text:
## JavaLifeSearch

For scripts to aid with computation or simulation in cellular automata.
A for awesome
Posts: 2084
Joined: September 13th, 2014, 5:36 pm
Location: Pembina University, Home of the Gliders
Contact:

### Re: JavaLifeSearch

The manual appears to mention the existence of "frozen unchecked" cells, which I should be able to create with X + I, but when I try that on my copy, nothing happens when I press "I". Is the problem with my copy of JLS, the manual, or my own misunderstanding?
praosylen#5847 (Discord)

x₁=ηx
V*_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

wildmyron
Posts: 1425
Joined: August 9th, 2013, 12:45 am

### Re: JavaLifeSearch

In case you hadn't figured it out yet, this seems to be an error in the documentation. 'i' and 'I' clear all unchecked cells in the selection, and 'o' and 'O' set all unset cells to unchecked. The frozen / unfrozen state is retained with 'i' and 'o' as indicated in the manual - you just need the opposite operation. As usual, 'Shift' applies the operation to all generations.
The latest version of the 5S Project contains over 226,000 spaceships. There is also a GitHub mirror of the collection. Tabulated pages up to period 160 (out of date) are available on the LifeWiki.

Sarp
Posts: 216
Joined: March 1st, 2015, 1:28 pm

### Re: JavaLifeSearch

It seems like the web page is broken, are there any alternative links?

Apple Bottom
Posts: 1034
Joined: July 27th, 2015, 2:06 pm
Contact:

### Re: JavaLifeSearch

Sarp wrote:It seems like the web page is broken, are there any alternative links?
Here's a ZIP file containing a saved copy of the JAR file for 1.7 and the accompanying manual:
JLS-1.7.zip
JLS 1.7 binary and manual
If you speak, your speech must be better than your silence would have been. — Arabian proverb

Catagolue: Apple Bottom • Life Wiki: Apple Bottom • Twitter: @_AppleBottom_

Proud member of the Pattern Raiders!

Sokwe
Moderator
Posts: 1669
Joined: July 9th, 2009, 2:44 pm

### Re: JavaLifeSearch

Apple Bottom wrote:Here's a ZIP file containing a saved copy of the JAR file for 1.7 and the accompanying manual
Thanks. I've updated the original post to link to your post.
-Matthias Merzenich

Entity Valkyrie
Posts: 247
Joined: November 30th, 2017, 3:30 am

### Re: JavaLifeSearch

How do I use JavaLifeSearch to find a suitable p3 reflector for this?

Code: Select all

x = 29, y = 25, rule = B3/S23
18bobo$19b2o$19bo6$o$3o$3bo$2b2o11b2o11bo$15b2o9b3o$6b3o17bobo$4b2o20b o$4b2obob2o$4b4o2bo$5bo4bo$6b4o$6b2o2$27b2o$28bo$25b3o$25bo!

EDIT: This is p51.

wildmyron
Posts: 1425
Joined: August 9th, 2013, 12:45 am

### Re: JavaLifeSearch

Entity Valkyrie wrote:How do I use JavaLifeSearch to find a suitable p3 reflector for this?

Code: Select all

x = 29, y = 25, rule = B3/S23
18bobo$19b2o$19bo6$o$3o$3bo$2b2o11b2o11bo$15b2o9b3o$6b3o17bobo$4b2o20b o$4b2obob2o$4b4o2bo$5bo4bo$6b4o$6b2o2$27b2o$28bo$25b3o$25bo!

EDIT: This is p51.
I'm not sure this problem is at a stage where JLS can be used to find a solution, but it depends very much on what you are trying to reflect, the timing of that reflection and where it needs to go. If I understand what you are trying to do correctly, then you want to use the p3 reflector to shuttle the glider which knocks out the FNG of the eastern herschel allowing the R-> H progression to work. What you need to do first is work out the timing and output lane of the reflector that's required, and then survey all the known p3 reflectors to see if there's anything that matches. If you find something but it doesn't fit, then you can use JLS to find an oscillator which uses the same mechanism and also fits in the space that is available. If there's nothing that matches then it is going to be very hard to find something starting with just JLS.

If you do want to tackle this problem then the way to do it would be to set up JLS with a period of 51 gen, and manually set the as much of the pattern as possible until you have the input and output gliders defined throughout the interaction. In this case you may need to work forwards from Gen 0 and backwards from the last gen to work out where and when the interaction will take place. In the middle you'll need to leave a number of cells unconstrained (which is where the interaction will take place) and then border that region with cells constrained to be p3. To start with there should be a thin border of p3 cells surrounded by a larger area of Unchecked p3 cells. I tackle these problems by starting with as small an area as possible for the interaction and gradually increase that area when no results are found. You'll see that there are errors where signals (including gliders) come into and go out of the conduits. These errors can be resolved with Unset cells in the last generation.

You can save a lot of time in setting up these searches by pasting in a pattern from Golly into JLS, manually setting the unknown areas throughout the evolution and letting it work out the subsequent generations everywhere else. I've attached a JLS file which sets up this kind of search from an adapted version of the pattern on the Gun Discussion thread (with alternate p3 sparker) combined with the pattern here. With the current setup the search finds 0 solutions after about 3 minutes. Note the Sort order used (in particular "Process all cells in a generation first") and the use of "Use combinations of solutions to prune search" in the Search Options. The later option has no effect on this search as it's set up, but as you expand the search it's a very useful option.

I suspect that even if you manage to find a solution to this problem it's going to be very difficult to make it fit with all the other circuitry you require, for example, there's no way it can coexist with the 2G -> H you used in the pattern from the Gun Discussion thread.

Good Luck
Attachments
B3S23-p3_reflector_for_p51_conduit.zip
Sample JLS setup for p3 reflector
The latest version of the 5S Project contains over 226,000 spaceships. There is also a GitHub mirror of the collection. Tabulated pages up to period 160 (out of date) are available on the LifeWiki.

Entity Valkyrie
Posts: 247
Joined: November 30th, 2017, 3:30 am

### Re: JavaLifeSearch

wildmyron wrote:
Entity Valkyrie wrote:How do I use JavaLifeSearch to find a suitable p3 reflector for this?

Code: Select all

x = 29, y = 25, rule = B3/S23
18bobo$19b2o$19bo6$o$3o$3bo$2b2o11b2o11bo$15b2o9b3o$6b3o17bobo$4b2o20b o$4b2obob2o$4b4o2bo$5bo4bo$6b4o$6b2o2$27b2o$28bo$25b3o$25bo!

EDIT: This is p51.
I'm not sure this problem is at a stage where JLS can be used to find a solution, but it depends very much on what you are trying to reflect, the timing of that reflection and where it needs to go. If I understand what you are trying to do correctly, then you want to use the p3 reflector to shuttle the glider which knocks out the FNG of the eastern herschel allowing the R-> H progression to work. What you need to do first is work out the timing and output lane of the reflector that's required, and then survey all the known p3 reflectors to see if there's anything that matches. If you find something but it doesn't fit, then you can use JLS to find an oscillator which uses the same mechanism and also fits in the space that is available. If there's nothing that matches then it is going to be very hard to find something starting with just JLS.

If you do want to tackle this problem then the way to do it would be to set up JLS with a period of 51 gen, and manually set the as much of the pattern as possible until you have the input and output gliders defined throughout the interaction. In this case you may need to work forwards from Gen 0 and backwards from the last gen to work out where and when the interaction will take place. In the middle you'll need to leave a number of cells unconstrained (which is where the interaction will take place) and then border that region with cells constrained to be p3. To start with there should be a thin border of p3 cells surrounded by a larger area of Unchecked p3 cells. I tackle these problems by starting with as small an area as possible for the interaction and gradually increase that area when no results are found. You'll see that there are errors where signals (including gliders) come into and go out of the conduits. These errors can be resolved with Unset cells in the last generation.

You can save a lot of time in setting up these searches by pasting in a pattern from Golly into JLS, manually setting the unknown areas throughout the evolution and letting it work out the subsequent generations everywhere else. I've attached a JLS file which sets up this kind of search from an adapted version of the pattern on the Gun Discussion thread (with alternate p3 sparker) combined with the pattern here. With the current setup the search finds 0 solutions after about 3 minutes. Note the Sort order used (in particular "Process all cells in a generation first") and the use of "Use combinations of solutions to prune search" in the Search Options. The later option has no effect on this search as it's set up, but as you expand the search it's a very useful option.

I suspect that even if you manage to find a solution to this problem it's going to be very difficult to make it fit with all the other circuitry you require, for example, there's no way it can coexist with the 2G -> H you used in the pattern from the Gun Discussion thread.

Good Luck
Thanks for the file. I didn't know how to set up JavaLifeSearch until now.

77topaz
Posts: 1497
Joined: January 12th, 2018, 9:19 pm

### Re: JavaLifeSearch

Could you please not quote entire page-long posts just to add a single line of response to the bottom?

LaundryPizza03
Posts: 907
Joined: December 15th, 2017, 12:05 am
Location: Unidentified location "https://en.wikipedia.org/wiki/Texas"

### Re: JavaLifeSearch

JLS's error detection is buggy when finding spaceships. For example, it prevents me from attempting to extend the following c/5o partial because of the top three sparks:

Code: Select all

x = 19, y = 14, rule = B3/S3
9bo2$7bo3bo$3b2o9b2o$5b2ob3ob2o$b2o3bo5bo3b2o$b2o3bo5bo3b2o$2bo3bo5bo
3bo$bo3bo7bo3bo$2b4o7b4o$2o5b5o5b2o$5bobo3bobo$4b2o7b2o$2bob2o2b3o2b2o
bo!

EDIT: Without the spaceship requirement, do you know why I'm getting only solutions where the rows behind the last functional one disappear after 1 period?

Code: Select all

x = 4, y = 3, rule = B3-q4z5y/S234k5j
2b2o$b2o$2o!

LaundryPizza03 at Wikipedia

The latest edition of new-gliders.db.txt and oscillators.db.txt have 31150 spaceships and 1205 oscillators from outer-totalistic rules. You are invited to help!

wildmyron
Posts: 1425
Joined: August 9th, 2013, 12:45 am

### Re: JavaLifeSearch

LaundryPizza03 wrote:
March 2nd, 2020, 1:45 am
JLS's error detection is buggy when finding spaceships. For example, it prevents me from attempting to extend the following c/5o partial because of the top three sparks:

Code: Select all

x = 19, y = 14, rule = B3/S3
9bo2$7bo3bo$3b2o9b2o$5b2ob3ob2o$b2o3bo5bo3b2o$b2o3bo5bo3b2o$2bo3bo5bo
3bo$bo3bo7bo3bo$2b4o7b4o$2o5b5o5b2o$5bobo3bobo$4b2o7b2o$2bob2o2b3o2b2o
bo!

This partial seems to work fine for me in JLS, but the search doesn't go very far before it's complete. Here are the settings which need to be adjusted from default to run a search (with the partial in the same orientation as shown above):
• Edit -> Properties -> Edit field:
• Columns (width) - 21 (or slightly larger odd value)
• Rows (height) - some number larger than 18 (50 is reasonable, less is OK, more gets awkward but will be necessary for long ships)
• Generations (depth) - 5
• Symmetry - Horizontal mirror
• Edit -> Properties -> Tiling/translation
• After the last generation is... Generation 0, shifted -1 cells down
• Edit -> Properties -> Rule
• B3/S3 (deselect S2)
• Select the top 14 rows and press 'a' to set cells to Off.
• Select the centre 19 columns of the top 14 rows and paste the partial pattern (Edit -> Paste or Ctrl-V)
• In order to run any reasonable search you also need to change the search order - Search -> Options -> Sorting
• Area - Vertical
• (Optional) Start at Column 10 (Should be the centre column [(width - 1) / 2] )
• Search -> Options -> Processing
• Display search status on screen - every 1 seconds (Personal preference)
This search won't get far - it ends almost immediately at width 23. If you keep just the top 7 rows of the partial you can run a decent search. (Still no results at width 23 though.)

Personally I find searching for vertically traveling spaceships in JLS / WLS awkward - the defaults are more tailored to leftward traveling ships. To set up such a search you just need to adjust the period, the displacement (set "After the last generation is..." to Generation 0, shifted -x cells to the right, where "x" is the desired displacement), and set symmetry to Vertical mirror (if desired). (And optionally change the sorting options to Start at Row r, where r is the centre row.)
EDIT: Without the spaceship requirement, do you know why I'm getting only solutions where the rows behind the last functional one disappear after 1 period?
I don't understand what you mean - you can't run an oscillator search with this partial...
The latest version of the 5S Project contains over 226,000 spaceships. There is also a GitHub mirror of the collection. Tabulated pages up to period 160 (out of date) are available on the LifeWiki.

LaundryPizza03
Posts: 907
Joined: December 15th, 2017, 12:05 am
Location: Unidentified location "https://en.wikipedia.org/wiki/Texas"

### Re: JavaLifeSearch

The spaceship search option is still proving unusably buggy for me. I'm trying to find a glide-symmetric 2c/8d in B368/S35678 by attaching a rear end to a wickstretcher. The spaceship is traveling northwest, so the correct option is to have the pattern shifted up 1 cell and left 1 cell, reflected diagonally backward. But then the ten cells highlighted in red and white at the northwest end of the pattern return an error, despite working exactly as intended. Even when specifying simple translation, it still doesn't work.

Code: Select all

x = 14, y = 14, rule = B368/S35678History
14B$3B4D7B$2B5AC6B$BD8A4B$BD8A4B$BD10A2B$BD10A2B$2BC10AE$3B9A2E$3B8A 3E$5B5A4E$6B3A5E$6B2A6E$8B6E!  That said, JLS works fine for searches that don't involve unknown moving patterns, though I'd still like to build a GUI for custom LLS searches because it's faster and more diverse. Code: Select all x = 4, y = 3, rule = B3-q4z5y/S234k5j 2b2o$b2o$2o!  LaundryPizza03 at Wikipedia The latest edition of new-gliders.db.txt and oscillators.db.txt have 31150 spaceships and 1205 oscillators from outer-totalistic rules. You are invited to help! wildmyron Posts: 1425 Joined: August 9th, 2013, 12:45 am ### Re: JavaLifeSearch LaundryPizza03 wrote: May 12th, 2020, 2:03 am The spaceship search option is still proving unusably buggy for me. I'm trying to find a glide-symmetric 2c/8d in B368/S35678 by attaching a rear end to a wickstretcher. The spaceship is traveling northwest, so the correct option is to have the pattern shifted up 1 cell and left 1 cell, reflected diagonally backward. But then the ten cells highlighted in red and white at the northwest end of the pattern return an error, despite working exactly as intended. Even when specifying simple translation, it still doesn't work. Code: Select all x = 14, y = 14, rule = B368/S35678History 14B$3B4D7B$2B5AC6B$BD8A4B$BD8A4B$BD10A2B$BD10A2B$2BC10AE$3B9A2E$3B8A
3E$5B5A4E$6B3A5E$6B2A6E$8B6E!

That said, JLS works fine for searches that don't involve unknown moving patterns, though I'd still like to build a GUI for custom LLS searches because it's faster and more diverse.
Unfortunately JLS doesn't fully support diagonal glide reflect spaceships. There was a brief mention of this issue at the end of page 1 of this thread. I'm not sure about the partial you are trying to extend (because you haven't shown it here) but as you note glide reflect with (-1,-1) does work in this rule. The glider in CGoL is glide reflect with (-1,0) and that doesn't work in JLS. Similarly, 2c/8d spaceships could be glide-reflect with (-2,0), and that doesn't work in JLS. It could be that your partial requires (-2,0) rather than (-1,-1).
The latest version of the 5S Project contains over 226,000 spaceships. There is also a GitHub mirror of the collection. Tabulated pages up to period 160 (out of date) are available on the LifeWiki.


text:
## Selection Sort

A selection sort, is in a certain sense somewhat similar to a bubble sort, in that it seeks to move extreme elements in sequence to one side of the array.

The first pass made by the algorithm traverses the entire array to find the position of the smallest element and then swaps that element to the beginning of the array.

In the second pass, knowing that the first element is already in the correct place, we visit all but that first element again to find the second-smallest element, and then swap that element to the second position in the array.

Knowing that the first two elements are now in their correct places, we visit the remaining elements to find the third-smallest element and swap it to the third position in the array.

If we continuing doing this -- after $n-1$ passes the entire array will be correctly sorted.

Below, we show an example of the second version (where we are finding small elements and moving them left, towards the beginning of the array.

=== First Pass ==============================

We are attempting to find the element that
should be at position 0 in the list:

5 2 4 1 9 3 7  min so far = 5, pos = 0
-

5 2 4 1 9 3 7  min so far = 2, pos = 1
-

5 2 4 1 9 3 7  min so far = 2, pos = 1
-

5 2 4 1 9 3 7  min so far = 1, pos = 3
-

5 2 4 1 9 3 7  min so far = 1, pos = 3
-

5 2 4 1 9 3 7  min so far = 1, pos = 3
-

5 2 4 1 9 3 7  min so far = 1, pos = 3
-

5 2 4 1 9 3 7  min so far = 1, pos = 3
-

5 2 4 1 9 3 7  min so far = 1, pos = 3
-

1 2 4 5 9 3 7  after swapping the element at position 3
with the element at position 0

=== Second Pass =============================

We are attempting to find the element that
should be at position 1 in the list:

1 2 4 5 9 3 7  min so far = 2, pos = 1
-            note: we ignore the previously placed 1
and start a new search for the next-
smallest value...

1 2 4 5 9 3 7  min so far = 2, pos = 1
-

1 2 4 5 9 3 7  min so far = 2, pos = 1
-

1 2 4 5 9 3 7  min so far = 2, pos = 1
-

1 2 4 5 9 3 7  min so far = 2, pos = 1
-

1 2 4 5 9 3 7  min so far = 2, pos = 1
-

1 2 4 5 9 3 7  after swapping the element at position 1
with the element at position 1
(yes, this is a bit silly, since 2 is

=== Third Pass =============================

We are attempting to find the element that
should be at position 2 in the list:

1 2 4 5 9 3 7  min so far = 4, pos = 2
-          note: we ignore the previously placed 1 and 2
and start a new search for the next-
smallest value...

1 2 4 5 9 3 7  min so far = 4, pos = 2
-

1 2 4 5 9 3 7  min so far = 4, pos = 2
-

1 2 4 5 9 3 7  min so far = 3, pos = 5
-

1 2 4 5 9 3 7  min so far = 3, pos = 5
-

1 2 3 5 9 4 7  after swapping the element at position 5
with the element at position 2

=== Fourth Pass =============================

We are attempting to find the element that
should be at position 3 in the list:

1 2 3 5 9 4 7  min so far = 5, pos = 3
-        note: we ignore the previously placed 1, 2, and 3
and start a new search for the next-
smallest value...

1 2 3 5 9 4 7  min so far = 5, pos = 3
-

1 2 3 5 9 4 7  min so far = 4, pos = 5
-

1 2 3 5 9 4 7  min so far = 4, pos = 5
-

1 2 3 4 9 5 7  after swapping the element at position 5
with the element at position 3

=== Fifth Pass =============================

We are attempting to find the element that
should be at position 4 in the list:

1 2 3 4 9 5 7  min so far = 9, pos = 4
-      note: we ignore the previously placed numbers 1-4
and start a new search for the next-
smallest value...

1 2 3 4 9 5 7  min so far = 5, pos = 5
-

1 2 3 4 9 5 7  min so far = 5, pos = 5
-

1 2 3 4 5 9 7  after swapping the element at position 5
with the element at position 4

=== Sixth Pass ============================

We are attempting to find the element that
should be at position 5 in the list:

1 2 3 4 5 9 7  min so far = 9, pos = 5
-    note: we ignore the previous placed numbers 1-5
and start a new search for the next-
smallest value...

1 2 3 4 5 9 7  min so far = 7, pos = 6
-

1 2 3 4 5 7 9  after swapping the element at position 6
with the element at position 5

===========================================

There is only one other value to consider (9), but there is only
one position he could be in -- and he's in it.  Thus, we are done
sorting the array.

### Implementation and Analysis

Again, the implementation of the algorithm is fairly straight-forward, using the helper methods less() and exch() mentioned previously. The version shown below is the one consistent with the example above, where small elements are swapped towards the beginning of the array.

   public static void selectionSort(Comparable[] a) {
int n = a.length;
for (int i = 0; i < n; i++) {
int minPos = i;
for (int j = i+1; j < n; j++) {
if (less(a[j],a[minPos])) {
minPos = j;
}
}
exch(a,i,minPos);
}
}

As for the cost, let us again focus on the number of comparisons and exchanges. With regard to comparisons made, we are always making $n-1$ comparisons in the first pass, $n-2$ comparisons in the second pass, $n-3$ in the third, and so on... Thus, we have a total number of comparisons given by:

$$(n-1) + (n-2) + (n-3) + \cdots + 3 + 2 + 1 = \frac{n(n-1)}{2} \sim \frac{n^2}{2}$$

Importantly, note that the running time to sort $n$ elements with a selection sort is not affected by the order of the elements -- it will be quadratic time, even if the input is already sorted!

Now let us consider the number of exchanges. Since we know that

• an exchange is only made at the end of each pass,
• the number of elements decreases by one with each pass, and
• the placement of the final element doesn't require an exchange
it must be the case that the number of exchanges is given by

$$n-1 = O(n)$$

Since there are only a linear number of exchanges for sorting $n$ elements, the "data movement" in a selection sort is minimal.

Note, the bubble sort actually faired a bit better in terms of comparisons, as while it was also $O(n^2)$ on average, there were times (like when the array is already partially ordered) when far fewer comparisons are made. However, when we consider the number of exchanges, we see that selection sort far surpasses the lowly bubble sort.

format: plain


text:
How do you write the complex number in trigonometric form 4-4sqrt3i?

Mar 18, 2017

$z = 8 \left[\cos \left(\frac{2 \pi}{3}\right) + i \sin \left(\frac{2 \pi}{3}\right)\right]$

Explanation:

$\left(x , y\right) \to r \left(\cos \theta + i \sin \theta\right)$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{r = \sqrt{{x}^{2} + {y}^{2}}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{and } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{\theta = {\tan}^{-} 1 \left(\frac{y}{x}\right)} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{here "x=4" and } y = - 4 \sqrt{3}$

$\Rightarrow r = \sqrt{{\left(4\right)}^{2} + {\left(- 4 \sqrt{3}\right)}^{2}} = \sqrt{64} = 8$

$\text{now } 4 - 4 \sqrt{3}$ is in the 2nd quadrant so we must ensure that
$\theta$ is in the 2nd quadrant.

$\Rightarrow {\tan}^{-} 1 \left(\frac{4 \sqrt{3}}{4}\right) = {\tan}^{-} 1 \left(\sqrt{3}\right) = \frac{\pi}{3}$

$\Rightarrow \theta = \left(\pi - \frac{\pi}{3}\right) = \frac{2 \pi}{3} \leftarrow \textcolor{red}{\text{ in 2nd quadrant}}$

$\Rightarrow 4 - 4 \sqrt{3} i = 8 \left[\cos \left(\frac{2 \pi}{3}\right) + i \sin \left(\frac{2 \pi}{3}\right)\right]$


text:
# How would you calculate the density of a substance which occupies 25.0mL and has a mass of 35.0g?

$\rho$ $\text{, Density}$ $=$ $\text{Mass"/"Volume}$
And thus $\rho$ , $=$ $\frac{35.0 \cdot g}{25.0 \cdot m L}$ $=$ ??g*mL^-1


text:
Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01k930bx153
 Title: Aligned Nonspinning Dipoles Contributors: Li, JasonNASA Keywords: neutron stars Issue Date: 21-Nov-2013 Abstract: Magnetic field lines and current sheets for an orbiting neutron star binary with the magnetic moments of both stars aligned with the rotation axis. The stars are not spinning, i.e., R_{LC,∗} = ∞. Fields are by and large confined to the half of the magnetosphere closer to their source star. This movie shows the corotating field pattern as the orbit progresses. URI: http://arks.princeton.edu/ark:/88435/dsp01k930bx153 Appears in Collections: Research Data Sets

Files in This Item:
File Description SizeFormat
t0sinf.mpeg13.88 MBMPEG


text:
Taking Hapmap Data To The Latest Genome Build
3
7
Entering edit mode
11.2 years ago

I would like to use the LD data in HapMap in combination with the latest genome annotation data in Ensembl 59. Unfortunately, if I am not wrong, HapMap rel. 27 is based on NCBI 36 coordinates, while latest ensembl uses the latest genome build (GRCh37). As far as I understand, the latest ensembl version with compatible coordinates would be 54, correct?

Edit:

Core question: how many SNPs (rd-ids) are re-annotated (deleted,renamed) between releases of dbSNP?

It seems like nobody has undertaken a full lift over of the HapMap bulk data to update all coordinates, at least I didn't find any information about this. So I was thinking about trying to do this.

This question is somewhat related http://biostar.stackexchange.com/questions/916/how-do-you-manage-moving-existing-projects-to-a-new-genome-build where the LiftOver tool was presented as a solution.

So here are my questions:

• Did anybody already try this, or would like to have this data, too?
• What would be the best approach to do the bulk conversion. For example running liftOver on the genomic coordinates, or is it be better to convert based on matching rs-snp ids?
• Is that a valid approach at all?

Any suggestions welcome.

Edit: One of the main concerns that I should mention, is that SNPs are re-named, deleted, positions changed. So I more and more get the impression, that both approaches, just mapping coordinates (the coodinates could be fine, but the SNP could have disappeared/renamed in dbSNP) or simply mapping the ids is not enough, even though it made be safer. I think Jorge's answer points into a good direction.

hapmap ensembl coordinates conversion genome • 6.4k views
4
Entering edit mode
11.2 years ago

The LD data look like this:

14430353 14441016 ASW rs2334386 rs9617528 1.0 0.0020 0.06 144
14430353 14564328 ASW rs2334386 rs7288972 1.0 0.0010 0.04 144
14441016 14564328 ASW rs9617528 rs7288972 1.0 0.0020 0.04 144
14805814 14809328 ASW rs7285246 rs12163493 1.0 0.0040 0.1 148
14805814 14870204 ASW rs7285246 rs8138488 0.088 0.0040 0.04 148

so, to re-map the data, for each snp I would sort the data on the SNP name and unix-join||sql with the SNP table from the UCSC.

1
Entering edit mode

the easiest way to be completely sure about that is to have a look to the merge data from dbSNP. for several reasons we are waiting to update to dbSNP 131, but I can tell you that we maintain a list of such merge information for HapMap using dbSNP 130, and the amount of rs codes merged (from dbSNP 126, which is HapMap's template) are ~1200. add to that figure a small number of rs codes that have been removed (unfortunately we do not keep track of that information), and you will be able to take your own decisions.

0
Entering edit mode

Thanks, Pierre. That looks like a viable solution. But what if rs-ids were changed, SNPs renamed, deleted, or whatever? I heard that happened, rarely, but still.

0
Entering edit mode

Michael, Pierre: Is this SNP re-annotation(as in renamining, deletion etc) common as in the case protein sequence revisions. Is there a way to track the changes in SNP annotations ?

0
Entering edit mode

@Khader I don't now how frequent this re-annotation of snps is, that was one of the reasons for asking this. If it was a few 10 I would not bother, but I am not sure. Possibly Jorge's answer contains the clue.

4
Entering edit mode
11.2 years ago

we have indeed come across this issue a few months ago, and we did considered then all the options mentioned on your post. if you are looking to integrate LD data, Pierre's solution is really interesting, but if you want to dig deeper (as I can guess from your comment to his answer) I can tell you what we did.

we work with several variational repositories (hapmap, 1000 genomes, perlegen, ...), and we have to do a huge normalization effort in order to merge seemlessly all this data. initially, we tried using liftOver, but we had some issues trying to understand all the information that was left out so we decided to study another option. and this option was to use dbSNP as template for all the rs codes we had. the main reason was that dbSNP maintains a record of the rs codes changes in all previous versions, so we were able to get all the data we needed for each rs snp (chromosome, position, validation status, gene presence, ...) from the latest dbSNP build's chromosome reports and merging information being sure that we weren't losing any data on the road.

the latest dbSNP build is currently 131, being mapped to GRCh37, so this has worked for us perfectly, but using Pierre's solution (merging hapmap's data with UCSC's) and adding the snp merging data from dbSNP should work too. please take into account that hapmap data is still using (even in the last release a few days ago) dbSNP's build 126, so using dbSNP's snp code merging information is almost mandatory if you are planning to work only at rs code level.

2
Entering edit mode
11.2 years ago

Just one minor point to add: We maintain a "SNP alias/Common name" field in order to incorporate a) names used in the literature (before or in deference to dbSNP IDs) or b) private, non-dbSNP variants.

I agree that dbSNP is the place to look for rs synonyms.

0
Entering edit mode

we do so in our systems too, as we use data from CEPH arrays and Perlegen, and we wanted to allow users to look for private codes if they wanted. also, as we work with 1000 genomes data, if we include information that hasn't been uploaded to dbSNP yet we have to use such field to identify somehow the variant (we use a "chromosome_position" format).


text:
# Concrete interpretations of higher (sheaf) cohomology groups

$H^1$ has an interpretation as torsors. But what about the higher $H^i$ (in the setting of algebraic geometry, and étale or flat cohomology)? For example $H^2(X, \mathbf{G}_m)$ is (often) isomorphic to the Brauer group, i.e. equivalence classes of Azumaya algebras.

-
What sort of coefficients are you thinking of? –  Tim Porter Feb 16 '11 at 21:48

Depending a bit on your context, try $n$-gerbes. That should handle all the usual cases. Look at papers by Larry Breen and more recently Aldrovandi and Noohi in Advances (Butterflies is the keyword to look for!).
I would say have a look at Duskin's paper '$K(\pi,n)$-torsors and the interpretation of "triple" cohomology' (pdf) and his student Glenn's paper 'Realization of cohomology classes in arbitrary exact categories' J. Pure Appl. Algebra, vol. 25, (1982) pp. 33-105. Also Duskin's 'Higher dimensional torsors and the cohomology of topoi : The abelian theory' Lecture Notes in Mathematics, Volume 753 (1979), pp255-279.


text:
# Bootstrapping for Linear Regression

You can view the code for this tutorial here.

In Homework 02, you fitted a linear regression model for your data, which may have looked something like this:

$f_{\hat{\theta}}(x) = \hat{\theta_0} + \hat{\theta_1}x_1 + \cdots + \hat{\theta_p}x_p$

Now, we would like to construct conﬁdence intervals for the estimated coefﬁcients $$\hat{\theta_0}, \hat{\theta_1}, \cdots \hat{\theta_p}$$ and perhaps infer the true coefficients of our model. Bootstrap is a computational method that allows us to calculate standard errors and confidence intervals for our parameters.

## Importing Libraries

As usual, we will want to use numpy, pandas, matplot, and seaborn to help us manipulate and visualize our data.

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns

## Our Data Set

In this example, I’ll be estimating the price of houses in King County, Washington.

You can obtain the dataset here.

There are 21 columns in this dataset, but for the purposes of this tutorial, we will just look at a couple. Let’s look at the following parameters to estimate price:

• sqft_living: the size, in square feet, of the living area of the house
• yr_built: the year in which the house was built

df = pd.read_csv("kc_house_data.csv", usecols=["price", "sqft_living", "yr_built"])

## Visualizing Our Data

Before doing anything, let’s get a little bit more familiar with our data. As we learned in Tutorial 02, first use head() to see the first five rows of our dataframe:

df.head()

pricesqft_livingyr_built
0221900.011801955
1538000.025701951
2180000.07701933
3604000.019601965
4510000.016801987

Instead of looking at the year built, we’ll look at the age of the house:

df["age of house"] = 2015 - df["yr_built"]

pricesqft_livingyr_builtage of house
0221900.01180195560
1538000.02570195164
2180000.0770193382
3604000.01960196550
4510000.01680198728

In reality, there’s also a column yr_renovated in the original dataset, but for simplicity, we will ignore this in this tutorial.

Let’s also create scatter plots to visualize the relationships between our variables:

plt.xlabel("sqft_living")
plt.ylabel("price")
plt.scatter(x=df["sqft_living"], y=df["price"])

plt.xlabel("age of house")
plt.ylabel("price")
plt.scatter(x=df["age of house"], y=df["price"])

## Fitting the Model

First, let’s organize our data into X and y, what we’re trying to predict (price, in our case).

X = df.loc[:, ["sqft_living", "age of house"]]
y = df.loc[:, "price"]

Note: Visually, we can see that the age of the home does not seem to be strongly correlated with the price of the home. In a real data analysis, we may want to investigate further and/or remove this from our regression.

Now, let’s use scikit-learn to perform linear regression (there’s no need to write the code for this on our own):

import sklearn.linear_model as lm

linear_model = lm.LinearRegression()
linear_model.fit(X, y)

print("""
intercept: %.2f
sqft_living: %.2f
age of house: %.2f
""" % (tuple([linear_model.intercept_]) + tuple(linear_model.coef_)))

intercept: -196929.07

sqft_living: 304.57

age of house: 2353.73

Above are the (estimates of) coefficients we get from our linear regression model. Now, we want to bootstrap our observations.

## Using Bootstrap

For the purposes of this tutorial, we can write a simple resampling function using random integers generated by NumPy (note that these are not true random numbers):

def simple_resample(n):
return(np.random.randint(low = 0, high = n, size = n))

Now, let’s write out a very general bootstrap function that takes in a bootstrap population (not the true population), some statistic, a resampling function (set default to our simple_resample), and the amount of replicates (set default to 10000):

def bootstrap(boot_pop, statistic, resample = simple_resample, replicates = 10000):
n = len(boot_pop)
resample_estimates = np.array([statistic(boot_pop[resample(n)]) for _ in range(replicates)])
return resample_estimates

Let’s just focus on the coefficient for sqft_living. We will sample with replacement from our bootstrap sample (our original data), and fit a new linear regression model to the sampled data. The coefficient for sqft_living will be used as our bootstrap statistic:

def sqft_coeff(data_array):
X = data_array[:, 1:]
y = data_array[:, 0]

linear_model = lm.LinearRegression()
model = linear_model.fit(X, y)
theta_sqft = model.coef_[1]

return theta_sqft

data_array = df.loc[:,  ["price", "age of house", "sqft_living"]].values

theta_hat_sampling = bootstrap(data_array, sqft_coeff)

## Constructing a Confidence Interval

First, let’s construct a histogram of our sampling distribution to get a visual approximation:

plt.hist(theta_hat_sampling, bins = 30, density = True)
plt.xlabel("$\\tilde{\\theta}_{sqft}$ Values")
plt.ylabel("Proportion per Unit")
plt.title("Bootstrap Sampling Distribution of $\\tilde{\\theta}_{sqft}$ (Nonparametric)");
plt.show()

Though we cannot direclty measure the true coefficient, we can construct a confidence interval to account for variability in the sample coefficient. If we construct a 95% confidence interval, we need to look at the 2.5th percentile and 97.5th percentile as our endpoints:

np.percentile(theta_hat_sampling, 2.5), np.percentile(theta_hat_sampling, 97.5)

(293.0643343501463, 316.5597894314288)


text:
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# Calling all Duke (Fuqua) Fall 2009 applicants!

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05 Oct 2008, 17:52
fall09 wrote:
Can anyone give tips on the 'Leader of consequence' essay?

Thanks

My approach (which isn't necessarily the best one) was to treat it as a long-term career goal essay, but instead of focusing on my career, I talked more about the impact I wanted to have.

So in my first essay I talked about wanting to work in a particular business function. In the last essay, I talked about using my new career to solve a major problem in my current industry. I also included an example from my past work experience where I tried to create change.

Does that help?

RF
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05 Oct 2008, 18:20
That helps refurb.But why do you think that is not the best approach?
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06 Oct 2008, 02:36
fall09 wrote:
That helps refurb.But why do you think that is not the best approach?

I only say that because the question is so open-ended. There are so many different ways to answer it that I can't say for certain mine is the best way.

In other words, if you think you've got a great idea on how to answer it, go for it!

RF
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Re: Calling all Duke (Fuqua) Fall 2009 applicants! [#permalink]

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06 Oct 2008, 10:08
raabenb wrote:
Interview Complete!

The interview was with a second year student.

Questions:

5-10 minute resume walkthrough.
Why MBA, why now?
Short term and long term goals?
Why Fuqua?
What will you contribute in and out of class?
What are your greatest strengths, weaknesses?
Give me an example of your teamwork.
How would you handle a difficult team member?
How would your colleagues describe you?
Give me an example of when your ethics were challenged.
If you do not get into any business schools, what will you do?

I think it went VERY well. The back and forth was great. We were both Seinfeld fans so we had some good laughs about Seinfeld references. Overall it lasted 45 min to 1 full hour.

Later in the day I did a campus tour and my tour guide was a guy I went to high school with in PA (I am still friend with his sister). We were totally weired out by how random it was.....

All in all, I had a GREAT experience. LOVED FUQUA.

Thanks for sharing your interview experience with us. I am very excited about my upcoming trip to Fuqua.....will let you guys know ..
VP
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06 Oct 2008, 15:35
Another application conundrum!

I've got essays 1-3 to fit on a single page, 11 point font, 1.5 line spacing and standard margins.

I'm having trouble fitting my fourth essay on two pages using the above format. Looking at the online application, the blurb about essay four says "2 page limit, please use a font no smaller than 10 point".

If I use 10 point, I can fit it all on (~1000 words). However, it's really small. I mean, I wouldn't want to have to read it.

Should I do more editing or submit it as 10 point font?

RF
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06 Oct 2008, 15:45
refurb wrote:
Another application conundrum!

I've got essays 1-3 to fit on a single page, 11 point font, 1.5 line spacing and standard margins.

I'm having trouble fitting my fourth essay on two pages using the above format. Looking at the online application, the blurb about essay four says "2 page limit, please use a font no smaller than 10 point".

If I use 10 point, I can fit it all on (~1000 words). However, it's really small. I mean, I wouldn't want to have to read it.

Should I do more editing or submit it as 10 point font?

RF

I think it would be good to have all the essays follow the same format, font size etc..
VP
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06 Oct 2008, 16:08
prospect wrote:
I think it would be good to have all the essays follow the same format, font size etc..

So I should make all the essays 10 point font?

Just kidding. I agree with you. I think any benefit I get from keeping the extra content will be lost by the adcom thinking "This guy is a jerk for making me read this small print!"

RF
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Re: Calling all Duke (Fuqua) Fall 2009 applicants! [#permalink]

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06 Oct 2008, 19:45
refurb wrote:
prospect wrote:
I think it would be good to have all the essays follow the same format, font size etc..

So I should make all the essays 10 point font?

Just kidding. I agree with you. I think any benefit I get from keeping the extra content will be lost by the adcom thinking "This guy is a jerk for making me read this small print!"

RF

shrink the margins some?
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Re: Calling all Duke (Fuqua) Fall 2009 applicants! [#permalink]

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07 Oct 2008, 02:41
ac8706 wrote:
refurb wrote:
prospect wrote:
I think it would be good to have all the essays follow the same format, font size etc..

So I should make all the essays 10 point font?

Just kidding. I agree with you. I think any benefit I get from keeping the extra content will be lost by the adcom thinking "This guy is a jerk for making me read this small print!"

RF

shrink the margins some?

I would do that if I was a line or two over the two page limit, but I'm more like 1/2 page over. I'd have to get rid of the margins all together!

RF
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07 Oct 2008, 06:03
I think you need to edit a bit then...sorry
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07 Oct 2008, 08:37
I attended the info session in Santa Monica last night. Only about 15 prospective students. In addition to an adcom officer, the associate dean made a surprise appearance (I think he coincidentally happened to be traveling to LA). There were also three alumni who attended.

A couple of takeaways:
1) During the presentation, they beat the "leader of consequence" bit to death. Based on this, I have no doubt that success on essay #4 is going to be CRITICAL to one's success on the application.
2) The staff and alumni were super duper friendly. I've been to probably 5-6 of these events over the last 2 years, and this was by far the friendliest group of people. The adcom was very warm and inviting and not intimidating at all. It was almost as if they were so thankful that we attended and wanted to give as much info on the program/process as possible.

As a (personal) side note, I spent a good deal of time chatting with the associate dean and the adcom member after the session. I seriously got a free 20 minute interview. My work experience is pretty interesting (especially considering what is going on with the financial/credit markets right now) and I felt like I really had a great opportunity to articulate my candidacy through my experiences. I hadn't planned to go into this whole spiel, but things just kind of went that direction. Not sure if these folks are coming to a town near you, but if there was a small turnout for the reception in LA, then you are likely to get some decent personal attention in another city as well.
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07 Oct 2008, 11:19
Dang, sound like a good info session. To bad I was in Hanover or I would have gone.
Director
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Re: Calling all Duke (Fuqua) Fall 2009 applicants! [#permalink]

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07 Oct 2008, 18:31
raabenb wrote:
Interview Complete!

The interview was with a second year student.

Questions:

5-10 minute resume walkthrough.
Why MBA, why now?
Short term and long term goals?
Why Fuqua?
What will you contribute in and out of class?
What are your greatest strengths, weaknesses?
Give me an example of your teamwork.
How would you handle a difficult team member?
How would your colleagues describe you?
Give me an example of when your ethics were challenged.
If you do not get into any business schools, what will you do?

I think it went VERY well. The back and forth was great. We were both Seinfeld fans so we had some good laughs about Seinfeld references. Overall it lasted 45 min to 1 full hour.

Later in the day I did a campus tour and my tour guide was a guy I went to high school with in PA (I am still friend with his sister). We were totally weired out by how random it was.....

All in all, I had a GREAT experience. LOVED FUQUA.

Nice write up - I'm glad to see the interview was straightforward.

Did you move Duke up in your list at all based on your visit?
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07 Oct 2008, 18:47
Fuqua was always tied for my top choice. I was even aiming for an EA submission but now I will have to hit Round 1. It really is a fun and exciting place.
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07 Oct 2008, 18:59
Cool I hope you get in.

I'm thinking about applying EA next year provided I like it when I visit this winter...so tough to choose though.
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Re: Calling all Duke (Fuqua) Fall 2009 applicants! [#permalink]

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08 Oct 2008, 07:39
I attended the info session in Dallas last night. There were around 15-18 prospective students, 3 alumni, one 2nd year student who had come down for the Texas info sessions ( which was really amazing) and one admissions rep.

The alumni were amazing, extremely friendly and very easy to talk to. And yes they did talk about the "leader of consequence" a lot and also about how much Fuqua values team work. The session was pretty long, started at 7 and ended at 9! The 2nd year student talked about the curriculum and different clubs at Fuqua, she was very enthusiastic about the Fuqua program which really helped.

Also came to know that all interviews will be conducted by the 2nd year students.
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08 Oct 2008, 11:39
Woo. Booked ticket to NC for the interview. Anyone know roughly how much it costs to take a cab from airport-Fuqua-airport? I'm getting a car rental for around 40 bucks...is that less than the cost of cab?

thanks
ac.
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Re: Calling all Duke (Fuqua) Fall 2009 applicants! [#permalink]

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08 Oct 2008, 11:49
My cab ride was $42! Close and less hassle! ac8706 wrote: Woo. Booked ticket to NC for the interview. Anyone know roughly how much it costs to take a cab from airport-Fuqua-airport? I'm getting a car rental for around 40 bucks...is that less than the cost of cab? thanks ac. _________________ "George is getting upset!" GMAT Club Premium Membership - big benefits and savings SVP Joined: 04 Dec 2007 Posts: 1689 Schools: Kellogg '11 Followers: 14 Kudos [?]: 198 [0], given: 31 Re: Calling all Duke (Fuqua) Fall 2009 applicants! [#permalink] ### Show Tags 08 Oct 2008, 11:52 Ooh. Was that$42 each way or round trip?
I'm actually flying in on Friday night then: airport-> hotel -> Sat AM to Fuqua -> back to airport. I know the hotel has a free shuttle to Fuqua so that should help lower the cost....

cheers,
ac.

raabenb wrote:
My cab ride was $42! Close and less hassle! ac8706 wrote: Woo. Booked ticket to NC for the interview. Anyone know roughly how much it costs to take a cab from airport-Fuqua-airport? I'm getting a car rental for around 40 bucks...is that less than the cost of cab? thanks ac. Director Joined: 16 May 2008 Posts: 885 Location: Earth Schools: Cornell '11 Followers: 8 Kudos [?]: 140 [0], given: 29 Re: Calling all Duke (Fuqua) Fall 2009 applicants! [#permalink] ### Show Tags 08 Oct 2008, 11:57$42 from airport to Fuqua, \$46 from Fuqua to the airport.
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Re: Calling all Duke (Fuqua) Fall 2009 applicants!   [#permalink] 08 Oct 2008, 11:57

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· Current postion: Home >> Academic Activities >> e-Forum on HENPIC >> Content
 HENPIC seminars in 2016. Thursday, Dec 08, 2016, 10:30 AM (Beijing time)  seminar The 55th HENPIC Seminar: New quantum effects in relativistic magnetohydrodynamics: topology, instability and self-similarity         Speaker：  Yi Yin (尹伊),MIT Date：Thursday, Dec 08, 2016, 10:30 AM (Beijing time) Download：http://pan.baidu.com/s/1geognuz (after Dec 04) abstract: Abstract:Chiral anomaly induces a family of macroscopic quantum behaviors in chiral medium, including the chiral magnetic effect. The application of these effects covers systems of enormous varieties and scales, ranging from the structure of primordial magnetic field in the early universe to charged particle correlation in heavy-ion collisions and negative magnetoresistivity in the newly discovered Weyl semimetal. In this talk, I will present three closely related aspects of new quantum effects present in fluids that contain chiral fermions: topology, instability and self-similarity. I will demonstrate the magnetic reconnections changing chirality of magnetic flux induces in the fluid a quantized electric current, a new kind of the \"chiral magnetic effect\". I further show self-similar inverse cascade driven by the  chiral magnetic current. Finally, I report a new type of instability in a magnetohydrodynamics due to anomaly.Refs.[1]Phys. Rev. Lett. 117 (2016) 152002, arXiv:1607.01513[2]Phys. Rev. Lett. 117 (2016) 172301,  arXiv:1606.09611[3]Phys. Rev. D 92 (2015), 125031, arXiv:1509.07790 Thursday, Nov. 10th, 2016, 10:30 AM (Beijing time)  seminar The 54th HENPIC Seminar: Overpopulated Glasma: Five Years After         Speaker：  Jinfeng Liao (廖劲锋),Indiana University Date：Thursday, Nov. 10th, 2016, 10:30 AM (Beijing time) Download：http://pan.baidu.com/s/1geognuz abstract: The approach toward equilibrium from the initial state in a heavy ion collision, has been a most challenging problem in heavy ion phenomenology, often referred to as the so-called “thermalization puzzle”. The tension lies particularly in that “rapid thermalization” requires strong scatterings while the matter at very early stage (characterized by the semi-hard saturation scale Qs) should be more or less weakly coupled. The key to reconcile such tension, as suggested in a paper (arXiv:1107.5296) five years ago, is that the matter formed shortly after the collision (as often referred to as the glasma) is a very dense, and in fact highly overpopulated system of gluons. The high overpopulation means the gluon occupation number is parametrically much larger than a system in thermal equilibrium with the same energy density. A number of key features of such overpopulated glasma outlined there has since been extensively studied, including: the emergence of a strongly interacting fluid even though with small elementary coupling constant, the approach toward hydrodynamic stage with finite longitudinal/transverse anisotropy, the rapid infrared local thermalization as well as the novel idea of a possible Bose-Einstein condensation . We review those conceptual ideas and highlight subsequent developments in recent years. [Refs]: arXiv:1107.5296; arXiv:1303.7214; arXiv:1305.2119;  arXiv:1503.07260; arXiv:1503.07263; arXiv:1609.02580. Thursday, Oct. 13rd, 2016, 10:30 AM (Beijing time)  seminar The 53rd HENPIC Seminar: Medium Induced Transverse Momentum Broadening in Hard Processes         Speaker：  Bin Wu (吴斌),Ohio State University Date：Thursday, Oct. 13rd, 2016, 10:30 AM (Beijing time) Download：http://pan.baidu.com/s/1geognuz abstract: In this talk I shall start with the double logarithmic correction to the transverse momentum broadening of high-energy parton in QCD matter. Such a double logarithmic term, averaged over the path length of the partons, can be taken as the radiative correction to the jet quenching parameter $\\hat{q}$ and contributes to radiative energy loss. Then, I shall talk about our recent work on deep inelastic scattering on a large nucleus. We find that one can factorize such a medium-induced double log and the vacuum radiation contribution, Sudakov double logs. Our derivations can be generalized  to  other  hard   processes, such  as  dijet  productions,  which  can  be  used  as  a   probe  to measure  the  medium p_T-broadening  effects  in  heavy-ion   collisions  when  Sudakov  effects  are  not overwhelming. Thursday, Sept. 08, 2016, 10:30AM (Beijing time)  seminar The 52nd HENPIC Seminar: Experimental study of chiral and matter-antimatter symmetries at RHIC         Speaker：  Aihong Tang,BNL, USA Date：Thursday, Sept. 08, 2016, 10:30AM (Beijing time) Download：http://pan.baidu.com/s/1geognuz abstract: Symmetries and the physics laws that they dictate are fundamental in describing the physical world. In this talk I discuss two fundamental symmetries that are well suited to be studied at RHIC, namely, the chiral symmetry and the matter-antimatter symmetry. Under the hot and dense condition at RHIC, quarks and gluons are set free from protons and neutrons, making it feasible for the chiral symmetry to be restored. A restored chiral symmetry is a necessary requirement for the Chiral Magnetic Wave (CMW), a novel QCD phenomena, to propagate. The CMW has experimental consequences - it leads to the separation of elliptic flow between charged pions, which will be discussed in this talk. On the other hand, the abundantly produced antimatter at RHIC offers a unique opportunity to study the matter-antimatter symmetry. In particular the nuclear force between two antinucleons has not been measured previously, although the corresponding force for nucleons or nuclei has been well studied for decades. In this talk I will discuss the measurement of the nuclear force between two antiprotons and compare to that between protons. As direct information on the interaction between two antiprotons, one of the simplest systems of antinucleons, this result provides an elemental ingredient for understanding the structure of more complex antinuclear and their properties. Thursday, August 11, 2016, 10:30 AM (Beijing time)  seminar The 51st HENPIC Seminar: Quarks, mesons, and the inverse magnetic catalysis in strong magnetic fields         Speaker：  Toru Kojo,CCNU Date：Thursday, August 11, 2016, 10:30 AM (Beijing time) Download：http://pan.baidu.com/s/1geognuz abstract: Recently numerical lattice QCD calculations in strong magnetic fields, |eB| >> Lambda_QCD^2, offer ample results which contradict with naive model calculations, posing theoretical challenges. I will discuss the following theoretical problems: the inverse magnetic catalysis, the B-dependence of chiral condensates, quark mass gap, meson spectra and wavefunctions, and the quark back-reaction on the gluon dynamics. I will discuss how to understand all these issues consistently, and also explain why the lattice results differ from typical model predictions. Thursday, July 21st, 2016, 10:30 AM (Beijing time)  seminar Experimental Search for Chiral Magnetic/Vortical Effects in Heavy-ion Collisions         Speaker：  Gang Wang (王刚),UCLA Date：Thursday, July 21st, 2016, 10:30 AM (Beijing time) Download：http://pan.baidu.com/s/1geognuz abstract: In ultra-relativistic heavy-ion collisions, the produced quark-gluon plasma facilitates the study of microscopic domains that bear interesting physics mechanisms, such as the chiral magnetic effect and the chiral magnetic wave. These mechanisms are theoretically conditioned on the chiral symmetry restoration and a strong magnetic field (both experimentally feasible), and have been investigated with experimental observables. In this talk, we will review the techniques to study this subject at RHIC and the LHC and discuss the evidence observed so far for the chiral magnetic/vortical effects. An outlook for further isobaric collisions will also be presented. Thursday, June 23rd, 2016, 10:30 AM (Beijing time)  seminar 49th HENPIC Seminar: Critical fluctuations near the QCD critical point         Speaker：  Jiang Lijia (姜丽佳),Peking University Date：Thursday, June 23rd, 2016, 10:30 AM (Beijing time) Download：http://pan.baidu.com/s/1geognuz abstract: Recently, the STAR collaboration has measured the energy dependent moments of net-proton multiplicity distributions in Au+Au collisions. The most exciting result is the large deviation of undefinedamp;#954;undefinedamp;#963;^2 from the unity at collision energy below 39 GeV within 0.4 < pT < 2 GeV/c. In this report, we first introduce a freeze-out scheme for the dynamical models near the QCD critical point through coupling the decoupled classical particles with the order parameter field. We calculate the correlated fluctuations of net protons on the hydrodynamic freeze-out surface. A comparison with the STAR data shows that our model calculations could roughly reproduce energy dependent cumulant C4 and undefinedamp;#954;undefinedamp;#963;^2 of net protons through tuning the related parameters. But the calculated C2 and C3 are always above the experimental data due to the positive contributions from the static critical fluctuations. In the later part of this talk,  We will further discuss the dynamical evolution of sigma field? cumulants based on Langevin dynamics. Our calculation of cumulants show the critical slowing down and memory effects near the critical point, which could solve the issue of static critical fluctuations on the sign problem of C3. Thursday, May 12th, 2016, 10:30 AM (Beijing time)  seminar The 48th HENPIC Seminar: Exploring the QCD phase diagram for a signature of the critical point         Speaker：  Jian Deng( 邓建),Shandong University Date：Thursday, May 12th, 2016, 10:30 AM (Beijing time) Download：http://pan.baidu.com/s/1geognuz abstract: Heavy ion collision experiments search for a critical point in the phase diagram of nuclear matter by measuring non-Gaussian moments of baryon number. Universality of critical phenomena predicts that non-Gaussian moments are enhanced near a critical point. We show that universality near a critical point implies a characteristic relation between higher order baryon susceptibilities. Including the individual enhancements of these susceptibilities near a critical point, the relation between them may be a consistent set of observations supporting the interpretation of baryon fluctuations data as arising from criticality. Thursday, Apr. 14th, 2016, 10:30 AM (Beijing time)  seminar The 47th HENPIC Seminar: Nonperturbative Computation of Open Heavy Flavor in Relativistic Heavy Ion Collisions         Speaker：  Min He(何敏),Nanjing University of Sci. undefinedamp; Tech. Date：Thursday, Apr. 14th, 2016, 10:30 AM (Beijing time) Download：http://pan.baidu.com/s/1geognuz abstract: We evaluate open heavy-flavor (HF) transport in relativistic heavy-ioncollisions by combining a strong-coupling treatment in both macro- andmicroscopic dynamics of the reaction (hydrodynamics andnon-perturbative HF interactions). The hydrodynamic evolution isquantitatively constrained by bulk-hadron spectra and elliptic flow.In the Quark-Gluon Plasma (QGP) phase, heavy-quark diffusioncoefficients are taken from a non-perturbative $T$-matrix calculationof heavy-light quark and heavy quark-gluon scattering. Theseinteractions lead to resonance formation close to Tc which isimplemented as a hadronization (recombination) mechanism on ahydrodynamic hypersurface. In the hadronic phase, the diffusion of HFmesons is treated with effective hadronic theory. We present acomprehensive study of open HF observables at RHIC and the LHC. Afair description of current experimental data on $D$, $D_s$, $B$mesons and HF electrons emerges from our nonperturbative approach, forboth the nuclear modification factor and elliptic flow. Somediscrepancies remain at high pt, indicative of radiative energy lossthat is to be included in our approach. Preliminary results fordielectrons from correlated $D$$D\\bar$ decay will also be reported. Thursday, Mar. 10th, 2016, 10:30 AM (Beijing time)  seminar The 46th HENPIC Seminar: Heavy flavor production in relativistic heavy ion collisions and Properties of sQGP medium         Speaker：  Dr. Xin Dong(董昕),LBNL Date：Thursday, Mar. 10th, 2016, 10:30 AM (Beijing time) Download：http://pan.baidu.com/s/1geognuz abstract: Heavy flavors are expected to offer unique sensitivity to study properties of the sQGP medium. I will review recent experimental achievements in heavy flavor measurements at RHIC and LHC. I will discuss what we have learned from these measurements on the interaction mechanisms between heavy flavor quarks and the sQGP medium as well as the medium transport properties. In the end, I will discuss future plans on heavy flavor programs at both RHIC and LHC. Thursday, Jan. 14th, 2016, 10:30 AM (Beijing time)  seminar The 45th HENPIC Seminar: Chiral symmetry restoration and chiral rotation in the presence of external electric field         Speaker：  Dr. Gaoqing Cao (曹高清),Fudan University Date：Thursday, Jan. 14th, 2016, 10:30 AM (Beijing time) Download：http://pan.baidu.com/s/1sjK6iN7 abstract: We systematically studied the chiral symmetry breaking and restoration in the presence of a pure electric field in the Nambu?ona-Lasinio (NJL) model at finite temperature and baryon chemical potential. In addition, we also studied the effect of the chiral phase transition on the charged pair production due to the Schwinger mechanism. The inverse catalysis effect of the electric field to chiral symmetry breaking is recovered. And the Goldstone mode is find to disperse anisotropically such that the transverse velocity is always smaller than the longitudinal one, especially at nonzero temperature and baryon chemical potential. As expected, the quark-pair production rate is greatly enhanced by the chiral symmetry restoration.   Furthermore, we studied the QCD vacuum structure under the influence of an electromagnetic field with a nonzero second Lorentz invariant I_2=Eundefinedamp;#8901;B at zero temperature. We will show that the presence of I_2 can induce neutral pion (undefinedamp;#960;_0) condensation in the QCD vacuum through the electromagnetic triangle anomaly. Within the frameworks of chiral perturbation theory at leading small-momenta expansion as well as the Nambu?Jona-Lasinio model at leading 1/N_c expansion, we quantify the dependence of the undefinedamp;#960;_0 condensate I_2. Previous：The 56th HENPIC Seminar: Recent $J/\\psi$ measurments from STAR experiment Next：HENPIC seminars in 2015.

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text:
HomeEnglishClass 12MathsChapterCoordinate Sysyem

O P Q R is a square and M ,N a...

# O P Q R is a square and M ,N are the middle points of the sides P Qa n dQ R , respectively. Then the ratio of the area of the square to that of triangle O M N is 4:1 (b) 2:1 (c) 8:3 (d) 7:3

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Text Solution

4:1 2:1 8:3 7:3

Let the coordinates of vertices O,P,Q,R be (0,0),(a,0)(a,a),(0,a), resepectively. Then we get the coordiantes of M as (a,a//2) and those of N as (a//2,a). Therefore, the area of DeltaOMA is
 (1)/(2)|{:(0,,0,,1),(a,,a//2,,1),(a//2,,a,,1):}|=(3a^2)/(8)
 The area of the sqaure is a^2. Hence, the required ratio is 8:3.


text:
£199.99 £139.99 for one year of Unlimited learning. Offer ends on 28 February 2023 at 23:59 (UTC). T&Cs apply

Linear algebra and polynomials

In this article we briefly introduce some of NumPy's linear algebra and
polynomial functionality.
© CC-BY-NC-SA 4.0 by CSC - IT Center for Science Ltd.

Linear algebra

NumPy includes linear algebra routines that can be quite handy.

For example, NumPy can calculate matrix and vector products efficiently (dot,
vdot), solve eigenproblems (linalg.eig, linalg.eigvals), solve linear
systems (linalg.solve), and do matrix inversion (linalg.inv).

A = numpy.array(((2, 1), (1, 3)))B = numpy.array(((-2, 4.2), (4.2, 6)))C = numpy.dot(A, B)b = numpy.array((1, 2))print(C)# output:# [[ 0.2 14.4]# [ 10.6 22.2]]print(b)# output: [1 2]# solve C x = bx = numpy.linalg.solve(C, b)print(x)# output: [ 0.04453441 0.06882591]

Normally, NumPy utilises high performance numerical libraries in linear
algebra operations. This means that the performance of NumPy is actually quite
good and not far e.g. from the performance of a pure-C implementations using
the same libraries.

Polynomials

NumPy has also support for polynomials. One can for example do least square
fitting, find the roots of a polynomial, and evaluate a polynomial.

A polynomial f(x) is defined by an 1D array of coefficients (p) with
length N, such that (f(x) = p[0] x^{N-1} + p[1] x^{N-2} + … + p[N-1]).

# f(x) = x^2 + random noise (between 0,1)x = numpy.linspace(-4, 4, 7)f = x**2 + numpy.random.random(x.shape)p = numpy.polyfit(x, f, 2)print(p)# output: [ 0.96869003 -0.01157275 0.69352514]# f(x) = p[0] * x^2 + p[1] * x + p[2]
© CC-BY-NC-SA 4.0 by CSC - IT Center for Science Ltd.


text:
# How to solve this?

1. Sep 10, 2005

### Werg22

Two simple waves but on is a Y function and the other a X function, on do you find the intersecting point?

y=cos(x)
x=cos(y)

cos^-1(x)=cos(x)

2. Sep 10, 2005

### VietDao29

You can use Newton's method to solve this:
$$x_n = \frac{f(x_{n - 1})}{f'(x_{n - 1})}$$
And the solution x is:
$$x = \lim_{n \rightarrow \infty} x_n$$
Newton's method
You can change the equation a bit so it's easier to take the dirivative of the function:
Since the graph of Arccos(x) is the reflection of the graph Cos(x) across the line y = x.
So the intersection of the two graph Arccos(x) and Cos(x) is right on the line y = x. So the equation can be changed to:
$$\cos(x) = x \Leftrightarrow \cos(x) - x = 0$$
Let f(x) = cos(x) - x.
So f'(x) = -sin(x) - 1.
Using the formula, you have:
$$x_n = \frac{\cos (x_{n - 1}) - x_{n - 1}}{-\sin (x_{n - 1}) - 1}$$
Since the two graph cos(x) and x will cut each other at some x lies between 0, and pi. So you just choose $$x_0 \in [0, \ \pi]$$, eg: x_0 = 0.5,...
Viet Dao,

Last edited: Sep 10, 2005


text:
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text:
Dear Uncle Colin,

I have the parametric equations $x = (t+1)^2$ and $y = \frac{1}{2}t^3 + 3$ and the lines $y = 16 - x$ and $x=1$. I need to find the area enclosed by the curve, these two lines and the $x$-axis, but my answer doesn’t agree with the book’s! Can you help?

- Frankly I’m Surprised How Errors Result

Hi, FISHER, and thanks for your message!

Before we begin, let’s sketch the diagram:

There are clearly two bits to integrate: a wiggly bit on the left and a triangle on the right. The triangle is probably easiest to begin with.

The triangle

We need to find the intersection point of the curve and the line, so that $(t+1)^2 = 13 - \frac{1}{2}t^3$.

Doubling and expanding: $2t^2 + 4t + 2 = 26 - t^3$, or $t^3 + 2t^2 + 4t - 24 = 0$.

This factorises as $(t-2)(t^2 + 4t + 12)$, and the only real solution to that is at $t=2$.

That corresponds to the point $(9,7)$; we can immediately see that the triangle has height of 7 and base of 7, and therefore an area of $\frac{49}{2}$.

The wiggle

I can see two reasonable ways to solve this, so let’s try both. The first, and I think easiest, is parametric integration; the second is to make it cartesian and integrate directly.

Parametric

When $x=1$, $t=0$, so we would need to calculate $\int_0^2 y \diff{x}{t} \dt$.

This works out to be $\int_0^2 (t^3 + 6)(t+1) \dt$, or $\int_0^2 t^4 + t^3 + 6t + 6 \dt$.

That’s $\left[ \frac{1}{5}t^5 + \frac{1}{4}t^4 + 3t^2 + 6t\right]_0^2$, which evaluates to $\frac{32}{5} + 4 + 12 + 12$; I get $\frac{172}{5}$.

Cartesian

Alternatively, we can rearrange the first equation to find that $t = x^{\frac{1}{2}}-1$.

In this case, $y = \frac{1}{2} \left( x^{\frac{1}{2}}-1\right)+3$, which we can expand: $y = \frac{1}{2} \left( x^{\frac{3}{2}} - 3x + 3x^{\frac{1}{2}} + 5\right)$, bringing the 3 inside the bracket.

We need $\int_1^9 y \dx$, which is $\frac{1}{2}\left[ \frac{2}{5}x^{\frac{5}{2} } - \frac{3}{2}x^2 + 2x^\frac{3}{2} + 5x\right]_1^9$.

Evaluating this, I get $\frac{1}{2}\left[ \frac{2}{5}\times 242 - \frac{3}{2}\times 80 + 2 \times 26 + 5 \times 8 \right]$.

This gives $\frac{242}{5} - 60 + 26 + 20$, or $\frac{172}{5}$ again. Phew.

Altogether

Finally, we need to add $\frac{172}{5}$ to $\frac{49}{2}$, which gives $\frac{344 + 245}{10} = 58.9$ square units.

Hope that helps!

- Uncle Colin


text:
Now showing items 198-217 of 508

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This is an easy read introduction to multifractals. We start with a thorough study of the Binomial measure from a multifractal point of view, introducing the main multifractal tools. We then continue by showing how to ...
• #### Inverse Measures, the Inversion formula, and Discontinuous Multifractals

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The present paper is part I of a series of three closely related papers in which the inverse measure m' of a given measure m on [0,1] is introduced. In the first case discussed in detail, both these measures are multifractal ...
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In a previous paper the authors introduced the inverse measure Âµâ   of a probability measure Âµ on [0,1]. It was argued that the respective multifractal spectra are linked by the 'inversion formula' ...
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We propose a new method for speckle reduction in synthetic aperture radar (SAR) imagery based on the embedded zerotree image compression algorithm. This new approach to denoising is inspired by the realization that the ...
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Traditional OFDM implementations use conventional Fourier filters for data modulation, via the IFFT operation. Much research suggests wavelet based OFDM provides performance gains, due to superior spectral containment ...
• #### Joint Distributions for Arbitrary Variables

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We compare the methods of Cohen (1971) and of Baraniuk and Jones (see Proc. IEEE ICASSP-93, p.320-323, 1993) for obtaining joint distributions for arbitrary variables. We show that the two methods produce identical results ...
• #### Joint Distributions of Arbitrary Variables Made Easy

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In this paper, we propose a simple framework for studying certain distributions of variables beyond time-frequency and time-scale. When applicable, our results turn the theory of joint distributions of arbitrary variables ...
• #### Joint Distributions of Arbitrary Variables Made Easy

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• #### Joint Distributions of Arbitrary Variables Made Easy

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• #### Joint signaling techniques and spectral optimization for symmetric bit-rate communication over self-NEXT-dominated channels

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We present a framework for maximizing the capacity of symmetric bit-rate communication services dominated by Gaussian crosstalk, in particular, digital subscriber line (DSL) services. We solve for optimal transmit power ...
• #### Joint Signaling Techniques for Crosstalk-Dominated Communication Channels

(1999-12-01)
We present a framework for maximizing the capacity (or bit rate) of symmetric bit rate communication services dominated by crosstalk, in particular digital subscriber line (DSL) services. We assume the DSL channel is a ...
• #### JPEG Compression History Estimation for Color Images

(2006-06-01)
We routinely encounter digital color images that were previously compressed using the Joint Photographic Experts Group (JPEG) standard. En route to the image's current representation, the previous JPEG compression's various ...
• #### JPEG Compression History Estimation for Color Images

(2003-09-01)
We routinely encounter digital color images that were previously JPEG-compressed. We aim to retrieve the various settings - termed JPEG compression history (CH) - employed during previous JPEG operations. This information ...
• #### JPEG Compression History Estimation for Color Images

(2006)
We routinely encounter digital color images that were previously JPEG-compressed. En route to the image's current representation, the previous JPEG compression's various settings—termed its JPEG compression history ...
• #### Lattice Algorithms for Compression Color Space Estimation in JPEG Images

(2001-08-01)
JPEG (Joint Photographic Experts Group) is an international standard to compress and store digital color images [5]. Given a color image that was previously JPEG-compressed in some hidden color space, we aim to estimate ...
• #### Learning minimum volume sets with support vector machines

(2006-09-01)
Given a probability law P on d-dimensional Euclidean space, the minimum volume set (MV-set) with mass beta , 0 < beta < 1, is the set with smallest volume enclosing a probability mass of at least beta. We examine the use ...
• #### Lifting Construction of Non-Linear Wavelet Transforms

(1998-10-01)
This paper analyzes non-linear wavelet transforms using the lifting construction. The lifting construction exploits a spatial-domain, prediction-error interpretation of the wavelet transform and provides a powerful framework ...
• #### A Limitation of the Kernel Method for Joint Distributions of Arbitrary Variables

(1996-02-01)
Recently, Cohen has proposed a construction for joint distributions of arbitrary physical quantities, in direct generalization of joint time-frequency representations. Actually this method encompasses two approaches, one ...


text:
# I What is "making the time integration redundant"?

1. Mar 11, 2016

### Happiness

Last edited: Mar 11, 2016
2. Mar 12, 2016

### haruspex

I don't pretend to know what half of this is about, but it looks to me that (28) can be got from (50) by differentiating wrt time. That certainly avoids the integration.

3. Mar 13, 2016

### vanhees71

4. Mar 13, 2016

### Happiness

I think I figured it out.

$\delta q_j=0$ when $t=t_1$ and $t=t_2$ since the end points are fixed as we vary the trajectory.

That leaves us with $\int_{t_1}^{t_2}\delta L\,dt = -\int_{t_1}^{t_2}Q_j^{NP}\delta q_j\,dt$.

By "making the time integration redundant", we have $\delta L = -Q_j^{NP}\delta q_j$.

Then by expressing $\delta L$ in terms of $\delta q_j$, we obtain (14) and subsequently (28).


text:
Working paper Open Access

# The need for a standard for the mathematical pronunciation of the natural numbers. Suggested principles of design. Implementation for English, German, French, Dutch and Danish

Colignatus, Thomas

### DataCite XML Export

<?xml version='1.0' encoding='utf-8'?>
<identifier identifierType="DOI">10.5281/zenodo.1418480</identifier>
<creators>
<creator>
<creatorName>Colignatus, Thomas</creatorName>
<givenName>Thomas</givenName>
<familyName>Colignatus</familyName>
<nameIdentifier nameIdentifierScheme="ORCID" schemeURI="http://orcid.org/">0000-0002-2724-6647</nameIdentifier>
<affiliation>Samuel van Houten Genootschap</affiliation>
</creator>
</creators>
<titles>
<title>The need for a standard for the mathematical pronunciation of the natural numbers. Suggested principles of design. Implementation for English, German, French, Dutch and Danish</title>
</titles>
<publisher>Zenodo</publisher>
<publicationYear>2018</publicationYear>
<subjects>
<subject>number sense, counting, arithmetic, mathematical ability, invalidity, design, standards, language, pronunciation, metastudy, number processing, numerical development, inversion effects, language-moderated effects, Google Translate, Child, Child Development, Educational Measurement,  Humans, Intelligence, Longitudinal Studies, Mathematics/education, Mathematics/methods, Mental Processes, Students</subject>
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<dates>
<date dateType="Issued">2018-09-14</date>
</dates>
<language>en</language>
<resourceType resourceTypeGeneral="Text">Working paper</resourceType>
<alternateIdentifiers>
<alternateIdentifier alternateIdentifierType="url">https://zenodo.org/record/1418480</alternateIdentifier>
</alternateIdentifiers>
<relatedIdentifiers>
<relatedIdentifier relatedIdentifierType="DOI" relationType="References">10.5281/zenodo.291979</relatedIdentifier>
<relatedIdentifier relatedIdentifierType="DOI" relationType="IsReferencedBy">10.5281/zenodo.1244063</relatedIdentifier>
<relatedIdentifier relatedIdentifierType="DOI" relationType="References">10.5281/zenodo.1244008</relatedIdentifier>
<relatedIdentifier relatedIdentifierType="DOI" relationType="IsVersionOf">10.5281/zenodo.774866</relatedIdentifier>
<relatedIdentifier relatedIdentifierType="URL" relationType="IsPartOf">https://zenodo.org/communities/re-engineering-math-ed</relatedIdentifier>
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<version>2.5</version>
<rightsList>
<rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
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<descriptions>
<description descriptionType="Abstract">
Current English for 14 is fourteen but mathematically it is ten &amp; four. Research on number sense, counting, arithmetic and the predictive value for later mathematical abilities tends to be methodologically invalid when it doesn&#39;t measure true number sense that can develop when the numbers are pronounced in mathematical proper fashion. Researchers can correct by including proper names in the research design, but this involves some choices, and when each research design adopts a different scheme, also differently across languages, then results become incomparable. A standard would be useful, both ISO for general principles and national implementations. Research may not have the time to wait for such (inter ) national consensus. This article suggests principles of design and implementations for said languages. This can support the awareness about the need for a process towards ISO and national consensus, and in the mean time provides a baseline for research.
</description>
<description descriptionType="Other">(a) May 14 2018: The update is to use "&" as the connective of the place value positions. Thus also for higher positions as e.g. 657 = six·hundred & five·ten & seven. The ampersand better is 1 fontsize smaller than the other text. See the developed software and http://thomascool.eu/Papers/NiceNumbers/Index.html  (b) June 28 2018: This research finds support at https://zwanzigeins.jetzt (c) August 20 2018: Better expression of the distinction between simplified 11 = ten & one for everyday use and non-simplified 11 = one.ten & one.one for clarification of the place value system. (d) September 14 2018: The hyphen is used for common expressions like twenty-one.</description>
</descriptions>
</resource>

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text:
# Supervised Learning

## In words...

In supervised learning, the computer is first given a training set of labeled data, i.e., of pairs of input patterns and corresponding labels. Then, the goal is to generalize, i.e., predict the correct label of previsouly unseen patterns. To achieve this goal, the computer applies a learning algorithm on the training set to obtain a predictive model. An expected behavior of these learning algorithms is that the larger the training set is, the better the predictive model should be.

In the sentence above, "better" needs to be defined. In supervised learning, the quality of a model is measured in terms of the risk, also known as the generalization error.

The theory that allows us to study learning machines is known as statistical learning theory and formalizes the subject in probabilistic terms. The introduction of a probabilstic framework is rather natural given that we want to make statements about a problem dealing with "previously unseen" (and thus unknown) objects.
The first step of this formalization is to consider a data pair (a pattern with its label) as a realization of a pair of random variables with a joint probability distribution (a random pair). Then, the following assumptions are usually made.

• The process generating the data pairs does not evolve: all data pairs (the ones available for training as well as the unseen ones) are identically distributed.
• All data pairs are drawn at random without influence from the previously observed data: all data pairs are independent.
• The probability distribution of the data pairs is unknown. If it was known, then we would have access to all the required information to compute the best predictions and there would be nothing left to learn.
• We have access to a sample of data pairs: the training sample is the only information available for learning.
This framework can be studied either in the deterministic or stochastic case.

There is also an additional assumption rarely explicited but always needed: the smoothness assumption stating that the label of a pattern very close to another cannot behave very differently compared with the label of the other pattern.

Given that the probability distribution of the data is unknown, the risk of a model cannot be computed and thus we cannot select the best model with minimal risk: the model must be learned from data only.

Learning the data by heart is a very easy task for a computer. But with respect to the goal that is to generalize, learning by heart is a bad idea. As a simple illustration, consider you take a course and learn by heart the solutions to all exercises given in that course, but without understanding the course itself. Then it is most likely that you would fail the exam, for which you would have to generalize what you learned during the course to solve new problems; and learning by heart does not help you do that.

If learning by heart is not the right way to go, learning a model that outputs correct predictions for the training data remains a well-founded idea, which is behind the Empirical Risk Minimization (ERM) principle at the basis of many learning algorithms.

Two categories of supervised learning problems can be distinguished based on the nature of the labels. If the labels can be any real number, then the problem is a regression one. Alternatively, if the labels can only take a finite number of values, then this is a classification problem.

## In pictures...

### Abstract view of supervised learning

Hover over the elements of the diagram to get additional information.

...

...

...

### Demos

You can also have a look at the drawing recognition demo to play with these effects on your own.

## In maths...

Given a training set of $N$ labeled examples, i.e., of $N$ pairs of input vectors and labels, $$\{ (\g x_1,y_1), \dots, (\g x_N,y_N) \} \in (\X\times \Y)^N,$$ the goal of supervised learning is to estimate a model $f : \X \rightarrow \Y$ that can output the prediction $f(\g x)$ of the label $y$ with minimum error.

In statistical learning theory, this problem is formalized in probabilistic terms as follows.

Let $(X,Y)$ be a random pair (a pair of random variables) taking values in $\X\times \Y$ with fixed but unknown joint probability distribution $P_{X,Y}(X,Y)$.
The training sample $$D = \{(X_i,Y_i)\}_{i=1}^N$$ is a sample of $N$ independent and identically distributed copies of $(X,Y)$.
Given a realization of $D$, called the training set, the goal is to find the function $f : \X \rightarrow \Y$ that minimizes the expected error, called the risk.

Given that $P_{X,Y}(X,Y)$ is unknown, the risk cannot be computed nor minimized and we have to find a surrogate pinciple to learn $f$. The most straightforward of such principles is the Empirical Risk Minimization (ERM) principle, at the basis of many learning algorithms. Another popular principle is the maximum likelihood inference principle.