Binary measurement

Estimates of phase diagrams can be made on the assumption of ideal behavior or with activity coefficient data based on binary measurements that ate more easily obtained. In such cases, clearly, it should be known that inteimolecular compounds do not form. 

To simplify further, let us assume that what is important about an individual s experiences can be mapped on only two dimensions, we can thus draw a graph, like Figure 5-1. Each small circle represents an observation at a single point in time of where a particular individual is in this two-dimensional psychological space, in this example, we have taken a total of twenty-two binary measures at various times. 

Y. Y. Shi, G. A. Miller, O. Denisenko, H. Qian, and K. Bomsztyk. Quantitative model for binary measurements of protein-protein interactions../. Comput. Biol., 14 1011-1023,2007. 

There are several reports in the literature that measure binary adsorption equilibria using gas chromatography [4,S,6]. In GC techniques the adsorbent is equilibrated with a continuous flow of carrier gas (gas 1). Then a pulse of gas 2 is injected at the column inlet. A peak of the gas 2 is eluted at the exit of the column after some time. Net retention time (or volume) is calculated from the first moment of the peak after correcting for void volume (by measuring the retention time of a non-adsorbing species). If the carrier gas is inert (i.e. helium) the net retention time is related to the pure component Henry s constant. Typical binary measurements reported so r use a mixture of the two gases as carrier and introduce a small perturbation in composition. The net retention volume is related to the thermodynamic properties by [4]... 

We used a typical GC setup and a mass spectroscopic detector. The only modification involves controlling column pressure between 20 - 1000 kPa. The following table lists the main features of the experimental system used. All previous attempts to use the GC technique for binary measurements were conducted at constant (atmospheric) pressure. The pure component isotherms are obtained form a conventional volumetric technique. 

If the terms b and care replaced in sucha way that Ujis the number of bits 1 of the object s, that is, a + b, and n the number of bits 1 of the object t, that is, a + c, the previous binary measures can take a different form. For example, the Tanimoto index can be written as... 

The most popular distance binary measures are Hamming and Tanimoto distances that are listed below (Table SIO), together with other distance measures on binary vectors. 

Measurements of almost any thermodynamic property of the binary mixture allows at least one of these parameters to be determined more precisely. It is usual to retain rii = 1 and to use the binary measurements to estimate. Typical values are ... 

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