text:
Introduction

This document will cover in depth the use of DoE experiments in R! We will focus our attention to measuring treatment effects, not variances.

Based on the work:
Lawson, John. Design and Analysis of Experiments with R. Chapman and Hall/CRC, 20141217. VitalBook file.

Definitions

• Experiment (also called a Run) is an action where the experimenter changes at least one of the variables being studied and then observes the effect of his or her actions(s). Note the passive collection of observational data is not experimentation.

• Experimental Unit is the item under study upon which something is changed. This could be raw materials, human subjects, or just a point in time.

• Sub-Sample, Sub-Unit, or Observational Unit When the experimental unit is split, after the action has been taken upon it, this is called a sub-sample or sub-unit. Sometimes it is only possible to measure a characteristic separately for each sub-unit; for that reason they are often called observational units. Measurements on sub-samples, or sub-units of the same experimental unit, are usually correlated and should be averaged before analysis of data rather than being treated as independent outcomes. When sub-units can be considered independent and there is interest in determining the variance in sub-sample measurements, while not confusing the F-tests on the treatment factors, the mixed model described in Section 5.8 should be used instead of simply averaging the sub-samples.

• Independent Variable (Factor or Treatment Factor) is one of the variables under study that is being controlled at or near some target value, or level, during any given experiment. The level is being changed in some systematic way from run to run in order to determine what effect it has on the response(s).

• Background Variable (also called a Lurking Variable) is a variable that the experimenter is unaware of or cannot control, and which could have an effect on the outcome of the experiment. In a well-planned experimental design, the effect of these lurking variables should balance out so as to not alter the conclusion of a study.

• Dependent Variable (or the Response denoted by Y) is the characteristic of the experimental unit that is measured after each experiment or run. The magnitude of the response depends upon the settings of the independent variables or factors and lurking variables.

• Effect is the change in the response that is caused by a change in a factor or independent variable. After the runs in an experimental design are conducted, the effect can be estimated by calculating it from the observed response data. This estimate is called the calculated effect. Before the experiments are ever conducted, the researcher may know how large the effect should be to have practical importance. This is called a practical effect or the size of a practical effect.

• Replicate runs are two or more experiments conducted with the same settings of the factors or independent variables, but using different experimental units. The measured dependent variable may differ among replicate runs due to changes in lurking variables and inherent differences in experimental units.

• Duplicates refer to duplicate measurements of the same experimental unit from one run or experiment. The measured dependent variable may vary among duplicates due to measurement error, but in the analysis of data these duplicate measurements should be averaged and not treated as separate responses.

• Experimental Design is a collection of experiments or runs that is planned in advance of the actual execution. The particular runs selected in an experimental design will depend upon the purpose of the design.

• Confounded Factors arise when each change an experimenter makes for one factor, between runs, is coupled with an identical change to another factor. In this situation it is impossible to determine which factor causes any observed changes in the response or dependent variable.

• Biased Factor results when an experimenter makes changes to an independent variable at the precise time when changes in background or lurking variables occur. When a factor is biased it is impossible to determine if the resulting changes to the response were caused by changes in the factor or by changes in other background or lurking variables.

• Experimental Error is the difference between the observed response for a particular experiment and the long run average of all experiments conducted at the same settings of the independent variables or factors. The fact that it is called “error” should not lead one to assume that it is a mistake or blunder. Experimental errors are not all equal to zero because background or lurking variables cause them to change from run to run. Experimental errors can be broadly classified into two types: bias error and random error. Bias error tends to remain constant or change in a consistent pattern over the runs in an experimental design, while random error changes from one experiment to another in an unpredictable manner and average to be zero. The variance of random experimental errors can be obtained by including replicate runs in an experimental design.

Condensed theory

DoE is used to distinguish between correlation and causality in a way that is cost efficient and accounts for most confounding effects and lurker effects.

Sequential strategies are used to determine what factors are most influencial and after that the changes in factors are quantified until finally optimal operating conditions are determined (most appropriate factor states to accomplish maximum treatment effect)

DoE Workflow

An effective experimental design will ensure the following:

• A clear objective
• An appropriate design plan that gaurantees unconfounded and unbiased factor effects
• A plan for data collection to enable estimation of variance and experimental error
• A stipulation to collect enough data to satisfy the objectives

In order to achieve this we must:

1. Define objectives
2. identify experimental units
3. Define a meaningful and measurable respnse or dependent variable
4. List the independent and lurking vbariables
5. Run pilot tests
6. Make a flow diagram of the experimental procedure
7. Choose the experimental design
8. Determine number of replicants
9. Randomize the experimental conditions to experimental units
10. Describe a method for data analysis with tested dummy data
11. Timetable and budget for resources

In particular it’s important to note that the time we have to run the experiment and the cost budget for the experiment will heavily impact the type of experimental design

When to use which design

Let’s summarise the theory to understand when we should use which experimental design:

Clearly our very first split depends on what we wish to investigate, the variances or the effects of different factors.

Design Name Acronym Index

RSE - random sampling experiment

FRSE - factorial random sampling experiment

NSE - nested sampling experiment

SNSE - staggered nested sampling experiment

CRD - completely randomized design

CRFD - completely randomized factorial design

CRFF - completely randomized fractional factorial

PB - Plackett-Burman design

OA - orthogonal array design

CRSP - completely randomized split plot

RSSP - response surface split plot

EESPRS - equivalent estimation split-plot response surface

SLD - simplex lattice design

SCD - simplex centroid design

EVD - extreme vertices design

SPMPV - split-plot mixture process variable design

RCB - randomized complete block

GCB - generalized complete block

RCBF - randomized complete block factorial

RBSP - randomized block split plot

PBIB - partially balanced incomplete block

BTIB - balanced treatment incomplete block

BIB - balance incomplete block

BRS - blocked response surface

PCBF - partially confounded blocked factorial

CCBF - completely confounded blocked factorial

LSD - Latin-square design

RCD - row-column design

Study factor effects

We start off with the objective of studying factor effects on treatment response. We will illustrate the basic workflows using a simple 1 factor CRD with 1 response.

Completely randomized design (CRD)

In completely randomized designs we consider only a single factor. For each possible state of this factor we have a treatment or group. The total number of experimental units n is equal to the number of treatments * the number of replications in of each treatment.

Replications are vital!
Without replications we couldn’t tell if the treatment effect was real or due to random manifistation of unmeasured effects.

Remember:
By randomly assigning treatments and replications we balance out the effects we are not aware of (law of large numbers fighting off lurker effects). We therefore assume any affects we do not account for are equally distributed accross treatments on average.

Sub-samples are not replicates!
Having two independant tasters taste/rate the same cake does not mean you have two replicates of that particular cake’s treatment.

Example

Test bread rise height caused by factor time:

We test 3 values for time with 4 replicates each (12 experimental units of 3 treatments with 4 replicates)

set.seed(234789)
f <- factor(rep(c(35,40,45),each = 4))
randomized_times <- sample(f,12)
allocation <- 1:12
design <- data.frame(allocated_loaf = allocation, time = randomized_times)
design
##    allocated_loaf time
## 1               1   40
## 2               2   45
## 3               3   35
## 4               4   40
## 5               5   40
## 6               6   45
## 7               7   45
## 8               8   45
## 9               9   35
## 10             10   40
## 11             11   35
## 12             12   35

Linear model used for CRD inference

Obviously we are only making inference about the mean effect within each treatment given the replications:
Cell mean model
$$Y_{ij} = \mu_i + \epsilon_{ij}$$

A more useful representation:
Effects model
$$Y_{ij} = \mu + \tau_i + \epsilon_{ij}$$
This formulation is more useful because $$\tau_i$$ is interpreted as the difference of the mean within treatment $$i$$ and the overall average.

If the design is executed properly the log likelihood function will be maximised if we minimise the sum of squares of residuals (linear regression).

BUT in R the lm() function will omit the first factor $$\tau_1$$ and derive coefficients relative to $$\mu + \tau_1$$:

bread_example <- daewr::bread

bread_example %>% lm(formula = height~time) %>% summary
##
## Call:
## lm(formula = height ~ time, data = .)
##
## Residuals:
##    Min     1Q Median     3Q    Max
## -1.812 -1.141  0.000  1.266  2.250
##
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept)   5.4375     0.7655   7.104 5.65e-05 ***
## time40        2.8125     1.0825   2.598   0.0288 *
## time45        2.8750     1.0825   2.656   0.0262 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.531 on 9 degrees of freedom
## Multiple R-squared:  0.5056, Adjusted R-squared:  0.3958
## F-statistic: 4.602 on 2 and 9 DF,  p-value: 0.042

So we can see the lm() function did not derive a coefficient for the time = 35 factor level. In this call the intercept is interpreted as $$\mu + \tau_1$$ and the other factor levels are all evaluated relative to this intercept:

Obviously from this equation it’s easy to derive e.g. $$\mu + \tau_2$$ by adding the 1st and second coefficients together…

Hypothesis test for No Treatment Effect

Now let’s test if the treatment (changing the time factor) has any affect on the response variable (the height of the baked bread):

\begin{align} H_0:& \tau_i = \tau_j \ \forall \ {i,j} \\ H_1:& \textrm{atleast 2 } \tau_i \textrm{'s differ} \end{align}

bread_example %>% aov(formula = height~time) %>% summary
##             Df Sum Sq Mean Sq F value Pr(>F)
## time         2  21.57  10.786   4.602  0.042 *
## Residuals    9  21.09   2.344
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

So we can see that the p-value here is the same as the p-value in the lm() summary and since it is < 0.05 we can safely reject $$H_0$$ and say different time factor levels had a significant impact on the response variable height.

Verify linearity assumption

Of course, using a lm() model assumes linearity and we should validate this assumed relationship between time and height:

Assumptions validation function

Validate_assumptions <- function(df, formula_ = NULL, model, factor, response) {
qq_plot <-
df %>%
ggplot(aes(sample = model %>% residuals))+
stat_qq()+
ggtitle("QQ plot of residuals")+
xlab("")+
ylab("")

Res_fac <- df %>%
ggplot()+
geom_point(aes(y = model %>% residuals(), x = df[,factor] ))+
ggtitle("Residuals VS factor levels") +
xlab("Residuals")+
ylab("Factor levels")

Res_fit <- df %>%
ggplot(aes(y = model %>% residuals(), x = model %>% predict))+
geom_point()+
ggtitle("Residuals VS fitted")+
xlab("Residuals")+
ylab("fitted")

Res_eu <- df %>%
ggplot(aes(y = model %>% residuals(), x = seq(nrow(df))))+
geom_point()+
ggtitle("Residuals VS experimental unit")+
xlab("Residuals")+
ylab("Experimental unit")

multiplot <- function(..., plotlist=NULL, file, cols=1, layout=NULL) {
library(grid)

# Make a list from the ... arguments and plotlist
plots <- c(list(...), plotlist)

numPlots = length(plots)

# If layout is NULL, then use 'cols' to determine layout
if (is.null(layout)) {
# Make the panel
# ncol: Number of columns of plots
# nrow: Number of rows needed, calculated from # of cols
layout <- matrix(seq(1, cols * ceiling(numPlots/cols)),
ncol = cols, nrow = ceiling(numPlots/cols))
}

if (numPlots==1) {
print(plots[[1]])

} else {
# Set up the page
grid.newpage()
pushViewport(viewport(layout = grid.layout(nrow(layout), ncol(layout))))

# Make each plot, in the correct location
for (i in 1:numPlots) {
# Get the i,j matrix positions of the regions that contain this subplot
matchidx <- as.data.frame(which(layout == i, arr.ind = TRUE))

print(plots[[i]], vp = viewport(layout.pos.row = matchidx$row, layout.pos.col = matchidx$col))
}
}
}

multiplot(qq_plot, Res_fac, Res_fit, Res_eu, cols=2)

}

Validate_assumptions(df = bread_example,model =  bread_example %>% lm(formula = height~time), factor = "time")

# qqnorm(y = bread_example %>% lm(formula = height~time) %>% residuals)

In this case we do seem to have a fairly normal response relationship but with some variability in the lower corner. Consider that we only have 12 points.

A more serious violation of assumption is heterogeneity of variances. In general when the linearity assumption is violated so will the homogeniety of variances assumption. To remedy this we can apply a transformation to the data to reconsile the linearity assumption.

Box-Cox Power Transformations

** When variation is relative to the mean observation within each treatment **

This transformation will change the data so that it is distributed normally. Normally distributed data has honogeneous variances

These transformations ensure that $$\sigma \propto \mu^{1 - \lambda}$$

To find $$\lambda$$ we can do:

box_cox <- boxcox(aov(bread_example,formula = height~time))

lambda = box_cox$x[which(box_cox$y == box_cox$y %>% max)] lambda ## [1] -0.5050505 Now we transform the data: bread_example_transformed <- bread_example %>% mutate(height = height^lambda) Let’s redo the normality validation on residuals: qqnorm(y = bread_example_transformed %>% lm(formula = height~time) %>% residuals()) And if we look at the hypothesis test with the now normally distributed data: bread_example_transformed %>% aov(formula = height~time) %>% summary ## Df Sum Sq Mean Sq F value Pr(>F) ## time 2 0.01732 0.008662 6.134 0.0209 * ## Residuals 9 0.01271 0.001412 ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Our new p-value is smaller which indicates that an observation as or more extreme than what we have is even more unlikely under the null hypothesis that there is no treatment effect. Distributional transformations ** When variation is relative to the mean observation within each treatment ** An alternative to box-cox power transformation OK, well let’s use the lognormal transformation and see the effect on the anova: bread_example_lognormal <- bread_example %>% mutate(height = log(height)) Let’s redo the normality validation on residuals: qqnorm(y = bread_example_lognormal %>% lm(formula = height~time) %>% residuals()) In this case we seem to fit the tail distribution better… And if we look at the hypothesis test with the now more? normally distributed errors: bread_example_lognormal %>% aov(formula = height~time) %>% summary ## Df Sum Sq Mean Sq F value Pr(>F) ## time 2 0.4598 0.22992 5.64 0.0258 * ## Residuals 9 0.3669 0.04077 ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 The p-value is again shifted towards 0.0258 which indicates with higher certainty that we reject the null hypothesis Alternatives to least squares regression Weighted linear model When we believe the heterogeneous variances are not related to the treatment mean we can use a weighted least squares Use sd() as weights within treatments: bread_example_Weighted <- bread_example %>% group_by(time) %>% mutate(sd_treatment = 1/sd(height)) bread_example_Weighted ## # A tibble: 12 x 4 ## # Groups: time [3] ## loaf time height sd_treatment ## <dbl> <fct> <dbl> <dbl> ## 1 1.00 35 4.50 1.04 ## 2 2.00 35 5.00 1.04 ## 3 3.00 35 5.50 1.04 ## 4 4.00 35 6.75 1.04 ## 5 5.00 40 6.50 0.485 ## 6 6.00 40 6.50 0.485 ## 7 7.00 40 10.5 0.485 ## 8 8.00 40 9.50 0.485 ## 9 9.00 45 9.75 0.735 ## 10 10.0 45 8.75 0.735 ## 11 11.0 45 6.50 0.735 ## 12 12.0 45 8.25 0.735 Now that we have the weights for each treatment we can use it in a weighted OLS: bread_example_Weighted %>% lm(formula = height~time,weights = bread_example_Weighted$sd_treatment) %>% summary
##
## Call:
## lm(formula = height ~ time, data = ., weights = bread_example_Weighted$sd_treatment) ## ## Weighted Residuals: ## Min 1Q Median 3Q Max ## -1.5543 -1.0203 0.0050 0.9611 1.5671 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 5.4375 0.5941 9.152 7.44e-06 *** ## time40 2.8125 1.0520 2.674 0.0255 * ## time45 2.8750 0.9220 3.118 0.0124 * ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 1.209 on 9 degrees of freedom ## Multiple R-squared: 0.5805, Adjusted R-squared: 0.4872 ## F-statistic: 6.226 on 2 and 9 DF, p-value: 0.02006 This gives us a p-value of 0.02006 which is very similar to the other transformed methods Creating a weighted OLS function So to generalize this for simple case of CRD: weighted_ols_anova <- function(df, formula_, factor, response) { factor_enq <- dplyr::enquo(factor) response_enq <- dplyr::enquo(response) # factor_quo <- dplyr::quo(factor) # response_quo <- dplyr::quo(response) df <- df %>% group_by(!!factor_enq) %>% mutate(sd_treatment = 1/sd(!!response_enq)) %>% ungroup # y = df %>% select(!!response_enq) %>% flatten_dbl # x = df %>% select(!!factor_enq) %>% flatten_dbl df %>% lm(formula = formula_, weights = sd_treatment) %>% anova # df %>% lm(y = y, x = x, weights = sd_treatment) %>% anova # return(df) } weighted_ols_anova(bread,height~time,time,height) ## Analysis of Variance Table ## ## Response: height ## Df Sum Sq Mean Sq F value Pr(>F) ## time 2 18.209 9.1047 6.2263 0.02006 * ## Residuals 9 13.161 1.4623 ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Generalized linear models Pol data using logistic link function assuming multinomial distribution Participants were asked to rank a treatment from 1 to 5 Data: mod_full <- MASS::polr(data = daewr::teach, formula = score ~ method, weight = count) mod_reduced <- MASS::polr(data = daewr::teach, formula = score ~ 1, weight = count) anova(mod_full,mod_reduced) ## Likelihood ratio tests of ordinal regression models ## ## Response: score ## Model Resid. df Resid. Dev Test Df LR stat. Pr(Chi) ## 1 1 294 885.9465 ## 2 method 292 876.2986 1 vs 2 2 9.64787 0.008035108 The reduced model predicts assuming only a global mean which conceptually means: $$y_{i,j} = \mu + \epsilon_{i,j} \ \ \ VS \ \ \ y_{i,j}=\mu + \tau_i + \epsilon_{i,j}$$ This shows that using different methods does make a difference compared to no particular method used. Because the p-value here rejects the null hypothesis that the two models are the same and therefore rejects the null hypothesis that all treatment effects are the same: $$\mu_i = \mu_j \ \forall \ {i,j}$$ How do we measure treatment effect? Let’s visualize the scores by method used # Predicted <- # daewr::teach %>% # mutate(predicted_score = mod_full %>% predict) # Predicted %>% # group_by(method) %>% # nest %>% # mutate(Histogram = data %>% map(~hist(.$score))) %>%
#   .Histogram

daewr::teach %>%
ggplot()+
geom_bar(aes(x = score,y = count),stat = "identity")+
facet_wrap(~method)+
ggtitle("Distribution of scores by method",subtitle = "Method 3 appears to outperform")

daewr::teach %>%
mutate_if(is.factor,as.numeric) %>%
group_by(method) %>%
summarise(mean_score = sum(score*count)/sum(count),
Total_votes = sum(count))
## # A tibble: 3 x 3
##    <dbl>      <dbl>       <dbl>
## 1   1.00       2.98        88.0
## 2   2.00       3.22       104
## 3   3.00       3.47       106

We can see that on average the 3rd treatment here would outperform the rest of the treatment groups from this designed experiment.

Test for assumption violations

We can’t repeat the usual battery of tests here since we are dealing with a categorical response and the idea of residual error should be defined differently from say $$y-\hat{y}$$.

In order to run the usual battery of validity tests we need the residuals of the fitted model. However, this is a categorical response experiment.

# Validate_assumptions(df = daewr::teach, model = mod_full)

Deternining the number of replicates

The idea of practical difference is important here. If the practitioner wants to monitor any difference in cell means larger than say 3 inches he would use the Fpower1 function with $$\Delta = 3$$.

Fpower1 calculates the power of the 1 way anova F distribution

Now we specify the number of replications we would like to calculate the power for given we know the variance of the experimental error $$\hat{\sigma}^2$$

If we assume the naive OLS this value is:

daewr::bread %>% lm(formula = height~time) %>% residuals() %>% var
## [1] 1.917614

Let’s assume the value $$\hat{\sigma}^2 = 1.917614$$

power <- Fpower1(alpha = rep(0.05, 6-2+1),
nlev = 3,
nreps = 2:6,
Delta = 3,
sigma = sqrt(1.917614)
)
power
##      alpha nlev nreps Delta    sigma     power
## [1,]  0.05    3     2     3 1.384779 0.2086501
## [2,]  0.05    3     3     3 1.384779 0.4366902
## [3,]  0.05    3     4     3 1.384779 0.6315614
## [4,]  0.05    3     5     3 1.384779 0.7730600
## [5,]  0.05    3     6     3 1.384779 0.8666144

This table then shows us that with as many as 6 replicates per treatment we can detect with ~87% accuracy a cell mean shift of 3 inches.

Based on the affordability in terms of time and money we can limit the factor under investigation using screening designs and perhaps limit the number of factors such that we get enough power out of the affordable number of replications.

Choosing optimal treatments

In general it is possible to construct hypothesis tests of comparisons before the design of experiments is carried out and responses are recorded but we will not focus on that here.

Instead we will assume the practitioner is interested in comparing treatments to one another in an unbiased way or compared to the current control treatment being used.

Unplanned Comparisons

When comparing specific treatments with one another after the experiment has been designed and carried out we must adjust for bias.

In R we can use the TukeyHSD function to compare cell mean shifts between different treatments

Sugarbeet dataset

This dataset is another CRD design. Let’s illustrate the TukeyHSD function here:

Sugerbeet_anova <- aov(yield ~ treat, data = daewr::sugarbeet)

Sugerbeet_anova
## Call:
##    aov(formula = yield ~ treat, data = daewr::sugarbeet)
##
## Terms:
##                    treat Residuals
## Sum of Squares  291.0050   29.5865
## Deg. of Freedom        3        14
##
## Residual standard error: 1.453727
## Estimated effects may be unbalanced
Sugerbeet_TukeyHSD <- TukeyHSD(Sugerbeet_anova, ordered = TRUE)

Sugerbeet_TukeyHSD
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
##     factor levels have been ordered
##
## Fit: aov(formula = yield ~ treat, data = daewr::sugarbeet)
##
## \$treat
##     diff        lwr       upr     p adj
## B-A  6.3  3.3122236  9.287776 0.0001366
## D-A 10.0  7.1655464 12.834454 0.0000004
## C-A 10.1  7.2655464 12.934454 0.0000003
## D-B  3.7  0.8655464  6.534454 0.0094231
## C-B  3.8  0.9655464  6.634454 0.0077551
## C-D  0.1 -2.5723484  2.772348 0.9995162

Here we can see that treatments C and D do not reject the null hypothesis that they have different cell means. However, the test also shows that no other treatments are considered the same and all reject at 5%.

Based purely on the confidence interval showed we could conclude that treatments C and D appear to be the most optimal if a higher mean in the response was required.

This function does not explicitly tell us what those means are, merely their differences.

Another, more conservative, function we can use is the SNK.test function from the agricolae package:

Sugarbeet_SNK <- SNK.test(Sugerbeet_anova, "treat", alpha = 0.05)

Sugerbeet_anova
## Call:
##    aov(formula = yield ~ treat, data = daewr::sugarbeet)
##
## Terms:
##                    treat Residuals
## Sum of Squares  291.0050   29.5865
## Deg. of Freedom        3        14
##
## Residual standard error: 1.453727
## Estimated effects may be unbalanced

This time we can clearly see the treatment means along with their summary statistics. As for rejection of the null hypothesis we can compare the M column in the groups output. Treatments that did not reject the null would have the same letters here.

Comparison to the current control treatment

To compare different treatments to the current control treatment we can use the function glht from the multcomp package

The glht function assumes that the 1st factor level is in fact the control treatment

Sugarbeet_glht <- glht(Sugerbeet_anova,linfct = mcp(treat = "Dunnett"), alternative = "greater")

Sugarbeet_glht %>% summary
##
##   Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: Dunnett Contrasts
##
##
## Fit: aov(formula = yield ~ treat, data = daewr::sugarbeet)
##
## Linear Hypotheses:
##            Estimate Std. Error t value Pr(>t)
## B - A <= 0   6.3000     1.0279   6.129 <1e-04 ***
## C - A <= 0  10.1000     0.9752  10.357 <1e-04 ***
## D - A <= 0  10.0000     0.9752  10.254 <1e-04 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- single-step method)

By specifying alternative = "greater" we can test the null hypothesis of the cell mean being greater than that of the control treatment using the Dunnett method.

Here we can again see that treatments C and D are superior to the control treatment A.


text:
Energy of particles in the nucleus

1. Dec 16, 2011

bharath666

1. Suppose that the potential seen by a neutron in a nucleus can be represented by a square well of width 10^(-12)cm with very high walls. What is minimum KE of the neutron in this potential ?

2. K.E = (1/2)mv^2

3. Its an isolated system, so it drops into its lowest energy state and the energy of the lowest state is higher than the minimum of potential energy. How to calculate the minimum potential energy with the width of well ? What to do with the width of well ?

2. Dec 17, 2011

Dick

I think you are supposed to estimate it using the Heisenberg uncertainty relation.

format: plain


text:
New Contributor

# Excel

Good day

Trust you are well

May you please assist, after i have made a pivot table on my excel and when i  sum up column B2: C3  and drag down its no carrying down the formula.I have to sum up each column separately. What formula do i use so i can drag down the answer. I remember we used to insert a D somewhere but i cant remember where. please assist?

=GETPIVOTDATA("Sum of Overdue + Due ";\$A\$4;"Legal Status ";"Domestic")+GETPIVOTDATA("Sum of Less Risk amount ";\$A\$4;"Legal Status ";"Domestic")

2 Replies


text:
Journal ArticleDOI

# Effect of grain network modifications due to additives on critical current (Ic) in Bi-2212 superconductor

01 May 1999-Physica C-superconductivity and Its Applications (North-Holland)-Vol. 316, Iss: 1, pp 119-128

Abstract: The presence of weak links in high-Tc superconductors is a major drawback in achieving high critical current densities The present study deals with the effect of additives (Ag, Ag2O and BaBiO3) on the weak link behaviour of Bi-2212 in bulk form It is observed that the addition of silver (Ag) metal powder improves the connectivity between the grains by proximity-effect and thereby enhances the current carrying capability at temperatures very close to Tc De Gennes and Clarke models have been invoked to establish that Bi-2212 containing insulating additives (BaBiO3 and Ag2O) show a superconductor–insulator–superconductor (S–I–S) type grain network and thereby enhance the weak link behaviour, whereas metallic Ag addition shows a superconductor–normal metal–superconductor (S–N–S) behaviour and is, therefore, a potential candidate for large scale applications Further support to this data is obtained from ac susceptibility studies carried out at different magnetic field strengths (01–40 Oe)
##### Citations
More filters

Journal Article
01 Jan 1988-Physical Review
Abstract: We calculate the transport critical-current density in a granular superconductor in magnetic fields below about 5 x 10/sup -3/ T. The field dependence in this region is assumed to be controlled by intragranular or intergranular Josephson junctions. Various model calculations are fitted to transport critical-current data on bulk Y/sub 1/Ba/sub 2/Cu/sub 3/O/sub 7/..sqrt../sub delta/ ceramic superconductors, whose average grain size somewhat exceeds 10 ..mu..m. The results yield an average junction cross-sectional area (thickness x length) of 4--6 ..mu..m/sup 2/. If the junctions are at the grain boundaries, a London penetration depth of about 150--300 nm is inferred, consistent with other estimates. We conclude that Josephson junctions are limiting the transport critical current in these samples and that they lie at the grain boundaries. The parameters of the fit are not consistent with Josephson junctions at twinning boundaries.

165 citations

Journal ArticleDOI
S. B. Mohamed, S. A. Halim1, H. AzhanInstitutions (1)
Abstract: The effect of doping on the superconductivity in Bi/sub 2/Pb/sub 0.6/Sr/sub 2/Ca/sub 2-x/R/sub x/Cu/sub 3/O/sub /spl delta// (R=Ba,Y,V,Zn,Sn) has been investigated by resistivity, ac susceptibility measurements and x-ray diffraction (XRD) analysis. All the dopants were incorporated in the calcium site with x ranging from 0.00 to 0.10. The temperature dependence of electrical resistance and ac susceptibility measurements was studied for these samples. The nature of the temperature dependence of the resistance curves indicates the presence of a superconducting transition between grains coupled by weak links. From the XRD data, it is observed that the volume percentage of the 2223 phase decreases with the increasing doping concentration. The presence of low T/sub c/ phase is also visible in the real component (/spl chi/'), of the susceptibility data, while the imaginary component (/spl chi/"), shows a shift towards lower temperature in the intergranular coupling peak, T/sub p/, as the dopant concentration increases. All the doping elements do not enhance the T/sub c/ zero but decreases its value from /spl sim/104 K to 88 K, 53 K, 79.6 K, 58 K and 53 K for Ba, Y, V, Zn and Y respectively for x=0.10. Barium doped samples are least affected by compositional variation and the zero resistance values are higher than that of the other doped samples.

10 citations

Journal ArticleDOI
Abstract: The production of bulk Bi2+xSr3-yCayCu 2O8+D (Bi-2212) superconductors for fault current limiter application was developed via a partial-melting route. Aiming high Ic (critical current), which is the essential superconducting characteristic for application of this material in the construction of Fault Current Limiters (FCL), the produced blocks have predominance of Bi-2212 phase (83 wt%), which characterizes with high values of zero and onset transport critical temperature of 92K and 97.5K, respectively. A relatively low transition width, DT, from the superconducting to the normal state of 5.5K, revealed a good intergrain connectivity. Consequently, current measurements on the blocks of Bi-2212 show promising Ic values of 230A and 850A for direct and alternate current, respectively. It is expected that further increases in the Ic values will depend on the elimination of an observed amorphous phase and further reduction of amount and grain sizes of secondary phases, still present in the blocks obtained by the proposed partial-melting route. This may be achieved by a further optimization of the partial-melting processing parameters.

6 citations

Journal ArticleDOI

3 citations

##### References
More filters

Journal ArticleDOI
Abstract: The properties of layered structures of superconducting (and non- superconducting) materials are studied, with emphasis on the related boundary- value problems. The experimental results are summarized, and theoretical interpretations are proposed for them. (T.F.H.)

1,031 citations

Journal ArticleDOI
01 Jun 1988-Physical Review B
TL;DR: It is concluded that Josephson junctions are limiting the transport critical current in these samples and that they lie at the grain boundaries.
Abstract: We calculate the transport critical-current density in a granular superconductor in magnetic fields below about 5 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}3}$ T The field dependence in this region is assumed to be controlled by intragranular or intergranular Josephson junctions Various model calculations are fitted to transport critical-current data on bulk ${\mathrm{Y}}_{1}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ ceramic superconductors, whose average grain size somewhat exceeds 10 \ensuremath{\mu}m The results yield an average junction cross-sectional area (thickness x length) of 4-6 \ensuremath{\mu}${\mathrm{m}}^{2}$ If the junctions are at the grain boundaries, a London penetration depth of about 150-300 nm is inferred, consistent with other estimates We conclude that Josephson junctions are limiting the transport critical current in these samples and that they lie at the grain boundaries The parameters of the fit are not consistent with Josephson junctions at twinning boundaries

215 citations

Journal ArticleDOI
M. F. Chisholm1, Stephen J. Pennycook1Institutions (1)
01 May 1991-Nature
Abstract: THE critical current density across individual grain boundaries in thin films of the high-Tc superconductor YBa2Cu3O7–δ (YBCO) has been found1–4 to be inversely proportional to lattice misorientation for tilts up to ∼10°. Reports of impurity segregation5,6 at grain boundaries, and variations in the chemical stoichiometry7,8, have led to the view that deviations from the ideal composition are responsible for the depressed superconducting order parameter at the boundary. Here we present images of YBCO grain boundaries obtained by a scanning transmission electron microscope in Z-contrast mode9,10, which show that chemical segregation does not necessarily occur at these boundaries. A simple model of the strain associated with the grain-boundary dislocations provides a reasonable physical explanation of the suppressed superconductivity. The surprisingly large effect of strain implied by our model has implications beyond critical currents, for the physics and applications of any thin-film YBCO structures involving strained epitaxial layers.

188 citations

Journal Article
01 Jan 1988-Physical Review
Abstract: We calculate the transport critical-current density in a granular superconductor in magnetic fields below about 5 x 10/sup -3/ T. The field dependence in this region is assumed to be controlled by intragranular or intergranular Josephson junctions. Various model calculations are fitted to transport critical-current data on bulk Y/sub 1/Ba/sub 2/Cu/sub 3/O/sub 7/..sqrt../sub delta/ ceramic superconductors, whose average grain size somewhat exceeds 10 ..mu..m. The results yield an average junction cross-sectional area (thickness x length) of 4--6 ..mu..m/sup 2/. If the junctions are at the grain boundaries, a London penetration depth of about 150--300 nm is inferred, consistent with other estimates. We conclude that Josephson junctions are limiting the transport critical current in these samples and that they lie at the grain boundaries. The parameters of the fit are not consistent with Josephson junctions at twinning boundaries.

165 citations

Journal ArticleDOI
Abstract: The resistance of thin-film lead-copper-lead junctions has been studied with the lead in the superconducting state. The junctions will sustain a supercurrent up to a certain critical value above which a voltage appears, rising smoothly from zero as the current is increased. The effect of a magnetic field upon the critical current has demonstrated that the sandwiches behave phenomenologically as Josephson junctions. The critical current rises rapidly as the temperature is lowered, decreases exponentially with increasing thickness of copper and mcreases with increase of the mean free path of the copper. A simplified version of the de Gennes theory of the proximity effect has been used to account quantitatively for this behaviour. The experiments show that the coherence length of the paired electrons in the copper increases as the temperature decreases, implying that thermal fluctuations govern the decay of the pairs. From the value of the decay length, the interaction parameter in copper is estimated to lie between +0$\cdot$06 and +0$\cdot$14. The properties of these junctions are compared with those of junctions with insulating barriers.

159 citations

##### Network Information
###### Related Papers (5)
15 Mar 2004, Physica C-superconductivity and Its Applications

01 Feb 2003, Solid State Communications

01 Jun 2002, Journal of Superconductivity

Abhijit Ray, T. K. Dey +1 more

01 Nov 2001, Journal of Magnetism and Magnetic Materials

A. Sedky, M.I. Youssif

01 Nov 2000, Physica C-superconductivity and Its Applications

Migaku Oda, T. Matsuzaki +2 more

##### Performance
###### Metrics
No. of citations received by the Paper in previous years
YearCitations
20141
20021
20011
19881


text:
Department of

# Mathematics

Seminar Calendar
for events the day of Monday, March 6, 2017.

.
events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    February 2017            March 2017             April 2017
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4             1  2  3  4                      1
5  6  7  8  9 10 11    5  6  7  8  9 10 11    2  3  4  5  6  7  8
12 13 14 15 16 17 18   12 13 14 15 16 17 18    9 10 11 12 13 14 15
19 20 21 22 23 24 25   19 20 21 22 23 24 25   16 17 18 19 20 21 22
26 27 28               26 27 28 29 30 31      23 24 25 26 27 28 29
30

Monday, March 6, 2017

4:00 pm in 245 Altgeld Hall,Monday, March 6, 2017

#### Stability, Eigenvalues and Index Theorems

###### Jared Bronski (Department of Mathematics, University of Illinois)

4:00 pm in 243 Altgeld Hall,Monday, March 6, 2017

#### Contact embeddings in three dimensions

###### Olguta Buse (Indiana University-Purdue University Indianapolis )

Abstract: We study neighborhoods of transversal knots in contact thee dimensional manifolds. By doing so, we introduce the concepts of capacity and shape for a three dimensional contact manifold $(M, \xi)$ relative to a transversal knot $K$. We will explain the connection with the existing literature and provide our main computation for the shape in the case of lens spaces $L(p,q)$ with a toric contact structure. The main tool used here are rational surgeries which will be explained through their toric interpretations based on the continuous fraction expansions of $p/q$. This is joint work with D. Gay.

5:00 pm in 241 Altgeld Hall,Monday, March 6, 2017

#### Embedding of Heisenberg group in L_1

###### Jeremy and Chris (UIUC)

Abstract: This is an introduction to a series of lectures showing that the Heisenberg group does not embed in (commutative) L_1


text:
Type Reference
Source SLScanner/FiniteAutomaton.cpp
Source SLScanner/DeterministicFiniteAutomaton.cpp
Test SLScanner/TestDeterministicFiniteAutomaton.cpp

## Definition

$S$ is the finite set of states in the recognizer, along with an error state $s_e$

$\Sigma$ is the finite alphabet used by the recognizer. Typically, $\Sigma$ is the union of the edge labels in the transition diagram.

$\delta(s, c)$ is the recognizer’s transition function. It maps each state $c\in \Sigma$ and each character $c ∈ \Sigma$ into some next state. In state si with input character $c$, the $FA$ takes the transition $s_i\rightarrow^c \delta (s_i, c)$.

$s_0\in S$ is the designated start state.

$S_A$ is the set of accepting states, $S_A\subseteq S$. Each state in $S_A$ appears as a double circle in the transition diagram.

## Design

According to the definition of Finite Automaton, I have designed the class FiniteAutomaton in below structure. Actually, starting state $s_0$ is always $s_0$, so I didn’t describe it explicitly in the class. Before building the class structrue, I decided to define some fundamental types for the internal elements of a finite automaton.

typedef int32_t State;
typedef char Alphabet;
typedef std::pair<State, Alphabet> Move;
typedef std::map<Move, State> TransitionSet;
typedef std::set<State> StateSet;
typedef std::set<Alphabet> AlphabetSet;
typedef enum {
Accepted = 1, NotAccepted = 0, Trapped = -1
} StateType;

Followings are some necessary elements for a finite automaton.

StateSet states;
TransitionSet transitions;
AlphabetSet alphabets;
StateSet acceptingStates;
State currentState;

And those values has been defined outside the FiniteAutomaton class.

const FiniteAutomaton::State StartState = 0;
const FiniteAutomaton::State TrapState = -1;

The FiniteAutomaton class is a base class for DeterministicFiniteAutomaton. And we can only use DFA to match the strings. So the most important part of the scanner is the fundamental DFA.

So I built the following function to simulate the actions of real DFA.

State transite(Alphabet input);
Silly::DeterministicFiniteAutomaton::State
Silly::DeterministicFiniteAutomaton::transite(Silly::DeterministicFiniteAutomaton::Alphabet input) {
if (isFinished) {
reboot();
isFinished = false;
}
if (alphabets.find(input) != alphabets.end() && transitions.find(Move(currentState, input)) != transitions.end()) {
State nextState = transitions[Move(currentState, input)];
currentState = nextState;
currentAlphabet = input;
return nextState;
} else {
currentState = TrapState;
return TrapState;
}
}

The transite function needs to check if the DFA has finished a match task executed by match function. And one transition means finding an accessible transition from all transitions. If it does not exist in the transitions, the DFA may cause a trap state to exclaim the match is not successful and it can not move to other states unless reboot is executed.

Actually the structure of a DFA is simple and you must manually set all the elements for the DFA by using the following constructor function.

DeterministicFiniteAutomaton(
StateSet states_,
TransitionSet transitions_,
AlphabetSet alphabets_,
StateSet acceptingStates_);

## Test

So I used following test case to check the availability of the DFA.

DeterministicFiniteAutomaton.SimpleTest:

Test Result:

String StateType TestResult
A12345 Accepted PASS
A Accepted PASS
Z3910 Accepted PASS
Z99999 Accepted PASS
Z9999D Trapped PASS
Trapped PASS
3232 Trapped PASS

DeterministicFiniteAutomaton.FloatNumberTest:

The definition of test DFA is omitted, you can reference it in the SLScanner/TestDeterministicFiniteAutomaton.cpp.

String StateType TestResult
0.13423231 Accepted PASS
0.1342E+213.4 Accepted PASS
+13 Accepted PASS
+13e-19 Accepted PASS
.234144 Trapped PASS
.234122.21310012. Trapped PASS
.234E NotAccepted PASS

DeterministicFiniteAutomaton.CamelCaseTest:

The definition of test DFA is omitted, you can reference it in the SLScanner/TestDeterministicFiniteAutomaton.cpp.

String StateType TestResult
HelloWorld Accepted PASS
GoodBoy Accepted PASS
GoodB NotAccepted PASS
GoodB8 Trapped PASS


text:
axiom-developer
[Top][All Lists]

## [Axiom-developer] [#103 solve(z=z, z) ] solve(z=z, z) should return [z=z

 From: Bill Page Subject: [Axiom-developer] [#103 solve(z=z, z) ] solve(z=z, z) should return [z=z] Date: Thu, 17 Feb 2005 17:09:17 -0600

Someone wrote:

This should return [ ] as in (1)

but I disagree. The (trivial) solution of 'z=z' for the variable 'z'
is obviously [z=z] just as the solution of 'w=z' for 'z'
is [z=w]
\begin{axiom}
solve(w=z,z)
\end{axiom}

Similarly, I think the only reasonable result of 'solve(0=0,z)'
is also [z=z]. So I agree that the result should be
that same as (1) except that the result of (1) is also wrong!

Note: These are the same as the results returned by Maple.
--


text:
another diameter-perimeter-area inequality

Recently I learnt that $$\inf\frac{diam(C)(per(C)-2diam(C))}{area(C)}=0$$ where the infimum is taken over all plane convex bodies $C$ (say, with non-zero area). In other words, there is no non-trivial (with $c>0$) inequality of the form $$diam(C)(per(C)-2diam(C))\geq c\cdot area(C),$$ that would hold for all $C$.

Now I'm wondering about inequalities of the form $$diam(C)(per(C)-(2-\epsilon)diam(C))\geq c_{\epsilon}\cdot area(C)$$ for $\epsilon>0$. Clearly, such an inequality is true for $c_\epsilon=\frac{4\epsilon}{\pi}$ (since $per(C)\geq2diam(C)$ and $diam(C)^2\geq4/\pi\cdot area(C)$).

The question is: what is the best $c_{\epsilon}$ for which the inequality holds? When would equality be achieved (it might depend on $\epsilon$)?

-


text:
# 6 hour ride 38.4 killometers

###### Question:

6 hour ride 38.4 killometers

### How many square units are in the greatest area that can be enclosed by a rectangle whose perimeter is 20 units?

How many square units are in the greatest area that can be enclosed by a rectangle whose perimeter is 20 units?...

### How do you write 0.056 as a rational number

how do you write 0.056 as a rational number...

### The biggest danger of relying on case-study evidence is that it A)is based on naturalistic observation.B)may be unrepresentative of what is generally true.C) overestimates the importance of operational definitions. D) leads us to underestimate the causal relationships between events

The biggest danger of relying on case-study evidence is that it A)is based on naturalistic observation.B)may be unrepresentative of what is generally true.C) overestimates the importance of operational definitions. D) leads us to underestimate the causal relationships between events...

### A new energy drink advertises 106 calories for 8 ounces. How many calories are in 12 ounces of the drink?

A new energy drink advertises 106 calories for 8 ounces. How many calories are in 12 ounces of the drink?...

### Question 1 How did the Leo Frank case impact Georgia society? The rise in antisemitism in Georgia that resulted from the case contributed to the reemergence of the Ku Klux Klan. The increase in migration from the north to Georgia in response to the case helped reinvigorate the state's economy. The state government struck down various discriminatory laws in response to the events of the case to protect religiou ethnic minorities. The federal government intervened to remove Georgia's governor from

Question 1 How did the Leo Frank case impact Georgia society? The rise in antisemitism in Georgia that resulted from the case contributed to the reemergence of the Ku Klux Klan. The increase in migration from the north to Georgia in response to the case helped reinvigorate the state's economy. The s...

### Project managers find many advantages in having diverse teams, as considering diverse perspectives in making decisions can help avoid major risks that a single perspective would not uncover. True False

Project managers find many advantages in having diverse teams, as considering diverse perspectives in making decisions can help avoid major risks that a single perspective would not uncover. True False...

### Mental health disorders may NOT affect...

Mental health disorders may NOT affect......

### This is for Health! Please help Which part of the brain is affected when a person experiences a "blackout" in which they can't remember entire events?

This is for Health! Please help Which part of the brain is affected when a person experiences a "blackout" in which they can't remember entire events?...

### Shelly got 60 questions correct on her math test.If she got 75% how many questions were on the test?

Shelly got 60 questions correct on her math test.If she got 75% how many questions were on the test?...

### Please help me with this biology question...... Predict what will happen to the shrinkage rate of shrinkage vacuole if Paramecium sp. put in a concentrated salt solution.

Please help me with this biology question...... Predict what will happen to the shrinkage rate of shrinkage vacuole if Paramecium sp. put in a concentrated salt solution....

### What does a bird , beetle and a fungus have in common

What does a bird , beetle and a fungus have in common...

### I will give the BRAINIEST Find the values of x and y in the diagram below

I will give the BRAINIEST Find the values of x and y in the diagram below...

### Creeping obesity is described as… A) Increased teenage obesity B) Gradual weight gain during aging C) Fat gained during teen years D) Obese grandparents

Creeping obesity is described as… A) Increased teenage obesity B) Gradual weight gain during aging C) Fat gained during teen years D) Obese grandparents...

### . Give an example for the following: a. horizontal merger b. vertical merger c. multinational corporation

. Give an example for the following: a. horizontal merger b. vertical merger c. multinational corporation...

### How many tons are in 5,000 lbs?

how many tons are in 5,000 lbs?...

### Find the slope of the line containing the given information (3/2,-3) and (1/2,-7)

Find the slope of the line containing the given information (3/2,-3) and (1/2,-7)...


text:
Software  ›   pipelines

# Customized Secondary Analysis using cellranger-dna reanalyze

The cellranger-dna reanalyze command re-runs copy number variation analysis on the read counts per bin per cell matrix, optionally with different parameters, a subset of cells, or structured by a user-provided Newick-formatted tree.

## Command Line Interface

These are the most common command line arguments (run cellranger-dna reanalyze --help for a full list):

ArgumentDescription
--id=IDA unique run ID string: e.g. AGG123_reanalysis
--cnv-data=H5Path of cnv_data.h5 from a previous cellranger-dna invocation (cellranger-dna cnv, cellranger-dna reanalyze, or cellranger-dna aggr).
--reference=PATHPath to a Cell Ranger DNA reference.
--csv=CSVPath of CSV file containing barcode subset definitions (see Configuration).
--description=TEXT(optional) More detailed sample description.
--tree=NEWICK(optional) Path to a Newick format tree file that defines the new tree structure. If this flag is not set, the data will be clustered as-is. Each leaf of this tree must correspond to a row in the CSV passed to --csv.
--soft-min-avg-ploidy=FLOAT(optional) Use a known lower limit on the average ploidy of the sample.
--soft-max-avg-ploidy=FLOAT(optional) Use a known upper limit on the average ploidy of the sample.

After specifying these input arguments, run cellranger-dna reanalyze. In this example, we're reanalyzing the results of an aggregation named AGG123:

$cd /home/jdoe/runs$ ls -1 AGG123/outs/*.h5 # verify the input file exists
AGG123/outs/cnv_data.h5
\$ cellranger-dna reanalyze --id=AGG123_reanalysis \
--cnv-data=AGG123/outs/cnv_data.h5 \
--csv=AGG123_reanalysis.csv \
--reference=/home/jdoe/refs/GRCh37

The pipeline will begin to run, creating a new folder named with the specified reanalysis ID (e.g. /home/jdoe/runs/AGG123_reanalysis). If this folder already exists, cellranger-dna will assume it is an existing pipestance and attempt to resume running it.

## Pipeline Outputs

A successful run should conclude with a message similar to this:

2019-05-06 21:40:29 [runtime] (run:local)       ID.AGG123_reanalysis.CNV_REANALYZER_CS.DLOUPE_PREPROCESS.fork0.join
2019-05-06 21:40:31 [runtime] (chunks_complete) ID.AGG123_reanalysis.CNV_REANALYZER_CS._POSTPROCESSING.MAKE_WEBSUMMARY
2019-05-06 21:40:37 [runtime] (join_complete)   ID.AGG123_reanalysis.CNV_REANALYZER_CS.DLOUPE_PREPROCESS

Outputs:
- HDF5 file with CNV data:          /home/jdoe/runs/AGG123_reanalysis/outs/cnv_data.h5
- Loupe visualization file:         /home/jdoe/runs/AGG123_reanalysis/outs/dloupe.dloupe
- CNV calls with imputation:        /home/jdoe/runs/AGG123_reanalysis/outs/node_cnv_calls.bed
- CNV calls without imputation:     /home/jdoe/runs/AGG123_reanalysis/outs/node_unmerged_cnv_calls.bed
- Per-cell summary metrics:         /home/jdoe/runs/AGG123_reanalysis/outs/per_cell_summary_metrics.csv
- Reanalyze specification:          /home/jdoe/runs/AGG123_reanalysis/outs/reanalyze.csv
- Analysis summary metrics:         /home/jdoe/runs/AGG123_reanalysis/outs/summary.csv
- Newick guide-tree for clustering: null

Pipestance completed successfully!

Refer to the Analysis page for an explanation of the output.

## Configuration

### Selecting Cells Using a List of Cell Barcodes

You may select your barcodes of interest for each group directly, using a separate barcodes file for each group.

A text editor or Excel may be used to construct the configuration CSV. Your spreadsheet may look something like this:

AB
1library_idbarcodes_csv
2normal/home/jdoe/normal_barcodes.csv
3tumor_primary/home/jdoe/tumor_primary_barcodes.csv
4tumor_metastases/home/jdoe/tumor_metastases_barcodes.csv

When you save this to CSV, it will look something like this:

library_id,barcodes_csv
normal,/home/jdoe/normal_barcodes.csv
tumor_primary,/home/jdoe/tumor_primary_barcodes.csv
tumor_metastases,/home/jdoe/tumor_metastases_barcodes.csv

The barcodes CSV files will each have one barcode entry per line, including the GEM well suffix (see GEM wells). Each such file will look something like:

AAACGGGTCAAAGTGA-1
AAAGATGCAATGGGAC-1
...
TTTGTCATCCGCACGA-1

### Selecting the Cells of a Group of Interest

You may use a Group ID, determined perchance by exploring the data in Loupe scDNA Browser, as a proxy for a list of barcodes. In this case, all constituent cells of that group will be included.

As before, a text editor or Excel may be used to construct the CSV. Your spreadsheet may look something like this:

AB
1library_idnode_id
2normal842
3tumor_primary912
4tumor_metastases919

When you save this to CSV, it will look something like this:

library_id,node_id
normal,842
tumor_primary,912
tumor_metastases,919

### Guiding Clustering with a Custom Newick Tree

If you define more than one group in the configuration CSV, you must also guide clustering by providing a Newick-formatted tree. For instance, if you have defined three groups in the CSV: normal, tumor_primary, and tumor_metastases, you may force the pipeline to arrange them with the normal tissue as an outgroup:

(normal,(tumor_primary,tumor_metastases));

## Common Use Cases

These examples illustrate how you may use cellranger-dna reanalyze in some common situations.

### 1. Impose Upper or Lower Limits on the Copy Number Variation Analysis

When the outputs of a cellranger-dna cnv suggest the use of the options for imposing upper or lower limits on the average ploidy, cellranger-dna reanalyze is the most suitable way to do so, avoiding the significant computational overhead of the read processing stages of the cellranger-dna cnv.

### 2. Omit Replicating or Noisy Cells from the Analysis

You may wish to omit noisy or replicating cells from the outputs of the analsis. These cells can be identified from the per_cell_summary_metrics.csv or from exploration in the Loupe scDNA Browser. From these sources, a barcodes.csv file (with one cell barcode per line) may be constructed containing only the cell barcodes of interest, which when employed with cellranger-dna reanalyze will produce outputs with only those cells.

### 3. Imposing a Structure on the Clustering

As show in the example above, you may impose a self-chosen tree structure on the clustering using a Newick-formatted tree.

• 1.0
• Cell Ranger DNA v1.1 (latest)