Introduction
In this post, we will analyze data extracted from a mobile application that offers users access to a wide range of recipes. Our objective is to extract valuable insights from this data to benefit the product team.
Can we identify a statistically significant disparity in the number of recipe views per session among PRO users across different primary platforms?
Data Cleansing and Preparation
- Our analysis will focus exclusively on customers classified as 'Pro.'
- Excluding Huawei as a platform due to its minimal traffic and non-significant status as a 'main platform.'
- Applying a filter to only consider the 'recipe.detail' event, assuming it signifies user interaction with the product.
- Eliminating any recipes lacking a valid recipe_id.
# Import necessary libraries
library(tidyverse) # For data manipulation and visualization
library(arrow) # For reading in Parquet data
library(lubridate) # For working with dates
# Filter out recipes without a recipe_id and consider only "pro" customers, excluding Huawei
filtered_recipes <- recipes %>%
filter(!is.na(recipe_id),
subscriptionstatus == 'pro',
platform != 'huawei',
name == "recipes.detail")
Exploratory Data Analysis
# Import necessary libraries
library(patchwork) # For joining multiple plots together
# Calculate and visualize views per session by platform and date
plot1 <- recipes %>%
group_by(date, platform) %>%
summarise(views_per_session = n() / n_distinct(sessionid)) %>%
ggplot(aes(date, views_per_session)) +
geom_line(aes(color = platform), size = 1.5) +
geom_text(aes(label = round(views_per_session, 2)), vjust = -1) +
scale_color_manual(values = c("#0072B2", "#009E73")) +
labs(title = "Views per Session by Platform and Date",
x = "",
y = "") +
theme_minimal() +
theme(plot.title = element_text(size = 20, face = "bold", hjust = 0.5),
axis.text = element_text(size = 14),
axis.title = element_text(size = 16),
panel.grid.major = element_blank(),
panel.grid.minor = element_blank())
# Calculate and visualize views per session by platform
plot2 <- recipes %>%
group_by(platform) %>%
summarise(views_per_session = round(n() / n_distinct(sessionid), 2)) %>%
ggplot(aes(platform, views_per_session)) +
geom_bar(aes(fill = platform), stat = "identity", width = 0.5) +
geom_text(aes(label = views_per_session), vjust = 1, size = 6) +
scale_fill_manual(values = c("#0072B2", "#009E73")) +
labs(title = "Views per Session by Platform",
x = "",
y = "") +
theme_minimal() +
theme(plot.title = element_text(size = 20, face = "bold", hjust = 0.5),
axis.text = element_text(size = 14),
axis.title = element_text(size = 16),
panel.grid.major = element_blank(),
panel.grid.minor = element_blank())
# Calculate and visualize views per session by platform and overall goal
plot3 <- recipes %>%
group_by(platform, overallgoal) %>%
summarise(views_per_session = round(n() / n_distinct(sessionid), 2)) %>%
filter(!is.na(overallgoal)) %>%
ggplot(aes(x = overallgoal, y = views_per_session, fill = platform)) +
geom_bar(stat = "identity", position = "dodge", width = 0.7) +
geom_text(aes(label = views_per_session, group = platform),
position = position_dodge(width = 0.7), vjust = 1, size = 4) +
theme_bw() +
theme(axis.text.x = element_text(angle = 45, hjust = 1, size = 12),
axis.text.y = element_text(size = 12),
axis.title = element_text(size = 14, face = "bold"),
strip.text = element_text(size = 14, face = "bold"),
strip.background = element_rect(fill = "lightgray", colour = "black", size = 1),
legend.position = "right") +
scale_fill_manual(values = c("#0072B2", "#009E73")) +
labs(title = "Views per Session by Platform and Overall Goal",
x = "",
y = "")
# Combine the plots
combined_plots <- (plot1 + plot2) / plot3
- There is a marginal variance observed between iOS and Android platforms when computing views per session.
- Sunday exhibits the highest user engagement, which gradually declines throughout the week, reaching its lowest point on Saturday.
- Both platforms demonstrate a strong preference for weight loss as the primary goal.
- However, given that this data encompasses only one week, it may not accurately reflect overall customer engagement.
Establishing Statistical Significance
To establish statistical significance between the two platforms, a sufficiently large sample is required. Consequently, we will assess the number of views per session at both the platform and user_id levels.
# Calculating average views per session on a user level for each platform
views_per_platform_session <- recipes %>%
group_by(platform, userid) %>%
summarise(views_per_session = n() / n_distinct(sessionid)) %>%
ungroup()
# Visualizing the distribution of our data
views_per_platform_session %>%
ggplot(aes(x = views, fill = platform)) +
geom_density(trim = FALSE) +
scale_fill_manual(values = c("#1a78ae", "#9c47a5")) +
labs(x = "Group", y = "Value", fill = "Group") +
facet_wrap(~platform) +
theme_bw() +
theme(
axis.line = element_line(size = 1),
axis.title = element_text(face = "bold"),
axis.text = element_text(size = 12, color = "black"),
legend.position = "bottom",
legend.title = element_blank(),
legend.text = element_text(size = 12),
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
panel.background = element_blank()
)
# Load necessary package
library(homogeneity)
# Perform homogeneity of variance test
homogeneity_test <- homogeneity_test(views ~ platform, data = views_per_platform_session)
- The distribution of our data deviates from a normal distribution.
- The Levene's test provides substantial evidence indicating unequal variances between the two groups.
- Given the non-normal distribution and disparate variances, a t-test cannot be employed.
- An alternative approach for our analysis is the Mann-Whitney U test, which is adept at accommodating outliers, as in our scenario, and offers straightforward interpretation.
- The Mann-Whitney U test requires fewer assumptions compared to parametric tests like the t-test, which mandate normal distribution and equal variances.
Conducting the Statistical Test
# Subset the data for the two platforms
android_data <- views_per_platform_session %>%
filter(platform == "android") %>%
select(views) %>%
extract()
ios_data <- views_per_platform_session %>%
filter(platform == "ios") %>%
select(views) %>%
extract()
# Perform the U test
u_test <- my_mann_whitney_test(android_data, ios_data)
# Print the test results
print(u_test)
# Perform a statistical test using the provided data
test_results <- perform_rank_sum_test(android_data, ios_data)
# Print the test results
print(test_results)
The test outcome reveals a p-value of 3.003e-15, indicating a statistically significant difference between the two groups. The alternative hypothesis suggests that the true location shift (median difference) is not zero. Thus, we can infer that a significant disparity exists between the Android and iOS data groups regarding the number of views per session.
Additionally, we can employ the Hodges-Lehmann estimator to quantify the magnitude of the difference. This estimator, a non-parametric technique, enables us to compute the median difference between the two groups.
# Calculate an effect size using the provided data
effect_size <- calculate_effect_size(android_data, ios_data)
# Print the effect size
print(effect_size)
##
## Cohen's d
##
## d estimate: -0.006311648 (negligible)
## 95 percent confidence interval:
## lower upper
## -0.02708118 0.01445788
Key Insights
- Our analysis reveals a statistically significant distinction in user engagement between iOS and Android users.
- However, the observed difference is minimal, potentially lacking practical significance or impact.
- The product team may choose to prioritize other factors that exert a more substantial influence on user engagement or conduct further investigations to understand the underlying reasons behind the marginal disparity between the two platforms.
Determining Recipe “Success“
- To gauge the popularity or success of a recipe, we will compute the geometric mean of both views per session and views per user.
- This approach assigns equal importance to both metrics while accommodating variations in their scales and highlighting recipes that demonstrate well-rounded performance across both measures.
- As a reference, the overall average popularity index stands at 1.22.
Data Preparation and Transformation
#loading our recipe usage data and creating week columns
recipe_usage <- read_parquet("data.parquet") %>%
mutate(wkday = wday(date,label= TRUE),
weekday_or_weekend = if_else(wkday %in% c("Mon","Tue","Wed","Thu","Fri"),"weekday","weekend"))
# Calculating usage metrics on recipe and weekday_weekend group level
df1 <- recipe_usage %>%
group_by(recipe_id,weekday_or_weekend) %>%
summarise(hits = sum(as.numeric(no_hits),na.rm = T),
sessions = sum(as.numeric(no_sessions),na.rm = T),
users = sum(as.numeric(no_users),na.rm = T),
views_per_session = hits/sessions,
views_per_user = hits/users) %>%
ungroup() %>%
mutate(popularity_index = sqrt(views_per_session*views_per_user)) %>% # Average of views_per_session and views_per_user will be our popularity index
mutate_if(is.numeric, ~round(.,2))
# Aggregating hits,sessions, and users on recipe level
df2 <- recipe_usage %>%
group_by(recipe_id) %>%
summarise(hits = sum(as.numeric(no_hits),na.rm = T),
sessions = sum(as.numeric(no_sessions),na.rm = T),
users = sum(as.numeric(no_users),na.rm = T))
# joining the two datasets together to get a final view
combined <- df1 %>%
select(recipe_id,weekday_or_weekend,popularity_index) %>%
pivot_wider(names_from = weekday_or_weekend,values_from = popularity_index) %>%
left_join(df2) %>%
rename(weekday_popularity_index = weekday,
weekend_popularity_index = weekend)
Weekends vs Weekdays
We will consolidate our data to examine the proportion of recipes that exhibit higher popularity on weekends compared to weekdays, as well as vice versa.
# Calculate the count of recipes popular on weekdays and weekends
popular_recipes <- combined %>%
summarise(recipes_popular_weekday = n_distinct(recipe_id[weekday_popularity_index > weekend_popularity_index]),
recipes_popular_weekend = n_distinct(recipe_id[weekend_popularity_index > weekday_popularity_index])) %>%
mutate_if(is.numeric, ~ round(., 2)) %>%
pivot_longer(cols = everything(), names_to = "category", values_to = "count")
# Create a bar chart
ggplot(popular_recipes, aes(x = category, y = count, fill = category)) +
geom_bar(stat = "identity") +
geom_text(aes(label = count), vjust = 1) +
theme_minimal() +
theme(axis.text.x = element_text(hjust = 1),
legend.position = "none") +
labs(title = "Count of Popular Recipes on Weekdays or Weekends",
x = "",
y = "") +
scale_fill_manual(values = c("steelblue", "lightblue", "darkred", "pink"))
It is intriguing to note that over 50% of recipes garner greater popularity on weekdays than on weekends, yet the popularity index remains nearly identical for both recipe categories. Now, let's delve into the data on a daily basis to gain further insights.
Daily Fluctuations in Popularity Index
# Calculate popularity index by date
popularity_index <- recipe_usage %>%
group_by(date, wkday) %>%
summarise(hits = sum(as.numeric(no_hits), na.rm = TRUE),
sessions = sum(as.numeric(no_sessions), na.rm = TRUE),
users = sum(as.numeric(no_users), na.rm = TRUE),
views_per_session = hits / sessions,
views_per_user = hits / users) %>%
ungroup() %>%
mutate(popularity_index = sqrt(views_per_session * views_per_user)) %>%
select(date, wkday, popularity_index)
# Create a line plot
ggplot(popularity_index, aes(date, popularity_index)) +
geom_line(color = "steelblue", size = 1) +
geom_text(aes(label = wkday), vjust = -0.5, size = 5) +
theme_minimal() +
labs(title = "Popularity Index by Date",
x = "",
y = "") +
theme(plot.title = element_text(hjust = 0.5),
axis.text.x = element_text(angle = 45, hjust = 1),
panel.grid.major = element_blank(),
panel.grid.minor = element_blank())
Key Insights
It is worth noting that we observe a higher number of popular recipes on weekdays (1073 recipes) compared to weekends (865 recipes).
This discrepancy can be attributed to a seasonal pattern within the data, where popularity is at its lowest on Sundays (average popularity index of 1.20) but reaches its peak on Mondays (average popularity index of 1.23). As the week progresses, popularity gradually declines until it rises again on Saturdays (average popularity index of 1.23). For the sake of our analysis, let's assume this difference is significant. Potential reasons for this trend include:
Weekend vs. weekday mindset: Users may perceive Sundays as a day for relaxation, indulgence, or spending time with family, resulting in lower engagement with the fitness recipe app. Conversely, Mondays often represent the start of a new week and a renewed focus on healthy routines, leading to increased app usage.
Meal planning: Many individuals plan their meals for the week on Sundays and Mondays. As the week progresses, users may already have their meal plans in place, resulting in less time spent on the app.
Motivation: Users might feel more motivated to pursue a healthy lifestyle at the beginning of the week. However, as the week progresses, this motivation could wane, leading to decreased engagement with the app.
The product team could consider the following actions:
Sunday: Since Sundays demonstrate the lowest popularity, provide users with meal planning tools and meal prep ideas to help them prepare for the upcoming week. Offer healthy recipes that can be prepared in larger quantities and easily reheated or repurposed for multiple meals throughout the week.
Monday: Capitalize on the peak popularity observed on Mondays by emphasizing fresh starts and motivation. Feature a "Recipe of the Week" that aligns with users' dietary preferences and is easy to prepare.
Tuesday to Friday: Focus on providing quick and easy recipes for lunch and dinner, suitable for users with limited cooking time during the workweek. Include healthy meal options that can be easily packed for lunch or prepared in advance.
Saturday: As popularity increases again on Saturdays, consider offering healthy brunch ideas or dishes suitable for social gatherings.
Additional Factors Affecting Popularity
Categorization by Difficulty
# Calculate popularity index by difficulty
popularity_index <- recipe_usage %>%
group_by(difficulty) %>%
summarise(hits = sum(as.numeric(no_hits), na.rm = TRUE),
sessions = sum(as.numeric(no_sessions), na.rm = TRUE),
users = sum(as.numeric(no_users), na.rm = TRUE),
views_per_session = hits / sessions,
views_per_user = hits / users) %>%
ungroup() %>%
mutate(popularity_index = sqrt(views_per_session * views_per_user)) %>%
mutate_if(is.numeric, ~round(., 2))
# Create a bar plot
ggplot(popularity_index, aes(x = difficulty, y = popularity_index, fill = difficulty)) +
geom_col() +
geom_text(aes(label = popularity_index)) +
scale_fill_brewer(palette = "Set2") +
theme_minimal() +
theme(axis.text = element_text(size = 12),
axis.title = element_text(size = 14, face = "bold"),
title = element_text(size = 16, face = "bold")) +
xlab("") +
ylab("") +
ggtitle("Popularity Index by Difficulty") +
guides(fill = FALSE)
User Preference for Easy (1.22 popularity index) and Normal (1.23 popularity index) Difficulty Recipes suggests that the team should prioritize increasing the availability of such recipes within the app. These recipes could be prominently featured on the main page or recommended to users, in contrast to harder recipes that exhibit a lower popularity index of 1.15.
Relationship between Number of Cooking Steps and Popularity
# Calculate popularity index by steps
d1 <- recipe_usage %>%
group_by(steps) %>%
summarise(hits = sum(as.numeric(no_hits), na.rm = TRUE),
sessions = sum(as.numeric(no_sessions), na.rm = TRUE),
users = sum(as.numeric(no_users), na.rm = TRUE),
views_per_session = hits / sessions,
views_per_user = hits / users) %>%
ungroup() %>%
mutate(popularity_index = sqrt(views_per_session * views_per_user)) %>%
mutate_if(is.numeric, round, 2)
# Create scatter plot with line and area
d1 %>%
ggplot(aes(x = steps, y = popularity_index)) +
geom_point(aes(size = hits), color = "maroon") +
geom_line() +
geom_area(data = d1 %>% filter(steps %in% c(3, 4, 5, 6, 7)), aes(x = steps, y = popularity_index), alpha = 0.3) +
labs(x = "", y = "", title = "Popularity Index by Steps", subtitle = "Size of points by number of hits") +
theme_bw() +
theme(plot.title = element_text(hjust = 0.5, size = 14, face = "bold"),
axis.title.x = element_text(size = 12),
axis.title.y = element_text(size = 12),
axis.text.x = element_text(size = 10),
axis.text.y = element_text(size = 10),
legend.position = "none",
legend.title = element_blank(),
legend.text = element_text(size = 10)) +
coord_cartesian(ylim = c(1, 1.3))
Upon reviewing the popularity index in relation to the number of steps required to cook a recipe, it becomes apparent that recipes with 3-7 steps are more popular, with an average popularity index of 1.23. There could be various reasons why recipes with a lower or higher number of steps have lower popularity. Here are some potential explanations:
- Complexity: Recipes with too few or too many steps might be perceived as overly simple or excessively complex. People may prefer recipes that provide a moderate challenge while still being manageable to follow.
- Time: Recipes with too few or too many steps could also involve insufficient or excessive preparation time, respectively. Individuals may favor recipes that are quick and easy to follow, while still yielding delightful results.
- Variety: Recipes with too few or too many steps might lack diversity in terms of flavors and ingredients. People may prefer recipes that strike a balance in flavors, textures, and incorporate a variety of ingredients to keep things interesting.
Exploring Portion Count
# Calculate popularity index by portion count
modified_recipe_usage <- recipe_usage %>%
group_by(portioncount) %>%
summarise(hits = sum(as.numeric(no_hits), na.rm = TRUE),
sessions = sum(as.numeric(no_sessions), na.rm = TRUE),
users = sum(as.numeric(no_users), na.rm = TRUE),
views_per_session = hits / sessions,
views_per_user = hits / users) %>%
ungroup() %>%
mutate(popularity_index = sqrt(views_per_session * views_per_user)) %>%
mutate_if(is.numeric, round, 2) %>%
top_n(15, hits)
# Create scatter plot with point size scaled by hits
ggplot(modified_recipe_usage, aes(x = portioncount, y = popularity_index)) +
geom_point(aes(size = hits), color = 'darkred') +
geom_line() +
labs(x = "Portion Count", y = "Popularity Index", title = "Popularity Index by Portion Count", subtitle = "Point size scales with hits") +
theme_bw() +
theme(plot.title = element_text(hjust = 0.5, size = 14, face = "bold"),
axis.title.x = element_text(size = 12),
axis.title.y = element_text(size = 12),
axis.text.x = element_text(size = 10),
axis.text.y = element_text(size = 10),
legend.position = "none",
legend.title = element_blank(),
legend.text = element_text(size = 10)) +
scale_x_continuous(breaks = seq(1, 30, 1))
Recipes within the 1-4 portion count range demonstrate the highest popularity, with an average popularity index of 1.23. Several factors may contribute to this phenomenon:
- Smaller households: Since many households consist of fewer individuals, recipes with smaller portion sizes tend to be more appealing.
- Individual preferences: Users may prefer cooking smaller portions to accommodate their personal tastes or dietary requirements.
- Meal preparation and planning: Smaller portion sizes can be convenient for users who engage in meal prep and planning, allowing them to prepare meals for one or a few days without experiencing food waste or compromising freshness.
- Ease of scaling: Recipes with smaller portions are often easier to scale up or down, enabling users to adapt them to their specific needs.
Are Longer Recipes with Lengthy Cooking Times Less Popular?
# Filter and process recipe usage data
modified_recipe_usage <- recipe_usage %>%
filter(preparationtime < 200) %>%
group_by(preparationtime) %>%
summarise(hits = sum(as.numeric(no_hits), na.rm = TRUE),
sessions = sum(as.numeric(no_sessions), na.rm = TRUE),
users = sum(as.numeric(no_users), na.rm = TRUE),
views_per_session = hits / sessions,
views_per_user = hits / users) %>%
ungroup() %>%
mutate(popularity_index = sqrt(views_per_session * views_per_user)) %>%
mutate_if(is.numeric, round, 2) %>%
top_n(10, popularity_index)
# Create scatter plot with point size scaled by hits
ggplot(modified_recipe_usage, aes(x = preparationtime, y = popularity_index)) +
geom_point(aes(size = hits), color = 'darkred') +
geom_line() +
labs(x = "Minutes", y = "Popularity Index", title = "Popularity Index by Preparation Time (Minutes)", subtitle = "Point size scales with hits") +
theme_bw() +
theme(plot.title = element_text(hjust = 0.5, size = 14, face = "bold"),
axis.title.x = element_text(size = 12),
axis.title.y = element_text(size = 12),
axis.text.x = element_text(size = 10),
axis.text.y = element_text(size = 10),
legend.position = "none",
legend.title = element_blank(),
legend.text = element_text(size = 10)) +
ylim(c(1.16, 1.5)) +
scale_x_continuous(breaks = seq(5, 200, 10))
Recipes with a cooking time of 25 minutes or less or less than 50 minutes exhibit higher popularity (1.25 popularity index) based on both their popularity index and the number of hits they receive. To enhance visual clarity and eliminate unnecessary noise, we have excluded outliers with cooking times exceeding 200 minutes.
Exploring the Impact of Recipe Tags on Recipe Success by Unnesting
# Process and visualize top 15 tags by popularity index
top20_rec <- recipe_usage %>%
separate_rows(tags, sep = ",") %>%
group_by(tags) %>%
summarise(hits = sum(as.numeric(no_hits), na.rm = TRUE),
sessions = sum(as.numeric(no_sessions), na.rm = TRUE),
users = sum(as.numeric(no_users), na.rm = TRUE),
views_per_session = hits / sessions,
views_per_user = hits / users) %>%
ungroup() %>%
mutate(popularity_index = sqrt(views_per_session * views_per_user)) %>%
mutate_if(is.numeric, round, 2) %>%
top_n(15, popularity_index) %>%
ggplot(aes(x = reorder(tags, popularity_index), y = popularity_index)) +
geom_bar(stat = "identity", fill = "#b20238") +
geom_text(aes(label = popularity_index), hjust = 5, size = 3.5, color = "white") +
coord_flip() +
labs(x = "", y = "", title = "Popularity Index of Top 15 Tags") +
theme_bw() +
theme(plot.title = element_text(hjust = 0.5, size = 14, face = "bold"),
axis.title.x = element_text(size = 12),
axis.title.y = element_text(size = 12),
axis.text.x = element_text(size = 10),
axis.text.y = element_text(size = 10),
legend.position = "top",
legend.title = element_blank(),
legend.text = element_text(size = 10))
# Process and visualize bottom 15 tags by popularity index
bottom20_rec <- recipe_usage %>%
separate_rows(tags, sep = ",") %>%
group_by(tags) %>%
summarise(hits = sum(as.numeric(no_hits), na.rm = TRUE),
sessions = sum(as.numeric(no_sessions), na.rm = TRUE),
users = sum(as.numeric(no_users), na.rm = TRUE),
views_per_session = hits / sessions,
views_per_user = hits / users) %>%
ungroup() %>%
mutate(popularity_index = sqrt(views_per_session * views_per_user)) %>%
mutate_if(is.numeric, round, 2) %>%
top_n(-15, popularity_index) %>%
ggplot(aes(x = reorder(tags, popularity_index), y = popularity_index)) +
geom_bar(stat = "identity", fill = "#0d1137") +
geom_text(aes(label = popularity_index), hjust = 5, size = 3.5, color = "white") +
coord_flip() +
labs(x = "", y = "", title = "Popularity Index of Bottom 15 Tags") +
theme_bw() +
theme(plot.title = element_text(hjust = 0.5, size = 14, face = "bold"),
axis.title.x = element_text(size = 12),
axis.title.y = element_text(size = 12),
axis.text.x = element_text(size = 10),
axis.text.y = element_text(size = 10),
legend.position = "top",
legend.title = element_blank(),
legend.text = element_text(size = 10))
# Combine the top and bottom plots
top20_rec + bottom20_rec
Drawing Insights from the Order of Tags, from Most to Least Popular:
- Casseroles, meat, and soup emerge as the top three tags, indicating that users prefer substantial and satisfying meals.
- The tag 'lunch' signifies users' interest in quick and convenient recipes suitable for midday meals.
- Popular tags such as 'high protein,' 'low fat,' and 'low calorie' suggest that users prioritize health-conscious choices and seek recipes that align with their dietary needs.
- The presence of multiple calorie tags (e.g., 500kcal, 400kcal, 300kcal) indicates users' preference for lower-calorie recipes that can assist in maintaining a healthy weight. However, extremely low-calorie options (e.g., 50kcal, 100kcal) might be less appealing, as they may not provide sufficient satiety, while excessively high-calorie recipes (e.g., 700kcal) may also be less favored.
- Tags such as 'clean eating' and 'detox' demonstrate popularity, indicating users' interest in incorporating healthier food choices into their diets.
- Tags related to baking and desserts appear towards the end of the list, suggesting that users prioritize nutritious meals over indulgent treats.
- Interestingly, 'breakfast' tags are less popular compared to 'dinner' and 'lunch,' possibly due to time constraints in the early morning.
Exploring Recipe Descriptions for Further Analysis
# Load necessary libraries
library(tidytext)
library(stopwords)
# Remove punctuations and numbers from description
recipe_usage <- recipe_usage %>%
mutate(description = str_replace_all(description, "[^[:alpha:][:space:]]", ""),
description = str_replace_all(description, "\\d+", ""))
# Create a tidy text data frame
tidy_description <- recipe_usage %>%
select(recipe_id, description, no_hits, no_sessions, no_users) %>%
unnest_tokens(word, description) %>%
anti_join(stop_words) %>%
filter(!is.na(word))
# View the top 15 most popular words
tidy_description %>%
group_by(word) %>%
summarise(hits = sum(as.numeric(no_hits), na.rm = TRUE),
sessions = sum(as.numeric(no_sessions), na.rm = TRUE),
users = sum(as.numeric(no_users), na.rm = TRUE),
views_per_session = hits / sessions,
views_per_user = hits / users) %>%
ungroup() %>%
top_n(15, hits) %>%
mutate(popularity_index = (views_per_session + views_per_user) / 2) %>%
mutate_if(is.numeric, round, 2) %>%
ggplot(aes(x = reorder(word, popularity_index), y = popularity_index)) +
geom_bar(stat = "identity", fill = "#e75874") +
geom_text(aes(label = popularity_index), hjust = 5, size = 5, color = "white", bold = TRUE) +
coord_flip() +
labs(x = "", y = "", title = "Popularity Index of Recipe Description Words", subtitle = "Top 15 most popular (hits) words from recipe descriptions") +
theme_bw() +
theme(plot.title = element_text(hjust = 0.5, size = 14, face = "bold"),
axis.title.x = element_text(size = 12),
axis.title.y = element_text(size = 12),
axis.text.x = element_text(size = 10),
axis.text.y = element_text(size = 10),
legend.position = "top",
legend.title = element_blank(),
legend.text = element_text(size = 10))
- Meal and dish are commonly used words that imply users are looking for a full, satisfying meal, rather than just a snack or side dish.
- Prepare and ingredients suggest that users are interested in learning how to cook and create new dishes from scratch.
- Delicious implies that taste is an important factor in recipe selection, which is not surprising since the ultimate goal of cooking is to create tasty meals.
- Time and easy suggest that users are looking for recipes that are not too time-consuming or complicated to prepare.
- Day implies that users may be interested in recipes that are suitable for a particular time of day, such as breakfast, lunch, or dinner.
- Salad and protein suggest that users may be interested in healthy recipes that incorporate fresh ingredients and provide balanced nutrition.
- Perfect and fresh imply that users are looking for recipes that are high-quality and satisfying.
- Tip suggests that users may be interested in learning cooking techniques and tricks to improve their skills.
Conclusion
This analysis provides insights into the dynamics of a real-world product analytics project, emphasizing the generation of actionable insights from the data. Rather than a generic exploratory data analysis, the focus here is on driving specific actions from stakeholders based on our analysis.
Recommendations for Each Day of the Week:
Sunday: As Sundays exhibit lower popularity, consider providing users with meal planning tools and meal prep ideas to help them prepare for the upcoming week. Offer healthy recipes that can be prepared in bulk, facilitating reheating or repurposing for multiple meals throughout the week.
Monday: Capitalize on the peak popularity on Mondays by emphasizing fresh starts and motivation. Feature a "Recipe of the Week" that aligns with users' dietary preferences and is easy to prepare.
Tuesday to Friday: Cater to users with limited cooking time during the workweek by focusing on quick and easy recipes for lunch and dinner. Include healthy meal options that are convenient for packing lunch or preparing in advance.
Saturday: Responding to the increased popularity on Saturdays, consider offering healthy brunch ideas or dishes suitable for social gatherings.


{% extends 'program_base.html' %} {% load commonmark %} {% load static %} {% block extra_head %} {% endblock %} {% block title %} Schedule | {{ block.super }} {% endblock %} {% block program_content %} No javascript? Don't worry, we have a HTML only version of the schedule! Redirecting you there now. Click here if you are not redirected.
No javascript? Don't worry, we have a HTML only version of the schedule! Redirecting you there now.
Click here if you are not redirected.


Seroquel is prescribed for schizophrenia and other similar personality disorders. I myself am prescribed Seroquel and Effexor for Major Depression and Borderline Personality Disorder.....I'm also diagnosed with Antisocial Personality Disorder, but thats besides the point. Anyways, the maximum daily dosage is 800mg, but the usual dosage is between 100mg and 600mg. I, myself, take 300mg nightly right before bed. Seroquel is in the antipsychotic class of drugs and it is HIGHLY sedative. I have been taking it well over a year now and it still knocks me out.
Seroquel does NOT make me high or even give me a slight euphoria. BUT, if I want to sleep, Seroquel is just what the doctor ordered.  DON'T take Seroquel and drive, or mix with alcohol or any other sedative drugs, unless you have a death wish. I have high tolerance for drugs, legal and illegal, but I do not underestimate Seroquel.
Experience Reports are the writings and opinions of the individual authors who submit them.
Some of the activities described are dangerous and/or illegal and none are recommended by Erowid.


Next update will have bug fixes, some pretty items n' stuff...and hair!!
edit: please ignore the hugeness of the guy's shield. Its from an earlier shot.
Moderator: Joe M.
marzuku wrote:JeeZes what an upgrade:)
BTW STAFFS ETC dont Le SorcererS need that ?
Karl G. wrote:marzuku wrote:JeeZes what an upgrade:)
BTW STAFFS ETC dont Le SorcererS need that ?
Yes, they do! In fact, I'm planning on adding them soon--the problem is that the attacks work completely differently for staves, and I only recently figured out how to make that work. Fortunately, this will mean that I can add other 2H weapons, bows, and attack styles fairly easily!
thadiusofx3 wrote:I'll make some cool staves and 2h weapons if need be
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Inquire.
A paper-themed responsive survey form template using CSS Grid and Flexbox, by
Pius Wong
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Hello! Help us learn more about you.
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attendance policy, rehearsals, personnel
I feel strongly that all your orchestra's members should be expected to attend every rehearsal for a concert they will perform in. Sporadic attendance and a lackadaisical attitude toward attendance among your players damages both the musical product and the social cohesion of the group. Amateur players, especially, need consistency during rehearsals. It's easy for them to get confused when they aren't sitting next to the person they usually sit with, an important solo or the cues they rely on aren't being played, or the overall sound balance is off. Furthermore, your orchestra is meant to be fun, so people should feel like they're among a group of friends, not a group of strangers who pop in and out whenever they please. Your musicians should view rehearsals as a serious commitment.
 They will inevitably have to miss rehearsal once in a while. 95% of your musicians will be fine most of the time. They will be committed and responsible about rehearsals and communicate expected absences to the personnel manager and their section leader. The other 5% are the flaky ones who unexpectedly miss rehearsal without warning, who can't follow through on their commitment to the group, or who simply disappear (yes, this actually happens). It is for these people that you should have an attendance policy. The policy won't necessarily encourage them to be more responsible, but it will give your personnel manager some guidelines to follow and will make any decisions seem less arbitrary if the player has to be asked to sit out a concert or to leave the group.
After a good bit of debate on the subject, the RCO decided on the following for our attendance policy: "Musicians are expected to attend all rehearsals. If a musician misses more than two for a given concert cycle, this warrants a discussion with the Personnel Manager and/or Music Director, and they can ask the musician to sit out the concert if they decide it's warranted." Since we generally have about eight rehearsals for each concert, missing two means missing 25%. We left the policy very flexible, however, to allow each case to be considered individually after a thoughtful discussion with the musician to understand their situation. We will have to see how this policy pans out in the future.
Don't wait too long to decide and implement your attendance policy. During your first year, you will likely have to be pretty forgiving, since your players will only be just beginning to work your orchestra into their regular schedules. However, if lax attendance takes hold at the beginning, it could be much more difficult to tighten it up later.
Note: You will most likely need the occasional "special" player, like harp or saxophone or contrabassoon, that isn't part of your regular contingent. Your regular attendance policy may or may not apply to these special players; either way, this subject deserves your considered attention as well.


# File vendor/plugins/rails_sql_views/lib/rails_sql_views/connection_adapters/abstract/schema_statements.rb, line 9 def create_view(name, select_query, options={}) if supports_views? view_definition = ViewDefinition.new(self, select_query) yield view_definition if options[:force] drop_view(name) rescue nil end create_sql = "CREATE VIEW " create_sql << "#{name} (" create_sql << view_definition.to_sql create_sql << ") AS #{view_definition.select_query}" create_sql << " WITH #{options[:check_option]} CHECK OPTION" if options[:check_option] execute create_sql end end


The First Piano
Reference Links
Bartolomeo Cristofori
Gottfried Silbermann
google.com
Bonus work for video link, order/unordered lists, tables
List of steps to make a sandwitch
- Get Bread, Toast bread (optional)
- use favorite Jelly/butter
- spread on side bread
- Put both bread together and enjoy
List of 5 bands/musicians
- Yanni
- Kennedy
- Edward Elgar.
- George Enescu.
| Class |
Name |
| Mammal |
Tiger |
| Recptiles |
Lizard |
| Birds |
Eagle |


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Blake Austin Griffin is an American professional basketball player for the Los Angeles Clippers of the National Basketball Association.
Find Out MoreBlake Austin Griffin (born March 16, 1989) is an American professional basketball player for the Los Angeles Clippers of the National Basketball Association (NBA). He played college basketball for the Oklahoma Sooners, when he was named the Consensus National Player of the Year as a sophomore. Griffin was selected first overall by the Clippers in the 2009 NBA draft, and has since been a five-time NBA All-Star and a four-time All-NBA selection.
| 2016 - 17 | MPG | FG% | 3P% | FT% | PPG | RPG | APG | BPG |
|---|---|---|---|---|---|---|---|---|
| POSTSEASON | 33 | 49 | 66.7 | 100 | 20.3 | 6 | 2.3 | 0.3 |
| CAREER STATS | 35.2 | 51.8 | 29.9 | 67.3 | 21.5 | 9.4 | 4.1 | 0.6 |


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XXHeadXX
The database used by the search forms is the same data that is used to generate the printed SCA Armorial and SCA Ordinary. It is a flat text file roughly 6 megabytes in size. The file format is documented online.
The database is protected by copyright, but that broad blanket permissions have been granted for verbatim redistribution and personal use. See the copyright notice for details.
You should be able to download the database via HTTP from XXWebDataUrlXX (not compressed). XXTrailerXX XXTrailer2XX XXCloseHtmlXX


Simon Grand, Wolfgang Jonas, [eds], Ranulph Glanville, Warren Weaver, Herbert A. Simon, Charles Owen, Christopher Frayling, Bruce Archer, Alain Findeli, Ken Friedman, John Chris Jones, Simon Grand, Friedrich Nietzsche, Peter Galison, Michael Gibbons, Camille Limoges, Helga Nowotny, Simon Schwartzman, Peter Scott, Martin Trow, Michel Callon, Hans-Jörg Rheinberger, Bruno Latour, John Law, Julian Bleecker, Anthony Dunne
Not the complete work in PDF form, but an enticing summary, especially with work by Anthony Dunne, Herbert Simon, Nietzsche, Bruno Latour in the same volume about design research. Wild.


--- title: "[Understanding Analysis by Stephen Abbott] - [Chapter 3 Basic Topology of R] - [3.2 Open and Closed Sets]" published: true tags: RealAnalysis ---
Definition 3.2.1 (open). A set \(O \subseteq \mathbb{R}\) is open if for all points \(a \in O\) there exists an \(\epsilon\)-neighborhood \(V_\epsilon (a) \subseteq O\)
Example 3.2.2
Theorem 3.2.3
Definition 3.2.4 (limit point). A point \(x\) is a limit point of a set \(A\) if every \(\epsilon\)-neighborhood \(V_\epsilon (x)\) of \(x\) intersects the set \(A\) at some point other than \(x\).
Theorem 3.2.5. A point \(x\) is a limit point of a set \(A\) if and only if \(x = \lim a_n\) for some sequence \((a_n)\) contained in \(A\) satisfying \(a_n \neq x\) for all \(n \in \mathbb{N}\)
Definition 3.2.6. A point \(a \in A\) is an isolated point of \(A\) if it is not a limit point of \(A\)
Definition 3.2.7 (closed) A set \(F \subseteq \mathbb{R}\) is closed if it contains its limit points.
Theorem 3.2.8. A set \(F \subseteq \mathbb{R}\) is closed if and only if every Cauchy sequence contained in \(F\) has a limit that is also an element of \(F\).
Theorem 3.2.10 (Density of \(\mathbb{Q}\) in \(\mathbb{R}\)). For every \(y \in \mathbb{R}\), there exists a sequence of rational numbers that converges to \(y\).
Definition 3.2.11. Given a set \(A \subseteq \mathbb{R}\), let \(L\) be the set of all limit points of \(A\). The closure of \(A\) is defined to be \(\overline{A} = A \cup L\)
Theorem 3.2.12 For any \(A \subseteq \mathbb{R}\), the closure \(\overline{A}\) is a closed set and is the smallest closed set containing \(A\).
Theorem 3.2.13 A set \(O\) is open if and only if \(O^\complement\) is closed. Likewise, a set \(F\) is closed if and only if \(F^\complement\) is open.
Theorem 3.2.14


Will defeat BJP govt in assembly speaker's election: NCP
The Shiv Sena-Nationalist Congress Party-Congress combine will defeat the new Bharatiya Janata Party-led government in Maharashtra during the assembly Speaker's election, the NCP said on Saturday night, indicating that most of its MLAs were intact, hours after senior leader Ajit Pawar joined hands with the BJP and took oath as deputy of Chief Minister Devendra Fadnavis.
In the 288-member Legislative Assembly, the BJP government will have to prove that it has the backing of 145 legislators, NCP chief spokesperson Nawab Malik on Saturday night told reporters that the government has been given time till November 30 to prove its numbers.
"The government has been given time till November 30. We will defeat them in the Speaker's election itself. We are sure the Shiv Sena-Congress-NCP will form the government," Malik said.
He made the remarks after emerging from a meeting of NCP MLAs in Mumbai.
Accounting for the party MLAs, he said five of the total 54 MLAs were not in touch with the party while six others were on their way to Mumbai.
"Remaining (43) MLAs have already reached (Mumbai)... All our MLAs will stay at a hotel in Mumbai," he added.
After the meeting, the NCP MLAs were taken to a hotel in suburban Powai.
Fadnavis and Ajit Pawar were sworn in a hush hush ceremony at Raj Bhavan by Governor Bhagat Singh Koshyari at 8 am after dramatic midnight developments, leading to the lifting of the 12-day President's rule in Maharashtra.
Ajit's political shocker came at a time when the Sena, the Congress and the NCP had almost finalised formation of a coalition government under Sena president Uddhav Thackeray as the chief minister.
Later in the night, the NCP sacked Ajit Pawar as its legislature party head, saying his move was not in line with the party's policies.
Earlier, NCP chief Sharad Pawar said the Congress, the NCP and the Sena, along with independents and smaller parties, have the support of 169 to 170 MLAs, and they were ready to form the government.
Malik said the list of NCP MLAs submitted by Ajit Pawar to the governor before taking oath was actually a letter signed by the party MLAs when they attended a meeting earlier.
Some of the MLAs, who were present with Ajit Pawar during the oath-taking ceremony, later pledged their loyalty to Sharad Pawar.
The number of legislators, if any, backing Ajit remains a mystery.
In the 288-member House, the BJP has 105 MLAs, the Shiv Sena 56, the NCP 54 and the Congress 44.


@BaboonGasser @2ndOldest Haha wtf i was just wondering about what the f a MHP pattern was ahahah
Cryptoon27-Jul-18 09:38 PM
@jorian yeah shitsite for sure thats why I only bought 0,007 btc worth, but had it in my wallet like an hour later or so
shak3nbak327-Jul-18 09:51 PM
KMD noob question: in order to receive monthly rewards do I have to sign in to the wallet once a month, or have a transaction of 10+KMD per month?
CHMEX27-Jul-18 09:53 PM
You have to send the complete balance to your self.
Once you login to agama there is a claim button which will do exactly that
shak3nbak327-Jul-18 09:56 PM
Thanks, but I've already been able to claim twice, but I thought I read somewhere that in order to keep receiving rewards that you have to have at least one transaction per month
siu - Chainmakers27-Jul-18 09:57 PM
At least one per year
CHMEX27-Jul-18 09:57 PM
Yes that is correct in about 41 days you will have to claim it once a month. This change is activated with block 1m(edited)
Rewards
Currently, the rewards mechanism will cap the amount of accrued rewards after 1 year. For example, if the coins sit in the same address for more than a full year, the amount of rewards will stop accruing at 5% total. This mechasism is being changed to cap the amount of accrued rewards after 1 month. This means in order to receive the maximum amount of rewards, a user must claim them at least once per month. This in turn, changes the amount of rewards to 5.1% per year.
This change is being made to encourage users to be active and use KMD more often.
shak3nbak327-Jul-18 10:01 PM
Thanks for the explanation!
siu - Chainmakers27-Jul-18 10:03 PM
CHMEX27-Jul-18 10:03 PM
Np
Hollowman900027-Jul-18 10:34 PM
@FishyGuts there can be no yin without a yang
1
FishyGuts27-Jul-18 10:35 PM
@Hollowman9000 - the Mark Hanna Pattern, I will always use that now.
Facebook going full MHP
I’d link a photo of the stock chart but you all know im sure. .
Waves had the potential to be what looked like the top decentralized exchange on the market with a strong user base and transaction flow.  Alternative is to you some tricky ways of viral marketing. but for viral oyu need outstanding idea + outstanding execution + maybe even some luck while making some movie/add.
media are not really free media - they live from adds
alternative would be media living from donations - but somehow does not work that way
jl777c28-Jul-18 08:25 AM
living from ads is fine, but when 90% is paid placement it seems a bit wrong
passcombo.com 🏴☠🏴28-Jul-18 08:25 AM
and sponsors also liek to impact messages
I agree it's wrong i nthe sense of false information / wrong education. And in my view marketing should have educational part very important.
here I feel good point to sell my old propaganda - creating decentralized media/forum platform could give a chance to change that also and bring new possibilities and I find it one of most important challanges for internet nation as what we really discussed here is not media nor ads. It's information processing by masses of people. And current information processin is far from reality as we can see, also because tools missing so people can organize better way. Some tools are slowly being built by some teams, hope someone will do it right.
KomodoWorld28-Jul-18 09:05 AM
not sure if it's worse being ignored or get misleading hit pieces like it happened to Waves


Chaity Group is a state of the art facility equipped with most modern equipment’s. It is a vertically integrated manufacturer of fabric and garments with foreign experts at different units. Most of the latest technologies have provided the unit a leading edge in the field of knit manufacturing.
Chaity Group is striving hard to become a perfect modern facility, where quality required will be superlative. Chaity group has set the pace for changing global customer demands for textiles and has focused its attention to select core products. Such a focus has enabled the company to play a dominant role in the global textile arena. With its presence across the textile value chain, the company endeavors to be a one-stop supplier for leading garment brands.


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Active since 2014
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Radiology support is a team effort. It is information technology and radiology working together. teams consisting of Radiolog Support Analysts, PACS Administrators and Health Technology Management working with Radiology Technologists and Radiologists to care for the patient.


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{% extends "base.html" %} {% block title %}About the Athens Docket Project{% endblock %} {% block content %}
More to come...
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The source code used to build this site is open sourced under the Apache 2.0 license, and is available from our github repository.


{{pr.author}} wants to merge {{pr.source | limitTo: 42}}{{pr.source.length > 42 ? '...' : ''}} into {{pr.target}}


{% assign today = page.date | date: '%s' %} {% assign start = page.startDate | date: '%s' %} {% assign secondsSince = today | minus: start %} {% assign hoursSince = secondsSince | divided_by: 60 | divided_by: 60 %} {% assign daysSince = hoursSince | divided_by: 24 | plus: 2 %}


Pick and drag ++ allows dynamic drag with scaling, copy, rotation and flip operations. It actually feels like you have hold of the segments and can do whatever you want with them.


Next: tooling, Previous: documentation index, Up: Top [Index]
(version: development)
Cedille’s type theory is called the Calculus of Dependent Lambda Eliminations (CDLE). It is somewhat rare in being a Curry-style type theory. Coq and Agda are based on Church-style theories. The difference is that in a Curry-style (aka extrinsic) type theory, type annotations are merely hints to the type checker, and the “real” terms (the subjects of metatheoretic analysis, for example) are completely unannotated. Thus, such annotations can be erased during compilation and during formal reasoning; in particular during conversion checking, where the type checker tests whether two terms are definitionally equal. In contrast, with Church-style (aka intrinsic) type theory, the annotations are “really there”, and must be preserved during compilation and conversion.
For an example, consider the polymorphic identity function Λ X : ★ . λ x : X . x. In Church-style type theory, the binder introducting the type variable X and the annotation giving the classifier for x are truly part of the term, and the theory itself does not allow for them to be erased. In contrast, in a Curry-style type theory like CDLE, those annotations are just hints to help the type checker see how to assign the type ∀ X : ★ . X ➔ X to λ x . x. The type theory has a notion of erasure, and conversion compares the erasures of terms rather than the annotated terms.
The starting point for Cedille is a Curry-style version of the Calculus of Constructions (CC). Coq is based on several extensions of CC, notably with a predicative universe hierarchy (Luo’s Extended Calculus of Constructions), and with a primitive system of inductive datatypes (the Calculus of Inductive Constructions of Paulin-Mohring and Werner). Cedille has neither the universe hierarchy nor the inductive types. The universe hierarchy is omitted to avoid additional metatheoretic and implementation complexity, which has not been justified to my (Aaron’s) satisfaction by examples. So it is omitted not for any really fundamental reason (that we know of). Omitting the system of primitive inductive types, however, is one of the chief goals of Cedille, and will be discussed more below.
The language is divided into three layers: terms, types, and kinds. Terms are the programs we intend eventually to execute, or to use as proofs. Types describe programs, and under the Curry-Howard isomorphism which Cedille makes use of, can be seen as formulas to be proved. Kinds are the classifiers for types. So in Cedille we have
term : type : kind
From CC, Cedille inherits the following type constructs:
See unicode shortcuts for how to type these symbols in Cedille mode.
To the above constructs, Cedille adds the following, discussed more below:
In (Curry-style) type theory, an intersection type T ∩ T’ can be assigned to a term t iff both T and T’ separately can be assigned to t. Dependent intersection types, introduced by Kopylov in this paper, extend this idea to allow the type T’ to reference the term t (i.e., the subject of typing) via a bound variable x. Kopylov’s notation for this is x : T ∩ T’. Cedille uses the notation ι x : T . T’ for the same concept.
One very helpful way to think of these types is that they allow the type T’ of t to refer to t itself, but through a weaker view; namely, the type T. So if you are writing some function f, say, the type T’ you give for f can mention f itself – which seems insane (as in insane dependent typing) – but sanity is preserved by the fact that T’ is only allowed to reference f through some other type T.
In Cedille, dependent intersections are used to derive inductive datatypes, using a critical observation of Leivant’s from this paper. Suppose one is trying to prove the natural-number induction principle for a specific number N; that is, for any predicate P on natural numbers, if the base and steps cases hold, then P holds for N. What would the proof look like for this? One would assume predicate P, assume P 0 (base case) and ∀ n : Nat . P n ➔ P (S n) (step case), and prove P N by apply the step case N times to the base case. Leivant’s remarkable observation is that this proof, seen through the lens of the Curry-Howard isomorphism, is
Λ P . λ z . λ s . s (... (s z))
where s is applied N times. This erases exactly to the Church-encoding of N. This means that using the Church-encoding we can view a number N two ways: as an iterator of type ∀ X : ★ . X ➔ (X ➔ X) ➔ X – call this type cNat – and as a proof of its own induction principle, which we can see as some kind of dependent enrichment of the first type:
∀ P : cNat ➔ ★ . P 0 ➔ (∀ n : cNat . P n ➔ P (S n)) ➔ P N
Calling this second type, as a predicate on N, Inductive, the crucial role of dependent intersection types is to allow us to define Nat as
ι N : cNat. Inductive N
This definition seems to allow one to prove universality of predicates on cNats – not Nats! But universality of Nat-predicates turns out to follow from this, in several different ways. See language-overview/induction-for-church-nats.ced for one example.
The type { t ≃ t’ } is a primitive equality type, between untyped terms. The meaning of such a type is that t and t’ are beta-eta equal (where any necessary instantiations of variables bound outside the equation are applied to t and t’). Cedille provides a primitive operation to rewrite with such equalities (namely ρ), and to prove them when the sides of the equation can be seen themselves to be beta-eta equal (without instantiating variables bound outside the equation); this is β.
In more detail: whenever t and t’ are beta-eta equal, the type-assignment system of CDLE considers any term to inhabit type { t ≃ t’ }. In Cedille, β is an annotated term inhabiting that type; β itself erases to λ x . x. If one wishes to pick a different unannotated term t1 to inhabit an obviously true equation like this, then one writes β{t1}. We call this the Kleene trick, after Stephen Cole Kleene’s similar approach to realizing true equations by any number whatsoever. Here, any term proves an obviously true equation. This has the intriguing side effect of giving Cedille a type for all terms, even ones otherwise untypable. Thus Cedille is Turing-complete: any closed term can be assigned type { λ x . x ≃ λ x . x }. In principle type checking becomes undecidable at this point, because checking whether two terms of pure untyped lambda calculus are beta-eta equal is undecidable. In practice, however, we think of the type checker as having some bound on the number of steps of beta-eta-normalization it will perform on the sides before testing for alpha-equivalence. This bound is currently up to the user to enforce by terminating the tool if it is taking too long.
Rewriting is performed by a construct ρ t - t’. Here, t should prove an equation { t1 ≃ t2 }. Then the type synthesized from or used to check t’ will be rewritten to replace any subterm beta-eta equal to t1 with t2. If we are typing the ρ-term in synthesizing mode, then we rewrite the type of t’ by replacing all subterms convertible with t2 with t1 (so we rewrite right to left). If we are typing the ρ-term in checking mode, then we rewrite the incoming (contextual) type to replace all subterms convertible with t1 with t2 (so we rewrite left to right).
See language-overview/equational-reasoning.ced for examples.
For unannotated terms, the type ∀ x : T . T’ (which can be written T ➾ T’ when x does not occur free in T’) introduces x of type T into the typing context, but otherwise does not affect the subject of typing. So such an x is purely specificational, and cannot appear in the unannotated term. In annotated terms, we use the construct Λ x : T . t to introduce this x, which may appear in annotations (only). An example is specifying the length of a vector as an erased argument to a function like map on vectors. In this case, the function does not need to use the length of the vector to compute the result. The length is only used specificationally, to state that the lengths of the input and output vectors are the same.
If one has a term t of type ∀ x : T . T’ and wishes to instantiate x with some term t’, the notation in Cedille is t -t’.
Finally, one sometimes wishes to give a binding for a more complex specificational term for use within an expression. To facilitate this Cedille has notation for erased let-bindings {x : T = t} - t2, where x is the bound variable, t1 its definition, and t2 and expression where x is in scope. The syntax for ordinary let-bindings is [x : T = t1] - t2
As already mentioned, the above constructs of Cedille are sufficient
to derive induction for a class of datatypes, including parametrized
and indexed ones, that are useful for programming and proving in
practice. Starting with Cedille 1.1, we have added direct support for
datatype notations. One can declare datatypes using syntax similar to
that of languages like Coq or Agda, and define functions using pattern
matching and pattern-matching recursion. Unlike Coq and Agda (as
implemented at the time of writing), though, Cedille’s datatype
notations elaborate to Cedille Core (see See tooling), which does
not have any built-in notion of datatypes, only the pure type theory
of CDLE. One additional difference from the datatype notations of Coq
and Agda is that Cedille’s pattern-matching recursion supports
histomorphic recursion, where one can iteratively extract subdata from
a pattern variable and then make a recursive call (on the extracted
subdata). This subsumes nested pattern-matching, although we do not
at present support nested-pattern syntax (we are considering possibly
adding this in a subsequent release). For examples of the basics of
datatypes in Cedille, see language-overview/datatypes.ced
, and
for an example of histomorphic recursion see language-overview/cov-pattern-matching.ced
.
The syntax and semantics of Cedille are described in this document on arXiv. You can also find this in the docs/semantics subdirectory of this distribution.
The paper first showing how to derive induction for an inductive type in Cedille is here.
Next: tooling, Previous: documentation index, Up: Top [Index]


Laravel is an open-source project and anyone may contribute to Laravel for its improvement. We welcome contributors, regardless of skill level, gender, race, religion, or nationality. Having a diverse, vibrant community is one of the core values of the framework!
To encourage active collaboration, Laravel currently only accepts pull requests, not bug reports. "Bug reports" may be sent in the form of a pull request containing a failing unit test. Alternatively, a demonstration of the bug within a sandbox Laravel application may be sent as a pull request to the main Laravel repository. A failing unit test or sandbox application provides the development team "proof" that the bug exists, and, after the development team addresses the bug, serves as a reliable indicator that the bug remains fixed.
The Laravel source code is managed on Github, and there are repositories for each of the Laravel projects:

Discussion regarding bugs, new features, and implementation of existing features takes place in the #laravel-dev
IRC channel (Freenode). Taylor Otwell, the maintainer of Laravel, is typically present in the channel on weekdays from 8am-5pm (UTC-06:00 or America/Chicago), and sporadically present in the channel at other times.
The #laravel-dev
IRC channel is open to all. All are welcome to join the channel either to participate or simply observe the discussions!

Before sending pull requests for new features, please contact Taylor Otwell via the #laravel-dev
IRC channel (Freenode). If the feature is found to be a good fit for the framework, you are free to make a pull request. If the feature is rejected, don't give up! You are still free to turn your feature into a package which can be released to the world via Packagist.
When adding new features, don't forget to add unit tests! Unit tests help ensure the stability and reliability of the framework as new features are added.

Pull requests for bugs may be sent without prior discussion with the Laravel development team. When submitting a bug fix, try to include a unit test that ensures the bug never appears again!
If you believe you have found a bug in the framework, but are unsure how to fix it, please send a pull request containing a failing unit test. A failing unit test provides the development team "proof" that the bug exists, and, after the development team addresses the bug, serves as a reliable indicator that the bug remains fixed.
If are unsure how to write a failing unit test for a bug, review the other unit tests included with the framework. If you're still lost, you may ask for help in the #laravel
IRC channel (Freenode).

Note: This section primarly applies to those sending pull requests to the laravel/framework repository, not Liferaft applications.
All bug fixes should be sent to the latest stable branch. Bug fixes should never be sent to the master
branch unless they fix features that exist only in the upcoming release.
Minor features that are fully backwards compatible with the current Laravel release may be sent to the latest stable branch.
Major new features should always be sent to the master
branch, which contains the upcoming Laravel release.
If you are unsure if your feature qualifies as a major or minor, please ask Taylor Otwell in the #laravel-dev
IRC channel (Freenode).

If you discover a security vulnerability within Laravel, please send an e-mail to Taylor Otwell at <a href="mailto:taylorotwell<EMAIL_ADDRESS>All security vulnerabilities will be promptly addressed.

Laravel follows the PSR-0 and PSR-1 coding standards. In addition to these standards, the following coding standards should be followed:
<?php
.{
must be on the same line as the class name.


B.B. King Museum expanding to add space for his vehicles
INDIANOLA, Miss. (AP) - Work is starting on a $2.5 million expansion of a Mississippi Delta museum dedicated to a native son who became a blues legend.
A groundbreaking ceremony was held Tuesday for new space at the B.B. King Museum and Delta Interpretive Center in Indianola.
The museum opened in 2008 near the area where King grew up. The 15-time Grammy winner died in 2015 and is buried on the museum grounds.
The 4,500-square-foot (418-square-meter) addition will house King’s tour bus and two of his vehicles, a Rolls Royce Silver Shadow and a custom painted Chevy El Camino.
The museum says in a news release that other artifacts acquired since his death are being preserved and cataloged, including a guitar given to King by guitarist and inventor Les Paul.
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Please read our comment policy before commenting.


Miley Cyrus
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23
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Adore You (Remix)
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Everybody Hurts
When your day is long And the night, the night is yours alone When you're sure you've had enough Of this life, well hang... -
JUST STAND UP!
Beyonce: The heart is stronger than you think, It’s like it can go through anything. And even when you think it can’t it... -
Don't Call Me Angel (Charlie's Angels)
[by:Trap_Girl] 作曲 : Max Martin/Alma-Sofia Miettinen/Ariana Grande/Lana Del Rey/Miley Cyrus/Savan Kotecha/Ilya Salmanzad... -
Wrecking Ball
We clawed, we chained, our hearts in vain We jumped, never asking why We kissed, I fell under your spell A love no one c... -
Adore You
作曲 : Oren Yoel/Stacy Barthe 作词 : Oren Yoel/Stacy Barthe Baby baby, are you listening? One dream, where you've been? I ... -
Don't Dream It's Over
[by:Lenn03] There is freedom within There is freedom without Try to catch a deluge in a paper cup There's a battle ahead... -
Nothing Breaks Like a Heart
作曲 : Miley Cyrus/Mark Ronson/Maxime Picard/Conor Szymanski/Ilsey Juber/Clement Picard/Thomas Brenneck 作词 : Miley Cyrus... -
FU
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Fly On The Wall
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No Freedom
Take it by your silence I'm free to walk out the door By the look in your eyes I can tell You don't think I'll be back f... -
Younger Now
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Unholy
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Party Up The Street
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Just Stand Up (Miley Cyrus ...)
作词 : SHANKS, JOHN/UNKNOWN Beyonce: The heart is stronger than you think It's like it can go through anything And even w... -
Come Get It Bae
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When I Look At You
Everybody needs inspiration Everybody needs a soul Beautiful melody, when the nights alone Cause there is no guarantee ... -
You'll Always Find Your Way Back Home
You wake up, it's raining and it's monday Looks like one of those rough days Time's up, you're late again, so get out th... -
SMS (Bangerz)
[by:蠢梨Sherry] 作曲 : Sean Garrett/Miley Cyrus/Marquell Middlebrooks/Mike L. Williams II 作词 : Sean Garrett/Miley Cyrus/Ma... -
Overboard (Live)
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Summertime Sadness
[by:北野斌] Kiss me hard before you go Summertime sadness I just wanted you to know That baby you're the best I got my red ... -
The Best of Both Worlds
Oh yea Come on You get the limo out front Have the styles, every shoe, every color Yea when you're famous it can be kind... -
Nightmare
[by:废柴机器人] [Verse 1] Hey! Feels like I'm asleep, but I’m awake In this dream I never see your face I'm just a step behin...  -
Do My Thang
作曲 : Miley Cyrus/Kyle Edwards/William Adams/Jean-Baptiste/Michael McHenry/Ryan Buendia 作词 : Miley Cyrus/Kyle Edwards/W... -
Bang Me Box
[by:工作婊] I sleep with the door open if you want to come in while I'm sleeping I'm always sleeping naked cause I wake up ...  -
See You Again
I've got my sights set on you, And I'm ready to aim, I have a heart that will, Never be tamed, I knew you were something... -
The Climb
I can almost see it. That dream I'm dreamin' but There's a voice inside my head saying you'll never reach it. Every step... -
We Can't Stop
[0-1:59.400]It's our party we can do what we want It's our party we can say what we want It's our party we can love who ... -
Mother's Daughter
[by:Trap_Girl] 作曲 : Miley Cyrus/Andrew Wyatt/Alma Miettinen 作词 : Miley Cyrus/Andrew Wyatt/Alma Miettinen Hallelujah, I... -
Twerk
I came up in this party time to twerk I came up in this party & I’m turnt I came up in this party time to twerk Twerk, t... -
Slide Away
作曲 : Miley Cyrus/Andrew Wyatt/Alma Miettinen 作词 : Miley Cyrus/Andrew Wyatt/Alma Miettinen Wooh, wooh, wooh Wooh, wooh,... -
Party in the U.S.A.
I hopped up the plane at LAX With the dream, my card again Welcome to the land of fame Am I gonna fit in? Jumped in the ... -
Butterfly Fly Away
You tuck me in, turn out the light Left me safe and sound at night Little girls depend on things like that Brushed my t... -
wrecking ball
We clawed, we chained our hearts in vain We jumped, never asking why We kissed, I fell under your spell A love no one co... -
Stay
Well it’s good to hear your voice I hope you’re doing fine And if you ever wonder I’m lonely here tonight Lost here in t... -
Hands Of Love
[by:紫ha123] [ar:Miley Cyrus] [ti:Hands Of Love] When the white flag sails, covered in streaks of blood There'll be an en... -
Jolene
[by:Valkubus] Jolene, Jolene, Jolene, Jolene I'm begging of you please don't take my man Jolene, Jolene, Jolene, Jolene ... -
Nothing Compares To Wrecking Ball (Robin Skouteris Mix)
[by:ChaseEndlessly] [by:E-Lyric] [offset:-100] We clawed, we chained our hearts in vain We jumped, never asking why We k... -
I Thought I Lost You
<MILEY>Nobody listens to me, don’t hear a single thing I've said Say anything to soothe me, anything to get you from my ... -
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Nanny Service
Lili, a native of Baja who was born in Mulege and raised in La Paz, has lived in many places like Brownsville, Texas. She is a trained certified babysitter, a yoga instructor for kids as well as adults. She is also the co-founder and manager at Baja Kids Lab.
Her career with children started in the summer of 2001 at the Center of Psychological and Alternative Therapies in Toluca City, where she worked as teacher's assistant with a group of twenty or more special learning needs children between the ages of 5 and 12.
Later on, in 2013, she received several certifications:
For a wedding, we will surely make the day less stressful by creating an environment where the children can have their own "wedding time party." We will provide board games, arts and crafts, as well as toys and play games (treasure hunts, lawn bowling, Frisbee golf, etc.)
For corporate events, conferences, conventions or trade-shows: our babysitting team fits each client's budget, when parents have the option to bring their children, clients report higher attendance. We work hand-in-hand with event planners, DMC’s and venues to arrange all the childcare needed to provide a seamless transition between the parents and nanny staff.
In-villa babysitting service: your children will be looked after in the safety of your own vacation rental, Airbnb or event venue! Every sitter arrives with a bag of games, books, and age-appropriate activities. In addition upon request, they have sitters who can care for families of children with special needs or speak other languages.
Whether you need a bilingual babysitter for a couple of hours or a full team of them while on vacation, from La Paz to Los Cabos, Los Barriles or anywhere in between, you can be sure your children will be in great hands with Lili and her team.
Her career with children started in the summer of 2001 at the Center of Psychological and Alternative Therapies in Toluca City, where she worked as teacher's assistant with a group of twenty or more special learning needs children between the ages of 5 and 12.
Later on, in 2013, she received several certifications:
- the Baby Care Certification by First AID Web Inc. and National Health Safety Foundation
- Babysitter Lessons and Safety Training by the American Academy of Paediatrics, USA
- Infant First Aids recognition by the Mexican Red Cros
- and the Yoga Kids Families Instructor Certification by Rainbow Kids Yoga and Yoga Alliance, more recently
For a wedding, we will surely make the day less stressful by creating an environment where the children can have their own "wedding time party." We will provide board games, arts and crafts, as well as toys and play games (treasure hunts, lawn bowling, Frisbee golf, etc.)
For corporate events, conferences, conventions or trade-shows: our babysitting team fits each client's budget, when parents have the option to bring their children, clients report higher attendance. We work hand-in-hand with event planners, DMC’s and venues to arrange all the childcare needed to provide a seamless transition between the parents and nanny staff.
In-villa babysitting service: your children will be looked after in the safety of your own vacation rental, Airbnb or event venue! Every sitter arrives with a bag of games, books, and age-appropriate activities. In addition upon request, they have sitters who can care for families of children with special needs or speak other languages.
Whether you need a bilingual babysitter for a couple of hours or a full team of them while on vacation, from La Paz to Los Cabos, Los Barriles or anywhere in between, you can be sure your children will be in great hands with Lili and her team.


| Temperature rise |
Poleward/deeper waters shifts |
Less in situ fishery biomass |
[
7]
|
|
|
Less local catch |
|
| Temperature rise; low upwelling |
Nutrient reduction |
Less primary productivity |
[
32]
|
| Temperature rise; low rainfall |
Low phytoplankton due to low riverine input |
Less biomass |
|
| Temperature rise; decreased upwelling, fishing |
Low phytoplankton due to low riverine input |
Less local catch |
|
| Temperature rise, salinity, upwelling |
Poleward shift |
Less local catch |
[
22]
|
| Temperature rise/decrease; increase/decreased upwelling |
Increased turbulence and reduced plankton |
Reduced catches |
[
33]
|
| Temperature and sea level rise |
Acidification |
Less coral reefs |
[
34]
|
| Temperature rise |
Not specified |
Not specified |
[
35]
|
| Ocean CO
2 sequestration
|
Acidification |
Echinoderms: low biomass |
[
36]
|
|
|
Mollusks: low biomass |
|
|
|
Crustaceans: low biomass |
|
|
|
Fish: possible effects on larval survival |
|
| Temperature rise, fishing mortality |
Decreased plankton |
Mid pelagic fish: increased biomass |
[
37,
38]
|
|
|
Small pelagics: less biomass |
|
|
|
Cephalopods: less biomass |
|
|
|
Bivalves: less biomass |
|
| Temperature, salinity, windfields, oxygen, acidification |
Poleward shift, change in productivity and trophic structure of communities |
Not specified |
[
6,
22]
|
| Upwelling, temperature |
Changes in fished stock productivity |
Changes in catchability, particularly short-lived species |
[
22]
|
| Wind, upwelling, salinity |
Effects on plankton and fish dynamics |
Change in biomass of small fishes |
[
39]
|
|
|
Change in biomass of top predatory fish |
|
| Temperature, rainfall |
Habitat loss.
Direct: temperature for species with limited thermal ranges.
Indirect: poleward movement, habitat changes and more diseases
|
Urchins: habitat expansion, increased biomass |
[
40]
|
|
|
Lobsters: low biomass (affected by urchins) |
|
|
|
Abalones: low biomass |
|
|
|
Organic reef species: unchanged |
|
|
|
Prawns and crabs: increased biomass |
|
| N/S |
Poleward shifts |
Slight decrease in Mexican marine catches |
[
5]
|
| Temperature, CO
2 sequestration
|
Poleward shifts, acidification, ecosystem disruptions, changes in primary productivity |
Less biomass, hence overfishing |
[
22]
|
| Wind stress |
Deep euphotic zone and increased offshore transport |
High primary productivity, variable phenology |
[
41]
|


SensorOverlord_Walkthrough.Rmd
This short tutorial is intended for microscopists who have:
A basic knowledge of R,
access to ratiometric images in their experimental system of interest, and
an interest in making accurate, quantitative measurements of \(E_{GSH}\), pH, or the concentration of a ligand.
The sensorOverlord package is available on GitHub. You can install it in R via the devtools
package. To install the devtools
package, run install.packages("devtools")
.
To install the most recent version of the sensorOverlord package from GitHub:
devtools::install_github("apfeldlab/sensoroverlord")
You can confirm your installation of sensorOverlord
with packageVersion
:
packageVersion("sensorOverlord") #> [1] '0.2.0'
To use the SensorOverlord framework, you need to have access to a midpoint potential for your sensor.
For redox sensors, the midpoint potential is \(E_0\). For pH sensors, the midpoint potential is \(pKa\). For ligand-binding sensors, the midpoint is \(pKd\).
The value of these midpoint potentials are almost always reported in the paper in which the sensor of interest was first published.
Note that, for ligand-binding sensors, papers often report \(Kd\). \(pKd = -log_{10}(Kd)\) so, to convert \(Kd\) to \(pKd\), use the log10
function:
kD <- 5*10e-6 pKd <- -log(kD)
sensorOverlord requires as input:
You can obtain these parameters in one of three ways:
Upload a digitized spectra. sensorOverlord
can programatically obtain these input values from a digitized spectra.
Use a provided spectra. We have created a MongoDB database containing many the spectra of many published redox, pH, and ligand-binding sensors.
Provide the parameters directly. These parameters can be measured empirically, as explained in Romero 2014.
Option 1: Upload a digitized spectra
If you have excitation-emission spectra data for your each of your sensor’s two states, you can upload those into R.
For example, you could have a .csv file with three columns:
Oftentimes with digitized spectra, the \(\lambda\) values recorded in states A and B are not identical. In that case, you can use a .csv file with four columns:
spectra <- read.csv("my_spectra.csv")
Once you have uploaded your spectra, you can use the sensorOverlord::spectraMatrixFromValues
function to create a Spectra
object:
spectra_object <- spectraMatrixFromValues( lambdas_minimum = spectra$lambda, values_minimum = spectra$values_A, lambdas_maximum = spectra$lambda, values_maximum = spectra$values_B )
or
spectra_object <- spectraMatrixFromValues( lambdas_minimum = spectra$lambda_A, values_minimum = spectra$values_A, lambdas_maximum = spectra$lambda_B, values_maximum = spectra$values_B )
You can use the newSensorFromSpectra()
function to turn the spectra object into a sensor object at a certain ratiometric wavelength pair:
sensor_object <- newSensorFromSpectra(spectra_object, c(510, 520), c(455, 465))
That sensor object will now contain estimates for the three required parameters:
Ra <- sensor_object@Rmin Rb <- sensor_object@Rmax delta2 <- sensor_object@delta
Option 2: Use a Provided Spectra
You can access all sensor information from the database with sensorOverlord::getDb()$find()
, which accepts JSON search queries. For more information, see the “Accessing and Manipulating the Database” vignette. For example:
deGFP1_information <- getDb()$find('{"sensor_name" : "deGFP1"}') print(deGFP1_information$sensor_readout) #> [[1]] #> [1] "emission ratiometric" print(deGFP1_information$sensor_midpoint) #> [[1]] #> [1] 8.02 print(deGFP1_information$lambda1_recommended) #> [1] 515 print(deGFP1_information$lambda2_recommended) #> [1] 460
The actual spectra information is in a list form, so you can use the apply
and unlist
functions to obtain the spectra:
library(data.table) deGFP1_spectra_information <- data.table( apply( deGFP1_information[c("lambda_min", "values_min", "lambda_max", "values_max")], 2, function(x) unlist(x)) )
Then, you can follow the same instructions as if you had provided the spectra yourself: create a spectra object, then a sensor object at a specific wavelength pair, and then extract the relevant parameters:
deGFP_spectra <- spectraMatrixFromValues(deGFP1_spectra_information$lambda_min, deGFP1_spectra_information$values_min, deGFP1_spectra_information$lambda_max, deGFP1_spectra_information$values_max) sensor_object <- newSensorFromSpectra(deGFP_spectra, c(510, 520), c(455, 465)) Ra <- sensor_object@Rmin Rb <- sensor_object@Rmax delta2 <- sensor_object@delta print(Ra) #> [1] 0.3330232 print(Rb) #> [1] 0.6447556 print(delta2) #> [1] 0.9611258
Option 3: Provide Parameters Directly
If you conducted the appropriate microscopy experiments, you may have also obtained exact values of \(R_a\), \(R_b\), and \(\delta_{\lambda2}\).
If that’s the case, you can use them to directly make a sensor object:
R_reduced <- 0.6 R_oxidized <- 5.2 delta2 <- 0.171 sensor_object <- new( "Sensor", Rmax = R_reduced, Rmin = R_oxidized, delta = delta2 )
In order to use the SensorOverlord framework, you need to have an estimate of the variability of your measurement of \(R\) in your system of interest.
There are various ways to accomplish this, as we detail in the Supplementary Information of the associated manuscript.
For example, you can simply plot the \(R\) values that you observed in a previous experiment in which you expected the \(R\) value to stay constant over some period of time. Then, you can estimate your error in \(R\) by looking at the standard error over that period.
In C. elegans, we find that the error is constant, but relative to the \(R\) value.
SensorOverlord can accommodate any error model that you find in your system. For example:
# Relative error of 2.8%, or 0.028*R error_relative <- function(x) x*0.028 # Absolute error of +/- 0.028 error_absolute <- function(x) 0.028 # Quadratic error error_other <- function(x) 0.0001 * x^2 + 0.028*x + 0.5
For more information about incorporating different error models, see the “Customizing Error Model” vignette. For now, this tutorial will assume that you are using a relative error.
After completing the pre-requisites, you should have access to a sensor object and an error model. E.g.
sensor_object <- new( "Sensor", Rmax = R_reduced, Rmin = R_oxidized, delta = delta2 ) my_error <- function(x) x*0.028
`
First, you’ll need to turn your generic sensor object into a specific redox, pH, or ligand-binding sensor. For example:
redox_sensor_object <- new( "redoxSensor", sensor_object, e0 = -265 )
Then, you can use the error_df()
method, defined on redoxSensor, pHSensor, and ligandSensor objects, to get a table of the inaccuracy of the sensor at different values of redox potential, pH, or p[Ligand].
redox_sensor_error <- error_df( redox_sensor_object, c(0.028), Emin = -300, Emax = -150 ) summary(redox_sensor_error) #> E Error Inaccuracy Rmin #> Min. :-300.0 Min. : 0.7329 Length:15001 Length:15001 #> 1st Qu.:-262.5 1st Qu.: 1.1032 Class :character Class :character #> Median :-225.0 Median : 3.4355 Mode :character Mode :character #> Mean :-225.0 Mean : Inf #> 3rd Qu.:-187.5 3rd Qu.:31.3965 #> Max. :-150.0 Max. : Inf #> Rmax Name #> Length:15001 Length:15001 #> Class :character Class :character #> Mode :character Mode :character #> #> #>
For more information, see ?error_df,redoxSensor-method
, or the method for your type of sensor.
You can export that table directly, or use it for further analysis.
sensorOverlord
can also compute the ranges of redox potential, pH, or ligand concentration that a sensor can measure to different accuracy thresholds:
# The redox potentials this sensor can measure, with an error in R of # 2% or 3%, to an accuracy of 1mV or 2mV accurate_ranges <- ranges_df(redox_sensor_object, inaccuracies = c(0.02, 0.03), thresholds = c(1, 2)) accurate_ranges #> Sensor_Name Minimum Maximum Inaccuracy error_thresh #> 1 Sensor_0.02 -252.89 -205.11 0.02 1 #> 2 Sensor_0.02 -264.09 -200.00 0.02 2 #> 3 Sensor_0.03 -243.66 -214.85 0.03 1 #> 4 Sensor_0.03 -257.68 -200.44 0.03 2
sensorOverlord
also provides some default plotting methods that work for all sensor objects.
plotProperty
will plot \(R\) vs the property of interest For example, for redox sensors, this will be \(R\) vs \(E_{GSH}\), the fraction of sensors in the oxidized state.
plotProperty(redox_sensor_object) #> Warning in log((object@delta * object@Rmax - object@delta * R)/(R - #> object@Rmin)): NaNs produced #> Warning: Removed 1 row(s) containing missing values (geom_path).
rangePlot
will plot the range of values a sensor can measure to a certain accuracy.
rangePlot(redox_sensor_object, ranges = accurate_ranges)
In the plot above, notice how the range of values the sensor can measure accurately expands when the error in R is 2% (“Sensor_0.02”) versus when the error in 3% (“Sensor_0.03”).
For more information on plotting methods, see the “Sensor Methods” section in the documentation reference.


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--- layout: default title: Bolt Developer Updates ---
Keep up to date with Bolt, what we’re actively working on, and what we’re thinking about in the near term.
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Privacy Policy
LeagueRepublic and GDPR
Please also see the LeagueRepublic Terms and Conditions. Our terms and conditions require all leagues and clubs who use LeagueRepublic within the EU to be GDPR compliant. Leagues are responsible for managing the "individual rights" of the individuals they are keeping data for in their leagues.
User's are not permitted to have a LeagueRepublic account (login / sign-in) unless they are 16 years old or over.
LeagueRepublic holds the following data on an individual with a LeagueRepublic account:
- Name
- Email address
- Encrypted login credentials
- Support questions history
This information is held by LeagueRepublic as the "Controller" for the purposes of:
- Allowing the user to sign into the LeagueRepublic system
- Provide the user with a platform for customer chat and support
This data is passed to the following external systems:
- Intercom platform for customer support, Intercom privacy
- Stripe to manage online payments, Stripe privacy
We do not pass this information to anyone else for marketing or any other purposes, so there is not an opt-in for any additional options.
LeagueRepublic holds data on league members on behalf of leagues
As a "Processor" LeagueRepublic holds personal data of league members who do not have a LeagueRepublic account, on behalf of leagues. For example, a League Administrator could create a "Player" in the system who won't have a LeagueRepublic account and therefore won't be able to sign-in to the LeagueRepublic system.
The following personal data of league members without LeagueRepublic accounts:
- Email address
- Mobile phone number
can be used by the LeagueRepublic to provide email notifications (after an opt-in) and result entry SMS message prompts. It will not be used for marketing purposes.
LeagueRepublic will not use the following personal data of league members collected by leagues for any purpose:
- Date Of Birth
- League reference numbers
- Address
Leagues and clubs are "Controllers" for the purposes of GDPR
A league may use many systems to manage their sports league and personal details about their members can cross many systems, some of which may be paper or spreadsheet based. For the purposes of GDPR a league is a "Controller" of this information and if it resides in the LeagueRepublic system then LeagueRepublic is a "Processor" of this information.
Leagues use LeagueRepublic to manage their day to day activities including:
- Scheduling
- Results management
- Statistics management
- People management for administrators, referees and players
Minimum personal data held within LeagueRepublic about league members in the league:
- Name
And optionally:
- Email address
- Date Of Birth
- League reference numbers
- Telephone contact details
- Address
LeagueRepublic provides leagues with the following tools
Display the league's own privacy policy
You can upload your own privacy policy under 'Site Builder > Documents'. In here you can state how and what personal data you collect and how you store, what you do with it, i.e. your purpose and which third parties you share the data with.
Leagues must comply with the GDPR "Individual Rights"
Right to be informed
This can be implemented in the league's privacy policy.
If the league uses the LeagueRepublic Player Registration system then consent can be obtained by requiring league members to accept the league's terms / privacy policy when registering for the league.
Right of access
Individuals have a right to access their personal data. LeagueRepublic provide a web page detailing personal information and related league sports data about an individual which a league can give to that individual.
Right to rectification
All data relating to an individual can be corrected by any League Administrator within a league.
Right to erasure
We provide the tools to completely erase a person in your league. There is no way to revert this. All personal data will be deleted and the player or person will have a first name and last name anonymised.
Right to restrict process
We provide the tools to restrict the processing of an individual. Their personal details will not be viewable within the administration system or the public sites and their first name and last name are anonymised.
Where we store your personal data
All LeagueRepublic data is stored using "Amazon Web Services (AWS)", they are a subsidiary of Amazon.com that provides a cloud computing platform for LeagueRepublic. AWS Privacy
All passwords are encrypted. The administration pages all operate under https, this means all communications between your browser and the website are encrypted.
Use of Intercom Services
We use third-party analytics services to help understand your usage of our services. In particular, we provide a limited amount of your information (such as your email address and sign-up date) to Intercom, Inc. ("Intercom") and utilize Intercom to collect data for analytics purposes when you visit our website or use our product. Intercom analyzes your use of our website and/or product and tracks our relationship so that we can improve our service to you. We may also use Intercom as a medium for communications, either through email, or through messages within our product(s). As part of our service agreements, Intercom collects publicly available contact and social information related to you, such as your email address, gender, company, job title, photos, website URLs, social network handles and physical addresses, to enhance your user experience. For more information on the privacy practices of Intercom, please visit Intercom privacy. Intercom's services are governed by Intercom's terms of use which can be found at Intercom terms.
Cookies
This policy gives the following information about cookies:
- what they are;
- which ones are used by www.leaguerepublic.com ("LR");
- the purposes for which they are used; and
- how you can manage and/or disable them.
Cookies are small text files which are placed on your device when you visit a website. They contain information that is transferred to your device's hard drive and help us to improve our site and to deliver a better and more personalised service to you. Cookies enable us to:
- estimate our audience size and usage pattern;
- store information about your preferences, and so allow us to customise our site according to your individual interests; and
- recognise you when you return to our site.
The cookies used on this website have been categorised based on the categories found in the ICC UK Cookie guide. A list of all the cookies used on this website by category is set out below.
Category 1 - Strictly Necessary Cookies
These cookies enable services you have specifically asked for.
These cookies are essential in order to enable you to move around the website and use its features, such as accessing secure areas of the website. Without these cookies, services you require, like results, statistics, standings and news cannot be provided.
| Cookie Name | Description | Expiry |
| JSESSIONID | This cookie contains a session ID which is a mechanism for distinguishing different users' visits when multiple users are visiting the website at the same time. It is essential for interactive use of the site. | On closing the web browser |
Category 2 - Performance Cookies
These cookies collect anonymous information about the pages visited by you
These cookies collect information about how visitors use a website, for instance which pages visitors go to most often, and if they get error messages from web pages. These cookies don't collect information that identifies a visitor. All information these cookies collect is aggregated and therefore anonymous. It is only used to improve how a website works.
| Cookie Name | Description | Expiry |
| __utma | This cookie is typically written to the browser upon the first visit to our site from that web browser. If the cookie has been deleted by the browser operator, and the browser subsequently visits our site, a new __utma cookie is written with a different unique ID. This cookie is used to determine unique visitors to our site and it is updated with each page view. Additionally, this cookie is provided with a unique ID that Google Analytics uses to ensure both the validity and accessibility of the cookie as an extra security measure. | 2 years from set/update |
| __utmb | This cookie is used to establish and continue a user session with our site. When a user views a page on our site, the Google Analytics code attempts to update this cookie. If it does not find the cookie, a new one is written and a new session is established. Each time a user visits a different page on our site; this cookie is updated to expire in 30 minutes, thus continuing a single session for as long as user activity continues within 30-minute intervals. This cookie expires when a user pauses on a page on our site for longer than 30 minutes. | 30 minutes from set/update |
| __utmc | This cookie operates in conjunction with the __utmb cookie to determine whether or not to establish a new session for the user. | On closing the web browser |
| __utmz | This cookie stores the type of referral used by the visitor to reach our site, whether via a direct method, a referring link, a website search, or a campaign such as an ad or an email link. It is used to calculate search engine traffic, ad campaigns and page navigation within our own site. The cookie is updated with each page view to our site. | 6 months from set/update |
Category 3 - Functionality Cookies
These cookies remember choices you make to improve your experience.
We do not use this type of cookie directly on our website.
We offer a support chat facility on our website via www.whoson.com , please visit their website for details of the Whoson privacy policy
Category 4 - Targeting / Advertising Cookies
These cookies collect information about your browsing habits in order to make advertising relevant to you and your interests.
LR does not directly store cookies related to advertising from our website. We serve adverts via Google DoubleClick for Publishers Small Business and Google Adsense. Please see Googles advertising privacy statements
Restricting and blocking cookies
If you wish to restrict or block the cookies which are set by our websites, or any other website, you can do this through your browser settings. The Help function within your browser should tell you how.
Alternatively, visit www.aboutcookies.org which contains comprehensive information on how to restrict or block the cookies on a wide variety of browsers. This site provides details on how to delete cookies from your computer as well as more general information about cookies.
For information on how to do this on the browser of your mobile phone you will need to refer to your handset manual.
Click here to opt out of being tracked by Google Analytics across all websites
Please be aware that restricting cookies may impact on the functionality of our website.
To obtain further information on the ICC (UK) UK cookie guide visit http://www.international-chamber.co.uk/our-expertise/digitaleconomy
Changes to our privacy policy
Any changes we may make to our privacy policy in the future will be posted on this page. This policy was last updated: 08 May 2018
Contact
Questions, comments and requests regarding this privacy policy should be addressed to LeagueRepublic, DJH Technology Ltd, Saturn Centre, Spring Road, Wolverhampton WV4 6JX or Contact Us


You have 1:00 seconds to answer five questions.
1. Lightning never strikes in the same place twice.
2. Goldfish only have a memory of three seconds.
True: False:3. Birds are dinosaurs.
True: False:4. The owner of the company that makes Segways died after accidentally driving his Segway off a cliff.
True: False:5. It costs the U.S. Mint more to make pennies and nickels than the coins are actually worth.
True: False: