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# SOCI8015 Lab 7: Normal Distribution & Confidence Intervals

We will use six packages for this lab. Load them using the following code:

library(dplyr)
library(sjlabelled)
library(sjmisc)
library(summarytools)
library(gmodels)
library(gplots)

# Import the 2012 AuSSa dataset.

This lab uses the 2012 AuSSa dataset. You can download the file of this dataset on the course website(iLearn). Download the data file and put it into your working directory. Then, run the following code:

aus2012 <-readRDS("aussa2012.rds")

The dataset is loaded as aus2012.

# How to create a variable of z-scores

We will make a new variable which is the standardised scores (z-scores) of wrkhrs(hours spent on work per week). std(data name, variable name, append = TRUE) from the sjmisc package will add a variable of standardised scores to your dataset. Run the following code.

aus2012 <- std(aus2012, wrkhrs, append = TRUE)

Then, you will see wrkhrs_z added to your dataset. The name of the new variables is always ‘old variable name_z’. Let’s check this newly created variable by running the following code:

aus2012 %>%
select("id", "wrkhrs", "wrkhrs_z") %>%
head()
## # A tibble: 6 x 3
##        id wrkhrs wrkhrs_z
##     <dbl>  <dbl>    <dbl>
## 1 2.01e15     NA    NA
## 2 2.01e15     NA    NA
## 3 2.01e15     NA    NA
## 4 2.01e15      7    -2.01
## 5 2.01e15      6    -2.08
## 6 2.01e15     NA    NA

Out of the aus2012 dataset, we select three variables: id, wrkhrs, and wrkhrs_z (If you don’t understand, see Creating a dataset of specific variables. head() shows data for the first six cases. Now you see the original and standardised scores of wrkhrs for the first six cases.

# How to compute the z-score of a specific value and its associated probabilities

In the week 8 lecture, you learned how to calculate the z-score of a specific value and find its associated probabilities using the standard normal table. This section will introduce how to perform this job in R.

Suppose that you want to get the z-score of respondents who work 50 hours per week and its associated probabilities. To do this job, you need to run the following code first. Run this code without changing anything.

getZ <- function(v1, v2){
score <- (v1 -mean(v2, na.rm = TRUE))/sd(v2, na.rm = TRUE)
prob <- pnorm(abs(round(score, digits = 2)))
cat(" 1. Z-score for", v1, ":", round(score, digits = 2))
cat("\n 2. The area between mean and Z-score (B)", ":", round(prob-0.5, digits = 4))
cat("\n 3. The area beyond Z-score (C)", ":", 0.5-round(prob-0.5, digits = 4))
}

This is a custom code that I made for computing the z-score of a specific value and its associated probabilities. After running this, you will see getZ in the tab of Environment.

Now, compute the z-score of respondents who work 50 hours per week and its associated probabilities using this function. getZ(value, data name$variable name) shows all the necessary information. getZ(50, aus2012$wrkhrs)
##  1. Z-score for 50 : 0.82
##  2. The area between mean and Z-score (B) : 0.2939
##  3. The area beyond Z-score (C) : 0.2061
• First, it shows the z-score.
• Second, it shows the areas between mean and z-score that corresponds to the B areas in the Standard Normal Table that I posted in week 8.
• Third, it shows the areas beyond Z-score that corresponds to the C areas in the Standard Normal Table.

# How to compute the confidence intervals for continuous variables

To compute confidence intervals, we use ci() from the gmodels package. ‘ci(data name$variable name, confidence = value, na.rm = TRUE)’ computes the confidence interval of a variable of your choice. For example, you can calculate the confidence interval of wrkhrs using the following code: ci(aus2012$wrkhrs, confidence = 0.95, na.rm = TRUE)
##   Estimate   CI lower   CI upper Std. Error
## 37.5182482 36.5568291 38.4796673  0.4899092

In the output, you may see a warning message saying “No class or unkown class. Using default calcuation”. Ignore this warning message. It will not affect your analytic outcome. As long as you see the confidence interval, it is fine. Estimate is the mean. CI Lower is the lower limit of confidence intervals, and CI Upper is the upper limit of confidence intervals. Std. Error is a standard error of a variable. In this output, the average is 37.52, the 95% confidence interval is the range between 36.56 and 38.48, and the standard error is 0.49.

na.rm = TURE’ means that cases with missing values are excluded in calculating the confidence intervals. ‘confidence = value’ set the confidence level. In this case, we use 0.95 because we want to get 95% confidence intervals. If you want to get the 90% confidence interval, change the value into 0.90 as in the below code.

ci(aus2012$wrkhrs, confidence = 0.90, na.rm = TRUE) ## Estimate CI lower CI upper Std. Error ## 37.5182482 36.7116392 38.3248571 0.4899092 # How to compute the confidence interval of proportions The confidence interval of proportions can be computed only for binary variables where values are either 0 or 1. Suppose that we want to calculate the 95% confidence intervals for the proportion of those who agree or strongly agree with the statement that a working mother can establish as warm and secure relationships with her children as a mother who does not work(fechld). First, we need to recode fechld into a binary variable in which 1 = “agree” and 0 = “don’t agree”. Before doing it, please check the labels for fechld in the codebook of the 2012 AuSSa. The below codes recode fechld in such a way (If you don’t understand them, see Recoding variables. aus2012 <- rec(aus2012, fechld, rec = "1:2=1; 3:5=0", append = TRUE) aus2012$fechld_r <- set_labels(aus2012$fechld_r, labels = c("agree" = 1, "don't agree" = 0)) Then, run the following code: ci(aus2012$fechld_r, confidence = 0.95, na.rm = TRUE)
##   Estimate   CI lower   CI upper Std. Error
## 0.68343949 0.66040651 0.70647247 0.01174267

The output shows the 95% confidence interval of the proportion of people who agree or strongly agree with the statement.

# How to compute confidence intervals for sub-groups

We often need to compute the confidence intervals for sub-groups such as male and female respondents. Suppose that we want to calculate the confidence intervals of working hours per week(wrkhrs) for men and women respectively. The first step is to create a dataset for each sub-groups. You learned how to do this in Creating a dataset of a sub-group. The below codes make two datasets, one for male and the other for female respondents.

aus2012.m <- aus2012 %>%
filter(sex==1)
aus2012.f <- aus2012 %>%
filter(sex==2)

Then, using these datasets, compute the 90% confidence intervals for men and women. The codes are:

ci(aus2012.m$wrkhrs, confidence = 0.9, na.rm = TRUE) # for male ## Estimate CI lower CI upper Std. Error ## 43.7266355 42.6159862 44.8372848 0.6737619 ci(aus2012.f$wrkhrs, confidence = 0.9, na.rm = TRUE) # for female
##   Estimate   CI lower   CI upper Std. Error
## 32.5876686 31.5609295 33.6144076  0.6230967

# How to visualise the confidence intervals between groups

Visualising the confidence intervals between groups could be a good way to examine the relationship between variables of groups and your choice. To do this, we use plotmeans() from the gplots package.

plotmeans(variable of your choice ~ to_label(group variable), data = data name, p = values for confidence levels, n.label = FALSE, connect = FALSE, xlab = “Label of X-axis”, ylab = “Label of Y-axis”)’ makes the plot of the confidence interval for all groups. The following code generates a plot of 90% confidence intervals for all gender categories.

plotmeans(wrkhrs ~ to_label(sex), data = aus2012, p = 0.90, n.label = FALSE,
connect = FALSE, xlab = "Gender", ylab = "Hours worked per week")

n.label = FALSE’ means that the plot does not show the total number of cases for each group. ‘connect = FALSE’ means that the plot does not make lines connected between the average for each group. If you want to draw a connected line, change it into ‘connect = TRUE’.

Note: If the plot is not displayed correctly (e.g., no confidence intervals), increase the size of plot areas. Move your cursor at the border between plot areas and console (see Figure 1). Then, move up while keeping clicking the left mouse button. This will increase the height of plot areas.

Move your cursor at the border between plot areas and right panes (see Figure 2). Then, move right while keeping clicking the left mouse button. This will increase the width of plot areas.

After increasing the size of plot areas, run the code for confidence interval plots again. It will show perfect plots.

# Lab 7 Participation Activity

No Lab Participation Activity this week. Completing R Analysis Task 2 will contribute to your participation mark.

The R codes you have written so far look like:

###############################################################################
# Lab 7: Normal Distribution & Confidence Interval
# 3/5/2021
# SOCI8015 & SOCX8015
################################################################################

library(dplyr)
library(sjlabelled)
library(sjmisc)
library(summarytools)
library(gmodels)
library(gplots)

# Import the 2012 AuSSA dataset

# How to create a variable of z-scores
aus2012 <- std(aus2012, wrkhrs, append = TRUE)

aus2012 %>%
select("id", "wrkhrs", "wrkhrs_z") %>%

# How to compute the z-score of a specific value and its associated probabilities
getZ <- function(v1, v2){
score <- (v1 -mean(v2, na.rm = TRUE))/sd(v2, na.rm = TRUE)
prob <- pnorm(abs(round(score, digits = 2)))
cat(" 1. Z-score for", v1, ":", round(score, digits = 2))
cat("\n 2. The area between mean and Z-score (B)", ":", round(prob-0.5, digits = 4))
cat("\n 3. The area beyond Z-score (C)", ":", 0.5-round(prob-0.5, digits = 4))
}

getZ(50, aus2012$wrkhrs) # How to compute confidence intervals of numbers ci(aus2012$wrkhrs, confidence = 0.95, na.rm = TRUE)
ci(aus2012$wrkhrs, confidence = 0.90, na.rm = TRUE) # How to compute the confidence interval of proportions aus2012 <- rec(aus2012, fechld, rec = "1:2=1; 3:5=0", append = TRUE) aus2012$fechld_r <- set_labels(aus2012$fechld_r, labels = c("agree" = 1, "don't agree" = 0)) ci(aus2012$fechld_r, confidence = 0.95, na.rm = TRUE)

# How to compute confidence intervals for sub-groups
aus2012.m <- aus2012 %>%
filter(sex==1)
aus2012.f <- aus2012 %>%
filter(sex==2)

ci(aus2012.m$wrkhrs, confidence = 0.9, na.rm = TRUE) ci(aus2012.f$wrkhrs, confidence = 0.9, na.rm = TRUE)

# How to visualise the confidence intervals between groups
plotmeans(wrkhrs ~ to_label(sex), data = aus2012, p = 0.90, n.label = FALSE,
connect = FALSE, xlab = "Gender", ylab = "Hours worked per week")
Last updated on 01 May, 2021 by Dr Hang Young Lee(hangyoung.lee@mq.edu.au)


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# What's New?

This brief guide outlines the new and changed features in the Rhino C/C++ SDK.

## Overview

The Rhino C/C++ SDK is not an abstract SDK. That is, the native classes and functions that are made available in the SDK are also used internally by Rhino. Thus, when the signatures of classes or functions change, all developers, both internal and external, are required to modify their source code to accommodate for the change. For this reason, the Rhino C/C++ SDK was not broken between Rhino 4 and 5. In doing this, plug-ins that worked in Rhino 4 also worked in Rhino 5.

A lot of time has passed since the Rhino 4 C/C++ SDK was made available. And although there was quite a bit of new functionality added to Rhino 5, some of it required some creative programming in order not to break backwards compatibility with Rhino 4.

In order to continue to move Rhino forward, breaking changes needed to be made to the SDK. The following document attempts to describe what has been added, what has changed, and how to deal with these changes.

## Breaking Changes

Although the breaking changes may seem numerous, most fall within the following categories.

### Visual Studio 2017

To write C++ plug-ins for Rhino 6, you will need Visual Studio 2017.

What’s really exciting is that the free Community edition of Visual Studio will work to build plug-ins for Rhino 6. Of course, you can also use either the Professional or Enterprise edition.

### Multi-Document Support

One of the primary goals for Rhino 6 was to consolidate the Rhino for Windows and Rhino for Mac source code into a single codebase. In order to do this, the source code had to become more multiple-document aware, as Rhino for Mac handle multiple documents. Note, Rhino 6 for Windows is still a single document application.

Thus, many SDK functions now require the developer to pass either a pointer or a reference to the active document or the active document’s runtime serial number.

An example of this is the CRhinoDisplayConduit class, which now requires the document serial number in which it will operate. In Rhino 5, you could enable a display conduit in a plug-in command as follows:

    CMyDisplayConduit conduit;
conduit.Enable();
context.m_doc.Redraw();

In Rhino 6, you need to do the following:

    CMyDisplayConduit conduit;
conduit.Enable(context.m_doc.RuntimeSerialNumber());
context.m_doc.Redraw();

A number of SDK functions have been modified to require some data from the active document. This is because SDK functions can no longer assume there is a single document.

An example of this is the RhinoPointInPlanarClosedCurve function, which now requires the absolute tolerance from the active document. In Rhino 5, you could use this function in a command as follows:

    int rc = RhinoPointInPlanarClosedCurve(point, closed_curve, plane);

In Rhino 6, you will need to do the following:

    double tolerance = context.m_doc.AbsoluteTolerance();
int rc = RhinoPointInPlanarClosedCurve(point, closed_curve, plane, tolerance);

### MFC Free

The Rhino 6 C/C++ SDK is now MFC free. That is, there are no longer any MFC classes or types used by Rhino class. By removing MFC from the Rhino SDK, plug-in that use MFC are no longer required to use the same version of MFC and Rhino.

Note, the core of Rhino continues to use MFC as before, including using the Doc/View framework. However, this implementation is no longer exposed to the SDK.

In general, there are three types of changes that you will need to know about:

#### Replacement of MFC classes with openNURBS equivalents

• ON_4iRect replaces CRect.
• ON_2iSize replaces CSize.
• ON_2iPoint replaces CPoint.

#### Replacement of MFC classes with Win32 equivalents

• HWND replaces CWnd.
• HDC replaces CDC.
• HFONT replaces CFont.

#### Classes no longer derived from MFC base classes

CRhinoDoc is no longer derived from CDocument.

CRhinoView is no longer derived from CView.

CRhinoApp is no longer derived from CWinApp.

Note, the Rhino Rhino 6 C/C++ SDK does include MFC user interface classes, such as CRhinoDialog, CRhinoDockBar, and more. To use these classes, define RHINO_SDK_MFC in your project’s stdafx.h file.

    // If you want to use Rhino's MFC UI classes, then
// uncomment the #define RHINO_SDK_MFC statement below.
// Note, doing so will requires that your plug-in is
// built with the same version of Visual Studio as was
// used to build Rhino.
#define RHINO_SDK_MFC

### Model Components

Rhino has a number of model components, such as layers, groups, render materials, dimensions styles, and more. Over the years, common properties, such as name, index, and id, have been added to these components, but done so in an inconsistent manner. For example, the method for obtaining the id of a layer was different than that of a render material.

The Rhino 6 C/C++ SDK contains a new ON_ModelComponent class that remedies this. Model component classes now inherit from this class.

Providing a consistent interface to common properties, however, means that the names of functions used to access these properties have changed.

For example, in Rhino 5, you could access the name of the current Layer as follows:

    const CRhinoLayer& current_layer = context.m_doc.m_layer_table.CurrentLayer();
ON_wString current_name = current_layer.LayerName();

In Rhino 6, you will need to do the following:

    const CRhinoLayer& current_layer = context.m_doc.m_layer_table.CurrentLayer();
ON_wString current_name = current_layer.Name();

As another example, in Rhino 5, you could access the id of a Group as follows:

    const CRhinoGroup* group = context.m_doc.m_group_table[0];
if (group)
ON_UUID group_id = group->m_group_id;

In Rhino 6, you will need to do the following:

    const CRhinoGroup* group = context.m_doc.m_group_table[0];
if (group)
ON_UUID group_id = group->Id();

### Annotations

For Rhino 6, there will be new implementations for all annotation objects, such as Text, Leaders, and Dimensions. The new implementations are much better organized than prior versions, plus provide new features such as Rich Text.

For more details, see Annotation Objects.

### Scoped and Strongly Typed Enums

C++11 provides some great new features for C++ programmers. One such feature is scoped and strongly typed enumerations, which ensures some measure of compatibility across compilers. They also make up for some shortcomings of old-style enums:

• Old-style enums do not have their own scope
• Old-style enums convert to integral types, which can lead to strange behavior
• You cannot specify the underlying integral type of an old-style enums

There are a number of places in the Rhino 6 C/C++ SDK were old-style enums have been converted to scoped and strongly typed enums by converting enum declarations to enum class. Enumerators of these types of enums require a qualified name such as enumname::enumerator when you refer to them.

For example, in Rhino 5, you could specify a unit system in millimeters as follows:

    ON_UnitSystem units(ON::millimeters);

In Rhino 6, you will need to do the following:

    ON_UnitSystem units(ON::LengthUnitSystem::Millimeters);

### ON_BOOL32 is obsolete

ON_BOOL32 was a 32-bit Boolean typedef that no longer exists. In general you should change occurrences of ON_BOOL32 to bool. However, in cases where you have used ON_BOOL32 in place of int, you must change ON_BOOL32 to int. Converting ON_BOOL32 to bool will be common and is what you should try if you are unable to determine which type you should use..

### Deprecation

Obsolete functions from Rhino 5 are marked as deprecated with a message to help accomplish the same goal through alternate functions in the Rhino 6 SDK. These deprecations will generate compiler warnings when plug-in code attempts to call these functions.

Functions marked as deprecated may or may not continue to work in Rhino 6. Thus, you should replace all calls to deprecated functions with calls to their replacements before distributing any plug-in.

In Rhino 7, all functions marked as deprecated in Rhino 6 will be removed.

### Other

Not all changes in the Rhino 6 C/C++ SDK could be tagged as deprecated. For example, if a member variable from a class were removed, or a feature was dramatically changed, then deprecation could not be used. These types of breakages will require more time to fix.

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# When Will N(d1) Be the Probability of Exercising an Option?

A proof by comparing change of measure with the Black-Scholes formula.

Written on September 26, 2018

Consider the value of a vanilla European call option:

Assuming constant interest rate:

we have:

Compare this with the Black-Scholes formula:

Since both formulas hold true for any choice of the parameters, we have:

In other words, $N(d_1)$ is the probability of exercising the option under the stock measure, while $N(d_2)$ is the probability of exercising the option under the T-forward measure (and of course, the risk-neutral measure as well).


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# Batch acknowledgement file

We describe the fields included in the batch acknowledgment (ACK) file.

After validating the submitted batch request file, an ACK file generates:

• If the batch request file successfully passes the validation check, the ACK file provides a report overview of the processed data.
• If one or more lines in the requested file do not pass the validation check, they are included in the generated ACK file so you can review them.

## ACK - Validation successful

After receiving a batch request file, the Adyen payments platform carries out a series of validation checks. If all validation checks are successful, a batch acknowledgment (ACK) file generates and returns with the fields described below.

FH,1.0,TEST,Company,TestCompany,CaptureOverAuthAmount,1,ws@Company.TestCompany,Modification,EchoData_BatchAck
R,2,8
N,NextFileSubmissionNumber,2

The File Header [FH] record marks the start of the ACK file.

Field # Format Description
1 Fixed value: FH. Record type identifier.
2 Numeric Version number.
This field enables version control for the release of future enhancements for batch processing.
3 Allowed values:
• TEST
• LIVE
It specifies the environment: either test or live/production.
4 Fixed value: Company Account type.
5 Alphanumeric Specifies the company account name.
6 Alphanumeric Submission platform.
The value specified in the file should match the corresponding value in the file name.
7 Numeric File sequence number.
The value specified in the file should match the corresponding value in the file name.
8 Alphanumeric The username of the API credential specified to connect to the Adyen SOAP service.
9 Allowed values:
• Authorisation
• Payout
• RefundWithData
• Modification
• PayoutModification
• AccountUpdater
File type.
Defines the type of transactions that are submitted for further processing.
10 Alphanumeric EchoData
In this field you can specify any data you may want to be returned with the result file. When this field is populated, its content is returned exactly as is. The Adyen payments platform does not use this data.
Maximum character length: 80 characters.

#### Record Line [R]

The File Trailer record specifies the number of blocks and lines in the ACK file.

Field # Format Description
1 Fixed value: R Record type identifier.
2 Numeric Number of processed blocks.
3 Numeric Number of processed line records.

#### Next File Submission Number [N]

This line specifies the number of the next file to process in a batch submission sequence. File sequence numbers are associated with the submission platform the files originate from, and they sequentially increment by one unit after each successful file submission.
The NextFileSubmissionNumber sub-line is always included in an ACK file, regardless of the file validation outcome:

• When a file in a batch process is submitted successfully and without errors, the submission number for the next file in the process increases sequentially.
• When a file in a batch process contains errors, the system tries to guess the submission number for the next file in the sequence. Therefore, this value may be incorrect.

A correct file in a batch submission process satisfies the following minimum requirements:

• The file name adheres to the naming conventions for batch acknowledgement files (ACK).
• The file data matches the expected data type and format.

The submission number is always incorrect when it is not possible to read or parse the header of a file. This can happen in the following cases:

• The file sequence number is missing or it is incorrectly formatted in the file name.
• The submission platform name is missing or it is incorrectly formatted in the file name.
• A database exception might occur during file insertion.
Field # Format Description
1 Fixed value: N Record type identifier
2 Fixed value: NextFileSubmissionNumber Record content definition.
3 Numeric The number corresponding to the next expected file in the submission sequence.

## ACK - Validation failed

When one or more validation errors occur, an error line gets generated per line in the requested file that did not pass validation.

E,L,5,5000,Invalid Merchant Account
E,L,6,5000,Invalid Merchant Account
N,NextFileSubmissionNumber,2

#### Error Line [E]

The File Header record contains marks the start of the ACK file.

Field # Format Description
1 Fixed value: E Record type identifier
2 Allowed values:
• FH
• L
• SL
• F
The record type where the error occurred:
• FH: the error occurred in the file header.
• L: the error occurred in a line record.
• SL: the error occurred in a sub-line record.
• F: the error occurred as the file was incomplete or unreadable.
3 Numeric The file line number where the error occurred.
4 Numeric The error code associated with the error.
5 Alphanumeric The error description.

#### Next File Submission Number [N]

This line specifies the number of the next file to process in a batch submission sequence. File sequence numbers are associated with the submission platform the files originate from, and they sequentially increment by one unit after each successful file submission.
The NextFileSubmissionNumber sub-line is always included in an ACK file, regardless of the file validation outcome:

• When a file in a batch process is submitted successfully and without errors, the submission number for the next file in the process increases sequentially.
• When a file in a batch process contains errors, the system tries to guess the submission number for the next file in the sequence. Therefore, this value may be incorrect.

A correct file in a batch submission process satisfies the following minimum requirements:

• The file name adheres to the naming conventions for batch acknowledgement files (ACK).
• The file data matches the expected data type and format.

The submission number is always incorrect when it is not possible to read or parse the header of a file. This can happen in the following cases:

• The file sequence number is missing or it is incorrectly formatted in the file name.
• The submission platform name is missing or it is incorrectly formatted in the file name.
• A database exception might occur during file insertion.
Field # Format Description
1 Fixed value: N Record type identifier
2 Fixed value: NextFileSubmissionNumber Record content definition.
3 Numeric The number corresponding to the next expected file in the submission sequence.


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3 edited body

I couldn't write this as a comment and I might be off base, but in Berger's paper Theorem 6 he proves that the list of real Lie groups acting transitively on the quadric $$x_1^2 + \dots + x_{n-h}^2 - x^2_{n-h+1} - \dots - x^2_{n} = 1$$ induced from a linear action on $\mathbb{R}^n$ are modulo a finite number of exceptions
1) $SO(n-h,h)$ $n \geq 2$

2) $T^1 \times SU(m/2-h/2,h/2)$, $SU(m/2-h/2,h/2)$ for some $m$ $m/2 \geq 2$

3) $SP(1) \times SP(m/4-h/2,h/2)$, $T^1 \times SP(m/4-h/2,h/2)$, $SP(m/4-h/2,h/2)$ $m/4 \geq 2$

Edit: since I still think the answer to your question is in Berger's list, I transcribe it completely as it can be found in [2]

signature (p,q): $SO(p,q)$
signature (2p, 2q) $U(p,q)$ and $SU(p,q)$
signature (4p,4q) $SP(1)SP(p,q)$ $SP(p,q)$
signature (n,n) $SO(n,\mathbb{C})$
signature (2n,2n) $SO(n, \mathbb{H})$

$G_2^\mathbb{C}$ $G_2$ and $G_2^2$ signatures (7,7), (7,0) and (4,3)

$Spin(7,\mathbb{C})$ $Spin(7)$ and Spin(4,3) signatures (8,8) (8,0) and (4,4).

you of course are interested in signature (p,1)p,2)

The point is that irreducible holonomies are the ones that act transitively on the unit sphere in the tangent space. And this seems to me as the problem you are asking for.

[2] Proc of Symp in pure mathematics 54 (1993) part 2. On the Holonomy of Lorentzian manifolds. Bergery and Ikemakhen

I couldn't write this as a comment and I might be off base, but in Berger's paper Theorem 6 he proves that the list of real Lie groups acting transitively on the quadric $$x_1^2 + \dots + x_{n-h}^2 - x^2_{n-h+1} - \dots - x^2_{n} = 1$$ induced from a linear action on $\mathbb{R}^n$ are modulo a finite number of exceptions
1) $SO(n-h,h)$ $n \geq 2$

2) $T^1 \times SU(m/2-h/2,h/2)$, $SU(m/2-h/2,h/2)$ for some $m$ $m/2 \geq 2$

3) $SP(1) \times SP(m/4-h/2,h/2)$, $T^1 \times SP(m/4-h/2,h/2)$, $SP(m/4-h/2,h/2)$ $m/4 \geq 2$

Edit: since I still think the answer to your question is in Berger's list, I transcribe it completely as it can be found in [2]

signature (p,q): $SO(p,q)$
signature (2p, 2q) $U(p,q)$ and $SU(p,q)$
signature (4p,4q) $SP(1)SP(p,q)$ $SP(p,q)$
signature (n,n) $SO(n,\mathbb{C})$
signature (2n,2n) $SO(n, \mathbb{H})$

$G_2^\mathbb{C}$ $G_2$ and $G_2^2$ signatures (7,7), (7,0) and (4,3)

$Spin(7,\mathbb{C})$ $Spin(7)$ and Spin(4,3) signatures (8,8) (8,0) and (4,4).

you of course are interested in signature (p,1)

The point is that irreducible holonomies are the ones that act transitively on the unit sphere in the tangent space. And this seems to me as the problem you are asking for.

[2] Proc of Symp in pure mathematics 54 (1993) part 2. On the Holonomy of Lorentzian manifolds. Bergery and Ikemakhen

1

I couldn't write this as a comment and I might be off base, but in Berger's paper Theorem 6 he proves that the list of real Lie groups acting transitively on the quadric $$x_1^2 + \dots + x_{n-h}^2 - x^2_{n-h+1} - \dots - x^2_{n} = 1$$ induced from a linear action on $\mathbb{R}^n$ are modulo a finite number of exceptions
1) $SO(n-h,h)$ $n \geq 2$

2) $T^1 \times SU(m/2-h/2,h/2)$, $SU(m/2-h/2,h/2)$ for some $m$ $m/2 \geq 2$

3) $SP(1) \times SP(m/4-h/2,h/2)$, $T^1 \times SP(m/4-h/2,h/2)$, $SP(m/4-h/2,h/2)$ $m/4 \geq 2$


text:
# Is this diophantine?

$\large {\begin{cases} xy+x+y=23\\ xz+x+z=41\\ yz+y+z=27 \end{cases}}$ Find the sum of positive integer solutions for $x,y,z$ of the system above.

×


text:
• ### The Flash ADC system and PMT waveform reconstruction for the Daya Bay Experiment(1707.03699)

April 9, 2018 physics.ins-det
To better understand the energy response of the Antineutrino Detector (AD), the Daya Bay Reactor Neutrino Experiment installed a full Flash ADC readout system on one AD that allowed for simultaneous data taking with the current readout system. This paper presents the design, data acquisition, and simulation of the Flash ADC system, and focuses on the PMT waveform reconstruction algorithms. For liquid scintillator calorimetry, the most critical requirement to waveform reconstruction is linearity. Several common reconstruction methods were tested but the linearity performance was not satisfactory. A new method based on the deconvolution technique was developed with 1% residual non-linearity, which fulfills the requirement. The performance was validated with both data and Monte Carlo (MC) simulations, and 1% consistency between them has been achieved.
• ### The high-speed after pulse measurement system for PMT(1404.6125)

April 24, 2014 hep-ex, physics.ins-det
A system employing a desktop FADC has been developed to investigate the features of 8 inches Hamamatsu PMT. The system stands out for its high-speed and informative results as a consequence of adopting fast waveform sampling technology. Recording full waveforms allows us to perform digital signal processing, pulse shape analysis, and precision timing extraction. High precision after pulse time and charge distribution characteristics are presented in this manuscript. Other photomultipliers characteristics, such as dark rate and transit time spread, can also be obtained by exploiting waveform analysis using this system.
• ### Energy Non-linearity study at Daya Bay(1403.1550)

March 25, 2014 hep-ex, physics.ins-det
The Daya Bay Reactor Neutrino Experiment has measured a non-zero value of the neutrino mixing angle $\theta_{13}$ with a significance of 7.7 standard deviations by a rate-only a nalysis. The distortion of neutrino energy spectrum carries additional oscillation information and can improve the sensitivity of $\theta_{13}$ as well as measure neutrino mass splitting $\Delta m^{2}$ . A rate plus shape analysis is performed and the results have been released in August at NuFact 2013. Detector energy non-linearity response study is crucial for the rate plus shape analysis. In this contribution, We present A brief description of energy non-linearity study at Daya Bay.


text:
# Browse Dissertations and Theses - Chemistry by Title

• (1991)
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• (1990)
Electron spin echo (ESE) methods are particularly useful for measuring weak electron-nuclear couplings in paramagnetic solids. Frequencies that correspond to nuclear transitions are manifested in the electron spin echo ...

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Scanning electrochemical microscopy (SECM) is a useful technique for exploring redox and ionic processes on active materials. Here we explore how conducting polymers (CPs) offer several advantages as probe electrode material, ...

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Because of their importance to energy production, understanding and improving catalytic materials is essential to further advances in their development and use. The following work discusses the experimental investigation ...

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Synthetic chemists are continually challenged to develop more efficient and selective methods for the synthesis of both simple and complex molecules. Traditionally, starting materials for synthesis are derived from petroleum ...

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text:
# Talor series expansion of roots of algebraic equation

1. Dec 3, 2012

### marellasunny

I have a algebraic equation like so:
x^2-1-εx=0

the roots are obviously-
x=ε/2±√(1+ε^2/4)

How can I expand the expression for the roots- as a taylor series?


text:
# apache_beam.io.fileio module¶

PTransforms for manipulating files in Apache Beam.

Provides reading PTransforms, MatchFiles, MatchAll, that produces a PCollection of records representing a file and its metadata; and ReadMatches, which takes in a PCollection of file metadata records, and produces a PCollection of ReadableFile objects. These transforms currently do not support splitting by themselves.

## Writing to Files¶

The transforms in this file include WriteToFiles, which allows you to write a beam.PCollection to files, and gives you many options to customize how to do this.

The WriteToFiles transform supports bounded and unbounded PCollections (i.e. it can be used both batch and streaming pipelines). For streaming pipelines, it currently does not have support for multiple trigger firings on the same window.

### File Naming¶

One of the parameters received by WriteToFiles is a function specifying how to name the files that are written. This is a function that takes in the following parameters:

• window
• pane
• shard_index
• total_shards
• compression
• destination

It should return a file name that is unique for a combination of these parameters.

The default naming strategy is to name files in the format $prefix-$start-$end-$pane-$shard-of-$numShards$suffix$compressionSuffix, where:

• $prefix is, by default, “output”. •$start and $end are the boundaries of the window for the data being written. These are omitted if we’re using the Global window. •$pane is the index for the number of firing for a window.
• $shard and$numShards are the current shard number, and the total number of shards for this window firing.
• \$suffix is, by default, an empty string, but it can be set by the user via default_file_naming.

### Dynamic Destinations¶

If the elements in the input beam.PCollection can be partitioned into groups that should be treated differently (e.g. some events are to be stored as CSV, while some others are to be stored as Avro files), it is possible to do this by passing a destination parameter to WriteToFiles. Something like the following:

my_pcollection | beam.io.fileio.WriteToFiles(
path='/my/file/path',
destination=lambda record: 'avro' if record['type'] == 'A' else 'csv',
sink=lambda dest: AvroSink() if dest == 'avro' else CsvSink(),
file_naming=beam.io.fileio.destination_prefix_naming())

In this transform, depending on the type of a record, it will be written down to a destination named ‘avro’, or ‘csv’. The value returned by the destination call is then passed to the sink call, to determine what sort of sink will be used for each destination. The return type of the destination parameter can be anything, as long as elements can be grouped by it.

class apache_beam.io.fileio.EmptyMatchTreatment[source]

Bases: object

How to treat empty matches in MatchAll and MatchFiles transforms.

If empty matches are disallowed, an error will be thrown if a pattern does not match any files.

ALLOW = 'ALLOW'
DISALLOW = 'DISALLOW'
ALLOW_IF_WILDCARD = 'ALLOW_IF_WILDCARD'
static allow_empty_match(pattern, setting)[source]
class apache_beam.io.fileio.MatchFiles(file_pattern: str, empty_match_treatment='ALLOW_IF_WILDCARD')[source]

Matches a file pattern using FileSystems.match.

This PTransform returns a PCollection of matching files in the form of FileMetadata objects.

expand(pcoll) → apache_beam.pvalue.PCollection[apache_beam.io.filesystem.FileMetadata][apache_beam.io.filesystem.FileMetadata][source]
class apache_beam.io.fileio.MatchAll(empty_match_treatment='ALLOW')[source]

Matches file patterns from the input PCollection via FileSystems.match.

This PTransform returns a PCollection of matching files in the form of FileMetadata objects.

expand(pcoll: apache_beam.pvalue.PCollection) → apache_beam.pvalue.PCollection[apache_beam.io.filesystem.FileMetadata][apache_beam.io.filesystem.FileMetadata][source]
class apache_beam.io.fileio.ReadableFile(metadata, compression=None)[source]

Bases: object

A utility class for accessing files.

open(mime_type='text/plain', compression_type=None)[source]
read(mime_type='application/octet-stream')[source]
read_utf8()[source]
class apache_beam.io.fileio.MatchContinuously(file_pattern, interval=360.0, has_deduplication=True, start_timestamp=Timestamp(1655688510.687020), stop_timestamp=Timestamp(9223372036854.775000), match_updated_files=False, apply_windowing=False)[source]

Checks for new files for a given pattern every interval.

This PTransform returns a PCollection of matching files in the form of FileMetadata objects.

MatchContinuously is experimental. No backwards-compatibility guarantees.

Initializes a MatchContinuously transform.

Parameters: file_pattern – The file path to read from. interval – Interval at which to check for files in seconds. has_deduplication – Whether files already read are discarded or not. start_timestamp – Timestamp for start file checking. stop_timestamp – Timestamp after which no more files will be checked. match_updated_files – (When has_deduplication is set to True) whether match file with timestamp changes. apply_windowing – Whether each element should be assigned to individual window. If false, all elements will reside in global window.
expand(pbegin) → apache_beam.pvalue.PCollection[apache_beam.io.filesystem.FileMetadata][apache_beam.io.filesystem.FileMetadata][source]
class apache_beam.io.fileio.ReadMatches(compression=None, skip_directories=True)[source]

Converts each result of MatchFiles() or MatchAll() to a ReadableFile.

This helps read in a file’s contents or obtain a file descriptor.

expand(pcoll: apache_beam.pvalue.PCollection[typing.Union[str, apache_beam.io.filesystem.FileMetadata]][Union[str, apache_beam.io.filesystem.FileMetadata]]) → apache_beam.pvalue.PCollection[apache_beam.io.fileio.ReadableFile][apache_beam.io.fileio.ReadableFile][source]
class apache_beam.io.fileio.WriteToFiles(path, file_naming=None, destination=None, temp_directory=None, sink=None, shards=None, output_fn=None, max_writers_per_bundle=20)[source]

Write the incoming PCollection to a set of output files.

The incoming PCollection may be bounded or unbounded.

Note: For unbounded PCollections, this transform does not support multiple firings per Window (due to the fact that files are named only by their destination, and window, at the moment).

WriteToFiles is experimental. No backwards-compatibility guarantees.

Initializes a WriteToFiles transform.

Parameters: path (str, ValueProvider) – The directory to write files into. file_naming (callable) – A callable that takes in a window, pane, shard_index, total_shards and compression; and returns a file name. destination (callable) – If this argument is provided, the sink parameter must also be a callable. temp_directory (str, ValueProvider) – To ensure atomicity in the transform, the output is written into temporary files, which are written to a directory that is meant to be temporary as well. Once the whole output has been written, the files are moved into their final destination, and given their final names. By default, the temporary directory will be within the temp_location of your pipeline. sink (callable, FileSink) – The sink to use to write into a file. It should implement the methods of a FileSink. Pass a class signature or an instance of FileSink to this parameter. If none is provided, a TextSink is used. shards (int) – The number of shards per destination and trigger firing. max_writers_per_bundle (int) – The number of writers that can be open concurrently in a single worker that’s processing one bundle.
MAX_NUM_WRITERS_PER_BUNDLE = 20
DEFAULT_SHARDING = 5
expand(pcoll)[source]


text:
July 22, 2004

Three ways to loop flatness

Posted by Urs Schreiber

Today I was contacted by Luiz Agostinho Ferreira who kindly called my attention to the paper

Orlando Alvarez & Luiz. A. Ferreira & J. Sánchez Guillén : A New Approach to Integrable Theories in any Dimension (1998)

that regrettably I was not aware of before but which discusses matters that are relevant for my recent work hep-th/0407122 on strings in nonabelian 2-form backgrounds.

The above paper is motivated from generalizing the method of Lax pairs from 1+1 to higher dimensions. Integrable field theories in 1+1 dimensions admit the construction of a certain connection on 1+1d spacetime which is flat iff the equations of motion hold, so that all holonomies of that connection around, say, ${S}^{1}$ space, are preserved in time and hence are conserved charges.

The idea is to generalize this procedure to $d=1+p$ dimensional field theories by constructing $p$-holonomies for $p>1$ which associate group elements with a $p$-dimensional manifold, so that when the relevant $p$-curvature vanishes these are again homotopy invariants of these surfaces.

For $p=2$ this amounts to the study of connections on loop space, which is precisely what I was concerned with in the above mentioned paper (as discussed here before: I, II, III).

Ferreira et al. work on parameterized but based loop space, where all the loops have a given point in target space at parameter $\sigma =0,2\pi$ in common. This differs a little from the setup needed for string theory, where there is no requirement about this point. So the based loop space in that paper is a subspace of the full loop space relevant in string theory. But as far as I can see this does not restrict any of the constructions and statements made by Ferreira et al., they all generalize easily to unbased loop space.

That said, the first thing to observe is that the general form of the loop space connection used by Ferreira et al. (see their equation (5.1)) is precisely that which dropped out from the boundary state deformation which I used (my equation (1.2) and (3.15)), namely (in the notation adapted from Hofman’s paper but modified as in my equation (3.12))

(1)${d}^{\left(A\right)\left(B\right)}=d+i{\oint }_{A}\left(B\right)\phantom{\rule{thinmathspace}{0ex}}.$

Here $d$ is the exterior derivative on loop space $A$ is a 1-form and $B$ a 2-form, both taking values in a nonablelian Lie-algebra, on target space and the integral is that over the pull-back of $B$ over the loop with $A$-holonomies used to parallel tranport everything to the point $\sigma =0$.

I argued in my paper that local gauge transformation on loop space translate into sensible 2-level gauge transformations on target space only when $B=-{F}_{A}$, in which case it turns out that the above connection is flat, which again makes sense since it implies that toroidal worldsheets don’t see the nonabelian background.

But $B=-{F}_{A}$ is not the only condition which implies flatness of the connection on loop space. Alvarez, Ferreira and Guillén don’t need to mind consistency of any boundary state deformations, of course, and they find two further sufficient conditions for flatness.

With the above notation there is a simple calculus for dealing with differential forms on loop space which are multi-path-ordered integrals (studied intensively by Chen) over the loops. Using this one finds for the curvature

(2)${\left({d}^{\left(A\right)\left(B\right)}\right)}^{2}={\left(d+i{\oint }_{A}\left(B\right)\right)}^{2}={\oint }_{A}\left({d}_{A}B\right)+{\oint }_{A}\left({F}_{A},B\right)-{\oint }_{A}\left(B,{F}_{A}\right)-{\oint }_{A}\left(B\right){\oint }_{A}\left(B\right)\phantom{\rule{thinmathspace}{0ex}}.$

Only the first term is understandable from the purely target space perspective, since this is just the ‘pullback’ (on one index) of the $B$-field strength to the loop up to these $A$-holonomies and integration.

The other terms have no direct target space analog. In particular, the field strength ${F}_{A}$ of the $A$-field shows up all the time, due to the action of the exterior derivative on the $A$-holonomies.

Alvarez, Ferreira & Guillé demand that

(3)${F}_{A}=0$

in order for these terms to vanish.

This is natural from the point of view of integrable systems, but not so natural when we want to think of ${F}_{A}$ really as the field strength of a physical background gauge field, like in string theory, instead of as a auxiliary connection coming from a Lax-pair method. The authors show that several known integrable systems have ‘Lax pairs’ which satisfy this condition.

That it would help to have ${F}_{A}=0$ was also discussed by Christiaan Hofman in the above mentioned paper, who also discussed constraining it to zero.

(For the connection with $B=-{F}_{A}$ that I was discussing, however, we can have ${F}_{A}\ne 0$ and there is full cancellation of all the bothersome terms.)

So with ${F}_{A}=0$ two of the terms in the above expression for the curvature vanish. Alvarez, Ferreira & Guillén now also set what one might call ‘target space curvature of $B$’ equal to zero:

(4)${d}_{A}B=0\phantom{\rule{thinmathspace}{0ex}}.$

With this requirement, all that remains is the exterior product of the 1-form ${\oint }_{A}\left(B\right)$ with itself. If this were an abelian 1-form, then its exterior square would vanish automatically. So that’s one condition on $B$ (together with ${F}_{A}=0={d}_{A}B$) which would give a flat connection (their equation (3.16)).

The second choice discussed by these authors is obtained by demanding not only ${d}_{A}B=0$, but even stronger that $B$ is covariantly constant (their equation (3.18)). Then, as they show and as can easily be seen, $\left({\oint }_{A}\left(B\right){\right)}^{2}=0$ follows automatically.

So this are two sets of conditions on $A$ and $B$ which yield a flat metric on loop space without having $B=-{F}_{A}$ but with instead having ${F}_{A}=0$ and constancy constraints on $B$.

It is annyoing that I wasn’t aware of this work before and I will need to cite it in a revised version of my paper. But I also think that the insights in both papers are to a good part complementary. The form of the loop space connection in both cases is found to be the same, but different conditions on the vanishing of its curvature arise for applications in integrable systems as opposed to applications for the configuration space of relativistic superstring.

(Please note that I have only read this paper today and not all of it, so I have to apologize for any inaccuracies in the above summary. I’ll appreciate corrections and comments. More on how to use the String Coffee Table can be found here.)

Posted at July 22, 2004 5:46 PM UTC

TrackBack URL for this Entry:   http://golem.ph.utexas.edu/cgi-bin/MT-3.0/dxy-tb.fcgi/405

Re: Three ways to loop flatness

Ha! I mentioned that paper to you in my
mail of 9th July. ;-)

Posted by: Amitabha on July 23, 2004 8:41 AM | Permalink | Reply to this

Re: Three ways to loop flatness

Yes, I know. I did look at it, but very quickly only. I had gotten the wrong impression that these integrable systems are not what I was looking for. A mistake. But, ok, that’s life.

Anyway, thanks for mentioning this and other references!

Posted by: Urs Schreiber on July 23, 2004 9:08 AM | Permalink | PGP Sig | Reply to this

Even more flat connections on loop space

As I mentioned, the easiest way to see that the loop space connection $d+{\oint }_{A}\left(B\right)$ with $B=-{F}_{A}$ is flat is to realize that it is gauge equivalent to the trivial connection $d$ under conjugation with the open Wilson line of $A$ around the loop.

This immediately suggests to apply such gauge transformations on loop space to the flat connections studied by Ferreira et al. This would yield even more flat connections.

I think it is important to note that gauge equivalent connections on loop space have nontrivial effect on the physics of bounded surfaces. In particular, as I argued in my paper, the physics of open strings is not invariant under all gauge transformation on loop space.

I believe that the reason for this is nicely elucidated by the SCFT deformation technique which I am using. One lesson from this is that a pure unitary tranformation of the generator algebra for the closed string translates into nontrivial deformations of boundary SCFTs when the closed string is cut open to produce the open string.

A simple well known example for this is Hashimoto’s boundary state deformation for the abelian $A$-field background. Another is the more recent paper by Maeda et al.

Posted by: Urs Schreiber on July 23, 2004 12:12 PM | Permalink | PGP Sig | Reply to this

Re: Even more flat connections on loop space

I spent some time thinking about higher gauge theory on the lattice and multi-dimensional integrability fifteen years ago, when the term gerbe was not yet invented and branes were frowned upon by string theorists:

T A Larsson, “p-cell gauge theories, manifold space and multi-dimensional integrability”, Mod Phys Lett A 5 (1990) 255-264

Inspired by a discussion about gerbes on spr, I later wrote a review of this model with an important correction, so don’t bother to look at the original paper.

The model is a straightforward generalization of lattice gauge theory. Recall that in LGT one puts matrices, i.e. 2-index quantities, on links; an index is associated to each endpoint. LGT has a gauge symmetry at each vertex, and one constructs gauge-covariant Wilson lines by gluing adjascent links together, contracting indices at common endpoints.

My 2-LGT consists of putting 4-index quantities on plaquettes, associating an index to each edge. This model has a gauge symmetry at each edge, and gauge-covariant Wilson surfaces are obtained by gluing adjascent plaquettes together, contracting indices at common edges. An interesting feature is that the zero-3-curvature condition is the Yang-Baxter equation, which gives a connection to lattice integrability.

This model differs significantly from gerbes (I misunderstood that when I chose the title) in one respect: different Wilson surfaces take values in different spaces. If you glue links together you always end up with either zero or two endpoints, so any Wilson line is either a c-number or a two-index matrix. However, when you glue plaquettes together you can end up with a boundary of any length L (a well-defined notion on a lattice). Therefore, the amplitude for such a Wilson surface has L indices.

I still think this old model is quite cool. This two-form generalization of non-abelian gauge theory on the lattice is a well-defined statistical model, and if anyone has the energy it can be treated by standard methods such as Monte Carlo. It may even be useful for studying things like membranes in condensed matter. The thing I like most is its manifest locality; the terms in the action only involves plaquettes around a single cube, which is as local as it gets on thelattice. It seems to me that you can get in trouble with locality if you start from a loop space formulation.

Alas, I later learned that Nepomechie and Orland considered essentially the same model as early as 1984 (references in the eprint). So it seems that essentially the same idea keeps popping up in different guises (2-LGT, gerbes, multi-dimensional integrability, 2-categories, branes, etc.), but a striking breakthrough is still missing. This makes me somewhat pessimistic.

Posted by: Thomas Larsson on July 26, 2004 7:03 AM | Permalink | Reply to this

Re: Even more flat connections on loop space

My 2-LGT consists of putting 4-index quantities on plaquettes, associating an index to each edge.

I have had a look at your paper. Some points are not yet clear to me:

On p.4 you discuss the need for labels NE and SE. Why does only NE appear in (2.6)? Are the SE terms implicit in the ‘7 more terms’?

Does the expression in (2.6) act on ${V}^{\otimes n}$ or on ${⨂}_{\ell \in \delta \Sigma }{V}_{\ell }$?

In (2.8) it is understood that ${f}_{\mu }$ acts on ${V}_{\mu }$, right?

I can see the reasoning behind the construction in section 2. But except for the gauge transformation (2.8) it does not make use of any 1-form holonomy, does it? In this respect it seems to be rather different from loop space and gerbe approaches, right?

Indeed, you write:

This model differs significantly from gerbes […]

Therefore, the amplitude for such a Wilson surface has L indices.

I see. You seem to avoid the issue of ordering the nonabelian surface contributions by keeping track of the orientations of the steps that pull the string over the surface in terms of these indices. This way no 1-form is needed to relate the 2-forms at different points, roughly.

So this seems to be an approach strictly different from that by, for instance, Baez, Girelli & Pfeiffer.

Not that this implies anything. Your (2.7) is arguably a sensible generalization of the Wilson action.

Have you tried to work out its implications, e.g. its equations of motion? (This is not related to your section 4.6, is it?)

It seems to me that you can get in trouble with locality if you start from a loop space formulation.

I would think the nonlocality on target space that may appear is of the same general form as that generally associated with strings.

As far as I can see the 2-group as well as the loop space approach currently do not and perhaps (as indicated by the work by Girelli and Pfeiffer) cannot produce interesting higher generalizations of YM theory. But it does give insights into the general problem of assigning surface holonomy, which allows to study strings in nonabelian 2-form backgrounds.

(From my perspective, the fact that the effective field theory of such strings does not appear to be higher YM looks like an indication that higher YM is maybe not such a good idea after all, but of course that’s a pretty bold conclusion. :-)

So in particular with the argument given in the current entry I think that it is sufficient to have any flat connection on loop space in order to have a well defined surface holonomy of spherical surfaces, even when the second homotopy group of the target is nontrivial. As discussed by Ferreira et al. this alone is sufficient to get interesting physics.

Posted by: Urs Schreiber on July 26, 2004 11:37 AM | Permalink | Reply to this

Re: Even more flat connections on loop space

On p.4 you discuss the need for labels NE and SE. Why does only NE appear in (2.6)? Are the SE terms implicit in the ‘7 more terms’?

Yes. In 1-LGT, the action consists of two terms, corresponding to the two ways you can do parallel transport around the square. My action consists of terms which do parallel transport of a string segment around a diagonal of an elementary cube, as illustrated in figure 3. Since there are eight directed diagonals, each cube contributes eight terms.

Does the expression in (2.6) act on ${V}^{\otimes n}$ or on ${⨂}_{\ell \in \delta \Sigma }{V}_{\ell }$?

Huh, this looks akward without MathML support; I know I should install it, but I haven’t gotten around to do it. I’ll stick to old-fashioned Ascii notation and write @ for tensor product [Converted to itex so the rest of us can read it.].

Anyway, (2.6) is supposed to be a cube cut open along three edges, as the ones in figure 3. Each link gives a $V$, so it acts on $V\otimes V\otimes V$. The trace in (2.7) contracts the indices living on the three links.

In (2.8) it is understood that ${f}_{\mu }$ acts on ${V}_{\mu }$, right?

Yes, I should have written (${f}_{\mu }\otimes {f}_{\nu }$) rather than just ${f}_{\mu }{f}_{\nu }$.

I can see the reasoning behind the construction in section 2. But except for the gauge transformation (2.8) it does not make use of any 1-form holonomy, does it? In this respect it seems to be rather different from loop space and gerbe approaches, right?

Yes, but you can construct more complicated models which have 1-form connections as well - I think Orland did that.

The gerbe approach certainly uses both 1- and 2-form connections, but in loop space you only have a 2-form (i.e. a 1-form in loop space), haven’t you?

Indeed, you write:

“This model differs significantly from gerbes […]

Therefore, the amplitude for such a Wilson surface has L indices.”

I see. You seem to avoid the issue of ordering the nonabelian surface contributions by keeping track of the orientations of the steps that pull the string over the surface in terms of these indices. This way no 1-form is needed to relate the 2-forms at different points, roughly.

Yes.

So this seems to be an approach strictly different from that by, for instance, Baez, Girelli and Pfeiffer.

Yes, although this wasn’t clear to me when I wrote the eprint, which is why I used the buzzword “gerbe”.

Not that this implies anything. Your (2.7) is arguably a sensible generalization of the Wilson action.

Have you tried to work out its implications, e.g. its equations of motion? (This is not related to your section 4.6, is it?)

Well, (4.6) and (4.7) should be the equations of motion, but the classical continuum limit is very formal, and I am not completely happy with it.

One thing that I both like and dislike is the formally diff-and gauge-covariant curvature in (4.35), $F=\mathrm{dA}+\left[A,s\cdot A\right]$. $F=0$ formally becomes the classical Yang-Baxter equation in section 4.7. There is something right about this, since the quantum Yang-Baxter equation is the zero-curvature condition on the lattice. But this is also a difficulty, because the CYBE is an equation in $\mathrm{End}\left(V\otimes V\otimes V\right)$, which seems to break rotational symmetry down to cubic symmetry.

“It seems to me that you can get in trouble with locality if you start from a loop space formulation.”

I would think the nonlocality on target space that may appear is of the same general form as that generally associated with strings.

Yes, and this is something which has bugged me about string theory for the past 20 years. Say that you embed a loop in space (not spacetime) so that it looks like the figure “8”. Then one would expect an interaction at the intersection point, since the two strands are very close to each other. However, this would give an interaction between two points on the loop that are far apart along the loop. This effect is difficult to describe in worldsheet langauge, so people just ignore it AFAIU. But I think that it is important, provided that embedding space has low enough dimension. My guess that the critical dimension is four, since self-avoiding and unconstrained random walks have different fractal dimensions below that.

OTOH, if we start from a theory which has manifest locality in spacetime, like 1-LGT or 2-LGT, we are safe. Spacetime locality cannot be ruined by a reformulation in terms of nonlocal holonomy variables, although loop space locality is probably lost.

As far as I can see the 2-group as well as the loop space approach currently do not and perhaps (as indicated by the work by Girelli and Pfeiffer) cannot produce interesting higher generalizations of YM theory. But it does give insights into the general problem of assigning surface holonomy, which allows to study strings in nonabelian 2-form backgrounds.

I have not studied Pfeiffer’s papers in great depth, but I also got the impression that that line of thought runs into trouble.

My own biggest problem is that the formal continuum limit is awkward. However, maybe one can live without such a limit. A lattice model needs of course a continuum limit to be of interest, but not necessarily a classical one. Maybe one can simply define the full, non-perturbative quantum theory as the critical point of the lattice theory. This assumes, of course, that a second-order phase transition exists, which must be checked by simulations or otherwise.

Posted by: Thomas Larsson on July 27, 2004 8:38 AM | Permalink | Reply to this

Re: Even more flat connections on loop space

but in loop space you only have a 2-form (i.e. a 1-form in loop space), haven’t you?

Not quite. There is of course just a 1-form on loop space, but its definition in general involves a 2-form as well as a 1-form on target space.

You can see this discussed in detail in equations (3.12), (3.15) of hep-th/0407122 and in equation (1.4) and (5.1) of hep-th/9710147. The general idea can also be found in the expression at the top of p. 7 in hep-th/0207017.

Roughly, the 1-form on loop space is obtained by integrating the 2-form on target space over the loop. But in the nonabelian case this integral alone would be ill-defined, since it involves addition of elements sitting in different fibers. This is cured by using a 1-form to parallel transport the 2-form to a given point on the loop, before adding up. In symbols:

(1)$\mathrm{loop}\mathrm{space}\mathrm{connection}={\int }_{0}^{2\pi }{W}_{A}\left(0,\sigma \right){B}_{\mu \nu }\left(\sigma \right)\left(\frac{\partial }{\partial \sigma }{X}^{\nu }\left(\sigma \right)\right){W}_{A}\left(\sigma ,0\right)\phantom{\rule{thinmathspace}{0ex}}{\mathrm{dX}}^{\mu }\left(\sigma \right)$

Here ${W}_{A}$ is the holonomy of the 1-form $A$ along the loop.

In the my paper mentioned above I show that this construction need not to be postulated but follows from a boundary state deformation analysis of the string.

But the general connection on loop space is even more general. This can be seen by simply making a loop-space gauge transformation of the expression above. In general the result of such a gauge transformation won’t have this form anymore, but will need several target space 1- and 2-forms for its description.

This is not the case for precisely the connections for which $B=-{F}_{A}$, where ${F}_{A}$ is the field strength of $A$. Only in this case does hence a gauge transformation on loop space have the interpretation of a 2nd order gauge transformation on target space. $B=-{F}_{A}$ (and two of its generalizations) is also the only known case for nontrivial $A$ which makes the connection on loop space flat, which is good, because it is related to the existence of unique surface holonomies induced by the loop space holonomy. This I discuss in the newly added section 3.4 of hep-th/0407122

Well, (4.6) and (4.7) should be the equations of motion

How do you see this? These equations are derived in the context of gerbes, right? But, as you say, your approach is different from gerbes.

Say that you embed a loop in space (not spacetime) so that it looks like the figure ‘8’. Then one would expect an interaction at the intersection point, since the two strands are very close to each other. However, this would give an interaction between two points on the loop that are far apart along the loop. This effect is difficult to describe in worldsheet langauge, so people just ignore it AFAIU.

True. String interactions are not directly related to string self-intersections, but only to the topology of the parameter space, so to say. But I wouldn’t say that anything is ignored here. After all, the dynamics of the string is what drops out e.g. from the ‘t Hooft limit or Wilson line dynamics in gauge theory.

I have not studied Pfeiffer’s papers in great depth

I haven’t compared the details, but it seems to me that what they are doing is, morally at least, precisely what you are doing, only that they allow for a non-vanishing 1-form together with their 2-form.

In particular, in section 2.5, in figure 2 and in the text below equation (3.25) they explain how they compute the surface holonomy of a little cube, much as envisioned in your paper.

Note that they claim that consistency of this whole setup requires their equation (2.10), which implies that (2.37) must be the unit, which again implies the condition $B=-{F}_{A}$ (3.25) mentioned above. I don’t know if this can be circumvented somehow. If not, it would mean that your approach is consistent only for $B=0$, because you set $A=0$.

But I haven’t worked that out in detail. Maybe you can have a look at it and tell us what you think.

the formal continuum limit is awkward

If the way Girelli and Pfeiffer compute the surface holonomy of a little lattice cube is the same as how you do it, then the continuum limit would be their equation (3.27) (for $A=0$). Actually, i think it might be different. It would be good to understand how different precisely.

Posted by: Urs Schreiber on July 28, 2004 2:23 PM | Permalink | PGP Sig | Reply to this

Re: Even more flat connections on loop space

I have sat down and looked through the literature again.

What you, Thomas, propose in equation (2.6) of your math-ph/0205017 as the surface holonomy of a cube is precisely the same construction as described by Pfeiffer and Girelli in section 2.5 of their hep-th/0309173 for the case of the tetrahedron and applied to the cube in equation (3.26) except for the fact that they have actions of the edge holonomy in their expression, which are missing in yours.

In other words, we obtain your equation (2.6) for the 3-curvature from Girelli&Pfeiffer’s (3.26) when we set $g=1$ throughout in their equation, i.e. when the 1-form connection vanishes.

If this is correct, then the continuum limit of your field strength should be, according to Pfeiffer’s (3.28)

(1)$G={d}_{A}B{=}_{\left(\mathrm{for}A=0\right)}\mathrm{dB}\phantom{\rule{thinmathspace}{0ex}}$

i.e. just the ordinary exterior derivative of the 2-form. (This would mean that the curvature which you discuss in your equation (4.48) would be something else. BTW, where does this expression come from?)

Note the discussion at the end of Girelli&Pfeiffer’s section 2.5, which explains the heuristic meaning of the 1-form holonomies which they have in their expression for the curvature.

Now in principle one could set $g=1$ and get your expression as a special case of Girelli&Pfeiffer’s. But there is a theorem that the combination of the gauge group $G$ of the edges with the group $H$ of the surfaces into a crossed module is a Lie 2-group if (and apparently only if) Pfeiffer’s equation (2.10) holds

(2)$t\left(h\right)={g}_{2}\cdot {g}_{1}^{-1}\phantom{\rule{thinmathspace}{0ex}}.$

Here $h$ is the group label of a surface and ${g}_{1}$ and ${g}_{2}$ that of its source and its target edge. $t$ is the homomorphism which maps $H$ to $G$. In the simplest case $H=G$ and we can just forget about $t$.

This equation apparently goes back to John Baez’ proposition 5 in hep-th/0206130, where it is implicit in the condition

(3)$\mathrm{target}\left(h,g\right)=t\left(h\right)g\phantom{\rule{thinmathspace}{0ex}},$

where $\left(h,g\right)$ is the surface with the source edge labeled by $g$ and the surface labeled by $h$.

It is obvious that the above condition

(4)$t\left(h\right)={g}_{2}\cdot {g}_{1}^{-1}$

is nothing but the finite version of

(5)$B=-{F}_{A}\phantom{\rule{thinmathspace}{0ex}}.$

This means that this condition (which from the loop space perspective is special due to a couple of properties) ensures that the 2-form theory one is dealing with is really a 2-group theory.

So I conclude from that that the 2-form YM action which you give is reasonable, but does not give us a 2-form gauge theory involving a 2-Lie group, that would require $B=-{F}_{A}$ and since $A=0$ in your approach we would be left with the trivial case $B=0$.

But of course one should ask if anything forces us to satisfy the condition of 2-groups! I have seen nowhere any statement why we should want to deal with a 2-group.

- From the loop space and string theory perspective I know that $B=-{F}_{A}$ is what we should probably want to have, due to some facts which I have mentioned before. But we know from Alvarez, Ferreira & Sánchez Guillén that there are other reasonable (namely flat) connections on loop space which do not have $B=-{F}_{A}$. Instead these have ${F}_{A}=0$, which means that locally a gauge transformation will turn this into something along the lines of your idea. They showed that such 2-form theories indeed do describe a couple of integrable models. This proves that there is certainly a physical application for 2-form theories which don’t satisfy $B=-{F}_{A}$ and hence are not 2-group theories, strictly.

Posted by: Urs Schreiber on July 28, 2004 5:18 PM | Permalink | PGP Sig | Reply to this

Re: Even more flat connections on loop space

Urs wrote:
But of course one should ask if anything
forces us to satisfy the condition of
2-groups! I have seen nowhere any
statement why we should want to deal with a 2-group.

There is no absolutely compelling reason. However, if you do have a `non-Abelian string’, you will want to build its world-sheet by adding infinitesimal surfaces. You know that inifinitesimal squares can be added in two ways, either along an edge or at a corner. So if each
little square corresponds to some group element, there should be two composition laws for those elements. Which should commute if the string world-sheet is to be independent of how you have added the little bits of surface. Then you either get an Abelian group (or F=0), or you get a 2-group. Maybe other structures are possible, but I haven’t seen any.

Posted by: Amitabha on July 29, 2004 1:29 PM | Permalink | Reply to this

Re: Even more flat connections on loop space

Yes, thanks for pointing this out. Thomas Larsson was concerned with writing down 3-curvatures, and to do just that one does not necessarily need a unique surface holonomy. But of course one would probably run into serious problems with a 2-form theory which does not admit a unique notion of surface holonomy. Probably the continuum limit of Thomas Larsson’s theory won’t be well defined when the surface holonomy of a big cube cannot be computed from small cubes.

Posted by: Urs Schreiber on July 29, 2004 1:45 PM | Permalink | PGP Sig | Reply to this

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text:
## Precalculus (6th Edition) Blitzer

$6x-(-2x)$ $8x$
The product of 6 and x is simply them multiplied together: $6x$. Two times $x$ is $2x$. Negative two times $x$ is $-2x$. The difference between $6x$ and $-2x$ is the second subtracted from the first: $6x-(-2x)$, which equals $8x$.


text:
# Angular momentum and Noether's theorem

Studying the lagrangian formulation of Noether's theorem and came upon how the invariance under rotations gives conservation of angular momentum.

Whilst setting up the problem the notes state that if a potential only depends on the distance between 2 points, namely $V(|r_i-r_j|)$, then you can apply the transformation:

$$\textbf{r}\rightarrow \textbf{r}+\epsilon T\textbf{r}$$

where $\epsilon$ is a small variation, $\textbf{r}$ is just a vector and $T$ is a rotation matrix. I'm confused about the fact that the notes state that $T$ is an anti-symmetric matrix, I thought rotation matrices where orthogonal.

You are absolutely right, a rotation matrix should be orthogonal. However, when we investigate symmetry transformations, we often like to consider infinitesimal variations, as they are often much easier to investigate.

Consider then a orthogonal matrix $R$, the rotation matrix. The rotation transformation is written as follows :

$$\vec{r}\rightarrow R\vec{r}$$

Now, let us consider an infinitesimal rotation. Since it is infinitesimal, it must be very close to the "$0$" rotation, or in other words, the identity $I$. Thus, we must write it in some way as :

$$R = I+\epsilon T$$

Where $\epsilon$ is a small parameter. Now, we want to find which $T$ we should use. Obviously, a random matrix $T$ wouldn't work in general. We must enforce the fact that $R$ is a rotation, i.e. that $R^T R = I$ :

$$I = R^T R = (I+\epsilon T^T)(I+\epsilon T) = I+\epsilon(T+T^T)+O(\epsilon^2)$$

Here, we don't care about terms in $\epsilon^2$, as they are much smaller than terms in $\epsilon$. So, to enforce $R^T R = I$, we must have simply $T+T^T = 0 \Leftrightarrow T = -T^T$. This is exactly the condition of anti-symmetricity you were looking for !

Thus, for an infinitesimal rotation, we can conveniently write $R = I +\epsilon T$ with T antisymmetric. Note that we often use an even more compact notation, $R = e^{\epsilon T}$, which you can check is equivalent to the one you gave for small $\epsilon$.

P.S. : Physicist use yet another notation, where they write $R = I -i\epsilon (iT) = I -i\epsilon T'$, so we would have purely imaginary antisymmetric matrices. This is mainly because in this way, when you consider unitary matrices $U^\dagger U =I$, then the associated $T'$ is hermitian $T'^\dagger = T'$


text:
# Edexcel Pure Maths A-Level

The Pearson Edexcel Level 3 Advanced GCE in Mathematics consists of three externally-examined papers.

Paper 1 and 2 are pure mathematics and paper 3 is mechanics and statistics.

### Edexcel Pure Maths A-Level

Papers 1 and 2: Paper codes: 9MA0/01 and 9MA0/02

Both papers are 2 hour written exam papers which are weighted at 33.33% with a total of 100 marks. Calculators can be used.

Students must complete all assessment in May/June in any single year.

Further resources:

Edexcel A Level Pure Maths Specification

Please note: The AS Pure Maths content is contained within this module.

Check out the video tutorials for Edexcel Pure maths A-Level from the topic lists below.

## Pythagoras’ Theorem – Playlist

1. Pythagoras' theorem

## Algebraic Long Division – Playlist

1. Algebraic long division

## Exam Questions – Straight Lines

1. Exam Questions - Straight lines

## Asymptotes – Playlist

1. Asymptotes - horizontal and vertical types

## Identities – Half angle type – Playlist

1. Examples using half angle identities

## Identities – Triple angle type – Playlist

1. Identity for cos 3θ and sin 3θ

## Exam Questions – Mixed trigonometry

1. Exam Questions - Mixed trigonometry

## Modelling Curves of the form y=kxn and y=kax – Playlist

1. Modelling curves - Converting to linear form

## More Standard Differentials – Playlist

1. The trig functions, sec(x), cosec(x) and cot(x)

## The Reciprocal Function of dy/dx – Playlist

1. The reciprocal function of dy/dx

## Exponential Functions – Playlist

1. Differentiation: Exponential functions of the form y=ax

## Integrals of the form f[g(x)]g'(x) by inspection – Playlist

1. Integrating products of the form f[g(x)]g'(x) by inspection


text:
# Strategy-proofness of social choice function in two dimensions

Suppose the allocation space is the unit square $A=[0,1] \times [0,1] \in \mathbb{R}^2$. The outcome is a single point $x\in A$. Assume all agents have single-peaked preferences. That is, each agent $i$ has a preference ordering $\succeq_i$ over the outcomes; there exists a point $p_i=(x_i, y_i) \in A$ such that for all $x\in A \setminus \{p_i\}$ and all $\lambda \in [0,1)$, we have $(\lambda x + (1 − \lambda)p_i) \succ_i x$.

The social choice $f$ takes in the agents' preferences $(\succeq_1,\dots,\succeq_n)$, and output $x\in A$.

Why is the function $f(\succeq_1,\dots,\succeq_n)=(x_i,y_i)$ where $x_i$ and $y_i$ are the medians of the $x$ and $y$ coordinates, respectively, not strategy-proof?

What I think: In one dimension, we know that the median scheme is strategy-proof. I don't see how taking the median over each dimension is not?

In more than one dimension, however, you might get a better result by shifting the result's $x$ coordinate further away from your peak's $x$ coordinate – while that causes the result to end up further away from your acutal peak, you're then on a different line $\lambda x + (1 − \lambda)p_i$, which might be more favourable to you, since nothing in the premise constrains the relative ordering of points along different lines through the peak, so a point on one line further from the peak might be preferable to a point on another line closer to the peak.


text:
# 0.3 Learning objects for arrays in java  (Page 4/5)

 Page 4 / 5
• Initially, the variable fib of type integer array is allocated. As part of the same statement, the array object is created with its seven fields having the values in the initializer; the reference to the object is returned and stored in the variable fib .
• A reference to the array is passed as a parameter to the method first . The formal parameter a contains a reference to the same array pointed to by the actual parameter fib .
• A new array b of the same type as the parameter a but half the length is declared and allocated.
• Each iteration of the for-loop moves one element from the first half of a to the corresponding element in the array b .
• The reference to array b is returned. Although array referenced by b was allocated within the method call, it still exists after returning.
• There are no references to the original array so it is inaccessible. Jeliot does not visualize garbage collection so the arrayremains visualized in the Instance and Array Area until the end of the program.

Exercise Modify the program so that the original array remains accessible in a different field.

## Two-dimensional arrays

Concept A matrix can be stored in a two-dimensional array. The syntax is int[][] with two indices, the first for rows and the second for columns. To access an element of the array, expressions for the twoindices must be givien.

Program: Array06.java

// Learning Object Array06 //     two-dimensional arrayspublic class Array06 {     static int addElements(int[][] a) {        int sum = 0;         for (int i = 0; i < a.length; i++)             for (int j = 0; j < a[i].length; j++)                sum = sum + a[i][j];         return sum;    }      public static void main(/*String[] args*/) {        int[][] matrix = new int[2][2];         for (int i = 0; i < matrix.length; i++)             for (int j = 0; j < matrix[i].length; j++)                matrix[i][j] = i*matrix.length + j;         int sum = addElements(matrix);    } }

This program creates a $2×2$ matrix and computes the sum of its elements.

• A two-dimensional array is allocated, the reference to it is assigned to the variable matrix . The variable matrix contains one reference for each row, and the rows are allocated as separate objects.Note that Jeliot displays each row from top to bottom as it does for all objects!
• The elements of the array are initialized to (0,1,2,3) in a nested for-loop.The outside loop iterates over the rows and the inner loop iterates over the columns within an array.
• matrix.length is used to get the number of rows and matrix[i].length to get the number of columns in row i , which is the same for all rows in this program.
• The reference to the array is passed as a parameter to the method addElements , which adds the values of all the elements.
• The sum is returned from the method and assigned to the variable sum .

Exercise Modify the program perform the same computation on a $2×3$ matrix and on a $3×2$ matrix.

## Arrays of arrays

Concept A two-dimensional array is really an array of arrays; that is, each element of the array contains a reference to another array. Therefore, byusing only one index a one-dimensional array is obtained.

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
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text:
# Happy Halloween folks

## News

• October 31, 2001
Happy Halloween folks

Happy Halloween folks. . . . . . enough scary ass shit goin' on these days, huh ?. . . . . .but we take this day to make stuff extra scary for y'all. . . . a scary GGD pumpkin today in the Daily. . . . . . .along with another chance to get in on a DGQ. . . . . . .so. . . . let's get those masks on, bags out and eggs ready. . . . . it's a Halloween Daily. . . . . . BOO. . . . edition # 488. . . . . . . . .Happy Haunting . . . . . . .

First off. . . . . our pumpkin fest. . . . . .this letter sent in by Donna Wyatt of Edmonton, Alberta . . . . . . . she sends in this photo (Click on Picture #1), and she writes in a letter. . . . . .

Hi Guys, I just wanted to take a sec to show you what happens, when you have a little extra time and an extra pumpkin! Wish me luck explaining to the little ghosts and goblins, when they say... GOO GOO WHO?? :) Nothing like educating the neighborhood! :) Have a very SAFE and fun Halloween! Smooches, Donna xox. . . . . . .

thanks Donna. . . . . . . . .and from Misty Michalski of Elsinore, CA , comes this photo (click on Picture #2) and letter. . . . . .

Hi GOOS, Happy Halloween >=) Here's a picture of some Pumpkins I carved last year for Halloween. There the GOO pumpkins. I'm going to do new ones this year but I haven't taken a picture yet. Hope you like and that you have a really great holiday. Lots of Love, Misty D:) . . . . .

Scary?. . . . . . . . you bet. . . . . . . Better late than never. . . . . . . . thanks for sendin' those in folks. . . . . . . we're always lookin' at our mail. . . . . . we love hearin from y'all. . . . . really we do. . . . . . . . .

OK. . . . . . tomorrow we'll be givin' away another Daily Goo Quickie prize. . . . . . .. . . A DGQ. . . . . . . our way of keepin' GGD stuff circulatin' beyond the barriers of cash and commerce. . . . .a random sort of contest. . . . . . . .a free Australian Broadway EP to the winner, chock full of B-sides. . . . .here's how it works. . . . . .

We ask a question, and you send us your answer to that question through our WRITE THE GOOS page. . . . . .in the text section type the words DAILY GOO QUICKIE, followed by your answer. . . . . . . . .we'll take all of the correct answers received and put them in a random drawing on THURSDAY. . . . . don't enter more than once in a 24 hour period. . . . . got it ?. . . . . . .ok. . . . . here's the question. . . . . .

In the current winning streak, how many years in a row have the Yankees won the World Series pennant ?

That's it. . . . . a winner tomorrow . . . . . .

Happy Birthday to the followin' Daily Goo readers. . . . . . .Ashley Plack, Becky Smith, Chris Walsh, Derek Rowell, Elyse Mallimo, Kristine Martin, Lauren Mastrangelo, Melissa Lee, Phil Reid and Wendy Benning . . . . .

And there you have it. . . . . .don't scare yourselves too badly tonite. . . . . check the kids candy, hell, check your candy. . . . . . . . . .join us tomorrow for a DGQ winner. . . . . and the last day for enterin' the MONTHLY CONTEST FOR OCTOBER. . . . . . . . .ok. . . . . . . . we're outta here. . . . . beyond the grave. . . . . dig it ?. . . . . . . .

be spooky. . . . .

byebye

love

goo

on October 31, 2001 - 12:00am

Happy Halloween folks. . . . . . enough scary ass shit goin' on these days, huh ?. . . . . .but we take this day to make stuff extra scary for y'all. . . . a scary GGD pumpkin today in the Daily. . . . . . .along with another chance to get in on a DGQ. . . . . . .so. . . . let's get those masks on, bags out and eggs ready. . . . . it's a Halloween Daily. . . . . . BOO. . . . edition # 488. . . . . . . . .Happy Haunting . . . . . . .

First off. . . . . our pumpkin fest. . . . . .this letter sent in by Donna Wyatt of Edmonton, Alberta . . . . . . . she sends in this photo (Click on Picture #1), and she writes in a letter. . . . . .

Hi Guys, I just wanted to take a sec to show you what happens, when you have a little extra time and an extra pumpkin! Wish me luck explaining to the little ghosts and goblins, when they say... GOO GOO WHO?? :) Nothing like educating the neighborhood! :) Have a very SAFE and fun Halloween! Smooches, Donna xox. . . . . . .

thanks Donna. . . . . . . . .and from Misty Michalski of Elsinore, CA , comes this photo (click on Picture #2) and letter. . . . . .

Hi GOOS, Happy Halloween >=) Here's a picture of some Pumpkins I carved last year for Halloween. There the GOO pumpkins. I'm going to do new ones this year but I haven't taken a picture yet. Hope you like and that you have a really great holiday. Lots of Love, Misty D:) . . . . .

Scary?. . . . . . . . you bet. . . . . . . Better late than never. . . . . . . . thanks for sendin' those in folks. . . . . . . we're always lookin' at our mail. . . . . . we love hearin from y'all. . . . . really we do. . . . . . . . .

OK. . . . . . tomorrow we'll be givin' away another Daily Goo Quickie prize. . . . . . .. . . A DGQ. . . . . . . our way of keepin' GGD stuff circulatin' beyond the barriers of cash and commerce. . . . .a random sort of contest. . . . . . . .a free Australian Broadway EP to the winner, chock full of B-sides. . . . .here's how it works. . . . . .

We ask a question, and you send us your answer to that question through our WRITE THE GOOS page. . . . . .in the text section type the words DAILY GOO QUICKIE, followed by your answer. . . . . . . . .we'll take all of the correct answers received and put them in a random drawing on THURSDAY. . . . . don't enter more than once in a 24 hour period. . . . . got it ?. . . . . . .ok. . . . . here's the question. . . . . .

In the current winning streak, how many years in a row have the Yankees won the World Series pennant ?

That's it. . . . . a winner tomorrow . . . . . .

Happy Birthday to the followin' Daily Goo readers. . . . . . .Ashley Plack, Becky Smith, Chris Walsh, Derek Rowell, Elyse Mallimo, Kristine Martin, Lauren Mastrangelo, Melissa Lee, Phil Reid and Wendy Benning . . . . .

And there you have it. . . . . .don't scare yourselves too badly tonite. . . . . check the kids candy, hell, check your candy. . . . . . . . . .join us tomorrow for a DGQ winner. . . . . and the last day for enterin' the MONTHLY CONTEST FOR OCTOBER. . . . . . . . .ok. . . . . . . . we're outta here. . . . . beyond the grave. . . . . dig it ?. . . . . . . .

be spooky. . . . .

byebye

love

goo