Chapter 5 Statistical maps
5.1 Statistical distribution maps
The previous chapter demonstrated how the choice of a classification scheme can generate different looking maps. Your choice of classification breaks should be driven by the data. This chapter will focus on statistical approaches to generating classification breaks.
Many spatial datasets consist of continuous values. As such, one can have as many unique values as there are unique polygons in a data layer. For example, a Massachusetts median household income map where a unique color is assigned to each unique value will look like this:
Such a map may not be as informative as one would like it to be. In statistics, we seek to reduce large sets of continuous values to discrete entities to help us better “handle” the data. In the field of statistics, discretization of values can take on the form of a histogram where values are assigned to one of several equal width bins. A choropleth map classification equivalent is the equal interval classification scheme.
The histogram in the above figure is “flipped” so as to match the bins with the color swatches. The length of each grey bin reflects the number of polygons assigned their respective color swatches.
An equal interval map benefits from having each color swatch covering an equal range of values. This makes is easier to compare differences between pairs of swatches. Note that a sequential color scheme is used since there is no implied central value in this classification scheme.
5.1.1 Quantile map
While an equal interval map benefits from its intuitiveness, it may not be well suited for data that are not uniformly distributed across their range (note the disproportionate distribution of observations in each color a bin in the above figure). Quantiles define ranges of values that have equal number of observations. For example, the following plot groups the data into six quantiles with each quantile representing the same number of observations (Exceptions exist when multiple observations share the same exact value).
You’ll note the differing color swatch lengths in the color bar reflecting the different ranges of values covered by each color swatch. For example, the darkest color swatch covers the largest range of values, [131944, 250001], yet it is applied to the same number of polygons as most other color swatches in this classification scheme.
5.1.2 Boxplot map
The discretization of continuous values can also include measures of centrality (e.g. the mean and the median) and measures of spread (e.g. standard deviation units) with the goal of understanding the nature of the distribution such as its shape (e.g. symmetrical, skewed, etc…) and range. The boxplot is an example of statistical plot that offers both. This plot reduces the data to a five summary statistics including the median, the upper and lower quartiles (within which 50% of the data lie–also known as the interquartile range,IQR), and upper and lower “whiskers” that encompass 1.5 times the interquartile range. The boxplot may also display “outliers”–data points that may be deemed unusual or not characteristic of the bulk of the data.
Here, we make use of a divergent color scheme to take advantage of the implied measure of centrality (i.e. the median).
5.1.3 IQR map
The IQR map is a reduction of the boxplot map whereby we reduce the classes to just three: the interquartile range (IQR) and the upper and lower extremes. The map’s purpose is to highlight the polygons covering the mid 50% range of values. This mid range usually benefits from a darker hue to help distinguish it from the upper and lower sets of values.
The IQR map differs from the preceding maps shown in this chapter in that upper and lower values are no longer emphasized–whether implicitly or explicitly. While these maps consistently highlighted the prominent east-west gradient in income values with the higher values occurring in the east and the lower values occurring in the west, the IQR map reveals that the distribution of middle income households follows a pattern that is more dispersed across the state of Massachusetts.
5.1.4 Standard deviation map
If the data distribution can be approximated by a Normal distribution (a theoretical distribution defined by a mathematical function), the classification scheme can be broken up into different standard deviation units.
You’ll note from the figure that the income data do not follow a Normal distribution exactly–they have a slight skew toward higher values. This results in more polygons being assigned higher class breaks than lower ones.
5.1.5 Outlier maps
So far, emphasis has been placed on the distribution of values which attempts to place emphasis on the full range of values. However, there may be times when we want to place emphasis on the extreme values. For example, we may want to generate a map that identifies the regions with unusually high or unusually low values. What constitutes an outlier can be subjective. For this reason, we will rely on statistical techniques covered in the last section to help characterize regions with unusually high and/or low values.
<IP_ADDRESS> Boxplot outlier map
We can tweak the boxplot map from the last section by assigning darker hues to observations outside the whiskers (outliers) and a single light colored hue to all other values. By minimizing the range of color swatches, we place emphasis on the outliers.
You’ll note the asymmetrical distribution of outliers with a bit more than a dozen regions with unusually high income values and just one region with unusually low income values.
<IP_ADDRESS> Standard deviation outliers
In this next example, we use the +/- 2 standard deviation bounds from the Normal distribution to identify outliers in the income data. Hence, if the data were to follow a perfectly Normal distribution, this would translate to roughly the top 2.5% and bottom 2.5% of the distribution.
5.2 Mapping uncertainty
Many census datasets such as the U.S. Census Bureau’s American Community Survey (ACS) data are based on surveys from small samples. This entails that the variables provided by the Census Bureau are only estimates with a level of uncertainty often provided as a margin of error (MoE) or a standard error (SE). Note that the Bureau’s MoE encompasses a 90% confidence interval1 (i.e. there is a 90% chance that the MoE range covers the true value being estimated). This poses a challenge to both the visual exploration of the data as well as any statistical analyses of that data.
One approach to mapping both estimates and SE’s is to display both as side-by-side maps.
While there is nothing inherently wrong in doing this, it can prove to be difficult to mentally process the two maps, particularly if the data consist of hundreds or thousands of small polygons.
Another approach is to overlay the measure of uncertainty (SE or MoE) as a textured layer on top of the income layer.
Or, one could map both the upper and lower ends of the MoE range side by side.
5.2.1 Problems in mapping uncertainty
Attempting to convey uncertainty using the aforementioned maps fails to highlight the reason one chooses to map values in the first place: that is to compare values across a spatial domain. More specifically, we are interested in identifying spatial patterns of high or low values. What is implied in the above maps is that the estimates will always maintain their order across the polygons. In other words, if one polygon’s estimate is greater than all neighboring estimates, this order will always hold true if another sample was surveyed. But this assumption is incorrect. Each polygon (or county in the above example) can derive different estimates independently from its neighboring polygon. Let’s look at a bar plot of our estimates.
Note, for example, how Piscataquis county’s income estimate (grey point in the graphic) is lower than that of Oxford county. If another sample of the population was surveyed in each county, the new estimates could place Piscataquis above Oxford county in income rankings as shown in the following example:
Note how, in this sample, Oxford’s income drops in ranking below that of Piscataquis and Franklin counties. A similar change in ranking is observed for Sagadahoc county which drops down two counties: Hancock and Lincoln.
How does the estimated income map compare with the simulated income map?
A few more simulated samples (using the 90% confidence interval) are shown below:
5.2.2 Class comparison maps
There is no single solution to effectively convey both estimates and associated uncertainty in a map. Sun and Wong (Sun and Wong 2010) offer several suggestions dependent on the context of the problem. One approach adopts a class comparison method whereby a map displays both the estimate and a measure of whether the MoE surrounding that estimate extends beyond the assigned class. For example, if we adopt the classification breaks [0 , 20600 , 22800 , 25000 , 27000 , 34000 ], we will find that many of the estimates’ MoE extend beyond the classification breaks assigned to them.
Take Piscataquis county, for example. Its estimate is assigned the second classification break (20600 to 22800 ), yet its lower confidence interval stretches into the first classification break indicating that we cannot be 90% confident that the estimate is assigned the proper class (i.e. its true value could fall into the first class). Other counties such as Cumberland and Penobscot don’t have that problem since their 90% confidence intervals fall inside the classification breaks.
This information can be mapped as a hatch mark overlay. For example, income could be plotted using varying shades of green with hatch symbols indicating if the lower interval crosses into a lower class (135° hatch), if the upper interval crosses into an upper class (45° hatch), if both interval ends cross into a different class (90°-vertical-hatch) or if both interval ends remain inside the estimate’s class (no hatch).
5.2.3 Problem when performing bivariate analysis
Data uncertainty issues do not only affect choropleth map presentations but also affect bivariate or multivariate analyses where two or more variables are statistically compared. One popular method in comparing variables is the regression analysis where a line is best fit to a bivariate scatterplot. For example, one can regress “percent not schooled”” to “income”” as follows:
The \(R^2\) value associated with this regression analysis is 0.2 and the p-value is 0.081.
But another realization of the survey could produce the following output:
With this new (simulated) sample, the \(R^2\) value dropped to 0.07 and the p-value is now 0.322–a much less significant relationship then computed with the original estimate! In fact, if we were to survey 1000 different samples within each county we would get the following range of regression lines:
These overlapping lines define a type of confidence interval (aka confidence envelope). In other words, the true regression line between both variables lies somewhere within the dark region delineated by this interval.
References
The Bureau’s MoE can be computed from the SE as follows: \(MoE = 1.645 \times SE\)↩


Adopt A Family Marin
Over the last 30 years, Adopt A Family has helped to prevent the road to homelessness which families face. Their goal is no homeless children living in Marin. They help families stay stable in their fight against poverty.
You can find them
In the real world, here: 35 Mitchell Blvd Suite 16, San Rafael, CA
Through email here<EMAIL_ADDRESS>Remember:
You should contact Adopt A Family Marin before donating any items.


Lady Musgrave Island
Brad, Bec and I travelled up to Bundaberg today, a short trip for Oz at only 1 hour and 20 mins, but not before bumping into the Hornchurch geezers at the bus station at Hervey Bay! They'd done the job on their hair, slappin' on the old Sunnin in the hope of turning it blonde, but it had gone ginger. Had to laugh. Loudly.
The hostel we arrived at was superb, run by a real old couple, Mom-and-Pop type place, complete with Bible in every room. Just in case my Satanic side came out. We'd decided to travel the 400 kms or so up the coast so that Bradley and Bec could get a look at the Great Barrier Reef - Brad was off to NZ soon, and Bec probably won't make it up this way again.
The $105 day trip took us 2 1/2 hours off the coast to Lady Musgrave Island, named after some bint who was the wife of a state governor, or something. Well, it's at least better than Fraser Island, named after the wife of the bloke who pranged his ship there. The island, when we arrived, was just like a desert island, funnily enough. We could see the waves breaking on the outer reef, a strange sight to see out in the middle of the ocean. Also strange was that the water was only 6m deep. After a brief little trip in the semi-submersible, we spent the rest of the day snorkelling on the coral reef, checking out all the little fishes. The trip organisers did a fish feed at one point, so I leapt in the water to get a better look; I got thumped on the back almost immediately by a huge trout! The bloke pointed out all the different fish to the onlookers, whilst throwing fish food on me. "There's a trout", he said, "There's a stripy, and over there is a mad English bloke". Fair enough.
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| MonadRun | | Portability | portable | | Stability | experimental | | Maintainer | Ralf Laemmel, Joost Visser |
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| Description |
| This module is part of StrategyLib, a library of functional strategy
combinators, including combinators for generic traversal. This module
provides non-strategic functionality for running monads and unlifting
monad transformers.

This function runs one monad, and puts its value in another. This is
basically a monadic version of the run function itself. Note that the two
monads are unrelated, so none of the effects of the incoming monad are
transferred to the result monad. |
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| Unlifting monad transformers |
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| class MonadUnTrans s t | t -> s where |
| Just as a base monad can be run to remove the monad, so can a transformed
monad be unlifted to remove the transformer and obtain the original monad. | | | Methods | | unlift :: Monad m => s a b -> t m a -> m b | | The overloaded function unlift for monad transformers takes as first
argument an algebra just like the run function for base monads. For
each monad transformer, the same algebra is used as for the base monad
of which the transformer is the parameterized variant. |
| | | Instances | |
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| Monadic choice combinators that confine the partiality effect |
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| Monadic choice |
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| mplus' :: (Monad m, MonadUnTrans MaybeAlg t) => t m b -> m b -> m b |
| Monadic choice combinator that confines the partiality effect to
the first argument. This is a variation on mplus which allows
the partiality effect to spread to both arguments and to the result. |
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| mswitch |
| :: (Monad m, MonadUnTrans MaybeAlg t) | | | => [t m b] | choice branches | | -> m b | otherwise | | -> m b | result | | Monadic choice combinator. Generalization of mplus' that takes a list
of choice arguments rather than a single one. |
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| mayswitch :: Monad m => [MaybeT m b] -> m b -> m b |
| Specialization of mswitch for MaybeT. |
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| Monadic function choice |
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| mchoice' :: (Monad m, MonadUnTrans MaybeAlg t) => (a -> t m b) -> (a -> m b) -> a -> m b |
| Monadic function choice combinator that confines the partiality effect
to the first argument. This is a variation on mchoice which
allows the partiality effect to spread to both arguments and to the
result. |
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| mchoices :: (Monad m, MonadUnTrans MaybeAlg t, MonadPlus (t m)) => [a -> t m b] -> (a -> m b) -> a -> m b |
| Monadic function choice combinator. Generalization of mchoice' that
takes a list of choice arguments rather than a single one. |
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| Implementation variants |
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| mswitch0 :: (Monad m, MonadUnTrans MaybeAlg t) => [t m b] -> m b -> m b |
| Implementation variant of mswitch in terms of foldr. |
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| mswitch1 :: (Monad m, MonadUnTrans MaybeAlg t) => [t m b] -> m b -> m b |
| Implementation variant of mswitch with mplus' expanded: |
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| mswitch' :: (Monad m, MonadUnTrans MaybeAlg t, MonadPlus (t m)) => [t m b] -> m b -> m b |
| Implementation variant of mswitch where the unlift is postponed
to the very end. |
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| Produced by Haddock version 0.6 |


The amount of the deposit. If you specify an Amount value, you must include AmountOperator
Tells the response to return tickets in ranges based on the Amount value. This string/value pair is required if you specify an Amount value. There is no AmountOperator setting for greater-than or less-than an Amount value.
The end of the period over which to return deposit tickets, in ISO 8601 format
Optional. The total number of deposit tickets to return in the array. Limit is a 32-bit integer value that can return over 4 billion tickets (4 thousand million). If Limit is not specified, all tickets are returned.
The ID of the Order Management System on which the deposit tickets reside
The ID of the operator of the trading venue.
Optional. The deposit ticket at which to start returning the array of deposit tickets, starting from 0, the most recent deposit ticket, and working backwards in time.
The start of the period over which to return deposit tickets, in ISO 8601 format.
The current status of the deposit. One of:
Note: The value of Status is an integer in the request for GetAllDepositTickets. In the response, it is a string..
The ID of a single deposit ticket that is unique across the Order Management System. By including a value for TicketId, you limit the returned information to a single ticket.
The name of the user making the deposit
Generated using TypeDoc
The ID of the account
{number}
AllDepositTicketsRequest


Before Change
self._trainable_weights = []
if not hasattr(self, "_non_trainable_weights"):
self._non_trainable_weights = []
if not hasattr(self, "losses"):
self.losses = []
if not hasattr(self, "constraints"):
self.constraints = {} // dict {tensor: constraint instance}
self.built = False
After Change
batch_input_shape = tuple(kwargs["batch_input_shape"])
elif "input_shape" in kwargs:
if "batch_size" in kwargs:
batch_size = kwargs["batch_size"]
else:
batch_size = None
batch_input_shape = (batch_size,) + tuple(kwargs["input_shape"])
self.batch_input_shape = batch_input_shape


Step 2: Develop (Javascript)
In this step, we’ll accomplish a few things.
- Add a click listener to our follow button
- Set a follow state on element
- Have an image show up in our profile photo
- Properly disconnect our element
First, let’s listen for clicks on the button in our element. The best place to add the click listener to the button is in the constructor. According to the W3C Custom Elements draft section called “2.2 Requirements for custom element constructors”:
In general, the constructor should be used to set up initial state and default values, and to set up event listeners and possibly a shadow root.
Since the base Rhelement class that we’re extending already sets up the shadow root, all we need to do is set up our click listener.
import Rhelement from '../rhelement/rhelement.js';
/*
* DO NOT EDIT. This will be autopopulated with the
* html from rh-cool-element.html and css from
* rh-cool-element.scss
*/
const template = document.createElement('template');
template.innerHTML = ``;
/* end DO NOT EDIT */
class RhCoolElement extends Rhelement {
constructor() {
super('rh-cool-element', template);
this.button = this.shadowRoot.querySelector('button');
this.button.addEventListener('click', this._clickHandler);
}
_clickHandler(evt) {
console.log('Button clicked!!!');
}
}
window.customElements.define('rh-cool-element', RhCoolElement);
In our constructor, we run querySelector
on our shadowRoot
to locate our button. Then we add the click listener, this._clickHandler
. Note the underscore before the method name. This is a convention that you’ll find in other custom elements where the author is trying to signal that this method is meant to be a private method.
Refresh your demo page, click the button and you should see the following result.
Now that the click handler is set up, let’s set a following state on our element to keep track of whether or not the user is following this profile. We’ll update the constructor
with a couple lines of code.
constructor() {
super('rh-cool-element', template);
this.following = false;
this._clickHandler = this._clickHandler.bind(this);
this.button = this.shadowRoot.querySelector('button');
this.button.addEventListener('click', this._clickHandler);
}
We did two things here. First we set the state of following
to false on our element. We also bound this
to our click handler so we can continue to use this
and refer to our element in the _clickHandler
.
Getter, Setter, and Element State
Next, let create a getter and a setter for the following
property of our element. The setter will enable us to reflect the state of following to an attribute on rh-cool-element
. The getter will provide us with the value of that attribute. Let’s use following
as the attribute to reflect the state.
set following(value) {
const isFollowing = Boolean(value);
if (isFollowing) {
this.setAttribute('following', '');
} else {
this.removeAttribute('following');
}
}
get following() {
return this.hasAttribute('following');
}
Now that we have the following getter and setter wired up, let’s update the _clickHandler
method to toggle the following state.
_clickHandler() {
this.following = !this.following;
}
So now when we click the follow button, we should see the following
attribute set and unset as we toggle the button.
Observed Attributes
Let’s do one more thing with the follow state. Let’s update the button text to “Unfollow” when this.following
is true and be “Follow” when this.following
is false. In this part, we’ll introduce a new concept: observing attributes. Observing attributes is an easy way to tell your custom element to perform an action when an attribute your observing changes. In this case, we want to know when the following
attribute has changed. When it does, we’ll change the text of our follow button. To observe an attribute, add this code to the top of your class.
static get observedAttributes() {
return ['following'];
}
observedAttributes
should return an array of attributes that you want to observe. In this case, we’ll observe the following
attribute. To react to a change in the attributes were observing, we need to set up the attributeChangedCallback
method.
attributeChangedCallback(name, oldValue, newValue) {
switch (name) {
case 'following':
this.button.textContent = this.following ? 'Unfollow' : 'Follow';
break;
}
}
All this code does is check which attribute changed and if it was the following
attribute, we update our button text. Pretty straight-forward. Now our button should reflect the state of following
in our element. With everything wired up, our UI should now look like this when we click the follow button.
Two more things and then we’re done. Next, let’s use a photo-url
attribute to pass in a photo url for our profile pic. Once again we can use observedAttributes
and the attributeChangedCallback
to handle this. So with just a few updates to those two methods, we can add our profile pic.
Let’s first add a reference to our #profile-pic
container in the constructor by setting this.profilePic
.
constructor() {
super('rh-cool-element', template);
this.following = this.hasAttribute('following') || false;
this._clickHandler = this._clickHandler.bind(this);
this.button = this.shadowRoot.querySelector('button');
this.button.addEventListener('click', this._clickHandler);
this.profilePic = this.shadowRoot.querySelector('#profile-pic');
}
Here is the update to observedAttributes
.
static get observedAttributes() {
return ['following', 'photo-url'];
}
And the updates to the attributeChangedCallback
.
attributeChangedCallback(name, oldValue, newValue) {
switch (name) {
case 'following':
this.button.textContent = this.following ? 'Unfollow' : 'Follow';
break;
case 'photo-url':
this.profilePic.style.backgroundImage = `url(${newValue})`;
break;
}
}
Now we need to update our demo page (/demo/index.html
) and add the photo-url
attribute with a URL to a profile pic so we can see everything working.
<rh-cool-element photo-url="https://avatars2.githubusercontent.com/u/330256?s=400&u=de56919e816dc9f821469c2f86174f29141a896e&v=4">
Kyle Buchanan
</rh-cool-element>
And finally, we need to modify /src/rh-cool-element.scss
and update the background-size property on #profile-pic
.
#profile-pic {
width: 50px;
height: 50px;
border: 2px solid #333;
border-radius: 50%;
background-color: #efefef;
margin-bottom: 16px;
background-size: contain;
}
The final result should look like this.
Great! Almost done. We have one last step which is cleaning up our event listeners when our web component is disconnected.
Disconnected Callback
It’s a good idea to clean up any event listeners that you’ve added to your web component. One of the lifecycle callbacks that are run on web components is disconnectedCallback
and this is where we run our cleanup code. In our case, all we need to do is remove the click listener that we added to our follow button.
disconnectedCallback() {
this.button.removeEventListener('click', this._clickHandler);
}
Wrap-up
And that’s it! We’re all done. To summarize, we’ve built a brand new web component that extends a base element. We built some HTML, added some custom style, and added some interactivity to our component. With this element we just scratched the surface of what’s possible with custom elements.
For reference, here’s the final Javascript code for our element.
import Rhelement from '../rhelement/rhelement.js';
/*
* DO NOT EDIT. This will be autopopulated with the
* html from rh-cool-element.html and css from
* rh-cool-element.scss
*/
const template = document.createElement('template');
template.innerHTML = ``;
/* end DO NOT EDIT */
class RhCoolElement extends Rhelement {
static get observedAttributes() {
return ['following', 'photo-url'];
}
constructor() {
super('rh-cool-element', template);
this.following = this.hasAttribute('following') || false;
this._clickHandler = this._clickHandler.bind(this);
this.button = this.shadowRoot.querySelector('button');
this.button.addEventListener('click', this._clickHandler);
this.profilePic = this.shadowRoot.querySelector('#profile-pic');
}
disconnectedCallback() {
this.button.removeEventListener('click', this._clickHandler);
}
set following(value) {
const isFollowing = Boolean(value);
if (isFollowing) {
this.setAttribute('following', '');
} else {
this.removeAttribute('following');
}
}
get following() {
return this.hasAttribute('following');
}
_clickHandler() {
this.following = !this.following;
}
attributeChangedCallback(name, oldValue, newValue) {
switch (name) {
case 'following':
this.button.textContent = this.following ? 'Unfollow' : 'Follow';
break;
case 'photo-url':
this.profilePic.style.backgroundImage = `url(${newValue})`;
break;
}
}
}
window.customElements.define('rh-cool-element', RhCoolElement);
Now that we have all of the code working for our rh-cool-element
, we need to make sure we have tests written to ensure that our element is going to work as it changes in the future. We’ll take care of that in the next step.


|
Bullet Collision Detection & Physics Library
|
Public Member Functions | |
| InitJointsLoop (btSequentialImpulseConstraintSolverMt *solver, btTypedConstraint **constraints) | |
| void | forLoop (int iBegin, int iEnd) const BT_OVERRIDE |
| Public Member Functions inherited from btIParallelForBody | |
| virtual | ~btIParallelForBody () |
Public Attributes | |
| btSequentialImpulseConstraintSolverMt * | m_solver |
| btTypedConstraint ** | m_constraints |
Definition at line 627 of file btSequentialImpulseConstraintSolverMt.cpp.
|
inline |
Definition at line 632 of file btSequentialImpulseConstraintSolverMt.cpp.
|
inlinevirtual |
Implements btIParallelForBody.
Definition at line 637 of file btSequentialImpulseConstraintSolverMt.cpp.
| btTypedConstraint** InitJointsLoop::m_constraints |
Definition at line 630 of file btSequentialImpulseConstraintSolverMt.cpp.
| btSequentialImpulseConstraintSolverMt* InitJointsLoop::m_solver |
Definition at line 629 of file btSequentialImpulseConstraintSolverMt.cpp.


--- title: "Simple Way to Make Ultimate No-Sugar Peach Preserves Tasty" slug: no-sugar-peach-preserves description: "No-Sugar Peach Preserves Recipe - Delicious peach preserves/jam for those watching carbs or for diabetics. Step-by-Step Guide to Make Award-winning No-Sugar Peach Preserves Tasty" date: 2021-04-16T13:20:36Z image: https://cdn.statically.io/img/images.media-allrecipes.com/userphotos/6968354.jpg thumbnail: https://cdn.statically.io/img/images.media-allrecipes.com/userphotos/6968354.jpg cover: https://cdn.statically.io/img/images.media-allrecipes.com/userphotos/6968354.jpg author: Agustina ratingvalue: 4.7 reviewcount: 206 recipeingredient: - "3 cups peeled and chopped peaches" - "¾ cup water" - "1 (1.75 ounce) package fruit pectin (such as Sure-Jell®)" - "½ cup sucralose sugar substitute (such as Splenda®)" recipeinstructions: - "Fill a canner pot half-full with water and bring to a simmer. Wash jars and rings in warm soapy water; rinse with warm water. Place lids in a saucepan off the heat; pour boiling water on top. Let stand until ready to use." - "Measure 3 cups of peaches into a 6- or 8-inch saucepot. Stir in 3/4 cup water. Gradually add pectin, stirring until well blended. Bring mixture to a boil over high heat, stirring constantly. Boil exactly 1 minute, stirring constantly. Remove from heat. Stir in sucralose. Skim foam off the surface of the jam using a metal spoon." - "Ladle jam immediately into the prepared jars, filling to within 1/8-inch from the tops. Wipe jar rims and threads. Cover with lids and rings; screw bands tightly. Place jars on an elevated rack in the canner. Lower the rack to cover the jars with 1 to 2 inches of water, adding more boiling water if necessary. Cover and bring water to a simmer." - "Process the jam for 10 minutes. Remove jars and place upright on a towel to cool completely, 2 to 3 hours. Check seals by pressing the middle of lid with your finger; if lid springs back, lid is not sealed and refrigeration is necessary." categories: - "Side Dish" - "Sauces and Condiments Recipes" - "Canning and Preserving Recipes" - "Jams and Jellies Recipes" - "Recipes" tags: - "side dish" - "sauces and condiments recipes" - "canning and preserving recipes" - "jams and jellies recipes" katakunci: no-sugar peach preserves, side dish, sauces and condiments recipes, canning and preserving recipes, jams and jellies recipes, . nutrition: 24 calories recipecuisine: Western preptime: "P0DT0H20M" cooktime: "P0DT0H25M" totaltime: "P0DT2H45M" recipeyield: "3 8-ounce jars" recipecategory: - Side Dish - Sauces and Condiments Recipes - Canning and Preserving Recipes - Jams and Jellies Recipes quotes: Who needs love when you can eat all the chocolate in the world. ---
No-Sugar Peach Preserves - Hello everybody, I hope youre having an amazing day today. It is me again Agustina , welcome to our recipe site. Today, Im gonna show you how to prepare a special dish, No-Sugar Peach Preserves. One of my favorites food recipes. For mine, I am going to make it a little bit unique. This will be really delicious.
No-Sugar Peach Preserves is Delicious peach preserves/jam for those watching carbs or for diabetics.
No-Sugar Peach Preserves is one of the most popular of current trending foods on earth. It is easy, it is quick, it tastes yummy. It is enjoyed by millions every day. its simple, its fast, it tastes yummy. No-Sugar Peach Preserves is something which I have loved my whole life. They are fine and they look wonderful. They are fine and they look fantastic. No-Sugar Peach Preserves is something which I have loved my whole life.
To begin with this recipe, we have to first prepare a few ingredients. You can cook No-Sugar Peach Preserves using 4 ingredients and 4 steps. Here is how you can achieve it.
So that is going to wrap it up for this exceptional food No-Sugar Peach Preserves recipe. Thanks so much for your time. Im confident you will make this at home. Theres gonna be more interesting food at home recipes coming up. Dont forget to bookmark this page in your browser, and share it to your loved ones, friends and colleague. Thanks again for reading. Go on get cooking!


Install and Start Using the Python SDK with Couchbase Server
The Couchbase Python SDK allows Python applications to access a Couchbase cluster. The Python SDK offers a traditional synchronous API as well as integration with twisted, gevent, and asyncio. It depends on the C SDK, libcouchbase, which it uses for performance and reliability.
First, install libcouchbase following the instructions here: https://developer.couchbase.com/server/other-products/release-notes-archives/c-sdk.
When libcouchbase is installed, please follow these instructions:
Installing on Linux
# Only needed during first-time setup:
sudo apt-get install build-essential python-dev python-pip
sudo pip install couchbase
# Only needed during first-time setup:
sudo yum install gcc gcc-c++ python-devel python-pip
sudo pip install couchbase
RHEL/CentOS distributions may not provide the python-pip package in the base repositories.
It may be found in the EPEL repository.
|
Installation on Mac OS X
To install the library on Mac OS X, first install the de-facto package manager for OS X: homebrew. Once homebrew is configured:
brew update # get list of latest packages
brew install python
pip install couchbase
| The above example uses the Python supplied by homebrew and not the vendor-supplied Python which ships with OS X. The Python SDK will still work with the vendor-supplied Python (though pip install may be a privileged command), but it is recommended to use Homebrew’s Python instead. |
Installing on Microsoft Windows
The Couchbase Python SDK is available as an executable installer for Windows. This contains all the required dependencies, including C SDK development files.
-
Check your Windows architecture (32-bit or 64-bit) and make sure the required version of Python is installed.
-
Download the Couchbase Python SDK installer for your platform and Python version from https://pypi.python.org/pypi/couchbase#files.
-
Run the installer and follow any instructions given.
| Installation by means of pip will not work on Windows. |
Hello Couchbase
The code snippet below shows how the Python SDK may be used for some common operations.
from couchbase.cluster import Cluster
from couchbase.cluster import PasswordAuthenticator
cluster = Cluster('couchbase://localhost')
authenticator = PasswordAuthenticator('username', 'password')
cluster.authenticate(authenticator)
cb = cluster.open_bucket('bucket-name')
cb.upsert('u:king_arthur', {'name': 'Arthur', 'email'<EMAIL_ADDRESS>'interests': ['Holy Grail', 'African Swallows']})
# OperationResult<RC=0x0, Key=u'u:king_arthur', CAS=0xb1da029b0000>
cb.get('u:king_arthur').value
# {u'interests': [u'Holy Grail', u'African Swallows'], u'name': u'Arthur', u'email'<EMAIL_ADDRESS>## The CREATE PRIMARY INDEX step is only needed the first time you run this script
cb.n1ql_query('CREATE PRIMARY INDEX ON bucket-name').execute()
from couchbase.n1ql import N1QLQuery
row_iter = cb.n1ql_query(N1QLQuery('SELECT name FROM bucket-name WHERE ' +\
'$1 IN interests', 'African Swallows'))
for row in row_iter: print(row)
# {u'name': u'Arthur'}
Connecting
To connect to a Couchbase bucket, you must use Couchbase Role-Based Access Control (RBAC). This is fully described in the section 6.0@server:security:security-authorization.adoc. An authenticator, containing username and password, should be defined, and then passed to the cluster. Following successful authentication, the bucket can be opened.
from couchbase.cluster import Cluster
from couchbase.cluster import PasswordAuthenticator
cluster = Cluster('couchbase://localhost')
authenticator = PasswordAuthenticator('username', 'password')
cluster.authenticate(authenticator)
bucket = cluster.open_bucket('bucket-name')
Once defined, the authenticator can be passed to other clusters, as appropriate.
See Managing Connections Using the Python SDK with Couchbase Server for more connection options and details about the connection string.
Document Operations
Document operations, such as storing and retrieving documents, can be done using simple methods on the Bucket
class such as Bucket.get
and Bucket.upsert
.
Simply pass the key (and value, if applicable) to the relevant methods.
rv = bucket.get('document-id')
print(rv.value)
bucket.upsert('document-id', {'application': 'data'})
N1QL Queries
Couchbase N1QL queries are performed by creating a N1QLQuery
object and passing that to the Bucket.n1ql_query()
method:
from couchbase.n1ql import N1QLQuery
query = N1QLQuery("""SELECT airportname, city, country FROM `travel-sample` """
"""WHERE type="airport" AND city=$my_city""", my_city="Reno")
for row in bucket.n1ql_query(query):
print(row)
API Reference
The API reference is generated for each release and can be found linked from the release notes for your version of the Python SDK.
Most of the API documentation can also be accessed via pydoc
.
Release Notes
Information on new features, fixes, known issues as well as information on how to install older release versions is in the release notes.
PyPy support
Because the Python SDK is written primarily in C using the CPython API, the official SDK will not work on PyPy.
An unofficial module, couchbase_ffi uses ffi rather than the CPython C API to implement the internals of the library, and may be used with pypy.
Contributing
Couchbase welcomes community contributions to the Python SDK. The Python SDK source code is available on GitHub.


The latest version is opentheory 1.4 (release 20230321), and can be downloaded in the following formats:
Please see the install notes for help installing and running the opentheory tool.


← Back to the list of examples
This step-by-step guide will quickly get you started on Leaflet basics, including setting up a Leaflet map, working with markers, polylines and popups, and dealing with events.
View example on a separate page →
Before writing any code for the map, you need to do the following preparation steps on your page:
<link rel="stylesheet" href="leaflet/leaflet.css" />

body
close tag):

div
element with a certain id
where you want your map to be and make sure it has defined width and height:

Now you're ready to initialize the map and do some stuff with it.
Let's create a map instance, set its view to the center of London and add a pretty CloudMade tile layer to it. First we'll initialize the map:
var map = new L.Map('map');
By default (as we didn't pass any options when creating the map instance), all mouse and touch interactions on the map are enabled, and it has zoom and attribution controls.
Next we'll create a tile layer to add to our map, in this case it's a CloudMade tile layer with Fresh style. Creating a tile layer usually involves setting the URL template for the tile images (get yours at CloudMade), the attribution text and the maximum zoom level of the layer:
var cloudmadeUrl = 'http://{s}.tile.cloudmade.com/YOUR-API-KEY/997/256/{z}/{x}/{y}.png',
cloudmadeAttrib = 'Map data © 2011 OpenStreetMap contributors, Imagery © 2011 CloudMade',
cloudmade = new L.TileLayer(cloudmadeUrl, {maxZoom: 18, attribution: cloudmadeAttrib});
Finally we'll set the map view to the center of London at 13th zoom level and add our tile layer (see the resulting map above):
var london = new L.LatLng(51.505, -0.09); // geographical point (longitude and latitude)
map.setView(london, 13).addLayer(cloudmade);
Make sure this code is below both the map div
and leaflet.js
inclusion, or in a window.load
or document.ready
event handler.
Besides tile layers, you can easily add other things to your map, including markers, polylines, polygons, circles, and popups. Let's add a marker:
var markerLocation = new L.LatLng(51.5, -0.09);
var marker = new L.Marker(markerLocation);
map.addLayer(marker);
Adding a circle is the same (except for specifying the radius in meters), but lets configure it by passing options as a third argument when creating the object (the second argument is the radius in pixels):
var circleLocation = new L.LatLng(51.508, -0.11),
circleOptions = {
color: 'red',
fillColor: '#f03',
fillOpacity: 0.5
};
var circle = new L.Circle(circleLocation, 500, circleOptions);
map.addLayer(circle);
Add a polygon is easy too:
var p1 = new L.LatLng(51.509, -0.08),
p2 = new L.LatLng(51.503, -0.06),
p3 = new L.LatLng(51.51, -0.047),
polygonPoints = [p1, p2, p3];
var polygon = new L.Polygon(polygonPoints);
map.addLayer(polygon);
Popups are usually used when you want to attach some information to a particular object on a map. Leaflet has a very handy shortcut for this:
marker.bindPopup("Hello world!
I am a popup.").openPopup();
circle.bindPopup("I am a circle.");
polygon.bindPopup("I am a polygon.");
Try clicking on our objects. The bindPopup
method attaches a popup with the specified HTML content to your marker so the popup appears when you click on the object, and the openPopup
method (for markers only) immediately opens the attached popup.
You can also use popups as layers (when you need something more than attching a popup to an object):
var popup = new L.Popup();
popup.setLatLng(new L.LatLng(51.5, -0.09));
popup.setContent("I am a standalone popup.");
map.openPopup(popup);
Here we use openPopup
instead of addLayer
because it handles automatic closing of a previously opened popup when opening a new one which is good for usability.
Every time something happens in Leaflet, e.g. user clicks on a marker or map zoom changes, the corresponding object sends an event which you can subscribe to with a function. It allows you to react to user interaction:
map.on('click', onMapClick);
function onMapClick(e) {
alert("You clicked the map at " + e.latlng);
}
Each object has its own set of events — see documentation for details. The first argument of the listener function is an event object — it contains useful information about the event that happened. For example, map click event object (e
in the example above) has latlng
property which is a location at which the click occured.
Lets improve our example by using a popup instead of an alert and formatting the location string:
map.on('click', onMapClick);
var popup = new L.Popup();
function onMapClick(e) {
var latlngStr = '(' + e.latlng.lat.toFixed(3) + ', ' + e.latlng.lng.toFixed(3) + ')';
popup.setLatLng(e.latlng);
popup.setContent("You clicked the map at " + latlngStr);
map.openPopup(popup);
}
Try clicking on the map and you will see the coordinates in a popup. View the full example →
Now you've learned Leaflet basics and can start building map apps straight away! Don't forget to take a look at the detailed documentation or other examples.
© 2011 CloudMade. Map data © 2011 OpenStreetMap contributors, CC-BY-SA.


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This test demonstrates how <set> elements change text properties on a <text> element. For each of the text properties being tested, 3 <set> elements are set. The first <set> element acts directly on the <text> element. The second <set> element acts on a <g> containing children. The third <set> element acts on an <a> containing children. In each case the test validates that the animated value set on the <g> and <a> elements is inherited by the <text> element. All the <set> elements have a begin attribute set to 0s with an offset of 1s after end. So, the animation will apply 1s after the document is loaded and will repeat every 1s after the animation ends.
The first <set> validates the transform property. When applied to the <text> element, the letter A will be translated to the right every 1s, in the <text> column. When applied to the <g> element, the letter A inherits the transform value and is translated to the right every 1s, as seen in the <g> column. When applied to the <a> element, the letter A inherits the transform value and is translated to the right every 1s, as seen in <a> column.
The second <set> validates the text-anchor attribute. When applied to the <text> element, the anchor position of letter A is moved from start to end. When applied to the <g> and <a> element, the property is inherited and hence the anchor position of letter A is moved from start to end in the second row.
The third <set> validates the font-size attribute. The font size of letter A is changed from 20 to 30. When applied to <g> and <a> elements, the letter A inherits the font-size and hence in row 3, letter A has a font-size of 30 in all 3 right columns of row 3.
The fourth <set> validates the font-family attribute. The font-family is changed from default to serif. When applied to <g> and <a> elements, the letter A inherits the font-family attribute and hence in row 4, letter A has serif font-family in all 3 columns.
The fifth <set> validates the font-style attribute. The font-style is changed from normal to italic. When applied to <g> and <a> elements, the letter A inherits the font-style attribute and hence in row 5, letter A is animated to italic in all 3 columns.
The sixth <set> validates the font-weight attribute. The font-weight is changed from normal to bold. When applied to <g> and <a> elements, the letter A inherits the font-weight attribute and hence in row 6, letter A is changed to bold on the right.


Enter the Rat
Your order total is:
Your pizza will be delivered to this address:
Thank you
for choosing
Pizza Rat.
Re-enter the Rat
Pick your pie!


Gecode::Int::Rel::ReEqBnd< View, CtrlView > Class Template Reference
[Integer propagators]
#include <rel.hh>
Inherits ReBinaryPropagator< View, PC_INT_BND, CtrlView >.
Detailed Description
template<class View, class CtrlView>
class Gecode::Int::Rel::ReEqBnd< View, CtrlView >
Reified binary bounds consistent equality propagator.
Requires
#include "gecode/int/rel.hh"
Definition at line 267 of file rel.hh.
Public Member Functions | |
| virtual Actor * | copy (Space *home, bool share) |
| Copy propagator during cloning. | |
| virtual ExecStatus | propagate (Space *home, ModEventDelta med) |
| Perform propagation. | |
| virtual Reflection::ActorSpec | spec (const Space *home, Reflection::VarMap &m) const |
| Specification for this propagator. | |
Static Public Member Functions | |
| static void | post (Space *home, Reflection::VarMap &vars, const Reflection::ActorSpec &spec) |
| Post propagator according to specification. | |
| static Support::Symbol | ati (void) |
| Mangled propagator name. | |
| static ExecStatus | post (Space *home, View x0, View x1, CtrlView b) |
| Post bounds consistent propagator . | |
Protected Member Functions | |
| ReEqBnd (Space *home, bool share, ReEqBnd &p) | |
| Constructor for cloning p. | |
| ReEqBnd (Space *home, View x0, View x1, CtrlView b) | |
| Constructor for posting. |
Constructor & Destructor Documentation
template<class View, class CtrlView>
| Gecode::Int::Rel::ReEqBnd< View, CtrlView >::ReEqBnd | ( | Space * | home, | |
| bool | share, | |||
| ReEqBnd< View, CtrlView > & | p | |||
| ) | [inline, protected] |
template<class View, class CtrlView>
| Gecode::Int::Rel::ReEqBnd< View, CtrlView >::ReEqBnd | ( | Space * | home, | |
| View | x0, | |||
| View | x1, | |||
| CtrlView | b | |||
| ) | [inline, protected] |
Member Function Documentation
template<class View, class CtrlView>
| Actor * Gecode::Int::Rel::ReEqBnd< View, CtrlView >::copy | ( | Space * | home, | |
| bool | share | |||
| ) | [inline, virtual] |
template<class View, class CtrlView>
| ExecStatus Gecode::Int::Rel::ReEqBnd< View, CtrlView >::propagate | ( | Space * | home, | |
| ModEventDelta | med | |||
| ) | [inline, virtual] |
template<class View, class CtrlView>
| Reflection::ActorSpec Gecode::Int::Rel::ReEqBnd< View, CtrlView >::spec | ( | const Space * | home, | |
| Reflection::VarMap & | m | |||
| ) | const [inline, virtual] |
template<class View, class CtrlView>
| void Gecode::Int::Rel::ReEqBnd< View, CtrlView >::post | ( | Space * | home, | |
| Reflection::VarMap & | vars, | |||
| const Reflection::ActorSpec & | spec | |||
| ) | [inline, static] |
template<class View, class CtrlView>
| Support::Symbol Gecode::Int::Rel::ReEqBnd< View, CtrlView >::ati | ( | void | ) | [inline, static] |
template<class View, class CtrlView>
| ExecStatus Gecode::Int::Rel::ReEqBnd< View, CtrlView >::post | ( | Space * | home, | |
| View | x0, | |||
| View | x1, | |||
| CtrlView | b | |||
| ) | [inline, static] |
The documentation for this class was generated from the following files:
- gecode/int/rel.hh (Revision: 7290)
- gecode/int/rel/eq.icc (Revision: 7348)


--- layout: archive title: Zulip Chat Archive permalink: /stream/116395-maths/topic/closure.20under.20colimits.html ---
Suppose C is a category.{u v}
that has_colimits
and I have a family A_i of objects of C indexed by a Type v
. I also have (let's say for simplicity) a fixed J which is a small_category.{v}
. I want to construct the closure of the objects A_i under colimits of shape J, as a new family also indexed on a Type v
. Is it possible?
I was going to use an inductive type of course, but in order to write down the data needed in the inductive constructor, I also need to know what the actual objects in C are (that is, the values of the indexed family), because a diagram involves morphisms in C between those objects. So I end up with an inductive-recursive definition.
I thought about adding the value of the object as an index of the type, but then it won't live in the right universe.
The only thing I can think of is to do some manual transfinite recursion up to an ordinal of large enough cofinality (I know... that's my solution to everything).
{% endraw %}Last updated: Apr 24 2020 at 19:02 UTC


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Delta flight evacuated after smoke fills cabin: 'There was smoke everywhere'
by Michael BartiromoA Delta Air Lines flight out of Madrid was evacuated prior to takeoff on Tuesday after smoke began filling the cabin.
The plane, which was bound for New York, was reportedly delayed for two hours following the evacuation, per Flight Aware.
STUDY CLAIMS ONE AIRLINE IS MORE LIKELY TO BUMP PASSENGERS
“The @delta plane got on fire in the back,” one passenger claimed in a Twitter post that contained footage of the incident. “There was smoke everywhere.”
FOLLOW US ON FACEBOOK FOR MORE FOX LIFESTYLE NEWS
The Twitter user, who identified himself as Paz, also claimed that passengers were not immediately allowed off the plane once the smoke was detected, and that he had “not stopped coughing” as of posting the tweet on Tuesday.
A representative for Delta was not immediately available to verify whether the cause of the smoke had been identified.
CLICK HERE TO GET THE FOX NEWS APP
Delta did, however, confirm on social media that its maintenance teams were investigating the incident.
“Thank you for this information and I see that our Maintenance Teams are currently working on this issue,” the airline tweeted at Paz. “Thank you for sharing.”


This package contains an alternative to the standard javadoc doclet It's meant to be prettier and more interactive than the standrad javadoc format. Also it uses JOT templates & CSS, so is much easier to customize than standard javadoc format.


WELCOME
TO DELANI STUDIO
AMAZING PEOPLE ARE MAKING AMAZING DESIGNS IN A FUN ENVIRONMENT
AMAZING PEOPLE ARE MAKING AMAZING DESIGNS IN A FUN ENVIRONMENT
When you work with us, you are a part of a team of committed collaborators. All aspects of our software development process are intergrated,interactive and agile
Our approach unifies design,development and product management to create exceptional products.
We start each project by understanding your business goals,the user's needs and the product requirement.
Then we help translate them into effective and elegant solutions.
Before we sign a contract or write a line of code our team will spend the necessary time needed to understand your product vision
The outcome of this scoping session is a proposal or high-level statement of work
based on your requirements, we can provide a complete offering or just the pieces you read.
Our design practice offers a full range of services including brand strategy, interaction and visual design and user experice testing.
Throughout yourproject, our designers create and implement visual design and workflows, solicit uswer feedback and work with you to make sure what gets build is what is needed
All engineers are fluent in the latest enterprise, mobile and web development technologies.
They collaborate with yournteam to write ad improve code on daily basis, using proven practices such as test-driven development and pair programming.
Planning and development is interactive. Because we are constantly coding and testing, the products we build are always ready to go live
This interactive process allows for change as business requirements evolve


"All the DJ's keep complaining
The tunes run much too long
So I went and wrote myself
a 26-second song."
The tunes run much too long
So I went and wrote myself
a 26-second song."
— Shel Silverstein, 26 Second Song
A Single Stanza Song sounds like a case of Second Verse Curse or a Chorus-Only Song, but there is one big difference: There really is only one stanza.
If there were ever other lyrics, they are lost to history. If these lyrics are repeated, it becomes Looped Lyrics (and if it repeats too much, Broken Record).
Contrast Second Verse Curse, Chorus-Only Song and Something Something Leonard Bernstein.
Examples:
open/close all folders
Alternative Rock
- Aside from the rap break in the middle, Dirty Harry by Gorillaz has only a single, six-line verse.
I need a gun to keep myself from harmThe poor people are burning in the sunThey ain't got a chanceThey ain't got a chanceI need a gun 'cause all I do is dance'Cause all I do is dance
- The title track of Coldplay's Parachutes, which only runs 46 seconds.
- The full song: "In a haze, a stormy haze, / I'll be 'round, I'll be loving you always. / Always. / Here I am and I'll take my time, / here I am and I'll wait in line always. / Always."
- They Might Be Giants:
- John Flansburgh did a few of these with his side project band Mono Puff: "Nixon's The One" has just 2 lines, "Dr. Kildare" has 4 lines of lyrics in the middle of an otherwise instrumental song, "Distant Antenna" has a single prose paragraph of text spoken over the music.
- "Minimum Wage" from Flood consists of the title, followed by a "HYAH!" and a whip-crack, then a little over half a minute of instrumental music.
- Most of the songs in "Fingertips" from Apollo 18 are only long enough for one verse. Some are only long enough for a single line, like "Who's That Standing By My Window?" and "The Day That Love Came to Play".
- There are several of these on TMBG's album Nanobots, such as "Destroy The Past".
- "Michigan" and "Nevada" from John Linnell's solo project State Songs are both a single verse, although the latter is followed by six minutes of a diminuendo-ing marching band.
- "The Famous Polka" is about 75 seconds of instrumental music, followed by a single stanza:
A famous person wears the same size water skis as me
She's got three cars, as many years I've lived in this city
Her hair is blonde and mine is brown, they both start with a "b"
But when the phone inside her rib cage rings, it's not for me
But when the phone inside her rib cage rings, it's not for me
HEY!
- "Elizabeth My Dear" by The Stone Roses. 30 words, less than a minute long, and extremely creepy.
- Phish's "The Divided Sky" has multiple composed sections and goes on for over ten minutes but the sole lyrics are, "Ah, divided sky, the wind blows high."
- This seems to be a trend with them, as several of their most famous songs - "You Enjoy Myself", "Run Like An Antelope" and "Weekapaug Groove" especially - are around 10 minutes long but have only one or two lines.
- Nine Inch Nails has two on The Downward Spiral: "Big Man With A Gun" and the Title Track.
- Harry and the Potters' "This Book Is So Awesome" is something like 28 seconds long.
- This is one of the reasons why San Pedro band the Minutemen had that name.
- "Tautou", the first track on Brand New's album Deja Entendu. The lyrics are "I'm sinking like a stone in the sea/I'm burning like a bridge for your body"
- The Pixies' "Stormy Weather" from Bossanova. "It is time, oh oh, it is time for stormy weather." Over and over. Not even a stanza, just a line.
- From the same album there's "Ana", which does have a whole stanza - it's one six line verse repeated a few times:
She's my fave
Undressing in the sun
Return to sea - bye
Forgetting everyone
Eleven high
Ride a wave - The reason for this is that it's an acrostic - If you put the first letter of every line together, it spells "surfer".
- From the same album there's "Ana", which does have a whole stanza - it's one six line verse repeated a few times:
- "Little Tiny Song" by Barenaked Ladies/The Brothers Creeggan:
Hey, I'm a cow, I'm curious
Hey watch me now, I'm furious
Hey, I'm a cow, I'm full of hate
Hey watch me now, I'm on your plate - "New Day Rising" by Hüsker Dü repeats its title all throughout the song, in various styles, shouting being the most prominent. "If I Told You" is also an example.
- "Cigarette" by Ben Folds Five.
- "Skeleton's Lullaby", a bonus track on Ludo's album Prepare The Preparations.
- "Nature Anthem" by Grandaddy.
- "There She Goes" by The La's.
- "Tender Lumplings" on Oingo Boingo's final studio album:
O listen, tender lumplings, let me take your little hand
I'll take you from this hell-hole to the promised land
But don't blame me, O children, if those promises don't keep
'Cuz promises, like lives, can be bought so very cheap - Feeder have two: "20th Century Trip" from Polythene (1997) and the inter-track "Space" from Silent Cry (2008):
Fading like someone who's given up on life
You've gotta know, know how that feels
People will always change, never stay the same
We've got to believe, we've got to believe - "Woods" by Bon Iver is the same four lines repeated with increasing levels of orchestration.
I'm lost in the woodsI'm down on my mindI'm building a stillTo slow down time
- "A Lady" by Tally Hall. Most of the song is an arrangement of gentle, harp-like piano notes and "aahs" aside from these lyrics:
I know a ladyShowed me that I was a gentlemanWait for the girl to blossom intoColors that grow where you can
- "#1 Hit Jam" by Brian Jonestown Massacre is a five minute song where the only lyrical content is "Hey, you".
Avant-garde
- Buckethead's three/four-line, 26-second song, "Taxidermy Tots". The lyrics go "Mom says I'm the best at playin' with taxidermy / That's why I'm gonna taxidermy you / Shouldn't have said those mean things to me last night / (cough cough) WHHHHAAAUUGGGHHHH"
- The Residents did a whole album of songs (about three dozen of them) that were one verse and one chorus long, all of which came in at one minute or less. They promoted it by buying time on a local Top 40 station and having the entire album played as advertisements.
- Yoko Ono's "Don't Worry, Yoko (Mummy's Only Looking For A Hand In The Snow)" is just "Don't worry" repeated over and over.
Blues-Rock
- Both of Blind Faith's hits, "Can't Find My Way Home" and "In The Presence of the Lord", consist of a single verse repeated three times with a solo between the second and third iteration.
- "People Are Strange" by The Doors is the same verse and chorus repeated three times.
Christian Rock
- Relient K's "Crayons Can Melt On Us For All I Care". The full lyrics are: "I just wasted ten seconds of your life."
Classical
- Every movement of J.S. Bach's Mass in B Minor is a Single Stanza Song because each movement is taken from a section of the Lutheran Mass. Such sections are made up of short phrases, such as "Kyrie eleison" (Lord have mercy).
Comedy / Parody
- "Harvey The Wonder Hamster" by "Weird Al" Yankovic.
- Subverted in Weird Al's "This Song's Just Six Words Long," a parody of George Harrison's "Got My Mind Set On You." Harrison's song nearly fits this trope itself; Weird Al's version is not only longer than six words, but none of the stanzas repeat.
- Sandra Boynton, children's writer, created "The Shortest Song in the Universe".
The shortest song in the universe
Really isn't much fun
It only has one puny verse
... and then it's done! - "This Song Is Boring" by Darryl Rhoades and the Hahavishnu Orchestra.

- Roger Miller's "Husbands and Wives" is almost an example, as it consists of the same verse twice, but the first time around, he adds "A woman and a man, a man and a woman / Some can, some can't, and some can." Brooks & Dunn's cover plays it straight, since it adds that line both times.
- "Heartland" by George Strait.
Dance
- "Don't Let the Man" by Fatboy Slim:
...and the sign said "Long-haired freaky people need not apply"...
- The line is said twenty times in roughly four minutes.
- And pretty much any other lyrical song by him. "Right about now, the funk soul brother / Check it out now, the funk soul brother"
Dance-Punk
- "HEY! HO!  - the entirety of the lyrics from Art vs. Science's "Flippers".
Dark Cabaret
- "672" by the Dresden Dolls: "Six-hundred-seventy-two (repeat 3 times) OHHHHHHHHHHHHHHHHHHH / Some day they'll find about you too..." And no, Amanda Palmer never explains what the hell that's supposed to mean.
Disco
- The Silver Convention had songs that had only six different words:
- "Fly Robin Fly":
Fly, robin, fly
Fly, robin, fly
Fly, robin, fly
Up, up to the sky! - "Get Up And Boogie":
That's right!
Get up and boogie!
Get up and boogie!
(instrumental line)
(more instrumental, then) That's right!
(instrumental, then) Boogie!
(instrumental, then) Boogie!
(two more instrumental lines and then) That's right!
(etc. etc. etc.)
- "Fly Robin Fly":
Electronic / Techno
- The Prodigy:
- "Smack My Bitch Up" consists of the eponymous lyrics over the same short techno loop about a zillion times.
- "Breathe" just has the one verse as well.
- "Poor Leno" by Röyksopp contains only a few repeated lines sung by Erlend Øye, one of the members of Kings Of Convenience.
- The Daft Punk song "Around the World", as recited in this Diesel Sweeties strip.
- "Harder, Better, Faster, Stronger" is pretty much just various permutations of:
Work it harder, make it better
Do it faster, makes us stronger
more than ever, Hour after
Our work is never over
- "Harder, Better, Faster, Stronger" is pretty much just various permutations of:
- "Old Piano" by Frou Frou:
What's that you're saying there?  - "Five Ways To Run" by The Crystalline Effect:
You can watch in silence, the world go by
You can feel the sadness that makes you cry
You can take action for what is right
You can inspire - The lyrics of Eric Prydz's "Call on Me" consist entirely of a looped lyric sampled up from Steve Winwood's "Valerie".
- Covenant has many, such as "Shelter", "Flux", "One World, One Sky", "The Men", "Kairos", et al.
- "Going Nowhere" by Cut Copy:
I can't think straight
Help me now before it's too late
Now what do I care?
'Cause we're going nowhere...
Experimental Rock
- "European Son" by The Velvet Underground has two very short stanzas before launching into a ten minute jam.
Folk
- "White Winter Hymnal" by Fleet Foxes is one verse repeated three times.
- A Hawk and a Hacksaw: "Laughter in the Dark"'s only lyrics are "Mean what you say, and say what you...". "For Slavoj"'s only lyrics are "I love you", repeated several times.
- "The Michael Jordan of Drunk Driving" by Andrew Jackson Jihad is just over 20 seconds and consists of four lines
Funk
- Parliament had some songs like this. For example, "Supergroovalisticprosifunkstication" only has two lines:
Give the people what they want, when they want, and they wants it all the time
Give the people what they need, when they need, and the need is yours and mine
Throwdown
Make me do the throwdown- Sometimes this would overlap with Spoken Word in Music; songs would only have a chorus, but someone would be speaking between each chorus.
Grindcore
Grunge
- "Stain" by Nirvana:
Well he never bleeds and he never fucks
And he never leaves 'cause he's got bad luck.
Well he never reads and he never draws.
And he never sleeps 'cause he's got bad luck, yeah
I'm a stain, I'm a stain, I'm a stain, I'm a stain- As well as "School."
Verse: Won't you believe it, It's just my luck
Chorus: No recess
Bridge: You're in high school again
Repeat as necessary
- As well as "School."
Hard Rock
- Bang Camaro pretty much is this trope
Hardcore Punk
- "I'm Shipping Up to Boston" by the Dropkick Murphys. One verse and one chorus repeated.
Heavy Metal
- "Power Of The Power Of The Power (Of The Great Sword)" by NanowaR.
Hip Hop
- On Eric B. and Rakim's breakthrough hit "Paid in Full" Rak's rap is a single 24-line stanza with no chorus or break.
- Lindsey Stirling's "Stars Align" is mostly instrumental, but has some vocals in the form of da-ing followed by "when the stars align". This is repeated a couple times without changes.
 This is all she says, ad nauseam.
Hymns
- The Christian Doxology (Only four lines long).
- Several modern worship songs fit this bill.
- "Shout to the Lord." One verse plus one chorus. Repeat as desired.
- "Shout to the Lord" is practically a novel compared to some of the songs of the Taizé Community. Check out "Jesus Remember Me" on this page, for example. As meditation music, they're supposed to be repetitive and somewhat hypnotic to focus the worshipper on prayer.
- "Down to the River to Pray" is a weird example of this, it's almost like a single multiple choice stanza song. The words are
As I went down in the river to pray
Studying about that good ol' way
And who shall wear the starry crown/robe and crown?
Good Lord show me the way!
O sisters/brothers/fathers/mothers/sinners let's go down
Let's go down, come on down
O sisters/brothers/fathers/mothers/sinners let's go down
Down in the river to pray
National Anthems
- The anthems of Japan, San Marino and Jordan each have four lines. They are the world's shortest.
- The national anthem of Germany is the third/last stanza of the 1841 poem "Das Lied der Deutschen" (also known as "Deutschlandlied"), whose three stanzas have been used in various constellations as national anthem since 1922.
- The Israeli national anthem is actually just a single sentence, and then another for the refrain, even though it runs about the typical length for an anthem. However, it also borders on Second Verse Curse, because the words are actually taken out of a ten stanza song.
New Age
- The winning song of the Eurovision Song Contest in 1995 was Norway's entry, Nocturne performed by Secret Garden. The song consisted of just 24 words.
New Wave
- Ladytron's "Seventeen". They only want you when you're seventeen, when you're twenty-one, you're no fun.
- Ladytron tends to repeat lyrics in nearly all of their songs, but it's most noticeable in "Seventeen".
- The title of The Police song "Voices Inside my Head" already forms half of the entire lyrics, the other half being "...echo things that you said."
Pop
- Herman's Hermits' "I'm Henry the Eighth I Am" - also a Looped Lyrics song.
Second verse, same as the first!
- "Night Boat to Cairo" by Madness has only one verse; the rest of the lyrics are just random interjections of the title and "all aboard!".
- Herbie Hancock's "Rockit":
Don't stop it
Rock it
Don't stop it - The Rainbow's "Balla Balla" consists of the line "My baby baby balla balla" followed by a chorus of repeated "balla"s.
Post-Metal
- Most songs by the post-metal band Isis, despite being upwards of 8 minutes long in some cases, often have one verse, sang one time somewhere in the middle of the song.
Post-Punk
- The closing track on Lifter Puller's first self-titled LP, "Mono", has only one stanza before entering a progressively louder and louder noise-rock section.

Power Metal
- Several of the songs on Blind Guardian's Nightfall in Middle-Earth. One of them, "Nom the Wise" consists of just the spoken lines: "Thus he died, Nom the Wise. Lord of the Caves and Friend of Man. Fair and noble, most beloved of the Noldor race. He paid the price, he redeemed the Oath. Farewell, my friend, farewell." Another one consists of the single sung line: "A dark seed of evil is grown."
Power Pop
- Fountains of Wayne's "Yours and Mine".
Progressive Rock
- The lyrics to the 2nd movement of "I've Seen All Good People" by Yes are simply one line repeated several times.
- "White Car" from Drama has just four lines in it.
- Traffic's "Dear Mr. Fantasy" consists of one verse repeated three times.
- The single version of "Eve of the War" from Jeff Wayne's Musical Version of The War of the Worlds has just an Epic Instrumental Opener and one verse:
The chances of anything coming from MarsAre a million to one, he saidThe chances of anything coming from MarsAre a million to one, but still they come!
- Downplayed in the album version, which does still have only one sung verse, but features Richard Burton's spoken narration as well. And averted altogether by the 1989 hit remix, which has the narration but not the singing.
Punk Rock
- The Living End's 34-second song "Ready" features the lyrics:
Well if she's not that kind to you,
Don't ya think we're through buddy?

I don't wanna walk around with you!
I don't wanna walk around with you!- "Now I Wanna Sniff Some Glue":
Now I wanna sniff some glue
Now I wanna have somethin' to do
All the kids wanna sniff some glue
All the kids want somethin' to do - "It's A Long Way Back":
You all alone
You by the phone
It's a long way back to Germany
It's a long way back to Germany - "I Wanna Be Sedated":
Twenty-twenty-twenty four hours to go I wanna be sedated
Nothin' to do and no where to go-o-oh I wanna be sedated
Just get me to the airport put me on a plane
Hurry hurry hurry before I go insane
I can't control my fingers I can't control my brain
Oh no no no no no
- "Now I Wanna Sniff Some Glue":
- Flipper's "Sex Bomb" - the only lyric printed in their album liner notes is "She's a sex bomb, my baby, yeah", and the vocals consist of variations on this one line, along with a few shouts of "Whoa!" or "yeah!" and a lot of horrifying screaming. For about eight minutes.
- Rocket From The Tombs' "Frustration" takes this to the extreme - the only lyric in the song is David Thomas yowling the title a few times.
Rock
- "Summer's Day Song" from McCartney II.
- The Beatles:
- "Why Don't We Do It In The Road?" consists of the same six-line verse sung three times. All six lines are simply the song's title except for the fifth line, which is "No one will be watching us."
- "Can You Take Me Back", the hidden song that immediately proceeds "Revolution 9" on the White Album.
- "Wild Honey Pie" from the White Album:
Honey Pie!
Honey Pie!
Honey Pie!
Honey Pie!
Honey Pie!
Honey Pie!
Honey Pie!
Honey Pie!
I love you!
Honey Pie! - "You Know My Name (Look Up The Number)" uses three different arrangements using the vocals then follows with a jazzy piano arrangement with the sounds of harmuphing and coughing.
- "I Want You (She's So Heavy)" from Abbey Road has a single verse ("I want you / I want you so bad / I want you so bad it's driving me mad, it's driving me mad", repeat) played three times (the second time as an instrumental) alternating with the chorus, which consists solely of the words "She's so heavy".
- The Abbey Road closer "Her Majesty" consists of a single verse and only lasts 23 seconds.
Her Majesty's a pretty nice girl but she doesn't have a lot to say
Her Majesty's a pretty nice girl but she changes from day to day
I wanna tell her that I love her a lot, but I gotta get a belly full of wine
Her Majesty's a pretty nice girl, some day I'm gonna make her mine, oh yeah
Some day I'm gonna make her mine
- Sparks' "There's No Such Thing as Aliens". The lyrics consist mostly of the title, with two nearly identical stanzas in between.
- David Bowie's "Eight Line Poem" is... Well, an eight line poem.
- "Lightning Frightening", an outtake from 1971, is another example. One line repeated twice, chorus, lengthy instrumental part, repeat.
- "Guide Vocal" by Genesis, off their somewhat lackluster Duke album, is just over a minute long, and is one of the nastiest breakup songs ever (with the exception of the outright Ax-Crazy "Vow" by Garbage).
- Peter Gabriel recorded several single stanza songs over his solo career.
- The entirety of the lyrics of "Fourteen Black Paintings" from Us are as follows:
from the pain comes the dream
from the dream comes the vision
from the vision come the people
from the people come the power
from this power comes the change. - "Lead A Normal Life", from his third Self-Titled Album, is a single verse's worth of lyrics sandwiched between a lengthy instrumental intro and outro:
It's nice here with a view of the trees
Eating with a spoon?
They don't give you knives?
'Spect you watch those trees
Blowing in the breeze
We want to see you lead a normal life - "We Do What We're Told (Milgram's 37)", from So:
We do what we're told
We do what we're told
We do what we're told,
Told to do.
We do what we're told
We do what we're told
We do what we're told,
Told to do.
One doubt
One voice
One war
One truth
One dream
- The entirety of the lyrics of "Fourteen Black Paintings" from Us are as follows:
- The ''only'' lyrics of Roky Erickson's "I walked with a zombie" are "I walked with a zombie last night" - that's verse, chorus, everything. Unless you count the backing vocals ("He walked with a zombie").
- "Passive Manipulation" by The White Stripes is Meg singing the following verse, looped for thirty seconds:
Women, listen to your mothers
Don't just succumb to the wishes of your brothers
Take a step back, take a look at one another
You need to know the difference between a father and a lover - Bob Dylan's "All The Tired Horses" consists of the chorus girls singing the lines "All the tired horses in the sun/How'm I supposed to get any ridin' done?/Hmmm." This hasn't stopped dylanologists from examining and interpreting them at length.
- "Colour My World" by Chicago starts with a piano solo and ends with a flute solo, and has this verse in the middle:
As time goes on, I realize
Just what you mean to me
And now, now that you're near
Promise your love that I've waited to share
And dreams of our moments together
Colour my world with hope of loving you- Reportedly, Frank Sinatra expressed interest in covering the song, on the condition that composer James Pankow write a second verse. Pankow respectfully declined.
- "T-Bone" by Neil Young has 2 lines and various permutations of it:
Got Mashed Potato
Ain't Got No T-Bone- Even the lyric book itself tells you to repeat the line in order to save space.
- Steely Dan's "The Fez" has one stanza repeated three times:
No, I ain't gonna do it without my fez on, oh no
Don't make me do it without my fez on, oh no
That's what I am
Please understand
I wanna be your holy man - Frank Zappa's "Willie The Pimp" consists of one stanza, followed by a nine-minute jam.
- Billy Joel's "Souvenir" is one stanza with a short piano motif on either end.

Rock and Roll
- "Naked, If I Want To" by Moby Grape. Four lines (in an ABCB rhyme scheme), 51 seconds long.
- "Hey" by The Sensational Alex Harvey Band ("I knew we had/to say goodbye/when I felt that warmth/against my thigh.... HEY! is that you pissing on my leg?")
- "Runaway" by Del Shannon is one of the most awesome old time rock'n'roll songs ever, being the obvious genesis of hard rock (particularly punk). It also has a second verse consisting entirely of an organ solo with no words whatsoever.
- The Rock-a-Teens "Woo Hoo", famously covered by Japanese all-girl band The <IP_ADDRESS>'s in Kill Bill Volume 1. It goes only "woo-hoo, woo-hoo-hoo" over and over and over.
Stoner Metal
- "Lick Doo", the hidden track on Kyuss's Welcome to Sky Valley.
Thrash
- S.O.D. has "The Ballad of Jimi Hendrix", consisting of a few seconds of the intro to Purple Haze followed by the words "You're dead".
Traditional
- "Happy Birthday to You!" might be an example.
- The Portuguese version averts this. It's a full-fledged poem with four quatrains, although people usually only sing the first two - yet it's not uncommon in Portugal to sing the third one after the clapping.
- This is the song that doesn't end/ Yes, it goes on and on, my friend
- An old perverted Brazilian song: "coelhinho, se eu fosse como tu, tirava a mão do bolso e enfiava a mão no... coelhinho, se eu fosse como tu..." (translation with an added word to make sense: "bunny rabbit, if I were you sass, I'd take the hand off the pocket and into the...")
- Parodied by Neil Innes's "Short Blues", which abruptly ends after one line of lyrics.
Uncategorized
- I Love Beijing Tiananmen is a strange example. the lyrics stay the same but the tune changes.
Examples from other media:
Film
- The song "I Am Sad, So Very, Very Sad" by Crash and the Boys in Scott Pilgrim vs. The World consists of only the words "Soooooo sad!". The song only lasts about five seconds. In the graphic novels, it's said to last less than one.
- Here's to you, originally written by Ennio Morricone for the movie Sacco e Vanzetti, and later featured in the game Metal Gear Solid 4.
Here's to you, Nicola and Bart
Rest forever here in our hearts
The last and final moment is yours
That agony is your triumph
Opera / Theatre
- The musical Wicked has one when the students sing about Dear Old Shiz.
- The musical She Loves Me has the very brief recurring chorus "Thank You, Madam".
- A similar recurring chorus was "Poor Joe" from Allegro: only 8 bars long.
- "Day By Day" from Godspell has only about six lines of lyrics. "Prepare Ye" has only a single line.
- Much of Godspell is like this. The finale consists of 9 lines of lyrics, and "All for the Best" is two characters singing one stanza each on top of each other repeatedly.
- "Our State Fair" from Rodgers and Hammerstein's State Fair has a four-line refrain and no verse, not even an unused one.
- "I'm Like The Bluebird" from Anyone Can Whistle is a Two Stanza Song. The stanzas are four lines long and nearly identical.
- The title song of The Pajama Game.
- "Wintergreen for President" from Of Thee I Sing has two lines of lyrics, not counting repetitions of the title or wordless snatches of other campaign songs:
He's the man the people choose;
Loves the Irish and the Jews.
Video Games
- The lyrics to the beatmania IIDX song "thunder" are composed of two whole sentences (albeit stretched out over eight measures each), both of which are identical save for two words, and are repeated twice in the 2 1/4-minute game version and even more in the extended 5:43 version:
I'm drifting through the mists of love to find out where my heart belongs
I'm drifting through the mists of love to find the place my heart belongs - The credits song for Prince of Persia: The Sands of Time has only one verse and one chorus.
Web Original
- "A Bug Fell In Love With A Cat" by Songs to Wear Pants To. In fact the title is the lyrics in their entirety. There's also "Don't Feel Bad", where the lyrics consist of the single line "Don't feel bad, it's better than being shot in the face".
- "Red Like Roses", the Red theme from RWBY has just one verse; the rest is instrumental.
Red like roses fills my dreams and brings me to the place you rest
White is cold and always yearning, burdened by a royal test
Black the beast descends from shadows
Yellow beauty burns gold
Western Animation
- The credits theme to The Raccoons, "Run with Us", was this at first, but was later turned into a full-length song.
- Many, if not all of Jem and the Holograms' songs (and the ones by The Misfits, and The Stingers for that matter).
- The first song at the beginning of The Rescuers, "The Journey", is mostly instrumental but with one stanza.
Who will rescue me?
I'm lost at sea without a friend.
This journey, will it ever end?
Who will rescue me?


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How do I think? How do I process information? What strategies enhance my learning the most? What are my biggest obstacles when it comes to learning? These are all questions that have been cycling through my head ever since I embarked on my DBC journey. So I took the Gregorc Thinking Style quiz to help me answer these questions. I have to say that the results seem to be pretty much spot on. My thinking style can best be described as Concrete Random. I am most comfortable taking in information that I can see, hear, or touch and organizing that information in chunks. However, not every aspect of Concrete Random Thinking applies to me; nobody is purely one type of thinker. So what aspects do apply?
How does any of this apply to my experience at DBC? I have found that my trial and error approach to problem solving is really helpful in coding exercises. Coding is definitely a process where you try one method, then maybe another, then another, and another...until you solve your problem. What I have struggled with so far is getting myself into a routine and trying to stay on task to finish all of the work in a timely manner. I've had to write out schedules for myself and stick to those schedules. I've completed all of my tasks so far, but I feel like I am often racing against the clock.
So can I expand and change the way that I think and learn? Can anyone? Absolutely! It's all about having a growth-mindset. It's about stepping out of your comfort zone every now and again and challenging yourself.


PRESENTLY I'M IN PARAGUAY BUT BY NEXT WEEK I WILL BE IN CHINA FOR INVESTMENT PROJECTS WITH MY OWN SHARE OF THE TOTAL SUM. MEANWHILE,I DIDN'T FORGET YOUR PAST EFFORTS AND ATTEMPTS TO ASSIST ME IN TRANSFERRING THOSE FUNDS DESPITE THAT IT FAILED US SOME HOW.   SO FEEL FREE AND GET IN TOUCH WITH MY SECRETARY AND INSTRUCT HIM WHERE TO SEND THE AMOUNT TO YOU. PLEASE DO LET ME KNOW IMMEDIATELY YOU RECEIVE IT SO THAT WE CAN SHARE THE JOY AFTER ALL THE SUFFERNESS AT THAT TIME.   REGARDS, MR MOZIE RAPHAEL ELOKA PETERS EMAIL;eloka_peters005@ummah.org