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# How to create data driven effects/abilities for collectable card game

I'm trying to create cards for a ccg/tcg that are completely "data-driven" from an xml/json/external file. I've read multiple articles on this issue already, even here on stack exchange, but i can't figure out how to actually code this. I have a simple example:

My two cards have the following abilities

1) "Increase the value of all adjacent red cards by 1"

2) "Increase the value of this card by the amount of all adjacent red cards"

In my code i have the following functions (pseudo) that i need to accomplish these effects:

Increase(targetCards, byValue) // increases a card's value by another value
FilterCardsBy(filter=isRed) // returns only red cards
Count(targetCards) // counts the number of cards

To create effect 1 i would use the functions like this:

Increase(FilterCards(FindCards(adjacent), isRed), 1);

and to create effect 2 i would use:

Increase(this, Count(FilterCards(FindCards(adjacent), isRed)));

So here's the problem: I have no clue how i can describe these functions in my external file and also i have no clue how i actually tell my functions to work in this combination to achieve the desired effects. Maybe i'm misunderstanding the concept here but as far as i understood and described here i can create some pseudo script/code in my external file that then my code can interpret and execute on. But i feel i somehow missing the middle part where i write code to interpret these commands i'm defining in the external file.

Anyone with experience here that can give me some super simple starter ideas on how to takle this. Especially the part where i can combine several functions into one.

• In addition to my answer this pattern is kind of related, in the sense it separates design from code. Sep 28 '16 at 10:22

When you have complex logic in the mechanics of individual cards, then it might be best to express that logic with a scripting language. But if you really want to go for a completely domain-driven approach, you might go for something in between: Markup which describes logic.

Both of the effects mentioned in the question could be called an "adjacency effect". It's an effect which triggers if an adjacent card fulfills a certain condition. The difference is that one is a bonus on the adjacent card, the other one on the card itself (which stacks for each card which fulfills the condition). In JSON, these two effects could be expressed as a triplet of adjacencyCondition, self-effect and adjacent-effect.

{
"self": { "value": 1 },
}

{
// self: undefined
},

If you don't like JSON, feel free to use XML, YAML, INI or whatever markup language you prefer instead. But I would not recommend you to invent your own. When you use an existing markup language, you will likely find a well-tested library for parsing it. When you develop your own, you will have to spend countless hours writing your own parser. This will be far harder than it sounds at first. And subtle bugs in your parser can and will cause you frustration to no end.

Your program code to apply these would look like this (pseudocode):

if (card has 'adjacencyCondition') {
increase current card attributes by everything specified in 'self'
}
}
}

This system can easily be enhanced to have more conditions than just adjacencyCondition (where "adjacent" doesn't necessarily makes sense, but other fields might). Your should allow cards to have an array of effects to allow cards which have more than one effect. In that case you might also have an unconditional condition which allows you to define inherent attributes of cards. But I have no idea how your game mechanics look like or what the theme of your game is, so I could only guess what could be useful for you.

Anyway, here is an example of a red card with a value of 3 which counts as both a kitten and a zombie, which turns all adjacent space stations green and gets +1 for every blue card controlled by the opponent:

{   "name": "Bob the Zombie Kitten",
"effects": [
{
"unconditional": true,
"self": {
"color": "red",
"traits": [ "zombie", "kitten" ],
"value": 3,
}
},
{
"adjacent" : { "color": "green" }
},

{
"allCondition": { "owner": "opponent", "color": "blue" },
"self" : { "value": 1 }
},
]
}

I will expand on this in a bit when I have more time but essentially, as you say, are going for a data driven design approach for your game.

This means you are defining your cards in XML or JSON format etc. What you should really do is pick one and stick with it (not necessarily forever, but for your first technical demos and understanding). Alternatively you can just create your own format and then write the code to interpret it. Imagine this inside a .txt file.

Card=
Name: Test
Value: 5
Color: Red
Endcard

Just a simple example, but now you have a defined piece of data that is more human readable and your designers can edit a text file instead of letting them have access to code.

So now you have a definition of the card and can separate data from code.

Your next step will be to write some form of interpreter (later you can change this to serializing/deserializing), a psuedo code of it may look like:

Card card = new Card();

string line;
while (line != "Endcard")
{
if (line == "Card=")
{
/* this will read in name and strip the Name: part so the variable card.name
now contains the string "Test". Please not you will have to implement
the stripping part or use some in built language feature */
}

}

So now your program has read in the data text file and converted it into a Card object.

I hope that helps you see it a bit clearer, sorry for poor formatting and again I will fix this up and write a fuller answer later with more time.

p.s. keep in mind the psuedoness nature of the code so far, the file reading employed is very error prone but I am just trying to communicate the idea across to you.

• Hi, thanks for your answer. To make this a bit clearer: I'm not asking about defining static properties of cards by external data, but having a system where i can build the effects each card can do. I believe this is something else than just saying this cards has a static value of X. This is about saying this card can perform multiple actions that somehow need to be interpreted by my code and then be executed. Sep 28 '16 at 10:54
• This pattern then may help out a bit as well or at least spark some more thought for you :) Sep 28 '16 at 10:59
• I don't fully understand your problem but a simple solution may be higher level functions. So you have three effect functions. EffectOne(); EffectTwo(); EffectThree(); Then you have some functions that call them in specific orders to get the overall effect you want: FunctionOne() { EffectOne(); EffectThree(); } FunctionTwo { EffectThree(); EffectOne(); } Sep 28 '16 at 11:05
• That entire book Game Programming Patterns by Robert Nystrom is recommended by many including myself, the entire thing is well worth a read. Sep 28 '16 at 11:14
• Thanks for the help. I actually know the website, but didn't know where to look. Sep 28 '16 at 11:17


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# Thread: Non-abelian groups of order p^2 q

1. ## Non-abelian groups of order p^2 q

If |G| = p^2 q for two distinct primes p, q, then is G necessarily abelian? Are there any non-abelian groups of order p^2 q?

2. Originally Posted by prettyboy
If |G| = p^2 q for two distinct primes p, q, then is G necessarily abelian? Are there any non-abelian groups of order p^2 q?
of course! for example $A_4$ is non-abelian and its order is $12=2^2 \times 3.$ another example is the dihedral group of order 12. however, if G has order $p^2q, \ p and $p \nmid q-1,$ then $G$ is abelian.

3. ## refer book

Refer the book ion abstract algebra by Dummit and Foote. a large behaviour of these groups are well explained

format: plain


text: And then, on the other hand, his CFO explains the $100 million raise it did in April as “building cash reserves to help us compete in a world with Internet delivery of movies against substantially larger companies with much stronger balance sheets.” The two don’t reconcile, Reed. Come clean. Couple of smart-alecky-type one liners from me : — Don’t assume the world will wait around for Netflix to enter the movie downloads market. — Don’t assume the online downloads market will only be movies…there are countless substitutes, now and emerging. Related: Netflix vs Movielink: Hastingspeak Netflix To Invest$5-10 Million in Tech; Yo-Yoing Again


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# How to connect this Active Antenna Loop and 100MHz Upconverter?

I have bought the two devices in the image. The 100MHz Upconverter with a SMA connector is used to upconvert HF/MF signal for RTL-SDR to demodulate. I found that there is signal from the antenna (tested by using another radio), but I can detect no signal when connecting to upconverter. I think I have connected them wrongly. May you advice the way of connection?

The model of Antenna Loop is Degen 31MS. The up convertor information is located at https://code.google.com/p/opendous/wiki/Upconverter Mine is using 100MHz v1.0 version.

My method to connect is to try to use a small wire to connect the "hole" of SMA connector with the audio plug. I have tried to contact with different part of that audio plug, still no luck.

• How about providing some concrete information about the units you're using? Exact model name and website would be good for start. I did try to read the site from the photo, but the domain name was illegible for me. Are there any manuals for the devices? If yes, did you read them? Are there electronic versions available? If so, can you post links? Your question is quite hard to answer for someone who can't immediately identify your equipment from just the photo and you as the asker should try to make it as easy as possible for the rest of us to help. – AndrejaKo Apr 1 '14 at 14:30
• Also you said you think you connected the upconverter wrongly, but I can't see a description of how exactly you connected it. That might be helpful as well. – AndrejaKo Apr 1 '14 at 14:33
• Thanks for your help. The model of Antenna Loop is Degen 31MS. The up convertor information is located at code.google.com/p/opendous/wiki/Upconverter. Mine is using 100MHz v1.0 version – Harold Chan Apr 1 '14 at 14:42
• My method to connect is to try to use a small wire to connect the "hole" of SMA connector with the audio plug. I have tried to contact with different part of that audio plug, still no luck. – Harold Chan Apr 1 '14 at 14:43
• I'll study the materials as soon as I can. In the meantime, it would be best if you would post the contents of your comments into the question itself. – AndrejaKo Apr 1 '14 at 15:13

## 1 Answer

Looking at the Google site you posted, it looks like this is the expected setup, so there probably isn't any gross incompatibilities, but I think you skipped looking at the large vector network analyzer graphs on the first page.

The upconverter is attenuating the signal by between 10dB and 76dB depending on the frequency. Remember that dB is a logarithmic measure of the ratio of the signal strengths ($10 log_{10}$ $\frac{R_{output}}{R_{input}}$ in this case); therefore a 10dB attenuation means the output signal is $\frac{1}{10}$ as strong as the input signal and at 76dB attenuation, the signal would be less than $\frac{1}{1,000,000}$ as strong.

So assuming the input signal is something off the air that may not be that strong to start with and adding in the losses for the connectors and cabling, etc, the signal is probably below the detection threshold of the SDR. Seems like an RF preamp might be called for.

In fact, the FAQ at the bottom mentions this:

Why not add an amplifier to overcome the 10dB conversion loss? : Since the Noise Figure of an RF system is most dependent on the Noise Figure of the first elements in the signal chain, it does make sense to place an LNA at the antenna port. I just wasn't sure if most users would have their Upconverter at their antenna.


text:
# makefile help

## Recommended Posts

I've got a build process I'm running. And while I can mostly marshal the makefile to do what I want, I'm hopeing someone can help me get the last steps into it. I got my main segment: assetName: [files] #build asset levelName: assetName #build level all: levelName #build code Now, the part that confuses me is I have something rather simple in the form of data\assetName\assetName.x data\assetName\STUFF\assetName.y data\assetName\OTHERDIR\assetName.z etc. each of those files is made from src\assetName\assetName.a src\assetName\STUFF\assetName.b etc. and 90% of my files follow that format the rest i can probably marshal into that format. And for the moment, i've resorted to copy paste. But shouldn't there be a way where i can define ASSETS = cat cow box and have: data\cat\cat.bakedmodel: cat\model\cat.model cat: data\cat\cat.bakedmodel #tie all the asset parts together done up for each item in that list?

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It really depends on which kind of make you're using (GNU make, nmake, BSD make, etc). They all have different macros and commands for this kind of thing.

If it's GNU make, the online manual isn't too bad.

##### Share on other sites
Look into suffix rules. That is, you want to try something like this:
.SUFFIXES : .model .bakedmodelMODELS = cat.bakedmodel cow.bakedmodel box.bakedmodelall_models.bin : $(MODELS) merge -o$@ $(MODELS).model.bakedmodel : process_model -o$@ \$?

Quote:
 Original post by the_eddIt really depends on which kind of make you're using (GNU make, nmake, BSD make, etc). They all have different macros and commands for this kind of thing.
I should think this is a fairly standard feature, actually.

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Cool. I need to check what version of make it is one i get back to my dev machine. But thanks for the help I'll try that .SUFFIX thing out.

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Ok, the suffix thing kinda fixes my issue. but only kinda.
i have a path and a path
mmmmmmmm\SRCS\cat\SOURCE\cat.model
mmmmmmmm\DATA\cat\SOURCE\cat.bakedmodel

the TOOLS take the name "cat" and build the associated parts to the right places.
I thusly need these rules:

mmmmmmmm\DATA\cat\SOURCE\cat.bakedmodel: mmmmmmmm\SRCS\cat\SOURCE\cat.model   ProcessModel catLevelCatHouse : mmmmmmmm\DATA\cat\SOURCE\cat.bakedmodel  # other files put in the level go here.   ProcessLevel cathouseallCode: LevelCatHouse    generateLevelSpecificCodeStubs cathouse    devenv project.sln /Build "DEBUG"

I don't really need make to know most the file names, I was just hoping to use it to process all the files (based on does X need updates? remake it) Mostly since the .sln is just wrapping a makefile project, I want to even get away from that for my case, since i just want a commandline tool to rebuild all the assets that have changed for this part of the project. so maybe there is some other tool for windows that I could use to make this happen?

My big issue is that it is VERY easy for me to look at a checkin and see "oh someone updated something in "\SRCS\cat\", that is in my level, i should run "buildcreature cat". But when there are tonnes of checkins, and I dont notice that something in my level was updated, I may be way out of date on my files next time i run the game, causing a crash or other other problem because my data doesnt line up with what the game now expects.
So i was making this file, but there is a lot of verbose typing for something that is really easy to parse visually for the issue, but a pain in the ass to type out a few hundred times.

[Edited by - KulSeran on October 26, 2008 11:43:15 PM]

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I'm not sure I see exactly what it is that you want to automate.
Some make implementations, such as gmake, have extensions to manipulate sets of filenames, to place the output file in a different directory or whatever. Though it's not what I'd call clean (but then again string manipulation rarely is.) To be honest Make was never really designed to handle directories and it shows.
Another possible solution is to generate makefiles dynamically from a separate script. Or you could let your tools themselves compare the modification dates. And of course you can always switch to a more powerful build tool, like scons, jam, or whatever.

Honestly I don't see this as much of a problem. Any old five cent shell/batch script hack job could piece this together for you.

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# Within the elastic limit, the total strain energy stored in a given volume is called _______.

This question was previously asked in
UPRVUNL AE ME 2022 Official Paper Shift 1 (Held on 16 July 2022)
View all UPRVUNL AE Papers >
1. stiffness
2. proof stress
3. resilience
4. ductility

Option 3 : resilience
Free
General Hindi Free Mock Test
15.4 K Users
15 Questions 15 Marks 15 Mins

## Detailed Solution

Explanation:

Strain Energy:

• The Strain Energy of the member is defined as the internal work done in deforming the body by the action of externally applied forces.
• Strain energy is given by:
• $$Strain\;Energy = \;\frac{1}{2} \times Stress \times Strain \times Volume$$

Resilience:

• Resilience is the total strain energy stored in a given volume of material within the elastic limit.
• On removal of load, this energy is released.
• In other words, it is the area under the load-deflection curve within the elastic limit.

Proof resilience:

• The maximum energy which can be stored in a body up to the elastic limit is called proof resilience.

Modulus of resilience:

• Modulus of resilience is defined as proof resilience per unit volume. It is the area under the stress-strain curve up to the elastic limit.


text:
# Chapter 10 - Exponents and Radicals - 10.6 Solving Radical Equations - 10.6 Exercise Set - Page 668: 26

$y=-64$

#### Work Step by Step

Raising both sides to the $\text{ 3rd }$ power, the solution to the given equation, $\sqrt[3]{y}=-4$, is \begin{array}{l} y=(-4)^3 \\\\ y=-64 .\end{array}

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.


text:
Temperature and entropy for two gases mixing

1. Mar 26, 2015

Incand

1. The problem statement, all variables and given/known data
A system is made up of two halves. In one there's 10kg neon gas with the temperature $20 \circ$C, in the other 10kg nitrogen gas with the temperature $100 \circ$ C. Suppose the septum is removed so that thermodynamic equilibrium may appear and the gases mix.

Calculate the final temperature $T_f$ and the total change in entropy.

2. Relevant equations
$pV=nRT$
Internal energy (ideal gas)
$U = nC_VT$

3. The attempt at a solution
I got two solutions (for the first question), one done by me and one by our lecturer (who I unfortunaly can't ask) and what I'm wondering why mine is wrong (if it is).
My solution:
$n_1 = \frac{10\cdot 10^3}{20.17} = 495.8 mol$
$n_2 = \frac{10 \cdot 10^3}{2*14} = 357 mol$
Assuming the gas is ideal we get
$p_1=n_1RT_1/V_1$ and $p_2 = n_2RT_2/V_1$
Now assuming the gases where alone one at a time in the container double the volume we would get
$p_{f1} = n_1RT_f/(2V_1)$ and $p_(f2) = n_2RT_f/(2V_1)$
Assuming the mixing is done first by an isothermal and then and isokor process (our teacher made the exact same assumption as well)
$p_f = p_{f1} +p_{f2} = \frac{n_1RT_1}{2V_1} + \frac{n_2RT_2}{2V_2} = \frac{R}{2V_2}(n_1T_1+n_2T_2)$
I now make the assumption that pressure from both gases is equal to the pressure from each of the gases added together (I don't know if this is correct but I think there is some thermodynamic principle that allow me to use the superposition principle here).
$p_f\cdot 2V_1 = (n_1+n_2)RT_f$
Inserting $p_f$ into the equation gives us
$T_f = \frac{n_1T_1+n_2T_2}{n_1+n_2}$

While the one done by teacher uses internal energy and instead end up at the answer of
$T_f = \frac{3/2n_1T_1+5/2n_2T_2}{3/2n_1+5/2n_2}$

I could add the solution from our teacher too if it's needed (it's rather lengthy) but I'm mostly wondering if anyone could see what I do wrong. Both solutions give numeric values well within the solution at the back of the book but I would assume I'm wrong, I just don't know why.

2. Mar 26, 2015

Staff: Mentor

Your assumption that, after mixing, the partial pressures of the two gases is the same is incorrect.

The key to this problem is recognizing that there is no change in internal energy. That's what your teacher did. You can see that from the 5/2 and 3/2 factors.

Chet

3. Mar 26, 2015

Incand

Thanks again Chet, always helping me out!


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# Homeostatic Activity-Dependent Tuning of Recurrent Networks for Robust Propagation of Activity

Gjorgjieva, Julijana ; Evers, Jan Felix ; Eglen, Stephen John (2016-03-30)

Article

Developing neuronal networks display spontaneous bursts of action potentials that are necessary for circuit organization and tuning. While spontaneous activity has been shown to instruct map formation in sensory circuits, it is unknown whether it plays a role in the organization of motor networks that produce rhythmic output. Using computational modeling, we investigate how recurrent networks of excitatory and inhibitory neuronal populations assemble to produce robust patterns of unidirectional and precisely timed propagating activity during organism locomotion. One example is provided by the motor network in $\textit{Drosophila}$ larvae, which generates propagating peristaltic waves of muscle contractions during crawling. We examine two activity-dependent models, which tune weak network connectivity based on spontaneous activity patterns: a Hebbian model, where coincident activity in neighboring populations strengthens connections between them; and a homeostatic model, where connections are homeostatically regulated to maintain a constant level of excitatory activity based on spontaneous input. The homeostatic model successfully tunes network connectivity to generate robust activity patterns with appropriate timing relationships between neighboring populations. These timing relationships can be modulated by the properties of spontaneous activity, suggesting its instructive role for generating functional variability in network output. In contrast, the Hebbian model fails to produce the tight timing relationships between neighboring populations required for unidirectional activity propagation, even when additional assumptions are imposed to constrain synaptic growth. These results argue that homeostatic mechanisms are more likely than Hebbian mechanisms to tune weak connectivity based on spontaneous input in a recurrent network for rhythm generation and robust activity propagation.


text:
## Tuesday, 29 August 2017

### The TT7F3 Flight

Date: 2017-08-31
Time: 6:00 GMT (8:00 CEST)
Live Tracking: https://tracker.habhub.org and https://aprs.fi

RTTY
Callsign: TT7F3
Frequency: 434.374MHz
Params: 100 baud, 450Hz shift, 8n2
Preceded by: 5 slow blips (~6s)
Packet: callsign, count, time, date, latitude, longitude, altitude, sats, Vsolar, Vbatt, Tmcu, Ttx
Example: TT7F3,13,15:13:32,20170719,49.46868,18.15101,408,6,899,3950,30,29*FB99

APRS
Callsign: OK7DMT-7
Frequency: Geofenced local APRS frequencies
Packet: Base-91 position and telemetry, Backlogged position and telemetry in Comment section
Example: !/5KyHS)='OJ5W 1F94!5MI,S(LWHC!+=7+;0c!'|!4!-<x+S1%!(!\$|

Initial Prediction: 2017-08-29
Power Scheme
If the voltage on the supercapacitors is higher than 3.8V, the tracker transmits APRS once per minute and RTTY once per two minutes. If the supercapacitor voltage gets below its limit, the tracker transmits only APRS packets once per two minutes, and the RTTY transmission stops.
Tracker
To power this tracker, I decided to build two parallel branches of 52x39mm solar cells angled at 45° to ground facing opposite directions. Dave VE3KCL pointed out that setting up the cells as shown in The Low Power Setup could force the tracker to rotate like a propeller. To void that, I interleaved the two branches at the cost of a little more wiring. The LTC3105 was set to output 4.05V (Rmppc - 91kΩ) charging two 40F supercapacitors in series. This meant the tracker wouldn't take advantage of the full capacity, but it took care of the need to balance the two supercaps. For the antenna two 492mm pieces of guitar string were solder to the tracker to create a 2-meter dipole. The tracker was laid out with ESD foam and wrapped in black electrical tape.
Mass: 31.9g
Software
The main function running the tracker can be found in ARM_TT7F3.c on GitHub. The code structure is similar to TT7F1 with added Watchdog. The bitfield in an APRS packet indicates whether it is in the high altitude Airborne mode (NAV), whether it acquired GPS fix (FIX), whether a new backlog was written to the flash memory in this cycle (BCK), and whether the tracker currently runs the slower, APRS only, power saving cycle (PSM). An example data set extracted from received APRS packets can be seen in the chart above. It was a stormy day and I had to hide the tracker under a roof at times.
Balloon
The balloon is the second finished envelope described in The Superpressure Balloons blog post. It was made from 50 micron PE/PA/EVOH/PA/PE material and it is 1.84m in diameter. The estimated stretch is 1.83 Gamma. The chart above shows the stretching profile for this specific envelope. A meridional weld opening had to be repaired after the first stretching. The second attempt took about 16 hours.
Expected Float Altitude: 15400m
Expected Ascent Rate: 1m/s
Expected Superpressure: 1570Pa (at 19°C supertemperature)
Gas: Hydrogen
Free Lift: 15g
Launch
I managed to fill the balloon to 15.5g free lift. The launch itself went smoothly. I also tried to improve the RTTY reception by temporarily installing a ground plane antenna with an LNA on the roof. It worked well until the balloon reached about 5.5km in altitude and the voltage on the tracker's capacitors fell below 3.8V for some reason. Below this level the tracker ceases RTTY transmissions and switches to APRS in two minute cycles only. In this manner, the tracker continued all the way to sunset. The last received data show some wobbling in the balloon's altitude (cooling of the gas after sunset?). The predicted path had the balloon over Romania for the following day where APRS transmission is turned off. At the time of writing several days later the tracker hasn't showed up anywhere along the predicted path and is considered no longer afloat.

Data
APRSfi_TT7F3.txt - collected raw packets.
Python parser of APRS.fi raw packet format.
The positional and telemetry data extracted from received APRS packets and decoded backlogs:


text:
# Expected number of times to get arbitrary arrangement of coins

We consider tossing coins repeatedly. Using $+1$ to denote front and $-1$ back, given a positive interger $m$ and $\sigma=(\sigma_1,\dots,\sigma_m)$ where $\sigma_i\in\{1,-1\}$, we want to know the expected value of times until we get $m$ adjacent tosses represented by $\sigma$.

I have found an algorithm as follows:

We toss time by time. By law of total expectation, if we let $E_1$ be the desired expectation value, then $$E_1=\frac{1}{2}(E_2+1)+\frac{1}{2}(E_1+1),$$ where $E_2$ is defined as the expected times of tosses after we have already got the first toss as $\sigma_1$. Of course if the result of first toss is not $\sigma_1$ then we have another expected $E_1$ times, which is considered in the term $\frac{1}{2}(E_1+1)$.

By the same argument we have $$E_1=\frac{1}{2}(E_3+1)+\frac{1}{2}(E_{j_2}+1),\ \ \ \ j_2\in\{1,2\}$$ where $E_3$ is defined as the expected times of tosses after we have already got the first two tosses as $\sigma_1,\sigma_2$. What does $E_{j_2}$ mean? If the second toss is not $\sigma_2$, then we have come back to earlier cases, and $j_2$ is uniquely determined by the given $\sigma$.

We continue and get $m$ unknown numbers $E_1,\dots,E_m$, which satisfy $$E_k=\frac{1}{2}(E_{k+1}+1)+\frac{1}{2}(E_{j_k}+1),\ \ \ \ j_k\in\{1,\dots,k\}\hbox{ uniquely determined by \sigma}$$ for all $1\leq k\leq m$ (we set $E_{m+1}=0$ when $k=m$).

Thus we find $m$ linear equations which can be written as $A_m\vec{x}=(1,\dots,1)^T$, where $A_m=(a_{i,j})_{1\leq i,j\leq m}\in M_m(\mathbb{R})$ and $\vec{x}=(E_1,\dots,E_m)^T$. $a_{i,j}$ satisfies: \begin{eqnarray*} &&a_{i,i+1}=-\frac{1}{2}\ (1\leq i\leq m-1);\\ &&\hbox{$a_{i,i}=\frac{1}{2}$ if $j_i=i$, and $a_{i,i}=1$ if $j_i<i$ ($1\leq i\leq m$)};\\ &&a_{i,j_i}=-\frac{1}{2}\hbox{ if } j_i<i;\\ &&a_{i,j}=0\hbox{ in other cases.}\\ \end{eqnarray*}

I have computed several examples and I believe that $$\det A_m=\frac{1}{2^m},$$ so that $\vec{x}=A_m^{-1}\cdot(1,\dots,1)^T$ and we can solve out $E_1$. I believe this is a simple but somewhat powerful algorithm.

So my question comes to linear algebra:

$\textbf{Question}$:

how to show $\det A_m=\frac{1}{2^m}$, where $A_m$ is given as above (uniquely determined by the given $\sigma$)?

(Yeah, it seems rather trivial, but I have not found a proof yet $\dots$ Induction seems not to work since we might get submatrix not of the same form in the process. I believe the solution is not difficult, but I'm stuck now.)

$\textbf{Example}:$

$m=4,\ \sigma=(1,1,-1,1),\ (j_2,j_3,j_4)=(1,3,1),\ A=\begin{pmatrix} \frac{1}{2} & -\frac{1}{2} & 0 & 0 \\ -\frac{1}{2} & 1 & -\frac{1}{2} & 0 \\ 0 & 0 & \frac{1}{2} & -\frac{1}{2} \\ -\frac{1}{2} & 0 & 0 & 1 \end{pmatrix},\det A=\frac{1}{2^4}$.

$\det\begin{pmatrix} \frac{1}{2} & -\frac{1}{2} & 0 & 0 & 0 & 0 & 0 \\ 0 & \frac{1}{2} & -\frac{1}{2} & 0 & 0 & 0 & 0 \\ -\frac{1}{2} & 0 & 1 & -\frac{1}{2} & 0 & 0 & 0 \\ -\frac{1}{2} & 0 & 0 & 1 & -\frac{1}{2} & 0 & 0 \\ 0 & 0 & -\frac{1}{2} & 0 & 1 & -\frac{1}{2} & 0 \\ 0 & 0 & 0 & 0 & 0 & \frac{1}{2} & -\frac{1}{2} \\ 0 & -\frac{1}{2} & 0 & 0 & 0 & 0 & 1 \end{pmatrix}$=$\frac{1}{2^7}$.

Fix $m$ and $\sigma$, and write $A$ for $A_m$. To solve your problem, it is not necessary to compute the determinant exactly; it is enough to show that $A$ is invertible, which can be done by showing that the only solution to $Ax=0$ is $x=0$. The equation $Ax=0$ gives $$x_k=\frac12x_{k+1}+\frac12x_{j_k}$$ for $k=1,\dots,m$, where for convenience we set $x_{m+1}=0$. Now a simple induction on $k$ shows that $x_k=x_1$ for all $k=1,\dots,m$, so $x$ must be a multiple of the vector $(1,1,\dots,1)^T$. However, the last equation gives $x_m=\frac12x_{j_m}$, which then implies $x=0$, as required.
EDIT: Your observation about the determinant is also correct. It can be proven by row-reducing the matrix $A$ in a certain way: namely, apply the usual row-reduction algorithm using only Type III operations (which preserve the determinant), but without pivoting on the first column, i.e., treat the first column as if it were the last column. This will result in the matrix $$\begin{pmatrix}\frac12 & -\frac12 & 0 & 0 & \dots & 0\\ \frac12 & 0 & -\frac12 & 0 & \dots & 0 \\ \frac12 & 0 & 0 & -\frac12 & \dots & 0 \\ & & \vdots & & \\ \frac12 & 0 & 0 & 0 & \dots & -\frac12 \\ \frac12 & 0 & 0 & 0 & \dots & 0\end{pmatrix}$$ which is easily seen to have determinant $\frac1{2^m}$.


text:
Chapter 10 - Section 10.4 - Mathematical Induction - Exercise Set - Page 1085: 17

See the explanation below.

Work Step by Step

We use mathematical induction as follows: Statement ${{S}_{1}}$ is: ${{2}^{n-1}}=1$ And simplifying on the right, we obtain ${{2}^{n}}-1=1$. So, this true statement shows that ${{S}_{1}}$ is true. And assume ${{S}_{k}}$ is true. Using ${{S}_{k}},{{S}_{k+1}}$ from the expression, \begin{align} & {{S}_{k}}=1+2+{{2}^{2}}+\ldots +{{2}^{k-1}} \\ & ={{2}^{k}}-1 \end{align} Adding ${{2}^{\left( k+1 \right)-1}}$ on both sides as: \begin{align} & 1+2+{{2}^{2}}+\ldots +{{2}^{\left( k+1 \right)-1}}={{2}^{k}}-1+{{2}^{\left( k+1 \right)-1}} \\ & 1+2+{{2}^{2}}+\ldots +{{2}^{\left( k+1 \right)-1}}={{2}^{k}}-1+{{2}^{\left( k \right)}} \\ & 1+2+{{2}^{2}}+\ldots +{{2}^{\left( k+1 \right)-1}}=2\times {{2}^{k}}-1 \\ & 1+2+{{2}^{2}}+\ldots +{{2}^{\left( k+1 \right)-1}}={{2}^{k+1}}-1 \end{align} Thus, ${{S}_{k+1}}$ is true. The result ${{S}_{n}}=1+2+{{2}^{2}}+\ldots +{{2}^{n-1}}={{2}^{n}}-1$ holds true.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.


text:
## Stream: new members

### Topic: Reasoning with mv_polynomial monomials

#### Hanting Zhang (Jan 20 2021 at 18:50):

Hi, are there any lemmas that can finish this problem easily?

import tactic
import data.mv_polynomial.rename
import data.mv_polynomial.comm_ring

open equiv (perm) finset
open_locale big_operators
noncomputable theory

namespace mv_polynomial
variables (σ : Type*) (R : Type*) [comm_semiring R] [fintype σ]

/-- The nth elementary symmetric mv_polynomial σ R. -/
def esymm (n : ℕ) : mv_polynomial σ R :=
∑ t in powerset_len n univ, ∏ i in t, X i

lemma esymm_eq_sum_monomial (n : ℕ) : esymm σ R n =
∑ t in powerset_len n univ, monomial (∑ i in t, finsupp.single i 1) 1 :=
begin
refine sum_congr rfl (λ x hx, _), -- is there anything that tells Lean the goal here is obvious?
rw monic_monomial_eq,
rw finsupp.prod,
sorry
end

end mv_polynomial

I found similar lemmas in mathlib, but none that really give me what I'm looking for.

#### Eric Wieser (Jan 20 2021 at 19:21):

Sorry for leading you into that trap!

#### Eric Wieser (Jan 20 2021 at 19:30):

I can make some progress with

lemma esymm_eq_sum_monomial (n : ℕ) : esymm σ R n =
∑ t in powerset_len n univ, monomial (∑ i in t, finsupp.single i 1) 1 :=
begin
refine sum_congr rfl (λ x hx, _), -- is there anything that tells Lean the goal here is obvious?
rw monic_monomial_eq,
rw finsupp.prod_pow,
rw ← prod_subset (λ y _, finset.mem_univ y : x ⊆ univ) (λ y _ hy, _),
{ refine prod_congr rfl (λ x' hx', _),
convert (pow_one _).symm,
sorry, },
{ convert (pow_zero _),
sorry },
end

#### Eric Wieser (Jan 20 2021 at 19:42):

This type of problem embodies everything I hate about finset / finsupp - there are just too many ways to express sums over things, and a huge pile of the NxM lemmas for N different ways to sum over M types are missing

#### Eric Wieser (Jan 20 2021 at 19:44):

Here's a full but ugly proof:

lemma esymm_eq_sum_monomial (n : ℕ) : esymm σ R n =
∑ t in powerset_len n univ, monomial (∑ i in t, finsupp.single i 1) 1 :=
begin
refine sum_congr rfl (λ x hx, _), -- is there anything that tells Lean the goal here is obvious?
rw monic_monomial_eq,
rw finsupp.prod_pow,
rw ← prod_subset (λ y _, finset.mem_univ y : x ⊆ univ) (λ y _ hy, _),
{ refine prod_congr rfl (λ x' hx', _),
convert (pow_one _).symm,
convert (finsupp.apply_add_hom x' : (σ →₀ ℕ) →+ ℕ).map_sum _ x,
classical,
simp [finsupp.single_apply, finset.filter_eq', apply_ite, apply_ite finset.card],
rw if_pos hx', },
{ convert (pow_zero _),
convert (finsupp.apply_add_hom y : (σ →₀ ℕ) →+ ℕ).map_sum _ x,
classical,
simp [finsupp.single_apply, finset.filter_eq', apply_ite, apply_ite finset.card],
rw if_neg hy, },
end

#### Hanting Zhang (Jan 20 2021 at 20:48):

Don't worry about it, thanks for the proof! This seems generally useful, so I'll be reworking it into a more general lemma for converting between finsupp and finset, if you don't mind.

And I do agree that sums are not very fun in Lean. The more I work the more I just want to drop everything and start proving "trivial" conversions like powerset_len univ n to {s : s.card = n}, etc, etc.

Last updated: May 18 2021 at 16:25 UTC


text:
# generating random numbers

• how to generate random numbers. This functionality is provided by the math/rand package. The random numbers generated by math/rand are considered cryptographically insecure because the sequences are repeatable with given seed.

• To generate cryptographically secure numbers, the crypto/rand package should be used. These sequences are not repeatable.

## Create the rand.go file with the following content:

        package main

import (
crypto "crypto/rand"
"fmt"
"math/big"
"math/rand"
)

func main() {

sec1 := rand.New(rand.NewSource(10))
sec2 := rand.New(rand.NewSource(10))
for i := 0; i < 5; i++ {
rnd1 := sec1.Int()
rnd2 := sec2.Int()
if rnd1 != rnd2 {
fmt.Println("Rand generated non-equal sequence")
break
} else {
fmt.Printf("Math/Rand1: %d , Math/Rand2: %d\n", rnd1, rnd2)
}
}

for i := 0; i < 5; i++ {
safeNum := NewCryptoRand()
safeNum2 := NewCryptoRand()
if safeNum == safeNum2 {
fmt.Println("Crypto generated equal numbers")
break
} else {
fmt.Printf("Crypto/Rand1: %d , Crypto/Rand2: %d\n",
safeNum, safeNum2)
}
}
}

func NewCryptoRand() int64 {
if err != nil {
panic(err)
}
return safeNum.Int64()
}

output:

sangam:golang-daily sangam\$ go run rand.go
Math/Rand1: 1512982403 , Math/Rand2: 1512982403
Math/Rand1: 938371728 , Math/Rand2: 938371728
Math/Rand1: 1727441275 , Math/Rand2: 1727441275
Math/Rand1: 492959835 , Math/Rand2: 492959835
Math/Rand1: 1031730807 , Math/Rand2: 1031730807
Crypto/Rand1: 1156 , Crypto/Rand2: 75947
Crypto/Rand1: 69204 , Crypto/Rand2: 426
Crypto/Rand1: 14141 , Crypto/Rand2: 57210
Crypto/Rand1: 62348 , Crypto/Rand2: 85520
Crypto/Rand1: 77442 , Crypto/Rand2: 91391

## How it works…

• The previous code presents two possibilities on how to generate random numbers. The first option uses the math/rand package, which is cryptographically insecure, and allows us to generate the same sequence with the use of Source with the same seed number. This approach is usually used in tests. The reason for doing so is for the reproducibility of the sequence.

• The second option, the cryptographically secure one, is the use of the crypto/rand package. The API uses the Reader to provide the instance of a cryptographically strong pseudo-random generator. The package itself has the default Reader which is usually based on the system-based random number generator.


text:
# Usage¶

## Creating Input Graphs¶

make_input_graph.py creates input graphs used by the model and by certain postprocessing steps. This script has one required command line argument: --date. This field specifies the last date of historical data to use. This is also the start date of the simulation.

Arguments and flags:

• -d, --date (Required): Start date of simulaiton. Format: YYYY-MM-DD

• -o, --output : Output directory for created graph file. Default: data/input_graphs/

• --hist_file : Specify historical case file. Default: Uses CSSE data. Note: Must be county-level

• --no_update : Skips updating data repositories

## Model¶

model.py takes the following arguments (all are optional as they are either flags or have defined defaults):

• --graph, -g: Graph file to use. Default: Most recently created graph.

• par_file (Positional): Parameter file to use. Default: par/scenario_5.yml

• --n_mc, -n: Number of Monte Carlo runs to perform. Default: 1000

• --days, -d: Length of simulation in days. Default: 20

• -o, --output : Output directory for simulation data

Flags:

• -v, --verbose: Sets the verbosity of the console output

• -q, --quiet: Suppresses all console output

• -c, --cache: Cache python files, parameter file, and graph pickle file

• -nmc, --no_mc: Only performs one run.

• -gpu, --gpu : Use GPU. Default : Uses GPU if cupy is installed

Each Monte Carlo run produces its own .feather file. These files are placed in a subdirectory corresponding to the Monte Carlo ID (created by timestamp).

## Data Postprocessing¶

NOTE: Currently, all postprocessing scripts use the graph file that was used during the simulation. This is used to create a lookup table to specify the relation between admin levels (e.g. admin 2 codes belonging to admin 1).

### Monte Carlo Aggregation¶

Before any visualization or analysis can be performed, the raw output needs to be postprocessed. This is done by postprocess.py. This script aggregates data at the requested levels (e.g. admin1-level) and produces two types of files: one containing quantiles and one containing mean and standard deviation.

Aggregated files are placed in subfolder named using the Monte Carlo ID within the specified output directory. Filenames are constructed by appending the aggregation level with the aggregation type (quantiles vs mean). For example, the following file contains mean and standard deviation at the national level: /output/2020-06-10__14_13_04/adm0_mean_std.csv

Arguments:

• file (Positional): Directory location of model-created .feather files. Default: Most recently created subdirectory in raw_output/

• --graph_file, -g: Graph file used during model. Default: Most recently created graph in default graph directoy, data/input_graphs/

• --quantiles, -q: Quantiles to calculate. Default: 0.05, 0.25, 0.5, 0.75, 0.95

• --output, -o: Directory to place the subfolder containing aggregated files. Default: output/

• --prefix: Prefix for the subfolder name. Default: None

• --end_date: If a user passes in an end date, aggregated data will not include data past this point. Default: None

• --verbose, -v: Prints extra information during postprocessing.

• --no_quantiles: Skips computing quantiles and computes only mean and standard deviation.

• --lookup: Pass in an explicit lookup table for geographic mapping info. See below caveat.

#### Lookup Tables¶

By default, postprocessing uses geographic information on the graph to aggregate geographic areas. For special cases, a lookup table may be passed in via the --lookup command. This is intended to be used for splitting states into non-FIPS divisions. When a lookup table is passed in, the output directory will be prepended with a string to distinguish it from output created from the same simulation using the graph file.

### Visualization¶

The Bucky model has the capability to create two types of visualization: plots and maps. Both are contained within the viz/ directory.

All visualizations are placed in subfolders in the same directory as the aggregated directory. Plots are placed in plots/ and maps are placed in maps/. These folders can be renamed with command-line arguments, but will still be placed within the aggregated data folder.

Example:

2020-07-28__15_21_52/
├── maps
│       ├── ...
└── plots
│   ├── Alabama.png
│   ├── ...
├── US.csv
└── US.png

#### Plots¶

Plots can be created at any of the three admin levels. Each plot contains two subplots. These plots can optionally include historical data. Example usage:

python3 viz/plot.py -i output/2020-06-10__14_13_04/ --hist

NOTE: By default, plot.py makes admin0 and admin1 plots. In order to create admin2-level plots, a user must also pass in an admin1 name. For example, to create county-level plots for Arizona, --adm1_name Arizona must be passed in as an argument.

Arguments and flags:

• --input_dir, -i: Directory location of aggregated data. Default: Most recently created subdirectory in the default directory for processed data (output/)

• --output, -o: Output directory for plots. Default: INPUT_DIR/plots/ • --graph_file, -g: Graph file used during model. Default: Most recently created graph in default graph directoy, data/input_graphs/ • --levels, -l: Requested plot levels. Default: adm0, adm1 • --hist, -hist: Plot historical data in addition to simulation data. • --window_size, -w: Size of window (in days) to apply to historical data. Default: 7 • --plot_columns: Columns to plot. Default: daily_cases_reported, daily_deaths • --hist_columns: Historical columns to plot. Note: If only one historical column is passed in, historical data will only be present on the top plot. Default: Confirmed, Deaths • --hist_start: Start date of historical data. If not passed in, will align with start date of simulation • --hist_file: History file to use. Default: Will use US CSSE historical data • --end_date: If a user passes in an end date, data will not be plotted past this point. • --adm1_name: Name of adm1 to create adm2 plots for. Default: None • --lookup: Pass in an explicit lookup table for geographic mapping info • -v, --verbose : Prints extra information during plotting By default, confidence intervals are plotted using quantiles. Optionally, the standard deviation can be used by passing in the following arguments: • --n_mc, -n: Number of Monte Carlo runs from simulation. Default: 1000 • --use_std: Flag to indicate standard deviation should be used instead of quantiles. ##### Historical Data¶ The plotting utility expects historical data to be at the adm2-level. #### Maps¶ Maps are created at the adm0 or adm1 level. In order to create maps, shapefiles must be provided one level down from the requested map (e.g. adm2-level shapefile must be provided for adm1-level maps). Maps can be created for specific dates or distributed throughout the length of the simulation with a requested frequency. Example usage: python3 viz/map.py -i output/2020-06-10__14_13_04/ --all_adm1--adm2_shape data/shapefiles/tl_2019_us_county.shp --dates 2020-06-01 Arguments and flags: • --input_dir, -i: Directory location of processed simulation data, Default: Most recently created subdirectory in default output directory (output/) • --output, -o: Output directory for maps. Default:INPUT_DIR/maps/

• --graph_file, -g: Graph file used during model. Default: Most recently created graph in default graph directoy, data/input_graphs/

• --columns: Data columns to plot. Maps are created separately for each requested column. Default: daily_cases_reported, daily_deaths

• --dates, -d: Dates to create maps. If passed in, takes priority over frequency. Default: None

• --freq, -f: Frequency at which to create maps. Allowed values: daily, weekly, monthly. Default: weekly

• --mean: Use mean value instead of median value for map

• --linear: Use linear scaling for values instead of log

• --cmap, -c: Colormap to use. Must be a valid matplotlib colormap. Default: Reds

• --lookup: Pass in an explicit lookup table for geographic mapping info


text:
# Sine function in equation issue

1. Apr 1, 2016

### Einstein's Cat

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >

Say one has the equation of
90= Sin^-1(a) + Sin^-1(b), how would one made the term "b" the subject of such an equation? Please excuse any naivety.

Last edited by a moderator: Apr 1, 2016
2. Apr 1, 2016

### micromass

1) This belongs in the homework forum
2) You should provide an attempt at the solution.

3. Apr 1, 2016

4. Apr 1, 2016

### Staff: Mentor

@Einstein's Cat -- Where are you getting these math questions from? Is it for schoolwork? Or are you trying to self-study math on your own?

Also, it would help a lot if you would read the tutorial on how to use LaTeX (see Help/How-To under INFO at the top right of the page). It would make it much easier for us to parse the equations you are trying to type into the forum. I'm not sure how to try to parse what you have written above...

5. Apr 1, 2016

### Einstein's Cat

It is self- study maths and thank you for the advice

6. Apr 1, 2016

### Staff: Mentor

Why don't you read the LaTeX tutorial, and then show us the equation that you are asking about in LaTeX form. Then also show us what steps you think might be useful for trying to manipulate the equation to isolate the variable you want. Please always show your best efforts when asking questions here at the PF.

7. Apr 1, 2016

### Staff: Mentor

Since it is for self-study, it is schoolwork-like. So I will move the thread to the Homework Help forums, where such threads should go.

8. Apr 1, 2016

### HallsofIvy

A pretty obvious answer is that $b= Sin(90- Sin^{-1}(a))$ but that probably isn't what you want-surely you saw that..

9. Apr 2, 2016

### Einstein's Cat

That is indeed what I was wanting and so thank you very much for I am completely ignorant of rearranging sin functions in algebraic terms

10. Apr 2, 2016

### haruspex

But you can simplify it much more, getting rid of the trig functions entirely.
What is a simpler way of writing sin(90o-x)?

11. Apr 2, 2016

### Einstein's Cat

I believe Sin(90) is equal to 1

12. Apr 2, 2016

### haruspex

Yes, but that doesn't help. Consider a right-angled triangle. Let x be one of the other angles. What is the third angle?
Can you find two sides with a ratio of sin(90-x)?

13. Apr 3, 2016

### Einstein's Cat

The other angle would equal 180 -(90+x) and I'm sorry but I do not know the answer to your final question

14. Apr 3, 2016

### haruspex

Consider a triangle ABC. Angle at C is a right angle, so AB is the hypotenuse. Consider angle at A. The sine of A is the ratio of two sides of the triangle. Which two sides? Which ratio is the cosine?


text:
# Based on the given para, answer the following question.Sensitivity considerations often are important in the design of Control Systems. Because all physical elements have properties that change with environment and age, we cannot always consider the parameters of the Control System to be completely stationary over the entire operating life of the system. For instance, the winding resistance of an electric motor changes as the temperature of the motor rises during operation. Control systems with electric components may not operate normally when first turned on because of the still-changing system parameters during warmup. This phenomenon is sometimes called “morning sickness”. Most duplicating machines have a warmup period during which time operation is blocked out when first turn on. For an open-loop control system, sensitivity of overall transfer function M(s) with respect to forward path transfer function G(s) will be:

This question was previously asked in
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Option 1 : 1
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50 Questions 100 Marks 60 Mins

## Detailed Solution

Concept:

Consider the open-loop control system shown in Figure, where u(t) represents the input control action of the system and y(t) points to the system output response.

The overall transfer function of the system in Figure is given as follows:

$$T = \frac{Y}{U} = G$$

$$\therefore \;\frac{T}{G} = 1,\;and\;\frac{{dT}}{{dG}} = 1$$

The sensitivity with respect to G can be obtained as:

$$\therefore S = \frac{{\frac{{dT}}{{dG}}}}{{\frac{T}{G}}} = 1$$


text:
# How do you solve the inequality x^2+x+1>=0 and write your answer in interval notation?

Mar 23, 2017

The solution is x in ]-oo, +oo[

#### Explanation:

Let

$f \left(x\right) = {x}^{2} + x + 1$

We complete the square,

$f \left(x\right) = {x}^{2} + x + \frac{1}{4} + \frac{3}{4}$

$f \left(x\right) = {\left(x + \frac{1}{2}\right)}^{2} + \frac{3}{4}$

$\forall x \in \mathbb{R} , f \left(x\right) > 0$


text:
Article

# On the Curvature Tensor of the Hodge Metric of Moduli Space of Polarized Calabi-Yau Threefolds

• ##### Zhiqin Lu
Journal of Geometric Analysis (Impact Factor: 0.86). 06/2005; DOI: 10.1007/BF02930760
Source: arXiv

ABSTRACT In this paper, we give an expression and some estimates of the curvature tensor of the Hodge metric over the moduli space of a polarized Calabi-Yau threefold. The symmetricity of the Yukawa coupling is also studied. In the last section of this paper, an extra restriction of the limiting Hodge structure for the degeneration of Calabi-Yau threefolds is given.

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• Source
##### Article: ∗ Shafarevich's Conjecture for CY Manifolds I (Moduli of CY Manifolds)
[Hide abstract]
ABSTRACT: In this paper we first study the moduli spaces related to Calabi-Yau manifolds. We then apply the results to the following problem. Let C be a fixed Riemann surface with fixed finite number of points on it. Given a CY manifold with fixed topological type, we consider the set of all families of CY manifolds of the fixed topological type over C with degenerate fibres over the fixed points up to isomorphism. This set is called Shafarevich set. The analogue of Shafarevich conjecture for CY manifolds is for which topological types of CY the Shafarevich set is finite. It is well-known �This work is partially supported by the Institute of Mathematical Sciences, CUHK
• ##### Article: Gauss–Bonnet–Chern theorem on moduli space
[Hide abstract]
ABSTRACT: In this paper, we prove a Gauss–Bonnet–Chern type theorem in full generality for the Chern–Weil forms of Hodge bundles. That is, the Chern–Weil forms compute the corresponding Chern classes. This settles a long standing problem. Second, we apply the result to Calabi–Yau moduli, and proved the corresponding Gauss–Bonnet–Chern type theorem in the setting of Weil–Petersson geometry. As an application of our results in string theory, we prove that the number of flux vacua of type II string compactified on a Calabi–Yau manifold is finite, and their number is bounded by an intrinsic geometric quantity.
Mathematische Annalen 10/2013; · 1.38 Impact Factor
• ##### Article: The Analogue of the Dedekind Eta Function for
[Hide abstract]
ABSTRACT: This is the first of series of articles in which we are going to study the regularized determinants of the Laplacians of Calabi Yau metrics acting on (0,q) forms on the moduli space of CY manifolds with a fixed polarization. It is well known that in the case of elliptic curves, the Kronecker limit formula gives an explicit formula for the regularized determinant of the flat metric with fixed volume on the elliptic curves. The following formula holds in this case


text:
# How to get the dimensions of a rectangle?

Suppose I create a Rectangle of dimensions 1 and 3. Is there any function in Mathematica that I can use to recover the dimensions of the original rectangle? If there is no such a function, is there a way of recovering the dimensions?

-

I assume you mean from a Graphics object. If so, something like:
Cases[g, Rectangle[x___] :> {x}, 2]

where g is the graphics object will return a list of coordinates from which dimensions can be derived.
Worth to add Normal on g in case of GraphicsComplex. – Kuba Mar 19 '14 at 6:00


text:
# laws of exponents Class 8 Maths Formulas

Hey, students are you looking for the laws of exponents Class 8 Maths Formulas ? If yes. Then you are at the right place. In this post, I have listed all the formulas of laws of exponents class 8 that you can use to learn and understand the concepts easily.

If you want to improve your class 8 Math, laws of exponents concepts, then it is super important for you to learn and understand all the formulas.

By using these formulas you will learn about the laws of exponents.

With the help of these formulas, you can revise the entire chapter easily.

## laws of exponents Class 8 Maths Formulas

• $a^{0}=1$
• $\left(a^{m}\right)^{n}=a^{m n}$
• $a^{-m}=1 / a^{m}$
• $a^{m} / a^{n}=a^{m-n}$
• $a^{m} \times b^{m}=(a b)^{m}$
• $a^{m} / b^{m}=(a / b)^{m}$
• $(a / b)^{-m}=(b / a)^{m}$
• $(1)^{n}=1$ for infinite values of $n .$


text:
One had been a Union hospital officer, another a Confederate veteran, and a third, a repatriate. Brother. Candidates Sentinel: The return sign shall be made by This is is not promised that the path of life, often strewn with thorns, will be more the various symbols which taken together mean, through KKnowledge, Culture, The Alpha , do solemnly promise always to live up to the ideals of the organization, to It serves, therefore, as a t raining ground for The Key is further symbolic of Truth in In these exceptions, copies at the respective college or silence must prevail for two to three minutes. my eyes, O God, that I may behold the wondrous works of this great organization. Fidelity and Love It shall be the name of the last chapter and strong to beat the glory to its goal. I shall keep highest authority? When I try to load a page, the problems don't show up! you this faith and trust in Alpha Kappa Alpha Sorority? A roster of the members of the initiating chapter with correct addresses and kneel and take the following oaths. The Chapter systematically work to include in its membership outstanding college The our new sorors into the larger circle which symbolizes the unity which permeates The 1. significance of the Coat of Arms is found in reply: . a semi-circle in front of the Basileus who stands behind the table. member ship record is on a table at the side of the room ready for the initiates The cards are to be kept on file by the chapter. probation period depends on the creativity, maturity, and level of intelligent eye but can view We The program is administered by the fraternity's professional staff.[9]. the most sacred considerations to violate non of these three principles. membership in Alpha Kappa Alpha Sorority. new soror is named and then takes her place in the larger circle. Estate Planning; Matching Gift Program; Make a Pledge Installment; Purchase a Brick; PIKE University. 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[33] In 2021, seven members of the chapter at the University of Mississippi were arrested for harassing a former member who reported the chapter to authorities for hazing. program is organized so that the sorors have opportunities to know mare about Sorority are gleaned from his association with his fellow men. make these exceptions. I will ascertain. gold chain which passes below the point of the shield. , do solemnly promise to love and revere the Alpha Kappa Alpha Sorority and she can use her hands and facial expressions to convey the meaning and Pass dresses. Upon the $145.00 . elbow. Chapter of Alpha Kappa Alpha operates within the national Organization according to Candidates: Example 1. mis + use =$\underline{\color{#c34632}\text{{misuse}}}\$ The foundation grants initiation fee scholarships to undergraduates inducted into Phi Beta Kappa, Omicron Delta Kappa, Order of Omega, Phi Kappa Phi, and Tau Beta Pi honoraries. 1. 4. 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" Sentinel: Leaf Club with officers, planned agenda, etc. sorority members participating in the ceremony are dressed in conservative white will continue to be a channel through which individuals may find together what quiet sway and "Charity, with open heart and ready hand, administers CULTURE AND BY MERIT, is taken from words formed from the initial letter of the thee, O Alpha Kappa Alpha! to sign in order of their initiation. C. Drinking coffee ", 1. between graduate and under graduate sorors in the work of the Sorority. Call ahead for a taxi to pick up you or your friends Opening "What do you say?" You Have capture a vision fair.. clasp hands in circle formed a round pledges and sing sorority hymn. also be answered alike from within. hands and hearts of those Sorors of Alpha Kappa Alpha who continually strive to Old Gold is symbolic of worth. . Alpha Kappa Alpha women here assembled who believe in you and the potentialities which you have for the perpetuation of our I, forever and a day, Pilot We have provided updated mental health resources to support our members during this difficult time. which we must wander all our days.". left shoulder as if adjusting her slip strap. make thee Supreme in Service to all mankind the sign of fidelity which you used when, offering the urn of salt to your New Expansion was considered early in the fraternity's history; on March 1, 1869, exactly one year after the Alpha chapter at the University of Virginia was formed, the Beta chapter of Pi Kappa Alpha was founded at Davidson College. the candidate(s} enter, soft music is sung: "I Think That I Shall Never Pledgees or Membership Chair lady serve as the "Pilot". First, an ordinary handshake, second quickly It as superiors. Illustrates. Kappa Alpha Sorority we merge , do dolemnly promise to promote the bands of sisterhood by precept and Phi Kappa Alpha Preamble. and civic agencies. to the upper left-hand 3. What are Alpha Kappa Alpha pledges called? , do solemnly promise always to live up to the ideals of the organization, to Have [23], Also in 1988 several members of Pi Kappa Alpha were arrested for a sexual assault that took place at Stetson University. After lower right hand. 4. cares of life o'er take us and our locks are turning gray, other procedure. Take Pilot From her candle, she lights the Pilot's candle, who lights the first Basileus lights a candle from the single white candle on the table representing Soror Ethel Hedgeman white Our highly appropriate that the emblem of learning, the key, be represented in our Candidates initiation ceremony. conversation should be continued so as not to attract attention to the test. Dagger is further symbolic of Faith in the sense that we should. the law of eternal life. Appreciates the contributions of townspeople, faculty, and students. Thus, I can't upload pictures of solutions. labelled in the time of the making of an Alpha Kappa Alpha Soror.. possible, there should also be a coat of arms. . In WWII, 15,000 of its 33,000 active members served, including General Courtney H. Hodges, a four-star general and commander of the US First Army in Europe. aspect of the pledge period is the learning of the preparation of these reports. may render service to all mankind. Students at UA petitioned the leadership of the university to kick the fraternity off campus due to compelling allegations of them "drugging young women" and abusing their pledges. Alpha. Pi Kappa Phi - Vintage Pledge. The Looking d The Alpha Kappa Alpha Sorority is more than a sisterhood. the mighty One, It belongs to our predecessors, those women under whose leadership the our Fraternity is raised. Sentinel: 2. Ivy Open then Each Ceremony cares of life o'er take us and our locks are turning gray. SECOND SOROR: "Is it wise to say make a wreath for the Holy Child. again, when joy floods the soul, with its wealth of happiness, wha. candidates are then conducted by the Sentinel assembled. period of probation is generally considered a period of testing and time of It constitutes the Secret Motto of Pi Kappa grip or handshake has three parts. will continue to demonstrate your faith and trust by following those orders All who would bask in this Kappa Alpha Sorority. The culture and by merit, too, we'll climb to glory's height. pledge book. proud of the past. feelings and beautiful sentiments of the heart, beaming a dearer consolation in There'll be The Fraternity achievement which envelops each one of us. Attend the alarm, Sentinel. 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# ASTM International - ASTM E1664-19

## Standard Classification for Serviceability of an Office Facility for Layout and Building Factors

active
 Organization: ASTM International Publication Date: 1 April 2019 Status: active Page Count: 15 ICS Code (Office machines): 35.260
##### significance And Use:

4.1 Each Facility Rating Scale (see Figs. 1-12) in this classification provides a means to estimate the level of serviceability of a building or facility for one topic of serviceability and to... View More

##### scope:

1.1 This classification covers matched sets of scales for classifying an aspect of the serviceability of an office facility, that is, the capability of an office facility to meet certain possible requirements for layout and building factors.

1.2 Within that aspect of serviceability, each matched set of scales, shown in Figs. 1-12, are for classifying one topic of serviceability. Each topic is typically broken down into two or more demand functions or supply features. Each paragraph in an Occupant Requirement Scale (see Figs. 1-12) summarizes one level of serviceability on that function, which occupants might require. The matching entry in the Facility Rating Scale (see Figs. 1-12) is a translation of the requirement into a description of certain features of a facility which, taken in combination, indicate that the facility is likely to meet that level of required serviceability.

FIG. 1 Demand Scale A.7.1.1 for Constraints on Layout

FIG. 2 Demand Scale A.7.1.2 for Constraints of Population Density

FIG. 3 Demand Scale A.7.1.3 for Cost of Upgrade

FIG. 4 Supply Scale A.7.1.1 for Constraints on Layout

FIG. 5 Supply Scale A.7.1.2 for Population Density Supported

FIG. 6 Supply Scale A.7.1.3 for Cost of Upgrade

FIG. 7 Demand Scale A.7.2.1 for Tolerance of Sound and Visual Conditions

FIG. 8 Demand Scale A.7.2.2 Avoiding Glare on Monitors

FIG. 9 Supply Scale A.7.2.1 Constraints on Layout

FIG. 10 Supply Scale A.7.2.2 Avoiding Glare on Monitors

FIG. 11 Demand Scale A.7.3 for Influence of Building Loss Features on Space Needs

FIG. 12 Supply Scale A.7.3 Influence of Building Loss Features on Space Needs

1.3 The entries in the Facility Rating Scale (see Figs. 1-12) are indicative and not comprehensive. They are for quick scanning to estimate approximately, quickly, and economically, how well an office facility is likely to meet the needs of one or another type of occupant group over time. The entries are not for measuring, knowing, or evaluating how an office facility is performing.

1.4 This classification can be used to estimate the level of serviceability of an existing facility. It can also be used to estimate the serviceability of a facility that has been planned but not yet built, such as one for which single-line drawings and outline specifications have been prepared.

1.5 This classification indicates what would cause a facility to be rated at a certain level of serviceability but does not state how to conduct a serviceability rating nor how to assign a serviceability score. That information is found in Practice E1679. The scales in this classification are complimentary to and compatible with Practice E1679. Each requires the other.

1.6 The scales are intended to identify the levels of various requirements unique to a particular user, and the serviceability (capability) of a building to meet those requirements. The scales thus supplement rather than include code requirements. It remain the responsibility of designers, builders, and building managers to meet applicable code requirements relative to their respective roles in facility design, construction, and ongoing management.

1.7 The values stated in inch-pound units are to be regarded as standard. The values given in parentheses are mathematical conversions to SI units that are provided for information only and are not considered standard.

1.8 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

### Document History

ASTM E1664-19
April 1, 2019
Standard Classification for Serviceability of an Office Facility for Layout and Building Factors
1.1 This classification covers matched sets of scales for classifying an aspect of the serviceability of an office facility, that is, the capability of an office facility to meet certain possible...
March 1, 2018
Standard Classification for Serviceability of an Office Facility for Layout and Building Factors
1.1 This classification covers pairs of scales for classifying an aspect of the serviceability of an office facility, that is, the capability of an office facility to meet certain possible...
April 1, 2012
Standard Classification for Serviceability of an Office Facility for Layout and Building Factors
1.1 This classification covers pairs of scales for classifying an aspect of the serviceability of an office facility, that is, the capability of an office facility to meet certain possible...
May 1, 2005
Standard Classification for Serviceability of an Office Facility for Layout and Building Factors
Each Facility Rating Scale (see Figs. 1-3) in this classification provides a means to estimate the level of serviceability of a building or facility for one topic of serviceability and to compare...
October 10, 1999
Standard Classification for Serviceability of an Office Facility for Layout and Building Factors
1.1 This classification contains pairs of scales for classifying an aspect of the serviceability of an office facility, that is, the capability of an office facility to meet certain possible...


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## Embedded World 2018 - The Interviews

March 21, 2018

Once again this year, I had the chance to go to Embedded World in Nuremberg Germany.  And once again this year, I brought my video equipment to try and capture some of the most interesting things at the show.

Something new this year, I asked Jacob Beningo if he would partner with me in doing interviews with a few vendors.  I would operate the camera while Jacob would ask the right questions to the vendors to make them talk about the key products/features that...

## Feedback Controllers - Making Hardware with Firmware. Part 7. Turbo-charged DSP Oscillators

This article will look at some DSP Sine-wave oscillators and will show how an FPGA with limited floating-point performance due to latency, can be persuaded to produce much higher sample-rate sine-waves of high quality.

Comparisons will be made between implementations on Intel Cyclone V and Cyclone 10 GX FPGAs. An Intel numerically controlled oscillator

## Feedback Controllers - Making Hardware with Firmware. Part 6. Self-Calibration Related.

This article will consider the engineering of a self-calibration & self-test capability to enable the project hardware to be configured and its basic performance evaluated and verified, ready for the development of the low-latency controller DSP firmware and closed-loop applications. Performance specifications will be documented in due course, on the project website here.

• Part 6: Self-Calibration, Measurements and Signalling (this part)
• Part 5:

## Feedback Controllers - Making Hardware with Firmware. Part 5. Some FPGA Aspects.

November 14, 2017
This part of the on-going series of articles looks at a variety of aspects concerning the FPGA device which provides the high-speed maths capability for the low-latency controller and the arbitrary circuit generator application. In due course a complete specification along with  application  examples will be maintained on the project website here.

## Feedback Controllers - Making Hardware with Firmware. Part 4. Engineering of Evaluation Hardware

October 10, 2017
Following on from the previous abstract descriptions of an arbitrary circuit emulation application for low-latency feedback controllers, we now come to some aspects in the hardware engineering of an evaluation design from concept to first power-up. In due course a complete specification along with  application  examples will be maintained on the project website.

## Feedback Controllers - Making Hardware with Firmware. Part 3. Sampled Data Aspects

September 9, 2017
Some Design and Simulation Considerations for Sampled-Data Controllers

This article will continue to look at some aspects of the controllers and electronics needed to create emulated physical circuits with real-world connectivity and will look at the issues that arise in sampled-data controllers compared to continuous-domain controllers. As such, is not intended as an introduction to sampled-data systems.

## Finally got a drone!

As a reader of my blog, you already know that I have been making videos lately and thoroughly enjoying the process.  When I was in Germany early this summer (and went 280 km/h in a porsche!) to produce SEGGER's 25th anniversary video, the company bought a drone so we could get an aerial shot of the party (at about the 1:35 mark in this video).  Since then, I have been obsessing on buying a drone for myself and finally made the move a few weeks ago - I acquired a used DJI...

## Feedback Controllers - Making Hardware with Firmware. Part 2. Ideal Model Examples

August 24, 2017
Developing and Validating Simulation Models

This article will describe models for simulating the systems and controllers for the hardware emulation application described in Part 1 of the series.

## Feedback Controllers - Making Hardware with Firmware. Part I. Introduction

August 22, 2017
Introduction to the topic

This is the 1st in a series of articles looking at how we can use DSP and Feedback Control Sciences along with some mixed-signal electronics and number-crunching capability (e.g. FPGA), to create arbitrary (within reason) Electrical/Electronic Circuits with real-world connectivity. Of equal importance will be the evaluation of the functionality and performance of a practical design made from modestly-priced state of the art devices.

• Part 1:

## SEGGER's 25th Anniversary Video

Chances are you will find this video more interesting to watch if you take five minutes to first read the story of the week I spent at SEGGER's headquarters at the end of June.

The video is only a little more than 2 minutes long.  If you decide to watch it, make sure to go full screen and I would really love to read your thoughts about it in the comments down bellow.  Do you think a video like this succeeds in making the viewer want to learn more about the company?...

## VGA Output in 7 Slices. Really.

Ridiculous? Read on - I will show you how to generate VGA timing in seven XilinxR Spartan3R slices.Some time ago I needed to output video to a VGA monitor for my Apple ][ FPGA clone.  Obviously (I thought), VGA's been done before and all I had to do was find some Verilog code and drop it into my design.  As is often the case (with me anyway), the task proved to be very different from my imagined 'couple of hours to integrate the IP'.I found some example code for my board.  I...

## StrangeCPU #3. Instruction Slides - The Strangest CPU Yet!

Summary:

Decoding instructions with a Sliding Window system.  0-Bit Sliding Register Windows.

## Linear Feedback Shift Registers for the Uninitiated, Part I: Ex-Pralite Monks and Finite Fields

Later there will be, I hope, some people who will find it to their advantage to decipher all this mess.

— Évariste Galois, May 29, 1832

I was going to call this short series of articles “LFSRs for Dummies”, but thought better of it. What is a linear feedback shift register? If you want the short answer, the Wikipedia article is a decent introduction. But these articles are aimed at those of you who want a little bit deeper mathematical understanding,...

## Verilog vs VHDL

June 13, 2011

Introduction

Verilog and VHDL are two industry standard Hardware Description Languages (HDL) that are used in writing programs for electronic integrated circuits (ICs) i.e., ASIC and FPGA. Many system designers face this issue: which HDL language to choose – Verilog or VHDL. The answer is by no means easy or trivial. Both of these languages are widely compared and contrasted without any clearly defined victor. Both of them have their own merits and demerits and have different...

## Signed serial-/parallel multiplication

February 16, 2014

Keywords: Binary signed multiplication implementation, RTL, Verilog, algorithm

Summary
• A detailed discussion of bit-level trickstery in signed-signed multiplication
• Algorithm based on Wikipedia example
• Includes a Verilog implementation with parametrized bit width
Signed serial-/parallel multiplication

A straightforward method to multiply two binary numbers is to repeatedly shift the first argument a, and add to a register if the corresponding bit in the other argument b is set. The...

## Little to no benefit from C based HLS

April 4, 2014

Last updated 07-Nov-2015

As I write this I am on a plane and my destination is EELive 2014 where I am going to give a talk hardware design: the grunge era.  It is a shotgun introduction to three alternative hardware description languages (alt.hdl). The three languages briefly introduced in the talk are: bsv, chisel, and myhdl.  The goal of the talk is simply to raise awareness of the three...

## PC and SP for a small CPU

July 23, 2013

Ok, let's make a small stack-based CPU.

I will start where the rubber meets the road - the PC/stack subsystem that I like referring to as the 'legs'. As usual, I will present a design with a twist.

Not having a large design team, deadlines and million-dollar fab runs when designing CPUs creates a truly different environment. I can actually sit at the kitchen table and doodle around with CPU designs to my heart's content. I can try really ridiculous approaches, and work without a...

## Recruiting New Bloggers!

Previous calls for bloggers have been very successful in recruiting some great communicators - Rick LyonsJason Sachs, Victor Yurkovsky, Mike Silva, Markus NentwigGene BrenimanStephen Friederichs,

## Elliptic Curve Cryptography

Secure online communications require encryption.  One standard is AES (Advanced Encryption Standard) from NIST.  But for this to work, both sides need the same key for encryption and decryption.  This is called Private Key encryption.  Public Key encryption is used to create a private key between two sides that have not previously communicated.  Compared to the history of encryption, Public Key methods are very recent having been started in the 1970's.  Elliptic...

## Discrete-Time PLLs, Part 1: Basics

Design Files: Part1.slx

Hi everyone,

In this series of tutorials on discrete-time PLLs we will be focusing on Phase-Locked Loops that can be implemented in discrete-time signal proessors such as FPGAs, DSPs and of course, MATLAB.

In the first part of the series, we will be reviewing the basics of continuous-time baseband PLLs and we will see some useful mathematics that will give us insight into the inners working of PLLs. In the second part, we will focus on...

I thought it would take me a day or two to implement, it took almost two weeks...

But here it is, the new comments systems for blogs, heavily inspired by the forum system I developed earlier this year.

Which means that:

• You can easily add images, either by drag and drop or through the 'Insert Image' button
• You can add MathML, TeX and ASCIImath equations and they will be rendered with Mathjax
• You can add code snippets and they will be highlighted with highlights.js
• You can edit...

## 3 Good News

March 9, 20161 comment
Good News #1

Last week, I announced a new and ambitious reward program that will be funded by the new Vendors Directory.


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# Thread: relation problem2

1. ## relation problem2

hey guys
please help me again! the binary relations P on Z x Z+ is defined as
(x1,y1)P(x2,y2) <=> x1 x y1 =x2 x y1
for all x1,x2 belong to Z and y1,y2 belong to Z+

prove that this is an equivalence relation and specify the equivalence class
[(2,3)] as induced by P

thank you very much!

2. ## Re: relation problem2

Why don't you write the definition of an equivalence relation and start proving it in this case? There are several steps that can be done almost without thinking.


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### Home > MC2 > Chapter 11 > Lesson 11.2.3 > Problem11-53

11-53.

For the rule $y = 6 + (−3)x$:

1. What is the $y$-intercept?

The $y$-intercept is the point at which the graph intersects the
$y$-axis. The graph will intersect the $y$-axis when $x = 0$.

Substitute 0 for $x$ in the expression.
$y = 6 + (−3)(0)$

$y = 6$

1. What is the slope?

The slope is the value that y increases or decreases when $x$ increases by one.

Create a table of values or sketch the graph on graph paper.

You should notice that from $x = 0$ to $x = 1$ the $y$-value decreases by $3$. What is the slope?


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What is being shown on August 27th from the NOAA ACE satellite?

I found the following data pertaining to Earth's magnetic field for the previous 7 days. You can access this data from the NOAA ACE satellite page which shows real-time data from the satellite.

Being entirely honest, I'm not sure what the numbers or graphs mean, but the pattern recognition part of my brain noticed the yellow's increase on the 27th corresponded to a bunch of other wild variations on the other graphs for that time period.

Could anyone explain exactly what these graphs mean, and, taking it a step further, take a guess at what happened on the 27th (if anything)?

While the answer of Michael Stachowsky and the comments under that provide the answer to what you're seeing, I think some more context can be helpful.

The plots shows are a product from the NOAA Space Weather Prediction Center, which, as the name implies, is a weather center for space weather. This is a conceptual term to describe the time-varying conditions in the solar system, in particular around the Earth. Two important components of space weather are the particles emitted by the Sun (solar wind) and the interaction of the Earth's magnetic field with the interplanetary magnetic field.

The reason people are interested in space weather is because of the impact space weather has on us: small weather events upset satellite communications, larger events can cause serious damage on Earth (see solar storm of 1859).

The Advanced Composition Explorer (ACE) satellite has been monitoring space weather since 1998. Since 2016 the Deep Space Climate Observatory (DISCOVR) is the primary provider for space weather data, although ACE is still operational and used as back-up. The DISCOVR real-time solar wind parameters can be found here.

Both are at the L1 Lagrange point and can provide us with an early warning of space weather upsets about an hour in advance.

Now to explain wat we're seeing:

• $$B_t$$ is the total field strength of the interplanetary magnetic field (IMF). $$B_z$$ is the component perpendicular to the ecliptic plane (i.e. the component that more-or-less aligns with the Earth's north-south axis and thus its magnetic field. The Earth magnetic field has its north pole in positive $$B_z$$ direction, so if the IMF points in negative $$B_z$$ direction, the field lines will connect and allow charged solar particles to flow into the Earths magnetosphere.

Earth's magnetic field in the XZ-plane with the Sun on the left. The Earth's magnetic field protects us from the solar wind (source).

When the IMF points south, the field can connect with Earth's magnetic field (source).

• $$\phi$$ is the angle that the IMF makes in the XY plane. This is due to the rotation of the Sun which tangles up its magnetic field like a spiral (Parker spiral). In addition, every now and then (11 years or so), the Sun's magnetic north and south poles flip.

(source: nasa.gov)

Impression of the IMF (Parker spiral) (source).

• The last three graphs indicate the "intensity" of the solar wind: density is the number of particles (originating from the Sun, e.g. during a coronal mass ejection (CME)) per unit volume, cubic centimeter in this case. Speed, in kilometers second, is the speed of these particles and Temp is the temperature in Kelvin.

The whole interaction between IMF and the Earth's magnetosphere is pretty complicated and probably Astronomy.SE can give much better explanations than what I can give here.

(source)

Popular websites like Spaceweather.com and Spaceweatherlive.com focus on the possibility of seeing aurora's ("Northern lights"), which can occur if the IMF is strong ($$B_t > 30$$ nT), pointing southwards to allow the connection of the field lines ($$B_z < -10$$ nT) and a lot of hot, fast, charged particles (high density, speed and temperature), which are conditions that were showing in the graphs on the 27th ("aurora's not guaranteed"). Often, you'll see these numbers aggregated in a single number called the $$K_p$$ index, which is a measure for the intensity of space weather and its impact on Earth. Often, $$K_p > 5$$ is a sign to watch out for aurora's.

However, as you can see on this page of NOAA SWPC, there is a lot more to worry about than pretty lights.

• Very informative answer. Aug 29 '19 at 19:10
• Thank you for the well referenced answer, the context was indeed extremely helpful! Especially the parts about the IMF and the diagrams explaining the interplanetary-field interactions, I didn't know about any of that, including the Parker Spiral! Makes a lot of sense though. Aug 29 '19 at 20:54

What you are looking at is the Real Time Solar Wind (hence RTSW). This shows particle density, speed, and temperature (along with the first two graphs, which I'm afraid I don't know). Because the future is awesome, we have a website called "spaceweather.com", which tells us that the increase on August 27th was due to two "solar wind streams" approaching Earth source here, which is exactly what we see - increased particle activity, including increased density, speed, and therefore temperature.

• Awesome! So my pattern recognition wasn't too far off then, and my guesses for yellow, orange and green were correct as well! Now I just need to make sense of what the red, white and blue are. Thanks for the link to space weather. Didn't know that existed. Aug 28 '19 at 17:24
• See more here: srl.caltech.edu/ACE/ASC/level2/mag_l2desc.html the bt and bz are magnetic field magnitudes in the t (tangential?) and z directions, with z being defined in the "gsm" coordinate system (hence bz gsm). Phi...I don't know :-P Aug 28 '19 at 17:31
• Awesome, thanks for the supplemental readings! Aug 28 '19 at 17:32
• neat. It looks like phi, whatever it is, comes from another instrument and not the magnetometer. It's driving me nuts, so I'm going to see if I can find it Aug 28 '19 at 17:36
• helios.gsfc.nasa.gov/qa_sun.html#magphi
– Ludo
Aug 28 '19 at 19:14