Relative frequency of occurrence

When X represents a continuous variable quantity, it is sometimes convenient to take the total or relative frequency of occurrences within a given range of x values. These frequencies can then be plotted against the midvalues of x to form a histogram. In this case, the ordinate should be the frequency per unit of width x. This makes the area under any bar proportional to the probability that the value of x will he in the given range. If the relative frequency is plotted as ordinate, the sum of the areas under the bars is unity. 

Relative frequency of occurrence of D stability" Relative frequency of calms distributed above with D stability = 0.5753. 54,6058... 

FIGURE 6.39 Relative frequencies of occurrence of amino acid residues in m-helices, /3-sheets, and /S-turns in proteins of known structure. (Adapted from Belt, J E., and Belt, E. T, 1988, Proteins and. Enzymes, Englewood Cliffs, NJ Prentice-Hall.)... 

The possibility of obtaining single crystal diffraction patterns from regions of very small diameter can obviously be an important addition to the means for investigating the structures of catalytic materials. The difficulty arises that data on individual small particles is usually, at best, merely suggestive and at worst, completely meaningless. What is normally required is statistical data on the relative frequencies of occurrence of the various structural features. For adequate statistics, it would be necessary to record and analyse very large numbers of diffraction patterns. 

The computer program presented here can generate very different relative frequencies of occurrence of all amino acids (and stop codons) within a target set. One-pot, two-pot, and three-pot syntheses can be simulated. Optionally, correction factors can be included to compensate for the (possible) differences in chemical coupling efficiencies of the nucleotide synthons. Finally, the codon usage of three major expression microorganisms can be considered, treating rare codons as pseudo stop codons. 

Symmetry elements (in addition to identity) Relative frequency of occurrence in the CSD (%) ... 

For a numerical treatment of the relative frequency of occurrences for a similar curve defined by a lottery scheme, see Ehrenfest [2]. 

Once the theoretical yield of individual degradation acids have been calculated, their corresponding relative frequencies of occurrence can be obtained The figures are usually expressed in percent on a molar basis and are related to... 

Suppose that the following numbers denote the relative frequency of occurrence of each of the digits in the last significant figure of an instrument reading ... 

One important question regarding the distribution of measurements about their mean is the expected frequency of occurrence of an error as a function of the error magnitude. The most commonly utilized function, which describes well the relative frequency of occurrence of random errors in large sets of measurements, is given by Gauss formula (see also rel. (9) Section 5.2) ... 

This frequency function shows that the point of maximum frequency is obtained for the mean (when x = p), the distribution of positive and negative errors is symmetrical, and as the magnitude of the deviation from the mean increases, an exponential decrease in the frequency takes place. The errors with the relative frequency of occurrence given by rel. (5) have a so-called normal distribution N(n,o). Using the substitution ... 

For small sets of measurements it was found that the relative frequency of occurrence of random errors is not described so well by Gaussian distribution as by another frequency function named t or Student function, f(t, v) (where v = n -1 represents the degree of freedom of the sample) with a known expression [71] ... 

Graphs of s vs. number of revolutions are plotted. Also, the use of the usual chi-square test is illustrated for comparing distributions to determine whether a batch is randomly mixed. In addition, a table is given for classifying mixtures according to the relative frequency of occurrence of chi-square values. 

Based on our knowledge of herbicide modes of action and other characteristics, we are able to predict, with some confidence, which herbicides will have a high risk for resistance. There are wide margins for error due to uncertainty about genetic variability of weeds (i.e., the relative frequency of occurrence of different resistance mutations), the lack of knowledge on the primary sites or modes of action for certain herbicides, and the lack of understanding of cross-resistance between classes of herbicides. 

Fig. 61. Size and shape analysis of synaptic vesicles in S-type and F-type synapse. Diameters of both major and minor axis in each synaptic vesicle in both types of synapses were measured. Ordinate shows the length of the major axis, while the abscissa that of the minor axis of vesicles in each type of synapse. Diameters of vesicles in S-type synapse (white) are distributed around the 45-degree line between ordinate and abscissa, while those in F-type synapse (black) of both white and black circles indicates the relative frequency of occurrence. Elongation index ratio of average length of major versus minor axis of vesicles in S-type synapse was about 1.2, while that of F-type synapse was about 1.7. Uchizono (1965).

When a third strand is added, the relative frequencies of occurrence of the possible motifs reflect the same preferences for antiparallel compared with parallel, and for sequential strands to be adjacent in the structure. Tkble 15.3 shows the possible topologies for three consecutive strands that are adjacent in the same P sheet and their frequency of occurrence in our data set. The most commonly occurring pattern is the P meander (Figure 15.15), which consists of two consecutive P hairpin ( 4-1 ) connections. Many of these meanders exist as isolated units, i.e. no other strands are... 

The ratio n /N is sometimes called the relative frequency of occurrence of x in the first N trials. 

The distribution of random errors in these data is more easily understood if they are organized into equal-sized, adjacent data groups, or cells, as shown in Table a 1-2. The relative frequency of occurrence of results in each cell is then plotted as in Figure al-lA to give a bar graph called a histogram. 

Based on experimental observations, the theoretical models considered throw light on the origin of simple periodic phenomena and complex oscillations, including chaos, in biochemical systems. Besides illustrating the variety of molecular mechanisms producing oscillations at the cellular level, the models allow us to delineate in a qualitative and quantitative manner the conditions in which sustained oscillations occur. The theoretical approach thereby contributes to a better understanding of the physiological roles of such rhythms. Furthermore, in such an approach the relative frequency of occurrence of simple versus complex patterns of oscillations becomes amenable to quantitative assessment. Finally, theoretical models for biochemical and cellular... 

Fig. 13.5 Changes in the receiver response to offensive behavior without urine release (open bars) and to offensive behavior accompanied by urine release (solid bars). Responses are measured as changes in the relative frequency of occurrence of defensive (levels —2, — 1), neutral (level 0) and aggressive (levels 1-5) behaviors. Asterisks denote significant differences between the two conditions (double asterisk p < 0.01 modified after Breithaupt and Eger 2002)...

Computer-based implementations of Figure 16 may assume a Bayesian inferential framework for processing information. Frameworks for Bayesian inference require probability values as primary inputs. Because most events of interest are unique or little is known about their relative frequencies of occurrence, the assessment of probability values usually requires human judgment. Substantial... 

The relative frequency of occurrence of various corrosion forms depends on the type of industry and environment. One example from the chemical industry is shown in Table 7.1. In the heading we notice the high proportion of corrosion failures. The percentages of crevice corrosion and galvanic ( ) corrosion are surprisingly low. 

A way of characterizing the environment is to divide the execution into a set of runs, where a run is the execution of a function in the system. If runs are identical repetitions of each other, these runs form a run type. Variations of a system function are captured in different run types. The specification of the environment using run types is called the operational profile. The operational profile is a set of relative frequencies of occurrence of operations, where an operation is the set of run types associated with a system function. To simplify the identification of the operational profile, a hierarchy of profiles is established, each making a refinement of the operational environment. 

Figure 5. Relationship between karst forms (relative frequency of occurrences Y) and remoteness from lineament (index value—X).

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