• Introduction
• Methodology
  • Data preprocessing
  • Actogram and serie of bees activity
  • Analysis of p-values series
• Clasification
  • Functional splines curves of p-values
  • Clustering of p-value curves of bees
• Conclutions

The circadian clock of honey bees is important in complex physiological processes, such as spatiotemporal learning, time perception and sun-compass navigation. The study of honey bee circadian rhythms is of particular interest because similar to human.

The effect of temperature in the development of circadian rhythms in honey bee workers has yet to be explored. It is though that temperature at the center of the colony is important for the development of circadian rhythms in young honey bee workers.

Data preprocessing

The data used in this paper comes from two experimental groups, each of them with four monitors.

Let \(X_t=(x_1, x_2, \dots, x_n)\) be the activity series of a bee. We define

\[ t_{stable}=\max_{1 \leqslant t \leqslant n}\{t \mid p_{t-1} > p_t \hspace{0.2cm} and \hspace{0.2cm} p_{t}<0.05 \} \]

\[ y_i = x(t_i) + \epsilon_i \] \[ \chi(t) =\sum^K_{j=1} c_j\phi_{j}(t) = \Phi(t)c \] We say \(\Phi(t)\) is a basis system for \(\chi\)

\[ y_i = \beta_0 + \beta_1t_i + \beta_1t_1 + \beta_3t_3 + · · · + \]

#sdfsdf
library(ggplot2)
t=ggplot(data = data.frame(x=1,y=1), aes(x=NULL))+ theme(text=element_text(size = 24))

p1 = ggplot(mtcars, aes(x=wt, y=mpg))+geom_point(col="black")+
      labs(title = "Plot de Normalidad", x = "Teóricos", y = "Observados")
p2 = ggplot(mtcars, aes(x=wt, y=mpg))+geom_point(col="black")+
      labs(title = "Plot de Normalidad", x = "Teóricos", y = "Observados")+
      theme(text=element_text(size = 20))

library(gridExtra)
grid.arrange(p1, p2, ncol=2,top="Main Title")

##        id        num_awards           prog          math      
##  1      :  1   Min.   :0.00   General   : 45   Min.   :33.00  
##  2      :  1   1st Qu.:0.00   Academic  :105   1st Qu.:45.00  
##  3      :  1   Median :0.00   Vocational: 50   Median :52.00  
##  4      :  1   Mean   :0.63                    Mean   :52.65  
##  5      :  1   3rd Qu.:1.00                    3rd Qu.:59.00  
##  6      :  1   Max.   :6.00                    Max.   :75.00  
##  (Other):194

## 
## Call:
## lm(formula = p$math ~ p$prog)
## 
## Coefficients:
##      (Intercept)    p$progAcademic  p$progVocational  
##           50.022             6.711            -3.602

library("ggplot2")
library("gridExtra")
set.seed(1234)
dat <- data.frame(cond = factor(rep(c("A","B"), each=200)), rating = c(rnorm(200),rnorm(200, mean=.8)))

p <- ggplot(dat, aes(x=cond, y=rating)) + geom_boxplot()
p

• The Analysis of the circadian cycle of bees is a complex problem.
• Measurements of the data should not be very close because the time series may lose its tendency
• It was observed that the curves modeled by cubic splines help to determine the time and speed with which the bees using velocities in stable times.
• The use of periodograms is beneficial; however, it has its constrains.