Structured Communication and Collective Cohesion Measured by Entropy

by Arlin Cooper and Rush Robinett III
Albuquerque, New Mexico
 

Page:  1 | 2 | 3

 


The first step in normalizing the deviation from the equi-possible reference value (1/2n) at each module is to convert these inputs into qualitivity, q. Each positive input is converted by the first of the following equations; each negative is converted by the second.

(7)

Here, 2nl is the number of inputs to module l, and k is the total number of inputs in modules numbered less than l. This derives qualitivity for each primary input, ei, to each module, l.

In interval analysis, each equation has to be solved twice for interval numbers, once for the lower bound and once for the upper bound. The upper bounds of the positive qualitivities are derived from the upper bounds of the positive inputs and the upper bounds of the negative inputs. The lower bounds of the positive qualitivities are derived from the lower bounds of the positive inputs and the lower bounds of the negative inputs. The upper bounds of the negative qualitivities are derived from the lower bounds of the positive inputs and the lower bounds of the negative inputs. The lower bounds of the negative qualitivities are derived from the upper bounds of the positive inputs and the upper bounds of the negative inputs.

The second step provides for the calculation of entropy, additive inversion to match the polarity of the inputs (and to be compatible with quality), and linearization to compensate for the logarithmic function in the entropy calculation. The additive inversion is accomplished by subtracting the entropy from one. The linearization uses a quantity al, which is the average of all positive inputs to module l. Additive inversion is required in Equation 8, because each input represents a mode of communication with a particular entropy-reducing aim. The better this mode is, and the better it can be done, the higher the input value. In this step, the output of each module is calculated as:

(8)

The upper bound of each y output comes from the lower bound negative qualitivities and upper bound positive qualitivities. The lower bound of each output comes from the upper bound negative qualitivities and lower bound positive qualitivities.
 

"Interpersonal communication can temporarily reverse the ravages of entropy, and entropy can be used to develop a metric of the communication's degree of success."


The module outputs are the desired linearized inversed entropy. Importance (rank of contributors to the final result) and sensitivity (rank of most potential for improvement) can be derived by first using the mean value of each input in deriving a reference output. For importance, the mean value of each input is reduced by a fixed amount (the mean value), and the difference from the reference is computed. Then all inputs are ranked, normalized to one. For sensitivity, the mean value of each input is increased a fixed amount (to one), and the difference is computed. Then all inputs are ranked, normalized to one. Importance and sensitivity can be calculated at any point in the latent effects structure. For the example problem, we chose the final output for these computations in order to assess the ultimate effect of an important directive.

The inputs for this example structure are:

e1 = lack of deceit (conveying that the initiator will not give dishonest information to the recipient).
e2 = openness (conveying that the initiator will not hide information from the recipient).
e3 = goals (determining from the recipient what he or she would like to be doing professionally).
e4 = support (offering to find ways to help the recipient toward those goals).
e5 = dislike (aimed at finding what things about the job are most disliked).
e6 = like (aimed at finding what things about the job are most liked).
e7 = indirect (information about the person received from other sources).
e8 = skills (in order to improve job performance, the recipient must develop new skills).

The intent for this example is that the employee needs to improve job performance, or leave.

e9 = jobs (in order to be successful, the recipient should consider changing jobs).
e10 = example (offering an example of what another successful person is doing).
e11 = salary (salary treatment corresponds to job performance).
e12 = order (direct command).
e13 = demeanor (body language, where it is deemed necessary to reinforce order — e.g., stern expression).

Here are trial inputs for the example:

Table 1 — Example Inputs.

e1 = 0.2, 0.4

e2 = 0.3, 0.5

e3 = 0.7, 0.8

e4 = 0.3, 0.4

e5 = 0.3, 0.5

e6 = 0.7, 0.9

e7 = 0.6, 0.8

e8 = 0.5, 0.7

e9 = 0.5, 0.6

e10 = 0.6, 0.7

e11 = 0.4, 0.6

e12 = 0.8, 0.9

e13 = 0.7, 0.8

 

 

The outputs for the four modules are shown in Figure 3.

Figure 3 — Module Output Values for Example Problem.

The importance and sensitivity are shown in Figures 4 and 5.

Figure 4 — Importance Ranks for Example Inputs.

Figure 5 — Sensitivity Ranks for Example Problem.

Conclusion
Interpersonal communication can temporarily reverse the ravages of entropy, and entropy can be used to develop a metric of the communication’s degree of success. Interpersonal communication is so human-dependent that it is difficult to develop prescriptive communication methodology, and it is even more difficult to quantitatively analyze the process and measure its success. However, the work described in this article, based on entropy analysis, unique signal properties, and latent-effects relations, is a promising approach to improved communication strategy and success metrics. The work shows the importance of latent effects in establishing understanding through a common context and accumulated information, and the conveyance of information as background and as clear imperatives. Additional work could prove valuable. For example, we addressed only a subset of the interpersonal communication spectrum, and we have not yet completely validated the analytical approach. This additional work is planned as a follow-on effort.

Acknowledgment
The work documented in this article was supported by the National Nuclear Security Administration/Sandia National Laboratory Directed Research and Development program. Mike Dvorack, Glenn Kuswa, John Covan and Dave Menicucci helped in the development of and presentation of the concepts. Bob Roginski provided software development and support.

References

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Appendix: Example of Huffman Coding
In order to demonstrate Huffman coding, first assume six letters used in a message with the frequencies shown below, where they have been ordered from the lowest frequency at the top to the highest frequency at the bottom:

Letter

Frequency

S

4/65

I

1/13

N

7/65

T

8/65

P

12/65

E

29/65


The first two letters are given opposite values of the first encoding bit (e.g., 1 for S and 0 for I) and their frequencies are added for re-ranking and re-tabulation:

Letter

Frequency

N

7/65

T

8/65

S = 1, I = 0

9/65

P

12/65

E

29/65

The process continues:

Letter

Frequency

S = 1, I = 0

9/65

P

12/65

N = 0, T = 1

3/13

E

29/65

Letter

Frequency

N = 0, T = 1

3/13

S = 11, I = 10, P = 0

21/65

E

29/65

Letter

Frequency

E

29/65

N = 00, T = 01, S = 111, I = 110, P = 10

36/65

Letter

Frequency

N = 000, T = 001, S = 0111, I = 0110, P = 010, E = 1

1

 

Reading a coded word (e.g., TEST) from this encoding requires processing exactly the required number of bits for each character to get a match. For decoding, bits are considered sequentially until each coded character is identified unambiguously. For example, there are five characters whose code begins with 0, but beginning with 1 is unique to E. Therefore, 00110111001 cannot begin with E, but the other five letters are possible. Two letters begin with 00, so T is not decoded until the third digit. After this, the fourth bit must be E, since the other five characters start with 0. Then it takes four bits to distinguish S, and the last three bits are again decoded as T.

About the Authors
Arlin Cooper, a Senior Member of the System Safety Society, has worked at Sandia National Laboratories for 41 years, specializing in electronic component design, safety and security systems development and analysis, and mathematical algorithm development and assessment. He is a Senior Scientist and has a Ph.D. from Stanford University. He has authored numerous journal articles and three books, has contributed sections to several other books. He holds four patents.

Rush Robinett is currently Deputy Director of the Energy, Infrastructure and Knowledge Systems Center at Sandia National Laboratories. He has a Ph.D. in aerospace engineering from Texas A&M University. He has authored approximately 100 journal and conference articles, as well as two books, and has six patents. He is presently performing research in nonlinear control, optimization and information theory with respect to distributed decentralized systems including teams of people.

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