# Enhancing Recognition Memory in Virtual Memory Palaces Using Worlds-in-Miniature
## 4 Materials and Methods
### Measures  
This section describes the types and methods of data collection used for evaluation. The data are categorized into objective data and subjective data.  
Objective data include participants' memory performance evaluation data, consisting of short-term and long-term memory assessments collected after completing experiences with and without WIM. These data evaluate whether participants have correctly identified images included in the virtual memory palace, using a total of 60 images. The results are recorded as percentages, and this evaluation serves as a means to determine whether including WIM in the virtual memory palace improved memory performance or not. The data are stored after converting each participant's evaluation score into a percentile. The stored data are then analyzed using a forgetting curve model graph based on both short-term and long-term memory assessments.  
A graph was created using a method similar to the forgetting curve introduced by [PERSON] [31]. The forgetting curve provides a model for the exponential decay of memory retention over time. This model can be expressed as follows:  
\[R(t)=R_{0}\cdot e^{-kt} \tag{1}\]  
where \(R(t)\) is the memory retention at time \(t\), \(R_{0}\) is the initial retention, and \(k\) is the forgetting rate constant. To understand the relationship between short-term and long-term memory, we define the average forgetting rate \(s\) over a specific time interval \([0,t]\) as follows:  
\[s=\frac{M_{\text{short}}-M_{\text{long}}}{t} \tag{2}\]  
where \(M_{\text{short}}\) and \(M_{\text{long}}\) represent the measured retention rates at short-term and long-term intervals, respectively. To connect the average forgetting rate \(s\) with the forgetting curve model, we rewrite the retention difference, as follows:  
\[M_{\text{short}}-M_{\text{long}}=R_{0}-R_{0}\cdot e^{-kt}=R_{0}(1-e^{-kt}) \tag{3}\]  
Figure 5: Procedures of our experiment in the new virtual memory palace with Worlds-in-Miniature. (The faces of the characters have been blurred to prevent infringement of portrait rights).  
Substituting this into the definition of \(s\), we obtain the following:  
\[s=\frac{M_{\text{short}}-M_{\text{long}}}{t}=\frac{R_{0}(1-e^{-kt})}{t} \tag{4}\]  
This equation shows that \(s\) is influenced by both the forgetting rate constant \(k\) and the time interval \(t\). The parameter \(s\) represents the average forgetting rate over the interval \([0,t]\), while \(k\) characterizes the instantaneous forgetting rate in the Ebbinghaus forgetting curve. As \(t\to 0\), \(s\) approaches \(k\), making \(s\) a useful approximation of \(k\) over short intervals. This relationship provides a quantitative basis for comparing short-term and long-term memory retention within our experimental framework.  
By calculating \(s\) in relation to time (days) with short-term and long-term memory data, the curve can be generated. The relatively gentle slope of the curve suggests that the memory evaluation method used in this experiment employed a lenient image identification approach, resulting in slower rates of forgetting.  
Subjective data were collected through surveys and interviews. The surveys included the NASA-Task Load Index (NASA-TLX) 1998 (year) [32] and the Virtual Reality Sickness Questionnaire (VRSQ) [33], for experiments both with and without WIM. The Post-Study System Usability Questionnaire (PSSUQ) 3 (version) was additionally administered, but only for experiments with WIM [34].