influenced by possible reconstructions, adsorption, and charging, and the part of the electrolyte that deviates from the uniform ion distribution of the bulk electrolyte. The importance of these requirements becomes evident if we consider the theoretical modeling. If the interface model is chosen too small, then the excess charges on the electrode are not fuUy considered and/or, within the interface only part of the total potential drop is included, resulting in an electrostatic potential value at X = X2 that differs from the requited bulk electrolyte value < s-However, if we constrain such a model to reproduce the electrostatic potential... 

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