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Nijito
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Implements several stage commands for the Yarn scripts to use. More...
Public Member Functions | |
| void | AnimateStage (string[] args) |
| <<animate-stage ANIMATION [and wait]>> More... | |
| void | Background (string[] args) |
| <<background IMAGE [now|quickly|slowly] [and wait]>> More... | |
| void | ItemBox (string[] args) |
| <<itembox ITEM>> <<itembox hide [ITEM]>> More... | |
| void | Sound (string[] args) |
| <<sound SOUND-EFFECT [at VOLUME%] [and wait]>> More... | |
| void | StageFade (string[] args) |
| <<stage-fade to [black|white|IMAGE] [overlay] [now|quickly|slowly] [and wait]>> <<stage-fade out [overlay] [now|quickly|slowly] [and wait]>> <<stage-fade in [now|quickly|slowly] [and wait]>> More... | |
| void | Music (string[] args) |
| <<music TRACK [now|quickly|slowly]>> More... | |
| void | Wait (string[] args) |
| <<wait SECONDS>> More... | |
Implements several stage commands for the Yarn scripts to use.
These commands are generic commands, and they don't interact specifically with characters. Character commands are in the CharacterCommands class.
Note that, whenever you have a name of an asset (e.g. a music track or a sound effect) which contains a space, you must wrap it in double quotes.
For any command with options such as now, quickly, and slowly, these options control the relative speed of the movement. Note that the exact speed depends on the command being used.
For commands with wait or and wait options, those will cause the dialogue system to pause until the command finishes being carried out. This does nothing if now is also used. Also be careful of combining this with slowly too often; that might make things draggy.
| void Dialogue.VN.StageCommands.AnimateStage | ( | string [] | args | ) |
<<animate-stage ANIMATION [and wait]>>
Plays ANIMATION, which is an animation which has been set up on the stage in Unity.
If and wait is given when playing a looping animation, then dialogue pauses until the animation plays once.
Only one animation can play at a time, and specifying None (or an invalid animation) will cause the current animation to stop.
<<animate-stage Earthquake and wait>>
Play the "Earthquake" animation and wait for it to finish.
<<animate-stage None>>
Stop the current stage animation, if any.
| void Dialogue.VN.StageCommands.Background | ( | string [] | args | ) |
<<background IMAGE [now|quickly|slowly] [and wait]>>
Displays IMAGE in the background, where IMAGE is some background image that has been configured in Unity.
If IMAGE is None (or invalid), then a black background is shown instead.
<<background "Some Awesome Stage" now>>
Show "Some Awesome Stage" immediately.
<<background Home and wait>>
Show "Home," and wait until we finish fading into it.
| void Dialogue.VN.StageCommands.ItemBox | ( | string [] | args | ) |
<<itembox ITEM>>
<<itembox hide [ITEM]>>
In the first form, displays ITEM in an item box, where ITEM is the name of an item specified in Unity.
The second form hides the named item box. If no name is given, then all item boxes are hidden.
<<itembox EmployeesOnlySign>>
Display an item called "EmployeesOnlySign."
<<itembox hide EmployeesOnlySign>>
Hide the display for an item called "EmployeesOnlySign."
<<itembox hide>>
Hide whatever item(s) are currently being displayed, if any.
| void Dialogue.VN.StageCommands.Music | ( | string [] | args | ) |
<<music TRACK [now|quickly|slowly]>>
Cause background music named TRACK to start playing, where TRACK is the (case-insensitive) name for a song.
Tracks and their names are defined in Unity, so we can't put a full list here. If TRACK is None, the current song is stopped. If TRACK cannot be found, an error is sent to the debug console and it is treated as None.
If no song is playing, the new song will play immediately. If a song is playing, then the old one will fade out and the new song will begin to play after a short delay.
Options which control speed will alter the rate at which the songs fade.
<<music "Beautiful Lie">>
Plays a song named "Beautiful Lie." (No, we aren't ripping tracks from Danganronpa.)
<<music "Never Gonna Give You Up" now>>
Get Rick-Rolled without letting the previous song fade out.
<<music None>>
Stops the current track.
<<music None now>>
Stops the current track without any fade out.
| void Dialogue.VN.StageCommands.Sound | ( | string [] | args | ) |
<<sound SOUND-EFFECT [at VOLUME%] [and wait]>>
Plays SOUND-EFFECT once.
The list of sound effects (and their names) must be configured in Unity.
If given, VOLUME adjusts how loud the sound plays. Can be any percentage between 0% and 100%.
<<sound Beep>>
If the sound named "Beep" is configured, it's played.
<<sound "Breaking glass">>
If the sound named "Breaking glass."
<<sound Beep at 50%>>
Same as before, but "Beep" is played at half volume.
<<sound Beep wait>>
Same as before, but game waits until the sound finishes.
| void Dialogue.VN.StageCommands.StageFade | ( | string [] | args | ) |
<<stage-fade to [black|white|IMAGE] [overlay] [now|quickly|slowly] [and wait]>>
<<stage-fade out [overlay] [now|quickly|slowly] [and wait]>>
<<stage-fade in [now|quickly|slowly] [and wait]>>
In the first form, fades out to black, white, or IMAGE, where IMAGE is the name of an image that's been configured in Unity. If IMAGE is invalid, black is used instead.
The second form is a shortcut the first form that always fades to black.
In the third form, the fade effect is removed, showing everything.
If overlay is given, then everything, even the text box, is also hidden by the fade effect. Note that, even if this is given, the text box will be unhidden if any more dialogue is printed while we're faded out.
(Note that this is a great way to hide various other stage directions, like moving characters around, etc.)
<<fade out>>
Turns the screen black without hiding the dialogue box.
<<fade to white overlay now>>
Immediately turns the screen white, covering the dialogue box.
<<fade in now>>
Immediately fades back in.
| void Dialogue.VN.StageCommands.Wait | ( | string [] | args | ) |
<<wait SECONDS>>
Waits for SECONDS, and the continues to the next text box.
Note that this doesn't pause any on-going animations. It simply stops future text boxes and commands from triggering until the wait is over.
This is part of Yarn. See Yarn's documentation.
<<wait 2>>
Wait for 2 seconds.
<<wait 0.5>>
Wait for half a second.


About me
Hi, My name is Dohee Kim. I'm a master student in the School of Computing at KAIST, advised by Prof.Jongse Park. I'm a member of Computer Architecture and Systems Laboratory(CASys).
If you have any questions for me, contact me via my email. My email address is dhkim at casys.kaist.ac.kr
Research Interest
- Computer Architecture
- System for Machine Learning
- Edge-to-Cloud Computing
- Distributed Systems
- Approximate Computing
Education
- March 2020 - Current : M.S. in the School of Computing, KAIST
- March 2016 - February 2020 : B.S. in IT engineering, SMWU (Summa Cum Laude)


--- layout: post title: "Types + Properties = Software" description: "Combine a strong type system with Property-Based Testing to specify software." date: 2016-02-10 11:50 UTC tags: [Unit Testing, Software Design, F#, Article Series] image: "/content/binary/type-spectrum.png" image_alt: "A spectrum of languages, from most dynamic on the left, to most static on the right." --- {% include JB/setup %}
{{ page.description }}
When Kent Beck rediscovered Test-Driven Development (TDD) some twenty years ago, the original context was SmallTalk programming. When the concept of TDD began to catch on, it seemed to me to proliferate particularly in dynamic language communities like Python and Ruby.
It makes sense that if you can't get fast feedback from a compilation step, you seek another way to get feedback on your work.  Watching the NodeJS community from the side, it always seemed to me that TDD is an integral way of working with that stack. This makes sense.
This also explains why e.g. C# programmers were more reluctant to adopt TDD. That your code compiles gives a smidgen of confidence.
C# and Java programmers may joke that if it compiles, it works, but also realise that that's all it is: a joke. Automated testing adds another layer of safety on top of compilation. On the other hand, you may get by with writing fewer tests than in a dynamic language, because the static type system does provide some guarantees.
What if you had a stronger type system than what C# or Java provides? Then you'd have to write even fewer tests.
It can be useful to think about typing as a spectrum.
To the left, we have dynamically typed languages like JavaScript and Ruby. Python can be compiled, and Clojure is compiled, so we can think of them as being a little closer to the middle. Purists would want to point out that whether or not a language is compiled, and how statically typed it is, is two independent concerns, but the point of this spectrum is to illustrate the degree of confidence the type system gives you.
Java and C# are statically typed, compiled languages, but a lot of things can still go wrong at run-time. Just consider all the null pointer exceptions you've encountered over the years.
Further to the right are languages with Hindley–Milner type systems, such as F# and Haskell. These offer more safety from static typing alone. Such types are the subject of this and future articles.
I've put Haskell a bit to the right of F# because it has higher-order types. To the right of Haskell sits dependently-typed languages like Idris. To the far right, we have a hypothetical language with such a strong types system that, indeed, if it compiles, it works. As far as I'm aware, no such language exist.
It turns out that when you shift from a Java/C#-style type system to the stronger type system offered by F# or Haskell, you can further shift your design emphasis towards designing with types. You still need to cover behaviour with automated tests, but fewer are necessary.
With the algebraic data types available in F# or Haskell, you can design your types so that illegal states are unrepresentable. In other words, all values of a particular type are guaranteed to be valid within the domain they model. This makes it much easier to test the behaviour of your system with Property-Based Testing, because you can declaratively state that you want your Property-Based Testing framework (FsCheck, QuickCheck, etc.) to provide random values of a given type. The framework will give you random values, but it can only give you valid values.
In this series of articles, you'll see an example of this in F#:
The stronger a language's type system is, the more you can use static types to model your application's problem domain.  While states are guaranteed to be legal, transitions between states need not be. You can often use Property-Based Testing to ensure that the state transitions are correct. The combination of types and properties give you a simple, but surprisingly powerful way of specifying the behaviour of the software you create.


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I'm A Celeb's Ant McPartlin pictured back on set with Declan Donnelly for first time in two years
Ant McPartlin is back in Australia for the first time since taking last year off to deal with his addiction issues
by Louise Randell, https://www.mirror.co.uk/authors/louise-randell/I'm A Celebrity host Ant McPartlin has been pictured back with his co-host Declan Donnelly in Australia for first time since his drink-driving conviction.
Ant, 43, took last year off to deal with his personal demons following a car crash in London which forced him to address his addiction issues and head to rehab.
He was replace by Holly Willoughby on I'm A Celeb 2018, but he's now back for this year's show.
Ant arrived in Australia yesterday and has now reunited with Dec on their first trip to the jungle together in two years.
They shared a cute snap of themselves from the set as they prepare to get to work, captioning it simply: "G'Day."
Fans were thrilled to see the pair reunited Down Under, and praised Ant's bravery for getting his life back together.
One wrote: "It is always an amazing thing to see them together."
Another added: "Not long to go now.. so glad you are both back together where you belong.. my favourite show.."
A third commented: "So good to see the boys back together!! So excited."
Dec was the first of them to arrive Down Under for the 2019 series, bringing along his wife Ali and their daughter Isla.
Ant followed by landing in Oz last night and was seen walking through the airport with his girlfriend Anne-Marie Corbett.
The new stars of I'm A Celeb Extra Camp have also touched down in Brisbane, with Adam Thomas and Emily Atack joining Joel Dommett for this year's spin-off show.
The first contestant to arrive was Ian Wright.
Mirror Online excluisvely revealed the first pictures of the former
The opening episode of I'm A Celebrity airs next Sunday night at 9pm on ITV.
Do you have a story to sell? Get in touch with us at<EMAIL_ADDRESS>or call us direct 0207 29 33033


Josh Gold and I (Ben Heasly) talked about modeling animation in an explicit way. As of October2011, "animation" is handled by individual Drawable classes, which happen to update their internal state every time they draw().
This is fine for stimuli which appear to the subject to be stateless. This includes static stimuli like targets and even dynamic stimuli like random dot kinetograms.
But what about other kinds of animation? If a helicopter were to fly horizontally across the screen, it would be nice to model this animation explicitly. The experimenter should be able to say "fly from here to there" or "start flying to the right", instead of having to micromanage the flying behavior every frame, as part of task logic.
More parameters, not just position, should be "animatable". Size, color, and non-visual parameters like pitch or volume, might need to be "animated" along with position or instead of position.
Thoughts
So we would like to implement a clear model for organizing animation. The model would implicitly define what we mean by "animation" in the context of Snow Dots.
For the moment I'm just going to jot down notes from our conversation and my initial thoughts.
Animation Matrices
Let's say that "animation" means gradually changing a parameter over time. One way to specify gradual changes would be with a matrix of times and values to be applied to a parameter of a Drawable object: t0, value0; t1, value1; t2, value2; etc… In this case a draw() method could look up a value based on the current time and apply the value to a property. The value would change abruptly at t0, t1, and t2. Smooth animation would require a lot of values, or interpolation.
For uniform motion, it might be simpler to use a matrix of delta-values: t0, deltaValue0; t1, deltaValue1; t2, deltaValue2; etc… The parameter would "slide" at a different constant rate in each interval t0-t1, t1-t2, and t2-inf. However, since updates might occur at irregular intervals, it's not quite clear how to implement the sliding. It seems messy to try to interpolate between delta-values.
It would be up to the experimenter to compute an animation matrix which obeyed conventions.
There might also be utility methods for computing common types of animation matrices, such as a simple linear sweeps, or piecewise circular or sinusoidal motion.
Absolute values or delta-values could be applied to any public class property. It might be nice to apply values to class methods as well. Since incrementing a method is meaningless, methods could be animated only with absolute value matrices.
Using animation matrices would imply that only numerical values can be animated, which seems reasonable.
Class Model
Even simple animation matrices would require significant state management. When should the animation begin? How far along is it? What should happen when the matrix runs out of values? Which Drawable classes should be animated? Which of their properties should be updated? There's plenty of bookkeeping to do.
So I think it makes sense to define an Animator class. Each Animator instance could aggregate one or more animation matrices, pick values from them, and assign the same values to one or more Drawable objects. The Animator would assume that each aggregated Drawable had a similar interface.
Perhaps Animator should be a subclass of Drawable. This would make them relatively easy to drop into existing code. The Animator draw() method could look up values, deal them to aggregated Drawables, then invoke draw() on aggregated Drawables.
Aggregation
Dealing with the Animator---<>Drawable aggregation relationship would be somewhat tricky, since the same aggregation would need to exist on the client and server sides.
Perhaps TheDrawablesManager or AllRemoteObjectManagers should have a new method for "wiring up" an aggregation relationship on both client and server.
Such a method would need to know the outer and inner objects, and the property of the outer object which should receive the inner object. Both objects would need to belong to the same manager.
Getting this aggregation right would be important because we would want animation updates to occur on the server side. We would not want to send multiple property changes on every frame.
Remote object aggregation is a general problem for Snow Dots. Solving it might pay off elsewhere, too.
Bits and Pieces
However its implemented, animation would have several parts, including: * specify values and a time course for applying the values * specify which objects and object members should receive the values * specify when to start/restart animation * pick values and assign them each frame * decide what to do if we run out of values (freeze? loop?) * query the progress of ongoing animation * terminate animation for some reason * span the client and server
Wiring up an aggregation relationship would be great, but working with the objects would still require care. As of October2011, it's not possible to send an object through dotsTheMessenger. So for the client to access a member of the inner object, it needs to work with the inner object itself.
For example, consider an outerObject and an innerObject which both belong to a manager: manger.updateClientObjectProperties(outerObject); Would update properties for the outerObject on the client side, as expected. But it would not not update the properties of the inner object. The experimenter would also have to invoke manger.updateClientObjectProperties(outerObject.innerObject);
Dynamic stimuli like the random dot kinetogram, or new stimuli such as exploding particle systems (see demos/explodingBagOfMoney), will need a convenient mechanism for resetting to the beginning of their evolution. This might correspond to setting an internal-time variable to 0, then "animating" the internal-time, with respect to the "real" time.
dotsTheDrawablesManager already has a property called isAnimating, which determines whether it should invoke draw() methods and swap frame buffers during its runBriefly() method. This is a different sense of "animation".
We should make sure the senses don't conflict. Hopefully we can fold this "animating" behavior into the new model gracefully.
Restarting animation based on a delta-value matrix would not necessarily produce the same animation. The initial absolute value would have to be reset as well.
To help with this kind of usage, and other usages, it would be convenient if Animator had a setMany() method for dealing property vales to its inner Drawables. However, this would be similar to the setGroupProperty() method of dotsAllObjectManagers. Is there a good way to reuse this behavior without duplicating it?
An alternative would be to specify an initial value for each Drawable member while configuring the Animator, to be applied when the animator was reset. This would be less general than setMany(), and more clearly related to animation, as opposed to general object management.


ChROME
MATLAB(R) scripts implementing statistical closure modeling by the ROMES method
A novel technique for constructing a statistical closure model for reduced-order models (ROMs) applied to stationary systems is here implemented and tested on both linear and nonlinear stationary systems.
This MATLAB code enables to reproduce the methodology and the numerical experiments presented in the submitted article:
[[PMC19] S. Pagani, A. Manzoni, K. Carlberg. Statistical closure modeling for reduced-order models of stationary systems by the ROMES method, Preprint , 2019.]
Download and Installation
To install the library, extract the ZIP file or clone the git repository.
Run the script by running the setup file
setPath
License
Freely available subject to a BSD 2-Clause License.
Please cite this code by adding the following reference to your work:
[[PMC19] S. Pagani, A. Manzoni, K. Carlberg. Statistical closure modeling for reduced-order models of stationary systems by the ROMES method, Preprint , 2019.]
Development
LocalROM was developed and is currently maintained by Stefano Pagani
.
The code uses as submodule the redbkit toolkit:
[[redbKIT] F. Negri. redbKIT Version 2.2. http://redbkit.github.io/redbKIT/, 2016.]


Finding submission
A valid verification token should look like the following:
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If you successfully obtained such a token, please attach it to your submission within the correct field. The field should match the scope name.


Proof By Induction
Proof by induction, is a method of proving that is used to prove various formulas used in geometry. It is a direct proof, which sets the formula up like dominos. It proceeds to knock the first domino into the second, the second into the third, and so
on until it knocks all the dominos down.
Here, the example we will use is the formula for the sum of positive integers.
1+2+3+...+n=\frac{n(n+1)}{2}
Now, in order to prove this formula by induction, you will have to determine and prove each of these components: the base case and the inductive step.
The base case is going to be the first case in the sequence of cases that will ultimately prove that the formula is indeed correct. In this case, the sum of the first number will be the first case.
1=\frac{[1]([1]+1)}{2}=1
The inductive step will be to assume the equation to be true for $n=k$. Then to follow with a proof to show that same to be true for $k=n+1$. This is the most powerful step as it will show that if the base case is true, the rest must also be true. For
the case of the sum of n numbers, it will proceed to knock each of these statements until it reaches infinity.
If $n=1$ is true (the base case), then $n=2$ must be true
If $n=2$ is true, then $n=3$ is also true
If $n=3$ is true, then $n=4$ is also true
...
If $n=k$ is true, then $n=k+1$ is also true
We must start with the assumption that $S(n)=\frac{n(n+1)}{2}$ and prove that $S(n+1)=\frac{[n+1]([n+1]+1)}{2}$. That will complete the inductive step. A formal proof of the inductive step is given below.
| Statement |
Proof |
| $S(n)=1+2+...+n=\frac{n(n+1)}{2}$ |
Given |
| Suppose for any $k$, $S(k)=\frac{k(k+1)}{2}$ |
Statement 1 |
| $S(k+1)=1+2+...+k+(k+1)=\frac{k(k+1)}{2}+(k+1)$ |
Statement 1,Definition of Sum |
| $S(k+1)=\frac{k(k+1)}{2}+\frac{2(k+1)}{2}$ |
|
| $S(k+1)=\frac{[k+2](k+1)}{2}$ |
Factor $\frac{(k+1)}{2}$ |
| $S(k+1)=\frac{(k+1)(k+2)}{2}$ |
|
| $S(k+1)=\frac{[k+1]([k+1]+1)}{2}$ |
|
Ex. 1: Prove the following formula for the sum of the first $n$ square numbers: $S(n)=\frac{n(n+1)(2n+1)}{6}$
Base Case: $n=0$ works
S(0)=\frac{0(0+1)(20+1)}{6}=0
Inductive Step: $n=k+1$ works
| Statement |
Proof |
| $S(n)=\frac{n(n+1)(2n+1)}{6}$ |
Given |
| Suppose for any $k$, $S(k)=\frac{k(k+1)(2k+1)}{6}$ |
Statement 1 |
| $S(k+1)=\frac{k(k+1)(2k+1)}{6}+(k+1)^2$ |
Statement 1,Definition of Sum |
| $S(k+1)=\frac{k(k+1)(2k+1)}{6}+\frac{6(k+1)(k+1)}{6}$ |
|
| $S(k+1)=\frac{[k(2k+1)+6(k+1)](k+1)}{6}$ |
|
| $S(k+1)=\frac{[2k^2+k+6k+6](k+1)}{6}$ |
|
| $S(k+1)=\frac{[2k^2+7k+6](k+1)}{6}$ |
|
| $S(k+1)=\frac{(2k+3)(k+2)(k+1)}{6}$ |
|
| $S(k+1)=\frac{(k+1)(k+2)(2k+3)}{6}$ |
|
| $S(k+1)=\frac{[k+1]([k+1]+1)(2[k+1]+1)}{6}$ |
|
Another way to express both of these formulas is to use summation notation. The formula from Example 1 is this
\sum_{i=1}^{n} i^{2}=\frac{n(n+1)(2n+1)}{6}
The sum starts from replacing each instance of $i$ with $1$ in the equation (which is $1^2$) and continues to increment $i$ by $1$ until it reaches $n$ (which is $n^2$). This generates a sequence ${1^2,2^2,...,n^2}$. The capital sigma symbol says that
the numbers in the sequence are to be added together. Multiplying numbers in the sequence uses a capital pi symbol.
Ex. 2: Prove the following formula for a generalized geometric series of the form $\color{red}{a,ar,ar^2,...,ar^{n-1}}$
\sum_{i=0}^{n-1} ar^i=a\frac{1-r^n}{1-r}
Base Case: $n=1$ works
\sum_{i=0}^{1-1} ar^i=a
The other side also simplifies to $a$
a\frac{1-r^0}{1-r}=a\frac{1-r}{1-r}=a
Inductive Step: $n=k+1$ works
| Statement |
Proof |
|
\sum_{i=0}^{n-1} ar^i=a\frac{1-r^n}{1-r}
|
Given |
| Suppose for any $k$,
\sum_{i=0}^{k-1} ar^i=a\frac{1-r^k}{1-r}
|
Statement 1 |
|
\sum_{i=0}^{k} ar^i=a\frac{1-r^k}{1-r}+ar^{k}
|
Statement 1, Definition of Sum |
|
\sum_{i=0}^{k} ar^i=\frac{a}{1-r}[(1-r^k)+(1-r)r^{k}]
|
|
|
\sum_{i=0}^{k} ar^i=\frac{a}{1-r}[(1-r^k)+r^{k}-r^{k+1}]
|
|
|
\sum_{i=0}^{k} ar^i=\frac{a}{1-r}[1-r^{k+1}]
|
|
|
\sum_{i=0}^{k} ar^i=a\frac{1-r^{k+1}}{1-r}
|
|
Proof by induction could also prove certain features of geometry. One can also go about proving Euler's Formula by using three inductive proofs: one relates vertices and edges, another relates cycles and vertices, and a final relates cycles and faces.
Ex. 3: Prove Euler's Formula for the plane $V-E+F=2$
Proposition 3.1: For each acyclic (no loops on the graph), connected graph (a path exists from each vertex to every other vertex), $V=E+1$
Base Case: One Vertex is a connected graph
A graph with one vertex has no vertices. $[1]=[0]+1$
Inductive Step: Adding an edge adds one new vertex and a new edge to a connected graph is still a connected graph
| Statement |
Proof |
| Suppose an acyclic, connected graph has $k+1$ vertices, then a graph will have $k$ edges |
Given |
| Add a new vertex (called N) not on the graph and connect it with any vertex (called P) on the graph. The new graph is still connected |
Since we are assuming that the old graph has a path that connects P to any vertex, then there is a new path that connects from any vertex to P to N, making this new graph a connected graph. |
Proposition 3.2: For each connected graph with $k$ maximum, partitioned cycles and $V$ vertices, $E=V+k-1$
Base Case: A graph with no cycles and n vertices
This was already proved in Proposition 3.1 ( $V=E+1$ or $E=V-1$)
Inductive Step: Adding a cycle increases the number of edges by one.
| Statement |
Proof |
| Suppose a graph has $k$ cycles with $n$ vertices, then a graph will have $1+n+k$ faces |
Given |
| Connect two vertices called $P$ and $Q$ that are currently not connected by an edge . This new construction results in a new cycle. |
What this new edge does is create a new path that allows $P$ to go to itself through $Q$ (and for $Q$ to go through itself through $P$) creating a new cycle. |
Proposition 3.3: For each connected graph with $k$ maximum, partitioned cycles, the graph has $k+1$ faces
Base Case: Zero cycle graph has one face
An acyclic, connected graph has one face since none of the regions close in on itself.
Inductive Step: Adding a new cycle increases the number of faces by $1$
| Statement |
Proof |
| Suppose a graph has $k$ cycles, then a graph will have $k+1$ faces |
Given |
| Add a new cycle by connecting two vertices that are currently not connected by an edge. The new graph has an extra face. |
What this new edge does when it is connected by two adjacent vertices is split two regions in half, creating 2 faces from the preexisting face. |
Proof
Applying Proposition 3.2 and Proposition 3.3, for a connected graph with $k$ cycles and $n$ vertices.
$F=k+1$
$E=V+k-1$
$E=V+k+1-2$
$E=V+F-2$
$-V+E-F=-2$
$V-E+F=2$


Select the fleet which will be used to launch Jenkins workers. EC2 Spot Fleet and Auto Scaling Group are both supported.
By default, this list only includes active EC2 Spot Fleets and Auto Scaling Groups. If you need to see all fleets, click the checkbox below. The selected fleet will be in the list regardless of fleet state.
EC2 Spot Fleet specific: All non maintain
type fleets will be filtered out from this list.
More
about types.
If you are not sure about your fleet type, check its type via an API call or look in the console UI for
Maintain Target Capacity
being enabled.
AWS Permissions: The plugin requires certain AWS permissions for managing resources. You can check missing permissions by clicking the Test Connection button. The Test Connection button does not validate certain listed permissions such as TerminateInstances and UpdateAutoScalingGroup due to API restrictions. Check out the README for an inline IAM Policy.


This is the home page of Jon Arbuckle, a cartoon character who owns a cat named Garfield.
Quentin "Jon" Arbuckle is a fictional character from the Garfield comic strip by Jim Davis.
He has also appeared in the >animated television series Garfield and Friends, the computer-animated The Garfield Show, and two live-action/computer-animated
feature films.
Here are some useful things about Jon Arbuckle
- Jon's birthday is July 28
- He can play accordion, guitar, and bongos and sing
- His favorite music style is polka
- However, he's better known for his pets than his music
Here's a little information about Jon Arbuckle's pets
-
Garfield, the cat
- Garfield is an overweight tabby cat, noted for his laziness
- He has an intense passion for food, specifcally lasange
- He is often ridiculed for his weight
- One of Garfield's other passions is tormenting Odie
-
Odie, the dog
- Odie is a kind, if not slight unintelligent, yellow-furred dog
- His best known features are his large tongue
- And his ability to walk on 2 legs