Reduction of information

It would be highly desirable to reduce the individual facts in an information retrieval system to general principles just as the chemist has done in devising his empirical concepts mentioned pre-r viously. Such a reduction of information to its essential contents asks for insights, to transform information to knowledge. 

The purpose of this section is to show the reader how the different degree of reduction of information space (number of new variables) influences the final reproduction. As the procedures for the reduction depend on the type of data, i.e. smooth curves, discret distributions, and 2-dimensional patterns, we shall discuss each of them in appropriate subsections. The common property to all of them is the same representation in which they can be treated by the computer (see equation 4.1). 

Fig. 5.4 Example of the reduction of information space in discrete spectra mass (a) and C NMR (b) spectrum, chosen arbitrarily from a spectral inhouse database are represented similarly to the reproductions of the IR spectrum shown in Fig. 5.3. Only three reproductions with 65,129, and 257 coefficients, respectively, are shown in each case.

One approach to this situation is to research low latency update mechanisms across a group of participants, either by sophisticated communication schemes or the sheer reduction of information that has to be synchronized. A Virtual Reality application usually processes a lot of data for the visualization. In comparison to that, interaction events that actually steer the application are both, small in size and less frequent in comparison to video interrupts from the graphics hardware. A simple, but working approach is to share interaction events between collaborative applications in order to ensure data locking. This approach can be used for the synchronization of PC cluster based large displays and is depicted in the following section. 

In Chapter 1 we saw that only a rather small set of variables is required to completely specify the thermodynamic state of a system. How is the enormous reduction of information taking place as we go from a very large number of microscopic constituents and their motion in space and time to the macroscopic ctiuilibriiun behavior of matter ... 

Because of the substantial reduction of information associated with the transition between the micro- and macroworlds, one may readily conclude that the overwhelming amount of information buried in the detailed description of the spatio-temporal evolution of a inanyTpartielc system must be largely irrelevant for the thermod3mamics of an equilbrium system. In fact, one may suspect that it is the on-average behavior of the many-particle system what matters for its macroscopic properties, which, in turn, immediately suggests to employ statistical concepts. 

Notice also that, if we take our system as a quantum mechanical model for an ideal gas, the thermal state of the gas would be completely. specified by the density and temperature of the gtis (which would permit us to compute its pressure). Hence, in going from the microscopic to the macroscopic level of description, an enormous reduction of information from 0(10 ) down to only 2 degrees of freedom has taken place. 

In Chapter 2, we developed statistical thermodynamics as the central theory that enables ns in principle to calculate thermophysical properties of macroscopic confined flriids. A key feature of statistical thermodynamics is an enormous reduction of information that takes place as one goes from the microscopic world of electrons, photons, atoms, or molecules to the macroscopic world at which one performs measurements of thermophysical properties of interest. This information reduction is effected by statistical concepts such as the most probable distribution of quantum states (see Section 2.2.1). 

The wide variety of molecular structures usually requires a reduction of information together with the encoding process. Additionally, structural features should be encoded including properties that have a profound influence on the features to be investigated, such as molecular symmetry, physicochemical bond, or atomic or molecular properties like charge distribution, electronegativity, and polarizability of the compounds. Radial distribution functions and their derivatives have been found... 

Both the methodological part and the review of applications have shown the similarities and differences between effective Hamiltonians and pseudo-Hamiltonians. The similarities sometimes concern the purpose of the modelling (for instance the reduction to a minimal basis set) which may be attained in one way or another. They also concern the use of some reduction of information to a definite part (in general the lowest one) of the spectrum. This reduction is explicit in the effective Hamiltonian theory, through the choice of a model space, while in the pseudo-Hamiltonian approach it goes through the choice of a reduced distance between the exact Hamiltonian and the pseudo-Hamiltonian. 

But it must be clear that this reduction of information and this focus on some low part of the spectrum proceed differently and lead to completely different tools. The effective Hamiltonians appear as N-electron operators acting in well defined finite bases of iV-electron functions. The effective Hamiltonians obtained from the exact bielectronic Hamiltonian introduce three- and four-body interactions. They may essentially be expressed as numbers multiplied by products of creation and annihilation operators. In contrast, the pseudo-Hamiltonians keep an a priori defined analytic form, sometimes simpler than the exact Hamiltonian to mimic. For instance, the... 

In broad terms, where understanding already exists within the safety community, reducing uncertainty is focussed on presenting the correct information at the correct time (i.e. reduction of information uncertainty). Where understanding is lacking within the safety community, there are more fundamental issues that must be addressed to increase confidence (i.e. reduction of inadequate understanding). 

A further comment seems to be necessary concerning the phrase that the purpose of models is "to describe or to explain" an experimental phenomenon. Clearly, the most satisfactory descriptions of an experiment are the experimental curves themselves. The first step towards a model would be to reduce this usually very large amount of information by equivalently representing or simulating it in terms of as few and as simple relationships as possible, perhaps in the form of a mathematical formula. Such a reduction of information is stated by saying that a model describes an experiment. If we succeed, however, in establishing the description on the basis of the knowledge or at least of some intuitive assumptions about the specific molecular structure of the real system, we would call the model an explanation. 

IRRIIS. Integrated Risk Reduction of Information-based Infrastructure Systems (IRRIIS) (2006-2009), http //www.irriis. org/ [cited]... 

In general, the measures for uncertain quantities can be classified into representative values 971 and values to quantify the amount of uncertainty 11. For fuzzy quantities, the reduction of information is called defuzzification. This contribution shows information reducing measures for random and fuzzy variables. To avoid confusion, random variables Y G PfO.M) are defined by the CDF... 

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