# How to Understand Behavioral Patterns in Big Data: The Case of Human Collective Memory

## Abstract

**:**

## 1. Introduction

## 2. The Biexponential Pattern

## 3. Candia et al.’s Mechanistic Model

## 4. Alternative Mechanistic Models

#### 4.1. Structure of Alternative Process

#### 4.2. Additive Parallel Model

#### 4.3. Multiplicative Series Model

#### 4.4. Exponential Decay with Feedback

## 5. Frequency Interpretation of Process

#### 5.1. Exponential Decay as a Low Pass Filter

#### 5.2. Combining Low Pass Filters

#### 5.3. High Pass Filters Ignore Slowly Changing Inputs

#### 5.4. Feedback and Resonant Frequencies

## 6. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Biexponential decay of a signal in Equation (1). The same parameters are used for the plots on (

**a**) semi-log axes and (

**b**) log-log axes. The parameters for the curves from top to bottom are: $(a,b,c)=(0.35,0.005,0.408),(0.85,0.005,0.134),(0.85,0.05,0.143),(0.78,0.05,0.043)$. The parameters match Figure 2 of Candia et al. [9], associated with their parameterization given in Equation (2) and the parameter equivalences: $a=p+r$; $b=q$; $c=r/(p-q)$; and $N=1$. The inverse parameter equivalences are also useful: $p=(a+bc)/(1+c)$; $q=b$; and $r=c(a-b)/(1+c)$.

**Figure 2.**Alternative models that yield identical biexponential decay. The text describes each panel. The parameters can be matched to the generic model in Equation (1). with $r=c(a-b)/(1+c)$.

**Figure 3.**Frequency response of alternative models that yield identical biexponential decay. Each curve shows the relation between the frequency of input and the gain, which is the amount by which a process multiplies an input signal. The parameters match the red curve of Figure 1. The blue curve is the response of the total system, G, which is the same in all cases. The gain expresses the classic signal processing scale of $20{log}_{10}(\mathrm{gain})$. A value of zero corresponds to gain of one, which means that the process passes the signal without change. Values of less than zero reduce the signal intensity, and values above zero enhance the signal intensity. (

**a**) The combination of two low pass filters in Candia et al.’s model of Figure 2b. A similar pattern describes the additive parallel model in Figure 2c. (

**b**) The combination of high and low pass pass filters in series in Figure 2d. (

**c**) A low pass filter in green combined in a self-correcting feedback loop with a filter that enhances intermediate resonant frequencies in gold.

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Frank, S.A.
How to Understand Behavioral Patterns in Big Data: The Case of Human Collective Memory. *Behav. Sci.* **2019**, *9*, 40.
https://doi.org/10.3390/bs9040040

**AMA Style**

Frank SA.
How to Understand Behavioral Patterns in Big Data: The Case of Human Collective Memory. *Behavioral Sciences*. 2019; 9(4):40.
https://doi.org/10.3390/bs9040040

**Chicago/Turabian Style**

Frank, Steven A.
2019. "How to Understand Behavioral Patterns in Big Data: The Case of Human Collective Memory" *Behavioral Sciences* 9, no. 4: 40.
https://doi.org/10.3390/bs9040040