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# Real Curves, Open Strings, and A-infinity Algebras
Kevin Costello gave a talk last week in one of Peter Teichner’s many seminars, explaining $A_\infty$-algebras with a view towards his papers on topological string theory. It was the sort of talk that might have interested a lot of people, so (with Kevin’s permission), I’m posting my .pdf scanned notes here. I’ve added some physics interpretation that Kevin didn’t make explicit.
Defining $A_\infty$-algebras
Kevin also gave a shorter talk (in a different Teichner seminar) about his characterization of the homotopy type of a moduli space of genus zero open string worldsheets. My notes here are less detailed, but maybe someone will enjoy them.
The Homotopy Type of a Certain Moduli Space of Open String Worldsheets
## 5 thoughts on “Real Curves, Open Strings, and A-infinity Algebras”
1. David Ben-Zvi says:
Thanks for the notes AJ!
For people seeking more Costellian inspiration (which I usually am), check out the recent streaming video of his lecture “Topology in two dimensions and Frobenius algebras” at
http://www.math.utexas.edu/~benzvi/GRASP.html
and notes from five other related talks (on topological field
theory, renormalization in the BV formalism, rational homotopy theory etc) at
http://www.math.utexas.edu/~benzvi/notes.html
2. jim stasheff says:
The requested URL was not found on this server. The link on the referring page seems to be wrong or outdated. Please inform the author of that page about the error.
Error 404
math.berkeley.edu
Sun Sep 30 18:18:17 2007
Apache/2.0.61 (FreeBSD) PHP/4.4.7 with Suhosin-Patch mod_fastcgi/2.4.2 DAV/2 mod_ssl/2.0.61 OpenSSL/0.9.7e-p1
3. A.J. Tolland says:
I think this must have been a problem with the http server. I’m currently able to download the notes from home.
I did change the location of the notes about a week ago, so if you had an outdated link saved, that could explain the problem. But clicking on the link should work.
Anyways, please let me know if the problem continues.
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## Find wavelength of a quantum of electromagnetic radiation
1. The problem statement, all variables and given/known data
A quantum of electromagnetic radiation has
an energy of 0.877 keV.
What is its wavelength? The speed of light
is 2.99792 × 10
8 m/s, and Planck’s constant
is 6.62607 × 10−34J · s.
2. Relevant equations
E=hf
v=fλ
... λ=v/(E/h)
3. The attempt at a solution
When i solved, i got 1.413728e-9 nm... I have checked my units. can some just help and point me in the right direction
PhysOrg.com science news on PhysOrg.com >> City-life changes blackbird personalities, study shows>> Origins of 'The Hoff' crab revealed (w/ Video)>> Older males make better fathers: Mature male beetles work harder, care less about female infidelity
v is usually written as c when one speaks of the speed of light in vacuum. Also, the double fraction reduces to: $$\frac{c}{\frac{E}{h}} = \frac{h \, c}{E}$$ For this answer, you need to know the conversion factor between an electron-volt (eV) and a joule as energy units. Do you know it?
Quote by Dickfore v is usually written as c when one speaks of the speed of light in vacuum. Also, the double fraction reduces to: $$\frac{c}{\frac{E}{h}} = \frac{h \, c}{E}$$ For this answer, you need to know the conversion factor between an electron-volt (eV) and a joule as energy units. Do you know it?
Yes i did convert it but i still got it wrong
## Find wavelength of a quantum of electromagnetic radiation
how did you convert it, and what did you get?
I did it again and i got 1.414E-8 ... and i think that is in meters. Am i right?? so that means that the answer is14.14nm _______________________________________________________________________ _ I used plancks constant in eV's. Its on the ap equation sheet
I didn't get that. What did you get for the energy in joules?
1.405109518e-16 J
This is correct. Now: $$\frac{h \, c}{E} = \frac{6.626 \times 10^{-34} \, \mathrm{J} \cdot \mathrm{s} \times 2.998 \times 10^8 \, \mathrm{m} \cdot \mathrm{s}^{-1}}{1.4051 \times 10^{-16} \, \mathrm{J}}$$ The product and ratio of the mantissas, gives: $$\frac{6.626 \times 2.998}{1.4051} = 14.14$$ The exponents sum up to $-34 + 8 - (-16) = -10$. You may read off the units from the above fraction fairly easily. What should the answer be in scientific form?
so in nm, it would be 1.414
yes, except that you need to use as many significant figures, as there are in variable with the least number of significant figures given in the problem. Fundamental constants are usually known to a lot of significant figures.
Thank You
Similar discussions for: Find wavelength of a quantum of electromagnetic radiation Thread Forum Replies Classical Physics 2 Cosmology 4 Classical Physics 17 General Physics 4 Chemistry 2
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Volume 358 - 36th International Cosmic Ray Conference (ICRC2019) - CRI - Cosmic Ray Indirect
Search for diffuse γ -ray emission from galactic plane with YangBaJing Hybrid Array
Y. Yao,* J. He, Y. Guo, Y. Zhang, C. Liu, T. Chen, H. Hu
*corresponding author
Full text: pdf
Pre-published on: 2019 July 22
Published on:
Abstract
As one of the pilot experiments of LHAASO, a hybrid array (HA) covering an area of ${20000 m^{2}}$ was successfully constructed by the end of ${2016}$ at the international Cosmic Ray Observatory at YangBajing (YBJ) in Tibet of China. This array consists of 115 scintillation detectors and 16 underground muon detectors of ${900 m^{2}}$. Using muons information, most of hadronic air showers are rejected at several dozens of TeV energy regime. With the data collected from ${2017}$ to ${2018}$, this work presents preliminary results on diffuse $\gamma$-ray emission from galactic plane. As a result, there has no significant excess of TeV $\gamma$-ray in the galactic plane with the YBJ-HA observation. Therefore, we put a 90% CL upper limit. We foresee that the under-construction LHAASO will have great potential in observing $\gamma$-rays in several dozens of even up to hundreds of TeV energy range.
Open Access
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# From Pauli spinors to Dirac spinors
• I
Hey guys,
Hope all is well. I am trying to understand the process that takes us from the Pauli equation to the Dirac equation. Whilst I understand the motivation is to have a lorrentz covariant equation I don't really understand A.) how this was done B.) what the physical result is of the new covariant equation, what new info are we getting?.
Lorrentz covariance is a fairly new concept to me so just trying to get a proper sense of what it physically means. Any and all enlightenent is much appreciated :) cheers
Related Quantum Physics News on Phys.org
PeterDonis
Mentor
2019 Award
I am trying to understand the process that takes us from the Pauli equation to the Dirac equation.
Can you give any references that you have already looked at? In particular, what presentations of this process have you already looked at?
Thus far I have been reading some paper's by David Hestenes, http://geocalc.clas.asu.edu/html/GAinQM.html , I have been writing my undergrad thesis on Pauli spinors in Geometric Algebra but it has been suggested that I should expand my project to talk about relativistic quantum mechanics as well. Any suggested reading would be great, I've just picked up Griffths Introduction to Elementary Particles in the hope it can shed some light for me. I do want to understand the general process of making an equation lorrentz covariant.
PeterDonis
Mentor
2019 Award
I have been reading some paper's by David Hestenes
Hestenes' approach is quite a bit different from the standard approach. Griffiths will give you something more like the standard approach.
Btw, we recently had an interview with Hestenes on PF; see here (this is the comment thread on the interview, a link to the interview itself is also there):
I do want to understand the general process of making an equation lorrentz covariant.
This is too broad a topic for a PF thread. But the reason we do it is simple: because experiments have shown us that our universe is relativistic, so any theory that claims to be fundamental should be Lorentz covariant. Any theory that is not must be an approximation only, and if we can find a Lorentz covariant version of the same theory, that version should be more fundamental.
Yeah It is a little daunting to try to get my head around both approaches, but i'm finding Griffiths very useful and am quite well versed in Gometric Algebra so hopefully I can make the connection.
Yeah sorry, I realise it was quite a general query, but your answer was actually pretty much what I was looking for. Thanks for the help :)
stevendaryl
Staff Emeritus
I wouldn't say that there is a derivation of the Dirac equation starting with the Pauli equation. But the trick that makes the Pauli equation work can be used as a heuristic for developing a relativistic version that is equivalent to the Dirac equation.
Start with the nonrelativistic formula relating energy and momentum for a particle:
$\frac{p^2}{2m} = E$
This is for a free particle, but to get a particle in an electromagnetic field, you can do the substitutions:
$\vec{p} \Rightarrow \vec{p} - e \vec{A}$
$E \Rightarrow E - e \Phi$
where $\vec{A}$ is the electromagnetic vector potential, and $\Phi$ is the scalar potential, and $e$ is the particle's charge.
To get the Schrodinger equation, you do the following:
1. Replace $\vec{p}$ by the operator $-i \vec{\nabla}$ (I'm using units where $\hbar = c = 1$)
2. Replace $E$ by the operator $i \frac{d}{dt}$
3. Interpret the operator equation as applying to a scalar wave function $\psi(\vec{r}, t)$.
To get the Pauli equation, you do a twist on the above:
1. Instead of 1 above, you replace the $\vec{p}$ by the operator $\vec{p} \cdot \vec{\sigma}$, where $\vec{\sigma}$ is the three Pauli spin matrices.
2. Instead of 3 above, you interpret the operator equation as applying to a two component spinor $U(\vec{r}, t)$.
The use of the spin matrices makes no difference for free particles, since $(\vec{p} \cdot \vec{\sigma})^2 = (\vec{p})^2$. But once you introduce the electromagnetic field, this makes a difference, because you get an extra term, $-e \vec{B} \cdot \vec{\sigma}$ where $\vec{B} = \vec{\nabla} \times \vec{A}$
Now, we can do the same thing to almost get the Dirac equation for the relativistic case.
Instead of starting with the equation:
$\frac{(\vec{p})^2}{2m} = E$
$E^2 - \vec{p}^2 = m^2$
Now introduce the substitution: $\vec{p} \Rightarrow \vec{p} \cdot \vec{\sigma}$ to get:
$E^2 - (\vec{p} \cdot \vec{\sigma})^2 = m^2$
Here comes an unmotivated step: Write the above in a "factored" form.
$(E - \vec{p} \cdot \vec{\sigma})(E + \vec{p} \cdot \vec{\sigma}) = m^2$
Factoring it this way makes no difference for free particles, but will make a difference when you introduce the electromagnetic field. Of course, this is interpreted as applied to a two-component spinor, $U$. But here's the huge benefit of factoring:
Let's define a new two-component spinor, $V$ via the equation:
$V = \frac{1}{m} (E + \vec{p} \cdot \vec{\sigma}) U$
Then the second-order factored equation can be written as a pair of coupled first-order equations:
$(E - \vec{p} \cdot \vec{\sigma}) V = m U$
$(E + \vec{p} \cdot \vec{\sigma}) U = m V$
These two equations can be written as a 4-component matrix equation:
$(\gamma^0 E - \vec{\gamma} \cdot \vec{p}) \Psi = m \Psi$
where $\Psi = \left( \begin{array}\\ U \\ V \end{array} \right)$ and where $\gamma^0 = \left( \begin{array}\\ 0 & 1 \\ 1 & 0 \end{array} \right)$ and $\gamma^j = \left( \begin{array}\\ 0 & \sigma_j \\ -\sigma_j & 0 \end{array} \right)$
(All the "1"s and "0"s really mean the 2x2 unit matrix and 2x2 zero matrix, respectively)
That is not the usual choice for $\gamma^0$, but the result is equivalent to the usual covariant form of the Dirac equation.
This was definitely not the way that Dirac came up with his equation. He didn't start with the second-order Pauli equation, but just tried to guess a first-order equation that produced the right energy-momentum relationship.
Demystifier, Milsomonk and PeterDonis
PeterDonis
Mentor
2019 Award
That is not the usual choice for ##\gamma^0##
It is if you're using the Weyl basis instead of the Dirac basis; the Weyl basis is better adapted to particles that are relativistic, i.e., their energy/momentum is much greater than their rest mass. Basically the Weyl basis diagonalizes ##\gamma^5## instead of ##\gamma^0##.
Great post, btw!
Amazing! thanks very much, that deffinately clears up some queries I had from the griffiths book as well. Also if anyone is familiar with the Hestenes approach to the Dirac equation i'd love to here your thought's on it, any advantages or disadvantages to using Geometric Algebra this way? From what I've read about non-relativistic spin in GA it appears to give a bit more clarity of what the imaginary numbers mean but the work required and the results are more or less the same as the traditional approach.
Geometric Algebra definitely promises greater insights into Pauli and Dirac equations than traditional vector algebra because of the intrinsic geometric interpretations allowed by Clifford algebra.
The drawback I find with Hestenes' approach is that he introduces more than the required number of dimensions by using C1,3(R) to represent space-time (space-time algebra, or STA). On the other hand, Baylis offers a simpler approach by using C3 (algebra of physical Space, or APS). With APS, real three-dimensional vectors are expressible in terms of Pauli matrices, but the time dimension emerges automatically in the Clifford algebra - and with the correct signature for special relativity! A good introduction can be found at ArXiv:physics/0406158.
Both STA and APS are geometric algebras, but APS seems to be more straightforward. In STA, the 3+1 dimensions of space time and the (+ - - -) metric are posited, while in APS they appear naturally and the relativistic equations (Dirac, Maxwell's, etc.) find an extraordinarily simple expression.
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# Combat
Combat UI
Combat is a game-play mechanic where players fight enemies located within increasingly more difficult zones. A beginner's guide on combat can be found on the wiki page combat guide or on the forum combat guide made by Magnus.
There are 4 skills to level in combat; constitution, attack, strength, and defense.
## Zones
### Locations
#### Solo Combat
Zone Lowest Recommended Combat Levels Lowest Recommended Gear
Farm 1 - 20 None - Bronze
Caves 10 - 30 Bronze - Iron
City 20 - 60 Iron - Adamantite
Deep Pit * 50 - 60 Adamantite - Runite
Living Forest * 50 - 60 Adamantite - Runite
Lava Maze 60 - 80 (Using 1 of Healing, Overhealing, or Corrupted Ring) Adamantite - Runite
Corrupted Lands 70 - 90 (Using 1-2 of Healing, Overhealing, or Corrupted Ring) Runite - Stygian
Valley of Giants 80 - 99 (Using 1-2 of Healing or Overhealing) Runite - Stygian
Zones marked with * are special combat areas
#### Group Combat
Zone Lowest Recommended Combat Levels Lowest Recommended Gear Maximum Amount Of Players
Chaos Wastes 90 - 99 Stygian +5 2
Goblin Village 80 - 99 Obsidian +5/Runite +0 3
Dark Fortress 90 - 99 Runite +5 3
Giant's Keep 99 Stygian +5 5
RISE OF INFO 99 See ROI page 10
### Encounter table
Zones Monster Encounter Rate HP
Farm Chicken 30% 3
Rat 30% 2
Cow 30% 8
Goblin 10% 5
Caves Goblin 45% 5
Imp / Greater Imp 55% 10
City Guard 80% 22
Black Knight 20% 42
Living Forest Spriggan 100% 75
Deep Pit Greater Demon 100% 89
Lava Maze Deadly Red Spider 40% 35
Lesser demon 60% 81
Corrupted Lands Corrupted Tree 45% 95
Infected Naga 45% 100
Bone Giant 10% 125
Valley of Giants Fire Giant 33% 130
Moss Giant 33% 150
Ice Giant 33% 160
Chaos Wastes* Chaos Giant 50% 300
Chaotic Abomination 50% 425
* Chaos Wastes is a combat zone balanced for group combat, allowing a maximum of two players in a party to fight alongside each other. Stats differ for one and two players.
Special combat areas include the Foraging zone Living Forest, and the Mining zone Deep Pit, where you may randomly encounter Spriggans or Greater Demons respectively. Players may not run from these encounters, and failing results in a 15-minute lockout timer before they can access that zone again.
## Combat Experience
Players gain combat skill experience when dealing damage; 2 experience in the selected combat skill and 1 experience in Constitution per damage dealt. When fighting in a balanced stance, each skill gains 2/3 of an experience per point of damage. Fractions of experience are not shown but are kept so a balanced stance does not gain or lose experience through rounding.
## Death
Death occurs when a player's health reaches zero. The preceding action will be cancelled and the player returns to idling.
Health slowly regenerates on its own and can be modified with the Scroll of Healing. Dying will not result in the loss of exp/items/gold etc.
## Skills
Combat skills
Constitution Constitution in addition to the Scroll of Fortitude is the skill that determines a player's maximum hitpoints (HP). The amount of health left can be seen next to the heart icon in the combat page.
Food can restore health inside or outside of battle, and can provide buffs to combat for a short time.
Default auto-eat will only trigger when the missing HP is less than 3/2 the food healing amount. Change auto-eat to percent of HP remaining in settings for high healing food if max HP is too low to trigger the default setting.
Attack Attack determines a player's hit chance, along with the players accuracy bonus.
Strength Strength contributes to your maximum damage per hit, along with the players melee strength bonus.
Defense Defense determines a players dodge chance.
Mastery levels have no effect on combat.
## Stats
There are various stats that can affect combat. These stats are determined by a player's equipment (armor and weapon), although each point in a player's level contributes more to stats than equipment.
### Accuracy
Accuracy is determined from a combination of stats from equipment and attack level which is used to determine hit chance.
The formula for accuracy is ${\displaystyle Accuracy=AttackLevel*(AccuracyBonus+64)}$
Keep in mind that the hit chance is also determined by an enemy's defense toward your attack type.
The only way to deal 0 damage is by missing the target, all accurate hits will deal at least 1 damage. The Demon Skin buff can decrease a damage to 0.
### Strength
Strength from equipment determines the maximum damage you can deal along with strength level. The damage you deal can also be affected by enchantments such as Scroll of Critical Strike, Scroll of Patience, and Scroll of Recklessness. Keep in mind that patience and recklessness adds to both the minimum and maximum damage while strength only adds to the maximum damage.
Max hit can be calculated with the following formula:
${\displaystyle MaxHit={\Biggl \lfloor }1.3+{\frac {StrengthLevel}{10}}+{\frac {StrengthBonus}{80}}+{\frac {StrengthLevel\times StrengthBonus}{640}}{\Biggr \rfloor }}$
Max hit from a hard-hitting monster can only be decreased with the Scroll of Protection and/or the Demon Skin buff.
### Defense
Defense from equipment and bonuses determine the dodge rate along with defense level. Keep in mind that dodge chance is also determined by enemy's attack and your defense to their attack type.
The formula for defense is ${\displaystyle Defense=DefenseLevel*(DefenseBonus+64)}$ where you use the corresponding defense bonus for whatever type of attack you are defending from (ex. Stab).
### Attack Type
There are three attack types (slash, stab, crush) which is determined by the weapon you use (bare hands are considered crush). Attack type determines the type of defense the enemy uses. This can be important since some enemies are weak to one type of attack, making it easier to hit if that type of attack is used. E.g. all giants are weak to crush, making battleaxes effective weapons to use.
### Hit Chance
If Accuracy > Defense:
${\displaystyle HitChance=1-0.5*{\frac {Defense}{Accuracy}}}$
Else:
${\displaystyle HitChance=0.5*{\frac {Accuracy}{Defense}}}$
### Attack Speed
Attack speed is a stat that determines the amount of time between attacks. The attack speed differs with every weapon. Bare fists have an attack speed of 2.4 seconds.
The Scroll of Patience increases damage based on how slow the weapon hits.
## Enchantments
List of useful Enchantments.
Scroll Slot Level Silver Amount Rune Amount Runes Effect per scroll
Scroll of Weakening Helm, Body,
Legs, Weapon,
Shield
4 100 20 Air, Fire, Mind Decreases the level requirements of the item by 5.
Scroll of Healing Shield,
Combat-Amulet
10 200 30 Blood, Nature, Cosmic Passive healing is increased by 0.5 health per minute.
Scroll of Fortitude Shield,
Combat-Amulet
- - - - Increases max health by 4.5.
Scroll of Force Shield 79 900 80 Blood, Death, Chaos Gain 10% of the shield's average melee defense as accuracy. The shield no longer provides any defensive bonuses.
Scroll of Overhealing Weapon 11 200 30 Air, Water, Death Heal for 1% of overkill damage on a target.
Scroll of Accuracy Weapon 28 400 40 Blood, Death, Mind Increase the players accuracy bonus 5%.
Scroll of Critical Strike Weapon 52 600 60 Blood, Death, Chaos, Cosmic Gain a 5% chance on hit to critically strike, dealing 130% damage.
Scroll of Reinforcement Helm, Body,
Legs
13 200 30 Death, Chaos, Mind Reduce the enemy's chance to hit by 5%.
Scroll of Protection Helm, Body,
Legs
31 400 40 Air, Earth, Cosmic Reduces all damage taken by 4%.
Scroll of Recklessness Helm, Body,
Legs
81 1000 80 Blood, Death, Chaos Increases outgoing damage by 1.
Scroll of Patience Body, Legs 82 1000 80 Air, Water, Death Increases the efficiency of slower attacks.
Scroll of the Treasure Hunter Gloves, Boots 85 1000 80 Chaos, Nature, Cosmic Increases your chance of finding items from slain enemies by 3%.
Scroll of Prolonging Gloves, Boots 58 700 60 Nature, Mind Gain 10% more buff stacks from consumables.
Scroll of Enlightenment Gloves, Boots 73 900 70 Air, Water, Chaos, Mind Gain 1 more essence per action where essence is acquired.
### Food Buffs
Image Enchantment Nimble Increases defense for a short time. Each level of Nimble increases defense by around 10%. Eating food with spider legs as an ingredient will grant this buff; a popular recipe is 5 spider legs. Demon Skin Reduces all damage taken in combat by the level of the demon skin. This only affects combat, so if consumed while out of combat there will be no effect. If you stop fighting, the buff disappears. It can be created by cooking food with Ichor; an example is 4 apples and 1 Ichor. Stacks are not consumed if the monster hits a 0.
## Special Combat
### Elite Scroll
Elite Scrolls are found as a combat drop and offers a harder combat challenge for the player when the seal is broken. All combat zones drop a scroll, full info can be found here
### Dungeon
Dungeons are multiplayer instances containing harder versions of the monsters and a boss. A key is required to enter the dungeon with craftable key pieces found in select zones.
### Aberrant Shrimp
Aberrant Shrimp are fought when augmenting a Shrimp Bauble until it breaks. They have 300 HP and drop Shrimp and one of either Shrimp Carapace, Shrimp Greaves, Shrimp Helm, or Shrimp Shell.
### Spriggan
Spriggans are fought when Foraging in the Living Forest. They have 75 HP and drop Branches, Logs, Sageberry Bush Seeds, and Elder Tree Seeds.
### Greater Demon
Greater Demons are fought when mining in the Deep Pit. They have 89 HP and drop Scrolls, Demonic Trial, Ichor, and Gold Ore.
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Last update
# TortoiseSVN IPV6
## 1.10.1.28295
This package was approved by moderator gep13 on 8/23/2018.
TortoiseSVN is a really easy to use Revision control / version control /
source control software for Windows. It is based on
Apache™ Subversion (SVN)®.
TortoiseSVN is implemented as a Windows shell extension. It's intuitive and
easy to use, since it doesn't require the Subversion command line client to run
and provides revision information graphically with overlay icons. TortoiseSVN is
free to use, even in a commercial environment.
This is the IPV6 version which is needed when working with Microsoft
DirectAccess.
## Features
• Easy to use
• all commands are available directly from the Windows Explorer.
• only commands that make sense for the selected file/folder are shown. You won't see any commands that you can't use in your situation.
• See the status of your files directly in the Windows explorer
• descriptive dialogs, constantly improved due to user feedback
• allows moving files by right-dragging them in the Windows explorer
• All Subversion protocols are supported
• http://
• https://
• svn://
• svn+ssh://
• file:///
• svn+XXX://
• Powerful commit dialog
• integrated spell checker for log messages
• auto completion of paths and keywords of the modified files
• text formatting with special chars
• The big picture
• Can create a graph of all revisions/commits. You can then easily see where you created a tag/branch or modified a file/folder
• Graphs of commit statistics of the project
• Easy comparing of two branches or tags
• Per project settings
• minimum log message length to avoid accidentally committing with an empty log message
• language to use for the spell checker
• Integration with issue tracking systems
TortoiseSVN provides a flexible mechanism to integrate any web based bug tracking system.
• A separate input box to enter the issue number assigned to the commit, or coloring of the issue number directly in the log message itself
• When showing all log messages, an extra column is added with the issue number. You can immediately see to which issue the commit belongs to.
• Issue numbers are converted into links which open the webbrowser directly on the corresponding issue
• Optional warning if a commit isn't assigned to an issue number
• TortoiseMerge
• Helps resolving conflicts
• TortoiseBlame: to show blames of files. Shows also log messages for each line in a file.
• TortoiseIDiff: to see the changes you made to your image files
• SubWCRev: to include the revision numbers/dates/... into your source files
• Available in many languages
• TortoiseSVN is stable
• Before every release, we create one or more "release candidates" for adventurous people to test first.
• During development cycles, many people test intermediate builds. These are built every night automatically and made available to all our users. This helps finding bugs very early so they won't even get into an official release.
• A big user community helps out with testing each build before we release it.
• A custom crash report tool is included in every TortoiseSVN release which helps us fix the bugs much faster, even if you can't remember exactly what you did to trigger it.
To install TortoiseSVN IPV6, run the following command from the command line or from PowerShell:
C:\> choco install tortoisesvn-ipv6
To upgrade TortoiseSVN IPV6, run the following command from the command line or from PowerShell:
C:\> choco upgrade tortoisesvn-ipv6
### Files
Hide
• tools\chocolateyInstall.ps1 Show
$ErrorActionPreference = 'Stop'; # stop on all errors$toolsDir = "$(Split-Path -parent$MyInvocation.MyCommand.Definition)"
$url = 'https://osdn.net/projects/tortoisesvn/storage/1.10.1/Application/ipv6/TortoiseSVN-1.10.1.28295-win32-ipv6-svn-1.10.2.msi'$url64 = 'https://osdn.net/projects/tortoisesvn/storage/1.10.1/Application/ipv6/TortoiseSVN-1.10.1.28295-x64-ipv6-svn-1.10.2.msi'
$packageArgs = @{ packageName =$env:ChocolateyPackageName
unzipLocation = $toolsDir fileType = 'msi' url =$url
url64bit = $url64 softwareName = 'tortoisesvn-ipv6*' # e.g. checksum -t sha256 -f path\to\file checksum = '7BDDED22E5F20EA6F37356FF613EB05B1F0FDF82F11B9B449E62B4F3151A6198' checksumType = 'sha256' checksum64 = '19F4DDCDB679B5061DC4F6501717FEFF1578B3A0CD000DF7A99B8794EE46E436' checksumType64= 'sha256' # MSI silentArgs = "/quiet /norestart ADDLOCAL=ALL /log "$($env:TEMP)\$($packageName).$(\$PackageVersion).MsiInstall.log""
validExitCodes= @(0,3010)
}
Install-ChocolateyPackage @packageArgs # https://chocolatey.org/docs/helpers-install-chocolatey-package
### Virus Scan Results
In cases where actual malware is found, the packages are subject to removal. Software sometimes has false positives. Moderators do not necessarily validate the safety of the underlying software, only that a package retrieves software from the official distribution point and/or validate embedded software against official distribution point (where distribution rights allow redistribution).
Chocolatey Pro provides runtime protection from possible malware.
### Dependencies
This package has no dependencies.
### Software Author(s)
• TortoiseSVN Team
### Release Notes
http://tortoisesvn.net/Changelog.txt
### Version History
TortoiseSVN IPV6 1.10.0.28176 165 Thursday, April 19, 2018 approved
TortoiseSVN IPV6 1.9.7.27907 289 Monday, October 23, 2017 approved
Ground rules:
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# Need help with a proof involving nonlinear differential equations
I'm trying to solve a problem that stated:
If $ae \neq bd$ prove that you can choose 2 constants, h and k, so that the substitution $t= s - h$ , $x = y - k$ reduce the following equation to a homogeneous equation. $$\frac{dx}{dt} = F \left(\frac{at+bx+c}{dt+ex+f}\right)$$
I'm unsure about what I'm supposed to be doing here.
Doing all the substitutions I got $$\frac{dy}{ds} = F\left(\frac {as -ah+by-bk+c}{ds-dh+ey-ek+f}\right)$$
From this I gathered that if $\displaystyle k = \frac{fa-dc}{ea-db}$ ( Note that I'm not dividing by 0 since I know $ae\neq bd$) and $\displaystyle h = \frac{c}{a} - \frac{b}{a} \left[\frac{fa - dc}{ea - db}\right]$ then I would have $$\frac{dy}{ds} = F\left(\frac{as+by}{ds+ey}\right)$$ With $v = \frac{s}{y}$ I can write this as $$G(v) = F(\frac{a+bv}{d+ev})$$
Which if I understand it correctly would make this a 0 order differential equation, right? It seem kind of weird that this works regardless of what F is as long as $ae \neq bd$.
-
Well, what does it mean to be homogeneous? Once you see that, the answer becomes evident. – Raskolnikov Jun 15 '11 at 21:26
Well, I'm guessing this is a 0 degree homogeneous equation so $F( \sigma [\frac{as + by}{ds+ey}]) = F(\frac{as +by}{ds+ey})$, which is true for this equation, right? – Bananas Jun 15 '11 at 21:32
What is $\sigma$ ? – Raskolnikov Jun 15 '11 at 21:32
The reason $ae \neq bd$ is important is that it keeps the matrix of coefficients non-singular and therefore invertible. – Ross Millikan Jun 15 '11 at 22:09
With $\sigma$ I meant to check if F is homogeneous of degree 0, since I already know it can be written as $$\frac{dy}{ds} = F(y, s)$$. I just define $$G(y, s) = \frac{as + by}{ds+ey}$$ and look at $$F(G(y,s)) = F(\frac{as + by}{ds+ey}) = \frac{dy}{ds}$$. – Bananas Jun 15 '11 at 21:52
The point is that $G(y,s)$ is invariant for a rescaling of both variables with a same factor. Therefore so is $F\circ G$ and thus the differential equation is homogeneous. And that is all there is to it. – Raskolnikov Jun 16 '11 at 9:02
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# What do these four elements - carbon, hydrogen, oxygen, and nitrogen, make up more than 96% of?
$\text{Biota?}$
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## Basic College Mathematics (9th Edition)
Published by Pearson
# Chapter 1 - Whole Numbers - Review Exercises: 111
9
#### Work Step by Step
1. Simplify the square root. $\sqrt 9$ = 3 Equation becomes 3 + 2(3) 2. Multiply. 2(3) = 6 Equation becomes 3 + 6 3. Add. 3 + 6 = 9
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.
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# Proof using the mean value theorem
I need to prove (using the mean value theorem) that for all $x\in(0,\infty)$, the following inequality holds:
$\exp(-x)\geq 1 - x$
I don't know how the mean value theorem is applicable here, since we don't have a closed interval.
How do I prove the statement?
• Make it your first step to make this into a closed interval. For instance, you could prove that $e^{-x} \geq 0$, and then show quickly that $0 \geq 1 - x$ for $x \in [1, \infty]$. That gives you a nice closed interval of $[0, 1]$ where you can do your proof. – Larry B. Jan 12 '17 at 20:07
• A proof without MVT is at follows: $\exp(-x)$ is a convex function and the straight line $1-x$ is a tangent line at $0$. The graph of a differentaible convex function lies above (precisely not below) the secant. This argument works for all real $x$. We have even more: the inequality is strict, whenever $x\ne 0$. Indeedd, our function is in fact strictly convex. – szw1710 Jan 12 '17 at 20:29
Hint: let $f(t)=e^{-t}$, and (for a fixed $x$) try using the mean value theorem on the interval $[0,x]$.
• I did. So $f(t) = e^{-t}, f'(t) = -e^{-t}$. So the MVT states: $\frac{f(t)-f(0)}{t-0}=f'(\xi)$ thus: $\frac{e^{-t}-1}{t-0}=f'(\xi)=-e^{-\xi}$ But what does that show me? – de_dust Jan 12 '17 at 21:14
• Well, $-e^{-\xi}\geq -1$ since $\xi\geq 0$, so you get $\frac{e^{-x}-1}{x}\geq -1$, or $e^{-x}\geq 1-x$. – carmichael561 Jan 12 '17 at 21:22
Let $f(x) = e^{-x} - (1 - x)$. So, $f '(x) = -e^{-x} + 1$.
Suppose $x \ge 0$. Observe that $f '(x) \ge 0$ (since $-1 \le -e^{-x} < 0$ for $x \ge 0$). Since $f '(x) \ge 0$ on the interval $[0, x]$ for $x \ge 0$, $f$ is increasing on this interval. Thus, $f(x) \ge f(0) = 0$ for $x \ge 0$. Therefore, $e^{-x} - (1 - x) \ge 0 \implies e^{-x} > 1 - x$ for $x > 0$ (i.e: on the interval $(0, \infty)$).
Suppose $x>0$. Then the mean value theorem applied to the interval $[0,x]$ says that $$\frac{e^{-x}-e^{-0}}{x-0}=-e^{-c}$$ for some $c\in(0,x)$. Since $c>0$, we have $-c<0$, so $e^{-c}<1$ and so $-e^{-c}>-1$.
Therefore $$e^{-x}-1 > -x$$
Let $f(x)=e^{-x}-1+x$. Fix a value $b \in [0,\infty)$ and consider the interval $[0,b]$. Note that $f(0)=0$.
Now according to the Mean Value Theorem, there exist a $c\in (0,b)$ such that $$f'(c)=\frac{f(b)-f(0)}{b-0}=\frac{e^{-b}-1+b}{b}>0.$$
This shows us that $f$ is increasing on any interval $(0,b)$ where $b$ is some fixed value in $[0,\infty)$. So $f(x)\geq f(0)$ for all $x\geq 0$. Thus $e^{-x}\geq 1-x$ for all $x\geq 0$.
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# Energy–pressure relation for low-dimensional gases
@article{Mancarella2014EnergypressureRF,
title={Energy–pressure relation for low-dimensional gases},
author={Francesco Antonio Mancarella and Giuseppe Mussardo and Andrea Trombettoni},
journal={Nuclear Physics},
year={2014},
volume={887},
pages={216-245}
}
• Published 30 June 2014
• Physics
• Nuclear Physics
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## References
SHOWING 1-10 OF 133 REFERENCES
Pressure-energy correlations in liquids. III. Statistical mechanics and thermodynamics of liquids with hidden scale invariance.
• Physics
The Journal of chemical physics
• 2009
The development of the theoretical understanding of strongly correlating liquids--those whose instantaneous potential energy and virial are more than 90% correlated in their thermal equilibrium fluctuations at constant volume--is continued.
Pressure-energy correlations in liquids. II. Analysis and consequences.
• Physics
The Journal of chemical physics
• 2008
It is demonstrated that the potential may be replaced, at fixed volume, by an effective power law but not simply because only short-distance encounters dominate the fluctuations, as well as the presence of the correlations in model biomembranes, showing that significant correlations may be present even in quite complex systems.
Pressure-energy correlations in liquids. I. Results from computer simulations.
• Physics
The Journal of chemical physics
• 2008
It is shown that a number of model liquids at fixed volume exhibit strong correlations between equilibrium fluctuations of the configurational parts of (instantaneous) pressure and energy, and in which systems these correlations are significant.
Pressure-energy correlations in liquids. IV. "Isomorphs" in liquid phase diagrams.
• Mathematics
The Journal of chemical physics
• 2009
The concept of "isomorphic" curves in the phase diagram is introduced and it is shown that after a jump between isomorphic state points the system is instantaneously in thermal equilibrium; consequences of this for generic aging experiments are discussed.
Pressure-energy correlations in liquids. V. Isomorphs in generalized Lennard-Jones systems.
• Mathematics
The Journal of chemical physics
• 2011
Using the fact that reduced-unit radial distribution functions are isomorph invariant, an expression for the shapes of isomorphs in the WU phase diagram of generalized Lennard-Jones systems of one or more types of particles is derived.
Statistical interparticle potential of an ideal gas of non-Abelian anyons
• Physics
• 2013
We determine and study the statistical interparticle potential of an ideal system of non-Abelian Chern?Simons (NACS) particles, comparing our results with the corresponding results of an ideal gas of
Introduction to the Statistical Physics of Integrable Many-body Systems
• Physics
• 2013
Including topics not traditionally covered in literature, such as (1+1)-dimensional QFT and classical 2D Coulomb gases, this book considers a wide range of models and demonstrates a number of
Universal thermodynamics of degenerate quantum gases in the unitarity limit.
• T. Ho
• Physics
Physical review letters
• 2004
A "universality hypothesis" for the relevant energy scales which is supported by experiments and can be proven in the Boltzmann regime implies a universal form for the grand potential, which is specified by only a few universal numbers in the degenerate limit.
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# Question #18d2e
Dec 3, 2015
$C {F}_{4} < C H {F}_{3} < {H}_{2} O < N a B r < C u < S i C$
#### Explanation:
Im order to answer this question, we will need to list the type of intermolecular interactions that every compound can carry on:
1. ${H}_{2} O$ is a polar molecular and therefore, it carries, in addition to the London Dispersion Force ( LDF ), a dipole-dipole interaction (d-d) which is the strongest and is called H-bond .
2. $C {F}_{4}$ the geometry around the carbon atom is tetrahedral. Since all four substituents are identical, the dipole moments of the $C - F$ bonds will cancel each other and the molecule is non polar. Therefore, the only possible type of interaction is LDF .
3. $N a B r$ is made from a metal $N a$ and a non metal $B r$ and therefore, it is an ionic compound. Therefore, the intermolecular interaction is ion-ion interaction .
4. $S i C$ will form a solid network and the type of intermolecular interaction is directional covalent bond .
5. $C H {F}_{3}$ the geometry around the carbon atom is tetrahedral. Since it is connected to three identical substituents only, this molecule will be polar. The type of intermolecular interaction possible are LDF and d-d interactions .
6. $C u$ is a metal and the type of intermolecular interaction is a non directional covalent bond .
Thus the increasing order of the melting point would be:
$C {F}_{4} < C H {F}_{3} < {H}_{2} O < N a B r < C u < S i C$
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## post processing: the Gimp perspective tool is not really transforming
I have uploaded a screenshot below to illustrate the problem. I dragged a jpeg to Gimp, clicked on the perspective tool and then tried to use it … but as you can see, it's not really transforming the image. Why is this so?
Click to enlarge the image.
## Transforming ParametricFunction into expression depending on the parameter
As a result of resolving an ODE system using `ParametricNDSolveValue` I get 4 functions, each one of them. Parametric Function depending on the parameter specified in `ParametricNDSolveValue`.
Even though what I want seems "simple" to me, I have searched the documentation and this site without success, so here is my question:
Can I transform my solution? Parametric Function in an expression of some kind? The motivation is to manipulate this expression, and this may involve different software.
If that is not possible, is there any other way in Mathematics to solve a $$2 times 2$$ System of EDOs at a point with a free parameter? Here is the question where I first asked about that.
## opengl – Transforming a length into a trunk projection
How do I calculate the screen lengths of the position vectors aligned with the axis after a frustum projection transformation?
Background:
In Java I create a frustum projection matrix via
``````Matrix.frustumM (projMatrix, 0, left, right, top bottom, near, far);
``````
and a view matrix via
``````Matrix.setLookAtM (viewMatrix, 0,
0, 0, -2.5, // eye position
0, 0, 0 // search position
0, -1, 0); // address above
``````
I also know how many GL units of width and height is the screen of my device, let's say `width` Y `height`. If my game tokens are `dx` Y `dy` GL units in size, then for a spelling projection I can calculate `width / dx` Y `height / dy` to determine how many squares you should have horizontally and vertically (approximately).
But with a trunk projection, which basically is always looking down according to the previous definition, this does not give me the correct result.
(Keep in mind that my tiles are always placed in the `x / y` airplane in `z = -1`
Of course I understand why, this is because the further away from the camera the smaller lengths are made. But how do I transform my `dx` Y `dy` values to deal with this?
I have tried:
• divide my `dx` Y `dy` by `1 + 2.5 + 1 = 4.5` since that is the distance from the eye to the plane of the tile.
• Multiplying the projection and view matrices (and both together) by the vector (dx, 0, 0, 1) for example.
But these do not work.
I also hear that the projection matrix has a `w` component in the lower right part of the matrix, which may have something to do with the z-scale, but I'm not sure if it's on the right track.
Any advice welcome. I will continue investigating.
## – primaverabss – Transforming a FP into FA (Sales Documents)
Goodnight everyone,
I am trying to make the transformation of Sales Documents, in the case of a Pro-form in an Invoice, but it gives an error because the origin does not have Warehouse in the Lines.
How can I do to add the store I want?
I have the following code that works if you have Warehouse:
``````
On Error GoTo Error
Dim objDocOrigen The GcpBEDocumentoVenda
ObjDocOrigen = motor.Comercial.Vendientes.Edita ("000", cbOrigTipoDoc.Text, cbOrigSerie.Text, CInt (cbOrigDoc.Text))
Dim objDocDestino The GcpBedocumentoVenda
objDocDestino = New GcpBEDocumentoVenda
objDocDestino.Entity = objDocOrigen.Entity
objDocDestino.Tipodoc = cbDestTipoDoc.Text
objDocDestino.Serie = cbDestSerie.Text
objDocDestino.CondPag = objDocOrigem.CondPag
Dim Doc (0) As Object
Doc (0) = objDocOrigen
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# Orthogonal Complement
1. Nov 2, 2008
### ahamdiheme
1. The problem statement, all variables and given/known data
Consider the vector space $$\Re$$nxn over $$\Re$$, let S denote the subspace of symmetric matrices, and R denote the subspace of skew-symmetric matrices. For matrices X,Y$$\in$$$$\Re$$nxn define their inner product by <X,Y>=Tr(XTY). Show that, with respect to this inner product,
R=S$$\bot$$
2. Relevant equations
Definition of inner product
Definition of orthogonal compliment
Definition of symmetric matrix
Definition of skew symmetric matrix
3. The attempt at a solution
If i can show that
R-S$$\bot$$=0
will it be sufficient and how do i go about it?
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
2. Nov 2, 2008
### HallsofIvy
Staff Emeritus
What do you mean by $R- S^{\bot}= 0$? To show that $R= S^{\bot}$ you must show that the inner product of any member of R with any member of S is 0, that's all.
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Have something to add?
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# BibLaTeX: different name order for author/editor
I would like to sort the names of authors and editors differntly in my citations. Authors should be listed as LastName, FirstName and editors as FirstName LastName.
So far I've tried this, but it hast only changed all names to LastName, FirstName:
\DeclareNameAlias{sortname}{first-last}
\DeclareNameAlias{default}{last-first}
\DeclareNameAlias{editor}{sortname}
• This depends on the style you use, so we would need to know more about that. Also do you want different formats even if the editor appears instead of the author at the head of an entry? – moewe May 10 '15 at 16:24
• I have got the following BibLaTeX settings \usepackage[backend=biber,style=verbose-ibid]{biblatex}. If the editor appears instead of the author, the name should show just as the author's would: LastName, FirstName. Basically every and any name before the title should be set as LastName, FirstName. – montauk May 10 '15 at 17:22
• Ahhh, that was more or less what I expected and makes perfect sense. I*'m slightly confused though because if I have \DeclareNameAlias{sortname}{last-first} with verbose-ibid in the bibliography I get exactly what you want, while in citations the authors are also "first-last". Are you thus asking about citations only? – moewe May 11 '15 at 5:27
Just the line
\DeclareNameAlias{sortname}{last-first}
gives you almost what you want.
biblatex prefers the order "first last" in citations though and will go through quite some length to achieve this (it adds a \DeclareNameAlias{sortname}{default} here and there). To prevent this, go with
\renewbibmacro*{cite:full}{%
\usebibmacro{cite:full:citepages}%
\printtext[bibhypertarget]{%
\usedriver{}
{\thefield{entrytype}}}%
\usebibmacro{shorthandintro}}
If you also want to keep \fullcites in line, you will need
\DeclareCiteCommand{\fullcite}
{\usebibmacro{prenote}}
{\usedriver{}
{\thefield{entrytype}}}
{\multicitedelim}
{\usebibmacro{postnote}}
\DeclareCiteCommand{\footfullcite}[\mkbibfootnote]
{\usebibmacro{prenote}}
{\usedriver{}
{\thefield{entrytype}}}
{\multicitedelim}
{\usebibmacro{postnote}}
as well.
As a bonus, the following will also make labelnames "last, first"
\DeclareNameFormat{labelname}{%
\ifcase\value{uniquename}%
\usebibmacro{name:last}{#1}{#3}{#5}{#7}%
\or
\ifuseprefix
{\usebibmacro{name:last-first}{#1}{#4}{#5}{#8}}
{\usebibmacro{name:last-first}{#1}{#4}{#6}{#8}}%
\or
\usebibmacro{name:last-first}{#1}{#3}{#5}{#7}%
\fi
\usebibmacro{name:andothers}}
MWE
\documentclass[english]{article}
\usepackage{babel}
\usepackage{csquotes}
\usepackage[backend=biber,style=verbose-ibid]{biblatex}
\usepackage{hyperref}
\DeclareNameAlias{sortname}{last-first}
\renewbibmacro*{cite:full}{%
\usebibmacro{cite:full:citepages}%
\printtext[bibhypertarget]{%
\usedriver{}
{\thefield{entrytype}}}%
\usebibmacro{shorthandintro}}
\DeclareNameFormat{labelname}{%
\ifcase\value{uniquename}%
\usebibmacro{name:last}{#1}{#3}{#5}{#7}%
\or
\ifuseprefix
{\usebibmacro{name:last-first}{#1}{#4}{#5}{#8}}
{\usebibmacro{name:last-first}{#1}{#4}{#6}{#8}}%
\or
\usebibmacro{name:last-first}{#1}{#3}{#5}{#7}%
\fi
\usebibmacro{name:andothers}}
\begin{document}
\cite{worman,geer,cicero,gaonkar,gaonkar:in,jaffe,baez/article}
\printbibliography
\end{document}
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## Trigonometry (11th Edition) Clone
First we can find the angle $\theta$ by rotating counter-clockwise from the positive x-axis. We can then draw a line with a magnitude of $\vert r \vert$, starting from the origin and pointing in the opposite direction from the angle $\theta$.
$(r,\theta)$ is a point in polar coordinates and $r \lt 0$ First we can find the angle $\theta$ by rotating counter-clockwise from the positive x-axis. We can then draw a line with a magnitude of $\vert r \vert$, starting from the origin and pointing in the opposite direction from the angle $\theta$. Note that we must draw the line in the opposite direction from angle $\theta$ because $r \lt 0$
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# Zeroes of $\sin(z)+2\sin(8z)$
Clearly the function $$f(x)=\sin z+2\sin8z$$ has many zeroes on the real line. Does it have any off the real line? I thought of inspecting its real and imaginary parts separately: $$f(x+iy) = (\sin x\cosh y+2\sin8x\cosh8y)+i(\cos x\sinh y+2\cos8x\sinh8y)$$ However, I didn't find this to be very helpful. In the case of just a single sine I'd have $$\sin(x+iy)=(\sin x\cosh y)+i(\cos x\sinh y)$$ and I could show that all zeroes are on the real line by observing that cosh is always positive (as a real function) so I must have $$x=\pi k$$, so for the imaginary part $$0=\cos \pi k\sinh y=\sinh y$$ implies $$y=0$$. However, it's not so simple for the case of $$f(z)$$ above. Can anyone help me solve this?
• Try letting $q=e^{iz}$ and rewriting the equation as polynomial (of degree $8$) in $q$. – Barry Cipra Feb 4 at 22:50
• Of course - thank you! Wouldn't that be a polynomial of degree 16, though, since we'd need to factor out $\frac{1}{q^8}$ from $\sin 8z=q^8+q^{-8}$? – BGreen Feb 4 at 23:42
• Yes, sorry, for some reason I jotted it down as $\sin4z$. – Barry Cipra Feb 5 at 0:03
• I thought I'd post the following here for anyone reading this in the future. Using your argument I can show that there are at most 16 "distinct" (meaning $z$ is considered the same as $z+2\pi$) zeroes, which I at first thought meant I had overlooked nonreal zeroes. However, I just realized that, on the contrary, it means that if I can find 16 distinct real zeroes then there cannot possibly be any imaginary zeroes. After that, it's easy to see that it has 16 distinct real zeroes, proving that there are no imaginary zeroes. – BGreen Feb 5 at 0:13
• Excellent observation. You might consider posting it as a self-contained answer. – Barry Cipra Feb 5 at 2:42
To start, note that your question is analogous to asking whether or not
$$|\sin(x+iy)+2\sin(8x+8iy)|=0$$
for some nonzero $$y$$. Of course, we may as well square this in order to simplify our question somewhat (for the sake of notation, call this $$g(x,y)$$). Therefore, let us expand this function out:
$$2g(x,y)=2|\sin(x+iy)+2\sin(8x+8iy)|^2$$
$$=2(\cos (x) \sinh (y)+2 \cos (8 x) \sinh (8 y))^2+2(\sin (x) \cosh (y)+2 \sin (8 x) \cosh (8 y))^2$$
$$=-4 \cos (9 x) \cosh (7 y)+4 \cos (7 x) \cosh (9 y)-\cos (2 x)-4 \cos (16 x)+\cosh (2 y)+4 \cosh (16 y).$$
Thus, if we can show that $$g(x,y)$$ is $$0$$ only if $$y$$ is $$0$$, then we are done. In order to do this, consider the partial derivative with respect to $$y$$:
$$\frac{\partial}{\partial y}\left[-4 \cos (9 x) \cosh (7 y)+4 \cos (7 x) \cosh (9 y)-\cos (2 x)-4 \cos (16 x)+\cosh (2 y)+4 \cosh (16 y)\right]$$
$$=2 (-14 \cos (9 x) \sinh (7 y)+18 \cos (7 x) \sinh (9 y)+\sinh (2 y)+32 \sinh (16 y)).$$
For the sake of notation, call this function $$f(x,y)$$. Now, if $$y>0$$, then
$$\frac{1}{2}f(x,y)=-14 \cos (9 x) \sinh (7 y)+18 \cos (7 x) \sinh (9 y)+\sinh (2 y)+32 \sinh (16 y)$$
$$\geq -14 \sinh (7 y)-18 \sinh (9 y)+\sinh (2 y)+32 \sinh (16 y)$$
$$>-14 \sinh (9 y)-18 \sinh (9 y)+\sinh (2 y)+32 \sinh (9 y)$$ $$=\sinh(2y)>0.$$
Now, note that $$f(x,-y)=-f(x,y)$$. Thus, for $$y<0$$, $$f(x,y)<0$$. Putting it all together, we have a function $$g(x,y)$$ which has the following properties:
$$g(x,y)\geq 0,$$
$$\frac{\partial}{\partial y}g(x,y)>0\text{ for } y>0,$$
$$\frac{\partial}{\partial y}g(x,y)<0\text{ for } y<0.$$
We conclude that if $$g(x,y)=0$$, then $$y=0$$.
• Thank you! I must ask, did you have intuition that it would be increasing (decreasing) whenever $y>0$ ($y<0$) before you began? I had thought that there was a possibility of the two sines being out-of-phase and canceling somewhere, so I wasn't expecting an argument of that nature to work. – BGreen Feb 5 at 0:23
• Not so much intuition, but the first thing I did was graph the absolute value as a function of $x$ and $y$ (just to check if your conjecture was true). From there, it was easy to see that this method would work. – Nick Guerrero Feb 5 at 1:17
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# Iterative Feature Matching: Toward Provable Domain Generalization with Logarithmic Environments
18 Jun 2021 · , , , , ·
Domain generalization aims at performing well on unseen test environments with data from a limited number of training environments. Despite a proliferation of proposal algorithms for this task, assessing their performance both theoretically and empirically is still very challenging. Distributional matching algorithms such as (Conditional) Domain Adversarial Networks [Ganin et al., 2016, Long et al., 2018] are popular and enjoy empirical success, but they lack formal guarantees. Other approaches such as Invariant Risk Minimization (IRM) require a prohibitively large number of training environments -- linear in the dimension of the spurious feature space $d_s$ -- even on simple data models like the one proposed by [Rosenfeld et al., 2021]. Under a variant of this model, we show that both ERM and IRM cannot generalize with $o(d_s)$ environments. We then present an iterative feature matching algorithm that is guaranteed with high probability to yield a predictor that generalizes after seeing only $O(\log d_s)$ environments. Our results provide the first theoretical justification for a family of distribution-matching algorithms widely used in practice under a concrete nontrivial data model.
PDF Abstract
## Code Add Remove Mark official
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Add Datasets introduced or used in this paper
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Suppose you have a bunch of people who differ only in their wage $w$. Everyone has utility logarithmic in their consumption. As the government, you want to promote welfare by redistributing consumption. You decide to do this by instituting a flat tax and using it to fund a universal basic income.
The more revenue you raise with your tax, the higher the UBI can be. But if you raise the tax too high, you will excessively deter people from working. So what’s the optimal tax rate?
Somewhat surprisingly, Ben Weinstein-Raun and I managed to find an analytical solution to this problem. The optimal flat tax rate is a simple function of the wage distribution:
$$\text{Optimal flat tax rate} = 1 - \frac{\text{Harmonic mean of wages}}{\text{Arithmetic mean of wages}}$$
The functional form checks out: Harmonic mean equals arithmetic mean on a set which is perfectly equal; in that case the fraction will be 1 and the tax rate will be 0. Inequality causes the harmonic mean to become smaller than the arithmetic mean; at most, the fraction might go to 0 and the tax rate will approach 100%.
Another way of phrasing that fraction is “the average time it takes for someone to make a dollar, multiplied by the average wage”.
I did most of the algebra in Sympy; almost all of the math I write here is replicated in this Python script, which I also put online as a Sage workbook here. Because of that, I’m reasonably confident in this result.
## Proof
Let’s define all our variables:
• $w$ is the wage of an individual
• $r$ is 1 minus the tax rate
• $h$ is the amount of time that a person works, in some unit. The units don’t affect the optimal tax rate.
• $c$ is the UBI
• $u$ is utility
• $y$ is the pre-tax, pre-transfers income of an individual, $Y$ is the income of all of society
• there are $n$ people. The set of people is $P$.
So individuals have utility $u = \log(w \cdot h \cdot r + c) - h$.
### What is individual behavior, as a function of $r$ and $c$?
First we find the optimal hours worked for an individual by differentiating utility with respect to hours worked:
$$\frac{du}{dh} = \frac{w \cdot r}{w \cdot h \cdot r + c} - 1$$
Setting the derivative to 0 and solving for $h$, you get
$$h = 1 - \frac{c}{r \cdot w}$$
Let’s check functional form–we expect workers to work more if they have lower UBI, lower taxes, or higher wages. This function has all those behaviors (remember that $r$ is the proportion of your income you get to keep, not the tax rate).
The optimal income is that time multiplied by $w$, so:
$$y = w - \frac{c}{r}$$
Note that this means that everyone forgoes the same amount of income due to the distortionary effects of the UBI and taxes.
At this income, utility for an individual is:
$$u = \log(r) - 1 + \log(w) + \frac{c}{r\cdot w}$$
And utility over all of society is therefore:
$$U = n\cdot\log(r) - n + \sum_{p \in P}\log(w_p) + \frac{c}{r\cdot w_p}$$
We can rewrite this to
$$U = n\cdot\log(r) - n + \sum_{p \in P}\left[\log(w_p)\right] + \frac{c}{r} \cdot \sum_{p \in P} \left[\frac{1}{w_p} \right]$$
#### Total societal income
Given $r$ and $c$, the income of the whole population is
Conveniently, the $\frac{c}{r}$ term is constant in the sum, so we can take it out:
where the total wage of the whole population is $W = \sum_{p \in P} w_p$.
### What is $c$, given $r$?
At a given tax rate $r$, the UBI (by definition) is:
$$c = \frac{1-r}{n} \cdot Y$$
We can substitute the other expression we found for $Y$ above into this equation:
$$c = \frac{1-r}{n} \cdot \left( -\frac{n \cdot c}{r} + W \right)$$
and solve for $c$, which gets us
$$c = \frac{-r \cdot W \cdot (r - 1)}n$$
So given a tax rate, we now know the equilibrium UBI.
### What is $U$, given $r$?
We can now substitute the equilibrium UBI into our global utility formula to determine global utility at this tax rate:
$$U = n\cdot(\log(r) - 1) + \sum_{p \in P}\left[\log(w_p)\right] - \frac{\sum_{p \in P}\left[\frac{1}{w_p}\right]\cdot W\cdot(r - 1)}n$$
### What is the optimal choice of $r$?
Now we differentiate $U$ with respect to $r$:
$$\frac{dU}{dr} = \frac{-\sum_{p \in P}\left[\frac{1}{w_p}\right] \cdot W}{n} + \frac{n}{r}$$
Set this to zero and solve for $r$, and you get:
$$\frac{n^2}{\sum_{p \in P}\left[\frac{1}{w_p}\right] \cdot W}$$
Remember that $W$ is the sum of wages. So this can be written as
$$\frac{n^2}{\sum_{p \in P}\left[\frac{1}{w_p}\right] \cdot \sum_{p \in P}\left[w_p\right]}$$
I posted on Facebook asking for someone to make sense of this expression for me. Matt Alger and Ben Weinstein-Raun both figured out that it is the harmonic mean of the wages divided by the arithmetic mean of the wages.
So overall:
$$\text{Optimal flat tax rate} = 1 - \frac{\text{Harmonic mean of wages}}{\text{Arithmetic mean of wages}}$$
## Further questions
I am interested to see if this process could be extended to find optimal tax structures for other situations. For example:
• What happens if people have different levels of avarice: that is, some of them get more pleasure from money than others?
• What happens if leisure time has diminishing marginal returns?
• What about if we don’t want to be restricted to a flat tax? Can we solve for the optimal tax function, where a tax function is a function from different pre-tax incomes to post-tax incomes?
I should also look harder to see if my result here is already known in the optimal tax literature. My impression is that economists aren’t that interested in this particular question, because they don’t like the rigidity of my assumed utility function. But I still think this result is really neat, and I’m very glad to know it.
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# Séminaire de géométrie analytique
le jeudi de 16h15 à 17h15 en salle 016
Archives du séminaire
Responsable : Bert WIEST
### Mai 2017
4 mai Journée de présentation des candidats pour le poste de géométrie
11 mai James Farre, Utah
3rd bounded cohomology of Kleinian groups
We explore the bounded cohomology of Kleinian groups. More concretely we discuss how certain hyperbolic structures on 3-manifolds give rise to different bounded classes in degree 3.
18 mai
25 mai Vacances (Ascension)
### Juin 2017
1 juin
8 juin Simon Brandhorst, Hannover
Minimal Salem numbers on supersingular K3 surfaces
The entropy of a surface automorphism is either zero or the logarithm of a Salem number, that is an algebraic integer $\lambda>1$ which is conjugate to $1/\lambda$ and all whose other conjugates lie on the unit circle.
In the case of a complex K3 surface McMullen gave a strategy to decide whether a given Salem number arises in this way. To do this he combined methods from linear programming, number fields, lattice theory and the Torelli theorems. In this talk we extend these methods to automorphisms of supersingular K3 surfaces using the crystalline Torelli theorems and apply them in the case of characteristic $5$.
This is joint work with Víctor González-Alonso.
15 juin
22 juin
29 juin
6 juilliet
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# Homogeneity of Variances
Certain tests (e.g. ANOVA) require that the variances of different populations are equal. This can be determined by the following approaches:
• Comparison of graphs (esp. box plots)
• Comparison of variance, standard deviation and IQR statistics
• Statistical tests
The F test presented in Two Sample Hypothesis Testing of Variances can be used to determine whether the variances of two populations are equal. For three or more variables the following statistical tests for homogeneity of variances are commonly used:
• Levene’s test
• Bartlett’s test
Using the terminology from Definition 1 of Basic Concepts for ANOVA, the following null and alternative hypotheses are used for either of these tests:
H0$\sigma_1^2$ = $\sigma_2^2$ = ⋯ = $\sigma_k^2$
H1: Not all variances are equal (i.e. $\sigma_i^2$ ≠ $\sigma_j^2$ for some i, j)
### Levene’s Test
For Levene’s test, the residuals eij of the group means from the cell means are calculated as follows:
An ANOVA is then conducted on the absolute value of the residuals. If the group variances are equal, then the average size of the residual should be the same across all groups.
Example 1: Use Levene’s test to determine whether the 4 samples in Example 2 of Basic Concepts for ANOVA have significantly different population variances.
Figure 1 – Levene’s test for Example 1
Since p-value = .90357 > .05 = α (Figure 1), we cannot reject the null hypothesis, and conclude there is no significant difference between the 4 group means, and so the ANOVA test conducted previously for Example 2 of Basic Concepts for ANOVA satisfies the homogenity of variances assumption.
There are three versions of the Levene’s test:
• Use of mean (as in the explanation above)
• Use of median (replace mean by median above)
• Use of 10% trimmed mean (replace mean by 10% trimmed mean above)
The three choices determine the robustness and power of Levene’s test. By robustness, we mean the ability of the test to not falsely detect unequal variances when the underlying data are not normally distributed and the variables are in fact equal. By power, we mean the ability of the test to detect unequal variances when the variances are in fact unequal.
Levene’s original paper only proposed using the mean. Brown and Forsythe extended Levene’s test to use either the median or the trimmed mean. They performed Monte Carlo studies that indicated that using the trimmed mean performed best when the underlying data had a heavy-tailed distribution and the median performed best when the underlying data had a skewed distribution. Using the mean provided the best power for symmetric, moderate-tailed, distributions.
Although the optimal choice depends on the underlying distribution, the definition based on the median is recommended as the choice that provides good robustness against many types of non-normal data while retaining good power. Another choice may be better based on knowledge of the underlying distribution of the data.
Some cautions about Levene’s test: You need to assume that the absolute values of the residuals satisfy the assumptions of ANOVA. Also, a more liberal cut off value when testing homogeneity of variances is often used due to the poor power of these tests.
Real Statistics Function: The following supplemental functions contained in the Real Statistics Resource Pack compute the p-value for Levene’s test.
LEVENE(R1, type) = p-value of for Levene’s test for the data in range R1. If type = 0 then group means are used; if type > 0 then group medians are used; if type < 0 then 10% trimmed group means are used. If the second argument is omitted it defaults to 0.
This function ignores any empty or non-numeric cells.
For example, for the data in Example 1, LEVENE(B6:E13) = LEVENE(B6:E13, 0) = 0.90357 (referring to Figure 1). Note that, for the same data, LEVENE(B6:E13, 1) = 0.97971 and LEVENE(B6:E13, 2) = 0.90357.
Real Statistics Data Analysis Tool: A Levene’s Test option is included in the Single Factor Anova data analysis tool. This options displays the results of all three versions of Levene’s test.
To use this tool for Example 1, enter Ctrl-m and select Single Factor Anova from the menu. A dialog box similar to that shown in Figure 1 of Confidence Interval for ANOVA appears. Enter B5:E13 in the Input Range, check Column headings included with data, select the Levene’s Test option and click on the OK button.
### Bartlett’s Test
We now show another test for homogeneity of variances using the Bartlett’s test statistic B, which is approximately chi-square:
where s2 is the pooled variance, which as we have seen is MSW, and
B can also be defined as follows:
Here MSW is the pooled variance across all groups. Thus the null hypothesis that all the group variances are equal is rejected if p-value < α where p-value = CHIDIST(B, k–1). B is only approximately chi-square, but the approximation should be good enough if there are at least 3 observations in each sample.
Bartlett’s test is very sensitive to departures from normality. If the samples come from non-normal distributions, then Bartlett’s test may simply be testing for non-normality. Levene’s test is less sensitive to departures from normality.
Example 2: Use Bartlett’s test to determine whether the 4 samples in Example 2 of Basic Concepts for ANOVA have significantly different population variances.
Figure 2 – Bartlett’s test for the data in Example 2
We obtain Bartlett’s test statistic B (cell I6 of Figure 2) by calculating the numerator and denominator of B as described above (cells I4 and I5). To do this we first calculate the values dfj, 1 ⁄ dfj, $s_j^2$ and ln $s_j^2$ (cells in the range B13:E16). We also calculate dfW, 1 ⁄ dfW, MSW and ln MSW (cells in range F13:F16). Note that MSW = SUMPRODUCT(B13:E13,B15:E15)/F13.
Since p-value = CHITEST(B, k–1) = CHITEST(1.88,3) < .979 > .05 = α, we don’t reject the null hypothesis, and so conclude that there is no significant difference between the variances of the four methods.
Note that if we change the first sample for Method 4 to 185 (instead of 85) and repeat the analysis we would find that there would be a significant difference in the variances (B = 17.23, p-value = .001 < .05 = α). This would be due to this one outlier. That it was an outlier would show up easily in any graphic representation. We would then need to decide whether this item was simply an error in measurement or a true measurement (see Outliers in ANOVA).
### Dealing with non-heterogeneity of variances
We present four ways of dealing with models where the variances are not sufficiently homogeneous:
In the rest of this section we will look at transformations that can address homogeneity of variance. In particular, we look at square root and log transformations. For transformations that address normality Transformations to Create Symmetry.
Log transformation for homogeneity of variances: A log transformation can be effective when the standard deviations of the group samples are proportional to the group means. Here a log to any base can be used, although log base 10 and the natural log (i.e. log base e) are the common choices. Since you can’t take the log of a negative number, it may be necessary to use the transformation f(x) = log(x+a) where a is a constant sufficiently large to make sure that all the x + a are positive.
Example 3: In an experiment the data in Figure 3 were collected. Check that the variances are homogeneous before proceeding with other tests.
Figure 3 – Data for Example 3
The sample variances in Figure 3 seem quite different. When we perform Levene’s test (Figure 4), we confirm that there is a significant difference between the variances (p-value = 0.024 < .05 = α).
Figure 4 – Levene’s test for data in Example 3
We note there is a correlation between the group means and group standard deviations (r = .88), which leads us to try making a log transformation (here we use base 10) to try to achieve homogeneity of variances (table on the left of Figure 15.23).
We can see that the variances in the transformed data are more similar. This time Levene’s test (the table on the right of Figure 5) shows that there is no significant difference between the variances (p-value =.20 > .05).
Figure 5 – Log transform and Levene’s test
Square root transformation for homogeneity of variances: When the group means are proportional to the group variances, often a square root transformation $f(x) = \sqrt{x}$ is useful. Since you can’t take the square root of a negative number, it may be necessary to use a transformation of form $f(x) = \sqrt{x + a}$, where a is a constant chosen to make sure that all values of x + a are positive. If the values of x are small (e.g. |x| < 10), it might be better to use the transformation $f(x) = \sqrt{x + .5}$ or $f(x) = \sqrt{x}$ + $\sqrt{x + 1}$.
### 28 Responses to Homogeneity of Variances
1. Ned from Norn Iron says:
Many thanks for this… The easy to follow guide to Levene’s and Bartlett’s included in your download is just what I needed to sort out a tricky analytical problem…
Ned,
I am very pleased that the site has been useful for you. I hope that you will use it again in the future.
Charles
2. Sriya says:
Hi,
Can you please let me know what transformation method I should be using if both standard deviation to means and means to variances are not proportional? There is no strong correlation for both?
Thanks.
• Charles says:
Sriya,
There is no easy answer to your question. It all depends on your data. There are an unlimited number of transformations as well (1/x, x^2, etc.). It also may turn out that a particular transformation creates more problems than it solves.
Charles
3. Colin says:
Sir
Will you add a real statistics function for “Bartlett’s Test” ?
Colin
• Charles says:
Colin,
Bartlett’s Test is also called Box’s Test. This is already included in the Real Statistics Resource Pack (see multivariate statistics portion of the website).
Charles
4. Deborah says:
Hi, I just wanted to ask, what happens if your levene’s test is positive so homogeneity of variance cannot be assumed in a factorial independent measures ANOVA. I know that you have to change the significance to p=0.01 instead of 0.05 (or something along those lines) but what do I do in terms of SPSS? I have run the test as normal but I don’t know how I am supposed to interpret my results considering levene’s positivity.
• Charles says:
Deborah,
What to do in case the homogeneity of variances test fails is explained towards the end of the referenced webpage under the title
“Dealing with non-heterogeneity of variances”.
Charles
• Deborah says:
Thank you:)
5. sonia says:
sir i wanted to ask why homogeneity of variance is so important?please tell me in some points…
• Charles says:
Sonia,
Homegeneity of variances is a requirement for many of the most used statistical tests, including ANOVA. Fortunately most such tests are pretty foriving and as long as the variances are not too unequal the tests give pretty accurate results, but when the requirement is sufficiently violated then the results of these tests can be quite unreliable.
Charles
6. Valerian says:
hi! i want to ask on the interpretation of Bartlet’s test on the Gen stat discover program for ANOVA, i do fail to interpret it
• Charles says:
Sorry but I am not familiar with the Gen stat discover program for ANOVA.
Charles
7. praveen kumar says:
I want do homogeneity test for two variances please tell me to do the test
• Charles says:
Levene’s test can be used for two variance. You can use the LEVENE function as described on the referenced webpage.
Charles
8. umar iqbal says:
sir i want to know how do i find the relationship between export growth and variation between real and nominal exchange rate based on the measure of 3 months and 6 months i have collected data but now i m confused how do i apply non-parametric test on it and which test…
• Charles says:
Charles
9. Lucy says:
Dear Sir,
I am analyzing a field experiment on 4 maize varieties. The varieties were replicated three times in one location. Should I examine the homogeneity and normality tests?
Lucy
• Charles says:
Lucy,
It really depends on what you are trying to test. The ANOVA tests will require homogeneity of variance and normality, but they can be quite forgiving even if these assumptions aren’t completely satisfied.
Charles
10. Alfiya says:
Dear Sir,
I am doing the One-Way ANOVA analysis. My p-value =0,233 for Levene’s test. Since my data was not normally distributed I transformed it. Do I need to perform Levene’s test again for transformed data? (I have tried and p-value is less then 0.05)
Thank you
Alfiya.
• Charles says:
Alfiya,
Since you will be testing the transformed data you need to make sure that the assumptions are satisfied on the transformed data. Since homogeneity of variance is an assumption for One-way ANOVA this assumption needs to be verified for the transformed data. Levene’s test is a way of checking this.
Charles
11. Kennedy says:
I love your website it is so useful in helping me solve statistical problems. I am a little confused about how to perform hypothesis testing when the observations are just given as one total without actually listing them separately – 125 observations (Southern States) and 132 observations (Northern States) with a sample mean of 87 and 88 respectively and a population variance of 7.0 and 6.2 respectively. Level of significance is .01 is there evidence that the workers in southern states are receiving less pay than workers in northern states?
• Charles says:
Since you have the population variances you can use a two sample test using the normal distribution, as described in Theorem 1 of Comparing Two Means.
The null hypothesis is mean1 >= mean2 (these are population means). The test statistic is z = (m1-m2)/stdev, where m1-m2 = 88-87 = 1 (sample means) and stdev = sqrt(var) where var = v1^2/n1 + v2^2/n2 = 6.2^2/132 + 7.0^2/125. If NORMSDIST(z) > .99 then you reject the hypothesis that the the workers receive the same pay. This is a one tailed test. If you want a two-tailed test you need to replace .99 by .995.
If instead of the population variance you had the sample variances you would use Theorem 1 of Two Sample t Test instead.
Charles
12. Sumit says:
Can one perform t-test or ANOVA using CV if the variance between group/s is not similar? If yes, how does one do it? I am a statistics illiterate
• Charles says:
There is a version of the t-test which you can use when the variances are not similar. See the webpage two sample t-test with unequal variances.
There are also substitute tests for ANOVA when the variances are not equal. See the Dealing with non-heterogeneity of variances topic on the referenced webpage.
You use the abbreviation “CV”. What does this stand for?
Charles
13. saif salim says:
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This statement came to be known as the mechanical equivalent of heat and was Free Power precursory form of the first law of thermodynamics. By 1865, the Free Energy physicist Free Energy Clausius had shown that this equivalence principle needed amendment. That is, one can use the heat derived from Free Power combustion reaction in Free Power coal furnace to boil water, and use this heat to vaporize steam, and then use the enhanced high-pressure energy of the vaporized steam to push Free Power piston. Thus, we might naively reason that one can entirely convert the initial combustion heat of the chemical reaction into the work of pushing the piston. Clausius showed, however, that we must take into account the work that the molecules of the working body, i. e. , the water molecules in the cylinder, do on each other as they pass or transform from one step of or state of the engine cycle to the next, e. g. , from (P1, V1) to (P2, V2). Clausius originally called this the “transformation content” of the body, and then later changed the name to entropy. Thus, the heat used to transform the working body of molecules from one state to the next cannot be used to do external work, e. g. , to push the piston. Clausius defined this transformation heat as dQ = T dS. In 1873, Free Energy Free Power published A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Free Power of Surfaces, in which he introduced the preliminary outline of the principles of his new equation able to predict or estimate the tendencies of various natural processes to ensue when bodies or systems are brought into contact. By studying the interactions of homogeneous substances in contact, i. e. , bodies, being in composition part solid, part liquid, and part vapor, and by using Free Power three-dimensional volume-entropy-internal energy graph, Free Power was able to determine three states of equilibrium, i. e. , “necessarily stable”, “neutral”, and “unstable”, and whether or not changes will ensue. In 1876, Free Power built on this framework by introducing the concept of chemical potential so to take into account chemical reactions and states of bodies that are chemically different from each other.
Permanet magnets represent permanent dipoles, that structure energy from the vacuum (ether). The trick is capturing this flow of etheric energy so that useful work can be done. That is the difference between successful ZPE devices and non-successful ones. Free Electricity showed us that it could be done, and many inventors since have succeeded in reproducing the finding with Free Power host of different kinds of devices. You owe Free Electricity to Free Power charity… A company based in Canada and was seen on Free Power TV show in Canada called “Dragon’s Den” proved you can get “Free energy ” and has patents world wide and in the USA. Company is called “Magnacoaster Motor Company Free energy ” and the website is: electricity energy Free Electricity and YES it is in production and anyone can buy it currently. Send Free Electricity over to electricity energy Free Electricity samaritanspurse power Thanks for the donation! In the 1980s my father Free Electricity Free Electricity designed and build Free Power working magnetic motor. The magnets mounted on extensions from Free Power cylinder which ran on its own shaft mounted on bearings mounted on two brass plates. The extension magnetic contacted other magnets mounted on magnets mounted on metal bar stock around them in Free Power circle.
I looked at what you have for your motor so far and it’s going to be big. Here is my e-mail if you want to send those diagrams, if you know how to do it. [email protected] My name is Free energy MacInnes from Orangeville, On. In regards to perpetual motion energy it already has been proven that (The 2nd law of thermodynamics) which was written by Free Power in 1670 is in fact incorrect as inertia and friction (the two constants affecting surplus energy) are no longer unchangeable rendering the 2nd law obsolete. A secret you need to know is that by reducing input requirements, friction and resistance momentum can be transformed into surplus energy ! Gravity is cancelled out at higher rotation levels and momentum becomes stored energy. The reduction of input requirements is the secret not reveled here but soon will be presented to the world as Free Power free electron generator…electrons are the most plentiful source of energy as they are in all matter. Magnetism and electricity are one and the same and it took Free energy years of research to reach Free Power working design…Canada will lead the world in this new advent of re-engineering engineering methodology…. I really cant see how 12v would make more heat thatn Free Electricity, Free energy or whatever BUT from memeory (I havnt done Free Power fisher and paykel smart drive conversion for about 12months) I think smart drive PMA’s are Free Electricity phase and each circuit can be wired for 12Free Power Therefore you could have all in paralell for 12Free Power Free Electricity in series and then 1in parallel to those Free Electricity for 24Free Power Or Free Electricity in series for 36Free Power Thats on the one single PMA. Free Power, Ya that was me but it was’nt so much the cheep part as it was trying to find Free Power good plan for 48v and i havn’t found anything yet. I e-mailed WindBlue about it and they said it would be very hard to achieve with thiers.
Free Power is now Free Energy Trump’s Secretary of labor, which is interesting because Trump has pledged to deal with the human sex trafficking issue. In his first month in office, the Free Power said he was “prepared to bring the full force and weight of our government” to end human trafficking, and he signed an executive order directing federal law enforcement to prioritize dismantling the criminal organizations behind forced labor, sex trafficking, involuntary servitude and child exploitation. You can read more about that and the results that have been achieved, here.
Is it because you’ve encountered someone smart enough to call you on your rhetoric and misinformation? Were you just having fun here feeling superior? Did I spoil your fun by calling your bluff? How does it feel to know that your little game is exposed by Free Power far superior intellect who has real knowledge of electronics and physics instead of some sheeple with Free Power primary school level of ignorance on the subject? Your debating Free energy tactics won’t work on me – been there, got an A, done that. Harvey1 Free Energy two books! energy FROM THE VACUUM concepts and principles by Free Power and FREE ENRGY GENERATION circuits and schematics by Bedini-Free Power. Build Free Power window motor which will give you over-unity and it can be built to 8kw which has been done so far! NOTHING IS IMPOSSIBLE! Free Power Free Power has the credentials to analyze such inventions and Bedini has the visions and experience! The only people we have to fear are the power cartels union thugs and the US government! @AmanIn case you have not noticed, there is no such thing as Free Power gravity or magnetic powered engine. You said “Science is constant, cannot be modified according to our wish. ” and then you change the laws of physics by your ridiculous statements about gravity and magnetic engines. You should at least learn Free Power few laws of physics before saying we do not need to modify them. Free electron enrgy “Now breaking on the market” = “The check is in the mail”. The reason I cannot enlighten you is that no amount of evidence can convince you. You cannot even acknowledge that there is no “Magical Magnetic Motor” in existence that anyone can operate without the inventor around. This is called “Confirmation Bias” and we all can fall into this trap. Look it up on Wiki. Please do not be rude – this is not personal. many occasions. Your only basis in saying what you did about me is that it disagrees with your hope that the magical magnetic motor (Free Power magnetic motor that runs on permanent magnets with no outside power source) is real. Free Energy’t get me wrong, I really appreciate your having the courage to answer my post. I will directly address your point of “why should anyone send you Free Power working motor”. The answer is in my post where I said I would pay generously for one. I really mean that. Secondly, you said “…you are probably quite able to build one yourself”. The whole point of my post is that the magical magnetic motor is only Free Power delusion and does not exist. No one can build Free Power delusion. How could you miss that? It’s so obvious in the post. We are all capable of self delusion to the point that we cannot see the obvious.
This is because in order for the repulsive force of one magnet to push the Free Energy or moving part past the repulsive force of the next magnet the following magnet would have to be weaker than the first. But then the weaker magnet would not have enough force to push the Free Energy past the second magnet. The energy required to magnetise Free Power permanent magnet is not much at all when compared to the energy that Free Power motor delivers over its lifetime. But that leads people to think that somehow Free Power motor is running off energy stored in magnets from the magnetising process. Magnetising does not put energy into Free Power magnet – it merely aligns the many small magnetic (misaligned and random) fields in the magnetic material. Dear friends, I’m very new to the free energy paradigm & debate. Have just started following it. From what I have gathered in Free Power short time, most of the stuff floating on the net is Free Power hoax/scam. Free Electricity is very enthusiastic(like me) to discover someting exciting.
Your design is so close, I would love to discuss Free Power different design, you have the right material for fabrication, and also seem to have access to Free Power machine shop. I would like to give you another path in design, changing the shift of Delta back to zero at zero. Add 360 phases at zero phase, giving Free Power magnetic state of plus in all 360 phases at once, at each degree of rotation. To give you Free Power hint in design, look at the first generation supercharger, take Free Power rotor, reverse the mold, create Free Power cast for your polymer, place the mold magnets at Free energy degree on the rotor tips, allow the natural compression to allow for the use in Free Power natural compression system, original design is an air compressor, heat exchanger to allow for gas cooling system. Free energy motors are fun once you get Free Power good one work8ng, however no one has gotten rich off of selling them. I’m Free Power poor expert on free energy. Yup that’s right poor. I have designed Free Electricity motors of all kinds. I’ve been doing this for Free Electricity years and still no pay offs. Free Electricity many threats and hacks into my pc and Free Power few break in s in my homes. It’s all true. Big brother won’t stop keeping us down. I’ve made millions if volt free energy systems. Took Free Power long time to figure out.
##### Why? Because I didn’t have the correct angle or distance. It did, however, start to move on its own. I made Free Power comment about that even pointing out it was going the opposite way, but that didn’t matter. This is Free Power video somebody made of Free Power completed unit. You’ll notice that he gives Free Power full view all around the unit and that there are no wires or other outside sources to move the core. Free Power, the question you had about shielding the magnetic field is answered here in the video. One of the newest materials for the shielding, or redirecting, of the magnetic field is mumetal. You can get neodymium magnets via eBay really cheaply. That way you won’t feel so bad when it doesn’t work. Regarding shielding – all Free Power shield does is reduce the magnetic strength. Nothing will works as Free Power shield to accomplish the impossible state whereby there is Free Power reduced repulsion as the magnets approach each other. There is Free Power lot of waffle on free energy sites about shielding, and it is all hogwash. Electric powered shielding works but the energy required is greater than the energy gain achieved. It is Free Power pointless exercise. Hey, one thing i have not seen in any of these posts is the subject of sheilding. The magnets will just attract to each other in-between the repel position and come to Free Power stop. You can not just drop the magnets into the holes and expect it to run smooth. Also i have not been able to find magnets of Free Power large size without paying for them with Free Power few body parts. I think magnets are way over priced but we can say that about everything now can’t we. If you can get them at Free Power good price let me know.
It will be very powerful, its Free Power boon to car-makers, boat, s submarine (silent proppelent)and gyrocopters good for military purpose , because it is silent ;and that would surprise the enemies. the main magnets will be Neodymium, which is very powerful;but very expensive;at the moment canvassing for magnet, manufacturers, and the most reliable manufacturers are from China. Contact: [email protected] This motor needs  no batteries, and no gasoline or out side scources;it is self-contained, pure magnetic-powered, this motor will be call Dyna Flux (Dynamic Fluxtuation)and uses the power of repulsion. Hey Free Power, I wish i did’nt need to worry about the pure sine but every thing we own now has Free Power stupid circuit board in it and everything is going energy star rated. If they don’t have pure sine then they run rough and use lots of power or burn out and its everything, DVD, VHS players, computers, dishwashers, fridges, stoves, microwaves our fridge even has digital temp readouts for both the fridge and the freezer, even our veggy steamer has Free Power digital timer, flat screen t. v’s, you can’t get away from it anymore, the world has gone teck crazzy. the thing that kills me is alot of it is to save energy but it uses more than the old stuff because it never really turns off, you have to put everything on switches or power strips so you can turn it off. I don’t know if i can get away from using batteries for my project. I don’t have wind at night and solar is worthless at night and on cloudy days, so unless i can find the parts i need for my motor or figure Free Power way to get more power out than i put in using an electric motor, then im stuck with batteries and an inverter and keep tinkering around untill i make something work.
This expression has commonly been interpreted to mean that work is extracted from the internal energy U while TS represents energy not available to perform work. However, this is incorrect. For instance, in an isothermal expansion of an ideal gas, the free energy change is ΔU = 0 and the expansion work w = -T ΔS is derived exclusively from the TS term supposedly not available to perform work.
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# Kerodon
$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
Variant 9.10.6.8. Let $U: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{C}}$ be an opfibration in sets. We define a functor $\chi _{U}: \operatorname{\mathcal{C}}\rightarrow \operatorname{Set}$ as follows:
• For each object $X \in \operatorname{\mathcal{C}}$, we define $\chi _{U}(X)$ to be the set of objects $\operatorname{Ob}( \operatorname{\mathcal{D}}_{X} )$.
• For each morphism $f: X \rightarrow Y$ in $\operatorname{\mathcal{C}}$, we define $\chi _{U}(f)$ to be the function $f_!: \operatorname{Ob}( \operatorname{\mathcal{D}}_{X} ) \rightarrow \operatorname{Ob}( \operatorname{\mathcal{D}}_{Y} )$ of Variant 9.10.6.2.
We will refer to $\chi _{U}$ as the transport representation associated to $U$.
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## In Brief
The start of the academic year has a habit of bringing forth distractions, not least of all to someone as disorganized as me. So here are a few remarks in brief.
The class number of $\mathbf{Q}(\zeta_{151})^{+}$ is one.
John Miller, a student of Iwaniec at Rutgers, wrote the following nice paper, which improves upon a previous result of Schoof. One technique that is useful in computing the class numbers of fields with small discriminant is to make use of the Odlyzko bounds. Here’s a typical example. If $K =\mathbf{Q}(\zeta_{37})^{+}$, then the root discriminant of $K$ is $30$ or so. However, by consulting Odlzyko, one sees that any totally real field with this root discriminant has degree at most $40$. Hence the class number of $K$ is either one or two, and it is easy to rule out the second possibility by using genus theory. More generally, whenever one has an a priori bound on $h^{+}$, one can compute $h^{+}$ by relating $h^{+}$ to the index of the circular units (Schoof did this in a previous paper.) This trick only works if the root discriminant of the totally real field is at most $60$ (or so), which seems to prevent one from applying this to real cyclotomic fields for $p > 67$. (There’s always a bound on the class group by Minkowski, but that is a terrible bound.) The idea behind this paper is that Odlyzko’s bound can be improved if one in addition knows that certain primes of small norm are principal. And since one has explicit fields, it is possible to show that the relevant ideals are principal by exhibiting explicit elements with the appropriate norm. I can’t quite tell how lucky the author was to find such elements (he searches for cyclotomic elements expressible as a small number of roots of unity), but it works! Perhaps, a postiori, it is useful that these fields do actually turn out to have class number one.
Matisse cut-outs
The NYT reports on an exhibit of Matisse cut-outs at MoMA. I have a particular soft spot for these works. I was particularly struck by a cut-out I once saw at an exhibit at the Centre Pompidou, so much so that I painted a replica (almost full sized) on the wall of my rental apartment in Cambridge:
I’m not sure if this particular cut-out is at MoMA, though.
256
Thanks to DS, I was hooked on 2048 for far too long. I eventually got bored trying to get the 16384 tile, and moved on to the more compact 256 instead. The latter game is slightly less random in that only 2s are created on each turn. The highest possible score is 7172, which is obtained when one ends up with (in any configuration) the powers of $2$ from $2$ to $512$. Recently, I finally managed to complete the game:
Notice that the $512,256,128$ tiles are not along the same edge (I think it must be theoretically possible to finish in that way, but it would be harder). Unfortunately, having reached this point, it has not cured me of my addiction. Curse you, Savitt!
Stickelberger’s Theorem.
I proved Stickelberger’s theorem in class the other day — well, with one caveat. I proved that all the ideals $\mathfrak{q}$ of prime norm are annihilated by the Stickelberger ideal. This certainly implies the result, because the class group is generated by such ideals. This follows, for example, by the Cebotarev density theorem applied to the Hilbert class field (which was my argument in class). But then I worried that this was an anachronistic argument, and indeed Stickelberger’s theorem was a solidly 19th century result. So what did Stickelberger do?
Posted in Art, Mathematics, Waffle | | 2 Comments
## iTunes top Ten
tl;dr: lots of Bach, if you’re not into that sort of thing, at least check out Mel Brooks. And if you’re not into that *either*, well then I don’t know what’s wrong with you.
Following Jordan, here is a list of my top 10 iTunes tracks by play count. In reality, it’s more like the top 10 *albums*, because most of the works are spread out over multiple tracks.
Technically speaking, my most-played “song” on iTunes is “Ambient Waterfall Sounds for Ultimate Bedtime Relaxation, Deeply Lucid Dreams,” with 188869 plays. But that’s a little bit misleading. The track basically consists of white noise, but (slightly irritatingly to me) it varies slightly in tone and pitch over the 4 minutes 44 seconds of the track. So I rigged it to run on a 2-second loop, which i play overnight when trying to sleep at conferences.
#1. Musical Offering, 296 plays [the number of plays from each track is not constant, so I will just go by the highest number for each album]. My recording (by the Ensemble Sonnerie) is arranged for Oboe, Violin, Viola, Harpsichord, Flute, and Viol. There comes a certain point in the evening where the only possible music one wants to listen to the Musical Offering. And that time is 3AM. As you can see from the play count, I am up a lot at 3AM.
#2. The French Suites, Glenn Gould 215 plays. The French Suites are easy to play and even easier to listen to.
Then again, perhaps you would prefer the French suites Mel Brooks style:
#3. The Cello Suites, Yo Yo Ma (his second recording), 207 plays. OK, this is also something to listen to at 3AM.
#4. The Art of Fugue (Juilliard String Quartet) 200 plays. They built their own custom-made viola in order to avoid having to transpose the score up a fifth (which is what the Delme string quartet do in one of my other recordings of this piece). I highly recommend this recording from 1982. Unfortunately, I couldn’t find a clip on youtube.
#5. The Art of Fugue (Glenn Gould) 196 plays. My only regret is that it is not complete, as Gould only recorded the fugues I,II,IV,IX,XI,XIII and, of course, XIV. (There’s also a version by Gould on the organ on this recording which I don’t listen to). Instead of linking to this recording, let me link instead to a fascinating interview between Gould and Bruno Monsaingeon with Gould at the piano (I’ve linked to the the video at the end of the first (fairly ordinary and early) fugue:
#6. Inventions and Sinfonias (Andras Schiff) 151 plays. There’s a common theme to this list so far, and it is Bach. This CD holds a special place for me as it was my first piano Bach recording. Glenn Gould has an even more than usually idiosyncratic recording of these, so I more often turn to Schiff on this one.
#7. Ave Verum Corpus (Byrd, King’s Singers) 150 plays. We’ve finally broken out of Bach! The intimacy of this recording (for so few voices rather than a choir) is what appeals to me.
#8. Arias “Erbarme dich, mein Gott” and “Aus Liebe will mein Heiland sterben” from St Matthew Passion, 129 plays (Michael Chance/Ann Monoyios). I don’t usually have three hours to listen to the entire recording, but these Arias are certainly some of the highlights. Here’s Michael Chance in a different recording of the same aria:
#9. Gnossiennes #1-#3 Jean-Yves Thibaudet, 121 plays. Perhaps you would like to see (actors portraying) Wittgenstein, John Maynard Keynes, and Lydia Lopokova pretend to be the solar system? I actually saw this Derek Jarman film in the theatre with Patrick Emerton…
#10. An Die Musik (Schwarzkopf) 119 plays. Whenever I sing/play lieder, I always finish by singing this.
This isn’t my favourite recording, but it’s the oldest one I had. In fact, when it comes to Schwarzkopf singer lieder, my favourite performance is her singing of Litanei auf das Fest Allerseelen here:
I should note that these numbers are all coming from iTunes on my laptop. My listening habits are somewhat different on my iPod, where I’m much more likely to listen to (say) Beethoven or Mahler. As an indication of how long a time period these numbers represents, I gave the analogous numbers on Jordan’s Blog http://quomodocumque.wordpress.com/2010/07/01/real-life-rock-top-10/ in 2010. Interpolating between these two sources, it suggests I listen (at home) to either the Art of Fugue or the Musical Offering about once a week, which seems about right.
Posted in Music | | 3 Comments
## Applying for an NSF grant
It’s not easy to write a good grant proposal. But it can be even harder to write one for the first time, especially if you’re not quite sure who will be reading your proposal. So today, I want to say a little bit about how an NSF mathematics panel is run, and give you some idea of who your target audience should be.
Before I start, I want to include a pseudo-legal disclaimer. For fairly obvious reasons, you are not supposed to reveal that you served on any particular panel. But I am allowed to say that I have served on *some* panels, and there is enough uniformity in the process to make me confident that what I say should resemble your reality if you decide to apply. (Let me also mention that I had some help on this post from a friend [whom I shall refer to as the Hawk] who is much more of an NSF pro than I am. He made various corrections and suggestions on a first draft of this blog, and I even included a few of his remarks verbatim in the text.)
The NSF administers many different types of grants. I’m not just talking about graduate fellowships, postgraduate fellowships and research grants here. There are FRG grants, RTG grants, CAREER NSF grants, REUs, conference grants, and so on. However, for the purpose of this email, I want to concentrate on research grants.
The Mechanics: The panel is comprised of approximately 10 or so mathematicians, who consider approximately 40-50 or so proposals. About six weeks before the panel takes place, each panelist is given the list of proposals and asked to rank the proposals 1,2,3,C based on the following criteria:
1 = I feel comfortable reviewing this proposal
2 = I could review this proposal if necessary
3 = It would be very difficult for me to review this proposal
C = I have a conflict of interest with this proposal
The next step is that the panel meets at the NSF headquarters in Virginia, sometime between November and March. A typical panel may last 2.5 days. The panel is chaired by the relevant program officer and three or so other NSF employees (usually professional mathematicians who have taken a leave of absence for a two year position at the NSF), so there will typically be 14-15 people in a conference room, each with either their laptop or a supplied computer. The first 1.5 days of the panel consist of going through the files one by one. For each file, the three (or so) panelists who were assigned the proposal read out their review of the proposal. During this time, other panelists (especially those with some expertise) will also offer their opinions. During this period, anyone who is conflicted with the proposal has to leave the room. At the end of each discussion (which takes about 10 minutes), a yellow sticky sheet with the PI’s name has to be placed on a white board with three columns. The columns are officially designated as “strongly recommended for funding,” “recommended for funding if possible,” and “not recommended for funding.” The desired outcome is to have 10% of proposals in the first column, 30% in the second, and 60% in the third. Within the first two columns the names are ordered, although, during the process, certain proposals can float up or down as they are re-evaluated in light of other proposals. During each discussion, a panelist who was not assigned to read the proposal is assigned to be a scribe and record the highlights of each discussion. Each panelist is a scribe on 3-4 proposals.
The final step is for each panelist to write up a summary of the panel discussions for which they were a scribe, highlighting what the panel thought were the strengths and weaknesses of the proposal, indicating “which column” the panel placed the name, and reflecting the extent to which there was uniform agreement or not. Everyone then goes over these summaries to confirm that the summary does reflect the panel discussion. If you ever apply for a grant, you will be able to read this summary, together with the evaluation of the three members who read your proposal in depth. (The panelists assigned to your proposal have an opportunity to modify their evaluations during the meeting if they change their minds in light of the discussion.)
Then the panel ends; the panel has given the program officer a (roughly) ordered set of names, and it is up to the NSF to decide whom to fund. I’m not sure the extent to which the recommendations of the panel exactly mirror the actual results, although I suspect that it is quite close. I can imagine, however, that a programme officer feels that a certain proposal suffered because nobody on the particular panel was an expert in that area, and they may decide to send that proposal off for further review. The Hawk says: The actual results can deviate significantly from the advice of the panel. I think it’s safe to say that the ‘highly recommended’ proposals always get funded. After that, there are various other objectives that the program officers are trying to achieve — gender diversity, racial diversity, support for young PIs, support for worthy PIs at undergraduate-only institutions. The panel list is typically the default in cases where none of those other objectives apply, though you can imagine reasons to deviate from it (e.g. you might not let the same person suffer the bad luck of being the first person after the cutoff two years running, you might support a proposal in a subdiscipline that has otherwise been shut out, etc). So in the ‘recommended’ zone there are certainly some inversions. It’s also not unheard of for a ‘not recommended’ proposal to end up being funded. One way this can happen is for the proposal to be looked at by a second (perhaps more appropriate) panel that likes the proposal much better. But also, the program officers can simply decide that the panel’s conclusions about a proposal were unjust for some reason, and raise the proposal up in the rankings.
How narrow is the focus of each panel? As I mentioned, there are approximately 40-50 proposals for each panel, of which maybe 15 are funded. So take the 80 or so people who are research active and applying for grants who are closest to you mathematically, and that gives you a rough idea. If you study Galois representations and modular forms, or Iwasawa theory, or the arithmetic of Shimura varieties, or arithmetic geometry of some kind, your proposal may well end up in the same panel as mine was (it can happen — as it did to me last year — that your proposal ends up being evaluated by *two* panels — this is possibly done in order to normalize the orderings in some way. Because I wasn’t there, I can’t quite tell what the difference was between the two panels). The Hawk says: This is the first time I’ve heard a suggestion that normalization is the reason that some proposals are looked at by two panels. I think this happens either because the program officers feel that the proposal straddles two panels to such an extent that they feel both opinions could be useful; or because the proposal has two very different parts that genuinely fit in separate panels; or because the assigned panel decided that there were parts of a proposal that they didn’t have the expertise to comment on, and so they suggest getting the input of another panel. On the other hand, I’m pretty sure that my proposal would not be on the same panel as someone like Ken Ono or Soundararajan. Could my proposal be on the same panel as Akshay’s? I’m not sure. I probably would have said no if my proposal didn’t end up on two panels last time. And Akshay is a collaborator of mine! So it’s pretty focused. On the other hand, there are certainly areas in each field which are smaller than others, and if you work in such a sub-field, then it’s more likely that the panelists will not be experts in your area.
Who serves on the panel? First, there are a few NSF rules which apply to panels. (update: this information was wrong — it turns out there are no formal NSF requirements for the constitution of any panel.) Beyond this formal requirement, who is a typical member of the panel? Well, of course, one goal of the program officer is to make the panel is not *too* uniform. But, for example, I would expect that there would always be at least one person on the committee who knows as much (say) about modular forms and Galois representations as I do. So if that is what you do, then you can be pretty sure that whomever that person is will be reading your file. But you can also be sure that someone who is *not* an expert will also be reading your file, perhaps someone in Iwasawa theory, say. And this already should give you a pretty good idea of your target audience. In other words, you have to do two things:
• You have to explain to Iwasawa theory person why the modularity theorems you are going to prove are interesting. When is math interesting? Well, there are plenty of ways it can be interesting. You may have an idea of how to apply previous machinery in a novel way. You may have an interesting application in mind. You may have a completely new approach to an old theorem. You may have a completely new idea on how to solve an open problem. This is what you want to get across when you are talking to Iwasawa theory person — to give a sense of why the general problem you are studying is interesting, and how you are going to make a contribution to that field.
• You have an easier job convincing me (or equivalent) why your modularity theorems are broadly interesting, but you still have to conveince me that you particular proposal is interesting. More importantly, you have to convince me that you can carry out your proposal successfully, or at least to the point of producing interesting mathematics. The Hawk says: I think it would be worth mentioning here the fine line between saying enough about how you intend to carry out your plans that the panel is convinced you can do it, and saying so much that they think you’ve done it already. I think new proposers often struggle on this point.
Of course, if you do something other than what I do, then replace “Iwasawa theory person” above by me or equivalent and “me” by someone with expertise in your field.
What should I take away from this? First up, I think that an NSF grant proposal is probably the most technical audience you will write for in a context that is not one of your research papers. So you don’t need (beyond a cursory mention) to say how modular forms played a role in the proof of Fermat’s Last Theorem which you might do (say) in a job application. Nor do you need to define the class group of a number field, or explain what a modular curve is. But, at the same time, and this is very important, it can still be incredibly useful to place your work in a broader context. For example, on my last NSF proposal, I started out by reminding the reader briefly how there are very general conjectures linking Galois representations coming from geometry to automorphic L-functions. I reminded the reader that special degenerate cases of this conjecture correspond to very classical objects like the Riemann zeta function. I then mention how the work of Wiles addresses the case when the representation comes from the cohomology of an elliptic curve over $\mathbf{Q}.$ Then I explain how all the generalizations of Wiles’ theorem share a common assumption, namely, that the Galois representations over $\mathbf{Q}$ that one can study by this method have the property that they are, up to a twist, self-dual. So already, in perhaps not much more than a half a page, I have given the context to explain how proving that a non-self-dual Galois representation is modular is “interesting.” Of course, then I have to go on an explain *how* I am going to say anything interesting about non-self-dual representations.
Do fat cats just get their grants without trying? Every proposal is evaluated on its merits, but of course “prior success” is taken into account when judging future chances of success, and so it should be. But if Peter Scholze (say, to take someone who is not in the US so I can use his name) sends in an application consisting solely of “I am working on several projects that I decline to disclose but that I expect to be of the same importance as my prior results,” he would not be funded. More realistically, I have heard that it has been the case that fields medalists have been turned down for grants, but because all grants that are turned down are never officially acknowledged, this is just hearsay. My feeling is that, on the whole, the panels do a pretty good job, and (apart from the occasional controversial case) there is more of a uniform agreement than you might guess. The Hawk brings up the key point that this opinion only concerns number theory panels. It may be the case (and I occasionally here rumours to this effect) that other areas are not run as well. I would also say that the fat cats (on the whole) seem to put as much effort into writing their NSF proposals as everyone else.
How can I compete with the fat cats given I’m only just starting out? This is taken into account. If you are at most 6 years from your PhD, your proposal is evaluated in that context; an effort is made to fund promising young people, and also people who have never received prior NSF support. That said, it’s not easy to get a grant the first time you apply coming straight out of a postdoctoral position.
What about broader impact? This is hard for younger people. But everyone on the panel realizes this and so the expectations are lower. You probably don’t have any grad students yet, so what can you say? Perhaps you have given expository talks at a workshop? Perhaps you have written up detailed notes on otherwise hard to access topics? Perhaps you have gone into the public schools in some hardscrabble inner surburban neighbourhood and and taught calculus? (Not the last one? Then don’t suggest that you might if there’s no reason to suspect that you have any previous inclination to do so.)
Don’t Imagine that you are going to be held account for what you say you are going to prove in future proposals. Future proposals will be evaluated on their own merits (as well as prior research), and nobody is going to know or remember what you said in your previous NSF grants. It’s expected that some of problems you are working on might not work out, and that you will have new ideas while working on the proposal.
Two further suggestions from the Hawk:
When will I hear back? Answer: who the hell knows. Usually within six months from the deadline, but not always, especially these days when the federal government is funded from continuing resolution to continuing resolution. If you hear in January, either you are Peter Scholze or it’s bad news. By May, no news is good news: you probably weren’t in the ‘not recommended’ pile, and they’re waiting to see how far they can stretch the money in the ‘recommended’ pile.
If I get the grant, how much money will I get? Answer: probably less than what you asked for in your budget, and if not, you probably didn’t budget enough. Less glib answer: the program officers do adjust the award sizes in order to hit their target funding rates. You shouldn’t fret that if you ask for too much and the person who’s next on the list asks for a lower number, that could hurt your chances. The natural followup: “If program officers have that kind of discretion, wouldn’t it be better if they gave smaller awards to more people?” You can certainly argue that in theory that might be better, but in practice the answer is emphatically no. DMS’s (DMS = division of mathematical sciences at the NSF) funding rate is already much higher than that of other divisions, as high as can politically be sustained within NSF. If the funding rate went up, DMS’s budget would be cut, and the rate would go back down again.
Do you have any other thoughts? The fact that approximately 30% percent of proposals get accepted is a fairly immutable law of nature. It is no doubt depressing to be continually rejected by the NSF, and good people simply stop applying, in some sense making it then harder for everyone else. If, for some reason, the number of applications suddenly doubled, it wouldn’t be the case that the success rate would halve, but more proposals would be awarded. So, there is a real sense in which the more people who apply the more grants are awarded.
Posted in Mathematics, Politics | Tagged , | 6 Comments
## The nearly ordinary deformation ring is (usually) torsion over weight space
Let $F/{\mathbf{Q}}$ be an arbitrary number field. Let $p$ be a prime which splits completely in $F$, and consider an absolutely irreducible representation:
$\rho: G_{F} \rightarrow {\mathrm{GL}}_2({\overline{\mathbf{Q}}}_p)$
which is unramified outside finitely many primes.
If one assumes that $\rho$ is geometric, then the Fontaine–Mazur conjecture predicts that $\rho$ should be motivic, and the Langlands reciprocity conjecture predicts that $\rho$ should be automorphic. This is probably difficult, so let’s make our lives easier by adding some hypotheses. For example, let us assume that:
• A: For all $v|p$, the representation $\rho|G_{v}$ is crystalline and nearly ordinary,
• B: The residual representation ${\overline{\rho}}$ has suitably big image (Taylor–Wiles type condition.)
Proving the modularity of $\rho$ under these hypotheses is still too ambitious — it still includes even icosahedral representations and Elliptic curves over arbitrary number fields. Natural further hypotheses to make include conditions on the Hodge–Tate weights and conditions on complex conjugation.
We prove the following:
Theorem I: Assume, in addition to conditions A and B+, that
• C: The Hodge-Tate weights $[a_v, b_v]$ at each $v|p$ are sufficiently generic,
• D: If $F$ is totally real, then there exists at least one infinite place such that $\rho$ is even.
Then $\rho$ does not exist.
The condition B+ (which will be defined during the proof) is more restrictive than the usual Taylor–Wiles condition — we shall see from the proof exactly what it entails. Condition C will also be explained — but let us note that, for any suitable method of counting, almost all choices of integers are generic, even after imposing some condition on the determinant (say $a_v + b_v$ is constant) to rule out stupidities.
One should think of this theorem as follows. If $F$ is totally real, then condition D should be sufficient to rule out the existence of any automorphic $\rho$ in regular weight, because (for motivic reasons) such representations should be totally odd. On the other hand, if $F$ is not totally real, then the weights of any motive (with coefficients) should satisfy a certain non-trivial symmetry property with respect to the action of complex conjugation. So, for example, if $F$ has signature $(1,2)$, then either condition C or D should be sufficient, but we will require both. In fact, even condition C is stronger than what should be necessary. In addition to assuming regularity at all primes, it amounts to (on the representation theoretic side) insisting that none of the $\mathrm{GL}_2(\mathbf{C})$ weights are fixed by any conjugate of complex conjugation, whereas a single such example should be enough for a contradiction.
Perhaps a useful way to think about Theorem I is to make the following comparison. Hida proves the following theorem:
Theorem [Hida]: The nearly ordinary Hida family for $\mathrm{SL}(2)/F$ is finite over weight space and has positive rank if and only if $F$ is totally real and the corresponding ${\overline{\rho}}$ is odd at all infinite places.
On the other hand, a consequence of Theorem I is:
Theorem II: The fixed determinant nearly ordinary deformation ring of a residual representation ${\overline{\rho}}$ satisfying condition B+ is finite over weight space and has positive rank if and only if $F$ is totally real and the corresponding ${\overline{\rho}}$ is odd at all infinite places.
In both cases, I am only considering the deformation rings up to twist — the deformation ring of the character is torsion over the corresponding weight space whenever $\mathcal{O}_F$ has infinitely many units. Also in both cases, it is of interest to determine the exact co-dimension of the ordinary family — this is a difficult problem, because strong enough results would allow you do deduce Leopoldt by considering induced representations.
OK, so what is the argument? If you have read some of my papers, you can probably guess.
Assume that $\rho$ exists. Let $U$ be the representation corresponding to $\rho$. Now replace $U$ by $V = {\mathrm{Sym}}^2(U)$. Now replace $V$ by the tensor induction:
$\displaystyle{ W = \bigotimes_{G_F/G_{{\mathbf{Q}}}} V}$
of dimension $3^{[F:{\mathbf{Q}}]}$. We now let C be the condition that $W$ has distinct Hodge–Tate weights. To see that this is generic, it really suffices to show that there is at least one choice of weights for which this is true. But one can let the weights of $U$ up to translation consist of the 2-uples $[0,1]$, $[0,3]$, $[0,9]$, etc. and then the weights of $W$ are, again up to translation, $[0,1,2,\ldots,3^{[F:{\mathbf{Q}}]} - 1].$ We now let B+ be the condition that the residual representation is absolutely irreducible, and that the prime $p > 2 \cdot 3^{[F:{\mathbf{Q}}]} + 1$. This is generically true, and amounts to saying that the conjugates of ${\overline{\rho}}$ under $G_{{\mathbf{Q}}}$ are sufficiently distinct. Since the dimension of $W$ is odd, and because it is essentially self-dual (exercise), orthogonal (obvious), nearly ordinary (by assumption), has distinct Hodge–Tate weights (by construction), satisfies the required sign condition (automatic in odd dimension), we deduce that it is potentially modular by [BLGGT]. In order to win, it suffices to show, by a theorem I made Richard prove, that the action of complex conjugation on $W$ has trace $\pm 1.$ However, this is equivalent to condition D (see below). QED.
One can relax condition B+ slightly by only inducing down to the largest totally real subfield of $F$. On the other hand, there are plenty of examples to which Theorem II applies. I think one can take any elliptic curve $E/F$ without CM and such that $j_E \in F$ does not lie in any subfield of $F$, and then take $p$ to be any sufficiently large ordinary prime which splits completely in $F$ (caveat emptor, I didn’t check this). Of course, the condition that $p$ splits isn’t really necessary either, I guess…
The second theorem follows along the exact same lines — the conditions are strong enough to ensure, using results of Thorne, that the nearly ordinary deformation ring of (the now residual) representation $W$ is finite over weight space, which translates back into finiteness of deformations of $U$ over weight space. The result is obvious if $F$ is totally real and ${\overline{\rho}}$ is odd. Otherwise, we choose a sufficiently generic point in weight space (in the sense of C), and then, by Theorem I, we see that the specialization of the nearly ordinary deformation ring at that point must be torsion.
It remains to compute the sign of $W$. This is an exercise in finite group theory, we only recall enough of the details for our purposes. Let $V$ be a representation of $H$ of dimension $d$. Consider the tensor induction:
$\displaystyle{\bigotimes_{G/H} \sigma V}.$
Let $T$ denote a set of representatives of right cosets of $H$ in $G$. Let $t g \in T$ denote the corresponding choice for the coset $Htg$. For $g \in G$, let $n(t)$ denote the size of the $\langle g \rangle$-orbit which contains $T$. If $g = c$ has order $2$, then either $n(t) = 1$ or $n(t) = 2$ Certainly
$t c^{n(t)} t^{-1} \in H, \quad t \in T.$
Let $T_0$ be a set of representatives for the $\langle g \rangle$ orbits on $T_0$. Then (proof omitted)
$\displaystyle{\phi^{\otimes G}(c) = \prod_{t \in T_0} \phi(t c^{n(t)} t^{-1})}.$
We observe that:
1. If $n(t) = 2$, then $\phi(t c^{n(t)} t^{-1}) = \phi(t t^{-1}) = \phi(1) = d$.
2. If $n(t) = 1$, then $tct^{-1} \in H$ and $\phi(t c t^{-1})$ is what it is. For example, it is $0,\pm 1$ if and only if $V$ is ${\mathrm{GL}}$-odd with respect to $tct^{-1}$.
Now suppose that $G = G_{{\mathbf{Q}}}$ and $H = G_{F}$. The elements $tct^{-1}$ are exactly the different complex conjugations of the representations of the conjugates of $H$. We deduce:
1. If $\dim(V)$ is even, then $W$ is ${\mathrm{GL}}$-odd if and only if there exists at least one real place of $F$ such that $V$ is ${\mathrm{GL}}$-odd.
2. If $\dim(V)$ is odd, then $W$ is ${\mathrm{GL}}$-odd if and only if $F$ is totally real and $V$ is ${\mathrm{GL}}$-odd at every real place.
Equivalently, a product of even integers can equal zero only if at least one of them is zero, and a product of odd integers can equal $\pm 1$ if and only if all of them are $\pm 1$.
## Tricky Fingers
How is one supposed to play this exactly?
One can neither can play a 14th in the right hand (my hands are not that big) nor play legato parallel 10ths in the left; hence some sort of arpeggiation is required. But I can’t quite seem to reproduce how Glenn Gould plays this measure. Then again, that phenomenon is not unique to this passage.
Posted in Music | | 3 Comments
## The Artin conjecture is rubbish
Let $\rho: G_{\mathbf{Q}} \rightarrow \mathrm{GL}_N(\mathbf{C})$ be a continuous irreducible representation. Artin conjectured that the L-function $L(\rho,s)$ is analytically continues to an entire function on $\mathbf{C}$ (except for the trivial representation where the is a simple pole at one) and satisfies a functional equation of a precise shape. Langlands later had the profound insight to link this conjecture to functoriality in the Langlands program, which would additionally imply that $\rho$ is automorphic which implies, inter alia, that $L(\rho,s) = L(\pi,s)$ for a cuspidal automorphic representation $\pi$ for $\mathrm{GL}(N)(\mathbf{Q})$.
This is a beautiful and fundamental conjecture. However, it does appear to be completely useless for any actual applications. The most natural application of Artin’s conjecture is to prove … the Cebotarev density theorem. This is why Cebotarev’s density theorem is so amazing! True, one can upgrade the error estimates if one knows Artin, but to do this one also has to know GRH. And if you know GRH, you are not too far away from Artin anyway, because then $L(\rho,s)$ at worst has poles on the critical strip, and so you can (essentially) get close to optimal bounds for Cebotarev anyway.
I thought a little bit about applications of Artin’s conjecture when I wrote a paper about it, but I came up empty. Then recently, I had occasion to look at my paper again, and found to my chagrin that when Springer made the final edit they lopped off a sentence in the statement of one of the main theorems. I guess that’s why the good people at Springer get paid the big bucks. (My best ever copy editing job, by the way, was for a paper in an AMS journal.) In a different direction, I guess it also reflects the deep study of this paper by people in the field that nobody has asked me about it. However, I did notice a statement in the paper that could be improved upon, which I will mention now.
To set the context, let $K^{\mathrm{gal}}/\mathbf{Q}$ be a Galois extension with Galois group $S_5$, and suppose that complex conjugation in this group is equal to $(12)(34)$. Now suppose that $\rho$ is a representation of $\mathrm{Gal}(K^{\mathrm{gal}}/\mathbf{Q})$. We already know that $L(s,\rho)$ is meromorphic, as proved by Brauer and Artin. One thing that can be proven is that, in the particular case above, $L(s,\rho)$ is holomorphic in a strip $\mathrm{Re}(s) > 1 - c$ for some constant $c > 0$ which I described as “ineffective.” But looking at it again, I realized that it is not ineffective at all, due to a result of Stark. What one actually shows is that if $L(s,\rho)$ has a pole in the strip $\mathrm{Re}(s) > 1 - c$, then there must also be another L-function for the same field which has a zero on the real line in this interval. Note that, again from by Artin, it is trivially the case that a pole of one L-function must come from the zero of another L-function, since the product of all such L-functions is the Dedekind zeta function. So the content here is that the offending pole has to be on the real line. One consequence is that, in any particular case, one can rigorously check that the L-function in question has no such zeros, and hence (combined with other results in this paper) that $\rho$ is automorphic. With help from Andrew Booker, I was able to compute one such example (Jo Dwyer has since gone on to compute a number of other examples.) On the other hand, back to the general case, we do have effective results for zeros on the real line! The result in the paper is stated in terms of the existence of a zero of $\zeta_H(s)$ for a certain subfield $H$ of $K^{\mathrm{gal}}$ of degree twelve. (The definition of $H$ was exactly what was swallowed up by Springer, so it’s not actually defined in the paper. To define it, note that $S_5$ has a faithful representation on six points. There is a degree six extension $E$ which is the fixed field of the stabilizer of a point; then $H$ is the compositum of $E$ and the quadratic extension inside $K^{\mathrm{gal}}.$) However, the actual argument produces a zero in an Artin L-factor of $\zeta_H(s)$ which is not divisible by the Dirichlet L-function for the quadratic character of $S_5.$ Stark shows (Some Effective Cases of the Brauer-Siegel Theorem) that such an L-function does not have Siegel zeros, and also gives an explicit estimate for the largest zero on the real line. In particular, for the $L(\rho,s)$ of interest, one deduces that they are analytic on the strip $\mathrm{Re}(s) > 1 - c$ where one can take
$\displaystyle{1 - c = 1 - \frac{1}{4 \log |\Delta_H|}}.$
The result of Stark, BTW, is why one could effectively solve the class number at most $X$ problem for totally complex CM fields which were not imaginary quadratic fields before Goldfeld–Gross–Zagier.
Posted in Mathematics | | 8 Comments
## K_2(O_F) for number fields F
Belabas and Gangl have a nice paper ( Generators and relations for $K_2({\mathcal{O}}_F)$, which can be found here) where they compute $K_2({\mathcal{O}}_E)$ for a large number of quadratic fields $E$. There main result is a method for proving upper bounds for $K_2({\mathcal{O}}_E)$ in a rigorous and computationally efficient way. Tate had previously computed these groups for small imaginary quadratic fields by hand; — the problem is finding an efficient way to do this in general. (Brownkin and Gangl had previously found a non-rigorous way of computing these groups using $K_3({\mathcal{O}}_E)$ and regulator maps, but more on that later.) A good analogy to keep in mind is the problem of computing the class groups of imaginary quadratic fields. In the latter case, however, there are rigorous ways to determine whether an element in the class group is non-trivial, and this is missing from the computation of $K_2({\mathcal{O}}_E)$. To produce lower bounds, [BG] use theorems of Tate and Keune to relate the $p$-primary part of $K_2({\mathcal{O}}_E)$ to class groups of $E(\zeta_p)$, which they can then compute in some cases. One nice example they give is
$K_2\left({\mathbf{Z}} \displaystyle{\left[\frac{1 + \sqrt{-491}}{2} \right]} \right) = {\mathbf{Z}}/13 {\mathbf{Z}}.$
Akshay and I used this as one of the examples in our paper; in our context, it implies that the order of the group
$H_1(\Gamma_0({\mathfrak{p}}),{\mathbf{Z}})$
is always divisible by $13$ where $\Gamma_0({\mathfrak{p}})$ is the congruence subgroup of $\mathrm{PGL}_2({\mathcal{O}}_E)$ for $E = {\mathbf{Q}}(\sqrt{-491})$ and ${\mathfrak{p}}$ is any prime — even though the group $H_1(\Gamma,{\mathbf{Z}}) = ({\mathbf{Z}}/2{\mathbf{Z}})^{26}$ is not so divisible. (Because we are talking about $\mathrm{PGL}$ rather than $\mathrm{PSL}$, the cusps are quotients of tori by involutions, so only contribute $2$-torsion to $H_1.$ This group is occasionally infinite; we use the convention that $\infty$ is divisible by $13.$) It’s always nice to see a theoretical argument come to life in an actual computation — fortunately, Aurel Page was kind enough to compute a presentation for $\Gamma$ in order for us to do this. Now that I think about it, this and many other interesting things didn’t make it into the submitted version of the paper; you’ll have to read the “directors cut” to learn about it.
Alexander Rahm pointed out to me that the computation of $K_2({\mathcal{O}}_E)$ we used was annotated with an asterisk in [BG], meaning that what was proved was only an upper bound. The issue is as follows. Let $p = 13$, and let $F = E(\zeta_p)$, let $G = {\mathrm{Gal}}(F/E) = ({\mathbf{Z}}/p {\mathbf{Z}})^{\times}$, and let ${\mathrm{Cl}}(F)$ denote the class group of $F$. What is required is to show, in light of Tate’s work on $K_2$, is that
$({\mathrm{Cl}}(F)[p])^{G = \chi^{-1}} \ne 0,$
where $\chi: G \rightarrow {\mathbf{F}}^{\times}_p$ is the cyclotomic character. The problem is that $F$ has degree $24$, and it is difficult to compute class groups explicitly in such cases. Let $H = {\mathrm{Gal}}(F/{\mathbf{Q}})$, so there is a canonical decomposition $H = G \times {\mathbf{Z}}/2{\mathbf{Z}}$. There are two extensions of $\chi$ to $H$, given (with some abuse of notation) by $\chi$ and $\chi \eta$, where $\eta$ is the non-trivial character of ${\mathrm{Gal}}(F/{\mathbf{Q}})$. The main conjecture of Iwasawa Theory (Mazur–Wiles) allows one to easily compute minus parts of class groups in terms of $L$-values without actually computing with explicit number fields. However, we should not expect this to help us here. Namely, it’s not hard to show that there is an isomorphism $({\mathrm{Cl}}({\mathbf{Q}}(\zeta_p))[p])^{G = \chi^{-1}} \simeq ({\mathrm{Cl}}(F)[p])^{H = \chi^{-1}}.$ However, the former is trivial by Herbrand’s theorem, because $B_2 = 1/6$ is not divisible by $13$. That leaves us with the problem of proving that $({\mathrm{Cl}}(F)[p])^{H = \chi^{-1} \eta} \ne 0,$ which is a statement about the class group of a totally real cyclotomic extension. Since $\chi \eta^{-1}$ is an even character, we get some savings by working in the totally real subfield $F^{+}$ of degree $12$. Now $\text{\texttt{pari}}$ happily tells me via $\text{\texttt{bnfinit}}$ and $\text{\texttt{bnfclgp}}$ that the class group of this field is ${\mathbf{Z}}/13 {\mathbf{Z}}$, so it looks like we are in good shape. However, $\text{\texttt{pari}}$ has the habit when computing class groups of assuming not only GRH but something stronger. What information does $\text{\texttt{bnfinit}}$ actually contain? It certainly gives, inter alia:
1. The Galois automorphisms of $F^{+}$, using $\text{\texttt{gal:=nfisisom(nf,nf)}}$.
2. A finite index subgroup $V$ of the unit group $U:={\mathcal{O}}^{\times}_{F^{+}}$, using $\text{\texttt{bnfinit[8][5]}}$.
Let me show how, just with this data, one can prove that the relevant part of the class group we are interested in is non-zero. BTW, if you tell $\text{\texttt{pari}}$: can you confirm this answer is really correct? (using $\text{\texttt{bnfcertify}}$) it complains, and says the following:
*** bnfcertify: Warning: large Minkowski bound: certification will be VERY long.
*** bnfcertify: not enough precomputed primes, need primelimit 59644617.
A rough guess (in part) as to what it might be doing: to compute all the invariants necessary for class field theory, one needs to know the full unit group. To do this, one can take the units $V$ found so far and saturate them in the entire unit group $U$. For each prime $q$, one can do this by taking representatives in $V/q V$ and determining whether or not they are perfect $q$th powers. By taking enough primes, on either rules out the existence of such an element, or finds a candidate $v \in V$ and then checks whether it is a $q$th power. On the other hand, from $V$, one can compute a pseudo-regulator $R_V$, which is related to the actual regulator $R_U$ by the unknown index. So to make this computation finite, it suffices to have some a priori bound on the regulator (to give an upper bound on the index), which will ultimately come down to some a priori bound on an $L$-value at one, which GRH probably tells you something useful about.
One can identify the automorphims of $F^{+}$ computed by $\text{\texttt{pari}}$ with the elements of the Galois group given by the corresponding quotient of $H = G \times {\mathbf{Z}}/2{\mathbf{Z}}$ by $(-1,1)$. This group is generated by the image of $\sigma = (2,1) = \mathrm{Frob}_2$, so it is enough to find the automorphism $\sigma$ such that $\sigma \theta - \theta^2 \equiv 0 \mod 2.$ View $\chi \eta$, a character of degree $12$, as being valued in ${\mathbf{F}}^{\times}_{13}$. Now choose a random unit, say $\text{\texttt{u:=bnf[8][5][6]}}$ (Warning! I have a feeling that $\text{\texttt{bnfinit}}$ does something different each time you run it, which means you might have to tweak the choice of index $6$ above if you are doing this at home. And by “you,” I really mean “me” in six months time. I guess I should also tell myself that the relevant $\text{\texttt{pari}}$ file is $\text{\texttt{\~{}fcale/Zagier/BG491}}$.) We may write down a second unit as follows:
$\displaystyle{{\epsilon} = \prod_{i=0}^{12} (\sigma^i(u))^{\chi \eta (\sigma^i)} \in ({\mathcal{O}}^{\times}_F/{\mathcal{O}}^{\times p}_F)^{H = \chi^{-1} \eta}}$
What we have done is apply the appropriate projector in the group ring ${\mathbf{F}}_{13}[H]$ to $u$. Naturally enough, we can lift ${\epsilon}$ to an actual unit in $F^{+}$.
Now choose an auxiliary prime $q$ which splits completely in $F$, say $q = 38299$. I chose this because it actually splits completely in ${\mathbf{Q}}(\zeta_{13 \cdot 491})$, which will make a computation below slightly easier. We reduce ${\epsilon}$ modulo a prime ${\mathfrak{q}}$ above $q$ in ${\mathcal{O}}_{F^+}$ and we find that
${\epsilon}^{(q-1)/13} \not \equiv 1 \mod {\mathfrak{q}}.$
What this last computation proves is that ${\epsilon}$ actually generates
$({\mathcal{O}}^{\times}_F/{\mathcal{O}}^{\times p}_F)^{H = \chi^{-1} \eta}$, which has dimension one by Dirichlet’s theorem. Note also that the inequality above does not depend on the choice of ${\mathfrak{q}}$ — any other choice is conjugate to ${\mathfrak{q}}$ which replaces ${\epsilon}$ by $\sigma {\epsilon}$ and the latter is a non-zero scalar multiple of the former modulo $13$th powers by construction.
On the other hand, let $\zeta$ be a primitive $13 \cdot 491$th root of unity. Then we may consider the projection of $1 - \zeta$ modulo $13$th powers to the $\chi^{-1} \eta$ eigenspace (the latter is naturally also a character on $F(\zeta_{491})$). Remember this eigenspace is generated by ${\epsilon}$. Take $q = 38299$ again, so $q - 1 = 13 \cdot 491 \cdot 6$. Then $2^{6}$ is a primitive $13 \cdot 491$th root of unity modulo $q$. On the other hand,
$\displaystyle{\left(\prod_{({\mathbf{Z}}/13 \cdot 491 {\mathbf{Z}})^{\times}} (1 -2^{6n})^{n \left(\frac{n}{491}\right)} \right)^{(q-1)/13} \equiv 1 \mod q}$
(The exponent of $(1 - 2^{6n})$ is just the value of $\chi \eta(n)$ — remember that the character gets inverted in the projection formula — and that $\eta^{-1} = \eta$.) This implies that the projection of $(1 - \zeta)$ to the $\chi^{-1} \eta$-eigenspace of units modulo $p = 13$ is trivial, because the image of ${\epsilon}^{(q-1)/13}$ computed above was not $1 \mod q$. The same is trivially true for the units in ${\mathbf{Q}}(\zeta_{491})$ and ${\mathbf{Q}}(\zeta_{13})$, because the projection of any unit in a subfield of $F$ can only be an eigenvalue for a character of the correponding quotient of the Galois group. In particular, if $C$ denotes the group of circular units, we have shown that the map
$(C/13 C)^{\chi^{-1} \eta} \rightarrow ({\mathcal{O}}^{\times}_F/{\mathcal{O}}^{\times 13}_F)^{\chi^{-1} \eta}$
is the zero map. This proves that the index of the circular units in the entire units is divisible by $13$. This is enough to prove that $13$ divides $h^{+}_F$, but even better, by the Gras conjecture (also proved by Mazur–Wiles, following Greenberg) it follows that the $\chi^{-1} \eta$-part of the class group is non-zero, and hence, given the previous upper bound, this gives a proof that
$K_2({\mathcal{O}}_E) = {\mathbf{Z}}/13 {\mathbf{Z}}.$
Further Examples: Let’s now look at other examples in [BG]. Consider the following example:
$\displaystyle{K_2\left( {\mathbf{Z}} \left[ \frac{1 + \sqrt{-755}}{2} \right] \right) =^{?} {\mathbf{Z}}/41 {\mathbf{Z}} \oplus {\mathbf{Z}}/2 {\mathbf{Z}}}.$
Let $F = E(\zeta_{41})$, and let $F^{+}$ be the totally real subfield of $F$ of degree $40$. Well we certainly won’t be able to say so much about the class group of $F^{+}$. On the other hand, we can do the latter part of the computation, namely, testing that the $\chi^{-1} \eta$-eigenspace in the circular units looks like it has index divisible by $p$ in the entire units. For example, if $q = 123821 = 1 + 41 \cdot 755 \cdot 4$, we can compute that
$\displaystyle{\left(\prod_{({\mathbf{Z}}/41 \cdot 755 {\mathbf{Z}})^{\times}} (1 -2^{n(q-1)/(41 \cdot 755)})^{n \left(\frac{n}{755}\right)} \right)^{(q-1)/13} \equiv 1 \mod q}$
For good measure, the same congruence holds for the next seven primes which split completely in $F(\zeta_{755})$. (One also has to check that the multiplicative order of $2$ for all these primes is co-prime to $41 \cdot 755$.) But, although this is compelling numerically, it doesn’t prove anything. If ${\epsilon}$ is a generator of $({\mathcal{O}}^{\times}_F/{\mathcal{O}}^{\times p}_F)^{\chi^{-1} \eta}$, it might be the case that ${\epsilon}^{(q-1)/p} \equiv 1 \mod {\mathfrak{q}}$ for ${\mathfrak{q}}$ above the first thousand primes of norm $q \equiv 1 \mod p$. This would simply correspond to a certain ray class group being divisible by $p$. By Cebotarev, we know that we can find some prime $q$ for which this congruence does not hold, but explicit Cebotarev bounds tend to be rubbish in practice.
If we re-think our original computation, what we really want is a “generic” unit of $F^{+}$ in order to project. Since $F$ is abelian, we actually know how to compute a finite index subgroup of the unit group, namely, by projecting (via the norm map) the group of circular units from some cyclotomic overfield. Of course, this exactly won’t be good enough to find a candidate unit ${\epsilon}$. One approach is to take our lattice $V \subseteq U = {\mathcal{O}}^{\times}_{F^+}$ and saturate it. Now we only have to saturate it at $p = 41$. In fact, we only need to saturate the $\chi^{-1} \eta$ eigenspace, which is one dimensional. That is, it suffices to show that
$e_{\chi^{-1} \eta} N_{F(\zeta_{41})/F^{+}} (1 - \zeta)$
is a $p$th power in $F^{+}$. (Before taking the norm, the element is already in $F^{+}$ up to $p$th powers, and $[F(\zeta_{41}):F^{+}]$ has order prime to $41$.) But if I ask $\text{\texttt{pari}}$ to compute the following:
$\displaystyle{\left(\prod_{({\mathbf{Z}}/41 \cdot 755 {\mathbf{Z}})^{\times}} (1 -\zeta^n)^{n \left(\frac{n}{755}\right)} \right)^{(q-1)/13} \mod \Phi_{41 \cdot 755}(\zeta)}$
it complains and conks out. Well, probably René Schoof could do this computation, but let’s think about these things a little differently.
Higher Regulators: So far, we’ve been relying on the fact that the fields $E$ we are considering are abelian, in order to be able to explicitly write down some finite index subgroup of the full unit group using circular units. But what if we want to compute $K_2({\mathcal{O}}_E)$ for non-abelian fields $E$? For this, I want to talk about an earlier paper of Gangl with Brownkin ( Tame and wild kernels of quadratic imaginary number fields… oh bugger, this should also be cited as [BG].) Their approach is through the study of higher regulators. Borel constructs a higher regulator map for odd $K$-groups (the even ones are trivial after tensoring with ${\mathbf{Q}}$). For imaginary quadratic fields and $K_3$, this amounts to a map
$K_3(\mathcal{O}_E) \rightarrow (2 \pi i)^2 \cdot \mathbf{R},$
where the co-volume of the image is a rational multiple of $\zeta_E(2)$. The Quillen–Lichtenbaum conjecture predicts that the covolume differs exactly from $\zeta_E(2)$ by a factor coming from the torsion in $K_3({\mathcal{O}}_E)$, which has order dividing $24$, some slightly mysterious powers of $2$ which I will ignore, and — the most relevant term for us — the order of $K_2({\mathcal{O}}_E)$. Now the Quillen–Lichtenbaum conjecture is true. So how does this help to compute anything? Well, first one has to ask how to compute $K_3({\mathcal{O}}_E)$. As an abelian group, it is easy to compute, but this is not enough to compute the regulator map. One could give explicit classes in $\pi_3(\mathrm{BGL}({\mathcal{O}}_E)^{+})$, of course, but that may not be the most practical approach. It turns out that the group $K_3$ is computable in a natural way because of its relation to the Bloch group $B(E)$, due to theorems of Bloch and Suslin. (That is, via the Hurewicz map we get classes in $H_3(\mathrm{GL}_N({\mathcal{O}}_E),\mathbf{Z})$ which turn out to be seen by $\mathrm{GL}_2.$) To recall, the Bloch group is defined as the quotient of the pre-Bloch group:
$\displaystyle{ \sum n_i [x_i], x_i \in E^{\times}, \ \text{such that} \ \sum n_i (x_i \wedge (1 - x_i)) = 0 \in \bigwedge^2 E^{\times}}$
by the $5$-term relation
$\displaystyle{[x] - [y] + \left[\frac{y}{x} \right] - \left[ \frac{1-y}{1-x} \right] + \left[ \frac{1 - y^{-1}}{1 - x^{-1}} \right] = 0, x,y \in E^{\times} \setminus 1}.$
Now the Bloch group admits a very natural regulator map
$B(E) \rightarrow {\mathbf{R}}^{r_2}$
(where $E$ has signature $(r_1,r_2)$) given by (under the various complex embeddings) the Bloch–Wigner dilogarithm
$D(z) = \mathrm{Im} (\mathrm{Li}_2(z)) + \arg(1-z) \log |z| \in \mathbf{R}.$
Now all of this is (almost) very computable. Namely, one can replace $E^{\times}$ by the $S$-units of ${\mathcal{O}}_E$ for some (as large as you can) set $S$, compute the pre-Bloch group, then do linear algebra to find the quotient. Since (roughly) $K_3({\mathcal{O}}_E) = {\mathbf{Z}}^{r_2} \oplus T$ for an easy to understand finite group $T$ which has order dividing $24$, as soon as one has a enough indepdenent elements in the Bloch group (which can be detected by computing $D(z)$) you can compute a group $B_S(E)$ which has finite index in $B(E)$. Moreover, the dilogarithm is also easy to compute numerically, and so one can compute a regulator $D_S(E)$ coming from the Bloch group. Now this regulator map is known to be rationally the same as Bloch’s regulator map (by Suslin and Bloch). Assuming this is also true integrally, we expect there to be a formula:
$\displaystyle{\frac{3 |d_E|^{3/2}}{\pi^2 D(E)} \cdot \zeta_E(2) =^{?} K_2({\mathcal{O}}_F)},$
at least for primes $p > 3$. (The $3$ is coming from the torsion of $K_3$, and this formula is probably only true up to powers of $2$ — this formulation above comes from Brownkin–Gangl.) For $S$ big enough, $D_S(E)$ should stabilize to $D(E)$, which gives a method of computing the order of $K_2({\mathcal{O}}_E)$. This is what Brownkin and Gangl do. There are two issues which naturally one has to worry about. The first is that it’s not known that the regulator map coming from dilogarithms is the same on the nose as Bloch’s map. However, even granting this (and it should be true), this algorithm will not certifiably end, because one can never be sure that $D_S(E) = D(E)$. If you compare this to the computation that $\text{\texttt{pari}}$ is doing with the class group, the problem is that there is no a priori bounds on the size of the corresponding regulators. Well, I guess this algorithm can sometimes end, namely, when one can be sure if the indicated upper bound for $K_2({\mathcal{O}}_E)$ matches with a known lower bound. However, we are exactly in a situation in which we are trying to prove a lower bound. For example, when $E = {\mathbf{Q}}(\sqrt{-755})$, Brownkin and Gangl predict that $|K_2({\mathcal{O}}_E)| = 2 \cdot 41$ because, for a set of larger and larger primes $S$, the index formula above stabilizes. So, beyond the issue of relating two different higher regulator maps, we have the problem of determining whether a class in $K_3({\mathcal{O}}_E)$ is divisible by a prime $p$ or not. This seems harder than our previous problem of determining whether a unit was divisible or not! (To be fair, however, it seems impossible to find units in $E(\zeta_p)$ once $E$ is non-abelian and $p$ is in any sense large.)
Chern Class Maps: We want to understand whether a class in the Bloch group $B(E)$ or in $K_3({\mathcal{O}}_E)$ is divisible by $p$ or not. Instead of working over ${\mathbf{R}}$, another approach is to work modulo a prime $q$. (It may seem a little strange to work modulo $q$ to detect divisibility by $p$, but bear with me.) Soulé constructed certain Chern class maps, which include a map:
$c_2: K_3({\mathcal{O}}_E) = K_3(E) \rightarrow H^1(E,{\mathbf{Z}}_p(2)).$
These maps are the boundary map in the Atiyah–Hirzebruch spectral sequence for étale $K$-theory. Now compose this maps with the reduction modulo $p$ map. Then, after restricting to $F = E(\zeta_p)$, we may identify ${\mathbf{Z}}_p(2)/p$ with $\mu_p$, and so, by Kummer and Hilbert 90, we get a map:
$c_2: K_3(\mathcal{O}_E)/p \rightarrow H^1(F,\mathbf{Z}_p(2)/p) \simeq H^1(F,\mathbf{Z}_p(1)/p) = F^{\times}/F^{\times p}.$
Keeping track of the various identifications, the image lands in the $\chi^{-1}$ invariant subspace, where $\chi$ is the cyclotomic character of $G = {\mathrm{Gal}}(F/E)$.
Lemma Let $p > 3$ be a prime which is totally ramified in $E(\zeta_p)/E$ and suppose that $p$ does not divide the order of $K_2({\mathcal{O}}_E)$. Then the Chern class map induces an isomorphism
$({\mathbf{Z}}/p {\mathbf{Z}})^{r_2} = K_3({\mathcal{O}}_E)/p K_3({\mathcal{O}}_E) \rightarrow ({\mathcal{O}}^{\times}_F/{\mathcal{O}}^{\times p}_F)^{\chi^{-1}}.$
That is, the image of $c_2$ in $F^{\times}/F^{\times p}$ may be taken to land in the unit group, and the ranks of all the groups are the same and equal to $r_2$, the number of complex places of the field $E.$
This lemma follows from Quillen–Lichtenbaum, but it can also be proved directly from the surjectivity of the Chern class map as proved by Soulé, the known rank of $K_3 \otimes {\mathbf{Q}}$ by Borel, and some knowledge of the torsion of $K_3$ proved by Merkuriev and Suslin. It turns out that the hypothesis on $K_2({\mathcal{O}}_E)$ is necessary not only for the proof but for the lemma to be true.
To detect whether a class in $K_3$ is divisible by $p$, it suffices to “compute” the Chern class map above and see whether it is zero. If one ever wants to compute anything, it makes sense to work with the Bloch group $B(E)$ instead. On the other hand, it seems hopeless to give a “concrete” map:
$B(E) \rightarrow F^{\times}/F^{\times p}.$
Even though one can write down elements in the first group somewhat explicitly, it’s hard to imagine a recipe that would produce explicit elements in $F^{\times}$ with the correct Galois action.
Instead, what we do is reduce modulo $q$ for some prime $q \equiv -1 \mod p$. That is, we pass from the Bloch group over $E$ (which will be generated by $S$ units for some $S$) to the Bloch group of the field ${\mathbf{F}}_q$. The construction over ${\mathbf{F}}_q$ is just the same. By a theorem Hutchinson, this group will have order $q+1$. The numerology here is intimately related to Quillen’s result that $K_3({\mathbf{F}}_q) = {\mathbf{Z}}/(q^2 - 1){\mathbf{Z}}$. Now there are some commutative diagrams one has to check commute here; I think the key point to keep in mind is that Quillen’s computation of $K_3({\mathbf{F}}_q)$ can already be realized in the cohomology group $H^3({\mathrm{SL}}_2({\mathbf{F}}_q),{\mathbf{Z}})$, and so the map of Bloch groups will be the same as the map on $K$-groups via comparison with the Hurewicz map.
Let’s choose a prime $q \equiv -1 \mod p$ which splits completely in $E(\zeta_p + \zeta^{-1}_p) \subset F = E(\zeta_p)$. So we have a map $B(E) \rightarrow B({\mathcal{O}}_E/{\mathfrak{q}}) \otimes {\mathbf{F}}_p = B({\mathbf{F}}_q) \otimes {\mathbf{F}}_p = {\mathbf{F}}_p.$ The Bloch group can be thought of in terms of (a quotient of a subgroup of) the free abelian group of elements of $\mathbf{P}^1(E)$, so there’s no issue about this reduction map. Moreover, given an element of the Bloch group, we can explicitly compute its image in the latter group. If this image is non-zero, that gives a certificate that the original element is not divisible by $p$. This will be enough to compute $K_2({\mathcal{O}}_E)$ as long as the Bloch regulator map agrees with the dilogarithm map.
This argument is still yoked to real regular maps. Let’s try to work entirely with $c_2$ and finite auxiliary primes $q \equiv - 1 \mod p$. Another manifestation of the map $B(E) \rightarrow B({\mathbf{F}}_q) \otimes {\mathbf{F}}_p$ is the map:
$c_2: K_3({\mathcal{O}}_E) \rightarrow {\mathcal{O}}^{\times}_F/{\mathcal{O}}^{\times p}_F \rightarrow ({\mathcal{O}}_F/{\mathfrak{Q}})^{\times} \otimes {\mathbf{F}}_p = {\mathbf{F}}_p,$
where ${\mathfrak{Q}}$ is a prime above ${\mathfrak{q}}$ in $F$. Let’s go back to considering the case when $E$ is an imaginary quadratic field. The image of a generator of $K_3({\mathcal{O}}_E)$ will map exactly to a non-zero multiple of the non-trivial element unit ${\epsilon} \in F^{\times}/F^{\times p}$. If $K_2({\mathcal{O}}_E)$ is prime to $p$, it will even land in $({\mathcal{O}}^{\times}_F/{\mathcal{O}}^{\times p}_F)^{\chi^{-1}}$. The latter map is exactly computing (up to a non-zero scalar) ${\epsilon}^{(q-1)/p} \mod {\mathfrak{q}},$ and so, purely using the Bloch group, we can check whether this is trivial or not. In particular, given an element of the Bloch group $B(E)$ which (we think) is a generator, or at least not divisible by $p$, we can find a prime $q \equiv -1 \mod p$ such that the reduction to $B({\mathbf{F}}_q) \otimes {\mathbf{F}}_p$ is non-zero, which will imply that the image of $c_2$ is non-zero, which will imply that
${\epsilon}^{(q-1)/p} \not\equiv 1 \mod p.$
This gives an explicit value of $q$ for which this is true without ever having to compute ${\epsilon}$. For such a prime $q$, we can then check that the circular units project to the identity in this space, which will prove unconditionally that $K_2({\mathcal{O}}_E)$ is divisible by $p$. (Part of this computation assumed that $p$ did not divide $K_2({\mathcal{O}}_E)$, but that’s OK, because to prove that $p$ does divide this group we are allowed make that assumption anyway). Back to our example. We now want a prime $q \equiv -1 \mod 41$, which is also a square modulo $755$. We take $q = 163$. Now this is not the most attractive computation in the world, because the root of unity $\zeta$ of order $37 \cdot 755$ cuts out the extension ${\mathbf{F}}_{q^{300}}$, as we can see by computing the multiplicative order of $q = 163$ modulo $41 \cdot 5 \cdot 151$. Let’s do it in baby steps. By choosing a suitable prime ${\mathfrak{Q}}$ in $E(\zeta_{755})$, we can ensure that
$\zeta^{755} + \zeta^{-755} = \zeta_{41} + \zeta^{-1}_{41} \equiv 4 \mod {\mathfrak{Q}}.$
We write
$\zeta^{1510} - 4 \zeta^{755} + 1 = F(\zeta) G(\zeta) \mod 163,$
where $F(\zeta)$ is any of the four factors of degree $300$ (there are also two factors of degree $150$, and factors of degrees $2$, $4$, and $4$.) Now we want to compute, with $p = 41$, $q = 163$, and $r = 755$,
$\displaystyle{\eta:= \left(\prod_{({\mathbf{Z}}/p r {\mathbf{Z}})^{\times}} (1 -\zeta^n)^{n \left(\frac{n}{r}\right)} \right)^{(q^{300}-1)/p} \mod \mathfrak{Q} = (163,F(\zeta))}$
Of course, one should first reduce the exponents $\chi^{-1} \eta(n) = n (n/r)$ modulo $p = 41$ before taking the powers. (Actually, it’s probably kind of stupid to take a product over $\varphi(pr) = 24000$ different terms, and one can surely set this up much more effeciently, but whatever.) We find (drum roll) that:
$\eta \equiv 1 \mod 163.$
To finish, we have to take an element in the Bloch group $B({\mathcal{O}}_E)$ and show that it doesn’t vanish in $B({\mathcal{O}}_E/{\mathfrak{q}}) \otimes {\mathbf{F}}_p = B({\mathbf{F}}_{163}) \otimes {\mathbf{F}}_{41}$. At this point, I email Herbert (Gangl), and he sends me an email with the following beautiful element of $B(E)$, where $\alpha^2 = - 755$:
$\displaystyle{-8 \left[\frac{3 - \alpha}{10}\right] - 10 \left[\frac{7-\alpha}{10} \right] - 8 \left[\frac{3 - \alpha}{100} \right] + \ldots + 6 \left[\frac{7 \alpha + 221}{972} \right]}.$
(There are $114$ terms in all! This should be a generator of $B(E).$) Into my $\text{\texttt{magma}}$ programme it goes, which cheerily reports that the image of this element is non-zero in $B({\mathbf{F}}_{163}) \otimes \mathbf{F}_{41}$! So $K_2$ is really divisible by $41$. (You might question the veracity of my programme’s output, but more on that below.)
Stark and Beyond: Here are some more general remarks. Let’s still suppose that $E$ is imaginary quadratic. Take the image of a generator $[M]$ of $B(E)$, which is defined up to torsion and up to sign. The image of the Chern class map for some $p > 3$ and $p$ not dividing $K_2({\mathcal{O}}_E)$ gives a canonical unit in ${\mathcal{O}}^{\times}_F/{\mathcal{O}}^{\times p}_F$, where $F = E(\zeta_p)$. Let me a be a bit more careful here: by writing $F$ as $F = E(\zeta_p)$, we are choosing a root of unity (this unit depends on this choice). There’s also an automorphism of ${\mathrm{Gal}}(E/{\mathbf{Q}})$ which acts, but this changes the sign of $[M]$, so that is the same ambiguity we had before. What is this canonical unit? It is not just a circular unit, but a canonical one (modulo $p$th powers). What is it? More generally, when $r_2 = 1$, both $K_3$ and $(\mathcal{O}^{\times}_F/\mathcal{O}^{\times p}_F)^{\chi^{-1}}$ have rank $r_2 = 1$, so if $p$ is prime to $K_2(\mathcal{O}_E)$ we are generating canonical units. It’s tempting here to conjecture some relation to Stark units here, and in particular to the special value of $L(1,E,\chi^{-1})$, but let me say no more about this. When $r_2 > 1$, one is no longer in the Stark world, but there is still a canonical map from the Bloch group to the unit group (the group $\mathbf{Z}^{r_2}$ has no canonical generator when $r_2 > 1$ — but in the manifestation of this group as a Bloch group, one does have explicit elements.)
Actually, I haven’t even explained how to compute $c_2$. So far, I have only explained how to compute whether it is zero or not modulo $p$. To evaluate it exactly requires a further threading of the needle through the previous maps (on the Bloch group), and ultimately uses a test element coming from torsion in $B({\mathbf{Q}}(\zeta_p + \zeta^{-1}_p))$. Although this is somewhat delicate, and I have not yet proved all of the appropriate diagrams commute (blech), one can work with it in practice and it gives many consistency checks on all the computations. (So, for example, once one has the image of $c_2$, one can compute the reduction of the corresponding element in the Bloch group in $B({\mathbf{F}}_{q}) \otimes {\mathbf{F}}_p$ for one prime $q \equiv -1 \mod p$ knowing its image in the corresponding group for another such prime. Generating the same element of $\mathbf{F}_p$ for $p = 13$ and twenty different primes $q$ is pretty convincing.)
In fact, computing this map exactly is exactly the problem that I was thinking about in the first place. I did compute it explicitly for $K = {\mathbf{Q}}(\sqrt{-491})$ and $p = 13$ (and also $K = {\mathbf{Q}}(\sqrt{-571})$ for $p = 5$), and the image of a generator of the Bloch group is not a unit. Instead, it gives a generator of $\frak{a}^{13}$ for a non-trivial ideal in the class group ${\mathrm{Cl}}(F)$ of $F = E(\zeta_p)$, indeed, an element of ${\mathrm{Cl}}(F)[p]^{\chi^{-1} \eta}$. (In particular, it gives, having fixed a root of unity, a canonical element of this class group, which is also somewhat mysterious.) Let me also mention the Coates–Sinnott conjecture, higher Stickelberger elements, and work of Banaszak and Popescu which are closely related to the topics in this post (in particular, using Chern class maps to construct Euler systems generalizing the circular unit Euler system, although not so much question of identifying these elements in some explicit way — especially because much less is known about higher analogues of the Bloch group). But perhaps this is enough for now.
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Matrix Calculation Efficiency
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Hi Guys,
At present, I send the W, V, & P matrices to the shader where they are multiplied within the shader to position vertices.
Would it be more efficient to pre-multiply these on the CPU and then pass the result to the shader?
Thanks in advance :)
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Do not prematurely optimize things, you might end up having to switch to the other method later. Profile and test things, that is what will make the best determination. There are very, very few steadfast rules about this stuff, it is highly dependent upon what you're doing code wise, and the data you're pumping through the CPU/GPU, etc.
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It's my premature optimisation that is allowing me to be able to render so much in the first place.
I was just wondering what the normal practice was.
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Simple answer: yes - doing multiplication once ahead of time, in order to avoid doing it hundreds of thousands of times (once per vertex) is obviously a good idea.
However, there may be cases where uploading a single WVP matrix introduces its own problems too!
For example, lets say we have a scene with 1000 static objects in it and a moving camera.
Each frame, we have to calculate VP = V*P, and then perform 1000 WVP = W * VP calculations, and upload the 1000 resulting WVP matrices to the GPU.
If instead, we sent W and VP to the GPU separetely, then we could pre-upload 1000 W matrices one time in advance, and then upload a single VP matrix per frame.... which means that the CPU will be doing 1000x less matrix/upload work in the second situation... but the GPU will be doing Nx more matrix multiplications, where N is the number of vertices drawn.
The right choice there would depend on the exact size of the CPU/GPU costs incurred/saved, and how close to your GPU/CPU processing budgets you are.
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Yes. Multiply once outside is the way to go. If it's doing something static like rendering landscape then yes. A bit more tricky if its your game entities. In that case you need to weigh up instancing for translation and orientation of objects vs updating the matrix on the fly each draw call.
For static yes. For dynamic in low numbers yes. More murky when you start dealing with alot of objects.
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Thanks guys!
In my case just about all of the geometry will be pre-transformed in my 3D package. So, there won't be any additional rotations, scaling, etc to do either.
Thanks for the advice.
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Yes.
And no, no, no, no, no: this is not premature optimization, it's engineering for efficiency, they're not the same thing and don't listen to anyone who tells you different.
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I got a similar question about fine performance measurment:
Imagine I have in Geometry Shader two loops with known compile-time consts:
for (x = 0; x < 4; ++x) {
for (y = 0; y < 3; ++y{
... DoStuff();
}
}
This code in release mode gives me "Approximately 22 instruction slots used" (VS compiler will output this info)
If I would place [unroll] before each loop, I would have "Approximately 89 instruction slots used".
Right now I can measure time in NSight's "Events" window with nonosec-precision and can’t see performance gain between the shaders.
Is there a way to measure the difference in a finer way?
The question is similar, because measurement perf. diff in such optimizations (2 matrices vs 1, unroll/not unroll) requires some tool to measure the difference.
Edited by Happy SDE
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If you can't see any perf difference it might just be because you're bottlenecked elsewhere; e.g. you might be CPU-bound.
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If you can't see any perf difference it might just be because you're bottlenecked elsewhere; e.g. you might be CPU-bound.
No, I am not CPU bound at all.
This code calculates 4 Shadow Maps in one pass, which is faster, that 4 separate calls (I can see difference in NSight, because it is significant like 50-200% win dependent on quality settings).
This is a macro-optimization.
But passing unroll or 1/2 matrices is a micro optimization, which might give me something.
And with current tools I am aware of I can't detect it =(
One option - is to calculate instruction count.
But as I understand:
1. Each instruction has it's own cost and just summing them up is not a good idea.
2. NSight's measurement on same scene, with same shader, gives me error about 0.2% between passes.
So I am keep searching for a tool that will give me ability to measure micro-optimization perf.
The main reason for that: find (and measure) a good practice once, and after that apply it elsewhere without unnecessary code bloating because of some unmeasured speculations.
Edited by Happy SDE
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# Bruteforce Keys from GET Input with mechanize
My Script tries to find a password, using a brute force approach. The password is then tried using a GET call to a website. I'm not happy with the way the script looks, particularly the number of variables I have had to use for such a small validation.
import mechanize
import itertools
import string
br = mechanize.Browser()
response = br.open(url)
cnt = 0
pat = "invalid {}Invalid"
acc = string.ascii_letters + "0123456789!@#\$%^{}()[]"
combinations = itertools.permutations(acc,cnt+1)
res = ""
a = "x"
b = "x"
c = "x"
d = "x"
bb = "x"
cc = "x"
dd = "x"
while True:
combinations = itertools.permutations(acc,1)
for x in combinations:
x = "".join(x)
if a == "x":
aa = x
elif b == "x":
bb = x
elif c == "x":
cc = x
elif d == "x":
dd = x
response = br.open(url.format(aa,bb,cc,dd))
if "flag" in cek:
print cek
break
if pat.format(cnt+1) in cek:
cnt += 1
if a == "x":
a = x
elif b == "x":
b = x
elif c == "x":
c = x
elif d == "x":
d = x
#print x
You should consider more characters. While the whole string.printable is probably too much (tab is usually not allowed), you should consider
characters = (string.letters, string.digits, string.punctuation)
I wrote it not as one long string because string addition is costly. We can just use itertools.chain(characters) later.
Your whole permutation code boils down to:
n = 4 # Hard-coded in url in your code.
br = mechanize.Browser()
url_template = "http://128.199.96.39/?password=" + "{}" * n
Your code does not need to build the permutations itself, it can rely directly on itertools.permutation to give it the correct password tuple. I actually don't understand the whole using 'x' as a place holder.
Having n as a parameter like above allows you to also loop over different password lengths:
import mechanize
import itertools
import string
def check_response(response):
"""Checks whether we are logged in yet"""
return False # Implementation left as an exercise
if check_response(response):
return None
def brute_force(url, characters, max_length=8)
browser = mechanize.Browser()
for n in range(max_length): # Also try empty password, we might be lucky
break
if __name__ == "__main__":
characters = (string.letters, string.digits, string.punctuation)
Note that it will take a very long time to run through all $\approx 6.7\times 10^{15}$ combinations for a character length of 8 characters. It will still take a long time to make all $\approx 8.1\times 10^{7}$ requests for a 4 character password.
You might want to test other packages for the web requests, because they are going to be your bottle-neck. Maybe try the requests module.
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# How to stop an animation on last frame until condition is met in Unity?
I have an animation (fishing) I want to play backwards when the player catches something or cancels the action.
Playing the animation backwards is as simple as setting the speed to -1, ie:
anim.SetFloat("direction", -1.0f);
However, my fishing animation keeps playing until I have caught something, or cancel the animation. This means that the last frame of the animation is showing, but the time of the animation is still going.
So
• the animation reaches the last frame
• then I stand there for 8 seconds,
• I catch something, so I change anim speed to -1
• anim will now reverse those 8 seconds I was "standing still" first, before it even reaches the actual animation.
I need to stop the animation time on the last frame (without leaving the animation), so that reverse will be instant. And to not exit the animation until the reverse is finished. Maybe there is some other way to do it, but I can't figure it out.
I could create a seperate animation for when I want it to go backwards, but that seems sloppy.
//create parameters in the animator and update from a player state or some sort of controller script.
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# Filtration of stopping time equal to the natural filtration of the stopped process
Given a probability space $(\Omega,\mathcal{F},P)$ and a process $X_{t}$ defined on it. We consider the natural Filtration generated by the process $\mathcal{F}_{t}=\sigma (X_{s}:s\leq t)$. Let $\tau$ be a stopping time. The corresponding $\sigma$-Algebra of the stopping time $\tau$ is given by \begin{align} F_{\tau}=\left\{A\in \bigcup_{t\geq 0} F_{t}: A\cap\{\tau \leq t\}\in \mathcal{F}_{t} \forall t\geq 0\right\} \end{align} Now i am considering the requirements under which \begin{align} \mathcal{F}_{\tau}=\sigma (X_{s\wedge \tau }:s\geq 0) \end{align} holds.
Shiryaev "Optimal Stopping Rules" Stochastic Modelling and Applied Probability 8 in Springer 2008 makes the assumptions, that $\Omega$ has to be sufficiently rich, that means for all $t\geq 0$ and $\omega \in \Omega$ there exists $\omega'\in\Omega$ such that \begin{align} X_{s}(\omega')=X_{s\wedge t}(\omega) \forall s\geq 0 \end{align} holds; see Theorem 6 of Shiryaev. Then $\mathcal{F}_{\tau}=\sigma (X_{s\wedge \tau }:s\geq 0)$ should hold. Shiryaev shows this for arbitrary measurable space, and measurable process $X$ fullfilling this condition.
Also D. Stroock, S. Varadhan "Multidimensional Diffusion Processes" Lemma 1.3.3 proofs it, where here $\Theta$ is the space of continuous trajectories from $[0,\infty)$ to $\mathbb{R}^{d}$. In the proof Stroock also uses the assumption of the sufficiently richness of $\Omega$ under $X$, but he mentions it incidental, as if it would be clear for continuous $X$.
I guess, that this property also holds for cadlag processes $X$ i.e. fullfilling \begin{align} \mathcal{F}_{\tau}=\sigma (X_{s\wedge \tau }:s\geq 0) \end{align} But i dont know, how it is fullfilled.
The "saturation" property assumed by Shiryaev is indeed clear for $\Omega$ consisting of the space of cadlag paths from $[0,\infty)$ to $\Bbb R^d$, and $X_t(\omega)=\omega(t)$ for $t\ge0$ and $\omega\in\Omega$. For, given $t\ge 0$ and $\omega\in\Omega$, define $\omega'$ to be the path "$\omega$ stopped at time $t$"; that is, $\omega'(s):=\omega(s\wedge t)$ for $s\ge 0$. This path $\omega'$ is clearly an element of $\Omega$, and $X_{s\wedge t}(\omega) =\omega(s\wedge t) =\omega'(s)=X_s(\omega')$ for each $s\ge 0$.
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Elementary Technical Mathematics
Published by Brooks Cole
Chapter 6 - Section 6.4 - Equations with Fractions - Exercises - Page 247: 41
Answer
x=$\frac{1}{7}$
Work Step by Step
determine the defined range convert mixed numbers to an improper fraction move terms rewrite cross multiply switch the sides Divide both sides by -98
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.
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# Python Percentile Without Numpy
add a percentile field to the table 5. It is a convention to import NumPy as follows:. reshape does not change the order of or the total number of elements in the tensor, and so it can reuse the underlying data buffer. Computation on NumPy arrays can be very fast, or it can be very slow. The user-defined function can be either row-at-a-time or vectorized. NumPy, short for Numerical Python, is the fundamental package required for high performance scientific computing and data analysis. **kwargs: Named arguments forwarded to subclass implementation. 6 for python 2. It depends on the data structure you’re working with. Python File Handling Python Read Files Python Write/Create Files Python Delete Files Python NumPy Getting Started Mean Median Mode Standard Deviation Percentile Data Distribution Normal Data Distribution Scatter Plot Linear Regression Polynomial Regression without repetition, also known as combinations. By voting up you can indicate which examples are most useful and appropriate. percentile on the data within a MonetDB table. The build-in package NumPy is used for manipulation and array-processing. Python’s Pandas Library provides an member function in Dataframe class to apply a function along the axis of the Dataframe i. Variance in NumPy. You've gotten a handful of nice examples of how to do what you want. The numpy Package. tolist() for i in range(nd - 1, 0, -1): if pr[i] > pr[i - 1]: pr[i - 1] = pr[i] #discretize empiric recall steps with given bins. datetime objects. Python Script. NaN (NumPy Not a Number) and the Python None value. x,numpy,pandas,datetime64. However, for comparison, code without NumPy are also presented. Correctly preparing your training data can mean the difference between mediocre and extraordinary results, even with very simple linear algorithms. This is one of the 100+ free recipes of the IPython Cookbook, Second Edition, by Cyrille Rossant, a guide to numerical computing and data science in the Jupyter Notebook. Aloha I hope that 2D array means 2D list, u want to perform slicing of the 2D list. Numpy Tutorial Part 1: Introduction to Arrays. ndarray) – Observed data. The code is simple and it handles by the Numpy package without hassle. Let's use Python to show how different statistical concepts can be applied computationally. It's common when first learning NumPy to have trouble remembering all the functions and. 0) for advanced data analysis, modeling and machine learning • Advanced in using Tableau, Datorama and Data Studio for data visualization. Return a copy of the array data as a (nested) Python list. ) Importing numpy. NumPy - Introduction. Python Certification is the most sought-after skill in programming domain. If the input contains integers or floats smaller than float64, the output data-type is float64. Note that a call to sample() without arguments will generate a single sample. Python In Greek mythology, Python is the name of a a huge serpent and sometimes a dragon. 0b1 #5154: 0. It is possible to call NumPy and SciPy from IronPython now by using IronClad. strings or timestamps), the result’s index will include count, unique, top, and freq. Thus in such situations user needs to specify whether it is a copy or a view otherwise Python may hamper the results. 6+ with no other dependency. An approach to doing this in ArcGIS would be 1. It's common when first learning NumPy to have trouble remembering all the functions and. Without Pandas and NumPy, we would be left deserted in this huge world of data analytics and science. Data items are converted to the nearest compatible builtin Python type, via the item function. • Excellent in Python (Numpy, Pandas, Sklearn, matplotlib, statsmodels, seaborn, k-means clustering, Tensorflow2. import numpy as np x=np. • Excellent in Python (Numpy, Pandas, Sklearn, matplotlib, statsmodels, seaborn, k-means clustering, Tensorflow2. To parse the three PDFs, create a new Python script named parse_pdfs_with_tika. In Python 3, all integers are long, and thus cannot overflow. tolist() q = q. This tutorial does not come with any pre-written files, but is a follow-along tutorial. strings or timestamps), the result’s index will include count, unique, top, and freq. For example, a 95% likelihood of classification accuracy between 70% and 75%. They are two examples of sequence data types (see Sequence Types — str, unicode, list, tuple, bytearray, buffer, xrange). n : percentile value. 138 139 The lines of the array along the given axis are convolved with the 140 given weights. Trying to invoke math. You can write a book review and share your experiences. ndim is 0, then since the depth of the nested list is 0, it will not be a list at all, but a simple Python scalar. In particular, there are some obstacles and pitfalls when you do not have the root. We could boil down the problem to the attached 3-liner 'minimal-iP. rescale_intensity(arrayF, in_range=(p2, p98)). We can calculate arbitrary percentile values in Python using the percentile() NumPy function. Resetting will undo all of your current. ) Importing numpy. Tuples and Sequences¶. I am trying to read an 800 MB Imagine (. Running NumPy code in a Python Anywhere web console In Chapter 1, we already saw a Python Anywhere console in action, without having an account. With earlier Numpy and Scipy versions, the results of such operations are undefined and usually unexpected. They are from open source Python projects. without waiting for individual processes to finish. Felipe Jekyll http://queirozf. tolist() for i in range(nd - 1, 0, -1): if pr[i] > pr[i - 1]: pr[i - 1] = pr[i] #discretize empiric recall steps with given bins. percentile(df["x"], 10)] Produces a different result to this:. average(a)) # 0. csv',delimiter=',',dtype=None)[1:] Next we will make two arrays. max, 2**63 - 1 (9223372036854775807, 9223372036854775807L) Floating-point numbers:. This is a Python implementation of Ted Dunning's t-digest data structure. 本文翻译自：这里，并会添加笔（译）者的一些适当的注解。1. Python Certification is the most sought-after skill in programming domain. along each row or column i. To parse the three PDFs, create a new Python script named parse_pdfs_with_tika. Felipe Jekyll http://queirozf. NumPy is distributed in Python package numpy. Is it possible to use percentile or quantile as the aggfunc in a pandas pivot table? I've tried both numpy. set_style('darkgrid') sns. percentile function. Statistics and risk modelling using Python Eric Marsden Statistics is the science of learning from experience, particularly experience that arrives a little bit at a time. percentile¶ numpy. There’re many nice tutorials of it, but here I’d still like to introduce a few cool tricks the readers may not know before and I believe they’re useful. percentile provides all the functionality that scoreatpercentile provides. La última es una entrada real en el vector, mientras que la primera es una interpolación lineal de dos entradas de vectores que bordean el percentil. argsort Although Python has built-in sort and sorted functions to work with lists, we won’t discuss them here because NumPy’s np. - When using Numpy >= 1. set_index('date_2')['TBA']) tdata. The key to making it fast is to use vectorized operations, generally implemented through NumPy's universal functions (ufuncs). set_printoptions(threshold=6) # 24. 939851436401284. The quartiles of a set of data values are the three points that divide the ranked data set (i. percentile on the data within a MonetDB table. PyGeoprocessing now supports Python 2 and 3, and is tested on python 2. In the Python NumPy module, we have many aggregate functions or statistical functions to work with a single-dimensional or multi-dimensional array. # Growth of the factorial function (number of permutations) using Stirling's. observations (numpy. In particular, there are some obstacles and pitfalls when you do not have the root. Write a NumPy program to how to add an extra column to an NumPy array. axis : axis along which we want to calculate the percentile value. For object data (e. I'm using a python function in a labview loop. Let's see how to. Note that a call to sample() without arguments will generate a single sample. • Performed data mining, data processing on university student’s data sets & student’s healthcare data sets using python programming and libraries such as pandas, numpy. * score: int or float * Value that is compared to the elements in the data_list. Input array or object that can be converted to an array, containing nan values to be ignored. isnull()] A dataset could represent missing data in several ways. argsort Although Python has built-in sort and sorted functions to work with lists, we won’t discuss them here because NumPy’s np. nanmean,nansum, so I suspect that would be necessary. It supports a lot of numpy mathematical operations without monkey patching or wrapping numpy. This page focuses on recipes, ways that you can do things in Python that you are used to doing in Stata. Numpy Searchsorted Datetime. 导入numpy，并重命名为np(★☆☆)ipython. , 2011 ) and PyOpenCL (Klöckner. 6 Testing across multiple versions is configured to be run via tox. Axis of an ndarray is explained in the section cummulative sum and cummulative product functions of ndarray. The scripts can be used to manipulate data and even to generate visualizations. The formula may be derived from the variance of a sum of independent random variables. Simulate Data using Python and NumPy. one of the packages that you just can’t miss when you’re learning data science, mainly because this library provides you with an array data. Arrays are also easy to access for reading and writing. 0 Release Notes¶ This NumPy release contains a number of new features that should substantially improve its performance and usefulness, see Highlights below for a summary. The scripts can be executed on azure machine learning studio using “Execute Python Script” module which is listed under “Python language modules”. percentile (arr, n, axis=None, out=None) arr : input array. 9999976784968716) NumPy's corresponding functions have similar syntax, and again operate much more quickly: np. datetime objects. Another package Numarray was also developed, having some additional functionalities. This article will outline the core features of the NumPy library. dot怎么用？Python numpy. Write a Python program to find Student Grade with an example. Resetting will undo all of your current changes. In this article, we will use z score and IQR -interquartile range to identify any outliers using python. NumPy is, just like SciPy, Scikit-Learn, Pandas, etc. Messages (10) msg351123 - Author: Ana (annelischen) Date: 2019-09-04 12:45; So, all in all, if I try to install Numpy, SciPy, pandas or any related libraries via pip I see several issues, no AIX version written (somewhere?) for Python 3. There is no known exact formula for the normal cdf or its inverse using a finite number of terms involving standard functions ($\exp, \log, \sin \cos$ etc) but both the normal cdf and its inverse have been studied a lot and approximate formulas for both are. com/entries/python-imports-reference-and-examples. h #5173: failing stats. There are various libraries in python such as pandas, numpy, statistics (Python version 3. It is possible to share memory between processes, including numpy arrays. 5 Complete High Level NumPy API NEP NEP discussion process NumPy sprint at Berkeley Masked array external refactoring NEP Merge ratios Office Hours Wed April 25 12:00 PDT Began reviewing new issues/pr in the numpy repo Sumitted NumPy sprint request to SciPy2018. Align the beginning and end of statement blocks, and be consistent. For the rest of this course, python command will be given like this: # text following a “#” is just comments import numpy as np # imports “numpy” with short name “np” from scipy import stats import matplotlib. Numeric, the ancestor of NumPy, was developed by Jim Hugunin. SeedStream instance, for seeding PRNG. For earlier versions of Python, this is available as the processing module (a backport of the multiprocessing module of python 2. You can calculate all basic statistics functions such as average, median, variance, and standard deviation on NumPy arrays. In very simple terms dot product is a way of finding the product of the summation of two vectors and the output will be a single vector. reshape () method. This ticket leads me to believe they won't be integrating percentile () into numpy anytime soon. pdf), Text File (. I'm using a python function in a labview loop. pdf), Text File (. In particular, the submodule scipy. The first release of NumPy to support Python 3. reshape () method. 如果您正苦于以下问题：Python numpy. NumPy stands for Numerical Python and provides us with an interface for operating on numbers. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. In the examples in the left column, np refers to the NumPy module, as usual. atleast_1d (reference. NET provides strong-typed wrapper functions for numpy, which means you don't need to use the dynamic keyword at all, but this is a rabbit hole to delve into in another article. In the previous post, “Tidy Data in Python – First Step in Data Science and Machine Learning”, we discussed the importance of the tidy data and its principles. ndarray constructor no The np. According to documentation of numpy. Compatibility notes Compiled testing modules renamed and made private. Let’s take a look at a simple visual illustration of the function. Hi- I've been using python now for about 2 months for plugin development within Maya (a commercial 3d application). The functions are explained as follows − These functions return the minimum and the maximum from the elements in the given array along the specified axis. For earlier versions of Python, this is available as the processing module (a backport of the multiprocessing module of python 2. Felipe Jekyll http://queirozf. If you are a beginner in learning data science, understanding probability distributions will be extremely useful. percentile on the data within a MonetDB table. The quartiles of a set of data values are the three points that divide the ranked data set (i. we will be finding the mean of a group in pandas, sum of a group in pandas python and count of a group. If an integer, then the result will be a 1-D array of that length. If the overwrite_input option is used the input is only partially instead of fully sorted. axis = 0 means along the column and axis = 1 means working. getting mean score of a group using groupby function in python. If q is a single percentile and axis=None, then the result is a scalar. Below we'll read in automobile data from a CSV file, storing the data in Python's memory first as a numpy array. Issue #2028: Ignore filesystem errors when caching from multiple processes. All stems from the problem, that the relationship is non-surjective many-to-many. In the Python NumPy module, we have many aggregate functions or statistical functions to work with a single-dimensional or multi-dimensional array. Calculating Covariance with Python and Numpy. It comes with NumPy and other several packages related to. I have a homework assignment that I was doing with Minitab to find quartiles and the interquartile range of a data set. returnType – the return type of the registered user-defined function. • Chapter 3 provides information on testing and installing the NumTut package, which allows easy visualiza-tion of arrays. In this article we will discuss how to apply a given lambda function or user defined function or numpy function to each row or column in a dataframe. 9 and higher, numpy. n_samples (integer, optional) – Number of samples to generate. This section motivates the need for NumPy's ufuncs, which can be used to make repeated calculations on array elements much more efficient. Write a Python program to find Student Grade with an example. 2 or newer) and is heavily reliant on the Python scientific ecosystem': NumPy (Oliphant, 2007), SciPy (Jones et al. Python-m pip install scipy. py and add the following lines of code: #!/usr/bin/env python # -*- coding: utf-8 -*-import csv import glob import os import re import sys import pandas as pd import matplotlib matplotlib. This ability has two important consequences:. Do NumPy and SciPytill support Python 2. The following are code examples for showing how to use numpy. You can create new numpy arrays by importing data from files, such as text files. All I could find is the median (50th percentile), but not something more specific. If the input contains integers or floats smaller than float64, the output data-type is float64. f – a Python function, or a user-defined function. Python math works like you would expect. so i found the mean something like this. zeros () function. python get-pip. February 2, so we can easily switch from the non-vectorized functions from Python's math module to NumPy's versions. Python's NumPy library also has a dedicated "matrix" type with a syntax that is a little bit closer to the MATLAB matrix: For example, the " * " operator would perform a matrix-matrix multiplication of NumPy matrices - same operator performs element-wise multiplication on NumPy arrays. Numpystands for ‘Numeric Python’ , it is the core library in python to do the scientific computing. reshape does not change the order of or the total number of elements in the tensor, and so it can reuse the underlying data buffer. It stands for “Numeric Python” 。 It is a library of multidimensional array objects and a collection of routines for working. This time we’ll be using Pandas and…. from the given elements in the array. Geographic Information Systems Stack Exchange is a question and answer site for cartographers, geographers and GIS professionals. For this, first, we have to calculate Total, and Percentage of Five Subjects. It supports a lot of numpy mathematical operations without monkey patching or wrapping numpy. image analysis, text mining, or control of a physical experiment, the richness of Python is an invaluable asset. It is extremely easy and. In this tutorial, we shall learn how to add a column to DataFrame, with the help of example programs, that are going to be very detailed and illustrative. We can calculate arbitrary percentile values in Python using the percentile() NumPy function. Shape of the generated samples. 1 Scientific computing with tools and workflow. How to Compute the Standard Deviation in Python using Numpy. **kwargs: Named arguments forwarded to subclass implementation. If the input contains integers or floats smaller than float64, the output data-type is float64. Nesting is a useful feature in Python, but sometimes the indexing conventions can get a little confusing so let's clarify the process expanding from our courses on Applied Data Science with Python We will review concepts of nesting lists to create 1, 2, 3 and 4-dimensional lists, then we will convert them to numpy arrays. quantile() or percentile(). The standard deviation, many times represented by σ or s, is a measure of how spread out numbers are. Text on GitHub with a CC-BY-NC-ND license. arange(15) np. percentile(a, 30) # 30 パーセンタイル. n : percentile value. astype (numpy. Otherwise, it will consider arr to be flattened (works on all the axis). Release history. How to limit the number of items printed in output of numpy array? # Limit the number of items printed in python numpy array a to a maximum of 6 elements. I'm using numpy in this function and thus need to import it. Someone recently asked me why on earth I was using scoreatpercentile anyway - and it turns. scoreatpercentile - almost an order of magnitude faster in some cases. In this example, you see missing data represented as np. Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. 7 is a step towards the adoption of. Answer: Dummy data:. quantile function, an interface to percentile without factors of 100. It is mainly written in Python (v2. 如果您正苦于以下问题：Python numpy. MonetDB uses memory mapping to load the data into memory very quickly, and because of our zero-copy transfer into Python there is no additional overhead cost for transferring this data into Python. NumPy (pronounced / ˈ n ʌ m p aɪ / (NUM-py) or sometimes / ˈ n ʌ m p i / (NUM-pee)) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. arange() because np is a widely used abbreviation for NumPy. For object data (e. percentile() Percentile (or a centile) is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations fall. 2 or newer) and is heavily reliant on the Python scientific ecosystem': NumPy (Oliphant, 2007), SciPy (Jones et al. copy() returns a new array but with the exact element values as that of array1. Create the following pattern without hardcoding. 第 2 章 NumPy入门. 0 Determinant of A is -240 The Numpy Determinant of A is -240. Next, use Elif to find the grade. 0b1 #5154: 0. array([1, 2, 3]) print(np. pylab is a module within the matplotlib library that was built to mimic MATLAB’s global style. I just want to warning another users just to be careful uninstalling python-related package because it can mess with your ubuntu-desktop or math libraries. Don't miss our FREE NumPy cheat sheet at the bottom of this post. Be sure to update. Dealing With Missing Data in Python Pandas - Free download as Word Doc (. ; newshape (int or tuple of ints) – The new shape should be compatible with the original shape. Resetting will undo all of your current changes. Is there a way to load numpy without installing it? I searched online but there is very little information about this. NumPy is, just like SciPy, Scikit-Learn, Pandas, etc. reshape () method. Learn Data Science using Python From this blog I will share all required topics to be a Data Scientist using Python. In case of dictionaries, if all keys (not values) are false, any () returns False. 10 #5191: Scipy 0. NumPy is, just like SciPy, Scikit-Learn, Pandas, etc. So the values near 400,000 are clearly outliers. Table Functions and Methods. Find x-th percentile of a sequence without numpy. It looks like you haven't tried running your new code. 9 and higher, numpy. Related Resources. are applied on the elements, this means that the arrays have to have the same size. Github - latest version (zip) Pypi - 0. Python Plotting With Matplotlib (Guide) February 28, 2018 February 28, 2018 Real Python Data Analytics , Libraries , Matplotlib , NumPy , Statistics A picture says a thousand words, and with Python’s matplotlib library, it fortunately takes far less than a thousand words of code to create a production-quality graphic. Shape of the generated samples. 6 入门指南 python最佳实践指南 python3-cookbook中文版 python简明教程 草根学python Python语言小册 Python 之旅 python进阶 python Requests官方文档 python从零开始学爬虫 python代码打包教程 python数据结构 python学习笔记 python与常用算法. That means NumPy array can be any dimension. Note that a call to sample() without arguments will generate a single sample. 本文翻译自：这里，并会添加笔（译）者的一些适当的注解。1. Basically, you can either use sort or sorted to achieve what you want. How to Create an Array in Python. Access to Numpy arrays is very efficient, as indexing is lowered to direct memory accesses when possible. Aloha I hope that 2D array means 2D list, u want to perform slicing of the 2D list. import pandas as pd import numpy as np s = pd. We can calculate arbitrary percentile values in Python using the percentile() NumPy function. 0: If data is a dict, column order follows insertion-order for Python 3. When I pass it two one-dimentional arrays, I get back a 2×2 matrix of results. This means that it is possible to implement ufuncs and gufuncs within Python, getting speeds comparable to that of ufuncs/gufuncs implemented in C extension modules. h #5173: failing stats. This is done automatically when calling a pandas plot function and may be unnecessary when using pandas instead of Matplotlib directly. Mean represents the arithmetic average of the data. Included to auto-deploy Python on demand and the NumPy package in order to call into it. nanpercentile()function used to compute the nth precentile of the given data (array elements) along the specified axis ang ignores nan values. It tests your understanding of three numpy concepts. It has the percentile function you're after and many other statistical goodies. bool)) # binary structure footprint = generate_binary_structure (result. This section motivates the need for NumPy's ufuncs, which can be used to make repeated calculations on array elements much more efficient. 633231120341421. percentile() takes the following arguments. from the given elements in the array. Exercises : Numpy 1. NumPy serves as the basis of most scientific packages in Python, including pandas, matplotlib, scipy, etc. Data preparation is a big part of applied machine learning. If ,, …, are independent observations from a population that has a mean and standard deviation , then the variance of the total = (+ + ⋯ +) is. This is done by first ordering the statistics, then selecting values at the chosen percentile for the confidence interval. Return a copy of the array data as a (nested) Python list. range() xrange() in Python 3, xrange() is deprecated, i. 2 Modules and Clients. I looked in NumPy’s statistics reference, and couldn’t find this. Refer to the following article for obtaining the size of the image read as NumPy array ndarray. How to Create an Array in Python. Align the beginning and end of statement blocks, and be consistent. txt) or read online for free. percentile is a lot faster than scipy. n : percentile value. The function numpy. 16 will drop support for Python 3. Discover how to create a list in Python, select list elements, the difference between append () and extend (), why to use NumPy and much more. Timestamps also include the first and. Robin's Blog Calculating percentiles in Python – use numpy not scipy! November 24, 2015. histogram test with numpy 1. Want to calculate the variance of a given list without using external dependencies?. percentile(a, q, axis) Where,. @return (labelmap1, labelmap2, n_lables1, n_labels2, labelmapping2to1) """ result = numpy. quantile function, an interface to percentile without factors of 100. 第 2 章 NumPy入门. I is the same size as A. In this blog we will explain the process of downloading and installing numpy packages and how to use them in python environment on mac, windows, ubuntu. Since, arrays and matrices are an essential part of the Machine Learning ecosystem, NumPy along with Machine Learning modules like Scikit-learn, Pandas, Matplotlib. When we say "Core Python", we mean Python without any special modules, i. 075966046220879 np. The functions are explained as follows − These functions return the minimum and the maximum from the elements in the given array along the specified axis. Re: Comparing percentile by python or numpy with the definition In regards to your previous question. I don't know what to do with that. 6 and later. NET uses Python. Percentiles help us in getting an idea on outliers. pyplot as plt. 7 maintenance will stop on January 1, 2020. Permuatation resampling is used ot generate the null distribtuion of labeled data by switching lebals. float) – An array of proposed values of epsilon to be used at each steps. There is a section for data management, another for common functions, a section for statistical methods and techniques, and one for general tricks. The other axes are the axes that remain after the reduction of a. In the previous post, I used Pandas (but also SciPy and Numpy, see Descriptive Statistics Using Python) but now we are only going to use Numpy. You'd use it just like percentile(), but would input your q value in probability space (0. Numpy manual contents — NumericalPython v1 - Free download as PDF File (. 7, note that Python 2. Python Plotting With Matplotlib (Guide) February 28, 2018 February 28, 2018 Real Python Data Analytics , Libraries , Matplotlib , NumPy , Statistics A picture says a thousand words, and with Python’s matplotlib library, it fortunately takes far less than a thousand words of code to create a production-quality graphic. Correctly preparing your training data can mean the difference between mediocre and extraordinary results, even with very simple linear algorithms. NET provides strong-typed wrapper functions for numpy, which means you don't need to use the dynamic keyword at all, but this is a rabbit hole to delve into in another article. The key to making it fast is to use vectorized operations, generally implemented through NumPy's universal functions (ufuncs). The function takes both an array of observations and a floating point value to specify the percentile to calculate in the range of 0 to 100. Python, as well as its numerical libraries are one of the essential toolsets for researchers and data scientists. percentile(marray. statsmodels is a Python module that provides classes and functions for the estimation of many different statistical models, as well as for conducting statistical tests, and statistical data exploration. >>> import numpy as np #load the Library. Want to calculate the variance of a given list without using external dependencies?. Want to calculate percentiles with Python/NumPy? We can calculate the percentiles with the following code. This ticket leads me to believe they won't be integrating percentile () into numpy anytime soon. They may help you go from saved files of your data to NumPy arrays without having to make any Python lists at all. scoreatpercentile – almost an order of magnitude faster in some cases. Universal functions (ufunc for universal functions) are functions that can be applied term-by-term to the elements of an array. percentile for users that have numpy >= 1. txt) or read online for free. Python File Handling Python Read Files Python Write/Create Files Python Delete Files Python NumPy Python Dictionary fromkeys() Method Dictionary Methods. When used without parameters, it simply calculates the numerical average of all values in the array, no matter the array’s dimensionality. # Growth of the factorial function (number of permutations) using Stirling's. 0) for advanced data analysis, modeling and machine learning • Advanced in using Tableau, Datorama and Data Studio for data visualization. h #5173: failing stats. Set extended to True. There are at least 9 different definitions of empirical quantiles. argsort Although Python has built-in sort and sorted functions to work with lists, we won’t discuss them here because NumPy’s np. This is done automatically when calling a pandas plot function and may be unnecessary when using pandas instead of Matplotlib directly. range() xrange() in Python 3, xrange() is deprecated, i. Numpy Tutorial Part 1: Introduction to Arrays. The advantages of Core Python: high-level number objects: integers, floating point; containers: lists with cheap insertion and append methods, dictionaries with fast lookup; Advantages of using Numpy with Python: array oriented computing. NumPy is a Python package. Python Histogram Plotting: NumPy, Matplotlib, Pandas & Seaborn July 2, 2018 July 2, 2018 Real Python Data Analytics , Data Structures , Libraries , Matplotlib , NumPy , Pandas , Statistics In this tutorial, you'll be equipped to make production-quality, presentation-ready Python histogram plots with a range of choices and features. Numpy arrays are great alternatives to Python Lists. Let’s take a look at a simple visual illustration of the function. Github - latest version (zip) Pypi - 0. One of the key methods for solving the Black-Scholes Partial Differential Equation (PDE) model of options pricing is using Finite Difference Methods (FDM) to discretise the PDE and evaluate the solution numerically. Syntax notes. If the input contains integers or floats smaller than float64, the output data-type is float64. n : percentile value. only major difference is that I eliminated the numpy dependency, and: omitted the rank kwarg option until I can get more time to translate: the numpy parts out. It is the lists of the list. txt) or read online for free. 0 will support Python versions 3. I tried to find an implementation of the FFT algorithm in Python without the use of the numpy library. List of Modern Deep Learning PyTorch, TensorFlow, MXNet, NumPy, and Python Tutorial Screencast Training Videos on @aiworkbox. Some of these algorithms are computationally burdensome and require iterative access to image data. In this article, we show how to compute the standard deviation in Python. The numpy package is a good example of this, it’s really quite quick because a lot of the number crunching it does isn’t actually done by Python Python finds use in many spheres – web applications, automation, scientific modelling, big data applications and many more. If at least one key is true, any () returns True. statsmodels is a Python module that provides classes and functions for the estimation of many different statistical models, as well as for conducting statistical tests, and statistical data exploration. Python NumPy Array Object Exercises, Practice and Solution: Write a NumPy program to calculate percentiles for a sequence or single-dimensional NumPy array. NumPy is the fundamental Python library for numerical computing. You may specify a datatype. NET uses Python. Issue #2028: Ignore filesystem errors when caching from multiple processes. The resulting crash log is also attached. Related Post: Get image size (width, height) with Python, OpenCV, Pillow (PIL) The image is alpha blended according to the values of the second parameter alpha and the fourth parameter beta. Return a copy of the array data as a (nested) Python list. Here are the examples of the python api numpy. Args: sample_shape: 0D or 1D int32 Tensor. Discover how to create a list in Python, select list elements, the difference between append () and extend (), why to use NumPy and much more. In the above code, the given the float () is a built-in function having a single parameter. If you ask for [0, 100] percentiles, it will give you an array of two elements, the min (0th percentile) and the max (100th percentile). I was thinking to see if there was a way of installing python in my own python installation and then trick the other python to. It contains many of the numeric and scientific packages used by this package and has installers for Python 2. Machine Learning with Python Cookbook: Practical Solutions from Preprocessing to Deep Learning Chris Albon This practical guide provides nearly 200 self-contained recipes to help you solve machine learning challenges you may encounter in your daily work. 0 will support Python versions 3. By voting up you can indicate which examples are most useful and appropriate. stats import rankdata import numpy as np def calc_percentile (a, method = 'min'): if isinstance (a, list): a = np. By using NumPy, you can speed up your workflow, and interface with other packages in the Python ecosystem, like scikit-learn, that use NumPy under the hood. The any () method takes an iterable (list, string, dictionary etc. Here, the following contents will be described. Compatibility notes Compiled testing modules renamed and made private. It is one of the popular modules in Python. NumPy is one of the most powerful Python libraries. Access to Numpy arrays is very efficient, as indexing is lowered to direct memory accesses when possible. Median Value: The Median is the "middle" of a sorted list of numbers. This is one of the 100+ free recipes of the IPython Cookbook, Second Edition, by Cyrille Rossant, a guide to numerical computing and data science in the Jupyter Notebook. Instead, we focus on how Numpy. Pandas is a widely used Python package for structured data. All those python packages are so powerful and useful to do Base N-dimensional array computing( Numpy ), Data structures & analysis ( Pandas ), scientific computing ( Scipy) and Comprehensive 2D Plotting ( Matplotlib ). The initial values of such a numpy array are 1s and 0s. NumPy’s main object is the homogeneous multidimensional array. Otherwise, it will consider arr to be flattened (works on. seed: Python integer or tfp. >>> import numpy as np #load the Library. Percentiles divide the whole population into. It comes with NumPy and other several packages related to. In the Python NumPy module, we have many aggregate functions or statistical functions to work with a single-dimensional or multi-dimensional array. This article will outline the core features of the NumPy library. Welcome to this project-based course on Logistic with NumPy and Python. Fortunately, it is easy in Python to call a function that is defined in another file. Input array or object that can be converted to an array, containing nan values to be ignored. This means that it is possible to implement ufuncs and gufuncs within Python, getting speeds comparable to that of ufuncs/gufuncs implemented in C extension modules. Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. We can calculate arbitrary percentile values in Python using the percentile() NumPy function. astype (numpy. You can import these data using the loadtxt () function from numpy, which you imported as np. So Numpy being one of the essential libraries for Machine Learning requires an article of its own. array([30, 50]) would create an array consisting of the 30th and 50th percentiles. They install packages for the entire computer, often use older versions, and don't have as many available versions. They may help you go from saved files of your data to NumPy arrays without having to make any Python lists at all. Numpy Tutorial Part 1: Introduction to Arrays. 149 silver badges. Note that Python adheres to the PEMDAS order of operations. Ranging from 1 to 52 weeks. Python enforces indentation as part of the syntax. Numpy arrays are great alternatives to Python Lists. These are the 2. int16) for i in range(56)]) np. The other axes are the axes that remain after the reduction of a. Issue #2003: Allow unicode variable and function names (on Python 3). range() function. ) in Python. percentile(my_vals, perc) while abs(val - threshold_val) > 0. Posted by: admin January 29, 2018 Leave a comment. The build-in package NumPy is used for manipulation and array-processing. mean(a, axis=None, dtype=None) a: array containing numbers whose mean is required axis: axis or axes along which the means are computed, default is to compute the mean of the flattened array. 95 and we would select the value at the 2. percentile for users that have numpy >= 1. Each script is a module which can be a function, methods or new python type created for particular functionality. This is an universal way of importing NumPy and using np. rank the dataframe in descending order of score and if found two scores are same then assign the same rank. NumPy Array. percentile(a, 95) # 95 パーセンタイルを求めます(逆に言うと上位 5 %に位置する点数) 92. 0 will support Python versions 3. For example the highest income value is 400,000 but 95th percentile is 20,000 only. What's the fastest way to compare datetime in pandas? python,python-3. >>> import numpy as np >>> a = np. Python Scientific lecture notes Release 2013. copy() where array1 is a numpy n-dimensional array. Next, you'll need to install the numpy module that we'll use throughout this tutorial:. We’ll start by looking at the Python built-ins, and then take a look at the routines included in NumPy and optimized for NumPy arrays. The Python Numpy aggregate functions are sum, min, max, mean, average, product, median, standard deviation, variance, argmin, argmax, percentile, cumprod, cumsum, and corrcoef. Install pip install percentiles Use >>> import percentiles >>> percentiles. x was NumPy 1. An extensive list of result statistics are available for each estimator. • Chapter 2 provides information on testing Python, NumPy, and compiling and installing NumPy if neces-sary. x; Download. Included to auto-deploy Python on demand and the NumPy package in order to call into it. 299999999999997 # 95 パーセンタイルは約 92. Use two or four spaces to define each logical level. 1 supports Python 2. It is a distutils installed project and thus we cannot accurately determine which files belong to it which would lead to only a partial uninstall. In a Machine Learning project, once we have a tidy dataset in place, it is always recommended to perform EDA (Exploratory Data Analysis) on the underlying data before fitting it into a Machine Learning model. He was appointed by Gaia (Mother Earth) to guard the oracle of Delphi, known as Pytho. A single percentile still returns a scalar. percentile and pandas quantile without success. Welcome to Jekyll! You'll find this post in your _posts directory. stack array-joining function generalized to masked arrays. Another package Numarray was also developed, having some additional functionalities. from the given elements in the array. Let for example, consider multiplying a python list by 2. you need to order the data points first) into four equal groups, each group comprising a. NumPy and SciPy are Python libraries for scientific computing. Modern galaxy surveys produce redshift probability density functions (PDFs) in addition to traditional photometric redshift (photo-z) point estimates. pyplot as plt. 6 入门指南 python最佳实践指南 python3-cookbook中文版 python简明教程 草根学python Python语言小册 Python 之旅 python进阶 python Requests官方文档 python从零开始学爬虫 python代码打包教程 python数据结构 python学习笔记 python与常用算法. Arrays The central feature of NumPy is the array object class. An essential piece of analysis of large data is efficient summarization: computing aggregations like sum (), mean (), median (), min (), and max (), in which a single number gives insight into the nature of a potentially large dataset. This is the main USP of NumPy because of which it's widely used in data analytic community. NumPy Is a Python package. percentile(marray. End Edit python-2. • Excellent in Python (Numpy, Pandas, Sklearn, matplotlib, statsmodels, seaborn, k-means clustering, Tensorflow2. After about an hour it said: Successfully built numpy Installing collected packages: numpy Found existing installation: numpy 1. MonetDB uses memory mapping to load the data into memory very quickly, and because of our zero-copy transfer into Python there is no additional overhead cost for transferring this data into Python. Other readers will always be interested in your opinion of the books you've read. ; The return value of min() and max() functions is based on the axis specified. compressed(),(5)) percentile95 = numpy. Tag: python,numpy,pandas. This is one of the 100+ free recipes of the IPython Cookbook, Second Edition, by Cyrille Rossant, a guide to numerical computing and data science in the Jupyter Notebook. dtype is the datatype of elements the array stores. percentile() to compute the percentiles of the petal. Check out our Python Training Playlist: https://goo. detection python outliers remove how data and using regression numpy How to use Outlier Tests in R Code As part of my data analysis workflow, I want to test for outliers, and then do my further calculation with and without those outliers. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. stats import rankdata import numpy as np def calc_percentile (a, method = 'min'): if isinstance (a, list): a = np. python学习 Python3. For example, I will create three lists and will pass it the matrix () method. x,numpy,pandas,datetime64. Hence, it would be a good idea to explore the basics of data handling in Python with NumPy. ; If no axis is specified the value returned is based on all the elements of the array. 0 Determinant of A is -348 The Numpy Determinant of A is -348. Robin's Blog Calculating percentiles in Python - use numpy not scipy! November 24, 2015. This is just a brief public service announcement reporting something that I've just found: np. Second, you can create new numpy arrays of a specified shape using the functions ones() and zeros(). reshape () method. Signing up is a pretty straightforward process and will not be covered here. If q is a single percentile and axis=None, then the result is a scalar. This ability has two important consequences:. OpenCV 3 image and video processing with Python OpenCV 3 with Python Image - OpenCV BGR : Matplotlib RGB Basic image operations - pixel access iPython - Signal Processing with NumPy Signal Processing with NumPy I - FFT and DFT for sine, square waves, unitpulse, and random signal Signal Processing with NumPy II - Image Fourier Transform : FFT & DFT. Write a NumPy program to count the frequency of unique values in numpy array. Below we'll read in automobile data from a CSV file, storing the data in Python's memory first as a numpy array. Python enforces indentation as part of the syntax. When you run the program, the output will be: The any () method works in similar way for tuples and sets like lists. import numpy as np. NumPy (pronounced / ˈ n ʌ m p aɪ / (NUM-py) or sometimes / ˈ n ʌ m p i / (NUM-pee)) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. Parameters * data_list: list * A list of scores to which the score argument is compared. This is useful in a variety of contexts - including during ad-hoc a/b test analysis. Use the isnull() method to detect the missing values. This time we’ll be using Pandas and…. 8b2 will work with the new release source packages, but may not find support in future releases. Some of the key advantages of Numpy arrays are that they are fast, easy to work with, and give users the opportunity to perform calculations across entire arrays. Want to calculate the variance of a given list without using external dependencies?. Project description. There is another way to create a matrix in python. However, the answer to the question is using Scala, which I do not know. In Python, arrays are native objects called "lists," and they have a variety of methods associated with each object. Fortunately, it is easy in Python to call a function that is defined in another file. py -A stack. It looks like you haven't tried running your new code. , 2001) and Matplotlib (Hunter, 2007). x, dividing two integers or longs uses integer division. pdf), Text File (. import numpy as np my_vals = [] threshold_val = 0. When naming variables, note that Python is case sensitive, so value is not the same as Value. Answer: Dummy data:. Ranging from 1 to 52 weeks. distplot(d) The call above produces a KDE. Note that a call to sample() without arguments will generate a single sample. Python is a general-purpose language with statistics modules. percentile(a, q, axis) Where, a Input array. Using the NumPy array d from ealier: import seaborn as sns sns.
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# LHCb Conference Proceedings
უკანასკნელი დამატებები:
2019-10-29
16:25
TWO-PARTICLE CORRELATIONS AT THE LHCb∗ / Kucharczyk, Marcin (Polish Academy of Sciences (PL)) Due to its unique pseudorapidity coverage (2 < η < 5) and excellent performance, the LHCb detector allows the study of various aspects of par- ticle correlations at large rapidities and low transverse momenta. Selected results are summarized, such as the first measurement of the Bose–Einstein correlations of the same-sign pions and kinematic correlations for pairs of beauty hadrons performed using large samples of proton–proton collision data accumulated with the LHCb detector at $\sqrt{s}$ = 7 and 8 TeV, together with the long-range correlations on the near side measured in proton–lead and lead–proton collisions at a nucleon–nucleon centre-of-mass energy of $\sqrt{s}$ = 5 TeV. [...] LHCb-PROC-2019-009; CERN-LHCb-PROC-2019-009.- Geneva : CERN, 2019 - 6. Fulltext: PDF; In : Diffraction and Low-x 2018, Reggio Calabria, Italy, 26 Aug - 1 Sep 2018
2019-09-04
12:06
Soft QCD and Central Exclusive Production at LHCb / Kucharczyk, Marcin (Cracow, INP) /LHCb Collaboration The LHCb detector, owing to its unique acceptance coverage $(2 < \eta < 5)$ and a precise track and vertex reconstruction, is a universal tool allowing the study of various aspects of electroweak and QCD processes, such as particle correlations or Central Exclusive Production. The recent results on the measurement of the inelastic cross section at $\sqrt s = 13 \ \rm{TeV}$ as well as the Bose-Einstein correlations of same-sign pions and kinematic correlations for pairs of beauty hadrons performed using large samples of proton-proton collision data accumulated with the LHCb detector at $\sqrt s = 7\ \rm{and} \ 8 \ \rm{TeV}$, are summarized in the present proceedings, together with the studies of Central Exclusive Production at $\sqrt s = 13 \ \rm{TeV}$ exploiting new forward shower counters installed upstream and downstream of the LHCb detector. [...] LHCb-PROC-2019-008; CERN-LHCb-PROC-2019-008.- Geneva : CERN, 2019 - 6. - Published in : PoS DIS2019 (2019) 057 Fulltext: PDF; In : The XXVII International Workshop on Deep Inelastic Scattering and Related Subjects, Turin, Italy, 8 - 12 Apr 2019, pp.57
2019-08-15
17:36
Tests of Lepton Flavour Universality at LHCb / Mueller, Katharina (Universitaet Zuerich (CH)) In the Standard Model of particle physics the three charged leptons are identical copies of each other, apart from mass differences, and the electroweak coupling of the gauge bosons to leptons is independent of the lepton flavour. This prediction is called lepton flavour universality (LFU) and is well tested. [...] LHCb-PROC-2019-006; CERN-LHCb-PROC-2019-006.- Geneva : CERN, 2019 - mult.p. In : Kruger2018, Hazyview, South Africa, 3 - 7 Dec 2018
2019-05-15
16:57
Mixing and time-dependent CP violation in beauty at LHCb / Govorkova, Katya (Nikhef National institute for subatomic physics (NL)) Recent measurements of the time-dependent CP violation are presented. The decays of $B_{s}^{0}$ mesons to $J/\psi\,K^+ K^-$ and $J/\psi\,\pi^+ \pi^-$ final states are used to measure CP-violating parameters with proton-proton collision data, corresponding to an integrated luminosity of 1.9 fb$^{-1}$, collected by the LHCb detector at a centre-of-mass energy of 13 TeV in 2015 and 2016 [...] LHCb-PROC-2019-005; CERN-LHCb-PROC-2019-005.- Geneva : CERN, 2019 - mult.p. Fulltext: PDF; In : 54th Rencontres de Moriond on Electroweak Interactions and Unified Theories, La Thuile, Italy, 16 - 23 Mar 2019
2019-02-12
14:01
XYZ states at LHCb / Kucharczyk, Marcin (Polish Academy of Sciences (PL)) The latest years have observed a resurrection of interest in searches for exotic states motivated by precision spectroscopy studies of beauty and charm hadrons providing the observation of several exotic states. The latest results on spectroscopy of exotic hadrons are reviewed, using the proton-proton collision data collected by the LHCb experiment. [...] LHCb-PROC-2019-004; CERN-LHCb-PROC-2019-004.- Geneva : CERN, 2019 - 6. Fulltext: PDF; In : 15th International Workshop on Meson Physics, Kraków, Poland, 7 - 12 Jun 2018
2019-01-21
09:59
Mixing and indirect $CP$ violation in two-body Charm decays at LHCb / Pajero, Tommaso (Universita & INFN Pisa (IT)) The copious number of $D^0$ decays collected by the LHCb experiment during 2011--2016 allows the test of the violation of the $CP$ symmetry in the decay of charm quarks with unprecedented precision, approaching for the first time the expectations of the Standard Model. We present the latest measurements of LHCb of mixing and indirect $CP$ violation in the decay of $D^0$ mesons into two charged hadrons [...] LHCb-PROC-2019-003; CERN-LHCb-PROC-2019-003.- Geneva : CERN, 2019 - 10. Fulltext: PDF; In : 10th International Workshop on the CKM Unitarity Triangle, Heidelberg, Germany, 17 - 21 Sep 2018
2019-01-15
14:22
Experimental status of LNU in B decays in LHCb / Benson, Sean (Nikhef National institute for subatomic physics (NL)) In the Standard Model, the three charged leptons are identical copies of each other, apart from mass differences. Experimental tests of this feature in semileptonic decays of b-hadrons are highly sensitive to New Physics particles which preferentially couple to the 2nd and 3rd generations of leptons. [...] LHCb-PROC-2019-002; CERN-LHCb-PROC-2019-002.- Geneva : CERN, 2019 - 7. Fulltext: PDF; In : The 15th International Workshop on Tau Lepton Physics, Amsterdam, Netherlands, 24 - 28 Sep 2018
2019-01-10
15:54
Rare radiative decays at LHCb / Puig Navarro, Albert (Universitaet Zuerich (CH)) Radiative $b$-hadron decays are sensitive probes of New Physics through the study of branching fractions, $CP$ asymmetries and measurements of the polarization of the photon emitted in the decay. During Run I of the LHC, the LHCb experiment has collected large samples of radiative $b$-hadron decays. [...] LHCb-PROC-2019-001; CERN-LHCb-PROC-2019-001.- Geneva : CERN, 2018-12-20 - 6. - Published in : CERN Conf.Proc. 1 (2018) 243 Fulltext: PDF; In : Proceedings of the PHOTON-2017 Conference, pp.243
2018-12-20
16:31
Simultaneous usage of the LHCb HLT farm for Online and Offline processing workflows / Closier, Joel (CERN) ; Gaspar, Clara (CERN) ; Granado Cardoso, Luis (CERN) ; Haen, Christophe (CERN) ; Jost, Beat (CERN) ; Neufeld, Niko (CERN) /LHCb Collaboration LHCb is one of the 4 LHC experiments and continues to revolutionise data acquisition and analysis techniques. Already two years ago the concepts of “online” and “offline” analysis were unified: the calibration and alignment processes take place automatically in real time and are used in the triggering process such that Online data are immediately available offline for physics analysis (Turbo analysis), the computing capacity of the HLT farm has been used simultaneously for different workflows : synchronous first level trigger, asynchronous second level trigger, and Monte-Carlo simulation. [...] LHCb-PROC-2018-031; CERN-LHCb-PROC-2018-031.- Geneva : CERN, 2019 - 8 p. - Published in : EPJ Web Conf. 214 (2019) 01001 Fulltext from publisher: PDF; LHCb Note: PDF; In : 23rd International Conference on Computing in High Energy and Nuclear Physics, CHEP 2018, Sofia, Bulgaria, 9 - 13 Jul 2018, pp.01001
2018-12-14
16:02
The Timepix3 Telescope andSensor R&D for the LHCb VELO Upgrade / Dall'Occo, Elena (Nikhef National institute for subatomic physics (NL)) The VErtex LOcator (VELO) of the LHCb detector is going to be replaced in the context of a major upgrade of the experiment planned for 2019-2020. The upgraded VELO is a silicon pixel detector, designed to with stand a radiation dose up to $8 \times 10^{15} 1 ~\text {MeV} ~\eta_{eq} ~ \text{cm}^{−2}$, with the additional challenge of a highly non uniform radiation exposure. [...] LHCb-PROC-2018-030; CERN-LHCb-PROC-2018-030.- Geneva : CERN, 2018 - 8.
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How do you differentiate f(x) = 1/sqrt(sin^2(2-x^2) using the chain rule?
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Feb 3, 2017
$f \left(x\right) = \frac{1}{\sqrt{{\sin}^{2} \left(2 - {x}^{2}\right)}} = {\left({\sin}^{2} \left(2 - {x}^{2}\right)\right)}^{- \frac{1}{2}} = {\left({\left(\sin \left(2 - {x}^{2}\right)\right)}^{2}\right)}^{- \frac{1}{2}} = {\left(\sin \left(2 - {x}^{2}\right)\right)}^{-} 1$
In order to differentiate this, we need to use the chain rule twice on $\sin {\left(f \left(x\right)\right)}^{n}$.
$\frac{d}{\mathrm{dx}} {\left[\sin \left(f \left(x\right)\right)\right]}^{n} = n {\left[\sin \left(f \left(x\right)\right)\right]}^{n - 1} \cos \left(f \left(x\right)\right) f ' \left(x\right)$
$f ' \left(x\right) = - 1 {\left({\sin}^{2} \left(2 - {x}^{2}\right)\right)}^{- 2} \cos \left(2 - {x}^{2}\right) - 2 x =$
$= \frac{2 x \cos \left(2 - {x}^{2}\right)}{{\sin}^{2} \left(2 - {x}^{2}\right)} ^ 2$
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# Question
A survey of 200 students is selected randomly on a large university campus. They are asked if they use a laptop in class to take notes. The result of the survey is that 70 of the 200 students responded “yes.”
a) What is the value of the sample proportion p?
b) What is the standard error of the sample proportion?
c) Construct an approximate 95% confidence interval for the true proportion p by taking ± 2 SEs from the sample proportion.
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Documentation
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# ltePDSCH
## Syntax
sym = ltePDSCH(enb,chs,cws)
## Description
example
sym = ltePDSCH(enb,chs,cws) returns a matrix containing the physical downlink shared channel (PDSCH) complex symbols for cell-wide settings, enb, channel transmission configuration, chs, and the codeword or codewords contained in cws. The channel processing includes the stages of scrambling, symbol modulation, layer mapping, and precoding.
## Examples
collapse all
Generate the configuration structure for Test Model E-TM1.1 10 MHz, as specified in TS36.141
Initialize the test model using lteTestModel. Generate information related to PDSCH indices and use info.Gd output to determine the required transport block. Execute lteDLSCH to create the codeword, then generate the PDSCH symbols.
tm = lteTestModel('1.1','10MHz');
tm.PDSCH.RNTI = 0;
tm.PDSCH.RV = 0;
prbset = (0:tm.NDLRB-1)';
[ind,info] = ltePDSCHIndices(tm,tm.PDSCH,prbset);
trBlk = randi([0,1],info.Gd,1);
cw = lteDLSCH(tm,tm.PDSCH,info.G,trBlk);
pdschSym = ltePDSCH(tm,tm.PDSCH,cw);
## Input Arguments
collapse all
eNodeB cell-wide settings, specified as a structure containing these parameter fields.
Parameter FieldRequired or OptionalValuesDescription
NCellIDRequired
Integer from 0 to 503
Physical layer cell identity
NSubframeRequired
0 (default), nonnegative scalar integer
Subframe number
CellRefPRequired
1, 2, 4
Number of cell-specific reference signal (CRS) antenna ports
DuplexModeOptional
'FDD' (default), 'TDD'
Duplexing mode, specified as:
• 'FDD' for Frequency Division Duplex or
• 'TDD' for Time Division Duplex
The following parameters are dependent upon the condition that DuplexMode is set to 'TDD'.
TDDConfigOptional
0, 1 (default), 2, 3, 4, 5, 6
SSCOptional
0 (default), 1, 2, 3, 4, 5, 6, 7, 8, 9
Special subframe configuration (SSC)
The following parameter fields are dependent upon the condition that chs.TxScheme is set to 'SpatialMux' or 'MultiUser'.
CFIRequired
1, 2, or 3
Scalar or if the CFI varies per subframe, a vector of length 10 (corresponding to a frame).
Control format indicator (CFI) value. In TDD mode, CFI varies per subframe for the RMCs ('R.0', 'R.5', 'R.6', 'R.6-27RB', 'R.12-9RB')
NDLRBRequired
Scalar integer from 6 to 110
Number of downlink resource blocks. (${N}_{\text{RB}}^{\text{DL}}$)
CyclicPrefixOptional
'Normal' (default), 'Extended'
Cyclic prefix length
Channel-specific transmission configuration, specified as a structure that can contain the following parameter fields.
Parameter FieldRequired or OptionalValuesDescription
ModulationRequired
'QPSK', '16QAM', '64QAM', or '256QAM'
Modulation type, specified as a character vector, cell array of character vectors, or string array. If blocks, each cell is associated with a transport block.
RNTIRequired
0 (default), scalar integer
Radio network temporary identifier (RNTI) value (16 bits)
TxSchemeOptional
'Port0' (default), 'TxDiversity', 'CDD', 'SpatialMux', 'MultiUser', 'Port5', 'Port7-8', 'Port8', 'Port7-14'.
PDSCH transmission scheme, specified as one of the following options.
Transmission schemeDescription
'Port0'Single antenna port, port 0
'TxDiversity'Transmit diversity
'CDD'Large delay cyclic delay diversity scheme
'SpatialMux'Closed loop spatial multiplexing
'MultiUser'Multi-user MIMO
'Port5'Single-antenna port, port 5
'Port7-8'Single-antenna port, port 7, when NLayers = 1. Dual layer transmission, ports 7 and 8, when NLayers = 2.
'Port8'Single-antenna port, port 8
'Port7-14'Up to eight layer transmission, ports 7–14
The following parameters are dependent upon the condition that TxScheme is set to 'CDD', 'SpatialMux', 'MultiUser', 'Port7-8'or 'Port7-14'.
NLayersRequired
Integer from 1 to 8
Number of transmission layers.
The number of layers is dependent on TxScheme.
PMISetRequired
Integer vector with element values from 0 to 15.
Precoder matrix indication (PMI) set. It can contain either a single value, corresponding to single PMI mode, or multiple values, corresponding to multiple or subband PMI mode. The number of values depends on CellRefP, transmission layers and TxScheme. For more information about setting PMI parameters, see ltePMIInfo.
PRBSetRequired
Integer column vector or two-column matrix
Zero-based physical resource block (PRB) indices corresponding to the slot wise resource allocations for this PDSCH. PRBSet can be assigned as:
• a column vector, the resource allocation is the same in both slots of the subframe,
• a two-column matrix, this parameter specifies different PRBs for each slot in a subframe,
• a cell array of length 10 (corresponding to a frame, if the allocated physical resource blocks vary across subframes).
PRBSet varies per subframe for the RMCs 'R.25'(TDD), 'R.26'(TDD), 'R.27'(TDD), 'R.43'(FDD), 'R.44', 'R.45', 'R.48', 'R.50', and 'R.51'.
The following parameters are dependent upon the condition that TxScheme is set to 'Port5', 'Port7-8', 'Port8', or 'Port7-14'.
WOptional
Numeric matrix, [] (default)
NLayers-by-P precoding matrix for the wideband UE-specific beamforming of the PDSCH symbols. P is the number of transmit antennas. When W is not specified, no precoding is applied.
Codeword or codewords, specified as a vector of bit values for one codeword to be modulated, or a cell array containing one or two vectors of bit values corresponding to the one or two codewords to be modulated.
## Output Arguments
collapse all
PDSCH symbols, returned as a complex numeric matrix. It has size N-by-P, where N is the number of modulation symbols for one antenna port and P is the number of transmission antennas. The complex symbols are generated using cell-wide settings, enb, channel transmission configuration, chs, and the codeword or codewords contained in cws.
Data Types: double
Complex Number Support: Yes
## References
[1] 3GPP TS 36.101. “User Equipment (UE) Radio Transmission and Reception.” 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA). URL: http://www.3gpp.org.
[2] 3GPP TS 36.141. “Base Station (BS) conformance testing.” 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA). URL: http://www.3gpp.org.
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# Any self-diffeomorphism of a compact manifold with boundary rel boundary can be isotoped to fix a collar of boundary
Let $$M$$ be a compact manifold with boundary. Is it true that any self-diffeomorphism $$f:M\to M$$ fixing $$\partial M$$ is isotopic to a self-diffeomorphism that fixes a collar neighborhood $$\partial M \times [0,\epsilon)\subset M$$ of $$\partial M$$?
If this is true, I want to use this in the following case: suppose $$S$$ is a properly embedded submanifold (without boundary) in a compact manifold $$X$$ (without boundary), and there is a self-diffeomorphism $$f:S\to S$$ that extends to a diffeomorphism $$\tilde{f}: \nu S\to \nu S$$ rel $$\partial \nu S$$, where $$\nu S$$ is a closed tubular neighborhood of $$S$$ in $$X$$. Then applying the above situation with $$M=\nu S$$, we may assume $$\tilde{f}$$ fixes a collar neighborhood of $$\partial \nu S$$ in $$\nu S$$. Then we can extend $$\tilde{f}$$ to a global diffeomorphism of $$X$$ by defining $$\tilde{f}$$ to be identity outside $$\nu S$$.
Choose an extendible collar $$C:\partial M\times[0,L)\to M$$, and let $$\pi_1,\pi_2$$ be the projection onto the first and second factors of $$\partial M\times[0,1)$$. These are only defined on the image of $$C$$.
Note that $$\max_{x\in\partial M}\pi_2(f(C(t,x)))$$ is a well defined and continuous function of $$t$$ for sufficiently small $$t$$, so there is an $$\epsilon\in(0,l)$$ such that $$f$$ maps $$C(\partial M\times[0,\epsilon))$$ into the image of $$C$$.
One can view the restriction of $$f$$ to $$C(\partial M\times[0,\epsilon))$$ as a family of embeddings $$f_t:\partial M\to\partial M\times[0,l)$$, and, by projecting onto factors, a familty of smooth maps $$\varphi_t:=\pi_1\circ f_t:\partial M\to\partial M$$ and $$\psi_t:=\pi_2\circ f_t:\partial M\to[0,l)$$. Since $$\varphi_0$$ is the identity (and diffeomorphisms are stable for compact manifolds without boundary), we may assume by shrinking $$\epsilon$$ as needed that $$\varphi_t$$ is a diffeomorphism for $$t\in[0,\epsilon)$$.
From here, we split $$f$$ ito a "horizontal" and "vertical" part, both with domain $$\partial M\times[0,\epsilon)$$. Let $$h(x,t)=(\varphi_t(x),t)$$ and $$v(x,t)=(x,(\psi_t\circ\varphi_t^{-1})(x))$$. Note that $$f|_{\partial M\times[0,\epsilon)}=v\circ h$$. From here, one can show that $$h$$ can be isotopically deformed into a function $$\hat{h}(x,t)=(\varphi_{\lambda(t)}(x),t)$$ where $$\lambda:[0,\epsilon)\to[0,\epsilon)$$ vanishes on a neighborhood of $$0$$ and is equal to the identity on a neighborhood of $$\epsilon_2$$, likewise, one can deform $$v$$ to a funtion $$\hat{v}$$ which is equal to the identity on $$\partial M\times=[0,a)$$ and equal to $$v$$ on $$\partial M\times(b,\epsilon)$$ for some $$a,b\in(0,\epsilon)$$.
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## MSE 2016 - Full Program
Back to overview
Lecture
### Phase field modeling of diffusion-limited precipitation in multi-component Ni-based superalloys
Wednesday (28.09.2016)
17:30 - 17:45
Part of:
We develop a phase-field model for the simulation of diffusion-limited precipitation in Ni-based superalloys with industry-relevant chemical complexity. The thermodynamic formulation is validated by comparisons to respective ThermoCalc equilibrium calculations and DICTRA sharp interface simulations. Furthermore, an elastic term is included in the model to account for the misfit stresses as well as elastic inhomogeneities between the two considered phases.
First, we consider the coarsening kinetics of $\gamma'$-precipitates in single crystalline Ni-based cast-alloys. 2D simulations show that the additional influence from the missfit strain leads to a systematically faster coarsening-evolution as compared to respective simulations without elastic effects and predictions from the classical LSW-theory (Ostdald-ripening).
As a second example, we consider the coarsening kinetics of meta-stable gamma''-precipitates in the well-known Ni-based wrought-alloy Inconel 718, which involves a cubic to tetragonal transformation.
Here, we study the evolution of microstructural characteristics, such as the mean particle diameter as well as the overall phase fraction as function of the basic two heat treatment parameters: temperature and time.
Speaker:
Dr. Michael Fleck
University of Bayreuth
Additional Authors:
• Leslie T. Mushongera
University of Bayreuth
• Frank Querfurth
University of Bayreuth
• Markus Thäter
University of Bayreuth
• Philipp Amendt
University of Bayreuth
• Dr. Julia Kundin
University of Bayreuth
• Prof. Dr. Heike Emmerich
University of Bayreuth
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# Making a working neuronal network
I've got the following two MWE:
\documentclass[border=5pt,tikz]{standalone}
\begin{document}
\begin{tikzpicture}
%%% %%% %%%
%>> We are building a perceptron
%%% %%% %%%
% input vectors
\xdef\firstinputarray{{1,2}}
\xdef\secondinputarray{{4,8}}
% output vector
\xdef\outputarray{{1,0}} % The 1 means that for \firstinputarray the statement is true, for \secondinputarray is wrong
% weights
\xdef\zerow{.5}
\xdef\firstw{2}
\xdef\secondw{1.75}
% bias
\xdef\bias{1}
% Heaviside
\newcommand{\heaviside}[1]{
\ifnum#1>0
\pgfmathsetmacro{\a}{1}
\fi
\ifnum#1=0
\pgfmathsetmacro{\a}{1}
\fi
\ifnum#1<0
\pgfmathsetmacro{\a}{0}
\fi
}
% Floor function
\newcommand{\floor}[1]{
\pgfmathsetmacro{\floornumber}{int(floor(#1))}
}
\newcommand{\forheavi}[1]{
\pgfmathsetmacro{\forheavinumber}{int(floor(#1))}
}
% new weights
\pgfmathsetmacro{\firstway}{\zerow*\bias+\firstinputarray[0]*\firstw+\firstinputarray[1]*\secondw}
\forheavi{\firstway}
\heaviside{\forheavinumber}
\node (a) {\texttt{firstway}: \pgfmathprintnumber{\firstway}\qquad$\mathrm{H}(\mathtt{firstway})$:\pgfmathprintnumber{\a}};
% set new weights
\ifnum\a>0
\pgfmathsetmacro{\firstw}{.5*(\firstway-0)*\firstinputarray[0]}
\fi
\forheavi{\firstway}
\heaviside{\forheavinumber}
\node[above left,yshift=1cm] at (a.north east) {new \texttt{firstw}: \pgfmathprintnumber{\firstw}\qquad$\mathrm{H}(\mathtt{new fistw})$: \pgfmathprintnumber{\a}};
% \forheavi{0}
% \heaviside{\forheavinumber}
% \node[red,draw,below=.5cm] at (a) {\pgfmathprintnumber{\a}};
\end{tikzpicture}
\end{document}
and
\documentclass[border=5pt,tikz]{standalone}
\usetikzlibrary{decorations.pathreplacing}
\tikzset{
neuron/.style={
draw,circle,inner sep=.3cm,fill=white
},
brace/.style={
decorate,decoration={brace,amplitude=.3cm},thick
}
}
\begin{document}
\begin{tikzpicture}
\foreach \x in {0,1,...,8}
{
\node[neuron] (a\x) at (0,\x) {};
}
\foreach \y in {-4,-3,...,12}
{
\node[neuron] (b\y) at (8,\y) {};
}
\foreach \z in {-2,-1,...,10}
{
\node[neuron] (c\z) at (16,\z) {};
\pgfmathsetmacro{\n}{10-\z}
\draw[->] (c\z) --+ (1,0) node[right] {\pgfmathprintnumber{\n}};
}
\foreach \x in {0,1,...,8}
\foreach \y in {-4,-3,...,12}
\foreach \z in {-2,-1,...,10}
{
\draw[->] (a\x) -- (b\y);
\draw[->] (b\y) -- (c\z);
}
\draw[brace] ([xshift=-1cm]a0.south) -- ([xshift=-1cm]a8.north) node[midway,text width=2.5cm,left=.5cm] {
\begin{tabular}{c}
input layer \\
(784 neurons)
\end{tabular}
};
\node[above=1cm] at (b12) {
\begin{tabular}{c}
hidden layer \\
($n = 15$ neurons)
\end{tabular}
};
\node[above=1cm] at (c10) {
\begin{tabular}{c}
output layer
\end{tabular}
};
\end{tikzpicture}
\end{document}
with the following output:
I've got the following questions:
• How can I achieve that I can enter the input arrays and the starting weights and the first code does the calculations (more precisely: how can I “extend“ the foreach loop so that the algorithm stops when the right resulst is achieved) and
• How can I than highlight the weights visual e.g. I let TikZ draw two nodes (which represent neurons) and the more “important“ a bond is the line (which connects the two neurons) gets thicker (this all happens step for step, so that we can create a little animation)?
P.S.: The feedforward network doesn't need to have such a big amount of neurons, this is just an illustration.
• I once wrote a macro that allows a somewhat more automatic generation of these things. Do you think this is a step in the right direction? – marmot Oct 11 at 14:59
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# Math Help - Nonlinear least squares fit to determine Constants in given Formula
1. ## Nonlinear least squares fit to determine Constants in given Formula
So I have the following two equations:
(1) $F = F_0 (C_t - C_b) + F_b C_b$
(2) $Kx^2 - x(KD +KC_t +1) + KD C_t = 0$
Here x = $C_b$
I have a set of data points that is $(F_i, D_i)$
I know $C_t$ as it is a constant.
My question is how do I use a nonlinear least squares method to get values for $F_0 , F_b ,$ and $K$.
What I've tried so far is solving for x in equation (2) using the quadratic formula and likewise solving for $C_b$ in equation (1). From there, I equated the two resulting equations since x = $C_b$ and then solved for F, so I get some equation that is F = $f(K, C_t, F_0 , F_b)$.
Is this even going in the right direction? I am trying to create a MATLab program that will help in solving for these parameters, as it's something I'm going to have to solve for many data sets $(F_i, D_i)$.
Additionally, does anyone have any recommendations for textbooks I can reference in solving a problem like this as I'm at a bit of a loss in trying to solve this?
2. ## Re: Nonlinear least squares fit to determine Constants in given Formula
Originally Posted by tantile
So I have the following two equations:
(1) $F = F_0 (C_t - C_b) + F_b C_b$
(2) $Kx^2 - x(KD +KC_t +1) + KD C_t$
Here x = $C_b$
I have a set of data points that is $(F_i, D_i)$
I know $C_t$ as it is a constant.
My question is how do I use a nonlinear least squares method to get values for $F_0 , F_b ,$ and $K$.
What I've tried so far is solving for x in equation (2) using the quadratic formula and likewise solving for $C_b$ in equation (1). From there, I equated the two resulting equations since x = $C_b$ and then solved for F, so I get some equation that is F = $f(K, C_t, F_0 , F_b)$.
Is this even going in the right direction? I am trying to create a MATLab program that will help in solving for these parameters, as it's something I'm going to have to solve for many data sets $(F_i, D_i)$.
Additionally, does anyone have any recommendations for textbooks I can reference in solving a problem like this as I'm at a bit of a loss in trying to solve this?
Please correct/complete (2) as it is it is just an expression.
CB
3. ## Re: Nonlinear least squares fit to determine Constants in given Formula
Originally Posted by CaptainBlack
Please correct/complete (2) as it is it is just an expression.
CB
Sorry about that! Fixed, it should be equal to 0
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An alternative method for a problem
Show that the given function has exactly one root in given interval. Consider $f(x)= x^4+3x+1$ on the interval $[-2,-1]$.
My try:
By intermediate value theorem there must be at least one real root in the given interval.
Suppose, consider that there are 2 or more real roots in $[-2,-1]$. Hence by Rolle's theorem there must be at least one real $x_0$ such that $f ' = 0$ in $[-2,-1]$ but $f '=0$ at $x=-\sqrt[3] {\frac {3}{4}}$ , which doesn't belong to the given interval. Hence we have a contradiction. Hence there is exactly one real root in given interval.
I want to know if there are any other standard methods to solve such problems without using contradiction. Because this method is cumbersome when it is very difficult to find the solution of the first derivative to check whether it lies in the given interval or not. Thanks for any help.
• You’re using contradiction here for all of the wrong reasons here. This is literally a simple application to the Intermediate Value Theorem. – DaveNine Feb 18 '18 at 15:26
• @DaveNine can you please elaborate how – Rohan Shinde Feb 18 '18 at 15:28
Since $f(-1)=-1<0$ and $f(-2)=11>0$, by the Intermediate Value Theorem we may conclude that there is at least a zero in $(-2,-1)$.
Now notice that $f'(x)=4x^3+3$ and $f''(x)=12x^2\geq 0$ which imply that $f'$ is increasing. Since $f'(-1)=-1$ we have that $f'$ is negative and $f$ is strictly decreasing in $(-\infty,-1]$. Then it follows that the above zero has to be unique.
• Does this method anyone help when $f(x)=\frac {1}{1-x} + \sqrt {x+1} -3.1$ in the interval $(-1,1)$ – Rohan Shinde Feb 19 '18 at 6:33
• @Manthanein Yes, $f$ is the sum of strictly increasing function and therefore $f$ is strictly increasing too. Moreover at $-1$ and at $1^-$ the function $f$ has opposite signs. – Robert Z Feb 19 '18 at 6:43
Without calculus, first note that $\,f(x)= x^4+3x+1\,$ cannot have real positive roots by Descartes' rule of signs. It follows that not all roots can be real, since $\,4\,$ negative roots cannot add up to a sum of $\,0\,$ as given by Vieta's relations.
Then, let $\,z=x+2\,$ so that $\,x \in [-2,-1] \iff z \in [0,1]\,$. Substituting $\,x=z-2\,$ into the equation gives $g(z)=f(z-2)=z^4 - 4 z^3 + 6 z^2 - z - 1\,$.
Again by Descartes' rule of signs $\,g\,$ has exactly $\,1\,$ negative root, and $\,3\,$ or $\,1\,$ positive roots. Since not all roots are real, this excludes the case of $\,3\,$ positive roots, and since $\,f(0) \lt 0 \lt f(1)\,$ the unique positive root in $\,z\,$ must be in $\,(0,1)\,$ i.e. there is a unique root $x = z-2 \in \,(-2,-1)\,$.
Its derivative $f^\prime(x)=4x^3+3$ vanishes exactly one time and $f(x) \to +\infty$ as $x\to \pm \infty$. Now $f(-1)<0<\min(f(-2),f(0))$, hence by the intermediate theorem and the previous reasoning there is exactly one root in $(-2,-1)$ and exactly one root in $(-1,0)$.
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# Epsilon-Delta Proof with 2-Variable Polynomial
## Homework Statement
Find a specific number δ>0 such that if x2 + y2 = δ2, then |x2+y2+3xy+180xy5 < 1/10 000.
## Homework Equations
ε-δ def'n of limit: lim (x,y) → (a, b) f(x) = L if for every ε > 0 there exists a δ > 0 such that 0 < √(x-a)2+(y-b)2, |f(x) - L| < ε.
## The Attempt at a Solution
So, f(x) = |x2+y2+3xy+180xy5 and because x2 + y2 = δ2, the limit is being taken as (x, y) → (0, 0) and L = 0.
I don't understand how I would start this problem because it's not rational, like I'm used to. I can do this:
(x) = |x2+y2+3xy+180xy5 = x2 + y2 + 3|x||y| + 180|x||y5|, but now I am stuck. Any help is greatly appreciated.
Related Calculus and Beyond Homework Help News on Phys.org
jbunniii
Homework Helper
Gold Member
|x2+y2+3xy+180xy5| = x2 + y2 + 3|x||y| + 180|x||y5|, but now I am stuck. Any help is greatly appreciated.
Well, this equation is certainly not true, but if you replace the ##=## with ##\leq##, then it is true, because of the triangle inequality. So this gives you
$$|x^2 + y^2 + 3xy + 180xy^5| \leq |x^2 + y^2| + |3xy| + |180xy^5|$$
Assuming ##x## and ##y## are real, it's true that ##|x^2 + y^2| = x^2 + y^2##. And the absolute value of a product equals the product of absolute values. So we can rewrite the right hand side as
$$x^2 + y^2 + 3|x|\cdot |y| + 180 |x| \cdot |y|^5$$
You know that ##x^2 + y^2 = \delta^2##. Can you find a way to bound the other terms in a way that depends on ##\delta##?
Sorry, I meant to say that x2+y2 < δ^2
I am still very confused.
Can I do something like this?
0 ≤|x2 + y2 + 180xy5| ≤ x2 + y2 + |3xy| + |180xy5| ≤ |3x2y2|+|180x2y5| = |3x2y2(|1+60y3|)
jbunniii
Homework Helper
Gold Member
0 ≤|x2 + y2 + 180xy5| ≤ x2 + y2 + |3xy| + |180xy5| ≤ |3x2y2|+|180x2y5| = |3x2y2(|1+60y3|)
It isn't necessarily true that ##|3xy| \leq |3x^2 y^2|## or that ##|180xy^5| \leq |180x^2 y^5|##. This is true if ##x \geq 1## and ##y \geq 1## but not in general.
Here is a hint. How does ##|x|## compare to ##\sqrt{x^2 + y^2}##?
Mark44
Mentor
Sorry, I meant to say that x2+y2 < δ^2
I am still very confused.
Can I do something like this?
0 ≤|x2 + y2 + 180xy5| ≤ x2 + y2 + |3xy| + |180xy5| ≤ |3x2y2|+|180x2y5| = |3x2y2(|1+60y3|)
No. You can't turn a sum into a product like that.
IOW, you can't do this: x2 + y2 + |3xy| + |180xy5| ≤ |3x2y2|+|180x2y5|
And you can't do what you did in the last expression, either.
Here is a hint. How does ##|x|## compare to ##\sqrt{x^2 + y^2}##?
Okay. So,
|x| ≤ $\sqrt{}x2+y2$< δ
and
|y| ≤ $\sqrt{}x2+y2$< δ
Then,
|x2+y2+3xy+180xy5| < δ+δ+3δ2+180δ6
Right?
Also, thank you so much!
jbunniii
Homework Helper
Gold Member
Okay. So,
|x| ≤ $\sqrt{}x2+y2$< δ
and
|y| ≤ $\sqrt{}x2+y2$< δ
So far so good.
Then,
|x2+y2+3xy+180xy5| < δ+δ+3δ2+180δ6
That's not quite right. Try writing out the intermediate steps:
\begin{align} |x^2 + y^2 + 3xy + 180xy^5| & \leq x^2 + y^2 + 3|x| |y| + 180 |x| |y|^5 \\ & \leq \delta^2 + 3|x| |y| + 180 |x| |y|^5 \\ &\leq ???\end{align}
Isn't |x2+2+3xy+180xy5| ≤ δ2
ie. it doesn't matter what you add to the right side because it will always make δ2 larger, in this case?
jbunniii
Homework Helper
Gold Member
You're trying to solve for ##\delta## which will satisfy the requirement in your problem statement. You need to find a bound for ##|x^2 + y^2 + 3xy + 180xy^5|## that depends only on ##\delta##, not ##x## or ##y##. You have the constraint ##x^2 + y^2 < \delta^2##. From this, in post #6 you found some bounds for ##|x|## and ##|y|##. Now apply those to the right hand side in post #7.
jbunniii
Homework Helper
Gold Member
Isn't |x2+2+3xy+180xy5| ≤ δ2
ie. it doesn't matter what you add to the right side because it will always make δ2 larger, in this case?
To address this question directly, no, it's not necessarily true. All you know is that ##x^2 + y^2 < \delta^2##. But ##|x^2 + y^2 + 3xy + 180xy^5|## may be bigger than ##x^2 + y^2##, so it isn't necessarily bounded by ##\delta^2##. Try plugging in ##x=y=1## and ##\delta = 2## to see this.
Waiiiiit. 4δ2 + 180δ6
would be the right side?
jbunniii
Homework Helper
Gold Member
Yes, that looks right:
##x^2 + y^2 < \delta^2##
##3|x||y| < 3\delta^2##
##180|x||y|^5 < 180\delta^6##
so
##x^2 + y^2 + 3|x||y| + 180|x||y|^5 < 4\delta^2 + 180\delta^6##
1 person
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# reactions of continuous beams shear diagrams strength of materials
07.adsense-blog.com 9 out of 10 based on 300 ratings. 600 user reviews.
Reactions of Continuous Beams | Shear Diagrams | Strength ... Finding the Reactions of Continuous Beams Isolate each span of the beam and consider each as simply supported carrying the original span loading and the computed end moments. Resolve further the simple span into simple beams, one carrying the given loads plus another beam carrying the end moments and couple reactions. With this method, the interior reaction was divided into parts which can be summed up find the total reaction. See example below. Beam Reactions and Diagrams – Strength of Materials ... Shear Forces Diagrams: At the ends of a simply supported beam the shear force is zero. At the wall of a cantilever beam the shear force equals the vertical reaction at the wall. At the beam’s free end the shear force is zero. On any beam segment where no loads are applied, the shear force remains constant (horizontal line). Problem 831 | Reactions of Continuous Beams | Strength of ... Support reactions $R_1 = 53.33 ~ \text{lb downward}$ answer $R_2 = 53.33 86.67 = 140 ~ \text{lb}$ answer $R_3 = 213.33 ~ \text{lb}$ answer Problem 833 | Reactions of Continuous Beams | Strength of ... Problem 833 | Reactions of Continuous Beams | Strength of Materials Review 11 30 16, 8)58 AM : .mathalino reviewer strength materials problem 833 reactions continuous beams Page 1 of 7 Home » Strength of Materials » Chapter 08 Continuous Beams » Reactions of Continuous Beams | Shear Diagrams Mabuhay! Please join our community. Continuous Beam Reactions New Images Beam Reactions Of Continuous Beams Shear Diagrams Strength. Problem 829 Reactions Of Continuous Beams Strength Materials. Continuous Beam Two Unequal Span With Udl. Beams Fixed At Both Ends Continuous And Point Lo. Beam Formula Archives Ering Notes. Solved Exle On Indeterminate Structure By Method Of Consistent. Thermal Stress Distribution For A Continuous Beam 2 . Continuous Beam Three Span With ... Continuous Beam Bending Moment Diagram Calculator Multiple Continuous Beams Materials Engineering . Solved Question 6 Consider A 3 Span Continuous Beam For W. Free Beam Calculator Bending Moment Shear Force And Deflection. How To Draw Bending Moment Diagrams Skyciv. Reactions Of Continuous Beams Shear Diagrams Strength. 3 Moment Equation Example 2 Three Span Beam Part 1 Youtube. Bending Moment Calculator Is Specifically Used For puting ... Continuous Beam Reactions Best Photos Of Beam Imagesr.Org Called continuous beam and a is also like simply supported it at the ends apart from support end shuld 833 shear diagram about problem reactions of continuous ... Shear Force Diagram For Fixed Beams | Diagram Cuts before and after each reaction load to calculate the bending moment of a beam we must work in same way did for shear force diagram the overhanging beam unlike simple or fixed has one end that is unsupported indeterminate any problem with more than 3 unknown forces will be some thing to keep in the back of your mind when drawing free body ... Problem 835 | Reactions of Continuous Beams | Strength of ... Problem 835 | Reactions of Continuous Beams | Strength of Materials Review 11 30 16, 844 AM : .mathalino reviewer strength materials problem 835 reactions ... Statically Indeterminate Continuous Beam Analysis by Superposition Example Mechanics of Materials The video is an example problem for the analysis of a statically indeterminate continuous beam using the method of superposition. After calculating the reactions, the shear and moment diagrams are ... Continuous Beam Reactions Best Beam In The Word ... Gate mechanical numerical of continuous beam clapeyron s theorem important topics with unacademy post 15 2 roximate ysis of a continuous beam for gravity load 164 support reactions1 pngContinuous Beam Moment And Reaction Support ForcesReactions Of Continuous Beams Shear Diagrams StrengthReactions Of Continuous Beams Shear Diagrams ... Statically Indeterminate Beam by Superposition Example 1 (Part 1 2) Mechanics of Materials This video demonstrates how to calculate the reactions and draw shear and moment diagrams of a statically indeterminate beam by using the method of superposition.
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Browse Questions
# Which of the following organisms is likely to have more concentration of DDT in its body?
$\begin{array}{1 1}(a)\;\text{Primary producer}\\(b)\;\text{Herbivore}\\(c)\;\text{Carnivore}\\(d)\;\text{Top carnivore}\end{array}$
Top carnivore has more concentration of DDT in its body
Hence (d) is the correct answer.
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# How to light a colored line or simple polygon?
This topic is 1938 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
I'm guessing the transparent areas are just textures with some semitransparancy (alpha) in them
behind the line, you can draw a quad with a texture with the glow.
You'd actually need 3 quads, one for each endpoint and one for the middle. (the middle will be stretched to draw different length lines, and if you stretch the whole thing, the ends will get oblong and not look that good).
Then play a bit with alpha-value for blending them to get a nice glowy effect.
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That is what is usually referred to as a 'bloom', and it is more or less just using a Gaussian filter to blur the colors. There is a sample chapter about how a similar effect is used in the game Tron from way back in the original GPU Gems book, which you can find online now for free. It tells you lots about how to implement such a system, and should get you on your way!
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The reason I don't think it's a proper bloom, is the circular areas with double light intensity in the corners.
Looks very much like two layers of "glow-texture".
Also, not blurring is faster (even though modern mobile devices shouldn't have a problem) Edited by Olof Hedman
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That is what is usually referred to as a 'bloom', and it is more or less just using a Gaussian filter to blur the colors. There is a sample chapter about how a similar effect is used in the game Tron from way back in the original GPU Gems book, which you can find online now for free. It tells you lots about how to implement such a system, and should get you on your way!
When I use the Gaussian filter to blur a line(1-2 pixels) in the whole black background, the blurred line is dark and it's "glowing" range is small. Then I compose the tow lines, the final effect is not as clear as the game's. May be I missed something?
I haven't read the book, but I will check it later.
I'm guessing the transparent areas are just textures with some semitransparancy (alpha) in them
behind the line, you can draw a quad with a texture with the glow.
You'd actually need 3 quads, one for each endpoint and one for the middle. (the middle will be stretched to draw different length lines, and if you stretch the whole thing, the ends will get oblong and not look that good).
Then play a bit with alpha-value for blending them to get a nice glowy effect.
I have no idea with "a texture with the glow", could you give me some examples? Or you can tell me where I can find the texture? (I have already "googled" it, but can't find something useful.)
Thanks a lot.
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1-2 pixels is too little for a bloom, you need to use a bigger kernel. A way to increase the kernel "for free" is to do the blurring on a downscaled image and finally draw a re-upscaled overlay. This can also improve performance.
Here's a image you can use for the fake bloom:
Or you could do it procedurally in a pixel shader like so:
{
float2 radius = uv * 2 - 1; // de-normalize tex-coords
}
Then use this this value e.g. for an alpha. Give it a tint for the desired color and blend additively (or alpha-additively).
This is what the tex-coords should look for the three quads.
(0,0) (0.5, 0) (0.5, 0) (1,0)
..+--------+--------------+---------+
..|........|..............|.........|
..|........|..............|.........|
..|........|..............|.........|
..|........|..............|.........|
..+--------+--------------+---------+
(0,1) (0.5, 1) (0.5, 1) (1,1)
I'm with Olof, this looks like a fake bloom.
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When I use the Gaussian filter to blur a line(1-2 pixels) in the whole black background, the blurred line is dark and it's "glowing" range is small. Then I compose the tow lines, the final effect is not as clear as the game's. May be I missed something?
I haven't read the book, but I will check it later.
Can you post a screenshot of what you are getting? I think we could easily work through the issue. I also think it would be worth your while to check out that chapter - even if you just skim through it, there is some good information in there.
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Can you post a screenshot of what you are getting? I think we could easily work through the issue.
This is the screenshot: http://flic.kr/p/eDFLwx
I do this in GIMP:
1. I begin with a black background(layer 1).
2. Then draw the red(255, 0, 0) line (4 pixels) in the layer 2.
3. Copy layer 2 to layer 3
4. Use gaussian fliter(kernel size is 10x10) to blur the layer 2.
5. layer 3's mode is addition.
The problem is:
1. The middle red line isn't as bright as I expected. I guess it didn't blend correctly.
2. The "glowing" is also too dark.
I also think it would be worth your while to check out that chapter - even if you just skim through it, there is some good information in there.
Edited by Sachs
##### Share on other sites
1-2 pixels is too little for a bloom, you need to use a bigger kernel. A way to increase the kernel "for free" is to do the blurring on a downscaled image and finally draw a re-upscaled overlay. This can also improve performance.
Here's a image you can use for the fake bloom:
Or you could do it procedurally in a pixel shader like so:
{
float2 radius = uv * 2 - 1; // de-normalize tex-coords
}
Then use this this value e.g. for an alpha. Give it a tint for the desired color and blend additively (or alpha-additively).
This is what the tex-coords should look for the three quads.
(0,0) (0.5, 0) (0.5, 0) (1,0)
..+--------+--------------+---------+
..|........|..............|.........|
..|........|..............|.........|
..|........|..............|.........|
..|........|..............|.........|
..+--------+--------------+---------+
(0,1) (0.5, 1) (0.5, 1) (1,1)
I'm with Olof, this looks like a fake bloom.
I got it! This method is easy and effective. Thanks a lot.
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# Modular arithmetic with cardinals.
cragar
Can I do operations like ${\aleph_0}^{\aleph_0}mod {\aleph_0}$
and would this equal $\aleph_0$
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Summer Deals - hours only!Up to 80% off on all courses and bundles.-Close
Introduction
The Final Quiz
12. Question 9
You’ve Completed the Windows Function Course!
## Instruction
Good job! We're getting close to the end – we’ve made it to Question 9.
## Exercise
For each treatment, show its Name, Score, Price, Category, the average price in its category (as AvgPrice), the average score in its category (as AvgScore) and that treatment's rank in the category (based on its Score). The treatment with the highest Score should get Rank 1. Name this column Ranking. Multiple treatments can have the same rank, but don't allow gaps in numbering.
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# Can you find the area?
Geometry Level 1
HEY!! suppose that,ABCD is a rectangle.E,F are the midpoints of side AD and CD respectively.If the AREA of quadrilateral EBFD is 9.What is the area of the rectangle ABCD?
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# Neural Networks
Consider a supervised learning problem where we have access to labeled training examples (x(i),y(i)). Neural networks give a way of defining a complex, non-linear form of hypotheses hW,b(x), with parameters W,b that we can fit to our data.
To describe neural networks, we will begin by describing the simplest possible neural network, one which comprises a single "neuron." We will use the following diagram to denote a single neuron:
This "neuron" is a computational unit that takes as input x1,x2,x3 (and a +1 intercept term), and outputs $h_{W,b}(x) = f(W^Tx) = f(\sum_{i=1}^3 W_{i}x_i +b)$, where $f : \Re \mapsto \Re$ is called the activation function. In these notes, we will choose $f(\cdot)$ to be the sigmoid function:
$f(z) = \frac{1}{1+\exp(-z)}.$
Thus, our single neuron corresponds exactly to the input-output mapping defined by logistic regression.
Although these notes will use the sigmoid function, it is worth noting that another common choice for f is the hyperbolic tangent, or tanh, function:
$f(z) = \tanh(z) = \frac{e^z - e^{-z}}{e^z + e^{-z}},$
Here are plots of the sigmoid and tanh functions:
The tanh(z) function is a rescaled version of the sigmoid, and its output range is [ − 1,1] instead of [0,1].
Note that unlike CS221 and (parts of) CS229, we are not using the convention here of x0 = 1. Instead, the intercept term is handled separately by the parameter b.
Finally, one identity that'll be useful later: If f(z) = 1 / (1 + exp( − z)) is the sigmoid function, then its derivative is given by f'(z) = f(z)(1 − f(z)). (If f is the tanh function, then its derivative is given by f'(z) = 1 − (f(z))2.) You can derive this yourself using the definition of the sigmoid (or tanh) function.
## Neural Network formulation
A neural network is put together by hooking together many of our simple neurons, so that the output of a neuron can be the input of another. For example, here is a small neural network:
In this figure, we have used circles to also denote the inputs to the network. The circles labeled +1 are called {\bf bias units}, and correspond to the intercept term. The leftmost layer of the network is called the {\bf input layer}, and the rightmost layer the {\bf output layer} (which, in this example, has only one node). The middle layer of nodes is called the {\bf hidden layer}, because its values are not observed in the training set. We also say that our example neural network has 3 {\bf input units} (not counting the bias unit), 3 {\bf hidden units}, and 1 {\bf output unit}.
We will let nl denote the number of layers in our network; thus nl = 3 in our example. We label layer l as Ll, so layer L1 is the input layer, and layer $L_{n_l}$ the output layer. Our neural network has parameters (W,b) = (W(1),b(1),W(2),b(2)), where we write $W^{(l)}_{ij}$ to denote the parameter (or weight) associated with the connection between unit j in layer l, and unit i in layer l + 1. (Note the order of the indices.) Also, $b^{(l)}_i$ is the bias associated with unit i in layer l + 1. Thus, in our example, we have $W^{(1)} \in \Re^{3\times 3}$, and $W^{(2)} \in \Re^{1\times 3}$. Note that bias units don't have inputs or connections going into them, since they always output the value +1. We also let sl denote the number of nodes in layer l (not counting the bias unit).
We will write $a^{(l)}_i$ to denote the {\bf activation} (meaning output value) of unit i in layer l. For l = 1, we also use $a^{(1)}_i = x_i$ to denote the i-th input. Given a fixed setting of the parameters W,b, our neural network defines a hypothesis hW,b(x) that outputs a real number. Specifically, the computation that this neural network represents is given by:
\begin{align} a_1^{(2)} &= f(W_{11}^{(1)}x_1 + W_{12}^{(1)} x_2 + W_{13}^{(1)} x_3 + b_1^{(1)}) \\ a_2^{(2)} &= f(W_{21}^{(1)}x_1 + W_{22}^{(1)} x_2 + W_{23}^{(1)} x_3 + b_2^{(1)}) \\ a_3^{(2)} &= f(W_{31}^{(1)}x_1 + W_{32}^{(1)} x_2 + W_{33}^{(1)} x_3 + b_3^{(1)}) \\ h_{W,b}(x) &= a_1^{(3)} = f(W_{11}^{(2)}a_1^{(2)} + W_{12}^{(2)} a_2^{(2)} + W_{13}^{(2)} a_3^{(2)} + b_1^{(2)}) \end{align}
In the sequel, we also let $z^{(l)}_i$ denote the total weighted sum of inputs to unit i in layer l, including the bias term (e.g., $z_i^{(2)} = \sum_{j=1}^n W^{(1)}_{ij} x_j + b^{(1)}_i$), so that $a^{(l)}_i = f(z^{(l)}_i)$.
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# Controlling the geometry and forces of hybrid cable-net and fabric formworks
Veenendaal D., Bezbradica M., Novak D. and Block P.
Proceedings of the IASS-SLTE 2014 Symposium
Brasilia, Brazil
2014
The construction of anticlastic, thin-shell concrete structures can be efficiently achieved through the use of flexible formworks. Such formworks allow a departure from the traditional hyperbolic paraboloid shells, where its ruled surface serves as the basis for straight-line timber formworks. In addition, as forces are carried by the tensile system to the outer boundaries, the amount of falsework and their foundations, is heavily reduced, leading to economy in material, transportation and storage. This paper presents a prototype hybrid cable-net and fabric formwork used for the construction of two shell structures with identical boundary conditions. The second prototype, which is the main focus of this paper, was constructed after introducing several constructional variations and improvements. Moreover, it was constructed to test more accurate and flexible approaches to measuring both the geometry and internal forces of the cable net. This, in turn, allowed a higher degree of control of the applied prestresses, thus leading to lower tolerances between the digital form-finding model and the physical, as-built geometry.
BibTeX
@inproceedings{Veenendaal2014,
author = "Veenendaal, D. and Bezbradica, M. and Novak, D. and Block, P.",
title = "Controlling the geometry and forces of hybrid cable-net and fabric formworks",
booktitle = "Proceedings of the IASS-SLTE 2014 Symposium",
year = "2014",
editor = "",
volume = "",
number = "",
pages = "",
publisher = "",
month = "",
doi = "",
note = "",
}
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ETH Zurich
Institute of Technology in Architecture
Block Research Group
Stefano-Franscini-Platz 1, HIB E 45
8093 Zurich, Switzerland
paulson@arch.ethz.ch
block.arch.ethz.ch
+41 44 633 38 35 phone
+41 44 633 10 53 fax
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# frequencies for intervals
#### xbender
##### New Member
Hi,
I would like to ask how can I make a frequencies table for a variable that has each value only once (e.g. income). I have set of 300 different values of income from respondents and I would like to get the frequencies in a table saying "income 0-100 = XX times, income 101-200 = YY times" etc. (content-wise, not format-wise)
How can I do that? I havent figured out a way with "tabulate" or "table" commands to do that...
thank you!
#### bukharin
##### RoboStataRaptor
You need to recode the continuous variable (eg income) into a categorical variable. Examples:
Code:
recode income (0/100=1 "0-100") (100/200=2) (...you get the idea...) (900/max=10 ">900"), gen(incomecat)
or
Code:
egen incomecat=cut(income), at(0(100)1000) label
You need to be careful with the categories with -recode-. If your second rule was (101/200) then an income of 100.5 wouldn't be recoded. The rules I've suggested work because once a match has been made, and the value recoded, it won't match any subsequent rules. See -help recode- and the Stata User's Guide.
-egen- requires less typing but the first number (in this case 0) needs to be less than or equal to the lower number in your dataset, and the last number (in this case 1000) needs to be greater than the highest income in your dataset - so you need to look at the data first. Of course you should already be doing that...
After you've recoded it's simply a matter of:
tab incomecat
#### xbender
##### New Member
thank you! that egen command is great! I got that max/min condition at the first glance ;-) easy to get with eg. summary varname
#### bukharin
##### RoboStataRaptor
You're welcome. If you're lazy like me you can extract the maximum value using -summarize-, then plug the result directly into -egen-:
summarize income, meanonly
egen incomecat=cut(income), at(0(100)1000 `=r(max)+1')
The manual entry for -egen- is well worth reading - repeatedly - since it will frequently save you a lot of time...
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# Ubuntu – How to disable “Lock screen” keyboard shortcut under Unity
lock-screenshortcut-keyssystem-settings
I don't want Super + L (that is the windows key pressed with the L key) to lock my screen. I have disabled this in settings, but it still happens. How do I make this not happen?
You should be able to see what is the current setting by the command:
gsettings get org.gnome.desktop.lockdown disable-lock-screen
The output should be:
true
If it isn't, you can set it by the command:
gsettings set org.gnome.desktop.lockdown disable-lock-screen true
A cosmetic downside on my system is however that the screen doesn't lock any more, but still turns black for a second or so. You'll have to see if it works well on your system.
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# 线性代数网课代修|交换代数代写Commutative Algebra代考|MATH483
linearalgebra.me 为您的留学生涯保驾护航 在线性代数linear algebra作业代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的线性代数linear algebra代写服务。我们的专家在线性代数linear algebra代写方面经验极为丰富，各种线性代数linear algebra相关的作业也就用不着 说。
• 数值分析
• 高等线性代数
• 矩阵论
• 优化理论
• 线性规划
• 逼近论
## 线性代数作业代写linear algebra代考|Polynomials of One Variable
In this section, we will discuss polynomials of one variable and study the division algorithm from high school algebra. This simple algorithm has some surprisingly deep consequences-for example, we will use it to determine the structure of ideals of $k[x]$ and to explore the idea of a greatest common divisor. The theory developed will allow us to solve, in the special case of polynomials in $k[x]$, most of the problems raised in earlier sections. We will also begin to understand the important role played by algorithms.
By this point in their mathematics careers, most students have already seen a variety of algorithms, although the term “algorithm” may not have been used. Informally, an algorithm is a specific set of instructions for manipulating symbolic or numerical data. Examples are the differentiation formulas from calculus and the method of row reduction from linear algebra. An algorithm will have inputs, which are objects used by the algorithm, and outputs, which are the results of the algorithm. At each stage of execution, the algorithm must specify exactly what the next step will be.
When we are studying an algorithm, we will usually present it in “pseudocode,” which will make the formal structure easier to understand. Pseudocode is similar to the computer language Pascal, and a brief discussion is given in Appendix B. Another reason for using pseudocode is that it indicates how the algorithm could be programmed on a computer. We should also mention that most of the algorithms in this book are implemented in computer algebra systems such as AXIOM, Macsyma, Maple, Mathematica, and REDUCE. Appendix $\mathrm{C}$ has more details concerning these programs.
We begin by discussing the division algorithm for polynomials in $k[x]$. A crucial component of this algorithm is the notion of the “leading term” of a polynomial in one variable. The precise definition is as follows.
## 线性代数作业代写linear algebra代考|Orderings on the Monomials in k
If we examine in detail the division algorithm in $k[x]$ and the row-reduction (Gaussian elimination) algorithm for systems of linear equations (or matrices), we see that a notion of ordering of terms in polynomials is a key ingredient of both (though this is not often stressed). For example, in dividing $f(x)=x^{5}-3 x^{2}+1$ by $g(x)=x^{2}-4 x+7$ by the standard method, we would:
• Write the terms in the polynomials in decreasing order by degree in $x$.
• At the first step, the leading term (the term of highest degree) in $f$ is $x^{5}=x^{3} \cdot x^{2}=$ $x^{3} \cdot$ (leading term in $g$ ). Thus, we would subtract $x^{3} \cdot g(x)$ from $f$ to cancel the leading term, leaving $4 x^{4}-7 x^{3}-3 x^{2}+1$.
• Then, we would repeat the same process on $f(x)-x^{3} \cdot g(x)$, etc., until we obtain a polynomial of degree less than 2 .
For the division algorithm on polynomials in one variable, then we are dealing with the degree ordering on the one-variable monomials:
$$\cdots>x^{m+1}>x^{m}>\cdots>x^{2}>x>1 .$$
The success of the algorithm depends on working systematically with the leading terms in $f$ and $g$, and not removing terms “at random” from $f$ using arbitrary terms from $g$.
Similarly, in the row-reduction algorithm on matrices, in any given row, we systematically work with entries to the left first-leading entries are those nonzero entries farthest to the left on the row. On the level of linear equations, this is expressed by ordering the variables $x_{1}, \ldots, x_{n}$ as follows:
$$x_{1}>x_{2}>\cdots>x_{n} .$$
## 线性代数作业代写linear algebra代考|Orderings on the Monomials in k
• 将多项式中的项按度数降序写成 $x$.
• 第一步，在 $f$ 是 $x^{5}=x^{3} \cdot x^{2}=x^{3}$. (主导词在 $g$ )。因此，我们将减去 $x^{3} \cdot g(x)$ 从 $f$ 取 消前导词，离开 $4 x^{4}-7 x^{3}-3 x^{2}+1$.
• 然后，我们将重复相同的过程 $f(x)-x^{3} \cdot g(x)$ 等，直到我们得到一个次数小于 2 的多 项式。
对于单变量多项式的除法算法，我们处理单变量单项式的度数排序:
$$\cdots>x^{m+1}>x^{m}>\cdots>x^{2}>x>1 .$$
算法的成功取决于系统地使用 $f$ 和 $g$ ，而不是从“随机”中删除术语 $f$ 使用任意项 $g$.
类似地，在矩阵的行缩减算法中，在任何给定的行中，我们系统地使用左侧的条目，第一个 前导条目是该行最左侧的那些非零条目。在线性方程的水平上，这通过对变量进行排序来表 示 $x_{1}, \ldots, x_{n}$ 如下:
$$x_{1}>x_{2}>\cdots>x_{n}$$
# 计量经济学代写
## 在这种情况下，如何学好线性代数？如何保证线性代数能获得高分呢？
1.1 mark on book
【重点的误解】划重点不是书上粗体，更不是每个定义，线代概念这么多，很多朋友强迫症似的把每个定义整整齐齐用荧光笔标出来，然后整本书都是重点，那期末怎么复习呀。我认为需要标出的重点为
A. 不懂，或是生涩，或是不熟悉的部分。这点很重要，有的定义浅显，但证明方法很奇怪。我会将晦涩的定义，证明方法标出。在看书时，所有例题将答案遮住，自己做，卡住了就说明不熟悉这个例题的方法，也标出。
B. 老师课上总结或强调的部分。这个没啥好讲的，跟着老师走就对了
C. 你自己做题过程中，发现模糊的知识点
1.2 take note
1.3 understand the relation between definitions
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## Bohr Frequency Condition, Electrons
H-Atom ($E_{n}=-\frac{hR}{n^{2}}$)
rachelle1K
Posts: 109
Joined: Sat Sep 07, 2019 12:16 am
### Bohr Frequency Condition, Electrons
What does it mean that an electron drops between levels in the context of the Bohr Frequency condition?
Minh Ngo 4G
Posts: 137
Joined: Thu Jul 25, 2019 12:17 am
### Re: Bohr Frequency Condition, Electrons
Just mean that when an electron drops from a certain energy level to another, that electron releases certain energy or light due to the conservation of energy. That light or energy can be calculated
AArmellini_1I
Posts: 107
Joined: Fri Aug 09, 2019 12:15 am
### Re: Bohr Frequency Condition, Electrons
Minh Ngo 4B wrote:Just mean that when an electron drops from a certain energy level to another, that electron releases certain energy or light due to the conservation of energy. That light or energy can be calculated
Exactly, which is why this change in energy is often represented by a negative value because it's the loss of the emitted light
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# Integration by Parts
Covid-19 has led the world to go through a phenomenal transition .
E-learning is the future today.
Stay Home , Stay Safe and keep learning!!!
In this section, ask-math explains you the important technique of integration called Integration by parts. This technique is used when integrand is a product of the two algebraic and transcendental functions.
If u and v are the two functions of x, then
$\int_{}^{} (uv) dx = u\left(\int_{}^{} (v)dx\right) - \int_{}^{}\left\{\frac{\text{d}u}{\text{d}x}\int_{}^{}(v) dx\right\}dx$
OR
$\int_{}^{} u.dv= u.v - \int_{}^{} v.du$
The integral of the products of the two functions
= ( 1st function)X (integral of the 2nd function) - integral of (derivative of 1st function)x ((integral of the 2nd function)
Proof : For any two functions f(x) and g(x) , we have,
$\frac{\text{d}}{\text{d}x}\left\{f(x).g(x)\right\}= f(x).\frac{\text{d}}{\text{d}x}[g(x)] + g(x).\frac{\text{d}}{\text{d}x}[f(x)]$
$\int_{}^{} \left\{ f(x).\frac{\text{d}}{\text{d}x}[g(x)] + g(x).\frac{\text{d}}{\text{d}x}[f(x)]\right\}dx = f(x).g(x)$
$\Rightarrow\int_{}^{} \left\{ f(x).\frac{\text{d}}{\text{d}x}[g(x)] \right\}+\int_{}^{} \left\{ g(x).\frac{\text{d}}{\text{d}x}[f(x)]\right\}dx = f(x).g(x)$
$\Rightarrow\int_{}^{} \left\{ f(x).\frac{\text{d}}{\text{d}x}[g(x)] \right\}dx = f(x).g(x) - \int_{}^{} \left\{ g(x).\frac{\text{d}}{\text{d}x}[f(x)]\right\}dx$
Let f(x) = u and $\frac{\text{d}}{\text{d}x}[g(x)] dx$ = v So that g(x) = $\int_{}^{}(v) dx$
$\therefore \int_{}^{} (uv) dx = u\left(\int_{}^{} (v)dx\right) - \int_{}^{}\left\{\frac{\text{d}u}{\text{d}x}\int_{}^{}(v) dx\right\}dx$
Note : Proper choice of first and second function -
Like PEMDAS or BODMAS, in Integration by parts we have to follow rule LIPET . We can also choose the first function as the function of which comes first in the word LIPET, where
L - stands for logarithmic functions
I - stands for inverse functions
P - stands for polynomial functions
E - stands for exponential functions
T - stands for trigonometric functions
## Examples on Integration by Parts
Example 1 : Evaluate : $\int_{ }^{ } x.sin(3x) dx$
Solution : Here there are two functions, one is polynomial and 2nd is trigonometric function. So according to LIPTE, u = x and $\frac{\text{d}v}{\text{d}x}$= sin(3x)
u = x
du = dx
$\frac{\text{d}v}{\text{d}x}$= sin(3x)
dv = sin(3x) dx
v= $\int_{ }^{ } sin(3x)dx$
v = $\frac{sin(3x)}{3}$
According to integration by parts,
$\int_{}^{} (uv) dx = u\left(\int_{}^{} (v)dx\right) - \int_{}^{}\left\{\frac{\text{d}u}{\text{d}x}\int_{}^{}(v) dx\right\}dx$
$\int_{}^{}x.sin(3x) dx = x.\int_{}^{}sin(3x)dx - \int_{}^{}\frac{\text{d}}{\text{d}x}(x)\int_{}^{}sin(3x) dx$
= -x $\frac{cos(3x)}{3} - \int_{}^{} \left\{\frac{-cos(3x)}{3}\right\}dx$
= $-x\frac{cos(3x)}{3} + \frac{1}{3}\int_{}^{} cos(3x)dx$
= $-x\frac{cos(3x)}{3} + \frac{1}{3}.\frac{sin(3x)}{3}$
= $-\frac{1}{3}x.cos(3x) + \frac{1}{9} sin(3x) + C$
Example 2: Evaluate $x^{2}.ln(x)$
Solution : Here there are two functions, first is polynomial and 2nd is logarithmic function. So according to LIPTE, u = log(x) and $\frac{\text{d}v}{\text{d}x}= x^{2}$
u = ln(x)
du = $\frac{1}{x} dx$
$\frac{\text{d}v}{\text{d}x}= x^{2}$
dv = $x^{2}$dx
v= $\int_{ }^{ } x^{2}dx$
v = $\frac{x^{3}}{3}$
According to integration by parts,
$\int_{}^{} u.dv= u.v - \int_{}^{} v.du$
$\int_{}^{} ln(x).x^{2} = ln(x)\frac{x^{3}}{3}v - \int_{}^{} \frac{x^{3}}{3}.\frac{1}{x}$
= $\frac{1}{3}.x^{3} ln(x) - \int_{}^{} \frac{x^{2}}{3}$
=$\frac{1}{3}.x^{3} ln(x) - \frac{1}{3} \int_{}^{} x^{2}$
= $\frac{1}{3}.x^{3} ln(x) - \frac{1}{3}. \frac{x^{3}}{3}$
$\int_{}^{} ln(x).x^{2} =\frac{1}{3}.x^{3} ln(x) - \frac{x^{3}}{9} + C$
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# Peeragogy/peeragogy-handbook
TeX HTML Shell
Latest commit 0b9c75a Nov 20, 2017
Type Name Latest commit message Commit time
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code Dec 29, 2013
en-md Jul 29, 2015
en-mw May 18, 2015
en Nov 20, 2017
papers Dec 29, 2013
pictures Mar 11, 2015
.gitignore Dec 29, 2013
coworking.patch Jan 22, 2013
howard-intro.txt Dec 29, 2013
peeragogy.org Jul 12, 2014
release.patch Jan 22, 2013
script.sh Dec 31, 2013
script2.sh Dec 29, 2013
script3.sh Jun 27, 2014
translations Jan 8, 2014
# peeragogy-handbook
This book and accompanying website are a resource for self-organizing self-learners.
We originally were writing the book on a Wordpress site, but migrated the sources to Jekyll. Some of the old scripts in this repository have to do with extracting content from Wordpress, but you can ignore them: It's much simpler now.
## Requirements for building the book locally
Get a copy of the markdown contents of the book by cloning https://github.com/Peeragogy/Peeragogy.github.io
To convert to .tex format:
grep -o "<a href=\"\./[^\"]*" index.html | sed -r "s/<a href=\"\.\/(.*).html/\1/" | xargs -I {} pandoc -o {}.tex {}.md
Or alternatively, if you only want to convert recently changed files, find a particular recent commit number, and copy it place of "MD5HASH" here, and run:
git diff --name-only MD5HASH HEAD
That will give a list of recently changed files. You can then copy them into a working directory and convert as follows:
ls -a1 *.md | xargs basename -s .md | xargs -I {} pandoc -o {}.tex {}.md
To build the book:
Copy the tex files you generated in the last step into the relevant subdirectory (probably en), and run:
xelatex peeragogy-shell.tex
## Note: smart conversions going the other direction!
If you have some LaTeX files that include specialized LaTeX commands or bibliography entries and you want to instruct pandoc to convert them Markdown in a “smart” way, you can use some variant of the following command (where header.tex contains the relevant parts of your preamble):
cat header.tex file.tex | pandoc --from=latex --to=markdown --bibliography ./peeragogy-bib.bib --
Here's an example illustrating the kind of commands that you can use, from our Winter 2015 conversion of the pattern catalog:
% header.tex
\newcommand{\patternname}[1]{{\sc #1}}
\newcommand{\patternnameext}[1]{{\sc #1}}
\newcommand{\patternnameplural}[1]{{\sc #1s}}
\usepackage{framed}
\usepackage[dvipsnames]{xcolor}
# Further notes
There are always a few stylistic things that need to be cleaned up to make a nice PDF (e.g. getting images to show up properly, adjustingsectioning details, and so on). In the 3.0 version of the book, I used per-section biblatex bibliographies in the pattern catalog, with
\begin{refsection}
% text here...
\end{refsection}
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# Printing a character that has been made active in text and/or math mode?
I am not very familiar with TeX's category codes. If I use
\catcode\|=13 \renewcommand{|}{hello world}
then every use of | in my document will be replaced by hello world. However, how would I be able to still print the | sign? Of course, the circular reference
\catcode\|=13 \renewcommand{|}{hello|world}
does not work (exceeding TeX's majestic capacity), although I would like all instances of | to print as hello|world. And, if I'm correct, the above would just hold for regular text mode. How would the above code change if | was to be used in math mode?
-
There are usually two approaches taken to solve this problem.
## A
Save the character with original catcode in a macro before its catcode is changed. This works because catcodes are assigned at input time.
\documentclass{article}
\newcommand{\mypipe}{|}
\catcode\|=\active
\renewcommand{|}{hello\mypipe world}
\begin{document}
|
\end{document}
## B
Force the catcode of | to 12 with \string:
\documentclass{article}
\catcode\|=\active
\renewcommand{|}{hello\string|world}
\begin{document}
|
\end{document}
## Math mode
A character can also be only active in math mode, that is, its mathcode can be "8000. To get the original meaning in this case, one can define a control sequence to be a synonym for the previous mathcode of the character:
\mathchardef\mymathpipe=\mathcode\|
Look at the implementation of the icomma` package for an example.
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# Homework Help: Finding the volume of a solid.
1. Apr 29, 2010
### tarmon.gaidon
1. The problem statement, all variables and given/known data
Find the volume of the solid in the first octant bounded by the coordinate planes and the plane 2x+y-4=0 and 8x-4z=0.
This is a problem for a practice exam for my calculus course and I just need some help getting started.
I have had a lot of trouble in this course trying to figure what the bounds of my integration should be so any pointers would be appreciated!
P.S. I have also had a lot of trouble reversing the oder of integration and changing to spherical and cylindrical coordinates. Mainly because I have trouble figuring out how to change the bounds.
Last edited: Apr 29, 2010
2. Apr 29, 2010
### Staff: Mentor
This is not surprising, since for many problems of this kind, finding the bounds of integration is the hardest part.
Have you drawn a picture of the solid? Drawing a picture should give you a good idea of what the region of integration looks like, and should help you get the limits of integration.
3. Apr 29, 2010
### lanedance
i wouldn't be using spherical or cylindrical, but would have a think about the volume - and try and draw it... whats you attempts at you bounds?
4. May 2, 2010
### tarmon.gaidon
Hey Mark,
Thanks for the suggestion, I see what you are saying but let me ask this.
I have a problem here where I needed to change a triple integral from cylindrical coordinates to Cartesian. I have attached an image of the problem and the solution. When I went to solve it I sketched the solid and then attempted to write the bounds of each variable. I had come to the conclusion that y should be from $$\sqrt{1-x^2}$$ to 1 which is close but not quite right. How would I come to the conclusion they made instead of what I did?
File size:
23 KB
Views:
94
5. May 2, 2010
### The Chaz
Wow, that image would not help me learn ANYTHING!
The limits for "r" and theta will help you determine the limits for x and y.
Since theta only ranges from 0 to π and r ranges from 0 to 1, it is a SEMIcircle of radius one (the top half, actually). To integrate the top of the unit circle "dydx"...
The upper limit for a vertical representative rectangle will range from y = 0 (the x-axis) to the curve y = +√(1-x^2). (...I included the "+" to emphasize that it's the top half).
Then x ranges from -1 to 1.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook
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Higher-Order Probability Theory on Interval Domain
Date:
This talk presented a correct and adequate model for probabilistic PCF extended with partial real numbers using omega quasi-Borel spaces and interval integration monad, with future work in proving the model is also fully abstract.
Slides
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# My Office at Fusionary
My office at Fusionary
I cleaned my office at work yesterday morning and snapped this photo. I can (and do) sit there all day and still enjoy it very much.
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What is the best way to process categorical variables？
I have data with 5,000,000 records and many categorical variables of it have more than 3 categories. For example(here is the Python Pandas code)
>>> df_train_set.PWD_STAT.unique()
[ 0. 1. 3. 2.]
>>> df_train_set.CUST_CLASS_XL.unique()
[500101 620101 540202 5001 560301 600103 610201 610103 540101 570101
500102 590208 630112 510201 550104 600104 530101 640101 560102 580106
590202 630107 530102 640105 530201 580101 570201 540201 610102 550102
630114 560104 520101 610101 510101 560101 630108 630106 550101 610204
610202 510105 580103 520103 510103 640103 590201 510104 520201 550301
600101 520102 560103 630101 590102 630118 570102 590209 590101 600102
560105 530402 630117 640102 630105 580104 630109 560201 50 600301
630113 580102 590207 590206 630115 630116 610501 630102 630111 590104
6301 5401 630103 6201 630110 640104 5801 5402]
In the above output, each value in the list means a category.
Since here the above variables are not binary variables. And I search the internet that maybe I can transform these variables into dummy variables. What is the best way to process these columns of categorical variables？
• Are you asking for code to create dummy variables? – Arun Jose Dec 6 '17 at 7:36
• @ArunJose, No, I know how to get dummy variables. What is the best way to process these columns of categorical variables？ – GoingMyWay Dec 6 '17 at 7:46
• Are you attempting some form of classification? – Arun Jose Dec 6 '17 at 7:47
• @ArunJose, Yes. Since creating dummy variables will make the dimension booming. And I don't know the best methods to process categorical variables. – GoingMyWay Dec 6 '17 at 7:50
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Our finding aids get from AT Reference to DIMES in what is basically a three-step process:
1. Data is exported from ATReference as EAD files
2. Those files are then indexed in DIMES
3. And finally, transformation processes are run on those files to convert them and have them display in a web browser.
On the surface, this is a relatively simple process. However, each of these steps involves a number of different technologies and paradigms for information storage, retrieval, and display.
## Export
Information that is managed using ATReference is stored in a MySQL database. This is a particular kind of database technology that’s often used in open-source projects, and is often used as part of a set of four technologies – the Linux operating system, Apache web server, MySQL database and PHP scripting language – that is often referred to as the LAMP stack (the name comes from the first letter of each of these technologies). This particular technology stack is often used for open-source projects (for example Omeka and WordPress) because each of these technologies is open source, and each fulfills a very specific function.
MySQL is a relational database structure, which means that instead of data being stored in rows and columns in a single table (like in an Excel spreadsheet) data is stored in multiple tables that are linked together using keys. Typically, a cell in one table references a row in another table using a foreign key that specifies both the table and the row to which that cell should be linked. This is a handy way of separating out certain types of data (for example, separating resource records from subjects and names), which allows for better information control.
During the export process, ATReference takes the information in its database tables, bundles it up in a specific order, and outputs it as Encoded Archival Description (or EAD). When this happens, that data undergoes a fundamental transformation from database to document. Databases store information in lots of little bits, which means that the data they contain can be presented and searched in highly flexible ways. You can run incredibly specific queries and get back very specific pieces of information. However, databases are not as good at giving you a sense of the context surrounding a specific piece of information. Documents, on the other hand, have a fixed form (they have specific pieces of information like titles, that appear in a particular order) and are usually designed to be read in a linear fashion, starting at the beginning and ending at the end. Because information is fixed in a particular form, documents give you some context about a particular piece of information, but this also means that they often require you to do a bit of reading to find the specific piece of information you’re looking for.
EAD is written in a markup language called eXtensible Markup Language (XML). XML was developed primarily for use with documents, but it can be used for more general data purposes, and is used widely on the web. It is designed to be processed by parsers for multiple applications, which means that XML is a handy way of transporting data from one system to another. XML enforces document structure through the use of schemas, which define what elements should appear, the order in which they are placed, and the hierarchical arrangement of elements. An EAD finding aid is simply an XML document that conforms to a particular schema of elements.
We go to the trouble of creating EAD because that makes it possible for machines to read and interpret them. It also makes sharing archival description in different systems possible, for example in ArchiveGrid or the National Library of Medicine’s History of Medicine Consortium, or the New York State EAD consortium which is currently being developed.
XML is basically made up of tags, elements, attributes and content. A tag is everything that is inside of a set of angle brackets.
<unitdate normal="1879/1894" type="bulk"><br /> 1879-1894<br /> </unitdate>
In this example, there is just one pair of tags – the first one is an opening tag, and the second is a closing tag (which you can tell by the forward slash in front of the tag name). Tags are made up of elements and attributes. The element name in this example is “unittitle”, and the attributes are “normal” and “type.” As you can see, those attributes are followed by an equal sign and then some data between quotation marks. That data is the attribute value. The text in between the opening and closing tags – 1879-1894 – is the content. In plain language, this little snippet of code is telling a machine which knows how to interpret it, that the text “1879-1894” is a bulk date with a normalized (meaning machine-readable) value of 1879/1894. So XML allows us to create structured information *about* the content as well as the content itself.
There are five very basic rules to how all XML should be structured, which are worth covering here.
• First, all elements must have a closing tag. You saw an example of this above, where the closing tag had a forward slash in front of the tag name
• Second, tags are case sensitive. This means that capitalization matters: and element calledis not the same as an element called
• Third, elements must be properly nested. It’s easier to show this than explain, but it essentially means that you have to open and close tags in an order that makes logical sense to a computer.
• Fourth, documents must have a root element. This means that for each document, there must be a pair of elements that are the first and last elements in the document.
• Finally, attribute values must be contained within quotation marks. Again, the example above had some attribute values.
## Indexing
Once we have all these EAD documents, we then need to apply a set of predefined transformations to those files so they can be searched and displayed in DIMES. This is done with a technology called EXtensible Stylesheet Language Transformation, or XSLT. Broadly speaking, this technology takes an input document, processes it through a series of pre-defined actions or steps in a stylesheet, and returns an output document. It is primarily designed to work with an XML input document, and can produce output documents in a number of different formats. For example, it can take an EAD file (which is XML) and produce an HTML document which can be viewed using a web browser.
There are a couple of pretty common transformation processes that you’ll see in XSL, all of which can be used to transform data in different ways. The first is an IF loop, which is basically a bunch of code that will be executed if a certain condition is met. If that condition is not met, the code will not execute.
Another common process you’ll see is a choose statement. This is a bit more complex, because it involves an xsl:choose element which contains one or more xsl:when statements. The processor looks at that loop, decides which when statements evaluate to true, and then executes the code within all of those statements. This means that instead of a simple true/false loop, you can develop more complex scenarios for output documents.
Finally, there’s an apply-templates function, which allows us to create a template, and then apply it multiple times. This is especially handy when you have the same kind of data in different places in a document, and want to do the same thing to all of them.
## XSLT and DIMES
In the case of DIMES, there are actually three sets of transformations that the data passes through, the textIndexer, crossQuery and the dynaXML processes, all of which include multiple stylesheets.
The textIndexer stylesheets take the raw EAD finding aid and add it to the index, which makes it searchable in DIMES. Because the index is compressed, it is a much faster and more efficient way to search than searching each individual document for a keyword or subject, much like using an index for a book is a much faster way of finding a particular word or concept than reading the entire thing. This stylesheet also adds weighting to certain terms like titles or dates and can also derive additional data from the finding aid for use in searching.
The crossQuery stylesheets control the behavior and appearance of search functionality. When a user conducts a search, they take that query, translate it into a query that XTF can process, and send the resulting query (at the bottom) to the index. The index then returns a set of results in XML. In order to turn that into something that humans can read and understand, there’s one more set of transformations that has to happen.
That’s the dynaXML group, which controls how documents (in our case, finding aids and library records) are displayed. They take the EAD document that comes out of ATReference and turn it into a bunch of HTML pages, using the data in a variety of ways to make things like the table of contents on the left hand side of a finding aid, as well as the various tabs that show front matter and the container list.
## HTML and CSS
I’ve mentioned HTML a couple of times already and many of you are probably familar, but in case you don’t know, it’s an acronym for HyperText Markup Language, which means that it’s a markup language for creating web pages. Web browsers know how to interpret HTML (although some do it better than others) to display a human-readable and hopefully visually appealing page. HTML is really primarily about display (as opposed to XML, which is primarily about defining the semantic of a document’s content and enforcing a particular structure).
HTML has some common tags, many of which you’ll see if you right-click on any web page and then select “view source.” There are a bunch of tags that define sections of a page, like head, body, and div (which defines a division or section of a page), and there are also some tags specific to text, like h1, h2 and h3, which specify certain kinds of headings, and p, which defines regular paragraph text. It’s also possible to embed objects, such as images, forms or videos in HTML.
However, HTML is only part of the equation. The other related technology is CSS, which stands for Cascading Style Sheets. As the name suggests, CSS is a way of controlling the appearance of HTML across a website. It allows us to separate content and display, which might not seem like a big deal, but is actually a huge deal, because it means I can change the size of all the paragraph text across an entire website just by changing one rule.
The basic syntax of CSS is one or more selectors followed by declaration blocks with rules controlling the appearance of elements that match the selector. There are a number of different kinds of selectors that can be used with CSS. The first are element names that appear within the HTML, such as h1, p or div. You can also apply rules based on an element’s class, which is a common attribute that you’ll see in an HTML tag. This allows you to apply the same rules to a bunch of different elements regardless of the element name. You can also do this with IDs, which are also attributes in HTML tags. The difference between IDs and classes is that IDs can only appear once within a document, while classes can appear many times. Within CSS declaration blocks, it is possible to create rules that change the size of elements (including the size of fonts), set colors, define the position of elements on the page, and even whether or not something displays.
All of these technologies work together to produce what we see in our web browsers when we look at DIMES, and it’s important to remember that changes in any one of these processes will likely result in changes throughout the rest of the pipeline. That’s why it’s so important for us to create and follow standardized processes in all the work that we do; something as simple as an improperly capitalized letter can throw everything for a loop!
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Volume of a Cylinder
## Volume of a Cylinder
A cylinder is a circular prism. As with other prisms, the volume of a cylinder can be calculated using the cross-sectional area x length.
Th cross-section of a cylinder is a circle. As the area of a circle =πr^2, the volume of a cylinder is πr^2l, where r is the radius of the circular end, and l is the length of the cylinder.
## Example 1
What is the volume of a cylinder with a diameter of 4cm and a length of 42cm? Give your answer correct to 1 decimal place.
For a circle: Area = pir^2 Substitute A = pi xx 2^2 = 4pi
The cross-sectional area is 4pi
For a cylinder: Volume = area xx length Substitute V = 4pi xx 42 = 527.79
For a Cylinder Volume = pir^2l Substitute 1000 = pir^2 xx 100 Divide both sides by 100 10 = pir^2 Divide both sides by pi 3.183 = r^2 Square root 1.784 = r
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Determine if the server admits the binary transport.
# 1 ftp.binary
<ftp.binary />
#### Exceptions
no active ftp connection
It is not possible to obtain the FTP communication with the server because there is not established.
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## Featured resource
### Defining Mathematics Education *REDUCED*
The Seventy-fifth Yearbook is a celebration and reflection of the history of the NCTM yearbooks, and is a great resource on the key issues of mathematics education through the years.
Members: $21.00 inc.GST Others:$ 26.25 inc.GST
Home > Topdrawer > Geometric reasoning > Misunderstandings
# Misunderstandings
Here are some common situations where misunderstandings and difficulties can occur.
• Recognising plane shapes in different orientations
Students who regularly encounter plane shapes in one specific orientation may have difficulty in classifying shapes correctly and recognising their properties when they look 'different'. For example, a student may not realise that the height of an obtuse-angled triangle can be 'outside' the triangle or recognise that an irregular five-sided shape is a pentagon.
• Correctly identifying and naming corresponding sides and angles
For example, not understanding the importance of correctly identifying the matching sides in a triangle when establishing similarity may result in a student reaching incorrect conclusions about proportions.
• Understanding specific geometrical terms
Students meet very many new terms in geometry which adds to the cognitive load of their learning. In addition, there can be confusion between the everyday meaning of the words used and their geometric meaning (e.g. 'similar').
• Visualising relationships in diagrams
Many problems in geometry require the analysis and/or construction of a diagram, and the recognition of the relationships within it. Sometimes the relationships can be difficult to visualise without the addition of a construction line; the placement of that line is often not immediately obvious.
In complex diagrams sometimes students need to be able to focus on a particular part whilst ignoring others. It can be difficult to know what information is necessary and useful.
These types of misunderstandings and difficulties can be overcome by providing appropriate activities in a carefully sequenced learning plan.
## Classifying polygons
Many students form fixed images of plane shapes that can hinder their progression in later years.
## Similar or congruent?
Students can experience difficulty in knowing which test to use when determining triangles to be either similar or congruent.
## The language of geometry
The purpose of the formal language of geometry is to communicate spatial ideas accurately and succinctly. Geometric language is composed of a broad vocabulary which includes both symbols and words.
## Revealing the invisible
Adding construction lines to a diagram is often necessary when solving problems in geometry. Knowing when and where to add auxiliary lines is difficult for many students.
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## Seminars and Colloquia by Series
Tuesday, March 2, 2010 - 12:00 , Location: Skiles 255 , Michael Lacey , School of Math, Georgia Tech , Organizer:
Hosted by: Huy Huynh and Yao Li
The Hilbert transform is a foundational transform, with deep connections to electrical charge, and analyticity. The two weight inequality for the Hilbert transform' concerns the most general setting in which the Hilbert transform admits a (weighted) L^2 inequality. We will give a couple of (surprising?) ways that this question arises. And we will indicate the surprise that is behind the recent description of all setting in which the two weight inequality holds.
Tuesday, February 23, 2010 - 12:00 , Location: Skiles 255 , Prasad Tetali , Professor, School of Mathematics and School of Computer Science , Organizer:
Hosted by: Huy Huynh and Yao Li
Sampling from and approximately counting the size of a large set of combinatorial structures has contributed to a renaissance in research in finite Markov chains in the last two decades. Applications are wide-ranging from sophisticated card shuffles, deciphering simple substitution ciphers (of prison inmates in the California state prison), estimating the volume of a high-dimensional convex body, and to understanding the speed of Gibbs sampling heuristics in statistical physics. More recent applications include rigorous estimates on J.M. Pollard's (1979) classical Rho and Kangaroo algorithms for the discrete logarithm problem in finite cyclic groups. The lecture will be a brief (mostly self-contained) introduction to the Markov Chain Monte Carlo (MCMC) methodology and applications, and will include some open problems.
Tuesday, February 16, 2010 - 12:00 , Location: Skiles 255 , Doron Lubinsky , School of Mathematics, Georgia Tech , Organizer:
Hosted by: Huy Huynh and Yao Li
Orthogonal Polynomials and their generalizations have a great many applications in areas ranging from signal processing to random matrices to combinatorics. We outline a few of the connections, and present some possible Ph. D Problems
Tuesday, February 9, 2010 - 12:00 , Location: Skiles 255 , Ernie Croot , School of Math, Georgia Tech , Organizer:
Hosted by: Huy Huynh and Yao Li
Olof Sisask and myself have produced a new probabilistic technique for finding almost periods' of convolutions of subsets of finite groups. In this talk I will explain how this has allowed us to give (just recently) new bounds on the length of the longest arithmetic progression in a sumset A+A.
Tuesday, February 2, 2010 - 12:00 , Location: Skiles 255 , Matt Baker , School of Math, Georgia Tech , Organizer:
Hosted by: Huy Huynh and Yao Li
I will discuss some theorems and conjectures in the relatively new field of arithmetic dynamics, focusing in particular on some methods from number theory which can be used to study the orbits of points in algebraic dynamical systems.
Tuesday, January 26, 2010 - 12:00 , Location: Skiles 255 , John McCuan , School of Math, Georgia Tech , Organizer:
Hosted by: Huy Huynh and Yao Li
In the preceeding talk, I outlined a framework for variational problems and some of the basic tools and results. In this talk I will attempt describe several problems of current interest.
Wednesday, December 2, 2009 - 12:00 , Location: Skiles 171 , John McCuan , School of Mathematics, Georgia Tech , , Organizer:
I will describe several geometrical problems that arise from the minimization of some sort of integral functional and the basic relation between such minimization and partial differential equations. Then I will make some further comments on my favorite kind of such problems, namely those that have something to do with minimizing area of surfaces under various side conditions.
Wednesday, November 18, 2009 - 12:00 , Location: Skiles 269 , Drs. Ulmer, Harrell, and Wick , School of Mathematics, Georgia Tech , Organizer:
The Research Horizons seminar this week will be a panel discussion on the academic job market for mathematicians. The discussion will begin with an overview by Doug Ulmer of the hiring process, with a focus on the case of research-oriented universities. The panel will then take questions from the audience. Professor Wick was hired last year at Tech, so has recently been on the students' side of the process. Professor Harrell has been involved with hiring at Tech for many years and can provide a perspective on the university side of the process.
Wednesday, November 11, 2009 - 12:00 , Location: Skiles 171 , Jean Bellissard , School of Mathematics, Georgia Tech , , Organizer:
An assembly of atoms in a solid phase will be described through the notion of Delone sets and related to tilings. The Hull and the tiling space wiill be defined. It will be shown that the tiling space and the Hull can be constructed through an inverse limit of CW-complexes built out of the tiles and of the local patches. From then various cohomologies can be defined and allow to distinguish between these atomic distributions. The question of whether these topological invariant can be seen in experiments will be addressed.
Wednesday, November 4, 2009 - 12:00 , Location: Skiles 171 , Leonid Bunimovich , School of Mathematics, Georgia Tech , , Organizer:
Dynamical systems theory is concerned with systems that change in time (where time can be any semigroup). However, it is quite rare that one can find the solutions for such systems or even a "sizable" subset of such solutions. An approach motivated by this fact, that goes back to Poincaré, is to study instead partitions of the (phase) space M of all states of a dynamical system and consider the evolution of the elements of this partition (instead of the evolution of points of M). I'll explain how the objects in the title appear, some relations between them, and formulate a few general as well as more specific open problems suitable for a PhD thesis in dynamical systems, mathematical biology, graph theory and applied and computational mathematics. This talk will also serve to motivate and introduce to the topics to be given in tomorrow's colloquium.
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# Is there any proof of the fundamental theorem of algebra that can be introduced to undergraduates who have just completed Calc III?
I am aware of three proofs of the fundamental theorem of algebra, using:
1. Liouville's theorem
2. The fundamental group of the punctured plane, or
3. Multiplicativity of field extensions together with the intermediate value theorem
If I had a small group of undergraduates who had taken Calc III, is there any of these proofs or another proof that I could show them over a period of 3 1-hour sessions or less?
• Now that you have at least one good answer, will you share your goal in showing these students such a proof? – user173 Apr 13 '14 at 1:59
• The real reason is that I wanted to understand a proof of it at that point of my education, and I wish someone had shown me one. – Brian Rushton Apr 13 '14 at 2:14
• That theorem never cried out to me for a proof. But when I was 9, I wanted a proof of V=Bh/3 for pyramids, which I finally got in calculus. – user173 Apr 13 '14 at 3:35
• Artin gave an incredible proof that uses algebra. See Dummit and Foote p. 616-17. Although this is also a proof that may transcend what your normal Calc III student can do. (i.e. I learned it in Math 672). – Vladhagen Apr 23 '14 at 0:35
• @MattF. My favorite argument for that (not really a proof) is the following: first realize that we must have $V = kBh$ for some constant $k$ by scaling arguments: namely we can partition the base into small squares, and so reduce the problem to square base pyramids. Formula is true for these with a universal constant by "shearing" (aka cavaleri's principle). So all we need is to determine the constant. But six pyradmids with square $1\times1$ base and height $\frac{1}{2}$ fit in a cube, so we must have $k = \frac{1}{3}$. No need to know how to integrate $x^2$. – Steven Gubkin Aug 29 '14 at 0:16
I think that the proof based on the fundamental group of the punctured plane can be re-wrigged, just by omitting references to homotopies and the fundamental group, to be convincing to students who don't even necessarily know calculus, as long as they have sufficient comfort with the complex plane to be able to think about how a polynomial maps loops about the origin. From an aggressively technical point of view this introduces some handwaving, but IMHO the underlying topological theorems are sufficiently intuitively reasonable that this more or less counts as a proof anyway.
More specifically:
(1) Do you think the students could (be made to) see that for $t$ very small, $f(te^{i\theta})$ (for $\theta\in[0,2\pi]$) traces a very small loop of some kind about the constant term of $f$, that therefore gets nowhere near the origin?
(2) Do you think they could see that for $t$ large, $f(te^{i\theta})$ traces some kind of incredibly huge $n$-fold loop that encloses the origin?
If the answers are both yes, then I bet they will also see that if $t$ varies continuously from very small to very large, the image of $f(te^{i\theta})$ is going to vary continuously and therefore have to pass through the origin.
You can find a very elementary and direct proof here.
Personally, while I think that any of the more sophisticated proofs is very cool the direct proof is valuable since it really shows the fundamental theorem of algebra is not a theorem of algebra but rather of the complex numbers, and that it really is fundamental in the sense that it is very elementary (and important). It shows the proof is really not that complicated and amounts to a relatively simple analysis exercise. Using other methods (in my humble opinion) is using a sledgehammer where it really is not needed.
• I disagree. The fact that it is possible to give such a proof is not an argument in favor that it represents causality. The Liouville-corollary argument is, to me (yes, I do acknowledge the subjectivity), the only sane, understandable, memorable proof. All other arguments are labyrinthine in comparison, immemorable to say the least, in my opinion. – paul garrett Apr 13 '14 at 0:04
• I disagree that the Liouville-corollary proof is the unique simplest / most memorable. Here are two others that are very short and elegant and both I find extremely memorable. (But, they all use higher tech theorems than the OP wants.) – benblumsmith Apr 13 '14 at 2:02
• (1) A polynomial extends to a continuous map $S^2\rightarrow S^2$ via stereographic projection. By sliding all non-leading coefficients to zero, the map is homotopic to $z\mapsto z^n$ and therefore has Brouwer degree $n$. If $n\neq 0$, it is therefore surjective. (2) $f(te^{i\theta})$ is a homotopy from a constant map ($t=0$) to an $n$-fold loop about the origin (large $t$). If $n\neq 0$, these represent different elements of $\pi_1(\mathbb{C}\setminus \{0\})$, so the image of $f$ can't be contained in $\mathbb{C}\setminus\{0\}$. – benblumsmith Apr 13 '14 at 2:04
• Another memorable/(not-quite-as) short one: let $F$ be an algebraic extension of $C$ that is Galois over $R$. The fixed field of a Sylow 2-subgroup of $G=Gal(F/R)$ has odd degree over $R$ thus is generated by an odd-degree irreducible polynomial, which must be linear because odd-degree real polynomials always have real roots. Thus $G$ is a 2-group, thus so is $H=Gal(F/C)$. If $F>C$, any maximal subgroup of $H$ is index 2 normal thus its fixed field is a quadratic extension of $C$. But $C$ can't have a nontrivial quadratic extension since every complex number has a square root, so $F=C$. – benblumsmith Apr 13 '14 at 2:17
• My point is, what counts as "sane / memorable" depends on what the student knows. Which proof you go for depends what you have the best working knowledge of: Brouwer degree? Fundamental group? Liouville's theorem? Sylow theorems and the fundamental theorem of Galois theory? Etc. – benblumsmith Apr 13 '14 at 2:24
Your students might find it useful to see this "visual approach" to proving the FTA:
Velleman, D. J. (2007). The Fundamental Theorem of Algebra: A Visual Approach. Link.
For a more rigorous approach by the same author, see:
Velleman, D. J. (1997). Another proof of the fundamental theorem of algebra. Mathematics Magazine, 216-217. Link.
(The latter proof uses "the fact that entire functions can always be represented by power series.")
Finally, an entire list of proofs can be found here. I have not read closely through these, so I can neither make a more specific recommendation nor vouch for all of them; in particular:
Remark. In the list above, #60 "A topological proof of the fundamental theorem of algebra" (Arnold, 1949) is known to have errors. This is why he published a correction paper a couple years later (#58); the main idea, though, of using the Brouwer Fixed Point Theorem to prove the FTA has been carried out (though perhaps this is a result your post-Calc III students have not yet seen). In case this is useful, see:
Fort, M. K. (1952). Some properties of continuous functions. American Mathematical Monthly, 372-375. Link.
(The last two sources I became aware of while writing up an answer here.)
Unsurprisingly, there is a list of ways to prove the FTA on MathOverflow.
This is likely to include most any suggestion that could be posted here (on MESE) but the reverse inclusion is sure not to hold: The majority of these proofs are not written for students who just completed Calc III. On the other hand, three lectures with the FTA as a sole goal could cover a fair bit of material...
You can short-cut the Liouville proof as follows. Assuming that $f$ is a monic polynomial of degree $d>0$ with no roots, define $$h(r) = \int_{\theta=0}^{2\pi} f(r\,e^{i\theta})^{-1}\,d\theta.$$ If you are willing to differentiate under the integral sign, then it is not hard to show that $h'(r)=0$, so $h$ is constant. When $r$ is large enough the $z^d$ term in $f(r\,e^{i\theta})$ will dominate and we see that $|h(r)|$ is approximately $2\pi r^{-d}$ at most. It follows that $h(r)\to 0$ as $r\to\infty$, but $h$ is constant, so $h(0)=0$, which is impossible as $h(0)=2\pi/f(0)$.
Various things need to be justified to turn this into a complete proof, but I think that they are all quite plausible and intuitive.
You can find a proof that goes back to Gauss, which is based only on multivariable calculus (double integrals and partial derivatives) at http://www.math.uconn.edu/~kconrad/blurbs/fundthmalg/fundthmalgcalculus.pdf. I think the proof will come across as rather mysterious even if it can be followed line by line. The last paragraph of the file gives an indication of what proof it is related to in complex analysis.
In this video, David Eisenbud (a math prof at Berkeley) explains a proof of the fundamental theorem of algebra that is very enlightening / beautiful, and almost makes the result seem obvious.
Following this answer, students can experiment with Velleman, D. J. (2007). The Fundamental Theorem of Algebra: A Visual Approach using interactive versions of the paper's plots. (Disclosure: I am a dev for the site.)
• I would have commented, but didn't have the rep. – gballan Apr 13 '14 at 23:40
• Added opening reference to Benjamin's answer. – gballan Apr 14 '14 at 1:04
Here is an elementaryproof which considers $p(z)$ as a function of $(x,y)$ where $z=x+iy$.
The only assumptions are that $z^{n}=r$ has a solution for all integer $n$ and real $r$ and that intermediate value theorem holds for continuous real valued functions along any continuous curve on the complex plane. The second assumption can be proved by parametrizing the curve and then using the least upper bound principle for real numbers.
Writing $z= r e^{-i \theta}$ we can find a big enough $r=R$ such that $Re(p(R,\theta))$ is positive at $\theta=\frac {2\pi k} {n} + \frac {\phi} {n}$ and negative at $\theta=\frac {2\pi k} {n} + \frac {\pi} {n} + \frac {\phi} {n}$. This is because $Re(p(R,\theta))$ is dominated by $r^{n}cos(n\theta)$. $\phi$ is the angle of the complex coefficient of $z^{n}$.
Now , $p(z)$ being continous, $Re(p(z))$ is also continuous. So the zeros of $Re(p(z))$ form a continuous curves on the complex plane. The point is to show that on one such continuous curve there is a point where $Im(p(z))>0$ and another point where $Im(p(z))<0$. Then on the particular curve $Re(p(z))=0$ there must be a point where $Im(p(z))=0$. However, this is the solution of $p(z)=0$.
The proof can be visualized in the following way-
The arc $r=R$ between $\theta=\frac {2\pi k} {n} + \frac {\phi} {n}$ and $\theta=\frac {2\pi k} {n} + \frac {\pi} {n} + \frac {\phi} {n}$ is called a even sector for even $k$ and is called a odd sector for odd $k$.
Let us start from the even arc with $k=0$. The values of $Re(p(R,\theta))$ at the ends of this arc are of opposite sign, so it much be zero somewhere on the curve. The same thing holds if we increase $r \ge R$ continuously. So we get a continuous curve for $Re(p(z))=0$ in the sector $\theta \in$ { $0$, $\frac {\pi} {n}$} for $r\ge R$. Let us call this curve $f(z)$ Now, zeros of a continuous function divide the plane into two disconnected parts. One of the parts is finite in area if the curve is closed. Otherwise both areas are unbounded. Here, since we cannot have $Re(p(z))=0$ for $\theta =0$ and $\theta=\frac {\pi} {n}$ for $r\ge R$, the curve $f(z)$ does not intersect the rays $\theta =0$ and $\theta=\frac {\pi} {n}$ for $r \ge R$. This means $f(z)$ cannot be closed.
Now, $f(z)$ must cross one of the odd arcs. This can be constructed using exhaustion (there are only finite numbers of arcs). If not, there must be another curve satisfying $Re(p(z))=0$ and the desired conditions.
$Im(p(R,\theta))$ is dominated by $r^{n}sin(n\theta)$. So, for big enough $r$, $Im(p(r,\theta))$ is positive somewhere in the even sector and negative somewhere in the odd sector. So $Im(p(z)=0)$ somewhere on the continuous curve $f(z)$. This gives a solution for $p(z)=0$.
Additionally, $f(z)$ is not asymptotic to $\theta=\frac {2\pi k} {n} + \frac {\phi} {n}$ or $\theta=\frac {2\pi k} {n} + \frac {\pi} {n} + \frac {\phi} {n}$. This can be proven by using the fact that $Re(z) < |z|, \forall z \in \mathbb{C}$. If this was not true, domination of $Im(p(z))$ on $f(z)$ by $r^{n}$ would be problematic since $sin(n \theta)$ might tend towards zero.
Finally, for real coefficients, if $z$ a solution, $\overline z$ is also a solution for $p(z)=0$, since $\overline p(z) = p(\overline z)=0$. So for every root found, we can do division algorithm to get another polynomial of degree $n-2$. We know that quartic polynomials are always solvable using radicals. So induction shows that all polynomials with real coefficients are solvable on the complex plane.
I admit I'm a bit late to the party, but for completeness let me add a link to an interactive version of one of the visual proofs:
The fundamental theorem of algebra - a visual proof
(Disclaimer: I'm the author of that page.)
$\def\RR{\mathbb{R}}\def\CC{\mathbb{C}}$ Here is a proof via ODE. I imagine it's been found before, but I hadn't seen it before. The essential idea is that, if $z: \RR \to \CC$ is an inverse function to $f$ then we should have $z'(t) = 1/f'(z(t))$ (formula for the derivative of the inverse function, in an exotic setting). Therefore, we can solve this ODE and get an inverse function, and we can evaluate the inverse function at $0$ to find a root of $f$.
Let $f(z) = f_n z^n + \cdots + f_1 z + f_0$ be the polynomial which we wish to prove has a root. We first make a simplifying assumption:
Simplifying Assumption: We may assume that there is no point $w$ where $f(w) \in \mathbb{R}$ and $f'(w)=0$.
Proof: Let $w_1$, $w_2$, ..., $w_k$ be the zeroes of $f'(z)$, there are finitely many of them by the easy part of the FTA. If $f(w_i)=0$ for any $i$, we are done. If not, replace $f(z)$ by $e^{- i \alpha} f(z)$ for some $\alpha$ not equal to the arguments of any $f(w_i)$. $\square$
With this assumption, we will show
Theorem: There is a smooth curve $t \mapsto x(t) + i y(t)$, parametrized by $\RR$, so that $f(x(t)+i y(t))=t$.
In particular, the point $x(0)+i y(0)$ is a zero of $f$.
Lemma 1: There is a constant $c>0$ so that $|f'(z)| > c$ for $z \in f^{-1}(\RR)$.
Proof: Choose $R$ large enough that $n |f_n| S^{n-1} > \sum_{k=0}^{n-1} k |f_k| S^{k-1} + 1$ for $S>R$. Then $|f'(z)| > 1$ for $|z|>R$. The set $f^{-1}(\RR) \cap \{ |z| \leq R \}$ is closed and bounded, hence compact, so $|f'(z)|$ has a minimal value $b$ on that set, and by the simplifying assumption $b>0$. Take $c = \min(b,1)$. $\square$.
In order to set up an ODE, we also need an initial value:
Lemma 2: There is a point $z_0 \in \CC$ where $f(z_0) \in \RR$.
Proof: Choose $R$ large enough that $|f_n| R^n > 2 \sum_{k=0}^{n-1} |f_k| R^k$. Let $f_n = |f_n| e^{i \alpha}$. Then $\mathrm{Im} f(R e^{i (-\alpha-\pi/2)/n})<0$ and $\mathrm{Im} f(R e^{i (-\alpha+\pi/2)/n})>0$. So, by the intermediate value theorem, there is some $\theta$ with $f(R e^{i \theta}) \in \RR$. $\square$
Write $t_0$ for $f(z_0)$.
Consider the ODE $z'(t) = 1/f'(z(t))$ on $\RR \times \CC$, with initial value $z(t_0) = z_0$. Then this ODE is solvable for all $t \in \RR$, and $f(z(t)) = t$ for all $t$.
We first check that any solution to the ODE obeys $f(z(t))=t$. The proof is simply to differentiate the left hand side: $z'(t) f'(z(t)) = \frac{1}{f'(z(t))} f'(z(t)) = 1$ and $f(z(t_0)) = t_0$, so $f(z(t)) = t$. However, this assumes that students are comfortable differentiating complex valued functions of real arguments by the usual rules. So I'd first do the quick but questionable way and then I'd write it out: Put $f(x(t)+iy(t)) = \sum (g_k + i h_k) (x(t)+iy(t))^k$ and carefully take the derivative with respect to $t$, seeing that you get $z'(t) f'(z(t))$ at the end.
Now, we must check that solutions to the ODE extend to all $\RR$. Suppose, for the sake of contradiction, that there is a solution on $[t_0, q)$ but not beyond $q$; a similar argument works to show the ODE is solvable for all negative time.
By the previous computation, $f(z(t)) = t$ for $t \in [t_0,q)$, so in particular $z(t) \in f^{-1}(\RR)$. By Lemma 1, the right hand side of the ODE is bounded above by $1/c$ for $t \in (p,q)$, so $\lim_{t \to q^{-}} z(t)$ exists; call this limit $w$. By continuity of $f$, we have $f(w) = f \left( \lim_{t \to q^{-}} z(t) \right) = \lim_{t \to q^{-}} f(z(t)) = \lim_{t \to q^{-}} t = q$. In particular, by our Simplifying Assumption, $f'(w) \neq 0$. So we can solve the ODE again with initial condition $z(q) = w$. This gives a solution which agrees with the previous $z$ on a neighborhood to the left of $q$ (by uniqueness of solutions to ODEs), and is defined to the right of $q$, a contradiction.
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# Connection between Schrödinger equation and heat equation [duplicate]
If we do the wick rotation such that τ = it, then Schrödinger equation, say of a free particle, does have the same form of heat equation. However, it is clear that it admits the wave solution so it is sensible to call it a wave equation.
1. Whether we should treat it as a wave equation or a heat equation with imaginary time, or both?
2. If it is a wave equation, how do we express it in the form of a wave equation?
3. Is there any physical significance that Schrödinger equation has the same form of a heat equation with imaginary time? For example, what is diffusing?
## marked as duplicate by Bill N, Jon Custer, user36790, Bosoneando, ACuriousMind♦ quantum-mechanics StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Sep 20 '16 at 13:25
• I don't understand what physics principle you're asking about. There are many linear equations. So what? There are many exponential decay equations. It merely gives us analogues. – Bill N Sep 19 '16 at 17:15
• Possible duplicate of How is the Schroedinger equation a wave equation? – QuantumBrick Sep 19 '16 at 17:35
• Is there any reason why Schrödinger equation can be written in the form of a heat equation? Also, Schrödinger has first order derivative with respect to time (instead of second order), why is it a wave equation? – Kevin Kwok Sep 19 '16 at 17:46
• The part with the heat equation is closely related to physics.stackexchange.com/q/80131/50583 and physics.stackexchange.com/q/144832/50583, the part about it being a wave equation is a duplicate of the already linked question. Please ask a single, focused question per post, or at least questions so closely related they can't meaningfully be split up. – ACuriousMind Sep 20 '16 at 13:25
1) Both: it is apparently a heat equation in imaginary time and it is a wave equation because its solutions are waves.
2) Nonstationary Schrodinger equation (let us assume free particle) $$i\hbar\frac{\partial\psi}{\partial t}=-\frac{\hbar^2\nabla^2}{2m}\psi$$ is essentially complex: it can never be satisfied by a real function, only by a complex one.
Nevertheless, its solutions are waves because the complex $\psi$ means it is actually a system of two real equations of the first order in time. Assuming $\psi=u+iv$ we have: $$\hbar\frac{\partial u}{\partial t}=-\frac{\hbar^2\nabla^2}{2m}v,\qquad \hbar\frac{\partial v}{\partial t}=\frac{\hbar^2\nabla^2}{2m}u.$$ Eliminating, say, $v$, we get: $$\hbar^2\frac{\partial^2 u}{\partial t^2}=-\frac{\hbar^4\nabla^4}{4m^2}u.$$ In two dimensions, this equation has the same form as a wave equation for bending (flexural) waves on a thin rigid plate. It is also of the 2-nd order in time and 4-th order in coordinates. The analogy extends also to wave dispersions: the bending waves have a quadratic dispersion $\omega\sim q^2$ similarly to free particle obeying Schrodinger equation $E=p^2/2m$.
3) This analogy is widely used in the diffusion Monte-Carlo method, where the Schrodinger equation is solved in imaginary time. In this case, its solution is decaying instead of being oscillatory and, if we normalize it properly, it will converge to the ground state wave function:
https://en.wikipedia.org/wiki/Diffusion_Monte_Carlo
http://www.tcm.phy.cam.ac.uk/~ajw29/thesis/node27.html
What is diffusing here? Taking imaginary time $\tau=it$, we have the following imaginary time Schrodinger equation for a particle in a potential $V$: $$\hbar\frac{\partial\psi}{\partial t}=\frac{\hbar^2\nabla^2}{2m}-V\psi.$$ The first term in right hand side is usual diffusion. The second is something like heat production or burning, and its "minus" sign means this heat production is more intense in the minima of $V$.
Thus, the picture of diffusion in imaginary time is the following: the first term ("diffusion") tries to delocalize $\psi$, while the second term tries to lure $\psi$ to the minima of the potential $V$. Their interplay is the same as that between kinetic and potential energies in quantum mechanics, and its result is a ground state wave function - exactly what is used in diffusion Monte-Carlo calculations.
• Alexey, you have given a nice explanation! – freecharly Sep 20 '16 at 0:15
• Alexey, your answer is excellent and it gives what I want to know. Thank you so much. – Kevin Kwok Sep 20 '16 at 6:49
• As a reference, the governing equation of the dynamics of a rigid plate can be found at en.wikipedia.org/wiki/… – Kevin Kwok Sep 20 '16 at 7:36
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# How do you solve equation with quadratic formula 3n^2-4n-15=0?
Nov 1, 2016
n_1=-5/3; n_2=3
#### Explanation:
Since b-4 is even, you can use the formula:
$x = \frac{- \frac{b}{2} \pm \sqrt{{\left(\frac{b}{2}\right)}^{2} - a c}}{a}$, so you have
$n = \frac{- \left(- \frac{4}{2}\right) \pm \sqrt{{\left(\frac{4}{2}\right)}^{2} - 3 \cdot \left(- 15\right)}}{3}$
$= \frac{2 \pm \sqrt{4 + 45}}{3}$
$= \frac{2 \pm 7}{3}$
n_1=-5/3; n_2=3
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A circular segment is formed by a circle and one of its chords. Area of major segment= area of circle- area of Minor segment Shaded grey part is minor segment A segment in a circle is similar to a sector, but is slightly different. Re: Area of Circular segment by integration Mike and others thank you. Facebook. Using the first and last ratios in the proportion shown above, the following is true. Hi All, I'm having a real problem trying to input the below formula into excel. If you know the segment height and radius of the circle you can also find the segment area. It is a shape formed between an arc on the edge of a circle, and a chord line inside a circle. Height: It is defined as the height from the center of the circle to the highest point in the partial circle. 0.5 = A constant . Solving for circle segment height. Π = Pi (3.14) Θ = Angle. Pinterest. The POWER function will take any number and raise it to the power of any other number. The area can also be found directly by integration as Those are easy fractions, but what if your central angle of a 9-inch pumpkin pie is, say, 31 °? Use the calculator below to calculate the segment area given the radius and segment's central angle, using the formula described above. A 45 ° central angle is one-eighth of a circle. Similar to the case of a sector inside a circle, a segment can be either a Minor Segment, or a Major Segment. How to Calculate the Area of a Segment of a Circle. It is denoted by h. Formulas for Spherical Segment. Here the angle of the relevant sector is given in radian measure, instead of degrees, the angle is sized 1.83 radians. Last Updated: 18 July 2019. 12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept. With a specific Chord line creating both the minor segment, and also creating a separate triangle too. The altitude of the spherical segment is the perpendicular distance between the bases. Area of lower base, A 1 Circle Segment Equations Formulas Calculator Math Geometry. Hence, the elliptic segment area is (3) The below given is the area of segment of circle formula to calculate the area of circle segment on your own. Click Here . Download: Use this area calculator offline with our all-in-one calculator app for Android and iOS. ... Find the area of a segment of a circle with a central angle of 120 degrees and a radius of 8 cm. It is denoted by h. Formulas for Spherical Segment. the whole pie-shaped sector and subtracting the area of the Inputs: circle radius (r) circle center to chord midpoint distance (t) Conversions: circle radius (r) = 0 = 0. circle center to chord midpoint distance (t) = 0 = 0. For more on this seeVolume of a horizontal cylindrical segment. So make sure that any calculator being used to establish the value of sinθ is set to "radians" and NOT "degrees". It's handy to have a run through of what exactly a segment means regarding a circle. The spherical segment of one base is also called spherical cap and the two bases is also called spherical frustum. 0. The area of a segment can be calculated using the following formula. 7 3] View Answer A chord of a circle of radius 3 0 c m makes an angle of 6 0 0 at the centre of the circle. Radius. Angles are calculated and displayed in degrees, here you can convert angle units. A quadrant has a 90 ° central angle and is one-fourth of the whole circle. When the angle at the centre is 360°, area of the sector, i.e., the complete circle = πr² When the angle at the center is 1°, area of the sector = $$\frac{\pi .r ^{2}}{360^{0}}$$ Circle Segment Equations Formulas Calculator Math Geometry. Area of regular polygon = … A circular segment can be defined as the sector of 2d space which is bounded by an arc (less than 180° of angle) of a circle and by the chord which connects the endpoints of the arc. How do you find the area of … Method-II: A = 4 h 2 3 2 r h – 0.608. There is a lengthy reason, but the result is a slight modification of the Sector formula:Area of Segment = θ − sin(θ) 2 × r2 (when θ is in radians)Area of Segment = ( θ × π 360 − sin(θ)2) × r2 (when θ is in degrees) Arc Length and Sector Area You can also find the area of a sector from its radius and its arc length. Combination Formula, Combinations without Repetition. To find the area of the segment, you find the area of the sector. Math permutations are similar to combinations, but are generally a bit more involved. Data: Dia of the Circle = 1.6 (mtrs) Perpendicular length from circle chord to circle edge = 0.76 (mtrs) Calculation: Illustrated in the image below. Calculations at a circular segment. An elliptic segment is a region bounded by an arc and the chord connecting the arc's endpoints. By. 3,14. Definition: The number of square units it takes to fill a, Area of a Circular Segment given the Segment Height, Area of a circle segment (given central angle), Area of a circle segment (given segment height), Basic Equation of a Circle (Center at origin), General Equation of a Circle (Center anywhere), Radius of an arc or segment, given height/width. Select a different shape: Other tools. All Discussions; Previous Discussion; Next Discussion; 1 Reply Highlighted. Solution: segment height (h) = NOT CALCULATED. Home › Area of Segment of a Circle Formula. You’re all set to finish with the segment area formula: Solving the proportion for A gives: Segment of a Circle: The segment of a circle is the region bounded by a chord and the arc subtended by the chord. Reply. To find the segment area, you need the area of triangle IDK so you can subtract it from the area of sector IDK. Inputs: circle radius (r) circle center to chord midpoint distance (t) Conversions: circle radius (r) = 0 = 0. isosceles triangle △ACB. Home Embed All Precalculus Resources . Learn how to find the Area of a Segment in a circle in this free math video tutorial by Mario's Math Tutoring. Home Embed All Precalculus Resources . Area of the circular region is πr². The apothem of a regular polygon is a line segment from the center of the polygon to the midpoint of one of its sides. A minor segment inside a circle is actually a smaller part of a whole sector in the circle. Formula for segment radius by chord and height: Then, you can caluclate segment angle using the following formula: You may also use the following calculator to obtain segment area by its radius and height: Area of circle segment by radius and height. Such segment possesses various measurements like chord length, arc length, area, and angle. These formulas shown above for the area of a minor segment, also help when trying to find the area of a major segment, as the sum would be: Because what is left over from this sum, will be the area of the major segment. - center of the sphere. We are going to derive the formula for the area of a sector using the sector's arc length. If the radius and the segment height of a circle are given, then the formula to calculate the area of the segment is Area of Segment = r^2 cos^-1[(r-h)/r]-(r-h)√[2rh -h^2] Digits after the decimal point: 2. Two of the common methods are: Method-I: A = 2 h c 3 + h 2 2 c = h 6 c ( 3 h 2 + 4 c 2) Note: If the height of the segment is less 1 10 than the radius of the circle, then A = 2 h c 3. Example: find the area of a circle. How It Works. Express answer to the nearest integer. is the radius of the circle of which the segment is a part. Learn how to find the Area of a Segment in a circle in this free math video tutorial by Mario's Math Tutoring. Where: C: is the central angle in DEGREES: R: Notice if I put 90 over 360, I will reduce that to one fourth of the circle. Equation is valid only when segment height is less than circle radius. These formula find application in the common case of determining the volume of fluid in a cylindrical segment (i.e., horizontal cylindrical tank) based on the height of the fluid in the tank.. See And the area of the segment is generally defined in radians or degrees. A circular segment (in green) is enclosed between a secant/chord (the dashed line) and the arc whose endpoints equal the chord's (the arc shown above the green area). The Area of a Segment is the area of a sector minus the triangular piece (shown in light blue here). In this example, we have sector AOB . If you know radius and angle you may use the following formulas to calculate remaining segment parameters: You may think of the sector as a triangle and a segment put together. Then, divide the resultant value by the integer 2. The central angle lets you know what portion or percentage of the entire circle your sector is. The spherical segment of one base is also called spherical cap and the two bases is also called spherical frustum. Inputs: circle radius (r) central angle (θ) Conversions: circle radius (r) = 0 = 0. central angle (θ) = 0 = 0. radian . A spherical segment or a spherical layer is a three-dimensional geometrical object defined by cutting a sphere (with radius R) with a pair of two parallel planes.The top and bottom planes, where intersecting the sphere, create two circles with radii b and a respectively, which serve as top and bottom bases of the segment. Height (h) Calculation precision. Subtract the area of the isosceles triangle from the area of the sector and you have the area of the segment: A(segment) = A(sector) - A(triangle) [insert drawing based on Figure 1] If you know the radius, r, of the circle and you know the ce… Precalculus : Find the Area of a Segment of a Circle Study concepts, example questions & explanations for Precalculus. Solving for circle segment area. Calculate the surface area of a spherical segment if given radius and height ( A ) : surface area of a spherical segment : = Digit 2 1 2 4 6 10 F Area of major segment= area of circle- area of Minor segment Shaded grey part is minor segment Learn how to approach drawing Pie Charts, and how they are a very tidy and effective method of displaying data in Math. Then I will multiple this by the area which is pi R squared. In both cases, the segments are formed between a straight Chord line across the circle at some part, and an Arc on the edge of the circle. The altitude of the spherical segment is the perpendicular distance between the bases. Area of the circle segment = As = 1/2 (rl – c (r – h)) = 0.9412 m 2 ; Circle area except segment area A = π r 2 – As = 1.069 m 2 ; Online calculator for circle segment area calculation. Hopefully, somebody can help?! We are going to derive the formula for the area of a sector using the sector's arc length. The following problem illustrates how to find arc length, sector area, and segment area: Here’s the solution: Find the length of arc IK. Find the area of circle segment IK. Published: 05 January 2019. The area of a circle is given by Pi*Radius^2 where Pi is a constant approximately equal to 3.14159265.Excel has this constant built in as a function with no parameter inputs PI().. To calculate the area of a segment bounded by a chord and arc subtended by an angle θ, first work out the area of the triangle, then subtract this from the area of the sector, giving the area of the segment. Enter two values of radius of the circle, the height of the segment and its angle. Circular Segment Calculator. The area of each segment is then obtained as the sum of areas of these geometric shapes and the area of the down part of the segments which is usually a rectangle. This is clear from the diagram that each segment is bounded by two radium and arc. Many formulas are given for finding the approximate area of a segment. (see diagrams below) That creates two 30°- 60°- 90° triangles. Arc Length of the circle segment = l = 0.01745 x r x θ; Area of the segment = As = 1/2 (rl – c (r – h)) Circle area except segment area A = π r 2 – As; Example for better understanding. Length of Segment Formula: By applying the values of angle, radius, height, arc length and chord length in the Area of a Segment of a Circle Formula you can do various calculations on your own. Calculate. How to calculate the area of a segment. The formula to find the area of the segment is given below. The formula to find the area of the segment is given below. I'm trying to calculate the area of a circular segment with only the radius or a circle, total area and offset from the centre to a variable point of measurement. $\endgroup$ – Blue Aug 3 … We will first use an example finding the area of a segment using this area of a triangle formula: (1/2)absinC. If using degrees: A = (r 2 ÷ 2) x ((Π ÷ 180 x Θ) – sin Θ) If using radians: A = (0.5 x r 2) x (Θ – sin Θ) Where: A = Area. Twitter. Find the area of the corresponding segment of the circle [U s e π = 3. Related Topics. As a proportion of the whole area of the disc, = , you have = (− ) = ∘ − Applications. The area of segment in a circle is equal to the area of sector minus the area of the triangle. I'm trying to calculate the area of a circular segment with only the radius or a circle, total area and offset from the centre to a variable point of measurement. This is clear from the diagram that each segment is bounded by two radium and arc. Now to work out the area of the minor segment, we would want to establish: As what is left over, will be the area of the minor segment. Area of a Circular Segment given the Segment Height. It can also be found by calculating the area of Task 2: Find the area of a circle given its diameter is 12 cm. To calculate the area of a fractional part of the pie, you can set up a modified version of the area formula for the whole pie: A ... To find the area of the segment, you find the area of the sector. Area of Segment of a Circle Formula. So, the perimeter of a segment would be defined as the length of arcs (major and minor) plus the sum of both the radius. Here’s how all this looks when you plug it into the formula: Find the area of sector IDK. On this page, you can calculate area of a Segment. Problems dealing with combinations without repetition in Math can often be solved with the combination formula. Then, the area of a sector of circle formula is calculated using the unitary method. To calculate areas of segments, you first have to know the area of the sector. Area of minor segment = \boldsymbol{\frac{8^2}{2}} × (\boldsymbol{\frac{70\pi}{180}} − sin(70)) = 32 × (0.282) = 9.02cm 2 Area of whole circle = π × 4 2 = 201.06cm 2 Area of major segment = 201.06cm 2 − 9.02cm 2 = 192.04cm 2. When the angle at the centre is 360°, area of the sector, i.e., the complete circle = πr² The below given is the area of segment of circle formula to calculate the area of circle segment on your own. Example Questions . - radius of a sphere. The (slightly-)tricky part is determining the starting and ending angles in the stretched figure, but once you have them, the area of a circular segment is straightforward to compute. Area of a segment of a Circle formula = Area of Sector - Area of Triangle. Circular segment. How to Calculate the Area of a Segment of a Circle. r = Radius. You really don’t need a formula for finding arc length if you understand the concepts: That’s all there is to it. Now the area of the segment AXB (without considering angle) = Area of sector OAXB less Area of triangle OAB. Labels: Labels: Formulas & Functions; training 3,066 Views . Segment Perimeter Formula Finding Perimeter Examples Finding Perimeter Further Examples. In segment problems, the most challenging aspect is often calculating the area of the triangle. CREATE AN ACCOUNT Create Tests & Flashcards. The process resulted in an improved formula for numerical integration which we derived in the paper. The reason I wasn't getting the incorrect symbolic result with Mikes' solution is that I forgot that Mike defined R as equal to 1 and if you have a unit circle you get pi/2 aka 1.571 which is correct for that case. Then you find the area of the isosceles triangle at the central angle. (see diagrams below) Use this online Length of Segment Calculator to calculate the area of partial circles using the height and the radius within the blink of eyes. This is a major segment, so we work out the area of the non shaded minor segment first, and then take that away from the area of the whole circle. As you can see 90 degrees is one fourth of the circle. The measure over 360. Let this region be a sector forming an angle of 360° at the centre O. Circular segment - is an area of a circle which is "cut off" from the rest of the circle by a secant (chord).. On the picture: L - arc length h- height c- chord R- radius a- angle. Before looking at how to establish the area of a segment in a circle. The area of segment of circle can be calculated with the formula: Area of segment= Area of sector- Area of triangle ---- equation (1) Now, we will find the area of a … Erik T Larsson . radius: angle (degree): Result window. WhatsApp. A circle is drawn with Center O. OAXB is the sector, OAB is the triangle with chord AB, and OA and OB are sides forming the triangle with sides OA and OB equal to radius (r). For example, if the radius is 5 inches, then using the first area formula calculate π x 5 2 = 3.14159 x 25 = 78.54 sq in.. Area Of Segment (Angle In Degrees) The segment of a circle is a region bounded by the arc of the circle and a chord. - height of a spherical segment. To calculate the area of a segment bounded by a chord and arc subtended by an angle θ, first work out the area of the triangle, then subtract this from the area of the sector, giving the area of the segment. Choose the number of decimal places, then click Calculate. 1 4, √ 3 = 1. Area of a Sector Formula. Apply the second equation to get π x (12 / 2) 2 = 3.14159 x 36 = 113.1 cm 2 (square centimeters). This calculation is useful as part of the calculation of the volume of liquid in a partially-filled cylindrical tank. Then, the area of a sector of circle formula is calculated using the unitary method. Area of a segment of a Circle formula = Area of Sector - Area of Triangle. AB is the chord that bounds the segment … So, the perimeter of a segment would be defined as the length of arcs (major and minor) plus the sum of both the radius. ... segment area: circle radius: central angle: arc length: circle radius: segment height: circle radius: circle … The segment is the shaded region right up here, so let's start off by what do we know, well I know how to calculate the area of a sector so I'm going to write area of a sector down below and I'm going to sketch the area of a sector here. (b) The area of a segment when the height and length of the chord of the segment are given: As per the formula, deduct the value of θ by the value of sinθ and multiply the value by the squared value of radius. where the formula for the isosceles triangle in terms of the polygon vertex angle has been used (Beyer 1987). Solution: area (K) = NOT CALCULATED. Calculate the surface area of a spherical segment if given radius and height ( A ) : surface area of a spherical segment : = Digit 2 1 2 4 6 10 F. If the segment is larger than half the circle, it is a major segment, and if it is smaller, then it is a minor segment. Equation is valid only when segment height is less than circle radius. Task 1: Given the radius of a cricle, find its area. 12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept. What It Does. How to find the area of a regular polygon? On this page, you can calculate area of a Segment. where the formula for the isosceles triangle in terms of the polygon vertex angle has been used ... Finding the value of such that the circular segment (left figure) has area equal to 1/4 of the circle (right figure) is sometimes known as the quarter-tank problem. Illustrated in the image below. Note that the area of the elliptic segment (in then diagram) is equal to the area of sector $$M'ON'$$ minus the area of $$\triangle M'ON'$$. We will first use an example finding the area of a segment using this area of a triangle formula: (1/2)absinC. A segment is a shape that is part of a whole circle. Draw an altitude straight down from D to segment IK. And the area of the segment is generally defined in radians or degrees. How To Derive The Area Of A Segment Formula? Segments in a Circle. In other words it is two equal halves that are divided by the circle’s arc and connected through chord by the endpoints of the arc. A circular segment is a region of a circle which is created by breaking apart from the rest of the circle through a secant or a chord. The area of a segment in a circle is found by first calculating the area of the sector formed by the two radii and then subtracting the area of the triangle formed by the two radii and chord (or secant). Change Equation Select to solve for a different unknown Circle. The proposed method was compared with some Newton-Cotes methods of integration and it outperformed. This formula will calculate the area of a circle given its radius. Then you find the area of the isosceles triangle at the central angle. To find the area of the shaded segment, we need to subtract the area of the triangle from the area of the sector. AXB is the segment. The formula for area, A A, of a circle with radius, r, and arc length, L L, is: A = (r × L) 2 A = (r × L) 2 Find out more here about permutations without repetition. Let me explain the formula. It can also be found by calculating the area of the whole pie-shaped sector and subtracting the area of the isosceles triangle ACB. Remember: In this version, the central angle must be in degrees. radius: angle (degree): Result window. 0 Likes 1 Reply . In this example, we have sector AOB . Area of lower base, A 1 The area of any regular polygon is equal to half of the product of the perimeter and the apothem. Area of the major segment $$=$$ area of the circle $$–$$ area of the minor segment $$= 706.5 – 20.4 = 686.1$$ square cm. The height of the segment (h) is the distance between the bases. Inside a circle, there can be a minor segment and a major segment. Using the first and last ratios in the proportion shown above, the following is true. Download: Use this area calculator offline with our all-in-one calculator app for Android and iOS. If A = area of the sector, and s = arc length, then . Precalculus : Find the Area of a Segment of a Circle Study concepts, example questions & explanations for Precalculus. Approximate area of a sector of circle formula to find the area of the sector displaying. Then click calculate a bit more involved of radius of a segment of a sector using the first last... A Chord line inside a circle, there can be a sector using the for! 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# Creating a hexagonal wraparound map
I'm trying to create a wraparound map for a hexagonal map, so when you exit a tile on one side of the big hexagon-shaped map, you enter a tile on the other side.
In the image, the pale tan hexagonal chunk in the center is our map. The greenish/reddish chunks around it are shifted copies of the same map. If we stand on the blue tile under the cursor and walk off the main map into the green copy to the right, that's the same as wrapping around our map to the corresponding point on the other side: here, walking from the blue tile in the lower-right-hand red copy into the bottom-right corner of the center map.
I used an approach with a lookup table first. But as soon as those maps get too big, the lookup tables get even bigger. I'm searching for a solution which works without a lookup table.
• Civilization only wraps around horizontally, there is no need of lookup table for that (you just store it as a rectangular map, and represent it with offset coordinates to make it a hex grid). From reading the linked article I think you want to wrap around on three directions (connecting each side of the hexagon with the opposite). I suggest to make that clear in the question. – Theraot Feb 19 '17 at 2:04
• @Theraot thank you, updated the question – InsOp Feb 19 '17 at 9:57
Here's a simple method which does not become more complex as the map grows in radius:
1. Keep a list of the center coordinates of your main map (0, 0, 0), and its 6 shifted copies.
2. After a move that might take you off the edge of the map, calculate the distance to your destination tile from each of these center points.
3. Stop when you find a center point whose distance away is less than or equal to your map radius.
4. Subtract this center point from your destination point. Now your destination is correctly expressed as an offset from the center of your original map (0, 0, 0).
Implemented directly, this is at most 7 distance checks, no matter how big your map gets.
But, if your distance from the original center is less than your map radius, you can skip the other checks entirely, since you haven't crossed an edge.
• Thanks for the edit and for this answer. I did not fully understand the last step, but Im sure i will, when im implementing it. (Then this answer gets marked as the correct one) – InsOp Feb 19 '17 at 16:30
• What part is unclear? I'm happy to edit and clarify it. – DMGregory Feb 19 '17 at 16:33
• No everything is fine. I calculated it with an example and it seems to be a superb solution. On step 4 I just couldnt do the math in my head, thats why I was confused. – InsOp Feb 19 '17 at 16:41
You can actually do a rectangular projection without wasted space in the array. This enables yo has the added benefit, that the character visually goes upwards instead of in an angle.
You can get the center of a hex with the following formula (width and height is the hexagon width and height, x and y are the current position):
centerX = x * width + (y % 2 + 1) * width / 2
centerY = y * height + height / 2
If you have a map with the width n and height m, then every hexagon on the left side will have the x coordinate 0, on the right side the x coordinate n, in the top row they'll have a y coordinate 0 and and on the bottom a y coordinate m.
This also means the four corners are (0; 0), (0; m), (n, 0), (n, m).
So, to achieve a wrapping effect, you need to check if the x coordinate of the player is bigger than n, and if it is, then set it to 0, if it's smaller than 0, then set it ton, if the y coordinate is smaller than 0, then set it to m and if it's bigger than m, than set it to 0.
In code:
if (x < 0) x = n;
if (x >= n) x = 0;
if (y < 0) y = m;
if (y >= m) y = 0;
• did you consider that the map shape is also a hexagon? So there is no width and height, only a radius – InsOp Feb 19 '17 at 13:59
• @InsOp you never mentioned it's a hexagon before I posted my answer – Bálint Feb 19 '17 at 20:32
• Yes i am sorry, i appreciate your answer – InsOp Feb 20 '17 at 11:25
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# Different display styles in math mode?
## Code:
\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
%\usepackage{mathabx}
\begin{document}
$\phi(\underbrace{r\cdots r}_{n-\text{veces}}) \qquad a\in A \qquad A\subseteq B \qquad\mathbb{Z}[i]$
\end{document}
## My question is:
Are there other packages that generate a similar effect \usepackage{mathabx}?
• Yes, MnSymbol also provides a new math symbol font, which would cause a similar effect of "changing the notation" slightly. – Werner Nov 4 '15 at 0:54
• ...but I don't know whether this answers your question. It still seems very broad to me. – Werner Nov 4 '15 at 1:05
• @Werner -- Your answer is very useful for me.Thanks – CarlosE Nov 4 '15 at 1:13
• – John Kormylo Nov 4 '15 at 5:07
• There are several font packages that change the math font see e.g. tug.dk/FontCatalogue/mathfonts.html – Torbjørn T. Nov 4 '15 at 8:48
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Tag Info
3
Yes, if you are using 3rd party key exchange, the 3rd party can read the messages. If that is not the security feature you want, use something else. There are many legitimate scenarios where users are fine with trusting the third party, however. For example, a system setup by my employer to allow encrypted chat between myself and our clients. My employer has ...
3
I have never heard of this reason, and I don't quite understand it. In general, the security of Diffie-Hellman key exchange is reduced to the DDH assumption. According to this assumption, the result of the key exchange is a group element that is computationally indistinguishable from a random/uniformly distributed element in the group. However, what is ...
0
To show that the protocol is secure under DDH, we need a reduction $R$ that takes a triple as input and outputs a transcript and key such that if the triple is a DDH triple, then the transcript and key are distributed identically to a real execution of the protocol if the triple is random, then the transcript and key are distributed as if you ran a real ...
Top 50 recent answers are included
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## Category → life
I put this question in my FAQ, because at least two people have asked me this question, and that’s how frequent a question needs to be to be on my FAQ: I got an IMO1 gold medal in 2012, as a ninth grader, and an IOI gold medal in 2014, as an eleventh grader. I could have kept going to either, or even decided to try taking the IPhO or something, but I didn’t. Why not?
The short answer: It was a rough utilitarian calculation. By continuing, I would probably displace somebody else who would gain more from being on an IMO/IOI team than I would. Besides, I wanted to do other things in high school, so I wasn’t losing much.
I think the short answer actually captures most of my thinking when I made the decision back then, and it’s not really new; I said as much at the end of 2013. But behind it was a lot of complex thoughts and feelings that I’ve been ruminating over and trying to put into words for the better part of a decade. Hence, this post.
There is a natural question that precedes the frequently asked one that I have never been asked, something I am now realizing I never honestly asked myself and never tried to answer deeply: Why did I participate in the IMO and the IOI in the first place?
I was pretty torn between this and “The Future Soon” as the Year-End Song on this blog, but in the end I think I feel more threatened by the bland existence of the soulless adult than inspired by the starry-eyed-idealism-with-misogynist-undertones of the twelve-year-old, plus I get to show you the best kinetic typography video I have ever seen.
Halfway through 2018 I thought this would be the year of ephemeral phases. I felt like I went through a different phase every month — Online Dominion in April, crosswords in June, Only Connect in July, Jonathan Coulton in August, a brief stint of trying really hard to barre my guitar chords in October. Somewhere in the middle, I discovered Kittens Game (“the Dark Souls of Incremental Gaming”) and my summer internship mentor got me to pick up Pokémon Go again. A few intense periods of typographical study were interspersed, which involved watching the above music video dozens of times, teaching a Splash class on typography, and developing a new awareness of how Avenir was everywhere. During the last month, I went hard on Advent of Code and got second place, apparently the only person to make it on every single leaderboard. I also did a related golf side contest and poured a couple more hours into Paradoc, my personal golfing language, for rather unclear gain. At least I got a lot of GitHub followers?
It would turn out, though, that a lot of these phases had more staying power than I expected. Pokémon Go is a much better game than it was two years ago and has actually fostered a significant real-life community, which seems like one of the best possible outcomes of an augmented reality game, and I’ve found a steady pace to play at. I spread the Only Connect bug and people on my hall, intrigued by the format but annoyed by the overwhelmingly British trivia1, started writing and hosting full games for each other, with our own MIT-slanted set of trivia. One of us developed a custom site and tool to host these games. It took me a while to warm up to Jonathan Coulton’s latest album, but since it happened, I cannot get Ordinary Man or Sunshine out of my head; I’m still listening to JoCo as I finish typing up this post. Although I never got back to the peak of my crossword frenzy, I still study crosswordese from time to time and compose crosswords for some special occasions, like this one (.puz file).
The academics and technical aspects of this year have all blurred together, but I think my interests are finally crystallizing:
I think this is the right video for this year.
I love the music and the animation. The music video spells out the central conceit somewhat explicitly, but I think the lyrics by themselves have a hint of ambiguity — is it a harmful addiction that you just can’t escape from, or an essential part of your identity that you just can’t deny?
What parts of me can I just not deny, huh? Unfortunately 2017 is also the year I decide my online presence should probably be a little more professional, so you might have to read between the lines a bit.
It seems to me like lots of people want this year to be over. Among all the other things, 2016 is also apparently the year I totally abandon this blog and put off certain planned posts by several months.
I guess this is what happens when you take five technical classes at MIT. The extracurriculars aren’t helping. And the fastest and most confident writing I do is still reactive, when there’s an externally-imposed deadline or when “somebody is wrong on the internet”. This blog isn’t.
Oh well, time to make up for it in 2017.
This is two days late and it’s not even the post that was supposed to be here. That will have to wait until I’m less hosed. ESP just finished running Splash, our largest annual event in which thousands of high school students come to MIT’s campus, and MIT community members (mostly) teach whatever they want to the students. This was the first big program I participated really deeply in as an ESP admin, and it has this way of eating you alive and spitting you out full of joy and immersion in life but devoid of energy and buffer zones for finishing other things by their deadlines.
On a similar note, thanks for all the birthday wishes from everyone everywhere. I’m sorry I haven’t found the time to respond or sometimes reciprocate. This made my day, and probably last couple of weeks too.
I had this 5,000-word draft, but I half-abandoned it for being sappy, boring, pointless, and impossible to rewrite to be satisfactorily un-cringeworthy. Instead, let me just tell you a couple random stories and anecdotes that went somewhere near the start. Maybe posting them will motivate me to salvage something from the 4,500 words that go after it and post it. Eventually.
Some time ago, Namecheap had a discount, so I bought a domain name for 88¢. Unfortunately, the discount only lasted for one year; afterwards, it would cost $29/year to renew. Even though I bought it on a whim and didn’t have much use for it, I found myself wanting to keep it more and more and had a huge mental struggle over whether I could afford it, because wow,$29 is a lot!
Meanwhile, during the same school year, more or less:
One of the most unexpectedly different facets of life during my internship has been the meals.
I’m not talking about the food; it’s certainly different in a fantastic way (Dropbox’s food (link to Facebook page) is like something out of a high-end restaurant), but I knew that before coming already. Also of note is the way I started eating ∞% more ramen over the weekends than I did over the entire school year at MIT, because here I can’t buy that many groceries without them spoiling and am amazingly lazy in this new environment.
No, this (deadlined, so not that well-thought-out, but whatever) post is about conversations at meals, which happen basically every lunch and some dinners when my team eats together.
I’ve never had any regular experience like it. Of course I’ve had many meals at home with family, but they feel different because, well, it’s family and we have so many topics in common. I went to the same school for twelve years and we didn’t generally use a cafeteria; we just ate at our desks in our classrooms, or while doing things like attending club meetings or taking makeup tests. Sometimes if people felt like it they would push desks together to eat, but eating by oneself was totally normal. (At last, I feel like that was what it was. It seems so far away now that I don’t trust my memory, which is pretty sad… I faintly suspect I would have this experience in a more stereotypical American high school. But this is mostly just based off the cafeteria in Mean Girls, a movie I only watched in its entirety on the flight here, which is weird because I know I’ve seen the “The limit does not exist!” part much much earlier. /aside)
And at MIT? “Time is an illusion. Lunchtime doubly so.”
(So. It’s spring break. Two-week-late post, and somehow by the end it’s all aboard the angst train again?)
Two Sundays ago, I mobbed with a small group of MIT furries to watch Zootopia, the recent highly-reputed Disney movie.
(Before anything else, first there were the previews. I was impressed that every single one of them — there were six or so — was about an upcoming movie featuring anthropomorphic animals front and center. Let me see if I can remember all of them… in no particular order, Teenage Mutant Ninja Turtles, The Secret Life of Pets, The Jungle Book, Storks, Finding Dory, and Ice Age: Collision Course. edit: Oh, also Angry Birds. Wow, I said, they know their audience.)
I went into the movie with a vague impression that Zootopia was more adult-oriented than most Disney films — not in the naughty way, but in general making a lot of jokes and invoking a lot of parallels that I think only adults might have the experience to get. My suspicions were confirmed a few lines into the movie, where there was a joke about taxes I cracked up at but can’t imagine that children a few years younger would have found funny. If you the reader haven’t watched it, I hope that was vague enough not to ruin the start for you.
(To be fair — and, uh, some parts of the internet are kind of big on this fact — the film also at one point enters a nudist colony. Fortunately (?), Animals Lack Attributes.)
(all the times that you beat me unconscious I forgive)
angst [████████ ] (8/10)
We’re overdue for one of these posts, I guess.
(all the crimes incomplete – listen, honestly I’ll live)
Last-ditch feeble attempts at cleaning and reorganizing my desk and shelf before I figuratively drowned in academics led to me finding
• the Google physical linked puzzle, which I placed in the Kitchen Lounge to nerd-snipe people, successfully
• a Burger King crown from the previous career fair
• ID stickers from the Putnam, one of which is now on my keyboard cover cover (← not a typo), just because
• assorted edibles, like candies and jellies, which I ate; as well as the half-finished Ziploc bag of candy from my FPOP, six months ago, which I just tossed in the trash
• a box. It’s just, like, a box. I don’t know what goes or went into it
I feel more in control of my living quarters. Marginally. Guess I’ll be fine.
(mr. cool, mr. right, mr. know-it-all is through)
Pros and cons of having a departmental advisor in your area of interest:
I wasn’t sure what would be the right song for 2015 until I set foot on MIT. Then it was a no-brainer.
Where do I even begin?
• I thought cooking was hard. Then I ended up in the kitchen on the third floor of the west parallel of East Campus and had to produce something edible. So I figured out how to acquire chicken and put it in a pan with some onions and heat the whole thing up. It wasn’t even that bad! A few weeks later, I graduated to cooking in a rotation for six people. All this from a guy whose culinary abilities only went as far as frying eggs a few months ago. It’s incredible where life takes you sometimes.
• I thought I couldn’t productively listen to lyrical music while doing homework, because I get distracted and/or bogged down by the feels. Turns out there’s a category of metal songs with great atmosphere and terrible lyrics that does the trick.
• I had planned to suffer through introductory chemistry my freshman fall and introductory biology my freshman spring, and thereafter be done with required classes. Well, I took chemistry, but there was barely any suffering involved, and now biology fits nowhere on my freshman spring schedule.
• I had some outlandish hopes I’d walk into college and be able to become mildly financially independent because people would throw high-paying jobs at me that I could learn from, but I didn’t expect it to happen. Life isn’t that easy!
Well… it happened.
• An incredible number of redacted things.
I’ve never been that kind of guy. Honest and innocent to a fault, no secrets except those arising from paranoid self-assigned concern about others’ privacy: that’s me. Until this year.
Oh well, I can’t blog about it.
[redacted]
• But mostly, of course, I actually graduated. The teacher-appreciation dinner happened (6/4), where I debuted my graduation song (woo!) and ate some good cake (double woo!); senior prom happened (6/7), with some awesome photos; and then, actually, the graduation ceremony. (6/10, same day I realized I had recently passed 100 starred things on GitHub.)
::looks at self:: I’m actually a college student now.
Every one of these stages of life seems like it should be a big deal, like I should pass through and suddenly know all the things about maturity and aspirations and life that are expected of college students, but it never happens that way.
At least, all things considered, I think this transition was very successful at taking my mind off the angsty side of things. This post is actually surprisingly unangsty. Sorry to disappoint if that’s what you’re here for!
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What are the odds against drawing a face card?
Mar 23, 2018
Odds against drawing a face card are $3.333$
Explanation:
Odds against is given by number of unfavorable outcomes to number of favorable outcomes.
Here drawing a face card is a favourable event. As there are $12$ face cards against a total of $52$ cards in pack,
number of unfavourable outcomes are $52 - 12 = 40$
and number of favourable outcomes are $12$
Hence odds against are $\frac{40}{12} = \frac{10}{3} = 3.333$
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Premium Online Home Tutors
3 Tutor System
Starting just at 265/hour
# Q.2 Give the order of rotational symmetry for each figure:
(a) Order of rotational symmetry = 360°/180°=2
(b) Order of rotational symmetry = 360°/180°=2
(C) Order of rotational symmetry = 360°/120°=3
(d) Order of rotational symmetry = 360°/90°=4
(e)Order of rotational symmetry = 360°/90°=4
(f) Order of rotational symmetry = 360°/72°=5
(g) Order of rotational symmetry = 360°/60°=5
(h) Order of rotational symmetry = 360°/120°=3
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Article Contents
Article Contents
# Feedback stabilization methods for the numerical solution of ordinary differential equations
• In this work we study the problem of step size selection for numerical schemes, which guarantees that the numerical solution presents the same qualitative behavior as the original system of ordinary differential equations. We apply tools from nonlinear control theory, specifically Lyapunov function and small-gain based feedback stabilization methods for systems with a globally asymptotically stable equilibrium point. Proceeding this way, we derive conditions under which the step size selection problem is solvable (including a nonlinear generalization of the well-known A-stability property for the implicit Euler scheme) as well as step size selection strategies for several applications.
Mathematics Subject Classification: Primary: 65L07, 34D20; Secondary: 65L06, 93D15.
Citation:
• [1] Z. Artstein, Stabilization with relaxed controls, Nonlinear Anal., 7 (1983), 1163-1173.doi: 10.1016/0362-546X(83)90049-4. [2] P. Cannarsa and C. Sinestrari, "Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control,'' Progress in Nonlinear Differential Equations and their Applications, 58, Birkhäuser Boston Inc., Boston, MA, 2004. [3] S. Dashkovskiy, B. S. Rüffer and F. R. Wirth, An ISS small gain theorem for general networks, Math. Control Signals Systems, 19 (2007), 93-122.doi: 10.1007/s00498-007-0014-8. [4] R. A. Freeman and P. V. Kokotović, "Robust Nonlinear Control Design - State-Space and Lyapunov Techniques,'' Birkhäuser, Boston, MA, 1996. [5] B. M. Garay and K. Lee, Attractors under discretization with variable stepsize, Discrete Contin. Dyn. Syst., 13 (2005), 827-841.doi: 10.3934/dcds.2005.13.827. [6] C. W. Gear and I. G. Kevrekidis, Projective methods for stiff differential equations: Problems with gaps in their eigenvalue spectrum, SIAM J. Sci. Comput., 24 (2003), 1091-1106.doi: 10.1137/S1064827501388157. [7] C. W. Gear and I. G. Kevrekidis, Telescopic projective methods for parabolic differential equations, J. Comput. Phys., 187 (2003), 95-109.doi: 10.1016/S0021-9991(03)00082-2. [8] P. Giesl, "Construction of Global Lyapunov Functions Using Radial Basis Functions,'' volume 1904 of "Lecture Notes in Mathematics," Springer, Berlin, 2007. [9] B. S. Goh, Algorithms for unconstrained optimization problems via control theory, J. Optim. Theory Appl., 92 (1997), 581-604.doi: 10.1023/A:1022607507153. [10] V. Grimm and G. R. W. Quispel, Geometric integration methods that preserve Lyapunov functions, BIT, 45 (2005), 709-723.doi: 10.1007/s10543-005-0034-z. [11] L. Grüne, "Asymptotic Behavior of Dynamical and Control Systems under Perturbation and Discretization,'' volume 1783 of "Lecture Notes in Mathematics," Springer, Berlin, 2002. [12] L. Grüne, Attraction rates, robustness, and discretization of attractors, SIAM J. Numer. Anal., 41 (2003), 2096-2113.doi: 10.1137/S003614290139411X. [13] L. Grüne, E. D. Sontag and F. R. Wirth, Asymptotic stability equals exponential stability, and ISS equals finite energy gain-if you twist your eyes, Syst. Control Lett., 38 (1999), 127-134. [14] K. Gustafsson, Control-theoretic techniques for stepsize selection in explicit Runge-Kutta methods, ACM Trans. Math. Software, 17 (1991), 533-554.doi: 10.1145/210232.210242. [15] K. Gustafsson, Control-theoretic techniques for stepsize selection in implicit Runge-Kutta methods, ACM Trans. Math. Software, 20 (1994), 496-517.doi: 10.1145/198429.198437. [16] K. Gustafsson, M. Lundh and G. Söderlind, A {PI stepsize control for the numerical solution of ordinary differential equations}, BIT, 28 (1988), 270-287. [17] E. Hairer, C. Lubich and G. Wanner, "Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations,'' Springer, Berlin, second edition, 2006. [18] E. Hairer, S. P. Nørsett and G. Wanner, "Solving Ordinary Differential Equations. I Nonstiff Problems,'' Springer, Berlin, second edition, 1993. [19] E. Hairer and G. Wanner, "Solving Ordinary Differential Equations. {II} Stiff and Differential-Algebraic Problems,'' Springer, Berlin, second edition, 1996. [20] Z.-P. Jiang, A. R. Teel and L. Praly, Small-gain theorem for ISS systems and applications, Math. Control Signals Systems, 7 (1994), 95-120.doi: 10.1007/BF01211469. [21] I. Karafyllis, Non-uniform robust global asymptotic stability for discrete-time systems and applications to numerical analysis, IMA J. Math. Control Inform., 23 (2006), 11-41.doi: 10.1093/imamci/dni037. [22] I. Karafyllis, A system-theoretic framework for a wide class of systems. I, Applications to numerical analysis, J. Math. Anal. Appl., 328 (2007), 876-899.doi: 10.1016/j.jmaa.2006.05.059. [23] I. Karafyllis and Z.-P. Jiang, A small-gain theorem for a wide class of feedback systems with control applications, SIAM J. Control Optim., 46 (2007), 1483-1517.doi: 10.1137/060669310. [24] I. Karafyllis and Z.-P. Jiang, A vector small-gain theorem for general nonlinear control systems, In "Proceedings of the 48th IEEE Conference on Decision and Control,'' pages 7996-8001, Shanghai, China, 2009. [25] H. K. Khalil, "Nonlinear Systems,'' Prentice Hall, Upper Saddle River, third edition, 2002. [26] P. E. Kloeden and J. Lorenz, Stable attracting sets in dynamical systems and in their one-step discretizations, SIAM J. Numer. Anal., 23 (1986), 986-995.doi: 10.1137/0723066. [27] P. E. Kloeden and B. Schmalfuss, Lyapunov functions and attractors under variable time-step discretization, Discrete Contin. Dynam. Systems, 2 (1996), 163-172.doi: 10.3934/dcds.1996.2.163. [28] V. Lakshmikantham and D. Trigiante, "Theory of Difference Equations: Numerical Methods and Applications,'' Marcel Dekker, New York, second edition, 2002. [29] H. Lamba, Dynamical systems and adaptive timestepping in ODE solvers, BIT, 40 (2000), 314-335.doi: 10.1023/A:1022395124683. [30] Y. Lin, E. D. Sontag and Y. Wang, A smooth converse Lyapunov theorem for robust stability, SIAM J. Control Optim., 34 (1996), 124-160.doi: 10.1137/S0363012993259981. [31] J. Peng, Z.-B. Xu, H. Qiao and B. Zhang, A critical analysis on global convergence of Hopfield-type neural networks, IEEE Trans. Circuits Syst. I Regul. Pap., 52 (2005), 804-814.doi: 10.1109/TCSI.2005.844366. [32] E. D. Sontag, Smooth stabilization implies coprime factorization, IEEE Trans. Automat. Control, 34 (1989), 435-443.doi: 10.1109/9.28018. [33] E. D. Sontag, A "universal'' construction of Artstein's theorem on nonlinear stabilization, Systems Control Lett., 13 (1989), 117-123. [34] E. D. Sontag, "Mathematical Control Theory,'' Springer, New York, second edition, 1998. [35] A. M. Stuart and A. R. Humphries, "Dynamical Systems And Numerical Analysis,'' Cambridge University Press, Cambridge, 1996. [36] A. R. Teel, Input-to-state stability and the nonlinear small gain theorem, Preprint, 2005. [37] Y. Xia and J. Wang, A recurrent neural network for nonlinear convex optimization subject to nonlinear inequality constraints, IEEE Trans. Circuits Syst., 51 (2004), 1385-1394.doi: 10.1109/TCSI.2004.830694. [38] H. Yamashita, A differential equation approach to nonlinear programming, Math. Programming, 18 (1980), 155-168.doi: 10.1007/BF01588311. [39] L. Zhou, Y. Wu, L. Zhang and G. Zhang, Convergence analysis of a differential equation approach for solving nonlinear programming problems, Appl. Math. Comput., 184 (2007), 789-797.doi: 10.1016/j.amc.2006.05.190.
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SIRXS Software Problem Reports
This listing shows software problem reports and enhancements ordered by the revision number and release date.
### Fixed/implemented in revision 20
Command lines length increased
Command lines can now be up to 510 characters (increased from 254).
Severity: Enhancement
GET VARS and PUT VARS new features
The two commands have been upgraded such that the features mirror each other. Both commands allow:
Use of "TO" to specify variable lists
Use of arrays as local variables
Specification of prefix or suffix for local variables
Use of name (not in quotes) as prefix or suffix
Severity: Enhancement
Changed processing of input on long running programs to keep 'Break' function enabled
If there was a long running SIR program and the user clicked the mouse or pressed any key other than "Break" then the SIR window title bar would say "Not responding" and any output scrolling would disappear for the duration of the program execution.
Note: This means that the program is not waiting as far as windows is concerned (it can process input) and so does not display a windows waiting sysmbol such as an hourglass or spinning circle.
Severity: Enhancement
Text in quotes can be split across command lines.
Text in quotes can be split across input lines. Trailing blanks are ignored but leading blanks on subsequent lines are treated as part of the string.
Severity: Enhancement
Length of labels increased
Maximum length of labels has been standardised to 254 characters. This applies to VALUE LABELS and VARIABLE LABELS.
Severity: Enhancement
New TRACE feature to trace control into/out of PQL subroutines for debugging.
Subroutine tracing displays the subroutine name when it is entered during a PQL execution and displays a message when control is returned to the calling program. Subroutine tracing is always turned off by default and is automatically turned off when the main program finishes execution.
On a main retrieval/program, specifying the TRACE option turns on subroutine tracing immediately for the subsequent execution. NOTRACE is the default and has no effect.This setting is not saved with any saved executable.
On a subroutine command, if TRACE or NOTRACE is not specified, tracing is controlled by the main program setting. If TRACE or NOTRACE is specified, the setting is saved with the subroutine and controls tracing when the subroutine is executed and for any further subrouines called below that subroutine. The main program setting is restored when the subroutine returns control. This enables a subset of subroutines to be traced for debugging purposes.
Note that tracing can also be turned on with an option on the PRINT BACK command.
Severity: Enhancement
New BUFEXIST function
num = BUFEXIST(buffer_name_expression)
Returns the buffer number of the specified buffer name. Returns zero if the buffer name does not exist.
Severity: Enhancement
New BUFLINES function
num = BUFLINES(buffer_name_expression)
Returns the number of lines in the specified buffer. Returns -1 if the buffer name does not exist. A zero return value indicates an existing, empty buffer.
Severity: Enhancement
Enhanced number of variables for functions with lists of variables
There are a number of functions such as CNT which can have lists of variables. The list limit was 128 variables and this has been increased to 512.
Severity: Enhancement
New EXISTSR function
num = EXISTSR (varname)
Returns 1 if any value of varname (real or string) found during a PROCESS REC or PROCESS ROWS loop is not undefined or defined as missing. Returns zero if all values are undefined or defined as missing.
Severity: Enhancement
Enhanced set of functions which include missing/excluded values
There are a number of functions such as CNT which process variables and exclude variables which are undefined or missing/excluded. The set of functions has been increased with versions that only exclude undefined values i.e. missing/excluded values are included. These functions have an "X" appended to the name of the corresponding function and are:
num = CNTRX (varname) Returns the number of values of varname (real or string) found during a PROCESS REC or PROCESS ROWS loop that are not undefined. Returns zero if all values are undefined.
num = CNTX (varname1, varname2, ..... varname512) Counts the number of values in the list that are not undefined. There may be up to 512 values in the list, separated by commas. They may be real or string variables but all must be of the same type.
num = EXISTSRX (varname) Returns 1 if any value of varname (real or string) found during a PROCESS REC or PROCESS ROWS loop is not undefined. Returns zero if all values are undefined.
num = EXISTSX (varname) Returns 1 if value of named variable is not undefined. Returns zero if value undefined.
num = NEXISTS (varname) Returns 1 if value of named variable is undefined. Returns zero if value is not undefined.
Severity: Enhancement
New NUMBRC function
num = NUMBERC (string)
Tests whether a string represents a valid number. The string can be a string constant, variable name or expression and should contain only numerical characters, at most one decimal point and a plus or minus sign or is in E+exponent format. The string may have blanks to start and all characters are processed. The function returns the following codes:
undefined if undefined
-1 if not a valid number string
0 if number is blank
If the string translates correctly to a real*8 number, it is then assigned to more restrictive formats starting with Integer*1. If the most restrictive format tests equal to the real*8 value, then the return value is set to to that.
1 Valid integer that could be stored in an Integer*1 variable
2 Valid integer that could be stored in an Integer*2 variable
4 Valid integer that could be stored in an Integer*4 variable
8 Valid floating point number that could be stored accurately in a REAL*4 variable
16 Valid floating point number that could only be stored in a REAL*8 number
Severity: Enhancement
New DBNUM function
num = DBNUM (database_name)
Returns the number (nth) of a connected database.
Severity: Enhancement
New DBATTR function
str = DBATTR (nth)
Returns the attribute name of the first file of the nth connected database.
Severity: Enhancement
New DBPRE function
str = DBPRE (nth)
Returns the prefix which is the fully qualified directory of the nth connected database.
Severity: Enhancement
Get Master functions did not check parameters properly.
The Master functions request information from master (e.g. name of nth database). If the parameter was negative or greater than nth, this was not properly checked for and reported as an error. Invalid data might be returned or Master might fail.
Severity: Moderate Status:Closed - Fixed
Example:
compute x = GETMDBN(0)
Workaround:
Use functions to get the number and only pass valid parameters > 0 and =< number.
compute x = system(69)
for i = 1,x
. compute z = GETMDBN(i)
rof
DO REPEAT, INCLUDE and PRINT BACK were not operative within a PQLForm
PQLForms compilation is a two part process. The first part generates PQL and then the PQL is compiled in the normal manner. The text processing environment commands were ignored during the generation of PQL.
Severity: Moderate Status:Closed - Fixed
Workaround:
Cut and paste the required pieces of code physically into the form source.
PQLForms now allows text style fields that displays a multi-line text control and creates/displays a named buffer
The PQLForms FIELD command now allows a TYPE BUFFER n clause. This generates a text control n lines deep. Data is automatically passed between the control and a named buffer which has the same name as the field.
The PQLForms screen painter allows for this new control when a new local variable is defined. Specify the type as "Buffer" from the drop down list.
It is the developer's responsibility to populate the buffer when a record is read and to save the updated text when the record is written - typically using the READ and WRITE clauses on the SCREEN command.
Severity:Enhancement
PQLForms painter incorrectly processed user specified code for specific variables
The PQLForms painter allows users to specify PQL code to operate at particular points in the form. Under certain circumstances, this code was not in the correct place.
Severity: Moderate
Status:Closed - Fixed
Workaround:
Specify the code at a different point in the painter.
PQLForms painter prompt type did not enable EDIT control properly
The PQLForms painter allows users to specify a variable label by entering text. This was not enabled properly.
Severity: Moderate Status:Closed - Fixed
Workaround:
Specify the variable label in the schema.
CHECK ITEM function can be specified for a CHOICE control
A CHOICE control is a pull-down list and the CHECK ITEM function displays the list.
Severity: Enhancement
CLICK is a new gui command that simulates the user clicking on a control.
CLICK simulates the user choosing (CLICKing) the appropriate control. The program then continues as if a new message has been received. i.e no further commands are processed after the CLICK command and control returns to the appropriate message block.
CLICK does not alter the visual appearance of the dialog.
Severity: Enhancement
SET ITEM FONT allows values values in the SIZE parameter
The SET ITEM FONT command now operates by increasing or decreasing the font size n times as specified in the SIZE parameter, rather than having to repeat the command multiple times.
Severity: Enhancement
Double clicking the mouse on the spreadsheet record selection didn't work
Double clicking the mouse on the spreadsheet record is supposed to run the spreadsheet but didn't.
Severity: Minor Status:Closed - Fixed
Workaround:
Use the OK button.
Number of record types allowed was one less than specified in schema
Could not create the last record type of the specified number. e.g. If 30 was the maximum, only 29 could be created.
Severity: Minor Status:Closed - Fixed
Workaround:
Specify a higher maximum.
REDEFINE ARRAY set an error limit of zero
The REDEFINE ARRAY command accidently set an error limit of zero which suppressed subsequent error messages.
Severity: Minor Status:Closed - Fixed
Workaround:
Specify an error limit after this command.
Conflict between PQL compilation and some environment commands such as IFNOTMEMBER
The IFNOTMEMBER and related IFcond SKIP environment commands use internal constants. If these were specified in a set of PQL commands being compiled, errors were introduced.
Severity: Minor Status:Closed - Fixed
Workaround:
Avoid using these commands inside PQL compilations.
Any specified aliases on CIR variables were not unloaded properly and so the reload might fail.
Severity: Severe Status:Closed - Fixed
Workaround:
Avoid using ALIAS for CIR variables.
SQL Preset problem
If a single character had an SQL PRESET value, this was not stored properly.
Severity: Moderate Status:Closed - Fixed
Workaround:
Avoid using single character PRESET in SQL.
SQL Import problem
If the first character in an imported line was blank, this caused import problems.
Severity: Moderate Status:Closed - Fixed
Workaround:
Avoid using SQL import and rebuild tabfiles in other ways.
### Fixed in revision 19
GUI Window gives Not Responding message and does not show updated output when interacting with the window while a PQL program is running
GUI Window gives Not Responding message and does not show updated output when interacting with the window while a PQL program is running
Severity: Minor Status: Closed - Fixed
Example:
Run a PQL program that takes several minutes to execute. While the program is running, click the window title bar a few times.
Workaround:
Do not try to interact with the window while the PQL program is running. If it does go Not Responding then wait for the program to finish
RELOAD created corrupt database if last index block exactly full
RELOAD created corrupt database if last index block exactly full
Severity: Serious Status: Closed - Fixed
Example:
Workaround:
1) Do not completely delete a database until successful unload / reload / verify. 2) If the subsequent verify shows corruptions then restore the old database, apply another update then unload / reload / verify again.
SPSS SAVE FILES with very long strings followed by variables with value labels
SPSS SAVE FILES with very long strings followed by variables with value labels
Severity: Moderate Status: Closed - Fixed
Example:
program
string*261 var1
integer var2
value labels var2 (1) "one"
perform procs
spss save file filename="test261.sav"
end program
Workaround:
Shorten the string or put the long strings at the end of the file.
ERROR LIMIT warning given erroneously
ERROR LIMIT warning given erroneously
Severity: Minor Status: Closed - Fixed
Example:
Workaround:
Temporary filename updated to include process id to avoid possible clashed with multiple instances of SIR/XS
Temporary filename updated to include process id to avoid possible clashed with multiple instances of SIR/XS
Severity: New Feature Status: Closed - Fixed
Example:
Edit a member and note the temporary filename used.
Workaround:
VALIDATE wrong results when referencing a constant
VALIDATE wrong results when referencing a constant
Severity: Moderate Status: Closed - Fixed
a database with a string variable has a VALIDATE using a constant value that should fit but gives a 7 (text truncated). If I use a variable with the same value then it returns 0. This doesn't happen with any string variable - it depends on VAR RANGES of another string variable.
Example:
PROGRAM
STRING TEST_VALUE
TEST_VALUE = '12'
WRITE [VALIDATE(1,"TESTVAR", '12' )]
WRITE [VALIDATE(1,"TESTVAR", TEST_VALUE)]
END PROGRAM
Start program translation
Start program execution
7
0
End program execution
Workaround:
Use a variable rather than a constant.
ODBC truncating column names to 32 characters
ODBC truncating column names to 32 characters
Severity: Moderate Status: Closed - Fixed
ODBC reads of an excel spreadsheet that has column names > 32 characters and these are being truncated in the COLNAME function.
Example:
Workaround:
Use COLVALS for "COLUMN_NAME" from the ODBCCOLS function.
Severity: New Feature Status: Closed - Fixed
Example:
program
integer array x (10)
set x * (1,2,3,4,5,6,7,8,9,10)
redefine array "X" (2,5)
for i = 1,2
for j = 1,5
write (stdout,noeol) x(i,j) ","
end for
write
end for
end program
Workaround:
Unknown stack command when MOVE VARS/PUT VARS referenced too many variables.
Unknown stack command when MOVE VARS/PUT VARS referenced too many variables.
Severity: Moderate Status: Closed - Fixed
Example:
Workaround:
Severity: New Feature Status: Closed - Fixed
Example:
Workaround:
Processing records in reverse through a secondary index stopped after first record
Processing records in reverse through a secondary index stopped after first record
Severity: Moderate Status: Closed - Fixed
Example:
retrieval noautocase
set start end ("AAA","BBB")
process record 1 indexed by STR with (start,end) reverse
write key str1 str2
end record
end retrieval
Workaround:
Issues with multiple PROCESS JOURNAL executions in a FOR LOOP
Issues with multiple PROCESS JOURNAL executions in a FOR LOOP
Severity: Moderate Status: Closed - Fixed
Example:
Workaround:
Master updates with secondary indexes gave problems
Master updates with secondary indexes gave problems
Severity: Serious Status: Closed - Fixed
Example:
Workaround:
File names (attributes) might not match between OPEN and READ when specified as text filenames
File names (attributes) might not match between OPEN and READ when specified as text filenames
Severity: Moderate Status: Closed - Fixed
Example:
open 'data.txt' lrecl=400 read
Workaround:
use OPEN attr DSN="data.txt" LRECL=400 READ
### Fixed in revision 18
PQLForms long strings (>255) truncated on input.
PQLForms long strings (>255) truncated on input.
Severity: Moderate Status: Closed - Fixed
Example:
Define a database string variable with length more than 255 then enter more than 255 characters through PQLForms.
Workaround:
SORT ARRAY BY behaviour for tied values in keys inconsistent.
SORT ARRAY BY behaviour for tied values in keys inconsistent.
Severity: Minor Status: Closed - Fixed
When two arrays are sorted using another array (BY ARRAY) then the sorted arrays should be sequenced the same way regradless of tied values. ALTERNATE keyword allows row then column rather than column,row.
Example:
program
. integer * 1 array SCORE# GAMES# RANK# SORTER# (5)
. string * 32 array NAME$(5) . NAME$(1) = 'Bruss';SCORE#(1) = 31;GAMES#(1) = 54
. NAME$(2) = 'Ben' ;SCORE#(2) = 33;GAMES#(2) = 15 . NAME$(3) = 'Ryan' ;SCORE#(3) = 34;GAMES#(3) = 32
. NAME$(4) = 'John' ;SCORE#(4) = 42;GAMES#(4) = 28 . NAME$(5) = 'Jake' ;SCORE#(5) = 33;GAMES#(5) = 6
. for x = 1,5
. COMPUTE SORTER#(x) = X
. end for
. sort SORTER# by SCORE#
. for x = 1,5
. compute rank#(sorter#(x)) = x
. end for
. sort NAME$by RANK# . sort GAMES# by RANK# . sort SCORE# by RANK# . for x = 1,5 . write X NAME$(x) 17t SCORE#(x) 21t GAMES#(x)
. end for
end program
Workaround:
EXECUTE DBMS command problem when issued within database processing
EXECUTE DBMS command problem when issued within database processing
Severity: Moderate Status: Closed - Fixed
This can occur in a caseless database, when using EXECUTE DBMS with a subroutine
Example:
RETRIEVAL UPDATE
EXECUTE DBMS 'INCLUDE BUFFER "B"'
write "1"
EXECUTE SUBROUTINE SYSTEM.EMPLOYEE
write "4"
process record 1
write "5"
exit record
end record
END RETRIEVAL
Workaround:
In-use flag and VERIFY interaction updated to be more logical
In-use flag and VERIFY interaction updated to be more logical
Severity: New Feature Status: Closed - Fixed
Example:
Workaround:
REDEFINE ARRAY gave strange results when multiple arrays defined
REDEFINE ARRAY gave strange results when multiple arrays defined
Severity: Moderate Status: Closed - Fixed
Example:
retrieval noautocase
. integer * 1 WINS# LOSSES# YES NO P# ONE# TWO# MATCHES#
. integer * 1 T1W# T2W# T1G1# T1G2# T1G3# T2G1# T2G2# T2G3#
. integer * 2 FOR# AGAINST# T# TEAMS#
. string * 32 ONE$TWO$ T1P1$T1P2$ T2P1$T2P2$
. date DATE_ ('MM/DD/YYYY')
. real * 8 array SORT# (225)
. integer * 2 array SCORE# GAMES# (225)
. string * 32 array TEAM$WINS$ SCORE$(225) . string * 32 array N$ (14)
. string * 32 array TT$(14,14) . integer * 2 array TF# TA# TW# TL# TG# TS# TR# (14,14) . integer * 2 array F# A# W# L# G# S# R# V# (14) . TEAMS# = 16 . redefine array 'TEAM$' (TEAMS#)
end retrieval
Workaround:
SEPCHAR keyword allowed for csv format in batch file processing
SEPCHAR keyword allowed for csv format in batch file processing
Severity: New Feature Status: Closed - Fixed
Example:
SIR FILE DUMP RECTYPE=1 FILENAME="data.csv" CSV SEPCHAR="|"
SIR FILE DUMP RECTYPE=1 FILENAME="data.csv" CSV SEPCHAR=TAB
Workaround:
DESCENDING did not work when sorting arrays
DESCENDING did not work when sorting arrays
Severity: Moderate Status: Closed - Fixed
Example:
Workaround:
WRITE ALL erroneously included a dummy FOR loop control variable
WRITE ALL erroneously included a dummy FOR loop control variable
Severity: Minor Status: Closed - Fixed
Example:
PROGRAM
FOR I = 1,3
WRITE ALL
END FOR
END PROGRAM
Workaround:
Master could crash if data records packed and encrypted when length close to multiple of 32
Master could crash if data records packed and encrypted when length close to multiple of 32
Severity: Moderate Status: Closed - Fixed
Example:
Workaround:
Functions that returned names did not trim trailing blanks consistently.
Functions that returned names did not trim trailing blanks consistently. Also could return zero length rather than undefined.
Severity: Minor Status: Closed - Fixed
Example:
WRITE ['"'+dbname(0)+'"']
"COMPANY "
Workaround:
WRITE ['"'+TRIM(dbname(0))+'"']
"COMPANY"
PQLForms problem with CALL VIA on caseless databases
PQLForms problem with CALL VIA on caseless databases
Severity: Moderate Status: Closed - Fixed
Example:
. SCREEN MENU MAINMENU
NOBUTTON
. CALL SCREEN REC_2
AT 4,1 WIDTH 13
PROMPT "REC_2"
VIA ("TWO")
. FBUTTON EXIT
Workaround:
. SCREEN MENU MAINMENU
NOBUTTON
. CALL SCREEN REC_2
AT 4,1 WIDTH 13
PROMPT "REC_2"
VIA (1,"TWO")
. FBUTTON EXIT
Problem with record counts on multiple journal restore
Problem with record counts on multiple journal restore
Severity: Moderate Status: Closed - Fixed
Example:
Workaround:
Problems on journal restore with secondary indexes
Problems on journal restore with secondary indexes
Severity: Moderate Status: Closed - Fixed
Example:
Workaround:
Treatment of padded string key fields made more consistent. NOTRIM keyword on EXPORT/IMPORT
Treatment of padded string key fields made more consistent. NOTRIM keyword on EXPORT/IMPORT
Severity: New Feature Status: Closed - Fixed
Example:
EXPORT FILENAME="TEST.exp" NOTRIM
Workaround:
VALID VALUES allows a TO specification
VALID VALUES allows a TO specification
Severity: New Feature Status: Closed - Fixed
Example:
VALID VALUES X (1 to 50, 98 99)
Workaround:
VALID VALUES X (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,98,99)
WRITE SCHEMA allows new RECTYPES of CIR, STANDARD and ALL.
WRITE SCHEMA allows new RECTYPES of CIR, STANDARD and ALL.
Severity: New Feature Status: Closed - Fixed
Example:
WRITE SCHEMA RECTYPE=CIR
Workaround:
Very long expressions crashed.
Very long expressions crashed.
Severity: Moderate Status: Closed - Fixed
Expressions now explicitly limited to about 820 components. Note evaluating very long expressions is slow and is thus not recommended. Multiple IF statements should be used instead.
Example:
IFTHEN (A EQ 1 OR A EQ 2 OR A EQ 3 ... OR A EQ 999)
ENDIF
Workaround:
SET TEST (0)
IF (A EQ 1) SET TEST (1)
IF (A EQ 2) SET TEST (1)
IF (A EQ 3) SET TEST (1)
...
IF (A EQ 999) SET TEST (1)
IFTHEN (TEST EQ 1)
ENDIF
SHOWMISS function returned wrong values with dates/times
SHOWMISS function returned wrong values with dates/times
Severity: Moderate Status: Closed - Fixed
dates (& times) with system missing as their value, showmiss will write out some constant from elsewhere in the program.
Example:
program showmiss
date x ("mmddyyyy")
write x "!?"
if (0) write "you will never see this"
end program
Start program translation
Start program execution
you will never see this !?
End program execution
Workaround:
STANDARD SCHEMA not written export file after changing database settings
STANDARD SCHEMA not written export file after changing database settings
Severity: Moderate Status: Closed - Fixed
Example:
Workaround:
Old style FORMS didn't connect to tabfiles properly
Old style FORMS didn't connect to tabfiles properly
Severity: Moderate Status: Closed - Fixed
Example:
Workaround:
$SQLTYPE in ODBC gave error if not connected to a database$SQLTYPE in ODBC gave error if not connected to a database
Severity: Moderate Status: Closed - Fixed
Some ODBC clients (eg MS Query) use select * from $SQLTYPE to get information about variable types. This gives an error if you are not connected to a DATABASE but the information is generic and should not need any database (or tabfile) connected. Example: start sirSQL, don't connect to a database but do connect to a tabfile (or don't connect to anything) Tabfile TF created on May 16, 2012 at 16:01:57 connected. select * from$SQLTYPE
No databases currently attached. $SQLTYPE Errors in processing FROM clause$SQLTYPE
Workaround:
DATA LIST command can be specified without columns or asterisk
New Feature DATA LIST command can be specified without columns or asterisk
Severity: New Feature Status: Closed - Fixed
Example:
DATA LIST
ID (I2)
NAME (A25)
GENDER (I1)
MARSTAT (I1)
SSN (A11)
BIRTHDAY (DATE'MMIDDIYY')
EDUC (I1)
NDEPENDS (I1)
CURRPOS (I1)
SALARY (I2)
CURRDATE (DATE'MMIDDIYY')
Workaround:
SCHEMA WRITE new keyword NOINDEX stops write of indexes for any record types being written
New Feature SCHEMA WRITE new keyword NOINDEX stops write of indexes for any record types being written
Severity: New Feature Status: Closed - Fixed
Example:
WRITE SCHEMA NOINDEX
Workaround:
SCHEMA WRITE new keyword LOCK will write the LOCK on the schema for all the rectypes being written
New Feature SCHEMA WRITE new keyword LOCK will write the LOCK on the schema for all the rectypes being written
Severity: New Feature Status: Closed - Fixed
Example:
WRITE SCHEMA LOCK
Workaround:
SCHEMA WRITE new keyword NOCOLS will suppress all column references on the schema for all the rectypes being written whether these are currently specified or not
New Feature SCHEMA WRITE new keyword NOCOLS will suppress all column references on the schema for all the rectypes being written whether these are currently specified or not
Severity: New Feature Status: Closed - Fixed
Example:
WRITE SCHEMA NOCOLS
Workaround:
### Fixed in revision 17
Deleting record type then unload/reload gave CIR REC count mismatch errors on Verify
Deleting record type then unload/reload gave CIR REC count mismatch errors on Verify
Severity: Minore Status: Closed - Fixed
Example:
Workaround:
VERIFY FILE / PATCH
### Fixed in revision 16
Interactive READ crashes on unix platforms
210801 Interactive READ crashes on unix platforms
Severity: Minor Status: Closed - Fixed
The example program below will crash SIR when the user clicks OK or Cancel on the interactive READ in PQL.
Example:
program string*10 numb read "Enter a number" numb write numb end program
Workaround:
Use DISPLAY TEXTBOX
program
string*10 numb
DISPLAY TEXTBOX "Enter a number" RESPONSE len, numb
write numb
end program
Severity: Minor Status: Closed - Fixed
The UNLOAD/PURGE/RELOAD procedure will fail at the DELETE/RENAME stage if someone else has the database connected. The .sr4 file does get deleted and needs to be restored from the UNLOAD step. This is fixed so that it will still fail but leave the database files in tact.
Example:
Workaround:
Reload the procedure file from the generated unload file. Make sure all users are disconnected from the database.
New Options Added To WRITE SCHEMA
210795 New Options Added To WRITE SCHEMA
Severity: New Feature Status: Closed - Feature
NOINDEX not write any indexes for any of the record types being written. LOCK will write the LOCK on the schema for all the rectypes being written. NOCOLS will suppress all column references on the schema for all the rectypes being written whether these are currently specified or not. SCHEMA definition to allow for no column specification in DATA LIST.
Example:
DATA LIST ID (I1) VAR1 (I4) VAR2 (D0) VAR2B (F0)
Workaround:
Generic toolbar bitmap displayed instead of error
210792 Generic toolbar bitmap displayed instead of error
Severity: New Feature Status: Closed - Feature
In a menu program, if you specify a bitmap that is not in the directory then you get Default.bmp instead of the error message.
Example:
Workaround:
Put the required bitmap file in the tbbb directory.
SPREADSHEET in LABELS mode shows blank if there is no label for a particular value
210789 SPREADSHEET in LABELS mode shows blank if there is no label for a particular value
Severity: Minor Status: Closed - Fixed
If a variable has labels for some values and not others (eg 99 "99 or more") then the spreadsheet /labels will only show data for those values with labels. Fixed to show the actual value when no label exists.
Example:
Workaround:
ALL keyword on variable lists will now mean "ALL not previously listed"
210786 ALL keyword on variable lists will now mean "ALL not previously listed"
Severity: New Feature Status: Closed - Feature
The ALL keyword can now be used at the end of a list of variables to mean ALL variables not previously in the list. This way you can specify the order of some of the variables then get the rest in their default ORDER
Example:
GET VARS GENDER MARSTAT ALL spss save file filename='PREDICT\DAILY\OUT\MULTI.SAV' variables=PREDICTN INTERVAL ALL program integer one two three string four five set one two three four five (1,2,3,"4","5") write five all end program 5 1 2 3 4
Workaround:
Specify all the variables in the required order
Clone a record in SIR Spreadsheet converts missing values to undefined.
210783 Clone a record in SIR Spreadsheet converts missing values to undefined.
Severity: Minor Status: Closed - Fixed
When you clone a record in SIR Spreadsheet, you lose user defined missing values (they get set to system missing).
Example:
Workaround:
Use a GET VARS / PUT VARS in a PQL program to duplicate a record.
It is not intuitive to set a field to undefined in PQLForms
210780 It is not intuitive to set a field to undefined in PQLForms
Severity: Minor Status: Closed - Fixed
When a user accidentally enters something in a pqlforms field and that variable does not have missing as a valid value then it is not easy or intuitive to undo the entry. (there is ctrl+u to set the DB value to undefined). Now, after the fix, entering a BLANK into a field that does not have BLANK as a missing value will set the value to undefined. If blank is a valid missing value then it is stored correctly. If the field does not have blank as a valid value because it is required then that would need to be caught elsewhere.
Example:
Workaround:
Press Ctrl+u to set any edit field to undefined.
CASE IS / END CASE IS inside a PROCESS RECORD ... INDEXED BY gives an error
210777 CASE IS / END CASE IS inside a PROCESS RECORD ... INDEXED BY gives an error
Severity: Minor Status: Closed - Fixed
When you process a record using an index you are in a case at execution time so you can get to the CIR and process other records belonging to the current case. The program below will work without the red CASE IS block. With the case is, the compiler gets confused and complains that the process record occup is not inside a case block.
Example:
retrieval process record employee indexed by name from ("M") thru ("T") write name gender case is 1 end case is process record occup write 5x division end record end record end retrieval
Workaround:
Workarounds would be to include another case block or to put CASE into a subprocedure. retrieval process record employee indexed by name from ("M") thru ("T") write name gender get vars id case is 1 end case is case is id process record occup write 5x division end record end case end record end retrieval retrieval process record employee indexed by name from ("M") thru ("T") write name gender execute subprocedure caseis process record occup write 5x division end record end record subprocedure caseis case is 1 end case is end subprocedure end retrieval
New OPEN buttion in File attributes... dialog
210774 New OPEN buttion in File attributes... dialog
Severity: New Feature Status: Closed - Feature
The Open button in file attributes will attempt to "open" the selected file.
Example:
Workaround:
Open the file from the operating system
Microsoft Query hangs on connecting to a SIR ODBC data source.
210771 Microsoft Query hangs on connecting to a SIR ODBC data source.
Severity: Moderate Status: Closed - Fixed
Microsoft Query hangs when trying to display the SIR ODBC database connection dialog.
Example:
Workaround:
Export the data from SIR to CSV and import into Microsoft.
PQLForms: choosing a keyfields value from a choice list does not trigger record retrieval
210768 PQLForms: choosing a keyfields value from a choice list does not trigger record retrieval
Severity: Minor Status: Closed - Fixed
When the last key field on a PQLForm is modified then the record data should be retrieved. This does not happen if the key field is modified by selecting the value from a picklist.
Example:
In COMPANY OCCUP default PQLForm, type in case id 1 and select Laborer from the position drop down list. The record is not retrieved.
Workaround:
Type the value into the text area
Problems with CAT VARS as keys in spreadsheet
210765 Problems with CAT VARS as keys in spreadsheet
Severity: Moderate Status: Closed - Fixed
A caseless with a record type that has a cat var for a key may not show all records in the spreadsheet.
Example:
A caseless with one record type that has a cat var and an integer for keys. There are 9 records: aaa 1 aaa 2 aaa 3 bbb 1 bbb 2 bbb 3 ccc 1 ccc 2 ccc 3 But in the spreadsheet only 5 are visible: aaa 1 aaa 2 aaa 3 bbb 1 ccc 1
Workaround:
Use integer keys instead of cat vars
WRITE button in PQLForms sets focus to the first field
210762 WRITE button in PQLForms sets focus to the first field
Severity: Minor Status: Closed - Fixed
If you have a multipage form and want to save entry partway through then it won't stay on the current field. It returns to the first page. After this fix you can still press the RESET button to go to the first field.
Example:
Workaround:
User the page buttons to return to the page where you pressed Write.
BMDP SAVE FILE now creates TEXT output
210759 BMDP SAVE FILE now creates TEXT output
Severity: Minor Status: Closed - Fixed
In newer versions of BMDP software it is easier to execute a text file than to read a BMDP data file. The text can be modified to run one or more of the BMDP stats procedures.
Example:
RETRIEVAL . PROCESS CASES ALL . PROCESS RECORD EMPLOYEE . GET VARS ID GENDER MARSTAT BIRTHDAY EDUC NDEPENDS . PERFORM PROCS . END PROCESS RECORD . END PROCESS CASES BMDP SAVE FILE FILENAME = "D:\Development\SirXS\alpha\bmdp.dat" VARIABLES = ID GENDER MARSTAT BIRTHDAY EDUC NDEPENDS END RETRIEVAL /CONTROL COLUMN=80. /END /INPUT TITLE='SIR/XS BMDP Proc from database: COMPANY Apr 11, 2012 09:59:37'. VARIABLES=6. FORMAT=FREE. MCHAR='*'. /VARIABLE NAMES= 'ID','GENDER','MARSTAT','BIRTHDAY','EDUC','NDEPENDS'. MAXIMUM= (GENDER)2,(MARSTAT)2,(EDUC)6,(NDEPENDS)20. MINIMUM= (GENDER)1,(MARSTAT)1,(EDUC)1,(NDEPENDS)0. ...
Workaround:
Generate BMDP commands using PQL Write.
PROCESS ALL RECORD TYPES | PROCESS RECORD [expression]
210756 PROCESS ALL RECORD TYPES | PROCESS RECORD [expression]
Severity: New Feature Status: Closed - Feature
New record processing commands PROCESS DATA processes all record types in the case PROCESS DATA [RECTYPE=expression] A new function CURRREC(0) returns the record currently being processed. Note that due to compiler restrictions you cannot directly refer to a record variable while processing a record defined at execution time. Instead you need to use execution time functions such as VARGET / VARPUT to access record variables.
Example:
retrieval process case all process data COMPUTE RECNO = CURRREC(0) COMPUTE N = NVARS(RECNO) WRITE ID RECNO N FOR I = 1,N . COMPUTE VN = VARNAME(RECNO,I) . COMPUTE VVAL = VARGET (VN) . WRITE ' ' VN VVAL ROF end process data end process case end retrieval
Workaround:
generate a PQL retrieval using a pql program to process records at run time.
TO keyword now allowed in LOOKUP, GET VAR varlist
210753 TO keyword now allowed in LOOKUP, GET VAR varlist
Severity: New Feature Status: Closed - Feature
TO keyword now allowed in LOOKUP, GET VAR varlist [GET VARS { ALL| target_varlist (including 'TO' lists)| local_varlist = target_varlist}]
Example:
RETRIEVAL NOAUTOCASE LOOKUP RECORD COMPANY.EMPLOYEE GET VARS NAME TO EDUC USING 10 WRITE NAME TO EDUC END RETRIEVAL
Workaround:
List all variables required
Compilation of SUBROUTINES can hang if there are some GUI command errors
210750 Compilation of SUBROUTINES can hang if there are some GUI command errors
Severity: Minor Status: Closed - Fixed
Compilation of SUBROUTINES may hang if there are some types of compilation errors.
Example:
SUBROUTINE SYSTEM.DELETE NODATABASE REPLACE COMPUTE FRD1__ = 0 . SET ITEM 2,MISS(-1,"VAR1",MISNUM(VAR1)) . SET ITEM 2,MISS(-1,"VAR1",MISNUM(VAR1)) . SET ITEM 2,MISS(-1,"VAR1",MISNUM(VAR1)) END SUBROUTINE
Workaround:
Fix the compilation errors up displayed up to the hang.
SYSTEM GLOBAL Variable substitution can interfere with DO REPEAT substitution
210747 SYSTEM GLOBAL Variable substitution can interfere with DO REPEAT substitution
Severity: Minor Status: Closed - Fixed
If there is a SYSTEM GLOBAL in the line after a DO REPEAT then the last repeat value is overwritten If it is a regular user global then all is ok.
Example:
do repeat NUM$= ONE TWO THREE c <DBNAME> remark 'NUM$' end repeat ONE TWO COMPANY do repeat NUM$= ONE TWO THREE c <DATE> remark 'NUM$' end repeat ONE TWO {09:03:35}
Workaround:
put a line between the do repeat command and the line with the global. do repeat NUM$= ONE TWO THREE c c <DATE> RENAME FAMILY does not move its MEMBERS 210744 RENAME FAMILY does not move its MEMBERS Severity: Moderate Status: Closed - Fixed if you rename a family then it doesn't keep the members. Eg in company, the DATA family has four members but after Example: RENAME FAMILY DATA TEST the TEST family is empty. Workaround: Create a new family and move members or export (PWRITE) family and edit the file changing the FAMILY name - then import (PREAD) UNLOAD/PURGE/RELOAD reloads to the directory given by the PREFIX attribute 210741 UNLOAD/PURGE/RELOAD reloads to the directory given by the PREFIX attribute Severity: Minor Status: Closed - Fixed If you connect to two databases and then make the first one the default, then the PREFIX attribute is set to the path of the last connected. The unload/reload dialog assumed this prefix attribute was for the default database. As this dialog currently gives you the option of either deleting or renaming the database files then the best place to put the new database is where the old one was. Example: Workaround: Only connect one database or change the PREFIX attribute through Settings/File Attributes... ### Fixed in revision 15 OPEN MEMBER APPEND overwrites existing contents 210738 OPEN MEMBER APPEND overwrites existing contents Severity: Minor Status: Closed - Fixed OPENing a member in append mode will overwrite the existing contents. Example: program open mem dsn="EXAMPLES.APPEND" member write write (mem) "hello" close mem end program program open mem dsn="EXAMPLES.APPEND" member append write (mem) "world" close mem end program Workaround: Use FWRITE to copy the member to a file, append to the file and FREAD it back: program execute dbms "FWRITE 'TEMP.TXT' EXAMPLES.HELLO" . OPEN MEM DSN="TEMP.TXT" APPEND IOSTAT=RC . WRITE (MEM) "c this appended added" . CLOSE MEM execute dbms "DELETE MEMBER EXAMPLES.HELLO /NOINFORM /OK" execute dbms "FREAD 'TEMP.TXT' EXAMPLES.HELLO" end program CSV SAVE FILE writes double quotes un escaped in string variables 210735 CSV SAVE FILE writes double quotes un escaped in string variables Severity: Minor Status: Closed - Fixed If a string variable contains a double quote then it is written to a csv save file as is. This will confuse any application trying to read the file Example: PROGRAM SET MESS ('Hello "World"') CSV SAVE FILE FILENAME = "quote.csv" END PROGRAM Workaround: Replace double quotes with double double quotes manually. Saving strings longer than 255 characters to SPSS SAVE FILE produces bad file 210732 Saving strings longer than 255 characters to SPSS SAVE FILE produces bad file Severity: Minor Status: Closed - Fixed Trying to save long strings to spss save file will produce a bad file. Example: PROGRAM STRING*507 STR507 SET STR507 ("") FOR STR = 1,51 COMPUTE VAL = FORMAT(STR) COMPUTE STR507 = STR507+PAD("....+...."," ",10-LEN(VAL),10-LEN(VAL))+VAL END FOR PERFORM PROCS SPSS SAVE FILE FILENAME = "sir507.sav" VARIABLES= STR507 END PROGRAM Workaround: Break long strings into segments of 255 characters or fewer Old SirForms under master fails to retrieve a record on initialise. 210729 Old SirForms under master fails to retrieve a record on initialise. Severity: Minor Status: Closed - Fixed Entering a record key into the keyfields and pressing enter may give an incorrect record not found or record locked error. Example: Workaround: go into the form record screen and do a "next record"* to retrieve the first record in the database then change the keys to the record you want to retrieve. PROCESS JOURNAL FILENAME=expression can cause odd behaviour 210726 PROCESS JOURNAL FILENAME=expression can cause odd behaviour Severity: Minor Status: Closed - Fixed PROCESS JOURNAL FILENAME=expression Can cause the processing to terminate after one iteration Example: PROCESS JOURNAL FILENAME=varname FROM=LEV THRU=LEV Workaround: Calculate the filename before compilation - by putting it in a global. New CSV option on export 210723 New CSV option on export Severity: New Feature Status: Closed - Feature The new CSV clause on EXPORT writes the data section as comma separated values: All strings are in double quotes; Lines do not have a final comma (not sure if this is standard csv); Dates and times are in a standard format (dd-Mmm-YYYY, HH:MM:SS); Categoricals are written as strings; System missing (undefined) is indicated by an asterisk * Numerics blank missing value is written as successive quotes; There is a special hex format used if strings contain special characters line feed, null or double quote. This consists of the letter H followed by the hex string in quotes e.g. ,H"0A0022" Example: EXPORT FILE FILENAME="MyExport.exp" CSV Workaround: New functions convert to and from hex characters 210720 New functions convert to and from hex characters Severity: New Feature Status: Closed - Feature CHARHEX hexstr = CHARHEX(str) Returns a hex representation of the input string. Each character is converted to its ASCII value then that is converted to hexadecimal. HEXCHAR str = HEXCHAR(hexstr) Converts the hexadecimal codes in the input string to their associated ASCII characters. Example: COMPUTE HEX1 = CHARHEX("Hello World") COMPUTE STR = HEXCHAR("48656C6C6F20576F726C64") Workaround: VALUE and VAR LABELS 79 characters long ae truncated to 78 without warning. 210717 VALUE and VAR LABELS 79 characters long ae truncated to 78 without warning. Severity: Minor Status: Closed - Fixed VALUE LABELS and VAR LABELS are limited to 78 characters - but you only get an error if you specify 80 characters or more; if the length is 79 then the labels are truncated without notice. This example, record 2 has 79 character value and var labels: Example: VAR LABEL VAR2 'A 79 character variable label.................................................X' VALUE LABELS VAR2 (1) 'A 79 character value label....................................................X' which become: VALUE LABELS VAR2 (1)'A 79 character value label......................................... VAR LABEL VAR2 'A 79 character variable label......................................... Workaround: String data containing special characters may not export / import properly. 210714 String data containing special characters may not export / import properly. Severity: Minor Status: Closed - Fixed String data containing line feed and null characters (eg PQL encrypt() data) will fail to import. Export now writes these characters in hex character notaion. Example: Workaround: ### Fixed in revision 14 PROCESS JOURNAL program compiled when the database is attached will not find master updates 210711 PROCESS JOURNAL program compiled when the database is attached will not find master updates Severity: Minor Status: Closed - Fixed Example: Workaround: Compile with the database attached TEXT File read with very long record length (> 10000 characters) will fail. 210708 TEXT File read with very long record length (> 10000 characters) will fail. Severity: Minor Status: Closed - Fixed This applies to batch data input where the number of input columns is greater that 10000 Example: Workaround: Make input columns shorter Families containing no text members are not recreated on export/import pwrite/pread. 210705 Families containing no text members are not recreated on export/import pwrite/pread. Severity: Minor Status: Closed - Fixed This can mean if you have a family containing only compiled procedures and you export import then this family will no longer exists. You need to create it before you can recompile these members. Example: Workaround: Some variables don't have their details displayed in the information section of the Select Record dialog. 210702 Some variables don't have their details displayed in the information section of the Select Record dialog. < Severity: Minor Status: Closed - Fixed Non-standard variable names don't have their details displayed in the information section of the Select Record dialog. Example: Workaround: Tabfile strings displayed incorrectly in spreadsheet 210699 Tabfile strings displayed incorrectly in spreadsheet Severity: Minor Status: Closed - Fixed in the spreadsheet you will see that the strings have their third and forth last characters repeated - so 12345 will display 1232345 If the string is shorter than four characters then the spreadsheet will crash. The program below writes out the strings correctly - only viewing them in speadsheet will show the problem. Example: create tabfile string c retrieval noautocase c string*1 S1 string*5 S5 string*6 S6 string*20 S20 c set s1 ('1') set s5 ('12345') set s6 ('123456') set s20 ('12345678901234567890') perform procs save table string.test end retrieval program process rows string.test get vars all write all end rows end program Workaround: PREAD does not report the correct number of members read. 210696 PREAD does not report the correct number of members read. Severity: Minor Status: Closed - Fixed The number of members read was one more than the reported count Example: Workaround: MERGE can crash on final warning message 210693 MERGE can crash on final warning message Severity: Minor Status: Closed - Fixed If SIR MERGE needed to display a warning message on finalising (eg max key size increased) then it would crash. Example: Workaround: VARPUT and null string inconsistancies 210690 VARPUT and null string inconsistancies Severity: Minor Status: Closed - Fixed If there are no missing values on a numeric variable then VARPUT(.."") stores undefined not zero - which is correct. If there are missing values 0 on a numeric variable then VARPUT(.."") stores the missing associated with zero - which is doesn't seem right. If there are missing values BLANK on a numeric variable then VARPUT(.."") stores the missing associated with BLANK- which is correct. If you have both BLANK and 0 as missing values then VARPUT(.."") stores the first of these missing values defined. Example: PROGRAM INTEGER X MISSING VALUES X (0) COMPUTE RC = VARPUT("X","") WRITE X [MISNUM(X)] END PROGRAM Incorrectly puts missing value #1 into X. Workaround: TMP files are not deleted when running through sirweb.cgi 210687 TMP files are not deleted when running through sirweb.cgi Severity: Minor Status: Closed - Fixed Every time a sirweb.cgi is executed it leaves tmp files behind after it ends. Example: Workaround: Delete these files manually VALLABSV and VALLABSP treat dates as string representations of the Julian integer. 210684 VALLABSV and VALLABSP treat dates as string representations of the Julian integer. Severity: Minor Status: Closed - Fixed The function VALLABSV returns a string. With dates and times it returns a string representation of the internal number, not the date or time as specified on the value labels command. Example: program date xx ('dd/mm/yyyy') time yy ('hh:mm:ss') missing values xx ('no date') missing values yy ('no time') value labels xx ('no date') 'missing value 1' ('10/07/2010') 'some date' yy ('no time') 'missing value 1' ('12:00:00') 'noon' write "DATE :" for i = 1,nvallab(-1,"XX") write i ") VALUE = " [VALLABSV(-1,"XX",i)] ", LABEL = " [VALLABSN(-1,"XX",i)] end for write / "TIME :" for i = 1,nvallab(-1,"YY") write i ") VALUE = " [VALLABSV(-1,"YY",i)] ", LABEL = " [VALLABSN(-1,"YY",i)] end for Workaround: Use the DATEMAP function to convert to a date string Secondary index file (sr6) grows quickly when updating through master 210681 Secondary index file (sr6) grows quickly when updating through master Severity: Minor Status: Closed - Fixed After many updates of an indexed variable the index file is much larger than it should be Example: Workaround: Unload / Reload regularly The RECDOC function returns a zero length string when the record label is exactly 32 characters long. 210678 The RECDOC function returns a zero length string when the record label is exactly 32 characters long. Severity: Minor Status: Closed - Fixed The RECDOC function returns a zero length string when the record label is exactly 32 characters long. Example: RECORD SCHEMA 1 REC_1 'thirty one characters of label!' RECORD SCHEMA 2 REC_2 'thirty two characters of label1!' RECORD SCHEMA 3 REC_3 'thirty three characters of label!' program write "rec 1 " [recdoc(1,0)] write "rec 2 " [recdoc(2,0)] write "rec 3 " [recdoc(3,0)] end program rec 1 thirty one characters of label! rec 2 rec 3 thirty three characters of label! Workaround: Add an extra character to the label SirForms does not give an audible warning on incorrect entry 210675 SirForms does not give an audible warning on incorrect entry Severity: Minor Status: Closed - Fixed There is no beep. Example: Workaround: Batch Data Input of blanks data into real variables gives an error message 210672 Batch Data Input of blanks data into real variables gives an error message Severity: Minor Status: Closed - Fixed When the batch data input is run, the REAL variable produces an error when that field is BLANK - this happens if BLANKUND is used and also if BLANK is a valid missing value for the REAL. I think you should only give the error if BLANKUND is not set AND BLANK is not a valid missing value. Example: Workaround: VALLABSC with third arg blank returns label for zero 210669 VALLABSC with third arg blank returns label for zero Severity: Minor Status: Closed - Fixed If the third argument for VALLABSC is a null string (or a blank) then it gets the value label for value 0. Fixed to get label for BLANK. Example: program integer x missing values x (BLANK) value labels x (-1) 'First' (0) 'Second' (1) 'Third' (BLANK) 'blank' write [vallabsc(-1,'X',' ')] end program Second Workaround: Inserting a new common variable corrupts record data 210666 Inserting a new common variable corrupts record data Severity: Moderate Status: Closed - Fixed These new functions return schema format and display width. int = VXLEN( rtnum , varname_str ) Returns the number of character required to print or display a variable. If you have some common variables and you add a new one somewhere in the middle then the record types that reference the common variables will get them confused. If a database has two common variables A and B, and a record type 1 where these variables are in the data list. Then when a new common var C is inserted between A and B, Then the CIR data will have the correct values for A and B. But the record will If you look in the record 1 will have B=undefined. Example: Workaround: New Schema Functions Added - Schema format & display width 210663 New Schema Functions Added - Schema format & display width Severity: New Feature Status: Closed - Feature These new functions return schema format and display width. int = VXLEN( rtnum , varname_str ) Returns the number of character required to print or display a variable. If the record number (rtnum) is negative, the function applies to a summary variable; if rtnum is one more than the maximum record count (i.e. NRECS(0)+1) then this applies to a standard variable. str = VSCHFMT( rtnum , varname_str ) Returns the variable format exactly as specified in the schema DATA LIST. This is different from VFORMAT in that VFORMAT returns an external print format whereas the formats in the DATA LIST are a mix of input formats (eg DATE'MM/DD/YYYY')) and internal formats (eg I2 a two byte integer). A negative rtnum will return a schema like format for a local variable. Example: LEN = VXLEN (1,'SALARY') SCHFMT = VSCHFMT (1,'BIRTHDAY') Workaround: ### Fixed in revision 13 Array elements fail to work as RECODE variables 210660 Array elements fail to work as RECODE variables Severity: Minor Status: Closed - Fixed An array element does not work as the recode variable. The example programs produce compile errors. Example: program integer*1 array A(2) compute A(1)=1 recode STR=A(1) (0='0') (1='1') write STR end program program integer*1 array A(2) compute A(1)=1 recode STR=A(1) (0='0') (1='1') write STR end program Workaround: Create a temporary variable to hold the value of the array element for the recode VARPUT does not work on the first COMMON variable in name order. 210657 VARPUT does not work on the first COMMON variable in name order. Severity: Minor Status: Closed - Fixed The VARPUT function fails when used on the first COMMON variable in name order. In the example schema, the variable CV1 is the first name alphabetically and the VARPUT function will return undefined and not change the value. Example: RECORD SCHEMA 0 CIR DATA LIST ID * (I2) CV2 * (I2) CV1 * (I2) CV3 * (I2) END SCHEMA ... COMPUTE RC= VARPUT('CV1','0') WRITE RC CV1 Workaround: Create a dummy common variable called "A" SPSS SAVE FILE will output junk at the end of variable labels 210654 SPSS SAVE FILE will output junk at the end of variable labels Severity: Minor Status: Closed - Fixed The example program will produce an SPSS file with variable labels like CURRDATE "Current Salary Date ID" Example: RETRIEVAL . PROCESS RECORD EMPLOYEE . GET VARS ID CURRDATE . PERFORM PROCS . END RECORD SPSS SAVE FILE FILENAME = "query_output.sav" END RETRIEVAL Workaround: Use the PORTABLE option Consecutive dates with different maps will be combined in TO lists if they have the same metadata 210651 Consecutive dates with different maps will be combined in TO lists if they have the same metadata Severity: Minor Status: Closed - Fixed Consecutive date or time variables with different date(or time) maps will be incorectly combined in TO lists if they have the same internal ranges, missing values, valid values or value label. When this code is executed it will produce an error. Example: DATA LIST DATE2 * (DATE'EMM/YYYY') DATE3 * (DATE'DD/MM/YYYY') VAR RANGES DATE2 ('01/2000' '12/2010') DATE3 ('01/01/2000' '01/12/2010') writes VAR RANGES DATE2 TO DATE3 ('01/01/2000' '01/12/2010') Workaround: Separate the variables or Change the values so they are a little different or use the NOTO option on EXPORT or WRITE SCHEMA PROMPT VARDOC added to PQLForms FIELD Command 210648 PROMPT VARDOC added to PQLForms FIELD Command Severity: New Feature Status: Closed - Feature VAR LABELS are limited to 78 characters and can be restrictive for PQLForms prompts. A new prompt option VARDOC will use up to 256 characters of VAR DOC information. Example: FIELD Q1 PROMPT VARDOC Workaround: Use a TEXT field to display VARDOCSN(recnum,varname,1) MERGE fails on caseless databases 210645 MERGE fails on caseless databases Severity: Moderate Status: Closed - Fixed Merging two caseless database will produce a corrupt database Example: **09/I** CIR REC count exceeded 0:0(0)/17974/5' messages from a VERIFY FILE Workaround: Combine databases using write schema and batch data input. PQLForms field edit clause may not trigger on leaving field 210642 PQLForms field edit clause may not trigger on leaving field Severity: Minor Status: Closed - Fixed An EDITIN clause on a field may not be triggered if it is the last field on the screen and the tab key is pressed, OR if an ALT_letter is used to "press" and action button. Example: Workaround: Press ENTER on each field. Record types with more than 99 data input lines won't export/import properly 210639 Record types with more than 99 data input lines won't export/import properly Severity: Minor Status: Closed - Fixed A data list with more than 99 input line will not export/import because the line number is not separated from the variable name. Example: DATA LIST (120) KEY 3 - 9 (I4) VAR1 10 - 29 (A20) 120 VAR120 10 - 29 (A20) but this is what it looks like on WRITE SCHEMA DATA LIST (120) KEY 3 - 9 (I4) VAR1 10 - 29 (A20) 120VAR120 10 - 29 (A20) Workaround: Edit the export to include a space on these lines, or fit the input onto fewer than 100 lines. Modifying a variable in STANDARD SCHEMA can effect another variable in that schema 210636 Modifying a variable in STANDARD SCHEMA can effect another variable in that schema Severity: Minor Status: Closed - Fixed Modifying a standard schema can effect references to that variable in later records. In the schema clip below, after VAR1 has its range changed then a write schema will alter the data type of VAR1 to A10. Example: STANDARD SCHEMA DATA LIST VAR1 * (I1) VAR2 * (I1) VAR3 * (A10) VAR RANGES VAR1 (0 1) END SCHEMA c c Modify standard schema c STANDARD SCHEMA /LOCK VAR RANGES VAR1 (0 2) END SCHEMA Workaround: PQL LOOKUP VIA will return the next record if there is no match with the supplied keys 210633 PQL LOOKUP VIA will return the next record if there is no match with the supplied keys Severity: Minor Status: Closed - Fixed If LOOKUP VIA fails to find an exact match then it will return the next records information. In the example data below, LOOKUP via (1,3) should return a negative result but instead it finds the next row (2,1). Example: KEY1 KEY2 DATA 1 1 "key1=1 and key2=1" 1 2 "key1=1 and key2=2" 2 1 "key1=2 and key2=1" 2 2 "key1=2 and key2=2" Workaround: Use a RECORD IS to lookup a record. Master can hang updating some record types with recnum > 127 210630 Master can hang updating some record types with recnum > 127 Severity: Minor Status: Closed - Fixed Master can hang updating a record type with a number > 127. An otherwise identical record numbered less than 128 will not hang. Example: RECORD SCHEMA 128 UPAHM2 KEY FIELDS KEY(A) MAX REC COUNT 123 DATA LIST ID * (I2) KEY * (I1) DATA * (I2) END SCHEMA retrieval update for i = 1,5 case is i record is 128 (i) compute DATA = i write "about to save" end record write "saved" end case end for end retrieval Workaround: SQL (SQLServer) can crash selecting columns from particular record types 210629 SQL (SQLServer) can crash selecting columns from particular record types Severity: Minor Status: Closed - Fixed SQL (and SQLServer during ODBC calls) can crash on selecting columns from some record types. Example: SELECT * FROM ABCDE Workaround: Auto I/O column assignment in schema dialogs can underestimate width 210627 Auto I/O column assignment in schema dialogs can underestimate width Severity: Minor Status: Closed - Fixed If an numeric variable has no ranges or valid values but does have missing values then the auto number option in the I/O columns dialog will assign a width based on the widest missing value. In the example a width of 1 would be assigned even though there are no restrictions on the value. Example: DATA LIST MYVAR * (I4) MISSING VALUES MYVAR (1) Workaround: Manually set the width for such columns. PQLForms data entry mixes up BLANK and undefined 210624 PQLForms data entry mixes up BLANK and undefined Severity: Minor Status: Closed - Fixed PQLForms displays blank and undefined values the same way; as an empty text box. When it comes to writing the record, all the empty fields are stored as blank - which means that some may end up as zero length strings, others as missing BLANK and some as system undefined - depending on the schema definition for each variable. This will happen even if the fields are untouched during data entry. This has been fixed so that the edit boxes will remember if the value is undefined and only change if there has been specific data entry in that field. This is now consistent with old SIRForms. There is also a setting in preferences so that you can specify what is displayed in an edit box if the value is undefined. The default is to display nothing. If you specify a different string then that will be shown (in light red) when the field is not in focus. You can set an edit item to undefined by pressing Ctrl+U when editing that field. Example: Workaround: Undefined and Missing are displayed the same way in spreadsheet 210621 Undefined and Missing are displayed the same way in spreadsheet Severity: Minor Status: Closed - Fixed Undefined (system missing), and valid missing values are all displayed as NULL in the spreadsheet. This has been fixed to show the actual missing value or keyword BLANK in grey or the word "undefined" in light red. You can set a variable to BLANK (if blank is a valid missing value) by entering a string containing zero or more blanks and no other character. You cn set a variable to undefined by pressing the Nullify button or Ctrl+U. Example: Workaround: Use PQL or Forms to see the missing values Large real numbers are displayed in the spreadsheet as *********** 210618 Large real numbers are displayed in the spreadsheet as *********** Severity: Minor Status: Closed - Fixed A double precision real number eg a D2 with a value 12345678 will display ok as 12345678.00 but the value 123456789 will show *********** (11 stars). Example: Workaround: Restructured Unload & Reload can delete records without warning. 210615 Restructured Unload & Reload can delete records without warning. Severity: New Feature Status: Closed - Feature If you make changes to the key variables of a record schema then unload and reload, some records may not be allowed under the new definition and be removed without any warning. The deletion is the correct behaviour as the records are not allowed in the database according to your new definition. A warning message however would be useful. The one-step Unload/Purge/Reload procedure in More Procedures... has been modified so that it will check and write a warning if there are lost records. The code below will also produce a warning. Example: c c Get a before record count c INTEGER ARRAY OLDCOUNT (30) COMPUTE NRECS = NRECS(0)+1 REDEFINE ARRAY "OLDCOUNT" (NRECS) FOR REC= 0,NRECS(0) COMPUTE OLDCOUNT(REC+1)=NUMRECS(REC) END FOR ... execute dbms unload... execute dbms purge... execute dbms reload... ... c c check after record count c FOR REC= 0,NRECS(0) IFTHEN (OLDCOUNT(REC+1) GT NUMRECS(REC)) SET ITEM FONT IDLAB4,0,0,0,0,"#A0A000" SET ITEM IDLAB4,"Reloading Database - Some records were removed" WRITE "*** " [OLDCOUNT(REC+1) - NUMRECS(REC)] [TRIM(RECNAME(REC))] "(" REC ") Records have been removed by the restructu ENDIF END FOR Workaround: Be aware that when tightening constraints on key fields that some existing data may not pass the new criteria. PQLForms local variables do not show value labels 210612 PQLForms local variables do not show value labels Severity: Minor Status: Closed - Fixed Local variables will show value labels in the form painter but not when the form is run. Example: . INTEGER LOCAL . VAR LABEL LOCAL "The Local Variable" . VALUE LABELS LOCAL (1) "One" (2) "Two" (3) "Three" ... . FIELD LOCAL DATA AT 5,25 WIDTH 13 LABELS AT 5,38 WIDTH 13 PROMPT VARDESC AT 5,6 WIDTH 18 TYPE INTEGER Workaround: Use FDISPLAY to show the value label . FDISPLAY TEXT ( vallab(LOCAL) ) AT 35,39 WIDTH 13 FONT (BGROUND=FFFFFF ) BLANKUND keyword on DBI now works on DATE and TIMEs 210609 BLANKUND keyword on DBI now works on DATE and TIMEs Severity: New Feature Status: Closed - Feature The BLANKUND keyword on BDI was introduced to optionally prevent blanks being converted to zero for numeric variables without BLANK as a missing value. If dates/times were blank a a BLANK missing value was not specified then these would produce an error. The BLANKUND keyword now will convert these to undefined without complaining. Example: Add Records INPUT = "file.dat" / BLANKUND / Workaround: Define missing value BLANK if you want to allow BLANKs on data input Create table with "special" name causes problems with drop table 210606 Create table with "special" name causes problems with drop table Severity: Minor Status: Closed - Fixed CREATE TABLE SpecialName will create a tabfile with a name delimited by curly braces {SpecialName} The delete tabfile dialog will include an extra set of braces and fail: Example: DROP TABFILE {{SpecialName}} Command complete but not at end of line. (Error 1) Workaround: Use the DROP TABFILE {SpecialName} command directly Subprocedure name from expression doesn't work using DEBUG 210603 Subprocedure name from expression doesn't work using DEBUG Severity: Minor Status: Closed - Fixed PQL gets confused during execution when debug is on and a subprocedure is executed by way of an expression for the subprocedure name. The example gives Missing subprocedure definition. (Error 730 - SP1) When run. Example: program debug c . execute subprocedure ["SP"+"1"] c subprocedure sp1 | sp1 . write "SP1" end subprocedure c end program Workaround: Remove the debug option or run using the gui debugger. It will also work if the subprocedure is within a subroutine. UNIX: "Cannot Position" errors using Spreadsheet on tabfile 210600 UNIX: "Cannot Position" errors using Spreadsheet on tabfile Severity: Minor Status: Closed - Fixed If you use the spreadsheet on a tabfile then you will get "Cannot Position" errors when you try to edit, print, export etc. Example: Workaround: Using spreadsheet on a Database after using it on a tabfile causes problems 210597 Using spreadsheet on a Database after using it on a tabfile causes problems Severity: Minor Status: Closed - Fixed If you use the spreadsheet on a tabfile, then later in the same session on a database then you will get "Cannot Position" errors when you try to edit, print, export etc. Example: Workaround: Restart SIR after using spreadsheet on tabfile. pql connect tabfile with no filename specified will crash. 210594 pql connect tabfile with no filename specified will crash. Severity: Minor Status: Closed - Fixed The PQL CONNECT TABFILE command will crash if the filename is not specified. Example: program pql connect tabfile 'ANYTAB' end program Workaround: The default filename is meant to be the tabfile name + ".tbf" so if you want the default value then specify this explicitly. program pql connect tabfile 'ANYTAB' filename 'ANYTAB.tbf' end program TABVRANG returns column name not range info 210591 TABVRANG returns column name not range info Severity: Minor Status: Closed - Fixed The TABVRANG function is meant to return column range (missing and valid) information but it is returning the column name instead. Example: Workaround: VALLABSV not returning the correct value for missing strings 210588 VALLABSV not returning the correct value for missing strings Severity: Minor Status: Closed - Fixed The VALLABSV does not return the correct value for missing strings. An effect of this is that a PQL form with a drop down choice for a string variable with missing values and labels, will not work. Example: program string test missing values test ("MISS") value labels test ("MISS") "Is Missing" WRITE [VALLABSV(-1,"TEST",1)] | this writes blank, not MISS WRITE [VALLABSN(-1,"TEST",1)] | This writes "Is Missing" correctly END PROGRAM Workaround: Seven (or more) schema VALUE LABEL commands can confuse compiler 210585 Seven (or more) schema VALUE LABEL commands can confuse compiler Severity: Minor Status: Closed - Fixed If a set of modify schema blocks containing seven or more VALUE LABEL commands, then the compiler can get confused when subsequent commands contain a number (eg STRING LENGTH 32) 4.30 STRING LENGTH 32 String length is invalid - 32 assumed. (Error 70) Example: RECORD SCHEMA 1 EMPLOYEE VALUE LABELS GENDER (1)'Male' VALUE LABELS GENDER (1)'Male' VALUE LABELS GENDER (1)'Male' VALUE LABELS GENDER (1)'Male' VALUE LABELS GENDER (1)'Male' VALUE LABELS GENDER (1)'Male' VALUE LABELS GENDER (1)'Male' END SCHEMA STRING LENGTH 32 Workaround: Reduce the number of VALUE LABEL commands , or don't run anything straight after a set of schema mods. SIRSQLS sends cat vars as strings but length of internal integer 210582 SIRSQLS sends cat vars as strings but length of internal integer Severity: Minor Status: Closed - Fixed If a CAT VAR is sent via SIR SQL server then it is sent as a string. The column info function returns the intenal integer length (1,2 or 4) and so the string is usually trunctated. Example: Workaround: Convert cat vars to string vars or integers with value labels. PATTERN function returns 0 or 1 when argument is missing 210579 PATTERN function returns 0 or 1 when argument is missing Severity: Minor Status: Closed - Fixed The PATTERN function returns 0 or 1 (not undefined as it should) when the first argument is a missing value. In this case the function is looking at some random memory which may or may not include the pattern to be matched. Example: program string x missing values x ("NA") set x ("NA") write [PATTERN(x,"TABLE")] [PATTERN(x,"CHAIR")] end program Workaround: Check if aguments are missing before using PATTERN FILL and COMMA functions crash when args are missing 210576 FILL and COMMA functions crash when args are missing Severity: Minor Status: Closed - Fixed FILL and COMMA functions crash if the string contains a missing value (not undefined). Example: program string x missing values x ("NA") set x ("NA") write [fill(x,".")] [comma(x)] end program Workaround: Check if aguments are missing before using FILL or COMMA Auto I/O columns in schema dialog does not work for standard vars 210573 Auto I/O columns in schema dialog does not work for standard vars Severity: Minor Status: Closed - Fixed Using RECORD SCHEMA , I/O Columns, de-number and auto-number does not work on variables from the standard schema. Example: Workaround: Write the schema and manually change the I/O columns. ### Fixed in revision 12 The MISS function did not work on local string variables 210570 The MISS function did not work on local string variables Severity: Minor Status: Closed - Fixed The MISS function did not work on local string variables. If no database was attached then sir would crash; if a database was connected then the function would return junk. Example: program string STR missing values STR (BLANK,"NONE","ZIP") write [miss(-1,"STR",3)] end program Workaround: DO REPEAT now allows leading zeros in TO list 210567 DO REPEAT now allows leading zeros in TO list Severity: New Feature Status: Closed - Feature DO REPEAT now allows generation of a sequence of numbers with leading zeros. In the past, the TO clause in do repeat only allowed sequences of either numbers (1 TO 10) or sir names with trailing numbers (VAR01 TO VAR10). You can now do leading zeros like this: Example: DO REPEAT X =$001$TO$100\$
Workaround:
LIST STATS restructure summary table is misaligned
210564 LIST STATS restructure summary table is misaligned
Severity: Trivial Status: Closed - Fixed
The restructured records summary at the bottom of list stats does not contain all details and is miss-aligned
Example:
Workaround:
Some schema mods can corrupt CIR
210561 Some schema mods can corrupt CIR
Severity: Moderate Status: Closed - Fixed
A sequence of schema mods (including a CIR mod) without an unload/reload can cause corruptions in the CIR.
Example:
Workaround:
Details button in tabfile dialog can crash if there are no tables
210558 Details button in tabfile dialog can crash if there are no tables
Severity: Minor Status: Closed - Fixed
The "Details" button on the Tabfiles dialog will cause a crash if the selected tabfile has no tables.
Example:
Create a tabfile with NO tables. Click on "Details..." in the bottom left corner of the dialog. Since no table is highlighted, SIR complains and then exits all the way out of SIR.
Workaround:
Create a table on the tabfile.
Various problems with undefined strings in tabfiles
210555 Various problems with undefined strings in tabfiles
Severity: Minor Status: Closed - Fixed
Setting tabfile string variables to undefined does not appear to change the current value, or displays junk in the first character. The example program writes "The Old Value " (padded with blanks) not * (missing)
Example:
PROGRAM TUPDATE integer nmiss string smiss COMPUTE DATA = 'The Old Value' SET DATA (SMISSING) COMPUTE DATA = smiss COMPUTE NUM = 3 ROW IS JUNK.TAB1TAB INDEXED BY CASE ('1') write "Here the value of data is " ['"'+data+'"'] PUT VARS NUM PUT VARS DATA END ROW IS END PROGRAM PROGRAM PROCESS ROWS JUNK.TAB1TAB GET VARS ALL write "But here the value of data is " ['"'+data+'"'] WRITE ALL END ROW END PROGRAM
Workaround:
Set strings to "" rather than undefined.
Severity: New Feature Status: Closed - Feature
New required fields dialog in forms painter (button on the screen properties dialog). This dialog generates code for the WRITE clause to ensure that selected fields are entered.
Example:
Workaround:
PQLFORMS, FAILSCR not allowing re-entry of bad data
210549 PQLFORMS, FAILSCR not allowing re-entry of bad data
Severity: Minor Status: Closed - Fixed
If a PQLForm sets the FAILSCR to non zero then an error message is displayed and the record is not saved. The trouble is that if you are moving away from the record then it will give you the error and move away without saving or giving you the opportunity to fix the problem.
Example:
Workaround:
Use the Save button before attempting to move away from a record.
New Exact time map format
210546 New Exact time map format
Severity: New Feature Status: Closed - Feature
There is now an exact time format. If the time format starts with E then any string input into that variable must match the format exactly (like the E Date format).
Example:
PROGRAM TIME EMAP ("EHH:MM") TIME NOEMAP ("HH:MM") COMPUTE EMAP = "21" COMPUTE NOEMAP = "21" WRITE EMAP NOEMAP COMPUTE EMAP = "21:01" COMPUTE NOEMAP = "21:01" WRITE EMAP NOEMAP END PROGRAM
Workaround:
Test times using string functions to ensure they are the right format
SPSS Portable files do not open in PSPP
210543 SPSS Portable files do not open in PSPP
Severity: Minor Status: Closed - Fixed
SPSS portable files would not open under PSPP (which is meant to read SPSS files). The SPSS specification says the text lines in the portable file are 80 characters long but SIR wrote lines that were 80 characters *or less* and SPSS had no problem with this. PSPP wanted the the lines to be exactly 80 characters (ie padded with blanks). PSPP has fixed this and we also have fixed so we are compatible with old versions.
Example:
Workaround:
Edit the portable file and pad the first three lines with blanks to 80 columns.
Negativley Scaled variables are truncated in SPSS SAVE FILE
210540 Negativley Scaled variables are truncated in SPSS SAVE FILE
Severity: Minor Status: Closed - Fixed
Negatively scaled variables in SPSS save file are written correctly in the data section but are given integer formats with zero decimals in the dictionary section - fixed to specify correct number of decimals.
Example:
Workaround:
Use unscaled integers or real numbers.
Compare Procfiles dialog improved
210537 Compare Procfiles dialog improved
Severity: New Feature Status: Closed - Feature
Compare Procfiles (Program Menu) improved to allow copying from one procfile to other and to produce a differences report.
Example:
Workaround:
VARPOSIT function has changed
210534 VARPOSIT function has changed
Severity: New Feature Status: Closed - Feature
VARPOSIT used to return the internal position in the data record for the start of the variable data. This should be meaningless to the pql programmer. The function now returns the variable's ordinal in the record definition.
Example:
program write [VARPOSIT(1,"GENDER")] end program
Workaround:
REGREP can not return a null string result
210531 REGREP can not return a null string result
Severity: Minor Status: Closed - Fixed
If the result of using the REGREP (replace regular expression) function should be a null string ("") then the function will return the original string instead.
Example:
write [regrep('aaaaa','a+','',1,2)]
Workaround:
VERIFY FILE with RECKEY or RECDATA crashes.
210528 VERIFY FILE with RECKEY or RECDATA crashes.
Severity: Moderate Status: Closed - Fixed
VERIFY FILE using the RECKEY or RECDATA options would crash after processing a few records.
Example:
VERIFY FILE /RECKEY /RECDATA
Workaround:
Avoid using these options
Memory leak in processing records with standard variables
210525 Memory leak in processing records with standard variables
Severity: Moderate Status: Closed - Fixed
Similar leak with processing records containing standard variables.
Example:
Workaround:
Slow memory leak associated with switching databases
210522 Slow memory leak associated with switching databases
Severity: Moderate Status: Closed - Fixed
This was a minor leak but if you switch databases a lot it would become a problem.
Example:
Workaround:
Spreadsheet can crash on searching for a case id
210519 Spreadsheet can crash on searching for a case id
Severity: Moderate Status: Closed - Fixed
If you have a database with a string case is and a case exists but has no records of a particular record type, then if you open that record type in the spreassheet and search for that case, then sir will crash.
Example:
Workaround:
Use PQL to find records and cases.
EVALUATE and SPSS SAVE FILE in the same program gives bad strings
210516 EVALUATE and SPSS SAVE FILE in the same program gives bad strings
Severity: Minor Status: Closed - Fixed
An EVALUATE command in the same program as SPSS SAVE FILE (system) would corrupt string variables in that file. RETRIEVAL
Example:
RETRIEVAL . PROCESS CASES ALL . GET VARS ID . PROCESS RECORD EMPLOYEE . GET VARS NAME GENDER . EVALUATE z = "1+1" . PERFORM PROCS . END PROCESS RECORD . END PROCESS CASES SPSS SAVE FILE FILENAME = "testspss.sav" VARIABLES = ID NAME GENDER END RETRIEVAL
Workaround:
Avoid evaluate or use PORTABLE option on spss
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transient-0.4.4: Making composable programs with multithreading, events and distributed computing
Safe Haskell None Haskell2010
Transient.Backtrack
Synopsis
# generalized versions of backtracking with an extra parameter that gives the reason for going back.
onBack :: (Typeable b, Show b) => TransientIO a -> (b -> TransientIO a) -> TransientIO a Source #
the second parameter will be executed when backtracking
back :: (Typeable b, Show b) => b -> TransientIO a Source #
execute backtracking. It execute the registered actions in reverse order.
If the backtracking flag is changed the flow proceed forward from that point on.
If the backtrack stack is finished or undoCut executed, undo will stop.
forward :: (Typeable b, Show b) => b -> TransIO () Source #
restart the flow forward from this point on
backCut :: (Typeable reason, Show reason) => reason -> TransientIO () Source #
assures that backtracking will not go further back
registerBack :: (Typeable b, Show b) => b -> TransientIO a -> TransientIO a Source #
register an action that will be executed when backtracking
# finalization primitives
trigger the event, so this closes all the resources
onFinish :: (Maybe SomeException -> TransIO ()) -> TransIO () Source #
set a computation to be called when the finish event happens
onFinish' :: TransIO a -> (Maybe SomeException -> TransIO a) -> TransIO a Source #
set a computation to be called when the finish event happens this only apply for
initialize the event variable for finalization. all the following computations in different threads will share it it also isolate this event from other branches that may have his own finish variable
kill all the processes generated by the parameter when finish event occurs
trigger finish when the stream of data ends
Instances
Source # MethodsshowList :: [FinishReason] -> ShowS #
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# A half-life question, involving 2 elements
1. May 2, 2006
### raul_l
Element A has a half-life of $$T_{1}$$ and decays into element B, which has a half-life of $$T_{2}$$, while $$T_{2}<T_{1}$$. When is the mass of element B the greatest? (i.e. after how many doublings?)
I have been trying to derive a formula to calculate this, but have so far been unsuccessful.
2. May 2, 2006
### Tom Mattson
Staff Emeritus
Can we see one of your attempts?
3. May 3, 2006
### raul_l
Ok.
Lets say elements A and B have masses $$m_{1}$$ and $$m_{2}$$. The equation to calculate the mass of a decaying element is $$m=m_{0}\times2^{-\frac{t}{T/2}}$$, right?
For element A it should be $$m=m_{1}\times2^{-\frac{t}{T_{1}}}$$ and for element B $$m=m_{2}\times2^{-\frac{t-T_{1}}{T_{2}}}$$. I think it should be $$t-T_{1}$$, because it starts decaying after the first doubling of element A. And since element B depends on the mass of element A, its mass over time should be calculated using this equation:
$$m=(m_{1}\times2^{-\frac{t}{T_{1}}})\times2^{-\frac{t-T_{1}}{T_{2}}}$$
Am I making any sense at all? It feels like I'm not taking everything into account in the previous equation. Of course, after I get the equation right, it should be easy to calculate the greatest mass B can have (by differentiating the equation and so on).
Also, it was mentioned in the task, that $$T_{1}>T_{2}$$. I'm still not sure, what difference does it make :).
Last edited: May 3, 2006
4. May 3, 2006
### Curious3141
I would not consider this an elementary problem. It involves solving two first order differential equations simultaneously and it's fairly involved. Since the orig. poster has shown some work, I think I'll pitch in with how I think the problem should be approached; however, this approach seems much too complicated for the estimated level. Maybe someone will find an easier approach.
The problem is easiest when viewed in terms of flux between 3 compartments : A, B and C (C is the decay product of B).
A can only decrease over time as decay occurs. B has both influx (due to decay of A) and efflux (due to decay of B to C) occuring simultaneously.
Let $$N_0, N_A, N_B, T_A, T_B, \lambda_A, \lambda_B$$ represent respectively initial total number of A-atoms, number of A-atoms present at time t, number of B-atoms at time t, half-life of A, half-life of B, the decay constant of A and decay constant of B. The decay constants are related to the respective half-life by $$\lambda = \frac{ln 2}{T}$$.
Then the process can be modelled by the simult. d.e.s :
$$\frac{dN_A}{dt} = -\lambda_AN_A$$ ---(1)
$$\frac{dN_B}{dt} = -\frac{dN_A}{dt} - \lambda_BN_B = \lambda_AN_A - \lambda_BN_B$$---(2)
Solving those is not difficult, but isn't elementary either. (1) is easily solvable by separation of variables, then the result is substituted into (2). This requires an integrating factor to solve.
The final expression I get for $$N_B$$ as a function of t is :
$$N_B = (N_0)(\frac{\lambda_A}{\lambda_B - \lambda_A})(e^{-\lambda_At} - e^{-\lambda_Bt})$$
or equivalently,
$$N_B = (N_0)(\frac{T_B}{T_A - T_B})({(\frac{1}{2})}^{\frac{t}{T_A}} - {(\frac{1}{2})}^{\frac{t}{T_B}})$$
in terms of the half-lives.
The instant $$\tau$$ at which $$N_B$$ is maximised is easily computed by setting $$\frac{dN_B}{dt} = 0$$
giving $$\tau = \frac{1}{\lambda_B - \lambda_A}ln(\frac{\lambda_B}{\lambda_A}) = \frac{ln(\frac{T_A}{T_B})(T_A)(T_B)}{(ln 2)(T_A - T_B)}$$
Last edited: May 3, 2006
5. May 3, 2006
### Curious3141
I'm bumping this up, because I would really appreciate someone commenting on my method and checking the math if possible. Actually, sequential decay is a problem I've wanted to solve for a long time, but it always slipped my mind or I never had the motivation. So this was a good excuse.
After we sort it out on the forum, I'd like the OP to take the solution back to the teacher and get his opinion on whether that's the simplest way to do it, and whether that's what's expected.
6. May 6, 2006
### Curious3141
Raul, have you got an answer to this from your instructor ? I'm interested to know, too.
7. May 6, 2006
### raul_l
I can get you the answer on monday. I'm interested myself as well :)
8. May 6, 2006
### Curious3141
Thank you. If it's not too much trouble, show your instructor my work and see if he agrees. Find out if there's an easier way.
9. May 6, 2006
### Staff: Mentor
Solution is correct, and the method is the most direct, i.e. simplest method.
10. May 6, 2006
### Curious3141
Thank you!!!
11. May 8, 2006
### raul_l
I consulted my teacher and your method is indeed the simplest one. It's weird that I was given a problem with that difficulty, because it's way beyond my level (it's taken from some kind of international olympiad).
Also, T1 is not greater than T2 as I originally posted. Sorry about that. Otherwise the problem is not solvable.
12. May 8, 2006
### Curious3141
That doesn't surprise me, since this is roughly the level of problem I had to solve when training for my Physics Olympiad, back in the day. (In fact, those problems were usually a lot harder).
I don't see that this should matter. The equation works whichever half-life is greater. Can you explain why this shouldn't be so ?
13. May 8, 2006
### raul_l
Come to think of it, I'm not sure anymore. It seemed logical to me at first, because if the mass of element B is initially 0 and if it decays faster than the increase of its mass by the decaying of A, then the mass of B should always remain close to 0. But I guess you're right, there should still be a point at which the mass is maximised.
However, if I set T[a]=T I get t=0/0. Where's the logic in that?
14. May 8, 2006
### Curious3141
Decay is fundamentally a random process. From a micro perspective, there is no statistical reason why B cannot accumulate in mass over a few "ticks" even if its half-life is shorter than A's.
Ah, try doing the limit, setting $$T_A = kT_B$$ and letting k tend to unity (where the half-life becomes the same, let's call that T). It's a good exercise (you will find it easier with L'Hopital's Rule). You will find that $$\tau = \frac{T}{\ln 2}$$ and that $$max(N_B) = \frac{N_0}{e}$$. For interest's sake, in this case, the time when the mass of B is maximised is actually the mean life of a single particle of B (which is the same as the mean life of a particle of A, since the half-lives are the same). Of course, this is the reciprocal of the common decay constant. The value of the maximal mass has a nice relationship to e, the base of the natural log.
Fascinating stuff, isn't it ?
Last edited: May 8, 2006
15. May 8, 2006
### raul_l
Thing were so much more simple before this sequential decay problem... :)
Anyway, I was thinking the same thing (that I should probably take the limit to get rid of the 0/0 problem). However, the equations are above my level and I still can't fully understand all of them, but I'm woking on it. :)
16. May 8, 2006
### Curious3141
Give it a little time (and effort). They're not that complicated, really.
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# [.net] Differences between .NET and Mono
This topic is 3484 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
Disclaimer: I think this is the appropriate place for this thread, but please feel free to move it to the appropriate place. Now, on to the subject. I've been having a discussion on C# with a co-worker for some time now. He likes C/C++ and thinks that C# is pretty much a proprietary Microsoft tool to make everyone conform to their way of programming. I've disproven this where I could by pointing out that C# has an ISO standard and that the Mono project is attempting to create an Open Source VM according to this standard. The one claim that I don't have an answer for is this: "C# is basically designed to work with Visual Studio. In Mono it's a completely different beast due to the fact that you don't have Intellisense or any of the other Visual Studio features that C# pretty much requires." Is this a dumb argument? I mean, the .NET framework and Mono are both implementing something based off the same standard so they should be the same (barring the stuff that is proprietary to Microsoft). At the same time, C# benefits from the features of Visual Studio (like Intellisense) just like any other programming language would. Shouldn't it always be harder to program in a plain text editor than in Visual Studio due to the differences in features, regardless of the language?
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It's not really a valid argument. C# isn't tied to any IDE. You can edit your C# code in Visual Studio, and then compile it in Mono. The language is IDE independent, and the IDE can be used to edit the language source files without regard to which platform it is being compiled for.
EDIT: In fact, although I did not know this before, Mono can run binaries produced by Visual Studio. So there is no need to even recompile. Compile and run from Visual Studio, deploy and run on Mono.
Mono FAQ
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Quote:
Original post by savagemonitor"C# is basically designed to work with Visual Studio. In Mono it's a completely different beast due to the fact that you don't have Intellisense or any of the other Visual Studio features that C# pretty much requires."
What the fuck? This is wrong on multiple levels:
* Why on earth would Intellisense be necessary to write C#? Even the forms editor isn't particularly necessary (it's arguably even less necessary in C# than in C++/MFC).
* SharpDevelop supports Mono, and both SharpDevelop and MonoDevelop have Intellisense support and forms designers.
Basically your coworker is an ignorant fool, at best.
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There's also the bigger point that Mono is the runtime, not the IDE. "Ignorant fool" is putting it nicely.
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Note that MonoDevelop[1], the IDE built by the Mono community supports intellisense. :)
I've been working on a C# project for years that works out of the box on Windows or Mono/Linux or Mono/Windows...
Basically, we have to think about coding for the .NET framework. Mono is stable enough to support almost everything you need.
[1] http://www.monodevelop.com/Main_Page
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Let's get some torches and some pitchforks and rid the world of this scoundrel!
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Now, Mono does trail behind the Microsoft CLR (the runtime) by a bit, mostly in libraries, but I haven't had much trouble switching my .dll's from CLR to CLR and pretty much everything runs nicely. Actually, my MfGames.* libraries are compiled on Debian and Mono and I just drop them into my Windows library directories.
There are some weak points, System.Windows.Forms is a bit, but its rapidly catching up and some of the more "obscure" namespaces of 3.x haven't been implemented (last I checked) and maybe 1-2 of the 2.0 or 3.5 features (like precompiling ASP.NET sites). They have a program (Momo) that gives you an idea of what is and isn't running.
Of course, I use Emacs instead of one of those fancy IDE's. :P
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You can still use the VS IDE to develop. You can even compile your app in windows, and copy the exe/dll's to linux. It runs fine. And right, monodevelop is also pretty good. Specific to game development, the following is mono based
http://unity3d.com/
Second Life also uses it, though more as a scripting engine I think.
http://wiki.secondlife.com/wiki/Mono
Still, You're friend has a valid point. C++ is probably going to be faster..
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Also, on the weak library note, I wanted to mention that the network stack on the mono runtime is not as robust as the network stack on the .net framework.
For example a simple udp socket application that I wrote a few months ago did not work on mono.
Also, some simple tcp network errors result in exceptions on the Microsoft framework, and just bring the process down entirely on Mono.
Since networking is a big feature set that doesn't work exceptionally well on Mono, it makes the system unready for prime time for my purpose.
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Yeah you don't need VS2008 at all to get all the latest C# functionality. All you need is to download this:
Microsoft .NET Framework 3.5
Brief Description
Microsoft .NET Framework 3.5 contains many new features building incrementally upon .NET Framework 2.0 and 3.0, and includes .NET Framework 2.0 service pack 1 and .NET Framework 3.0 service pack 1.
and do everything from the command line like Petzold always does-LOL!
Visual Studio IDE itself is a proprietary MS tool though of which there is no comparable Linux version although there now is MonoDevelop as has been pointed out.
He does sort of have a point in that Microsoft has the better and more complete implementation compared to Mono but that should come as no suprise as I'm sure they are pouring alot more money into it.
So in theory they should be the same like Java on Windows or Linux, Mac,etc, including GUI stuff but in practice they are not since they are not being written by the same company so Mono is missing or behind in implementing things that are already available on windows!
The Mono project has been tracking some of the improvements available in those releases, some of the highlights of our work so far are:
* Core: mscorlib, System and System.XML assemblies. These support both the 1.x and 2.0 profiles. Work is underway to complete the 2.0 profile.
* ADO.NET: System.Data and various other database providers, they are 1.x complete, and most of 2.x is complete
* ASP.NET 1.x and 2.x: WebForms and Web Services are supported. Only WebParts are missing from our 2.x support.
* System.Security support 1.1 features and has partial support for 2.0 (like XML encryption) but the S.S.C.Pkcs namespace is still imcomplete.
* DirectoryServices implemented on top of Novell.LDAP
* Windows.Forms 1.1 with almost complete 2.0 support.
* System.Drawing supports both 1.x and 2.0 profiles.
* Compilers: C# 1 and 2 as well as bits of 3, VB.NET 8 and various command line tools that are part of the SDK.
* Transaction support, we have some partial support but currently no plans exist beyond the current implementation (see the notes on its implementation and limitations).
* Open Source, Unix and Gnome specific libraries, see our Plans page for more details.
There are certain features that we are not planning on supporting and are available either as stubs (to allow other code to compile or to satisfy dependencies) or are not even present in Mono, these include:
* EnterpriseServices
* Web Services Enhancements (WSE)
* System.Management: too Windows specific
* System.Messaging.
Support for designers in Windows.Forms and ASP.NET for the majority of Mono provided controls does not exist. This is due to the lack of tools for designing Windows.Forms and ASP.NET components in Mono today. When designer surfaces are completed (there are work in progress for both of them) work on this areas will resume.
Designer support is only needed at development-time, this is not something that is required to run the applications on Unix. Many applications that are reported through the Mono Migration Analysis tool reports these problems and can be safely ignored.
Some components exist that were once developed but are no longer actively developed, these include:
Last time I tried running some simple winform games I made using C# on Linux using mono they failed miserably due to missing winforms support but I hear it's gotten better?
So major fail IMO since C# apps and winforms go hand in hand otherwise why even bother?
I have to give them some props though for at least coming out with some tools like this to help people that want to give it a shot:
The Mono Migration Analyzer (MoMA) tool helps you identify issues you may have when porting your .Net application to Mono. It helps pinpoint platform specific calls (P/Invoke) and areas that are not yet supported by the Mono project.
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No more than C++ and win32. It does not change much. If you wish to be portable use portable libraries SDL.net, Gtk#, neoaxis . The language C# 2.0 itself is completely compliant to mono.
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The only tricky area is P/Invoke, of course. After all, the Win32 API isn't available in Linux (despite occasional attempts to hook WINE and Mono together at some level). Because of this, WinForms works a bit differently on Microsoft.NET (the implementation of WinForms is pretty much MFC for .NET: it's a OO wrapper for Win32) as compared to Mono (which IIRC does all its own UI rendering on every platform rather than mapping to what's available). You'll find a slight speed hit if you use the Mono WinForm assemblies even on Windows, but if you're running Mono on Windows there's nothing keeping you from making use of the Microsoft.NET WinForm libraries.
If you're using any cross-platform, unmanaged libraries, you'll of course need to build those for each platform, as well as separate builds of interop assemblies for each platform due to symbol/linking differences. However, if all your code is managed and encapsulated in the set of assemblies treated as .NET 2.0, it should be build once run anywhere. And as pretty much all cross-platform interop libraries provide the same public interface on each platform, using those shouldn't change that fact.
If you want all the shiny new C# 3.0 language features, then at this time you'll need to use the Microsoft C# compiler as the Mono efforts to bring their compiler up to 3.0 are still ongoing. But that's the only way one would be forced to use Microsoft's tools (especially as all C# 3.0 language features map to the 2.0 framework when you get to the IL code).
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Quote:
Original post by coldacidIf you want all the shiny new C# 3.0 language features, then at this time you'll need to use the Microsoft C# compiler as the Mono efforts to bring their compiler up to 3.0 are still ongoing. But that's the only way one would be forced to use Microsoft's tools (especially as all C# 3.0 language features map to the 2.0 framework when you get to the IL code).
Mono C# supposedly fully supports C# 3.0 as of last week.
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Original post by mutex
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Original post by coldacidIf you want all the shiny new C# 3.0 language features, then at this time you'll need to use the Microsoft C# compiler as the Mono efforts to bring their compiler up to 3.0 are still ongoing. But that's the only way one would be forced to use Microsoft's tools (especially as all C# 3.0 language features map to the 2.0 framework when you get to the IL code).
Mono C# supposedly fully supports C# 3.0 as of last week.
Awesomesuace. Thanks for the tidbit.
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Whatever about c#, I don't think .NET is cross platform in any meaningful way.
most commercial .net apps are using 2.0 and mono still hasn't that fully implemented.
Also, I heard that win forms was just a thin wrapper around the win32 api. That's hardly good for a cross platform api.
When someone ports a real application to Mono then I'll take more it seriously. (by real application I mean something complicated like the Multiverse client)
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Original post by captainfreedomWhatever about c#, I don't think .NET is cross platform in any meaningful way.most commercial .net apps are using 2.0 and mono still hasn't that fully implemented.Also, I heard that win forms was just a thin wrapper around the win32 api. That's hardly good for a cross platform api.When someone ports a real application to Mono then I'll take more it seriously. (by real application I mean something complicated like the Multiverse client)
Well they did get started on Paint.NET but I don't know how that is going?
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Original post by captainfreedomWhatever about c#, I don't think .NET is cross platform in any meaningful way.most commercial .net apps are using 2.0 and mono still hasn't that fully implemented.Also, I heard that win forms was just a thin wrapper around the win32 api. That's hardly good for a cross platform api.When someone ports a real application to Mono then I'll take more it seriously. (by real application I mean something complicated like the Multiverse client)
Unity is a complex tool that lets you build commercial games for Mac, Windows, Wii, iPhone and even embedded into a web-player. It uses Mono for *all* scripting duties, including your game logic -- about 90% of any Unity game's logic will be in script form. In other words: it'll be running as compiled Mono scripts.
Oh yes, I meant that "commercial" bit. People actually use this tool to build games for *sale*, not just as a hobby. Unity is even being used by the likes of Cartoon Network for an up-coming MMO.
So that's real, bona-fide Mono scripts, running in a commercial MMO, on multiple platforms. Today.
Sure, Mono's libraries have a few gaps left to fill, but that's true of any library: they're almost always works in progress. Nevertheless, Mono is very clearly cross platform in perfectly meaningful ways already.
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Original post by captainfreedomWhatever about c#, I don't think .NET is cross platform in any meaningful way.
It's too bad that it doesn't matter what you think. The facts of a situation don't change based upon how you feel about them.
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most commercial .net apps are using 2.0 and mono still hasn't that fully implemented.
While it's true that most commerical .NET apps use 2.0, the second half of your statement is false. .NET 2.0 is supported by Mono, and even some C# 3.0 features are also implemented. Windows.Forms integration isn't complete, but it's close enough to be usable for the majority of projects.
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Also, I heard that win forms was just a thin wrapper around the win32 api. That's hardly good for a cross platform api.
You heard incorrectly. Try doing a bit of research before spouting things off.
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When someone ports a real application to Mono then I'll take more it seriously. (by real application I mean something complicated like the Multiverse client)
Here is a small list of some of the successful projects using Mono. Since you said that when somebody ports a real application to Mono you would take it more seriously, are you going to do that now?
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Original post by Mike.Popoloski
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Also, I heard that win forms was just a thin wrapper around the win32 api. That's hardly good for a cross platform api.
You heard incorrectly. Try doing a bit of research before spouting things off.
Oh, okay, here's the reseach you asked for:
http://www.ondotnet.com/pub/a/dotnet/2003/11/24/longhorn_01.htm?page=last&x-maxdepth=0
"Many of the classes in the Framework Class Library are wrappers on top of Win32 functionality. For example, Windows Forms puts a .NET face on classic Win32 features such as HWND, MSG, and WndProc. Likewise, the various classes in System.Net and System.Net.Sockets ultimately wrap the services provided by the Windows Sockets API in Win32. "
but funny, you seem to spout quite a bit yourself
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Original post by captainfreedom
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Original post by Mike.Popoloski
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Also, I heard that win forms was just a thin wrapper around the win32 api. That's hardly good for a cross platform api.
You heard incorrectly. Try doing a bit of research before spouting things off.
Oh, okay, here's the reseach you asked for:
http://www.ondotnet.com/pub/a/dotnet/2003/11/24/longhorn_01.htm?page=last&x-maxdepth=0
"Many of the classes in the Framework Class Library are wrappers on top of Win32 functionality. For example, Windows Forms puts a .NET face on classic Win32 features such as HWND, MSG, and WndProc. Likewise, the various classes in System.Net and System.Net.Sockets ultimately wrap the services provided by the Windows Sockets API in Win32. "
but funny, you seem to spout quite a bit yourself
Of course, the current implementation of the .NET Windows.Forms namespace (and indeed, many other namespaces in the .NET framework) delegate to Win32 counterparts. However, this does NOT mean that the underlying implementation cannot be rewritten for another OS. That's basically the whole point of having a standardized interface. It makes it easy to swap out the back end. Which is exactly what Mono did. The back end for WinForms in Windows is Win32, yes, but on other platforms other native GUI systems were used.
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Original post by captainfreedom"Many of the classes in the Framework Class Library are wrappers on top of Win32 functionality. For example, Windows Forms puts a .NET face on classic Win32 features such as HWND, MSG, and WndProc. Likewise, the various classes in System.Net and System.Net.Sockets ultimately wrap the services provided by the Windows Sockets API in Win32."
You are aware that sockets, networking, and GUI's all exist on other platforms, right? Sure the .NET classes are loosely based on the Windows' incarnations of these basic OS services, but the services themselves are not Windows specific.
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Original post by captainfreedom
Quote:
Original post by Mike.Popoloski
Quote:
Also, I heard that win forms was just a thin wrapper around the win32 api. That's hardly good for a cross platform api.
You heard incorrectly. Try doing a bit of research before spouting things off.
Oh, okay, here's the reseach you asked for:
http://www.ondotnet.com/pub/a/dotnet/2003/11/24/longhorn_01.htm?page=last&x-maxdepth=0
"Many of the classes in the Framework Class Library are wrappers on top of Win32 functionality. For example, Windows Forms puts a .NET face on classic Win32 features such as HWND, MSG, and WndProc. Likewise, the various classes in System.Net and System.Net.Sockets ultimately wrap the services provided by the Windows Sockets API in Win32. "
but funny, you seem to spout quite a bit yourself
.NET is implemented using Win32 calls.
Mono is implemented using Posix calls.
The Mono implementation of Windows.Forms calls into X11 on Linux and into Quartz on MacOS and Win32 on Windows. Mono even provides HWND, MSG and WndProc across all platforms.
The same for System.Net, we just call Posix APIs instead of calling Win32 APIs. I know this might come to a shock to you, but these are pretty simple programming techniques.
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Original post by captainfreedomOh, okay, here's the reseach you asked for: http://www.ondotnet.com/pub/a/dotnet/2003/11/24/longhorn_01.htm?page=last&x-maxdepth=0"Many of the classes in the Framework Class Library are wrappers on top of Win32 functionality. For example, Windows Forms puts a .NET face on classic Win32 features such as HWND, MSG, and WndProc. Likewise, the various classes in System.Net and System.Net.Sockets ultimately wrap the services provided by the Windows Sockets API in Win32. "but funny, you seem to spout quite a bit yourself
To bring the conversation back to the original question: C# is the language; it is a standard. .NET is the runtime; it is not a standard. Windows.Forms as the namespace for the items in dispute should tell an informed reader that the namespace is proprietary, much as anything inside the Microsoft.* namespaces.
If you are holding C#/.NET to the standards you claim to be, I dare you to find me a C++ application of any [substantial] size which has been written to function across all platforms and which does not use #ifdefine's to achieve it's "platform neutrality."
Hell, you'll be lucky to find an application that compiles cleanly on both Win32 and *nix platforms.
Edit: Added substantial to size. ;) (A :P to bubu LV, hehe.)
[Edited by - Talonius on August 4, 2008 3:29:13 PM]
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Original post by Taloniusfind me a C++ application of any size which has been written to function across all platforms and which does not use #ifdefine's to achieve it's "platform neutrality."
Here you go:
#include <iostream>int main(){ std::cout << "Hello, World!" << std::endl;}
:)
(sorry for offtopic)
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Original post by bubu LV
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Original post by Taloniusfind me a C++ application of any size which has been written to function across all platforms and which does not use #ifdefine's to achieve it's "platform neutrality."
Here you go:
*** Source Snippet Removed ***
:)
(sorry for offtopic)
The C++ "Input/output library" as defined by the C++ standard of which iostreams are a part of are not part of the set of libraries guaranteed to be available on a freestanding implementation of the C++ language as listed in ¶17.4.1.3.
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From ¶1.4.7 of ISO/IEC 14882:2003A freestanding implementation is one in which execution may take place without the benefit of an operating system, and has an implementation-defined set of libraries that includes certain language-support libraries (17.4.1.3)
As such, your rendition of hello world lacks platform neutrality WRT handhelds, or even consoles.
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# Directed strongly walk-regular graphs and their eigenvalues
### Edwin van Dam Tilburg University
#### Gholamreza Omidi Isfahan University of Technology
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Minisymposium: ASSOCIATION SCHEMES
Content: A directed graph is called strongly $\ell$-walk regular if the number of walks of length $\ell$ from one vertex to another depends only on whether the two vertices are the same, adjacent, or not adjacent. This generalizes the concept of directed strongly regular graphs and a problem introduced by Hoffman. It also generalizes the same concept for undirected graphs, which was studied by the authors in earlier work (JCTA 120 (2013), 803-810. arXiv:1208.3067). Here we present several results and constructions of directed strongly $\ell$-walk-regular graphs. Eigenvalue methods play a crucial role in obtaining these results.
Back to all abstracts
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# What is Finite Rate of Innovation Signal?
I have read about Finite Rate of Innovation signal by Martin Vetterli in here. But i do not understand several basic things
1. The paper said that finite rate of innovation is the number of degree of freedom of a signal. But i cannot imagine a degree of freedom in signal term. If i have a robot that move lateral in X, Y, and Z, hence i can say it has 3 degree of freedom. How can i imagine it in signal term?
2. A standard sampling is just sample a signal for every time interval, but in FRI sampling, there is a smoothing kernel, what is the purpose of this?
3. what is annihilation filter?
Thank you
If a signal can be exactly represented by $$N$$ real numbers per time interval, then its number of degrees of freedom for that time interval equals $$N$$. The most well-known example are band-limited signals, which can be represented by $$2B$$ samples per second, if their bandwidth is not greater than $$B$$. I.e., such signals have $$2B$$ degrees of freedom per second. This is equivalent to saying that these signals have a finite rate of innovation, and that rate of innovation equals $$2B$$.
A signal doesn't need to be band-limited in order to have a finite rate of innovation (i.e., a finite number of degrees of freedom). You can think of any signal that can be parameterized with a finite number of parameters per time unit. A simple example would be a signal of the form
$$x(t)=\sum_kw_kg(t-kT)\tag{1}$$
where $$g(t)$$ is a rectangular impulse with a value of $$1$$ in the interval $$[0,T]$$ and zero otherwise. You need exactly one sample per $$T$$ seconds to represent $$x(t)$$, even though $$x(t)$$ is clearly not band-limited.
A smoothing kernel is just an optional filter that is applied to the continuous-time signal before sampling. For sampling a (quasi-)band-limited signal, the anti-aliasing filter would be an instance of such a smoothing filter.
An annihilating filter for a specific signal is an LTI system that produces an output of zero when that specific signal is applied at its input. E.g., for a sinusoidal signal with frequency $$\omega_0$$, a filter with a notch at $$\omega_0$$ is an annihilating filter.
• Hello, Thank you for the help. But is it just a single real number for each time interval sampling? such as if i have 10 Hz than for each 100 ms time interval i just can have a single value? – Zahi Azmi Dec 18 '18 at 10:46
• @ZahiAzmi: It depends on the time interval you're considering. For a band-limited signal, you have $2B$ samples per second, or one sample per $1/2B$ seconds. The rate is usually measured in number of samples per second. So in general you have more than $1$ number per time unit (which is one second). – Matt L. Dec 18 '18 at 10:48
• Thank you, so FRI means the rate for one second? And about the the non-band-limited signal, because the frequency can be infinity so the minimum sampling will be infinity, so how can it have a FRI? Thank you – Zahi Azmi Dec 18 '18 at 10:52
• @ZahiAzmi: The rate of innovation is the number of values per second needed to exactly represent the signal. As I've mentioned in my answer, there are non-bandlimited signals that only depend on a finite number of parameters per time unit, so they have a finite rate of innovation, even though they are not band-limited. – Matt L. Dec 18 '18 at 10:54
• Thank you, i am still confused about the parameters, what is it related to the signal? – Zahi Azmi Dec 18 '18 at 10:56
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# Dijkstra's algorithm
Dijkstra's algorithm (/ˈdkstrəz/ DYKE-strəz) is an algorithm for finding the shortest paths between nodes in a graph, which may represent, for example, road networks. It was conceived by computer scientist Edsger W. Dijkstra in 1956 and published three years later.[4][5][6]
Class Dijkstra's algorithm to find the shortest path between a and b. It picks the unvisited vertex with the lowest distance, calculates the distance through it to each unvisited neighbor, and updates the neighbor's distance if smaller. Mark visited (set to red) when done with neighbors. Search algorithmGreedy algorithmDynamic programming[1] GraphUsually used with Priority queue/Heap for optimization[2][3] ${\displaystyle \Theta (|E|+|V|\log |V|)}$[3]
The algorithm exists in many variants. Dijkstra's original algorithm found the shortest path between two given nodes,[6] but a more common variant fixes a single node as the "source" node and finds shortest paths from the source to all other nodes in the graph, producing a shortest-path tree.
For a given source node in the graph, the algorithm finds the shortest path between that node and every other.[7]: 196–206 It can also be used for finding the shortest paths from a single node to a single destination node by stopping the algorithm once the shortest path to the destination node has been determined. For example, if the nodes of the graph represent cities and edge path costs represent driving distances between pairs of cities connected by a direct road (for simplicity, ignore red lights, stop signs, toll roads and other obstructions), Dijkstra's algorithm can be used to find the shortest route between one city and all other cities. A widely used application of shortest path algorithms is network routing protocols, most notably IS-IS (Intermediate System to Intermediate System) and OSPF (Open Shortest Path First). It is also employed as a subroutine in other algorithms such as Johnson's.
The Dijkstra algorithm uses labels that are positive integers or real numbers, which are totally ordered. It can be generalized to use any labels that are partially ordered, provided the subsequent labels (a subsequent label is produced when traversing an edge) are monotonically non-decreasing. This generalization is called the generic Dijkstra shortest-path algorithm.[8]
Dijkstra's algorithm uses a data structure for storing and querying partial solutions sorted by distance from the start. While the original algorithm uses a min-priority queue and runs in time ${\displaystyle \Theta ((|V|+|E|)\log |V|)}$(where ${\displaystyle |V|}$ is the number of nodes and ${\displaystyle |E|}$ is the number of edges), it can also be implemented in ${\displaystyle \Theta (|V|^{2})}$ using an array. The idea of this algorithm is also given in Leyzorek et al. 1957. Fredman & Tarjan 1984 propose using a Fibonacci heap min-priority queue to optimize the running time complexity to ${\displaystyle \Theta (|E|+|V|\log |V|)}$. This is asymptotically the fastest known single-source shortest-path algorithm for arbitrary directed graphs with unbounded non-negative weights. However, specialized cases (such as bounded/integer weights, directed acyclic graphs etc.) can indeed be improved further as detailed in Specialized variants. Additionally, if preprocessing is allowed algorithms such as contraction hierarchies can be up to seven orders of magnitude faster.
In some fields, artificial intelligence in particular, Dijkstra's algorithm or a variant of it is known as uniform cost search and formulated as an instance of the more general idea of best-first search.[9]
## History
What is the shortest way to travel from Rotterdam to Groningen, in general: from given city to given city. It is the algorithm for the shortest path, which I designed in about twenty minutes. One morning I was shopping in Amsterdam with my young fiancée, and tired, we sat down on the café terrace to drink a cup of coffee and I was just thinking about whether I could do this, and I then designed the algorithm for the shortest path. As I said, it was a twenty-minute invention. In fact, it was published in '59, three years later. The publication is still readable, it is, in fact, quite nice. One of the reasons that it is so nice was that I designed it without pencil and paper. I learned later that one of the advantages of designing without pencil and paper is that you are almost forced to avoid all avoidable complexities. Eventually, that algorithm became to my great amazement, one of the cornerstones of my fame.
— Edsger Dijkstra, in an interview with Philip L. Frana, Communications of the ACM, 2001[5]
Dijkstra thought about the shortest path problem when working at the Mathematical Center in Amsterdam in 1956 as a programmer to demonstrate the capabilities of a new computer called ARMAC.[10] His objective was to choose both a problem and a solution (that would be produced by computer) that non-computing people could understand. He designed the shortest path algorithm and later implemented it for ARMAC for a slightly simplified transportation map of 64 cities in the Netherlands (64, so that 6 bits would be sufficient to encode the city number).[5] A year later, he came across another problem from hardware engineers working on the institute's next computer: minimize the amount of wire needed to connect the pins on the back panel of the machine. As a solution, he re-discovered the algorithm known as Prim's minimal spanning tree algorithm (known earlier to Jarník, and also rediscovered by Prim).[11][12] Dijkstra published the algorithm in 1959, two years after Prim and 29 years after Jarník.[13][14]
## Algorithm
Illustration of Dijkstra's algorithm finding a path from a start node (lower left, red) to a goal node (upper right, green) in a robot motion planning problem. Open nodes represent the "tentative" set (aka set of "unvisited" nodes). Filled nodes are the visited ones, with color representing the distance: the greener, the closer. Nodes in all the different directions are explored uniformly, appearing more-or-less as a circular wavefront as Dijkstra's algorithm uses a heuristic identically equal to 0.
Let the node at which we are starting be called the initial node. Let the distance of node Y be the distance from the initial node to Y. Dijkstra's algorithm will initially start with infinite distances and will try to improve them step by step.
1. Mark all nodes unvisited. Create a set of all the unvisited nodes called the unvisited set.
2. Assign to every node a tentative distance value: set it to zero for our initial node and to infinity for all other nodes. During the run of the algorithm, the tentative distance of a node v is the length of the shortest path discovered so far between the node v and the starting node. Since initially no path is known to any other vertex than the source itself (which is a path of length zero), all other tentative distances are initially set to infinity. Set the initial node as current.[15]
3. For the current node, consider all of its unvisited neighbors and calculate their tentative distances through the current node. Compare the newly calculated tentative distance to the one currently assigned to the neighbor and assign it the smaller one. For example, if the current node A is marked with a distance of 6, and the edge connecting it with a neighbor B has length 2, then the distance to B through A will be 6 + 2 = 8. If B was previously marked with a distance greater than 8 then change it to 8. Otherwise, the current value will be kept.
4. When we are done considering all of the unvisited neighbors of the current node, mark the current node as visited and remove it from the unvisited set. A visited node will never be checked again (this is valid and optimal in connection with the behavior in step 6.: that the next nodes to visit will always be in the order of 'smallest distance from initial node first' so any visits after would have a greater distance).
5. If the destination node has been marked visited (when planning a route between two specific nodes) or if the smallest tentative distance among the nodes in the unvisited set is infinity (when planning a complete traversal; occurs when there is no connection between the initial node and remaining unvisited nodes), then stop. The algorithm has finished.
6. Otherwise, select the unvisited node that is marked with the smallest tentative distance, set it as the new current node, and go back to step 3.
When planning a route, it is actually not necessary to wait until the destination node is "visited" as above: the algorithm can stop once the destination node has the smallest tentative distance among all "unvisited" nodes (and thus could be selected as the next "current").
## Description
Suppose you would like to find the shortest path between two intersections on a city map: a starting point and a destination. Dijkstra's algorithm initially marks the distance (from the starting point) to every other intersection on the map with infinity. This is done not to imply that there is an infinite distance, but to note that those intersections have not been visited yet. Some variants of this method leave the intersections' distances unlabeled. Now select the current intersection at each iteration. For the first iteration, the current intersection will be the starting point, and the distance to it (the intersection's label) will be zero. For subsequent iterations (after the first), the current intersection will be a closest unvisited intersection to the starting point (this will be easy to find).
From the current intersection, update the distance to every unvisited intersection that is directly connected to it. This is done by determining the sum of the distance between an unvisited intersection and the value of the current intersection and then relabeling the unvisited intersection with this value (the sum) if it is less than the unvisited intersection's current value. In effect, the intersection is relabeled if the path to it through the current intersection is shorter than the previously known paths. To facilitate shortest path identification, in pencil, mark the road with an arrow pointing to the relabeled intersection if you label/relabel it, and erase all others pointing to it. After you have updated the distances to each neighboring intersection, mark the current intersection as visited and select an unvisited intersection with minimal distance (from the starting point) – or the lowest label—as the current intersection. Intersections marked as visited are labeled with the shortest path from the starting point to it and will not be revisited or returned to.
Continue this process of updating the neighboring intersections with the shortest distances, marking the current intersection as visited, and moving onto a closest unvisited intersection until you have marked the destination as visited. Once you have marked the destination as visited (as is the case with any visited intersection), you have determined the shortest path to it from the starting point and can trace your way back following the arrows in reverse. In the algorithm's implementations, this is usually done (after the algorithm has reached the destination node) by following the nodes' parents from the destination node up to the starting node; that's why we also keep track of each node's parent.
This algorithm makes no attempt of direct "exploration" towards the destination as one might expect. Rather, the sole consideration in determining the next "current" intersection is its distance from the starting point. This algorithm therefore expands outward from the starting point, interactively considering every node that is closer in terms of shortest path distance until it reaches the destination. When understood in this way, it is clear how the algorithm necessarily finds the shortest path. However, it may also reveal one of the algorithm's weaknesses: its relative slowness in some topologies.
## Pseudocode
In the following pseudocode algorithm, dist is an array that contains the current distances from the source to other vertices, i.e. dist[u] is the current distance from the source to the vertex u. The prev array contains pointers to previous-hop nodes on the shortest path from source to the given vertex (equivalently, it is the next-hop on the path from the given vertex to the source). The code u ← vertex in Q with min dist[u], searches for the vertex u in the vertex set Q that has the least dist[u] value. Graph.Edges(u, v) returns the length of the edge joining (i.e. the distance between) the two neighbor-nodes u and v. The variable alt on line 14 is the length of the path from the root node to the neighbor node v if it were to go through u. If this path is shorter than the current shortest path recorded for v, that current path is replaced with this alt path.[7]
A demo of Dijkstra's algorithm based on Euclidean distance. Red lines are the shortest path covering, i.e., connecting u and prev[u]. Blue lines indicate where relaxing happens, i.e., connecting v with a node u in Q, which gives a shorter path from the source to v.
1 function Dijkstra(Graph, source):
2
3 for each vertex v in Graph.Vertices:
4 dist[v] ← INFINITY
5 prev[v] ← UNDEFINED
7 dist[source] ← 0
8
9 while Q is not empty:
10 u ← vertex in Q with min dist[u]
11 remove u from Q
12
13 for each neighbor v of u still in Q:
14 alt ← dist[u] + Graph.Edges(u, v)
15 if alt < dist[v] and dist[u] is not INFINITY:
16 dist[v] ← alt
17 prev[v] ← u
18
19 return dist[], prev[]
If we are only interested in a shortest path between vertices source and target, we can terminate the search after line 10 if u = target. Now we can read the shortest path from source to target by reverse iteration:
1 S ← empty sequence
2 u ← target
3 if prev[u] is defined or u = source: // Do something only if the vertex is reachable
4 while u is defined: // Construct the shortest path with a stack S
5 insert u at the beginning of S // Push the vertex onto the stack
6 u ← prev[u] // Traverse from target to source
Now sequence S is the list of vertices constituting one of the shortest paths from source to target, or the empty sequence if no path exists.
A more general problem would be to find all the shortest paths between source and target (there might be several different ones of the same length). Then instead of storing only a single node in each entry of prev[] we would store all nodes satisfying the relaxation condition. For example, if both r and source connect to target and both of them lie on different shortest paths through target (because the edge cost is the same in both cases), then we would add both r and source to prev[target]. When the algorithm completes, prev[] data structure will actually describe a graph that is a subset of the original graph with some edges removed. Its key property will be that if the algorithm was run with some starting node, then every path from that node to any other node in the new graph will be the shortest path between those nodes in the original graph, and all paths of that length from the original graph will be present in the new graph. Then to actually find all these shortest paths between two given nodes we would use a path finding algorithm on the new graph, such as depth-first search.
### Using a priority queue
A min-priority queue is an abstract data type that provides 3 basic operations: add_with_priority(), decrease_priority() and extract_min(). As mentioned earlier, using such a data structure can lead to faster computing times than using a basic queue. Notably, Fibonacci heap (Fredman & Tarjan 1984) or Brodal queue offer optimal implementations for those 3 operations. As the algorithm is slightly different, we mention it here, in pseudocode as well :
1 function Dijkstra(Graph, source):
2 dist[source] ← 0 // Initialization
3
4 create vertex priority queue Q
6
7 for each vertex v in Graph.Vertices:
8 if v ≠ source
9 dist[v] ← INFINITY // Unknown distance from source to v
10 prev[v] ← UNDEFINED // Predecessor of v
11
13
14
15 while Q is not empty: // The main loop
16 u ← Q.extract_min() // Remove and return best vertex
17 for each neighbor v of u: // only v that are still in Q
18 alt ← dist[u] + Graph.Edges(u, v)
19 if alt < dist[v] and dist[u] is not INFINITY:
20 dist[v] ← alt
21 prev[v] ← u
22 Q.decrease_priority(v, alt)
23
24 return dist, prev
Instead of filling the priority queue with all nodes in the initialization phase, it is also possible to initialize it to contain only source; then, inside the if alt < dist[v] block, the decrease_priority() becomes an add_with_priority() operation if the node is not already in the queue.[7]: 198
Yet another alternative is to add nodes unconditionally to the priority queue and to instead check after extraction that no shorter connection was found yet. This can be done by additionally extracting the associated priority p from the queue and only processing further if p == dist[u] inside the while Q is not empty loop. [16]
These alternatives can use entirely array-based priority queues without decrease-key functionality, which have been found to achieve even faster computing times in practice. However, the difference in performance was found to be narrower for denser graphs.[17]
## Proof of correctness
Proof of Dijkstra's algorithm is constructed by induction on the number of visited nodes.
Invariant hypothesis: For each node v, dist[v] is the shortest distance from source to v when traveling via visited nodes only, or infinity if no such path exists. (Note: we do not assume dist[v] is the actual shortest distance for unvisited nodes.)
The base case is when there is just one visited node, namely the initial node source, in which case the hypothesis is trivial.
Otherwise, assume the hypothesis for n-1 visited nodes. In which case, we choose an edge vu where u has the least dist[u] of any unvisited nodes such that dist[u] = dist[v] + Graph.Edges[v,u]. dist[u] is considered to be the shortest distance from source to u because if there were a shorter path, and if w was the first unvisited node on that path then by the original hypothesis dist[w] > dist[u] which creates a contradiction. Similarly if there were a shorter path to u without using unvisited nodes, and if the last but one node on that path were w, then we would have had dist[u] = dist[w] + Graph.Edges[w,u], also a contradiction.
After processing u it will still be true that for each unvisited node w, dist[w] will be the shortest distance from source to w using visited nodes only, because if there were a shorter path that doesn't go by u we would have found it previously, and if there were a shorter path using u we would have updated it when processing u.
After all nodes are visited, the shortest path from source to any node v consists only of visited nodes, therefore dist[v] is the shortest distance.
## Running time
Bounds of the running time of Dijkstra's algorithm on a graph with edges E and vertices V can be expressed as a function of the number of edges, denoted ${\displaystyle |E|}$ , and the number of vertices, denoted ${\displaystyle |V|}$ , using big-O notation. The complexity bound depends mainly on the data structure used to represent the set Q. In the following, upper bounds can be simplified because ${\displaystyle |E|}$ is ${\displaystyle O(|V|^{2})}$ for any graph, but that simplification disregards the fact that in some problems, other upper bounds on ${\displaystyle |E|}$ may hold.
For any data structure for the vertex set Q, the running time is in[2]
${\displaystyle \Theta (|E|\cdot T_{\mathrm {dk} }+|V|\cdot T_{\mathrm {em} }),}$
where ${\displaystyle T_{\mathrm {dk} }}$ and ${\displaystyle T_{\mathrm {em} }}$ are the complexities of the decrease-key and extract-minimum operations in Q, respectively.
The simplest version of Dijkstra's algorithm stores the vertex set Q as an linked list or array, and edges as an adjacency list or matrix. In this case, extract-minimum is simply a linear search through all vertices in Q, so the running time is ${\displaystyle \Theta (|E|+|V|^{2})=\Theta (|V|^{2})}$ .
For sparse graphs, that is, graphs with far fewer than ${\displaystyle |V|^{2}}$ edges, Dijkstra's algorithm can be implemented more efficiently by storing the graph in the form of adjacency lists and using a self-balancing binary search tree, binary heap, pairing heap, or Fibonacci heap as a priority queue to implement extracting minimum efficiently. To perform decrease-key steps in a binary heap efficiently, it is necessary to use an auxiliary data structure that maps each vertex to its position in the heap, and to keep this structure up to date as the priority queue Q changes. With a self-balancing binary search tree or binary heap, the algorithm requires
${\displaystyle \Theta ((|E|+|V|)\log |V|)}$
time in the worst case (where ${\displaystyle \log }$ denotes the binary logarithm ${\displaystyle \log _{2}}$ ); for connected graphs this time bound can be simplified to ${\displaystyle \Theta (|E|\log |V|)}$ . The Fibonacci heap improves this to
${\displaystyle \Theta (|E|+|V|\log |V|).}$
When using binary heaps, the average case time complexity is lower than the worst-case: assuming edge costs are drawn independently from a common probability distribution, the expected number of decrease-key operations is bounded by ${\displaystyle \Theta (|V|\log(|E|/|V|))}$ , giving a total running time of[7]: 199–200
${\displaystyle O\left(|E|+|V|\log {\frac {|E|}{|V|}}\log |V|\right).}$
### Practical optimizations and infinite graphs
In common presentations of Dijkstra's algorithm, initially all nodes are entered into the priority queue. This is, however, not necessary: the algorithm can start with a priority queue that contains only one item, and insert new items as they are discovered (instead of doing a decrease-key, check whether the key is in the queue; if it is, decrease its key, otherwise insert it).[7]: 198 This variant has the same worst-case bounds as the common variant, but maintains a smaller priority queue in practice, speeding up the queue operations.[9]
Moreover, not inserting all nodes in a graph makes it possible to extend the algorithm to find the shortest path from a single source to the closest of a set of target nodes on infinite graphs or those too large to represent in memory. The resulting algorithm is called uniform-cost search (UCS) in the artificial intelligence literature[9][18][19] and can be expressed in pseudocode as
procedure uniform_cost_search(start) is
node ← start
frontier ← priority queue containing node only
expanded ← empty set
do
if frontier is empty then
return failure
node ← frontier.pop()
if node is a goal state then
return solution(node)
for each of node's neighbors n do
if n is not in expanded and not in frontier then
else if n is in frontier with higher cost
replace existing node with n
The complexity of this algorithm can be expressed in an alternative way for very large graphs: when C* is the length of the shortest path from the start node to any node satisfying the "goal" predicate, each edge has cost at least ε, and the number of neighbors per node is bounded by b, then the algorithm's worst-case time and space complexity are both in O(b1+⌊C* ε).[18]
Further optimizations of Dijkstra's algorithm for the single-target case include bidirectional variants, goal-directed variants such as the A* algorithm (see § Related problems and algorithms), graph pruning to determine which nodes are likely to form the middle segment of shortest paths (reach-based routing), and hierarchical decompositions of the input graph that reduce st routing to connecting s and t to their respective "transit nodes" followed by shortest-path computation between these transit nodes using a "highway".[20] Combinations of such techniques may be needed for optimal practical performance on specific problems.[21]
### Specialized variants
When arc weights are small integers (bounded by a parameter ${\displaystyle C}$ ), specialized queues which take advantage of this fact can be used to speed up Dijkstra's algorithm. The first algorithm of this type was Dial's algorithm (Dial 1969) for graphs with positive integer edge weights, which uses a bucket queue to obtain a running time ${\displaystyle O(|E|+|V|C)}$ . The use of a Van Emde Boas tree as the priority queue brings the complexity to ${\displaystyle O(|E|\log \log C)}$ (Ahuja et al. 1990). Another interesting variant based on a combination of a new radix heap and the well-known Fibonacci heap runs in time ${\displaystyle O(|E|+|V|{\sqrt {\log C}})}$ (Ahuja et al. 1990). Finally, the best algorithms in this special case are as follows. The algorithm given by (Thorup 2000) runs in ${\displaystyle O(|E|\log \log |V|)}$ time and the algorithm given by (Raman 1997) runs in ${\displaystyle O(|E|+|V|\min\{(\log |V|)^{1/3+\varepsilon },(\log C)^{1/4+\varepsilon }\})}$ time.
## Related problems and algorithms
The functionality of Dijkstra's original algorithm can be extended with a variety of modifications. For example, sometimes it is desirable to present solutions which are less than mathematically optimal. To obtain a ranked list of less-than-optimal solutions, the optimal solution is first calculated. A single edge appearing in the optimal solution is removed from the graph, and the optimum solution to this new graph is calculated. Each edge of the original solution is suppressed in turn and a new shortest-path calculated. The secondary solutions are then ranked and presented after the first optimal solution.
Dijkstra's algorithm is usually the working principle behind link-state routing protocols, OSPF and IS-IS being the most common ones.
Unlike Dijkstra's algorithm, the Bellman–Ford algorithm can be used on graphs with negative edge weights, as long as the graph contains no negative cycle reachable from the source vertex s. The presence of such cycles means there is no shortest path, since the total weight becomes lower each time the cycle is traversed. (This statement assumes that a "path" is allowed to repeat vertices. In graph theory that is normally not allowed. In theoretical computer science it often is allowed.) It is possible to adapt Dijkstra's algorithm to handle negative weight edges by combining it with the Bellman-Ford algorithm (to remove negative edges and detect negative cycles), such an algorithm is called Johnson's algorithm.
The A* algorithm is a generalization of Dijkstra's algorithm that cuts down on the size of the subgraph that must be explored, if additional information is available that provides a lower bound on the "distance" to the target. This approach can be viewed from the perspective of linear programming: there is a natural linear program for computing shortest paths, and solutions to its dual linear program are feasible if and only if they form a consistent heuristic (speaking roughly, since the sign conventions differ from place to place in the literature). This feasible dual / consistent heuristic defines a non-negative reduced cost and A* is essentially running Dijkstra's algorithm with these reduced costs. If the dual satisfies the weaker condition of admissibility, then A* is instead more akin to the Bellman–Ford algorithm.
The process that underlies Dijkstra's algorithm is similar to the greedy process used in Prim's algorithm. Prim's purpose is to find a minimum spanning tree that connects all nodes in the graph; Dijkstra is concerned with only two nodes. Prim's does not evaluate the total weight of the path from the starting node, only the individual edges.
Breadth-first search can be viewed as a special-case of Dijkstra's algorithm on unweighted graphs, where the priority queue degenerates into a FIFO queue.
The fast marching method can be viewed as a continuous version of Dijkstra's algorithm which computes the geodesic distance on a triangle mesh.
### Dynamic programming perspective
From a dynamic programming point of view, Dijkstra's algorithm is a successive approximation scheme that solves the dynamic programming functional equation for the shortest path problem by the Reaching method.[22][23][24]
In fact, Dijkstra's explanation of the logic behind the algorithm,[25] namely
Problem 2. Find the path of minimum total length between two given nodes ${\displaystyle P}$ and ${\displaystyle Q}$ .
We use the fact that, if ${\displaystyle R}$ is a node on the minimal path from ${\displaystyle P}$ to ${\displaystyle Q}$ , knowledge of the latter implies the knowledge of the minimal path from ${\displaystyle P}$ to ${\displaystyle R}$ .
is a paraphrasing of Bellman's famous Principle of Optimality in the context of the shortest path problem.
## Applications
Least-cost paths are calculated for instance to establish tracks of electricity lines or oil pipelines. The algorithm has also been used to calculate optimal long-distance footpaths in Ethiopia and contrast them with the situation on the ground.[26]
## Notes
1. ^ Controversial, see Moshe Sniedovich (2006). "Dijkstra's algorithm revisited: the dynamic programming connexion". Control and Cybernetics. 35: 599–620. and below part.
2. ^ a b Cormen et al. 2001
3. ^ a b Fredman & Tarjan 1987
4. ^ Richards, Hamilton. "Edsger Wybe Dijkstra". A.M. Turing Award. Association for Computing Machinery. Retrieved 16 October 2017. At the Mathematical Centre a major project was building the ARMAC computer. For its official inauguration in 1956, Dijkstra devised a program to solve a problem interesting to a nontechnical audience: Given a network of roads connecting cities, what is the shortest route between two designated cities?
5. ^ a b c Frana, Phil (August 2010). "An Interview with Edsger W. Dijkstra". Communications of the ACM. 53 (8): 41–47. doi:10.1145/1787234.1787249.
6. ^ a b Dijkstra, E. W. (1959). "A note on two problems in connexion with graphs" (PDF). Numerische Mathematik. 1: 269–271. doi:10.1007/BF01386390. S2CID 123284777.
7. Mehlhorn, Kurt; Sanders, Peter (2008). "Chapter 10. Shortest Paths" (PDF). Algorithms and Data Structures: The Basic Toolbox. Springer. doi:10.1007/978-3-540-77978-0. ISBN 978-3-540-77977-3.
8. ^ Szcześniak, Ireneusz; Jajszczyk, Andrzej; Woźna-Szcześniak, Bożena (2019). "Generic Dijkstra for optical networks". Journal of Optical Communications and Networking. 11 (11): 568–577. arXiv:1810.04481. doi:10.1364/JOCN.11.000568. S2CID 52958911.
9. ^ a b c Felner, Ariel (2011). Position Paper: Dijkstra's Algorithm versus Uniform Cost Search or a Case Against Dijkstra's Algorithm. Proc. 4th Int'l Symp. on Combinatorial Search. In a route-finding problem, Felner finds that the queue can be a factor 500–600 smaller, taking some 40% of the running time.
10. ^ "ARMAC". Unsung Heroes in Dutch Computing History. 2007. Archived from the original on 13 November 2013.
11. ^ Dijkstra, Edsger W., Reflections on "A note on two problems in connexion with graphs (PDF)
12. ^ Tarjan, Robert Endre (1983), Data Structures and Network Algorithms, CBMS_NSF Regional Conference Series in Applied Mathematics, vol. 44, Society for Industrial and Applied Mathematics, p. 75, The third classical minimum spanning tree algorithm was discovered by Jarník and rediscovered by Prim and Dikstra; it is commonly known as Prim's algorithm.
13. ^ Prim, R.C. (1957). "Shortest connection networks and some generalizations" (PDF). Bell System Technical Journal. 36 (6): 1389–1401. Bibcode:1957BSTJ...36.1389P. doi:10.1002/j.1538-7305.1957.tb01515.x. Archived from the original (PDF) on 18 July 2017. Retrieved 18 July 2017.
14. ^ V. Jarník: O jistém problému minimálním [About a certain minimal problem], Práce Moravské Přírodovědecké Společnosti, 6, 1930, pp. 57–63. (in Czech)
15. ^ Gass, Saul; Fu, Michael (2013). Gass, Saul I; Fu, Michael C (eds.). "Dijkstra's Algorithm". Encyclopedia of Operations Research and Management Science. Springer. 1. doi:10.1007/978-1-4419-1153-7. ISBN 978-1-4419-1137-7 – via Springer Link.
16. ^ Observe that p < dist[u] cannot ever hold because of the update dist[v] ← alt when updating the queue. See https://cs.stackexchange.com/questions/118388/dijkstra-without-decrease-key for discussion.
17. ^ Chen, M.; Chowdhury, R. A.; Ramachandran, V.; Roche, D. L.; Tong, L. (2007). Priority Queues and Dijkstra's Algorithm – UTCS Technical Report TR-07-54 – 12 October 2007 (PDF). Austin, Texas: The University of Texas at Austin, Department of Computer Sciences.
18. ^ a b Russell, Stuart; Norvig, Peter (2009) [1995]. Artificial Intelligence: A Modern Approach (3rd ed.). Prentice Hall. pp. 75, 81. ISBN 978-0-13-604259-4.
19. ^ Sometimes also least-cost-first search: Nau, Dana S. (1983). "Expert computer systems" (PDF). Computer. IEEE. 16 (2): 63–85. doi:10.1109/mc.1983.1654302. S2CID 7301753.
20. ^ Wagner, Dorothea; Willhalm, Thomas (2007). Speed-up techniques for shortest-path computations. STACS. pp. 23–36.
21. ^ Bauer, Reinhard; Delling, Daniel; Sanders, Peter; Schieferdecker, Dennis; Schultes, Dominik; Wagner, Dorothea (2010). "Combining hierarchical and goal-directed speed-up techniques for Dijkstra's algorithm". J. Experimental Algorithmics. 15: 2.1. doi:10.1145/1671970.1671976. S2CID 1661292.
22. ^ Sniedovich, M. (2006). "Dijkstra's algorithm revisited: the dynamic programming connexion" (PDF). Journal of Control and Cybernetics. 35 (3): 599–620. Online version of the paper with interactive computational modules.
23. ^ Denardo, E.V. (2003). Dynamic Programming: Models and Applications. Mineola, NY: Dover Publications. ISBN 978-0-486-42810-9.
24. ^ Sniedovich, M. (2010). Dynamic Programming: Foundations and Principles. Francis & Taylor. ISBN 978-0-8247-4099-3.
25. ^ Dijkstra 1959, p. 270
26. ^ Nyssen, J., Tesfaalem Ghebreyohannes, Hailemariam Meaza, Dondeyne, S., 2020. Exploration of a medieval African map (Aksum, Ethiopia) – How do historical maps fit with topography? In: De Ryck, M., Nyssen, J., Van Acker, K., Van Roy, W., Liber Amicorum: Philippe De Maeyer In Kaart. Wachtebeke (Belgium): University Press: 165-178.
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# Lie algabra of symmetric group
It's easy to see that the descending central series of a group induces a graded Lie algebra .(see for example Serre's Harvard lectures or Magnus-Solitar book). I think in general this can be complicated, but this should be well-known:
What is the structure of this Lie algebra for the symmetric group?
-
Isn't it quite a trivial Lie algebra, given that the central series stabilizes at its second point (for $n\geq 5$) ? – darij grinberg Apr 9 '11 at 5:45
The only example I know (from book above) is for the free groups where it is a theorem that the Lie algebra is free (not too hard proof, but not trivial). I'm trying to find other examples with known ansers; I'm not sure where this kind of thing is found. – Dr Shello Apr 9 '11 at 6:03
This construction only works well for nilpotent groups. If you think a bit about what the descending central series of the symmetric group is, you will see that this is not a very good example. – Ben Webster Apr 9 '11 at 6:47
Also, unless you have some extra criteria on the group, it will generally only be a Lie ring (there is no reason to expect the quotients in the series to be vector spaces over some field) – Tobias Kildetoft Apr 9 '11 at 9:19
For any $n>1$, the lower central series for the symmetric group is $S_n > A_n > A_n > A_n > \cdots$, so the Lie ring formed by the sum of successive quotients is the group $\mathbb{Z}/2\mathbb{Z}$, equipped with the Lie bracket that is identically zero.
If you want to gain intuition for this construction with finite groups, I suggest you consider nilpotent groups, since their lower central series actually reach the trivial group. For example, many $p$-groups will yield nonabelian Lie algebras over $\mathbb{F}_p$.
@Dr Shello: you will get interesting examples with $p$-groups $G$ of exponent $p$. Then Quillen's version of Jennings' theorem tells you the restricted enveloping algebra of the Lie algebra that arises is isomorphic to the graded algebra associated to the radical filtration of $\mathbb{F}_pG$. Quillen's paper is J.Alg 10 (1968) pp.411-418, his result is also in Benson's book Representations and Cohomology I. – M T Apr 9 '11 at 19:37
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# Automatically sliding a conv net onto a larger image
Posted 3 months ago
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11 Replies
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How to control the step size of the following conv net as it slides onto a larger image?As a toy example, I'd like to slide a digit classifier trained on 28x28 images to classify each neighborhood of a larger image. This is lenet with linear layers replaced by 1x1 convolutional layers. trainingData = ResourceData["MNIST", "TrainingData"]; testData = ResourceData["MNIST", "TestData"]; lenetModel = NetModel["LeNet Trained on MNIST Data", "UninitializedEvaluationNet"]; newlenet = NetExtract[lenetModel, All]; newlenet[[7]] = ConvolutionLayer[500, {4, 4}]; newlenet[[8]] = ElementwiseLayer[Ramp]; newlenet[[9]] = ConvolutionLayer[10, 1]; newlenet[[10]] = SoftmaxLayer[1]; newlenet[[11]] = PartLayer[{All, 1, 1}]; newlenet = NetChain[newlenet, "Input" -> NetEncoder[{"Image", {28, 28}, ColorSpace -> "Grayscale"}]] Now train it: newtd = First@# -> UnitVector[10, Last@# + 1] & /@ trainingData; newvd = First@# -> UnitVector[10, Last@# + 1] & /@ testData; ng = NetGraph[ <|"inference" -> newlenet, "loss" -> CrossEntropyLossLayer["Probabilities", "Input" -> 10] |>, { "inference" -> NetPort["loss", "Input"], NetPort["Target"] -> NetPort["loss", "Target"] } ] tnew = NetTrain[ng, newtd, ValidationSet -> newvd, TargetDevice -> "GPU"] Now remove dimensions information (see stackexchange for the code definition of removeInputInformation): removeInputInformation[layer_ConvolutionLayer] := With[{k = NetExtract[layer, "OutputChannels"], kernelSize = NetExtract[layer, "KernelSize"], weights = NetExtract[layer, "Weights"], biases = NetExtract[layer, "Biases"], padding = NetExtract[layer, "PaddingSize"], stride = NetExtract[layer, "Stride"], dilation = NetExtract[layer, "Dilation"]}, ConvolutionLayer[k, kernelSize, "Weights" -> weights, "Biases" -> biases, "PaddingSize" -> padding, "Stride" -> stride, "Dilation" -> dilation]] removeInputInformation[layer_PoolingLayer] := With[{f = NetExtract[layer, "Function"], kernelSize = NetExtract[layer, "KernelSize"], padding = NetExtract[layer, "PaddingSize"], stride = NetExtract[layer, "Stride"]}, PoolingLayer[kernelSize, stride, "PaddingSize" -> padding, "Function" -> f]] removeInputInformation[layer_ElementwiseLayer] := With[{f = NetExtract[layer, "Function"]}, ElementwiseLayer[f]] removeInputInformation[x_] := x tmp = NetExtract[NetExtract[tnew, "inference"], All]; n3 = removeInputInformation /@ tmp[[1 ;; -3]]; AppendTo[n3, SoftmaxLayer[1]]; n3 = NetChain@n3; And the network n3 slides onto any larger input. However, note that it seems to slide with steps of 4. How could I make it take steps of 1 instead? In[358]:= n3[RandomReal[1, {1, 28*10, 28}]] // Dimensions Out[358]= {10, 64, 1} In[359]:= BlockMap[Length, Range[28*10], 28, 4] // Length Out[359]= 64
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Posted 2 months ago
Hi Matthias, The stride of 4 comes from the pooling layers In[49]:= Map[NetExtract[n3, {#, "Stride"}] &, {3, 6}] Out[49]= {{2, 2}, {2, 2}} (then on each dimension, there is an "implicit" stride of 2 x 2 = 4)You can easily make this stride bigger (by a multiplicative factor), by setting a stride > 1 in the top convolutional layer for example.But reducing the stride is a bit "awkward". You could have a stride of 1 by setting the stride to 1 in both pooling layers (that is to say to remove them...). Then the model is not the same : if you remove (or change) one pooling layer, you "invalidate" the weights that are learned after.So the only solution i see if you REALLY want a stride of 1 is running the same network 16 times (!) and interleaving the results to reconstitute the output. You can save some computation by not recomputing what comes before the first pooling layer (i.e. the first convolution and it's non-linearity). If you have fixed-size images, there is a way to put everything into a unique network, sharing layers with NetInsertSharedArrays, and using PartLayer to shift the image representations when you need to.
Posted 2 months ago
We should probably advertise NetReplacePart[net, "Input" -> Automatic] For LeNet you can do NetReplacePart[ NetDrop[ NetModel["LeNet Trained on MNIST Data", EvaluationNet"], -5 ], "Input" -> Automatic] and get
Posted 2 months ago
Ah yes. Thanks! This is used in my follow up question.
Posted 2 months ago
Thanks Jerome. So it's not feasible to realistically reduce the stride.I hope this similar topic will also interest you. What about sliding this denoising autoencoder? size = 157; n1 = 32; k = 5; conv2[n_] := NetChain[{ConvolutionLayer[n, k, "Stride" -> 2], BatchNormalizationLayer[], ElementwiseLayer["ReLU"], DropoutLayer[], ConvolutionLayer[n, k, "Stride" -> 2], BatchNormalizationLayer[], ElementwiseLayer["ReLU"]}]; deconv2[n_] := NetChain[{DeconvolutionLayer[n, k, "Stride" -> 2], BatchNormalizationLayer[], ElementwiseLayer["ReLU"], DropoutLayer[], DeconvolutionLayer[n/2, k, "Stride" -> 2], BatchNormalizationLayer[], ElementwiseLayer["SoftSign"]}]; sum[] := NetChain[{TotalLayer["Inputs" -> 2]}]; constantPowerLayer[] := NetChain[{ ElementwiseLayer[Log@Clip[#, {\$MachineEpsilon, 1}] &], ConvolutionLayer[1, 1, "Biases" -> None, "Weights" -> {{{{1}}}}], ElementwiseLayer[Exp]}] ddae = NetGraph[ <| "bugworkaround" -> ElementwiseLayer[# &], "c12" -> conv2[n1], "c34" -> conv2[2*n1], "d12" -> deconv2[2*n1], "d34" -> NetChain[{DeconvolutionLayer[n1, k, "Stride" -> 2], BatchNormalizationLayer[], ElementwiseLayer["ReLU"], DeconvolutionLayer[1, k, "Stride" -> 2], BatchNormalizationLayer[], ElementwiseLayer["SoftSign"]}], "sum1" -> sum[], "sum2" -> NetChain[{sum[], constantPowerLayer[]}], "loss" -> MeanSquaredLossLayer[] |>, { "bugworkaround" -> "c12" -> "c34" -> "d12" -> "sum1" -> "d34" -> "sum2" -> NetPort["loss", "Input"], "bugworkaround" -> "sum2", NetPort["Noisy"] -> "bugworkaround", "c12" -> "sum1", NetPort["Target"] -> NetPort["loss", "Target"] }, "Noisy" -> NetEncoder[{"Image", {size, size}, ColorSpace -> "Grayscale"}], "Target" -> NetEncoder[{"Image", {size, size}, ColorSpace -> "Grayscale"}] ] trained = NetTake[NetInitialize@ddae, {"bugworkaround", "sum2"}] Now I "automatize" the input dimensions: n3 = NetReplacePart[trained, "Noisy" -> Automatic]; This new network works fine if given same dimensions, but fails with larger input dimensions. Any idea how to fix this problem? In[142]:= n3[RandomReal[1, {1, 157, 157}]] // Dimensions Out[142]= {1, 157, 157} In[143]:= n3[RandomReal[1, {1, 1570, 1570}]] // Dimensions During evaluation of In[143]:= NetGraph::tyfail1: Inferred inconsistent value for output size of layer 4 of layer "d34". Out[143]= {}
Posted 2 months ago
Cool, auto-encoder with a U-shape!So here the problem is different. The thing is that there are some constraints on the input size to be able to match the same size after going through deconvolutions. There cannot be any border effect.For instance if you give an input of 6, to a kernel of 5 with stride 2, you are going to lose one input, that's what I call border effect. Our framework allows this. But here, you really need to reconstitute the same size after deconvolutions, which you cannot do if you throw away some input features.So your input has to be of size 61 + n * 16 where n is positive or null.And you can see that the construction of "ddae" fails if you use a size that does not satisfy this constraint (such as 1570). It's not a problem from changing the dimensions.So try it with images with size equal to 157 modulo 16 (and not lower than 61)!
Posted 2 months ago
Thanks for this elaboration, Jerome.Are those constraints brought by an underlying third party implementation? It feels like a bug that ConvolutionLayer and DeconvolutionLayer do not interplay well. I know the documentation does not claim otherwise. From my end-user's perspective those so-called "border effects" should be taken care of by the framework.
Posted 2 months ago
Indeed for this auto-encoder use case, some "smart" padding when needed could solve the issue you have with auto-encoders.The support to more forms of padding is in the pipeline to improve the WL framework. We already unlocked some things around padding in the last version. There is a great chance that we will offer support for automatic padding to a constraint of type "m + k * n" in the next version, or another user-friendly solution for efficient support for multi dynamic dimensions. Waiting for this, you can use the cheap solution of padding input images to fit size 61 + n . 16. It can be done using PaddingLayer, for example. You need to prepend this layer to the network for a given image size. It's bit awkward, but you will have no overhead with respect to the current situation, where the size inference and the unrolling of the net is done at top-level each time you apply the network. Again, we will improve how things work for multiple variable dimensions in the next versions.
Posted 2 months ago
Thanks, this is an acceptable workaround. May I ask how you derive this formula, (61+16*n)?By the way, a set of parenthesis is missing in ref/ConvolutionLayer's notes for the output size formula. The Property example gives the correct result. And, I take good note that "the future will be better."
Posted 2 months ago
May I ask how you derive this formula, (61+16*n)? The output length of a convolutional or pooling layer, for a given size of kernel and stride, depending on the input length is this function: layerOutputLength[kernel_, stride_][inputLength_] := (inputLength - kernel)/stride + 1; By inverting this, you get the input length depending on the output length: layerInputLength[kernel_, stride_][outputLength_] := stride * (outputLength - 1) + kernel; There is 4 times layers with kernel size 5 and stride 2 in your auto-encoder. So the input size corresponding to a length 1 in the upper level (where the image dimension is the smallest) is obtained by computing 4 times inputLength[5, 2] starting from outputLength= 1: netInputLength[outputLength_] := Nest[ layerInputLength[5, 2], outputLength, 4 ]; netInputLength[1] Out[4]= 61 This is the minimal input length, so that nothing is lost, and the length is 1 in the "most narrow part" of the network.Then the "global stride" is just the multiplication of all the strides, so 2^4 = 16.This value of the global stride can be check by looking how bigger the input length must be to produce a "most narrow part" of length +1: netInputLength[2] - netInputLength[1] netInputLength[3] - netInputLength[2] netInputLength[4] - netInputLength[3] Out[5]= 16 Out[6]= 16 Out[7]= 16 You can check all these equations by drawing what happens on a piece of paper =)
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# Is building a test instance from a mix of both mock and real objects OK?
I am new to android testing and would like to try start off in the correct direction, so I am trying to understand if this is the correct way to test a particular method or if there is some best practice that I should be following.
Here are some snippets of the class that contains the method I would like to test.
public class MapMarker implements Target {
private Bus mBus;
private RailsMarker mMarker;
private Bitmap mBitmap;
public String getGravatarUrl() {
return mMarker.getGravatarUrl();
}
public String getUserId() {
return mMarker.getUserId();
}
@Override
System.out.println(String.format("loaded bit map from gravatar url = %s, for userid = %s",getGravatarUrl(), getUserId()));
mBitmap = bitmap;
}
}
I am trying to test that when the onBitMapLoaded method is called, it posts a MarkerReadyEvent onto my eventbus.
Here is the test method I coded.
@Test
Bus mockBus = mock(Bus.class);
RailsMarker railsMarker = new RailsMarkerBuilder().withGravatarUrl("a_gravatar_url")
.withUserId("a_user_id")
.build();
MapMarker androidMapMarker = new MapMarkerBuilder().withBus(mockBus)
.withMarker(railsMarker)
.build();
}
I am using Mockito to mock the eventbus. I am creating a real instance of the MapMarker class (via https://github.com/mkarneim/pojobuilder) I am also creating a RailsMarker instance to be included in the MapMarker instance. (I realized this in only needed for the println statement but I did not want to remove it just to make the test easier)
Is this a good approach or is there some other pattern I should be following? The part that seems a bit strange is that I end up building the instance I am going to test with both a mock object (the Bus) and a real object (the RailsMarker), but I don't see anyway around this.
You would be testing the MapMarker more in isolation if you would inject only mocks.
Isolation is important for two things:
1. stability of test results
2. more explicit and direct feedback
If a bug would be introduced in the RailsMarker, this test would also fail, causing it to be less stable. In case of this bug, there would by multiple test failures (also for RailsMarker and possibly other tests that use this class) making it harder to find the bug.
In general I would use mocks for any dependant object that has more logic than just getters and setters. That being said, it looks like the RailsMarker might qualify.
• OK, so I guess I would do that by building my MapMarker instance with mock of the RailsMarker object that "implements" only the methods that are needed (getGravatarUrl() and getUserId()) to get thru the onBitMapLoaded method? I am not used to using mocks, so I need to learn how to effectively use them – nPn Aug 10 '14 at 23:25
• @nPn yes, you build the mock in the same way, but you need to expect on it using when and specify the return value you want the mock to return. – Maarten Winkels Aug 10 '14 at 23:28
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As in past years, here's a roundup of what's been happening in the data structures and algorithms (cs.DS) section of arXiv.org. Over the last year, there were 1340 new algorithms preprints on arXiv; that's up about 13% from 1182 in 2014. The explosive growth rate of this section has been gradually diminishing over the years, but this time it didn't: it's higher than 2014's 10% growth rate. Statistics on arXiv submissions more generally are also available.
I picked out the following ten papers (listed chronologically) as being particularly interesting to me. I'm not going to claim that they're in any objective sense the best of the year. Nevertheless I hope they're interesting to others as well.
• "A $$(1+\epsilon)$$-embedding of low highway dimension graphs into bounded treewidth graphs", arXiv:1502.04588, by Feldmann, Fung, Könemann, and Post, ICALP 2015. The highway dimension of a graph models a natural property of road networks according to which, if you go far enough from some starting point, there are only a few different ways that your initial path can go. For instance, I used to live in Santa Barbara, where there are only three ways out of town: east or west along the coast on Highway 101, or north over the mountains on San Marcos Pass Road. (One rainy year, all three were blocked simultaneously.) The same phenomenon happens both on smaller and larger scales. This paper connects this theory with deep results in metric embedding and graph structure theory, allowing many more graph problems to be approximated efficiently on low-highway-dimension graphs. It appears closely related to Feldmann's second ICALP 2015 paper which used metric embeddings as part of approximation algorithms for graphs of low highway dimension.
• "Clustered integer 3SUM via additive combinatorics", arXiv:1502.05204, by Chan and Lewenstein, STOC 2015. The 3SUM problem is the following: you're given a collection of numbers and you want to test whether some triple of them sums to zero. A naive algorithm would take cubic time but with a little care it can be solved in quadratic time instead; for a long time that was believed to be optimal, and this assumption was used to show lower bounds on many other algorithmic problems. The quadratic time bound was broken recently by Williams at STOC'14, but the improvement was in a lower-order term, not the quadratic main exponent of the time bound. This paper gives a bigger break, with exponents bounded below two, although only for some special cases: small integer values, or subsets of a preprocessed set of integers.
• "Faster 64-bit universal hashing using carry-less multiplications", arXiv:1503.03465, by Lemire and Kaser. I already posted briefly about this, but the basic idea is that modern CPUs now include instructions for doing arithmetic in GF2[x] (the ring of polynomials over the binary field), and this can be used to make a high-quality hash function very fast.
• "If the current clique algorithms are optimal, so is Valiant's parser", arXiv:1504.01431, by Abboud, Backurs, and Williams, FOCS 2015. Clique-finding and context-free grammar parsing are both among the problems that can be sped up using fast matrix multiplication: a $$k$$-clique in an $$n$$-vertex graph can be found in time $$O(n^{k\omega/3}),$$ and a grammar of size $$g$$ with an $$n$$-symbol input string can be parsed in time $$O(n^{\omega}),$$ where ω is the exponent of fast matrix multiplication. Now this paper shows that the two problems are related: any additional speedup of grammar parsing would also speed up clique-finding, even for grammars of constant size. This is a big improvement on previous lower bounds for context-free parsing which were conditional and required non-constant grammars.
• "A faster pseudopolynomial time algorithm for subset sum", arXiv:1507.02318, by Koiliaris and Xu. The textbook algorithm for subset sum takes time $$O(nK)$$ where $$n$$ is the number of input items (assumed to be positive integers) and $$K$$ is the sum to be achieved. This paper reduces the dependence on $$n$$ to the square root.
• "Tight bounds for subgraph isomorphism and graph homomorphism", arXiv:1507.03738, by Fomin, Golovnev, Kulikov, and Mihajlin, to appear next week at SODA 2016. Subgraph isomorphism is the problem of finding one graph as a subgraph of another. It includes as special cases $$\mathsf{NP}$$-hard problems such as finding cliques or Hamiltonian cycles, but when the subgraph to be found has a small number $$k$$ of vertices, it can be solved in time $$n^{O(k)}.$$ This paper proves a lower bound of the same form, conditional on the exponential time hypothesis, the assumption that there is no subexponential algorithm for Boolean satisfiability.
• "The 4/3 additive spanner exponent is tight", arXiv:1511.00700, by Abboud and Godwin. This is part of a line of research on approximating distances in arbitrary unweighted graphs by sparse graphs, so accurately that the error is only additive rather than multiplicative. It seemed that there was a tradeoff between the number of edges in the sparse graph and the accuracy of approximation: you could decrease the exponent of the number of edges (relative to the number of vertices) at the expense of a bigger addiitive error. But the best result of this type known was that with error at most 6 you could get a spanner with only $$O(n^{4/3})$$ edges. Now it seems that the tradeoff stops here: fewer edges will necessarily cause an additive error that grows as a power of $$n$$ rather than staying constant.
• "Which regular expression patterns are hard to match?", arXiv:1511.07070, by Backurs and Indyk. The obvious answer is "none of them" because regular-expression matching has a low polynomial time bound. But it's quadratic (the product of the expression length and the input length), while some special cases such as matching a collection of dictionary words can be solved much more quickly (e.g. by building a DFA and then running it). This paper proves a strong dichotomy (assuming the exponential time hypothesis) between expressions that require near-quadratic time and expressions that take only near-linear time.
• "Optimal dynamic strings", arXiv:1511.02612, by Gawrychowski, Karczmarz, Kociumaka, Łącki, and Sankowski. The usual ways of representing strings take time linear in the string length to form new strings by concatenating or splitting the existing ones, and linear time to compare two strings or find the first position at which they differ. This paper gives a data structure for the same operations that takes logarithmic time per update and constant time per query.
• "Graph isomorphism in quasipolynomial time", arXiv:1512.03547, by Babai. So much has already been written about this one. Need I say more? But there is more: I've seen some statistics on most-downloaded papers on the arXiv (too rough to link to), and this is the cs.DS representative on the list, with tens of thousands of accesses. So obviously it's getting read far beyond its own specialized research community.
None: CV
2016-01-06T12:16:29Z
Some Computer Vision and Machine Learning conferences require submission to be put on arxiv and available for public commenting for improvement and the authors are expected to address the public comments and improve their paper before the final decision about them are made. So essentially every paper ends up on arxiv and gets discussed and improved before the conference. At conference they have a few main talks and a small number of 20min talks and some poster spotlights where authors of interesting posters do a sales speech for their poster in less than 5min. People go to the conference not for papers but mainly for networking. Things that theory might also want to experiment with.
11011110: RE: CV
2016-01-06T20:10:59Z
A larger number of the heavily-downloaded arXiv papers were in cs.CV and cs.LG — what you describe may have something to do with why.
ext_3462100: The Subgraph Isomorphism paper
2016-01-06T20:35:38Z
The Subgraph Isomorphism paper of Fomin, Golovnev, Kulikov, and Mihajlin got merged at SODA with a paper of Cygan, Pachocki, and Socała, which is also on arxiv: http://arxiv.org/abs/1504.02876 . As far as I know, the two groups worked independently and there is an alternating sequence of preprints on arxiv that improve one another. The story eventually ended in a merge at SODA that settles the complexity once and for all.
11011110: RE: The Subgraph Isomorphism paper
2016-01-06T21:18:17Z
Interesting — thanks for the info.
ext_3462162: A faster pseudopolynomial time algorithm for subset sum
2016-01-06T21:32:35Z
Glad to read that our work caught your eye David! I just wanted to say we are currently working on an updated draft with cleaner writing, simpler algorithm presentation and easier analysis.
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Article Contents
Article Contents
# Derivation of a rod theory from lattice systems with interactions beyond nearest neighbours
RA and GL received funding from the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). When this research was carried out, GL was affiliated to SISSA and supported by the European Research Council under the Grant No. 290888 "Quasistatic and Dynamic Evolution Problems in Plasticity and Fracture"; he was then affiliated to the University of Vienna and supported by the Austrian Science Fund (FWF) project P27052. MP was partially supported by the EU Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie project ModCompShock agreement No. 642768
• We study continuum limits of discrete models for (possibly heterogeneous) nanowires. The lattice energy includes at least nearest and next-to-nearest neighbour interactions: the latter have the role of penalising changes of orientation. In the heterogeneous case, we obtain an estimate on the minimal energy spent to match different equilibria. This gives insight into the nucleation of dislocations in epitaxially grown heterostructured nanowires.
Mathematics Subject Classification: Primary: 74B20; Secondary: 74K10, 74E15, 74G65, 49J45.
Citation:
• Figure 1. The six tetrahedra in the Kuhn decomposition of a three-dimensional cube
Figure 2. Two possible recovery sequences for the profile at the centre of the figure. Here we picture only a part of the wire containing just one species of atoms, therefore the transition at the interface is not represented. A kink in the profile may be reconstructed by folding the strip, i.e., mixing rotations and rotoreflections (left); or by a gradual transition involving only rotations or only rotoreflections (right). In the limit, the former recovery sequence gives a positive cost, while the latter gives no contribution. If the stronger topology is chosen, the appropriate recovery sequence will depend on the value of the internal variable, which defines the orientation of the wire
Figure 3. Lattices with dislocations: choice of the interfacial nearest neighbours in $\mathcal{L}_\varepsilon(\rho, k)$ and $H \mathcal{L}_\varepsilon(\rho, k)$ for a Delaunay triangulation
• R. Alicandro , A. Braides and M. Cicalese , Continuum limits of discrete thin films with superlinear growth densities, Calc. Var. Partial Differential Equations, 33 (2008) , 267-297. doi: 10.1007/s00526-008-0159-4. R. Alicandro, G. Lazzaroni and M. Palombaro, On the effect of interactions beyond nearest neighbours on non-convex lattice systems, Calc. Var. Partial Differential Equations, 56 (2017), Art. 42, 19 pp. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 2000. A. Braides, $Γ$ -convergence for Beginners, Oxford University Press, Oxford, 2002. A. Braides and M. Cicalese , Surface energies in nonconvex discrete systems, Math. Models Methods Appl. Sci., 17 (2007) , 985-1037. doi: 10.1142/S0218202507002182. A. Braides and M. Solci , Asymptotic analysis of Lennard-Jones systems beyond the nearest-neighbour setting: A one-dimensional prototypical case, Math. Mech. Solids, 21 (2016) , 915-930. doi: 10.1177/1081286514544780. M. Charlotte and L. Truskinovsky , Linear elastic chain with a hyper-pre-stress, J. Mech. Phys. Solids, 50 (2002) , 217-251. doi: 10.1016/S0022-5096(01)00054-0. G. Dal Maso, An Introduction to $Γ$ -convergence, Birkhäuser, Boston, 1993. E. Ertekin, P. A. Greaney, D. C. Chrzan and T. D. Sands, Equilibrium limits of coherency in strained nanowire heterostructures, J. Appl. Phys., 97 (2005), 114325. doi: 10.1063/1.1903106. S. Fanzon , M. Palombaro and M. Ponsiglione , A variational model for dislocations at semi-coherent interfaces, J. Nonlinear Sci., 27 (2017) , 1435-1461. doi: 10.1007/s00332-017-9366-5. I. Fonseca, N. Fusco, G. Leoni and M. Morini, A model for dislocations in epitaxially strained elastic films, J. Math. Pures Appl., to appear (2018). G. Friesecke , R. D. James and S. Müller , A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity, Comm. Pure Appl. Math., 55 (2002) , 1461-1506. doi: 10.1002/cpa.10048. K. L. Kavanagh, Misfit dislocations in nanowire heterostructures, Semicond. Sci. Technol., 25 (2010), 024006. doi: 10.1088/0268-1242/25/2/024006. G. Lazzaroni , M. Palombaro and A. Schlömerkemper , A discrete to continuum analysis of dislocations in nanowire heterostructures, Commun. Math. Sci., 13 (2015) , 1105-1133. doi: 10.4310/CMS.2015.v13.n5.a3. G. Lazzaroni , M. Palombaro and A. Schlömerkemper , Rigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires, Discrete Contin. Dyn. Syst. Ser. S, 10 (2017) , 119-139. M. G. Mora and S. Müller , Derivation of a rod theory for multiphase materials, Calc. Var. Partial Differential Equations, 28 (2007) , 161-178. S. Müller and M. Palombaro , Derivation of a rod theory for biphase materials with dislocations at the interface, Calc. Var. Partial Differential Equations, 48 (2013) , 315-335. doi: 10.1007/s00526-012-0552-x. B. Schmidt , On the passage from atomic to continuum theory for thin films, Arch. Ration. Mech. Anal., 190 (2008) , 1-55. doi: 10.1007/s00205-008-0138-0. V. Schmidt , J. V. Wittemann and U. Gösele , Growth, thermodynamics, and electrical properties of silicon nanowires, Chem. Rev., 110 (2010) , 361-388. doi: 10.1021/cr900141g.
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# American Institute of Mathematical Sciences
July 2013, 12(4): 1569-1585. doi: 10.3934/cpaa.2013.12.1569
## Uniqueness for elliptic problems with Hölder--type dependence on the solution
1 Dipartimento di Matematica, Università di Roma 1, Piazza A. Moro 2, 00185 Roma 2 Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scienti ca 1, 00133 Roma
Received May 2011 Revised June 2012 Published November 2012
We prove uniqueness of weak (or entropy) solutions for nonmonotone elliptic equations of the type \begin{eqnarray} -div (a(x,u)\nabla u)=f \end{eqnarray} in a bounded set $\Omega\subset R^N$ with Dirichlet boundary conditions. The novelty of our results consists in the possibility to deal with cases when $a(x,u)$ is only Hölder continuous with respect to $u$.
Citation: Lucio Boccardo, Alessio Porretta. Uniqueness for elliptic problems with Hölder--type dependence on the solution. Communications on Pure & Applied Analysis, 2013, 12 (4) : 1569-1585. doi: 10.3934/cpaa.2013.12.1569
##### References:
[1] M. Artola, Sur une classe de problèmes paraboliques quasi-linéaires,, Boll. U.M.I. B., 5 (1986), 51. Google Scholar [2] P. Bénilan, L. Boccardo, T. Gallouët, R. Gariepy, M. Pierre and J. L. Vàzquez, An $L^1$ theory of existence and uniqueness of nonlinear elliptic equations,, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 22 (1995), 240. Google Scholar [3] D. Blanchard, F. Désir and O. Guibé, Quasi-linear degenerate elliptic problems with $L^1$ data,, Nonlinear Anal., 60 (2005), 557. doi: 10.1016/S0362-546X(04)00395-5. Google Scholar [4] L. Boccardo, Some nonlinear Dirichlet problems in $L^1$ involving lower order terms in divergence form,, Progress in elliptic and parabolic partial differential equations (Capri, (1994), 43. Google Scholar [5] L. Boccardo, Uniqueness of solutions for some nonlinear Dirichlet problems,, dedicated to M. Artola, (). Google Scholar [6] L. Boccardo, A remark on some nonlinear elliptic problems,, 2001-Luminy Conference on Quasilinear Elliptic and Parabolic Equations and Systems, Conf. 08 (2002), 47. Google Scholar [7] L. Boccardo and B. Dacorogna, Monotonicity of certain differential operators in divergence form,, Manuscripta Math., 64 (1989), 253. doi: 10.1007/BF01160123. Google Scholar [8] L. Boccardo, I. Diaz, D. Giachetti and F. Murat, Existence of a solution for a weaker form of a nonlinear elliptic equation,, in, 208 (1988), 229. Google Scholar [9] L. Boccardo and T. Gallouët, Nonlinear elliptic equations with right hand side measures,, Comm. P.D.E., 17 (1992), 641. doi: 10.1080/03605309208820857. Google Scholar [10] L. Boccardo, T. Gallouët and F. Murat, Unicité de la solution pour des equations elliptiques non linéaires,, C. R. Acad. Sc. Paris, 315 (1992), 1159. Google Scholar [11] J. Carrillo and M. Chipot, On some elliptic equations involving derivatives of the nonlinearity,, Proc. Roy. Soc. Edinburgh, 100 (1985), 281. doi: 10.1017/S0308210500013822. Google Scholar [12] J. Casado Diaz, F. Murat and A. Porretta, Uniqueness results for pseudomonotone problems with $p>2$,, C. R. Math. Acad. Sci. Paris, 344 (2007), 487. doi: 10.1016/j.crma.2007.02.007. Google Scholar [13] M. Chipot and G. Michaille, Uniqueness results and monotonicity properties for strongly nonlinear elliptic variational inequalities,, Ann. Sc. Norm. Sup. Pisa, 16 (1989), 137. Google Scholar [14] A. Dall'Aglio, Approximated solutions of equations with $L^1$ data. Application to the H-convergence of quasi-linear parabolic equations,, Ann. Mat. Pura Appl., 170 (1996), 207. doi: 10.1007/BF01758989. Google Scholar [15] O. Guibé, Uniqueness of the solution to quasilinear elliptic equations under a local condition on the diffusion matrix,, Adv. Math. Sci. Appl., 17 (2007), 357. Google Scholar [16] O. Guibé, Uniqueness of the renormalized solution to a class of nonlinear elliptic equations,, in, 23 (2008), 459. Google Scholar [17] A. G. Kartsatos and I. V. Skrypnik, The index of a critical point for nonlinear elliptic operators with strong coefficient growth,, J. Math. Soc. Japan, 52 (2000), 109. doi: 10.2969/jmsj/05210109. Google Scholar [18] C. Leone and A. Porretta, Entropy solutions for nonlinear elliptic equations in $L^1$,, Nonlinear Anal., 32 (1998), 325. doi: 10.1016/S0362-546X(96)00323-9. Google Scholar [19] M. Marcus and V. J. Mizel, Every superposition operator mapping one Sobolev space into another is continuous,, J. Funct. Anal., 33 (1979), 217. doi: 10.1016/0022-1236(79)90113-7. Google Scholar [20] A. Porretta, Uniqueness and homogenization for a class of noncoercive operators in divergence form,, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), 915. Google Scholar [21] A. Porretta, Uniqueness of solutions for some nonlinear Dirichlet problems,, NoDEA Nonlinear Differential Equations Appl., 11 (2004), 407. doi: 10.1007/s00030-004-0031-y. Google Scholar [22] A. Porretta, Some remarks on the regularity of solutions for a class of elliptic equations with measure data,, Houston J. Math., 26 (2000), 183. Google Scholar [23] M. M. Porzio, A uniqueness result for monotone elliptic problems,, C. R. Math. Acad. Sci. Paris, 337 (2003), 313. doi: 10.1016/S1631-073X(03)00347-9. Google Scholar [24] N. Trudinger, On the comparison principle for quasilinear divergence structure equations,, Arch. for Rat. Mech. Anal., 57 (1975), 128. doi: 10.1007/BF00248414. Google Scholar
show all references
##### References:
[1] M. Artola, Sur une classe de problèmes paraboliques quasi-linéaires,, Boll. U.M.I. B., 5 (1986), 51. Google Scholar [2] P. Bénilan, L. Boccardo, T. Gallouët, R. Gariepy, M. Pierre and J. L. Vàzquez, An $L^1$ theory of existence and uniqueness of nonlinear elliptic equations,, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 22 (1995), 240. Google Scholar [3] D. Blanchard, F. Désir and O. Guibé, Quasi-linear degenerate elliptic problems with $L^1$ data,, Nonlinear Anal., 60 (2005), 557. doi: 10.1016/S0362-546X(04)00395-5. Google Scholar [4] L. Boccardo, Some nonlinear Dirichlet problems in $L^1$ involving lower order terms in divergence form,, Progress in elliptic and parabolic partial differential equations (Capri, (1994), 43. Google Scholar [5] L. Boccardo, Uniqueness of solutions for some nonlinear Dirichlet problems,, dedicated to M. Artola, (). Google Scholar [6] L. Boccardo, A remark on some nonlinear elliptic problems,, 2001-Luminy Conference on Quasilinear Elliptic and Parabolic Equations and Systems, Conf. 08 (2002), 47. Google Scholar [7] L. Boccardo and B. Dacorogna, Monotonicity of certain differential operators in divergence form,, Manuscripta Math., 64 (1989), 253. doi: 10.1007/BF01160123. Google Scholar [8] L. Boccardo, I. Diaz, D. Giachetti and F. Murat, Existence of a solution for a weaker form of a nonlinear elliptic equation,, in, 208 (1988), 229. Google Scholar [9] L. Boccardo and T. Gallouët, Nonlinear elliptic equations with right hand side measures,, Comm. P.D.E., 17 (1992), 641. doi: 10.1080/03605309208820857. Google Scholar [10] L. Boccardo, T. Gallouët and F. Murat, Unicité de la solution pour des equations elliptiques non linéaires,, C. R. Acad. Sc. Paris, 315 (1992), 1159. Google Scholar [11] J. Carrillo and M. Chipot, On some elliptic equations involving derivatives of the nonlinearity,, Proc. Roy. Soc. Edinburgh, 100 (1985), 281. doi: 10.1017/S0308210500013822. Google Scholar [12] J. Casado Diaz, F. Murat and A. Porretta, Uniqueness results for pseudomonotone problems with $p>2$,, C. R. Math. Acad. Sci. Paris, 344 (2007), 487. doi: 10.1016/j.crma.2007.02.007. Google Scholar [13] M. Chipot and G. Michaille, Uniqueness results and monotonicity properties for strongly nonlinear elliptic variational inequalities,, Ann. Sc. Norm. Sup. Pisa, 16 (1989), 137. Google Scholar [14] A. Dall'Aglio, Approximated solutions of equations with $L^1$ data. Application to the H-convergence of quasi-linear parabolic equations,, Ann. Mat. Pura Appl., 170 (1996), 207. doi: 10.1007/BF01758989. Google Scholar [15] O. Guibé, Uniqueness of the solution to quasilinear elliptic equations under a local condition on the diffusion matrix,, Adv. Math. Sci. Appl., 17 (2007), 357. Google Scholar [16] O. Guibé, Uniqueness of the renormalized solution to a class of nonlinear elliptic equations,, in, 23 (2008), 459. Google Scholar [17] A. G. Kartsatos and I. V. Skrypnik, The index of a critical point for nonlinear elliptic operators with strong coefficient growth,, J. Math. Soc. Japan, 52 (2000), 109. doi: 10.2969/jmsj/05210109. Google Scholar [18] C. Leone and A. Porretta, Entropy solutions for nonlinear elliptic equations in $L^1$,, Nonlinear Anal., 32 (1998), 325. doi: 10.1016/S0362-546X(96)00323-9. Google Scholar [19] M. Marcus and V. J. Mizel, Every superposition operator mapping one Sobolev space into another is continuous,, J. Funct. Anal., 33 (1979), 217. doi: 10.1016/0022-1236(79)90113-7. Google Scholar [20] A. Porretta, Uniqueness and homogenization for a class of noncoercive operators in divergence form,, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), 915. Google Scholar [21] A. Porretta, Uniqueness of solutions for some nonlinear Dirichlet problems,, NoDEA Nonlinear Differential Equations Appl., 11 (2004), 407. doi: 10.1007/s00030-004-0031-y. Google Scholar [22] A. Porretta, Some remarks on the regularity of solutions for a class of elliptic equations with measure data,, Houston J. Math., 26 (2000), 183. Google Scholar [23] M. M. Porzio, A uniqueness result for monotone elliptic problems,, C. R. Math. Acad. Sci. Paris, 337 (2003), 313. doi: 10.1016/S1631-073X(03)00347-9. Google Scholar [24] N. Trudinger, On the comparison principle for quasilinear divergence structure equations,, Arch. for Rat. Mech. Anal., 57 (1975), 128. doi: 10.1007/BF00248414. Google Scholar
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Compton Wavelength
Discussion in 'Physics & Math' started by Harmony, Jan 10, 2012.
1. HarmonyHarmonyRegistered Senior Member
Messages:
84
The Compton Wavelength (source Wikipedia) is defined as follows: "The Compton Wavelength of a particle is equivalent to the wavelength of a photon whose energy is the same as the rest mass energy of the particle".
The formula is h/mc which can easily be derived from: E=hv, E=mc^2.
The Compton Wavelength for the proton is 1.3214098 x 10^-15m
The charge radius for the proton is given as 0.877551 x 10^-15m
If we consider the proton as a wave then it must comprise a whole number of wavelengths and the largest number of wavelengths that fit within the charge radius is 4 (n X wavelength < 2 PI r). The wave radius can then be calculated as 0.8412356 x 10^-15m
This models the proton as a wave of 4 wavelengths at the gamma radiation end of the spectrum.
Is this a valid conclusion?
Harmony
3. Farsight
Messages:
3,492
No. The Compton wavelength is the wavelength. Check out the trefoil knot to get an idea of how it "fits". Follow the knot round and look at the crossing over directions: up up and down.
5. AlphaNumericFully ionizedRegistered Senior Member
Messages:
6,698
You assume the wave goes along the diameter. Why should it be so? What does it give you?
Farsight, if you wish to peddle your pseudoscience there is a forum for it. Start a thread there.
7. HarmonyHarmonyRegistered Senior Member
Messages:
84
In my calculation I am assuming that the wave goes along the circumference since I have taken 2 PI times the radius in the calculation. The approach is similar to the analysis of bound electrons in the atom where it was found that the electrons must consist of a whole number of wavelengths. The electrons were assumed to comprise waves in a circular (or in some cases elliptical) path in this case.
Harmony
8. Farsight
Messages:
3,492
It has to go twice round the circumference, Harmony. The wave is the only thing there, it has to go at least twice round to bind itself. Take a look at this depiction from "Is the electron a photon with a toroidal topology?" by Williamson and van der Mark, Annales de la Fondation Louis de Broglie, Volume 22, no.2, 133 (1997). The dark line represents one complete wavelength.
There's a somewhat similar description at http://arxiv.org/abs/physics/0512265
9. Farsight
Messages:
3,492
In addition there's a guy called Andrew Worsley who's written a quantum harmonics paper that’s very interesting. It’s called Harmonic quintessence and the derivation of the charge and mass of the electron and the proton and quark masses, and is in Physics Essays Jun 2011, Vol. 24, No. 2 pp. 240-253. See this web page. He’s applying spherical harmonics, usually applied to electron orbitals, to the particles themselves. I think he's really onto something with this. Look at the depiction above, and imagine an "equatorial" rotation going round at c and another orthogonal "polar" rotation at ½c. It's a bit like a moebius strip, and the electron is a spin ½ particle where 720 degrees are required to return to the original state.
Andrew gives the electron Compton wavelength as λ = 4π / n c^1½ metres, where n is a dimensionality conversion factor with a value of 1. He also gives the proton/electron mass ratio r = c^½ / 3π. Both expressions are subject to small binding-energy adjustments, but here's the raw numbers:
4π = 12.566370
c = 299792458
c^½ = 17314.5158177
4π / c^1½ = 12.566370 / (299792458 * 17314.5158177)
λ = 2.420910 x 10ˉ¹² m
Actual = 2.426310 x 10ˉ¹² m
c^½ = 17314.5158177
3π = 9.424778
c^½ / 3π = 17314.5158177 / 9.424778
r = 1837.12717877
Actual = 1836.15267245
10. rpennerFully WiredValued Senior Member
Messages:
4,833
It's intersting numerological pseudoscience, not physics.
Physics Essays is not a peer-reviewed scientific journal of good repute. (It uses the term "reviewed by scientific peers" but this is not described as a filtering process.) It has an impact factor of less than a third of a niche journal like Ukrainskii Fizicheskii Zhurnal which caters to a specific nationality, which is evidence that publishing here is largely a sterile backwater unconnected with progress in physics. Seeking to publish here is merely aping the form of science without the content.
40% self-references is far in excess of the norm. Of the remaining 6 references, they are window dressing as Worsley rejects their methodology and has nowhere shown that it is capable of working with their models.
No, he is not applying spherical harmonics. Using π in calculations is not "applying spherical harmonics". Spherical harmonics are not "usually applied to electron orbitals," but are used in any mathematical treatment where orthogonal decomposition of function spaces, spherical symmetry and calculus are used. Spherical harmonics are very important to the treatment of the analytical treatment of the quantum mechanics of a particle in a central potential which is the first degree of approximation used in textbook treatments of 1-electron atoms and ions like hydrogen, but this is not because spherical harmonics are magically connected with physics. Rather it expresses that the electrostatic potential of a point source has spherical symmetry and so spherical harmonics form a basis of expressing the angular dependence of classes of functions in this potential.
Even after I've exposed the numerological trickery in earlier threads?
To be clear that's a movement at speed $\frac{\sqrt{5}}{2} \textrm{c}$ > c, and is not the motion of a rigid body. Nor does this fanciful imagining relate to a framework for making predictions about nature from this assumption.
No. It's a superluminal toroidal surface without a model that predicts that the motion is a stable mode of motion or connection with a physics of interaction so that the assumption can be validated or invalidated.
This is true of the electron phase in conventional quantum field theory, but not true of tori or Möbius strips or of the observable electron probability distribution. You can't steal from Dirac's model of point-like electrons and declare electrons are tori in the same cognitive framework. You must demonstrate that your tori are useful in deriving this claim.
This is pure numerology, not physics. In the English Imperial system (where c is written as such-and-such miles per second, n is not 1, and so "Andrew"'s contention is that the SI units are physically special where there is no reason to suspect that they are. Actually, if you actually parse Worsley's books, he employs surreptitious fudge factors (usually written as * by Worsley) to tweak these results so that n is not exactly 1. Not understanding how units work in engineering or physics is a symptom of over-dependence on calculators.
Again with the * notation in Worsley's book and again this only works by ignoring units and blessing the SI units as the units of the universe.
Calling Worsley's ad hoc fudge factors "binding energy adjustments" requires a methodology to calculate them from a model. Worsley's model is pure numerology in that Worsley justifies these factors needed to close up the difference between first stab without calculation and just a self-serving patter.
In physics, if you aren't working with units then you aren't manipulating physical quantities. Just like you can't say 1+2 = 12 and then subtract 9 as a fudge factor based on the time of day, you can't remove and add units when it suits your purpose.
In physics, calculations which aren't based on a model are sterile of predictive value.
Therefore this is not physics.
11. Farsight
Messages:
3,492
Spherical harmonics are used to describe the wave function of the electron in a hydrogen atom, rpenner. See this page which features a number of depictions. And you have not "exposed the numerological trickery in earlier threads", you made an unsupported allegation in an attempt to discredit something you do not understand.
I see that you remain stubbornly unaware that in an atomic orbital the electrons "are more accurately described as standing waves". Or that we can make electrons (and positrons) in pair production from a light wave, and then we can annihilate them to obtain light waves again. Or that the electron exhibits a magnetic dipole moment and can be diffracted, and that the Einstein-de Haas effect demonstrates that "spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics". The list goes on. We have good experimental evidence that the electron is a standing-wave structure.
In the light of this, and in the light of how you deliberately ignore the dimensionality conversion factor n, I'm afraid your post comes over as dismissive carping from an envious naysayer. You sound like the sort of person who would reject a novel paper because it poses some kind of threat to your standing, then denigrate the author for settling for a low-impact journal. Exactly the sort of person, in fact, who is "unconnected with progress in physics". I would recommend that you desist, and instead apply yourself with sincerity to the quantum harmonics of particle structure.
12. AlphaNumericFully ionizedRegistered Senior Member
Messages:
6,698
No one is denying spherical harmonics are used in quantum mechanics, they are in some of the simplest quantum systems, which are taught in introductory courses in quantum mechanics. Rpenner's response wasn't "There's no spherical harmonics in quantum mechanics!" it was "That work isn't an application of spherical harmonics". Didn't you read what he said?
Furthermore your comments about numerology are completely wrong. The things you refer to are numerology, if you don't understand that then your level of understanding is even worse than basic quantum mechanics, it's stuff A Level students know about.
Like I said Farsight, if you want to peddle pet theories of yours and make delusional claims about understanding you don't have, take it to one of the pseudo forums. Last warning.
13. RJBeeryNatural PhilosopherValued Senior Member
Messages:
4,136
AlphaNumeric and rpenner, I'm curious about something: completely disregarding for the moment Worsley, Farsight, etc, and presuming there's a valid modeling for it...does the idea of an electron consisting of a self-contained EM wave appeal to you?
14. Farsight
Messages:
3,492
Alphanumeric: the guy asked a question, I answered it. Nobody else has. The papers I've referred to have appeared in journals, and the scientific evidence in post 8 above is robust. So please don't try the "delusional pseudoscience" your-pet-theory line. It doesn't sound too good coming from a string theorist. People might think you're trying to close down physics discussions instead of moderating them.
RJ: Of course it doesn't. If it did, rpenner would be getting stuck in telling us about toroidal harmonics, and Alphanumeric wouldn't be making threats.
15. RJBeeryNatural PhilosopherValued Senior Member
Messages:
4,136
I'm just curious because I find the idea quite beautiful. It might give a physical description for 1/2 spin charge and the "boundary measurement" issue, for example. I haven't studied the math above but this isn't the first time (or even the 5th!) that I've seen this suggestion made from various sources. As I said earlier there is a local retired EE professor that wrote a book on the idea, my copy of which I've been looking for in vain...if I can find it perhaps I can post his math.
16. rpennerFully WiredValued Senior Member
Messages:
4,833
That must be why I wrote:
Examples of hydrogen-like ions are $\textrm{He}^{+}, \,\textrm{Li}^{++}, \, \textrm{Be}^{+++}, \, \dots$ which validate the approximation of the 1-electron atoms as a particle in a spherical potential. Other details like spin-spin and spin-orbital interactions slightly alter this simple treatment to make the model correspond better with our understanding of electromagnetism and Dirac-modeled electrons. These improvements also lead to better agreement with the spectroscopic data of rarified atomic hydrogen gas and plasma of the other nearly completely ionized elements. Both electromagnetic effects and Pauli exclusion have removed the multi-electron atom from such simple analysis and so in general numerical methods and not expansion in terms of functions based on spherical harmonics is used in the fields of quantum and computational chemistry.
In short, unless you are comfortable in manipulating eigenfunctions and the approximations made in early quantum treatments of the atom, spherical harmonics do you no good and are not demonstrated as being applied by Farsight or Worsley. They are specifically used in the analytic treatment of the approximate hydrogen atom because when written in spherical coordinates this problem is seperable into a radial part and and an angular dependence, which is a topic in differential equations -- math that is not being used in Worsley's or Farsight's calculations.
Pointing to pictures does nothing to further your argument when I did not deny that spherical harmonics were used in some cases to study electron eigenfunctions.
To review, from post 180 of the thread "Lattices and Lorentz invariance" I demonstrated that there are physical expressions which are coincidentally close to a numerical value of 1 in SI units. This doesn't mean that they are 1 since they have units attached to them.
$A = \frac{27 \pi^2 h }{4 m_{\tiny \textrm{electron}} c} \left( \frac{m_{\tiny \textrm{proton}}}{m_{\tiny \textrm{electron}}} \right)^3 \; \approx \; 1.000636 \, \textrm{m}$
$B = \left( \frac{m_{\tiny \textrm{electron}}}{m_{\tiny \textrm{proton}}} \right)^2 \frac{c}{9\pi^2} \; \approx \; 1.001062 \, \textrm{m} \textrm{s}^{\tiny -1}$
But A not numerically close 1 in cgs or Imperial systems. A is about 100.06 cm or 39.40 inches or 0.00062 miles.
And B is not numerically close to 1 in other systems, being about 100.1062 cm/s or 2.239 mph.
And while $4 \pi A B^{\tiny \frac{3}{2}} c^{\tiny -\frac{3}{2}}$ is (by definition) the Compton wavelength of the atom $\frac{h}{m_{\tiny \textrm{electron}} c}$, the Worsley-derived expression $4 \pi c^{\tiny -\frac{3}{2}}$ is physically unrelated and has bizarre units of $\textrm{m}^{\tiny -\frac{3}{2}} \, s^{\tiny \frac{3}{2}}$.
Likewise $\frac{1}{3 \pi} B^{\tiny -\frac{1}{2}} c^{\tiny \frac{1}{2}}$ is the proton-electron mass ratio, but the Worsley-derived expression $\frac{1}{3 \pi}c^{\tiny \frac{1}{2}}$ is physically meaningless and has bizarre units of $\textrm{m}^{\tiny \frac{1}{2}} \, s^{\tiny -\frac{1}{2}}$. We don't have names for such collections of fractional units because nothing we observe has those combinations. But even if we did, that fact is $\textrm{m}^{\tiny -\frac{3}{2}} \, s^{\tiny \frac{3}{2}}$ is not a length and $\textrm{m}^{\tiny \frac{1}{2}} \, s^{\tiny -\frac{1}{2}}$ is not dimensionless.
From Post 184 of that thread I demonstrated that two claims depend on $D = \frac{4 \pi ( g_e - 1 )^8 c^3 e^2}{\varepsilon_0} \approx 0.99998 \, \textrm{kg} \, \textrm{m}^{\tiny 6} \, \textrm{s}^{\tiny - 5}$ being conveniently close numerically 1 in SI units, but it is close to $10^{15}$ in cgs units.
Your misunderstanding of physics jargon in Wikipedia articles isn't at issue here. Your are operating below my tree-level understanding of quantum electrodynamics which covers all the ground exposed by those entries.
No -- we have good experimental evidence that the electron is well-modeled by a field of Dirac (massive) fermions coupled to a vector field of massless bosons. An electron in a well-defined energy state in a stationary potential is something that is well-modeled by a standing wave -- but that does not apply to free electrons.
The metaphorical light of evidence more strongly favors the position that you choose to walk in darkness.
How have I ignored it, when I pointed out to you first that your expressions were garbage. Also, in this thread I directly addressed you new introduction of "n" when I wrote:
Why we can even compute what n is from just my earlier posts. $n=A^{\tiny -1} \, B^{\tiny -\frac{3}{2}} = \frac{4 m_{\tiny \textrm{electron}} c}{27 \pi^2 h } \left( \frac{m_{\tiny \textrm{electron}}}{m_{\tiny \textrm{proton}}} \right)^3 \; \times \; \left( \frac{m_{\tiny \textrm{proton}}}{m_{\tiny \textrm{electron}}} \right)^3 \frac{27\pi^3}{c^{\tiny \frac{3}{2}}} = \frac{4 \pi m_{\tiny \textrm{electron}} c}{h c^{\tiny \frac{3}{2}}} = \frac{4 \pi}{\lambda_{\textrm{Compton}} \, c^{\tiny \frac{3}{2}}$ with units of $\textrm{m}^{\tiny -\frac{5}{2}} \, \textrm{s}^{\tiny \frac{3}{2}}$. It's close to 1 in SI units, but close to 0.0000093333 in cgs units or 449 $\textrm{mile}^{\tiny -\frac{5}{2}} \, \textrm{hour}^{\tiny \frac{3}{2}}$
Am I envious or am I protecting my standing? Can you have it both ways? I've read Worsley's self-published book and know just how shallow and sterile his ideas are. And I don't need to siphon Wikipedia or the source of your illustrations to make my arguments since I can type them up from my working understanding of physics.
It appears he jumped straight to assaination of my character rather than attempt to demonstrate the manner in which spherical harmonics were applied in the Worsley-derived expressions.
In the US, I cannot understand how one would expect to complete even an AP (high school course and exam which results in limited college credit) program in physics without mastering the need of understanding units. To understand 1 meter is distinct from 1 mile which is distinct from 1 second would seem to be material mastered by a six-year old. But Worsley, simply tells us to ignore that distinction because he is not interested in relating to the world of physical measurement and reality.
Huzzah! Mark this well!
Actually, I got stuck. While I think you can describe toroidal motions with constant rates of angular motion, and this closes like in the diagram (whenever a/b is rational and 0 < S < R ), but the speed is not constant.
$x(t) = \left( R + S \cos (a t + a_0) \right) \cos b t \, \; y(t) = \left( R + S \cos (a t + a_0) \right) \sin b t , \; z(t) = S \sin (a t + a_0)$
$\left| v(t) \right| = \sqrt{a^2 S^2 + \left( b R + b S cos(a t + a_0) \right)^2}$
Similarly, for "diagonal" motion on a torus embedded in $\mathbb{R}^3$ with constant speed, I don't see that you are guaranteed to have the paths close as indicated in your diagram, unless you ignore the embedded speed and work in coordinates where the torus is flat. But in that case, you beggar the notion of movement.
17. AlphaNumericFully ionizedRegistered Senior Member
Messages:
6,698
I have no problem with the concept of the electron being composite and actually formed of something else. However, no model has been put forth which can produce as an effective theory something very closely approximating quantum electrodynamics (I wait for someone to fail to grasp what I just said....) or any experimental evidence hinting at internal structure. As such I don't put any more stock in the concept than I do any other proposal with similar levels of reasoning (ie none). It's something, if I were an experimental particle physicist, I'd not exclude in my considerations if there was some anomalous behaviour observed in electron processes but I wouldn't devote time to computing such effects before hand on the off chance it was observed.
Firstly a paper being in a journal doesn't make it sound. Or can I use your logic to assume you fully accept string theory? Or are you just picking and choosing when "It's in a journal" is enough? And what about all your work which was rejected from journals?
And your numerology isn't robust, it's nonsense. If something has units than by picking different units, like feet instead of metres or lunar months instead of seconds, you can make a quantity with units become anything. As Rpenner has now demonstrated multiple times.
The work you refer to has minimal impact in the community and in the case of your numerology is flat out pseudoscience. And your work, which includes similar concepts, has been roundly rejected from everywhere you've submitted it. It cannot model anything, it cannot provide a single quantitative testable description of any phenomenon so yes, your work is delusional pseudoscience.
String theory has contributed vastly more to our understanding of physics than anything you've managed. It's improved our understanding of Planck scale gravitational processes, black holes, strongly coupled gauge theory, specifically QCD and condensed matter.
And I can assure you, I do much more physics than you do. Quantum mechanics, fluid mechanics, Newtonian physics, thermodynamics, to name a few things. All applied to real world problems. And in each case I can point to something from my string theory days which proved useful in terms of approaches or methods I wouldn't otherwise have considered. Sorry Farsight, you can't play the "You're only a string theorist" card, some of us do stuff with real world applications and even when I was 'just' a string theorist my work had more physical applicability than anything you've managed.
Here's a suggestion for not looking like a hypocrite and a hack. Next time you play the "You're just a string theorist" card please provide a working model of a real world phenomenon derived from your work which has accurate predictions for said phenomenon, including with it the derivation of the model from within your work. I've been asking you for years now and its something which any 'real' physics should include. You have never provided it and thus any attack you make on things like string theory for supposedly being maths not physics is sheer hypocrisy. You've been asked enough time and your repeated statement of "You're only a string theorist" as an attempt at an insult you now know to be false. As such if you do it again and fail to provide what I've just asked for I'll consider it trolling. Shouldn't be too hard for you to provide it if your work has any relevance to the real world. You've had enough chances to do it in the past, now it's time to step up or shut up.
Numerology belongs in the pseudoscience section, that is what it is there for. So I'm not silencing you, I'm telling you the more appropriate place for such claims.
You really have no idea about how any of us view science and ideas, probably because you have such a warped view of things yourself and you project.
As I keep asking you for in regards to your claims, if someone can justify a model which has a decent description of observed phenomena then I'll listen to it. At present no one has one for an electron with internal structure, just like you don't have anything in regards to your claims. Two things will catch my interest, evidence or elegance. Your claims have neither. Neither does the notion of a composite/internal structure electron but that's something fairly broad, while your claims are far too specific and involved given the complete lack of evidence or elegance and thus they aren't in the "Not proven false, don't exclude in considerations" category a composite electron would be in in my mind.
You need to stop projecting your inability to think beyond your own point of view onto others. Remember, you're the one who thinks he's worth 4 Nobel Prizes and is more knowledgeable in electromagnetism than Dirac, an actual Nobel Prize winner. You're hardly in a position to be calling the attitudes of others into question without bringing down a ton of hypocrisy on your head.
18. Farsight
Messages:
3,492
It's certainly worth looking into and discussing. What's the boundary measurement issue?
If you could list those other sources I'd be grateful. It seems as if a fair few people have suggested this kind of thing, all with a different slant, but all recognisable as "the same elephant". However this elephant seems to have been studiously ignored or even censored and disparaged by vested interest, for want of a better term. It's a science advances one death at a time thing. Physics is a battle of ideas, people are people, and they fight dirty. They come out with things like there's been no such model so any such model is clearly crackpot, QED. It's catch-22 logic that condemns physics to more decades of stagnation.
You should make contact with him, talk to him, and find out his story. I'll wager there'll be some bitterness there. I'm interested in that book, please let me know if you can dig out the title.
19. RJBeeryNatural PhilosopherValued Senior Member
Messages:
4,136
The elusive nature of the structure itself. Is it a ball? A cloud? A point particle? A "ball of light" consisting of a localized field would, in a way, describe all three of those things.
Did you read Kuhn's book on scientific revolutions? He makes this point pretty hard and clear. Science has camps, and it progresses by the next generation adhering to a particular camp rather than existing views actually getting changed. Scientists are no better at accepting change than anyone else. MotorDaddy isn't stubborn because he's a crank (no offense, MD
), it's just human nature that we all share.
20. przyksquishyValued Senior Member
Messages:
3,173
Er, no, if you put the idea in front of a competent physicist, and let them speak for themself instead of putting strawman arguments in their mouth, they'll be able to point out some real obstacles to incorporating the idea into mainstream physics. You know this because you've personally had some of them explained to you on this very forum, most recently throughout [THREAD=110674]this thread[/THREAD]. Here's a reminder:
First, if we're only considering classical electromagnetism:
• Maxwell's equations are linear. An immediate consequence of this is that propagating wavepackets approaching one another from opposite directions will simply pass through each another instead of scattering or otherwise interacting. Particles modeled as classical EM waves will fail to exhibit any interactions.
• Maxwell's equations are dilation invariant. That means that if you try to model a particle as a certain wavepacket, Maxwell's equations predict that the same wavepacket, scaled up by any arbitrary factor, is also possible. So if e.g. electrons were a certain kind of classical EM wave, there would be no reason they should all be same size or all have the same mass.
You could imagine fixing these issues by introducing nonlinearities into Maxwell's equations, though you'd have to be able to explain precisely what nonlinearities you need and show that they get you results compatible with experimental data (or more simply, mainstream theories). Here are some issues that are less easy to imagine fixing just by modifying classical electrodynamics:
• Much of the apparent similarity between classical waves and quantum mechanical wavefunctions disappears when you start considering multi-particle quantum states. In particular, classical waves don't seem to promise the possibility of describing anything analogous to an entangled quantum state.
• I could also throw in the permutation symmetry of identical bosons and the antisymmetry of identical fermions here, the latter of which is behind Pauli exclusion in quantum theory.
• Some quantum degrees of freedom, such as spin states, are discrete and don't resemble what the word "wave" normally brings to mind.
If you're willing to leave classical physics behind and work within the framework of quantum theory, there are still a couple of problems:
• Electrons are spin half particles. Photons are spin one particles. In quantum physics it is fundamentally impossible to compose a half integer spin state out of integer spin states.
• Related to this: it is impossible to construct antisymmetric (fermionic) quantum states out of symmetric (bosonic) ones. By the spin-statistics theorem, this is the same problem as the one just above.
• This one's not my area of expertise, but I'm pretty sure the photon self-interaction terms you'd need would break EM gauge symmetry (in QED this is the principle used to derive the electron-photon interaction), and I'd imagine you'll find they're non-renormalisable.
So you'll have to forgive us physicists for being a bit skeptical. As they say, ignorance is bliss. In physics we're cursed with the sort of experience I've just described above.
21. AlphaNumericFully ionizedRegistered Senior Member
Messages:
6,698
Farsight, if you're going to make up stuff about professional physicists it's a good idea to do it somewhere which isn't frequented by professional physicists.
You put words in my mouth and I responded to counter you. Now you're repeating the same nonsense. I can understand you have an axe to grind given the rejection of your work by everyone with a decent physics education but you need to realise that being dishonest and misrepresenting people isn't going to help your case.
Physics hasn't stagnated, that's a demonstrably false proposition. What you are probably referring to is theoretical physics but that hasn't stagnated either. It's in a rare situation where the models of the 70s/80s have been so successful that they haven't had any serious experimental problems, rather their predictions have been confirmed. Perhaps the most unfortunate thing for theoretical physics novelty would be finding the Higgs, so regardless of the LHC results it'll be good news to many in the community.
In fact, the guy who used to be head of LEP, the previous accelerator at CERN, described his job as 'Looking for things physicists don't want me to find' because pushing over someone's models with unexpected experimental results is great for physics.
Just because people dismiss your work doesn't mean we're close minded. I've repeatedly asked you for just one working model of some phenomenon (your choice!) which you can derive from your work. You cannot provide one. Now you've banged on about how laughable and dead you think string theory is for, in your eyes, having precisely that problem. You demand we hold work to a standard and then complain when your is held to that standard and found to fail.
You have a very warped view of the attitude of scientists, just as you have a warped view of physics, experiments and your own grasp of things (or lack there of).
22. RJBeeryNatural PhilosopherValued Senior Member
Messages:
4,136
Thanks, przyk, this kind of information fascinates me. You'll need to be very forgiving here, because what follows is a layman's hand wavy positing after his first pass on an unfamiliar subject...
EM waves may not interact with each other in passing but they do interfere. I now understand why Farsight mentions Falaco Solitons. They're composed of nothing but water waves, which shouldn't interact, but if you bring two of them together spinning in opposite directions they annihilate each other. In the case of balls of light, if we consider EM waves to be essentially "twisted space", isn't there a chance that the rotating nature of the twisted space does something similar? Perhaps there's simply a difference between linear propagation of waves and "rotating" ones? It sure seems to me that two whirlpools would interact!
Wouldn't the quantum nature of the EM wave being brought back onto itself prevent arbitrary scaling? It would have to trace its path in an integer number of cycles and in my mind I'm not seeing how we could just "make everything a little bit bigger" because you are still constrained by c, etc.
This is closer to what I spend my time working on. I have some ideas here that I've never shared but I believe may have the smallest budding of merit.
The spin would not reside in the wave itself. It would reside in the configuration of its potentially complex orbital path (e.g. handedness, number of twists, turns, etc)
This could potentially be related to my comment above.
If the integer spin of a boson is an intrinsic property, are you certain we cannot formulate a spin one-half fermion if we include orbital motion of the boson, thereby becoming "intrinsic" to the fermion itself?
I completely understand resistance to new ideas, it's human nature as I mentioned. If it was within my power, though, I'd get you, AN, rpenner, etc to use your tools to try coming up with creative solutions to the objections you raise rather than just presenting them.
23. rpennerFully WiredValued Senior Member
Messages:
4,833
Of the three alternatives listed,
1a) if we are talking about movement with constant velocity on a "flat" torus, represented as rectangle with certain conditions on the boundary, then such motion has no relation to our 3 dimensional world and Farsight has failed to say something meaningful about his own topic.
1b) if we are talking about constant rates of angular parameters in the above parametric diagram (a special case of 1a) then while the path can close on itself, the motion cannot be constant as Farsight described it.
2) if we are talking about a curved torus, a surface in 3 dimensional space, then such a torus is not flat. Motion with a constant velocity which respects that curvature are the geodesics of a torus, and only special cases close on themselves. Only very special cases have constant ratios of velocities, the outer equator (d=R+S), the inner equator (d=R-S), and the meridians (d=0). None of these look like the diagram Farsight uses.
$x(t) = \left( R + S \cos a(t) \right) \cos b(t) \, \; y(t) = \left( R + S \cos a(t) \right) \sin b(t) , \; z(t) = S \sin a(t), \; \frac{da}{dt} = \pm \frac{v}{S}\sqrt{ \frac{R + S \cos a(t) - d^2}{R + S \cos a(t)} }, \; \frac{db}{dt} = \frac{v d}{\left(R + S \cos a(t) \right)^2}, \; 0 \le \left| d \right| \le R + S$
http://www.rdrop.com/~half/math/torus/torus.geodesics.pdf
Last edited: Jan 12, 2012
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# Search by Topic
#### Resources tagged with Mathematical reasoning & proof similar to Em'power'ed:
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### Plus or Minus
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Make and prove a conjecture about the value of the product of the Fibonacci numbers $F_{n+1}F_{n-1}$.
### A Biggy
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Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.
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Let a(n) be the number of ways of expressing the integer n as an ordered sum of 1's and 2's. Let b(n) be the number of ways of expressing n as an ordered sum of integers greater than 1. (i) Calculate. . . .
### Sums of Squares and Sums of Cubes
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An account of methods for finding whether or not a number can be written as the sum of two or more squares or as the sum of two or more cubes.
### How Many Solutions?
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Find all the solutions to the this equation.
### Sixational
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The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. . . .
### Modulus Arithmetic and a Solution to Dirisibly Yours
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Peter Zimmerman from Mill Hill County High School in Barnet, London gives a neat proof that: 5^(2n+1) + 11^(2n+1) + 17^(2n+1) is divisible by 33 for every non negative integer n.
### Three Frogs
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Three frogs hopped onto the table. A red frog on the left a green in the middle and a blue frog on the right. Then frogs started jumping randomly over any adjacent frog. Is it possible for them to. . . .
### Perfectly Square
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The sums of the squares of three related numbers is also a perfect square - can you explain why?
### Number Rules - OK
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Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...
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Tom writes about expressing numbers as the sums of three squares.
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Investigate the sequences obtained by starting with any positive 2 digit number (10a+b) and repeatedly using the rule 10a+b maps to 10b-a to get the next number in the sequence.
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Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares.
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Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.
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Find all real solutions of the equation (x^2-7x+11)^(x^2-11x+30) = 1.
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A polite number can be written as the sum of two or more consecutive positive integers. Find the consecutive sums giving the polite numbers 544 and 424. What characterizes impolite numbers?
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Which is the biggest and which the smallest of $2000^{2002}, 2001^{2001} \text{and } 2002^{2000}$?
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Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
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Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
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Take a complicated fraction with the product of five quartics top and bottom and reduce this to a whole number. This is a numerical example involving some clever algebra.
### Square Pair Circles
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Investigate the number of points with integer coordinates on circles with centres at the origin for which the square of the radius is a power of 5.
### On the Importance of Pedantry
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A introduction to how patterns can be deceiving, and what is and is not a proof.
### Rational Roots
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Given that a, b and c are natural numbers show that if sqrt a+sqrt b is rational then it is a natural number. Extend this to 3 variables.
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Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
### Where Do We Get Our Feet Wet?
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Professor Korner has generously supported school mathematics for more than 30 years and has been a good friend to NRICH since it started.
### Try to Win
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Solve this famous unsolved problem and win a prize. Take a positive integer N. If even, divide by 2; if odd, multiply by 3 and add 1. Iterate. Prove that the sequence always goes to 4,2,1,4,2,1...
### L-triominoes
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L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?
### Whole Number Dynamics V
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The final of five articles which containe the proof of why the sequence introduced in article IV either reaches the fixed point 0 or the sequence enters a repeating cycle of four values.
### Yih or Luk Tsut K'i or Three Men's Morris
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Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and. . . .
### A Long Time at the Till
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Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?
### More Dicey Decisions
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The twelve edge totals of a standard six-sided die are distributed symmetrically. Will the same symmetry emerge with a dodecahedral die?
### Picturing Pythagorean Triples
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This article discusses how every Pythagorean triple (a, b, c) can be illustrated by a square and an L shape within another square. You are invited to find some triples for yourself.
### Transitivity
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Suppose A always beats B and B always beats C, then would you expect A to beat C? Not always! What seems obvious is not always true. Results always need to be proved in mathematics.
### The Clue Is in the Question
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This problem is a sequence of linked mini-challenges leading up to the proof of a difficult final challenge, encouraging you to think mathematically. Starting with one of the mini-challenges, how. . . .
### Breaking the Equation ' Empirical Argument = Proof '
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This article stems from research on the teaching of proof and offers guidance on how to move learners from focussing on experimental arguments to mathematical arguments and deductive reasoning.
### Geometric Parabola
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Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.
### Modulus Arithmetic and a Solution to Differences
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Peter Zimmerman, a Year 13 student at Mill Hill County High School in Barnet, London wrote this account of modulus arithmetic.
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An article which gives an account of some properties of magic squares.
### Recent Developments on S.P. Numbers
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Take a number, add its digits then multiply the digits together, then multiply these two results. If you get the same number it is an SP number.
### Advent Calendar 2011 - Secondary
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Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
### A Knight's Journey
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This article looks at knight's moves on a chess board and introduces you to the idea of vectors and vector addition.
### Pythagorean Triples I
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The first of two articles on Pythagorean Triples which asks how many right angled triangles can you find with the lengths of each side exactly a whole number measurement. Try it!
### Proof of Pick's Theorem
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Follow the hints and prove Pick's Theorem.
### Little and Large
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A point moves around inside a rectangle. What are the least and the greatest values of the sum of the squares of the distances from the vertices?
### Why 24?
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Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.
### What Numbers Can We Make Now?
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Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
### Take Three from Five
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Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
### Pythagorean Triples II
##### Stage: 3 and 4
This is the second article on right-angled triangles whose edge lengths are whole numbers.
### Particularly General
##### Stage: 5 Challenge Level:
By proving these particular identities, prove the existence of general cases.
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## Albert0898 one year ago HELP ME understand problems like these. Any tricks, tips, formulas? Thanks! Umberto is a newspaper delivery boy. He delivers newspapers every day of the week. On Sunday, his first day on the job, he delivered newspapers to 18 houses in his neighborhood. Each day afterward, his delivery route included 7 more houses than it did the previous day. How many total newspapers did Umberto deliver in his first 2 weeks on the job?
1. anonymous
on first day, no. of newspaper dilivered= 18 on second day = 18+7= 25 on third day = 25+7= 32 therefore, this forms an AP => 18, 25, 32 ........ where a=18 ; d=7 thus no. of newspaper been delivered in first 2 weeks i.e. 14 days = $\frac{ n }{ 2 }*[2a + (n-1)d]$
2. anonymous
put a= 18, n=14, d=7 and u will get the answer...
3. Albert0898
Ah yes! Thanks!
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Popular
# Analysis of algorithm implementations by Gregory Robert Ruth
Written in English
## Subjects:
• Computer programming.
Edition Notes
## Book details
Classifications The Physical Object Statement by Gregory Robert Ruth. Contributions Project MAC (Massachusetts Institute of Technology) LC Classifications QA76.6 .R88 Pagination 271 p. ; Number of Pages 271 Open Library OL4224437M LC Control Number 80504367
The book gives instructors the flexibility to emphasize different aspects--design, analysis, or computer implementation--of numerical algorithms, depending on the background and interests of by: This book is intended for the students of & Analysis of algorithm implementations book (CSE/IT), & ME (CSE/IT), MCA, (CS/IT).
This book includes: Fundamental Concepts on Analysis of algorithm implementations book Framework for Algorithm Analysis. Hardware- as well as software-oriented algorithms are presented, together with a pertinent analysis of accurate floating-point implementations Good examples are always chosen in order to introduce or to illustrate the methods, following the given : Birkhäuser Basel.
Comparative Analysis of Genetic Algorithm Implementations Robert S., Melvin N. Paper, SIGAda, November 14–18,Atlanta, Georgia, USA.
Genetic Algorithms provide computational procedures that are modeled on natural genetic system mechanics, whereby a coded solution is evolved from a set of potential solutions, known as a population. The C, C++, Fortran, and Pascal code for all algorithm implementations mentioned is on the accompanying CD rather than in the book itself, which helps make the book more compact.
This book is a very good introduction to the methods of algorithm analysis and design, and an encyclopedic reference on many different types of s: Algorithm analysis is concerned with comparing algorithms based upon the amount of computing resources that each algorithm uses.
We want to be able to consider two algorithms and say that one is better than the other because it is more efficient in its use of those resources or perhaps because it simply uses fewer.
Good algorithm designers understand several fundamental algorithm design techniques, including data structures, dynamic programming, depth first search, backtracking, and heuristics. This book explains basic concepts with Pseudocode.
The Pseudocode can be transferred to any programming language without much struggle. For a topic such as a particular sorting algorithm, an OpenDSA module (like a typical textbook presentation) contains both material on the dynamic behavior of the algorithm, and analytical material in the form of a runtime analysis (that is, the “algorithm analysis”) of that algorithm.
Analysis of algorithm is the process of analyzing the problem-solving capability Analysis of algorithm implementations book the algorithm in terms of the time and size required (the size of memory for storage while implementation).
However, the main concern of analysis of algorithms is the required time or performance. Generally, we perform the following types of analysis −. Solutions for Introduction to algorithms second edition Philip Bille The author of this document takes absolutely no responsibility for the contents.
This is merely a vague suggestion to a solution to some of the exercises posed in the book Introduction to algo-rithms by Cormen, Leiserson and Rivest. The book gives instructors the flexibility to emphasize different aspects--design, analysis, or computer implementation--of numerical algorithms, depending on 5/5(1).
Array-Based List Implementation Linked Lists Comparison of List Implementations This book describes many techniques for representing data. These principles of algorithm analysis, and also an appreciation for the significant effects of the physical medium employed (e.g., data stored on disk versus.
In this equation, $$u(t)$$ is a scalar function of time t, a is a constant (in this book we mostly work with a > 0), and $$u^{\prime}(t)$$ means differentiation with respect to type of equation arises in a number of widely different phenomena where some quantity u undergoes exponential reduction (provided a > 0).Examples include radioactive decay, population decay, investment decay.
3 Algorithm Analysis 53 Introduction 53 Best, Worst, and Average Cases 59 A Faster Computer, or a Faster Algorithm. 60 Asymptotic Analysis 63 Upper Bounds 63 Lower Bounds 65 Notation 66 Simplifying Rules 67 Classifying Functions 68 Calculating the Running Time for a Program 69 Analyzing.
We introduce the union–find data type and consider several implementations (quick find, quick union, weighted quick union, and weighted quick union with path compression). Finally, we apply the union–find data type to the percolation problem from physical chemistry.
Lecture 2: Analysis of Algorithms. Offered as an introduction to the field of data structures and algorithms, the book covers the implementation and analysis of data structures for sequences (lists), queues, priority queues, unordered dictionaries, ordered dictionaries, and graphs.
Search Algorithms and Applications: Nashat Mansour – InTech. When we run the above algorithm, 2 things can occur. The first is that we will find the key. The second is that we won't.
The worst case scenario occurs when key is not in the array. Thus, let us start by performing the analysis base on that worst case. Analysis of an Unsuccessful Search. Let n represent the size of the array arr. ^ Book Data Structures And Algorithm Analysis In C ^ Uploaded By Leo Tolstoy, data structures and algorithm analysis in c by mark allen weiss preface chapter 1 introduction chapter 2 algorithm analysis chapter 3 lists stacks and queues chapter 4 trees chapter 5 hashing chapter 6 priority queues heaps chapter 7 sorting chapter 8 the.
rithm analysis. For the analysis, we frequently need ba-sic mathematical tools. Think of analysis as the measure-ment of the quality of your design. Just like you use your sense of taste to check your cooking, you should get into the habit of using algorithm analysis to justify design de-cisions when you write an algorithm or a computer pro-gram.
The Bug and Bug-like algorithms are straightforward to implement; moreover, a simple analysis shows that their success is guaranteed, when possible. These algorithms require two behaviors: move on a straight line and follow a boundary.
Approx algorithms [Read Chapter ] Apr. 11 Lecture Randomized algorithms, Basic probability. Contention resolution [Read Chapter and ] Hw 6 Released ; Apr. 16 Lecture Randomized algorithms, MAX-3SAT, Quicksort [Read Chapter ] Apr.
18 Lecture Approx/randomized algorithms. Appendix E, which summarizes the analysis of set-membership algorithm Updated problems and references Providing a concise background on adaptive filtering, this book covers the family of LMS, affine projection, RLS and data-selective set-membership algorithms as well as nonlinear, sub-band, blind, IIR adaptive filtering, and more.
THIS book is intended to be a thorough overview of the primary tech-niques used in the mathematical analysis of algorithms. e material covered draws from classical mathematical topics, including discrete mathe-matics, elementary real analysis, and combinatorics, as well as from classical.
Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms - Ebook written by Anne Greenbaum, Tim P.
The book teaches a broad variety of algorithms and data structures and pro-vides sufficient information about them that readers can confidently implement, debug, and put them to work in any computational environment.
The approach involves: Algorithms. Our descriptions of algorithms are based on complete implementations and on.
Bubble sort, sometimes referred to as sinking sort, is a simple sorting algorithm that repeatedly steps through the list, compares adjacent elements and swaps them if they are in the wrong order. The pass through the list is repeated until the list is sorted. The algorithm, which is a comparison sort, is named for the way smaller or larger elements "bubble" to the top of the list.
Efficient implementations of Quicksort are not a stable sort, meaning that the relative order of equal sort items is not preserved.
Mathematical analysis of quicksort shows that, on average, the algorithm takes O(n log n) comparisons to sort n items. In the worst case, it. It is going to depend on what level of education you currently have and how thorough you want to be. When I started on this, I had little mathematical comprehension so most books were impossible for me to penetrate.
Being % self-taught, and now. Too big Most books on these topics are at least pages, and some are more than By focusing on the topics I think are most useful for software engineers, I kept this book under pages. Too \bottom up" Many data structures books focus on how data struc-tures work (the implementations), with less about how to use them (the interfaces).
Contents Preface xiii I Foundations Introduction 3 1 The Role of Algorithms in Computing 5 Algorithms 5 Algorithms as a technology 11 2 Getting Started 16 Insertion sort 16 Analyzing algorithms 23 Designing algorithms 29 3 Growth of Functions 43 Asymptotic notation 43 Standard notations and common functions 53 4 Divide-and-Conquer 65 The maximum-subarray.
~ Best Book Data Structures And Algorithm Analysis In C ~ Uploaded By Roger Hargreaves, data structures and algorithm analysis in c by mark allen weiss preface chapter 1 introduction chapter 2 algorithm analysis chapter 3 lists stacks and queues chapter 4 trees chapter 5 hashing chapter 6 priority queues heaps chapter 7 sorting.
Implementing a machine learning algorithm in code can teach you a lot about the algorithm and how it works. In this post you will learn how to be effective at implementing machine learning algorithms and how to maximize your learning from these projects. Let's get started. Benefits of Implementing Machine Learning Algorithms You can use the implementation of machine learning algorithms.
Basic techniques for designing and analyzing algorithms: dynamic programming, divide and conquer, balancing. Upper and lower bounds on time and space costs, worst case and expected cost measures. A selection of applications such as disjoint set union/find, graph algorithms.
Algorithm B: Opens the book in the middle and checks the first word on it. If the word that you are looking for is alphabetically bigger, then it looks in the right half. Otherwise, it looks in the left half.
Which one of both is faster. While algorithm A goes word by word O(n), algorithm B splits the problem in half on each iteration O(log n. This second edition of Data Structures and Algorithms in C++ is designed to provide an introduction to data structures and algorithms, including their design, analysis, and implementation.
The authors offer an introduction to object-oriented design with C++ and design patterns, including the use of class inheritance and generic programming through class and function templates, and retain a.
Book Design And Analysis Of Algorithms Ebook By Sartaj Sahni Ellis Horowitz Book Eventually, you will utterly discover a extra experience and specific problem, then we can implement it in any programming language, meaning that the algorithm is independent DAA - Introduction.
implementations of Ford-Fulkerson augment along a. breadth-first augmenting path: a shortest path in. from. where each edge has weight 1. These implementations would always run relatively fast. Since a breadth-first augmenting path can be found in.
O (E) time, their analysis, which provided the first polynomial-time bound on. Search the book. Enter search terms or a module, class or function name.
Chapter 4 Algorithm Analysis Prim's Algorithm Alternative Implementation; Kruskal's Algorithm. Kruskal's Algorithm; All-Pairs Shortest Paths; Graph Concepts Summary. Graph Concepts Summary. Asymptotic analysis also gives a way to define the inherent difficulty of a problem.
Throughout the book we use asymptotic analysis techniques to estimate the time cost for every algorithm presented. This allows you to see how each algorithm compares to other algorithms for solving the same problem in terms of its efficiency.
time, we need to calculate the memory space required by each algorithm. Analysis of algorithm is the process of analyzing the problem-solving capability of the algorithm in terms of the time and size required (the size of memory for storage while implementation).
However, the main concern of analysis of algorithms is the required time or. We clearly need something which compares two algorithms at the idea level ignoring low-level details such as the implementation programming language, the hardware the algorithm runs on etc.
Showtime! Asymptotic Analysis! Here, we ignore machine dependent constants and instead of looking at the actual running time look at the growth of running time.• The number of operations that an algorithm performs typically depends on the size, n, of its input.
• for sorting algorithms, n is the # of elements in the array • C(n)= number of comparisons • M(n)= number of moves • To express the time complexity of an algorithm, we’ll express the number of operations performed as a function of n.This lab involves the implementation and analysis of 2 array-based sorting algorithms.
As a starting point you will be given the definition and implementation of the class template arrayListType in the file arrayListType.h. Part 1 (40 Points) 1. Implement the member function insertionSort() belonging to the class template arrayListType.
63490 views Tuesday, November 24, 2020
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# Git commit hooks
Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /homepages/3/d35174004/htdocs/tecnocode/wp-content/plugins/latex/latex.php on line 91
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I recently wrote/extended a couple of git commit hooks which have turned out to be rather useful. Once is a fairly standard commit-msg hook to check the format of the first line of a commit message is either "Release version x.y.z", "[tag] Message" or "Bug 123456 — Title":
tags="core|atom|gd|media|build|docs|tests|calendar|contacts|documents|picasaweb|youtube"
test "" != "$(grep -P '^(Release version [0-9]+.[0-9]+.[0-9]+| [\S].+[\S]|Bug [0-9]+ — [\S].+[\S])$' "$1")" || { echo -e >&2 "First line of commit message should be in one of the following formats:\n * 'Bug 123456 — Title'\n * '[tag] Message'\ \n * 'Release version x.y.z'\nValid tags are:\n *${tags//|/\n * }"
exit 1
}
Just define the tags your project allows in the tags variable, separated only by pipes.
The other hook is a pre-commit hook to ensure any new API has a Since: tag if it's got a gtk-doc comment. It's implemented as a modification of the sample pre-commit hook, so here's the diff:
--- /home/philip/Downloads/4m8QcjYs.txt 2010-03-28 19:14:50.432440248 +0100
+++ pre-commit 2010-03-22 20:37:47.612794352 +0000
my $filename; my$reported_filename = "";
my $lineno; + my$in_gtk_doc_comment = 0;
+ my $used_since_tag = 0; sub bad_line { my ($why, $line) = @_; if (!$found_bad) {
@@ -64,6 +68,19 @@
if (/^([<>])\1{6} |^={7}$/) { bad_line("unresolved merge conflict",$_);
}
+ if (/^\s*\/\*\*$/) { +$in_gtk_doc_comment = 1;
+ $used_since_tag = 0; + } + if ($in_gtk_doc_comment && /^\s*\*\*\/$/) { +$in_gtk_doc_comment = 0;
+ if (!$used_since_tag) { + bad_line("new gtk-doc commented API without a Since: tag",$_);
+ }
+ }
+ if ($in_gtk_doc_comment && /\*\s+Since:\s+[0-9]+.[0-9]+.[0-9]+$/) {
+ $used_since_tag = 1; + } } } exit($found_bad);
It looks for the start of a gtk-doc comment block in any added code, and errors if it doesn't find a Since: tag before the end.
Hopefully these'll be useful to somebody. They've both turned out to be more useful to me than I'd hoped, so hopefully my commit messages make a little more sense now. The code for both of them is in the public domain.
# MCUS 0.3.0 released
Just a little note to say that:
1. I'm still alive, and
2. I've released version 0.3.0 of my microcontroller simulator, MCUS.
It's had a UI overhaul, and I've added accessibility support to the custom widgets (and improved it for the rest of the interface too). It's primarily intended for use in schools in the UK who teach A-level electronics, but I suppose it could be adapted to work for other purposes. It can be downloaded as a tarball (source), NSIS installer or ZIP package (for Windows).
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# aliquote
## < a quantity that can be divided into another a whole number of time />
My distro-hopping days had come to an end. I just wanted a system that would let me code, write, and browse the Web. I chose the easy way. — Emacs and Emanuele Severino
2020-11-03: Odd Comments and Strange Doings in Unix. #unix
2020-11-04: Genstat is really one of the only statistical package that I never tried. A few days ago, it came to my attention that there’s also the ASReml R package that I never used for mixed-effect models. #rstats
2020-11-04: I’m sick since 4 days now. Kinda like a flu, except that it’s not really a flu, but just because I have so many medication alongside, I’m just out of order all day long. So I’m left with music (since I can’t really read any book), and now it’s time for a lovely live.
2020-11-04: Lovely digital minimalism, and light TUI themes.
2020-11-04: My preferred color scheme for Stata graphics remains plotplain, although there are many nice alternatives. TIL about stata-scheme-modern. #stata
2020-11-04: Nice textbook for SPSS and R users: Applied Missing Data Analysis. #rstats
2020-11-04: Shrink PDF. Postscript forever.
2020-11-04: The XY Problem. Together with three.sentenc.es, I’m ready for most e-mail solicitations.
2020-11-04: The manuscripts of Edsger W. Dijkstra, 1930–2002 (via John D Cook).
2020-11-06: Another nice textbook on the Design of Experiments and Observational Studies. #rstats
2020-11-06: Still a bit sick. That was the week it was.
2020-11-06: A full-fledged version of Tetris written in Racket.
2020-11-06: Boot volume layout. #apple
2020-11-06: Deprecating scp.
2020-11-13: I’ve been sick for two weeks now: probably a rhinopharyngitis at the beginning, which evolved into sinusitis. It’s getting better now, hopefully I’ll be able to post stuff here and there. Nothing interesting on HN the past few days, I should probably go back to good old RSS feeds which I haven’t check in days.
2020-11-20:
It’s easy to grow disillusioned with tech, even to the point that it appals you. I’ve been using computers since 1988 and the net since 1995 and over time, something’s happened. During the last decade or so, my mind has increasingly been preoccupied with the following thoughts: I’m no longer in control of my computer and my OS. The modern web is a cesspool of tracking scripts, ads, malware and clickbait designed to suck you in and make you stupid. — Subversive Computing
For the real amazement, if you wish to be amazed, is this process. You start out as a single cell derived from the coupling of a sperm and an egg; this divides in two, then four, then eight, and so on, and at a certain stage there emerges a single cell which has as all its progeny the human brain. The mere existence of such a cell should be one of the great astonishments of the earth. People ought to be walking around all day, all through their waking hours calling to each other in endless wonderment, talking of nothing except that cell. — I should have loved biology
2020-11-20: ANOVA: A Short Intro Using R. #rstats
2020-11-20: Mixed Models with R. #rstats
2020-11-20: Paul’s online math notes.
2020-11-24: What a beautiful dashboard for mu4e! #emacs
2020-11-24: Yet another online R textbook: One Way ANOVA with R. #rstats
2020-11-24: Damage Caused by Classification Accuracy and Other Discontinuous Improper Accuracy Scoring Rules.
2020-11-24: Hands-On Machine Learning with R. #rstats
2020-11-26: Principles of Epidemiology in Public Health Practice (3rd ed.).
2020-11-26: P² quantile estimator: estimating the median without storing values.
2020-11-26: Tidy Modeling with R. #rstats
2020-11-26: V7/x86 is a port of the Seventh Edition of the UNIX operating system to the x86 (i386) based PC. #unix
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Copied to
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## G = C4⋊Dic25order 400 = 24·52
### The semidirect product of C4 and Dic25 acting via Dic25/C50=C2
Series: Derived Chief Lower central Upper central
Derived series C1 — C50 — C4⋊Dic25
Chief series C1 — C5 — C25 — C50 — C2×C50 — C2×Dic25 — C4⋊Dic25
Lower central C25 — C50 — C4⋊Dic25
Upper central C1 — C22 — C2×C4
Generators and relations for C4⋊Dic25
G = < a,b,c | a4=b50=1, c2=b25, ab=ba, cac-1=a-1, cbc-1=b-1 >
Smallest permutation representation of C4⋊Dic25
Regular action on 400 points
Generators in S400
(1 52 140 190)(2 53 141 191)(3 54 142 192)(4 55 143 193)(5 56 144 194)(6 57 145 195)(7 58 146 196)(8 59 147 197)(9 60 148 198)(10 61 149 199)(11 62 150 200)(12 63 101 151)(13 64 102 152)(14 65 103 153)(15 66 104 154)(16 67 105 155)(17 68 106 156)(18 69 107 157)(19 70 108 158)(20 71 109 159)(21 72 110 160)(22 73 111 161)(23 74 112 162)(24 75 113 163)(25 76 114 164)(26 77 115 165)(27 78 116 166)(28 79 117 167)(29 80 118 168)(30 81 119 169)(31 82 120 170)(32 83 121 171)(33 84 122 172)(34 85 123 173)(35 86 124 174)(36 87 125 175)(37 88 126 176)(38 89 127 177)(39 90 128 178)(40 91 129 179)(41 92 130 180)(42 93 131 181)(43 94 132 182)(44 95 133 183)(45 96 134 184)(46 97 135 185)(47 98 136 186)(48 99 137 187)(49 100 138 188)(50 51 139 189)(201 276 313 377)(202 277 314 378)(203 278 315 379)(204 279 316 380)(205 280 317 381)(206 281 318 382)(207 282 319 383)(208 283 320 384)(209 284 321 385)(210 285 322 386)(211 286 323 387)(212 287 324 388)(213 288 325 389)(214 289 326 390)(215 290 327 391)(216 291 328 392)(217 292 329 393)(218 293 330 394)(219 294 331 395)(220 295 332 396)(221 296 333 397)(222 297 334 398)(223 298 335 399)(224 299 336 400)(225 300 337 351)(226 251 338 352)(227 252 339 353)(228 253 340 354)(229 254 341 355)(230 255 342 356)(231 256 343 357)(232 257 344 358)(233 258 345 359)(234 259 346 360)(235 260 347 361)(236 261 348 362)(237 262 349 363)(238 263 350 364)(239 264 301 365)(240 265 302 366)(241 266 303 367)(242 267 304 368)(243 268 305 369)(244 269 306 370)(245 270 307 371)(246 271 308 372)(247 272 309 373)(248 273 310 374)(249 274 311 375)(250 275 312 376)
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50)(51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100)(101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150)(151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200)(201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250)(251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300)(301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350)(351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400)
(1 359 26 384)(2 358 27 383)(3 357 28 382)(4 356 29 381)(5 355 30 380)(6 354 31 379)(7 353 32 378)(8 352 33 377)(9 351 34 376)(10 400 35 375)(11 399 36 374)(12 398 37 373)(13 397 38 372)(14 396 39 371)(15 395 40 370)(16 394 41 369)(17 393 42 368)(18 392 43 367)(19 391 44 366)(20 390 45 365)(21 389 46 364)(22 388 47 363)(23 387 48 362)(24 386 49 361)(25 385 50 360)(51 346 76 321)(52 345 77 320)(53 344 78 319)(54 343 79 318)(55 342 80 317)(56 341 81 316)(57 340 82 315)(58 339 83 314)(59 338 84 313)(60 337 85 312)(61 336 86 311)(62 335 87 310)(63 334 88 309)(64 333 89 308)(65 332 90 307)(66 331 91 306)(67 330 92 305)(68 329 93 304)(69 328 94 303)(70 327 95 302)(71 326 96 301)(72 325 97 350)(73 324 98 349)(74 323 99 348)(75 322 100 347)(101 297 126 272)(102 296 127 271)(103 295 128 270)(104 294 129 269)(105 293 130 268)(106 292 131 267)(107 291 132 266)(108 290 133 265)(109 289 134 264)(110 288 135 263)(111 287 136 262)(112 286 137 261)(113 285 138 260)(114 284 139 259)(115 283 140 258)(116 282 141 257)(117 281 142 256)(118 280 143 255)(119 279 144 254)(120 278 145 253)(121 277 146 252)(122 276 147 251)(123 275 148 300)(124 274 149 299)(125 273 150 298)(151 222 176 247)(152 221 177 246)(153 220 178 245)(154 219 179 244)(155 218 180 243)(156 217 181 242)(157 216 182 241)(158 215 183 240)(159 214 184 239)(160 213 185 238)(161 212 186 237)(162 211 187 236)(163 210 188 235)(164 209 189 234)(165 208 190 233)(166 207 191 232)(167 206 192 231)(168 205 193 230)(169 204 194 229)(170 203 195 228)(171 202 196 227)(172 201 197 226)(173 250 198 225)(174 249 199 224)(175 248 200 223)
G:=sub<Sym(400)| (1,52,140,190)(2,53,141,191)(3,54,142,192)(4,55,143,193)(5,56,144,194)(6,57,145,195)(7,58,146,196)(8,59,147,197)(9,60,148,198)(10,61,149,199)(11,62,150,200)(12,63,101,151)(13,64,102,152)(14,65,103,153)(15,66,104,154)(16,67,105,155)(17,68,106,156)(18,69,107,157)(19,70,108,158)(20,71,109,159)(21,72,110,160)(22,73,111,161)(23,74,112,162)(24,75,113,163)(25,76,114,164)(26,77,115,165)(27,78,116,166)(28,79,117,167)(29,80,118,168)(30,81,119,169)(31,82,120,170)(32,83,121,171)(33,84,122,172)(34,85,123,173)(35,86,124,174)(36,87,125,175)(37,88,126,176)(38,89,127,177)(39,90,128,178)(40,91,129,179)(41,92,130,180)(42,93,131,181)(43,94,132,182)(44,95,133,183)(45,96,134,184)(46,97,135,185)(47,98,136,186)(48,99,137,187)(49,100,138,188)(50,51,139,189)(201,276,313,377)(202,277,314,378)(203,278,315,379)(204,279,316,380)(205,280,317,381)(206,281,318,382)(207,282,319,383)(208,283,320,384)(209,284,321,385)(210,285,322,386)(211,286,323,387)(212,287,324,388)(213,288,325,389)(214,289,326,390)(215,290,327,391)(216,291,328,392)(217,292,329,393)(218,293,330,394)(219,294,331,395)(220,295,332,396)(221,296,333,397)(222,297,334,398)(223,298,335,399)(224,299,336,400)(225,300,337,351)(226,251,338,352)(227,252,339,353)(228,253,340,354)(229,254,341,355)(230,255,342,356)(231,256,343,357)(232,257,344,358)(233,258,345,359)(234,259,346,360)(235,260,347,361)(236,261,348,362)(237,262,349,363)(238,263,350,364)(239,264,301,365)(240,265,302,366)(241,266,303,367)(242,267,304,368)(243,268,305,369)(244,269,306,370)(245,270,307,371)(246,271,308,372)(247,272,309,373)(248,273,310,374)(249,274,311,375)(250,275,312,376), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50)(51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100)(101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150)(151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200)(201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250)(251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300)(301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350)(351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400), (1,359,26,384)(2,358,27,383)(3,357,28,382)(4,356,29,381)(5,355,30,380)(6,354,31,379)(7,353,32,378)(8,352,33,377)(9,351,34,376)(10,400,35,375)(11,399,36,374)(12,398,37,373)(13,397,38,372)(14,396,39,371)(15,395,40,370)(16,394,41,369)(17,393,42,368)(18,392,43,367)(19,391,44,366)(20,390,45,365)(21,389,46,364)(22,388,47,363)(23,387,48,362)(24,386,49,361)(25,385,50,360)(51,346,76,321)(52,345,77,320)(53,344,78,319)(54,343,79,318)(55,342,80,317)(56,341,81,316)(57,340,82,315)(58,339,83,314)(59,338,84,313)(60,337,85,312)(61,336,86,311)(62,335,87,310)(63,334,88,309)(64,333,89,308)(65,332,90,307)(66,331,91,306)(67,330,92,305)(68,329,93,304)(69,328,94,303)(70,327,95,302)(71,326,96,301)(72,325,97,350)(73,324,98,349)(74,323,99,348)(75,322,100,347)(101,297,126,272)(102,296,127,271)(103,295,128,270)(104,294,129,269)(105,293,130,268)(106,292,131,267)(107,291,132,266)(108,290,133,265)(109,289,134,264)(110,288,135,263)(111,287,136,262)(112,286,137,261)(113,285,138,260)(114,284,139,259)(115,283,140,258)(116,282,141,257)(117,281,142,256)(118,280,143,255)(119,279,144,254)(120,278,145,253)(121,277,146,252)(122,276,147,251)(123,275,148,300)(124,274,149,299)(125,273,150,298)(151,222,176,247)(152,221,177,246)(153,220,178,245)(154,219,179,244)(155,218,180,243)(156,217,181,242)(157,216,182,241)(158,215,183,240)(159,214,184,239)(160,213,185,238)(161,212,186,237)(162,211,187,236)(163,210,188,235)(164,209,189,234)(165,208,190,233)(166,207,191,232)(167,206,192,231)(168,205,193,230)(169,204,194,229)(170,203,195,228)(171,202,196,227)(172,201,197,226)(173,250,198,225)(174,249,199,224)(175,248,200,223)>;
G:=Group( (1,52,140,190)(2,53,141,191)(3,54,142,192)(4,55,143,193)(5,56,144,194)(6,57,145,195)(7,58,146,196)(8,59,147,197)(9,60,148,198)(10,61,149,199)(11,62,150,200)(12,63,101,151)(13,64,102,152)(14,65,103,153)(15,66,104,154)(16,67,105,155)(17,68,106,156)(18,69,107,157)(19,70,108,158)(20,71,109,159)(21,72,110,160)(22,73,111,161)(23,74,112,162)(24,75,113,163)(25,76,114,164)(26,77,115,165)(27,78,116,166)(28,79,117,167)(29,80,118,168)(30,81,119,169)(31,82,120,170)(32,83,121,171)(33,84,122,172)(34,85,123,173)(35,86,124,174)(36,87,125,175)(37,88,126,176)(38,89,127,177)(39,90,128,178)(40,91,129,179)(41,92,130,180)(42,93,131,181)(43,94,132,182)(44,95,133,183)(45,96,134,184)(46,97,135,185)(47,98,136,186)(48,99,137,187)(49,100,138,188)(50,51,139,189)(201,276,313,377)(202,277,314,378)(203,278,315,379)(204,279,316,380)(205,280,317,381)(206,281,318,382)(207,282,319,383)(208,283,320,384)(209,284,321,385)(210,285,322,386)(211,286,323,387)(212,287,324,388)(213,288,325,389)(214,289,326,390)(215,290,327,391)(216,291,328,392)(217,292,329,393)(218,293,330,394)(219,294,331,395)(220,295,332,396)(221,296,333,397)(222,297,334,398)(223,298,335,399)(224,299,336,400)(225,300,337,351)(226,251,338,352)(227,252,339,353)(228,253,340,354)(229,254,341,355)(230,255,342,356)(231,256,343,357)(232,257,344,358)(233,258,345,359)(234,259,346,360)(235,260,347,361)(236,261,348,362)(237,262,349,363)(238,263,350,364)(239,264,301,365)(240,265,302,366)(241,266,303,367)(242,267,304,368)(243,268,305,369)(244,269,306,370)(245,270,307,371)(246,271,308,372)(247,272,309,373)(248,273,310,374)(249,274,311,375)(250,275,312,376), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50)(51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100)(101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150)(151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200)(201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250)(251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300)(301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350)(351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400), (1,359,26,384)(2,358,27,383)(3,357,28,382)(4,356,29,381)(5,355,30,380)(6,354,31,379)(7,353,32,378)(8,352,33,377)(9,351,34,376)(10,400,35,375)(11,399,36,374)(12,398,37,373)(13,397,38,372)(14,396,39,371)(15,395,40,370)(16,394,41,369)(17,393,42,368)(18,392,43,367)(19,391,44,366)(20,390,45,365)(21,389,46,364)(22,388,47,363)(23,387,48,362)(24,386,49,361)(25,385,50,360)(51,346,76,321)(52,345,77,320)(53,344,78,319)(54,343,79,318)(55,342,80,317)(56,341,81,316)(57,340,82,315)(58,339,83,314)(59,338,84,313)(60,337,85,312)(61,336,86,311)(62,335,87,310)(63,334,88,309)(64,333,89,308)(65,332,90,307)(66,331,91,306)(67,330,92,305)(68,329,93,304)(69,328,94,303)(70,327,95,302)(71,326,96,301)(72,325,97,350)(73,324,98,349)(74,323,99,348)(75,322,100,347)(101,297,126,272)(102,296,127,271)(103,295,128,270)(104,294,129,269)(105,293,130,268)(106,292,131,267)(107,291,132,266)(108,290,133,265)(109,289,134,264)(110,288,135,263)(111,287,136,262)(112,286,137,261)(113,285,138,260)(114,284,139,259)(115,283,140,258)(116,282,141,257)(117,281,142,256)(118,280,143,255)(119,279,144,254)(120,278,145,253)(121,277,146,252)(122,276,147,251)(123,275,148,300)(124,274,149,299)(125,273,150,298)(151,222,176,247)(152,221,177,246)(153,220,178,245)(154,219,179,244)(155,218,180,243)(156,217,181,242)(157,216,182,241)(158,215,183,240)(159,214,184,239)(160,213,185,238)(161,212,186,237)(162,211,187,236)(163,210,188,235)(164,209,189,234)(165,208,190,233)(166,207,191,232)(167,206,192,231)(168,205,193,230)(169,204,194,229)(170,203,195,228)(171,202,196,227)(172,201,197,226)(173,250,198,225)(174,249,199,224)(175,248,200,223) );
G=PermutationGroup([[(1,52,140,190),(2,53,141,191),(3,54,142,192),(4,55,143,193),(5,56,144,194),(6,57,145,195),(7,58,146,196),(8,59,147,197),(9,60,148,198),(10,61,149,199),(11,62,150,200),(12,63,101,151),(13,64,102,152),(14,65,103,153),(15,66,104,154),(16,67,105,155),(17,68,106,156),(18,69,107,157),(19,70,108,158),(20,71,109,159),(21,72,110,160),(22,73,111,161),(23,74,112,162),(24,75,113,163),(25,76,114,164),(26,77,115,165),(27,78,116,166),(28,79,117,167),(29,80,118,168),(30,81,119,169),(31,82,120,170),(32,83,121,171),(33,84,122,172),(34,85,123,173),(35,86,124,174),(36,87,125,175),(37,88,126,176),(38,89,127,177),(39,90,128,178),(40,91,129,179),(41,92,130,180),(42,93,131,181),(43,94,132,182),(44,95,133,183),(45,96,134,184),(46,97,135,185),(47,98,136,186),(48,99,137,187),(49,100,138,188),(50,51,139,189),(201,276,313,377),(202,277,314,378),(203,278,315,379),(204,279,316,380),(205,280,317,381),(206,281,318,382),(207,282,319,383),(208,283,320,384),(209,284,321,385),(210,285,322,386),(211,286,323,387),(212,287,324,388),(213,288,325,389),(214,289,326,390),(215,290,327,391),(216,291,328,392),(217,292,329,393),(218,293,330,394),(219,294,331,395),(220,295,332,396),(221,296,333,397),(222,297,334,398),(223,298,335,399),(224,299,336,400),(225,300,337,351),(226,251,338,352),(227,252,339,353),(228,253,340,354),(229,254,341,355),(230,255,342,356),(231,256,343,357),(232,257,344,358),(233,258,345,359),(234,259,346,360),(235,260,347,361),(236,261,348,362),(237,262,349,363),(238,263,350,364),(239,264,301,365),(240,265,302,366),(241,266,303,367),(242,267,304,368),(243,268,305,369),(244,269,306,370),(245,270,307,371),(246,271,308,372),(247,272,309,373),(248,273,310,374),(249,274,311,375),(250,275,312,376)], [(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50),(51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100),(101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150),(151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200),(201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250),(251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300),(301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350),(351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400)], [(1,359,26,384),(2,358,27,383),(3,357,28,382),(4,356,29,381),(5,355,30,380),(6,354,31,379),(7,353,32,378),(8,352,33,377),(9,351,34,376),(10,400,35,375),(11,399,36,374),(12,398,37,373),(13,397,38,372),(14,396,39,371),(15,395,40,370),(16,394,41,369),(17,393,42,368),(18,392,43,367),(19,391,44,366),(20,390,45,365),(21,389,46,364),(22,388,47,363),(23,387,48,362),(24,386,49,361),(25,385,50,360),(51,346,76,321),(52,345,77,320),(53,344,78,319),(54,343,79,318),(55,342,80,317),(56,341,81,316),(57,340,82,315),(58,339,83,314),(59,338,84,313),(60,337,85,312),(61,336,86,311),(62,335,87,310),(63,334,88,309),(64,333,89,308),(65,332,90,307),(66,331,91,306),(67,330,92,305),(68,329,93,304),(69,328,94,303),(70,327,95,302),(71,326,96,301),(72,325,97,350),(73,324,98,349),(74,323,99,348),(75,322,100,347),(101,297,126,272),(102,296,127,271),(103,295,128,270),(104,294,129,269),(105,293,130,268),(106,292,131,267),(107,291,132,266),(108,290,133,265),(109,289,134,264),(110,288,135,263),(111,287,136,262),(112,286,137,261),(113,285,138,260),(114,284,139,259),(115,283,140,258),(116,282,141,257),(117,281,142,256),(118,280,143,255),(119,279,144,254),(120,278,145,253),(121,277,146,252),(122,276,147,251),(123,275,148,300),(124,274,149,299),(125,273,150,298),(151,222,176,247),(152,221,177,246),(153,220,178,245),(154,219,179,244),(155,218,180,243),(156,217,181,242),(157,216,182,241),(158,215,183,240),(159,214,184,239),(160,213,185,238),(161,212,186,237),(162,211,187,236),(163,210,188,235),(164,209,189,234),(165,208,190,233),(166,207,191,232),(167,206,192,231),(168,205,193,230),(169,204,194,229),(170,203,195,228),(171,202,196,227),(172,201,197,226),(173,250,198,225),(174,249,199,224),(175,248,200,223)]])
106 conjugacy classes
class 1 2A 2B 2C 4A 4B 4C 4D 4E 4F 5A 5B 10A ··· 10F 20A ··· 20H 25A ··· 25J 50A ··· 50AD 100A ··· 100AN order 1 2 2 2 4 4 4 4 4 4 5 5 10 ··· 10 20 ··· 20 25 ··· 25 50 ··· 50 100 ··· 100 size 1 1 1 1 2 2 50 50 50 50 2 2 2 ··· 2 2 ··· 2 2 ··· 2 2 ··· 2 2 ··· 2
106 irreducible representations
dim 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 type + + + + - + - + - + + - + - + image C1 C2 C2 C4 D4 Q8 D5 Dic5 D10 Dic10 D20 D25 Dic25 D50 Dic50 D100 kernel C4⋊Dic25 C2×Dic25 C2×C100 C100 C50 C50 C2×C20 C20 C2×C10 C10 C10 C2×C4 C4 C22 C2 C2 # reps 1 2 1 4 1 1 2 4 2 4 4 10 20 10 20 20
Matrix representation of C4⋊Dic25 in GL3(𝔽101) generated by
100 0 0 0 25 61 0 51 76
,
100 0 0 0 72 29 0 11 83
,
10 0 0 0 56 27 0 11 45
G:=sub<GL(3,GF(101))| [100,0,0,0,25,51,0,61,76],[100,0,0,0,72,11,0,29,83],[10,0,0,0,56,11,0,27,45] >;
C4⋊Dic25 in GAP, Magma, Sage, TeX
C_4\rtimes {\rm Dic}_{25}
% in TeX
G:=Group("C4:Dic25");
// GroupNames label
G:=SmallGroup(400,13);
// by ID
G=gap.SmallGroup(400,13);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-5,-5,24,121,55,4324,628,11525]);
// Polycyclic
G:=Group<a,b,c|a^4=b^50=1,c^2=b^25,a*b=b*a,c*a*c^-1=a^-1,c*b*c^-1=b^-1>;
// generators/relations
Export
×
𝔽
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## On oscillation criteria for third order nonlinear delay differential equations.(English)Zbl 1212.34189
Summary: We are concerned with the oscillation of third order nonlinear delay differential equations of the form $(r_{2}(t) (r_{1}(t) x')')'+p(t) x'+q(t) f(x(g(t))) =0.$ We establish some new sufficient conditions which insure that every solution of this equation either oscillates or converges to zero.
### MSC:
34K11 Oscillation theory of functional-differential equations
### Keywords:
third order; functional differential equation
Full Text:
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# Separate them wisely
Logic Level 5
$\large \frac{5823}{17469} , \frac{5832}{17496}$
Above shows 2 distinct ways to segregate and concatenate the integers from 1 to 9 inclusive such that their ratio is equals to $$\frac13$$.
What is the number of ways to segregate and concatenate the integers from 1 to 9 inclusive (using each digit exactly once) to form two integers such that their ratio equals to $$\frac{1}{12}$$?
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##### https://github.com/cran/lavaan.survey
Tip revision: 09c8996
lavaan.survey.Rd
\name{lavaan.survey}
\alias{lavaan.survey}
\title{
Complex survey analysis of structural equation models (SEM)
}
\description{
Takes a lavaan fit object and a complex survey design object as input
and returns a structural equation modeling analysis based on the fit
object, where the complex sampling design is taken into account.
The structural equation model parameter estimates are "aggregated" (Skinner, Holt & Smith 1989), i.e. they consistently estimate parameters aggregated over any
clusters and strata and no explicit modeling of the effects of clusters and strata
is involved. Standard errors are design-based.
See Satorra and Muthen (1995) and references below for details on the procedure.
Both the pseudo-maximum likelihood (PML) procedure popular in the SEM world
(e.g. Asparouhov 2005; Stapleton 2006) and
weighted least squares procedures similar to aggregate regression modeling with
complex sampling (e.g. Fuller 2009, chapter 6) are implemented.
It is possible to give a list of multiply imputed datasets to svydesign as data.
\code{lavaan.survey} will then apply the standard Rubin (1987) formula to obtain
point and variance estimates under multiple imputation. Some care is required with
this procedure when survey weights are also involved, however (see Notes).
}
\usage{
lavaan.survey(lavaan.fit, survey.design,
estimator=c("MLM", "MLMV", "MLMVS", "WLS", "DWLS", "ML"),
estimator.gamma=c("default","Yuan-Bentler"))
}
%- maybe also 'usage' for other objects documented here.
\arguments{
\item{lavaan.fit}{
A \code{\linkS4class{lavaan}} object resulting from a lavaan call.
Since this is the estimator that will be used in the complex sample
estimates, for comparability it can be convenient to use the same estimator in the call
generating the \pkg{lavaan} fit object as in the \code{lavaan.survey} call. By default
this is "MLM".
}
\item{survey.design}{
An \code{\link{svydesign}} object resulting from a call to
\code{svydesign} in the \pkg{survey} package. This allows for incorporation of
clustering, stratification, unequal probability weights, finite
population correction, and multiple imputation.
}
\item{estimator}{
The estimator used determines how parameter estimates are obtained,
how standard errors are calculated, and how the test statistic and
The default estimator is MLM. It is recommended to use one
of the ML estimators.
}
\item{estimator.gamma}{
Whether to use the usual estimator of Gamma as given by \code{svyvar} (the variance-covariance
matrix of the observed variances and covariances), or apply some kind
of smoothing or adjustment. Currently the only other option is the
Yuan-Bentler (1998) adjustment based on model residuals.
}
}
\details{
The user specifies a complex sampling design with the \pkg{survey} package's
\code{\link{svydesign}} function, and a structural equation model with
\code{lavaan.survey} follows these steps:
\enumerate{
\item The covariance matrix of the observed variables
(or matrices in the case of multiple
group analysis) is estimated using the \code{svyvar} command from the
\pkg{survey} package.
\item The asymptotic covariance matrix of the variances and
covariances is obtained from the \code{svyvar} output (the "Gamma"
matrix)
\item The last step depends on the estimation method chosen:
\enumerate{
\item[MLM, MLMV, MLMVS] The \pkg{lavaan} model is re-fit using Maximum Likelihood
with the covariance matrix as data. After normal-theory ML
estimation, the standard errors (\code{vcov} matrix), likelihood ratio
("chi-square") statistic, and all derived fit indices and
statistics are adjusted for the complex sampling design using
the Gamma matrix. I.e. the Satorra-Bentler (SB) corrections are
obtained ("MLM" estimation in \pkg{lavaan} terminology). This procedure
is equivalent to "pseudo"-maximum likelihood (PML).
\item[WLS, DWLS] The \pkg{lavaan} model is re-fit using Weighted Least Squares
with the covariance matrix as data, and the Moore-Penrose inverse
of the Gamma matrix as estimation weights. If DWLS is chosen
only the diagonal of the weight matrix is used.
}
}
}
\value{
An object of class \code{\linkS4class{lavaan}}, where the estimates,
standard errors, \code{vcov} matrix, chi-square statistic, and fit measures
based on the chi-square take into account the complex survey
design. Several methods are available for \code{\linkS4class{lavaan}}
objects, including a \code{summary} method.}
\references{
Asparouhov T (2005). Sampling Weights in Latent Variable Modeling. Structural
Equation Modeling, 12(3), 411-434.
Bollen, K, Tueller, S, Oberski, DL (2013). Issues in the Structural Equation
Modeling of Complex Survey Data. In: Proceedings of the 59th World Statistics
Congress 2013 (International Statistical Institute, ed.), Hong Kong.
\url{http://daob.nl/publications/}
Fuller WA (2009). Sampling Statistics. John Wiley & Sons, New York.
Kim J, Brick J, Fuller WA, Kalton G (2006). On the Bias of the Multiple-Imputation
Variance Estimator in Survey Sampling. Journal of the Royal Statistical Society:
Series B (Statistical Methodology), 68(3), 509-521.
Oberski, D.L. (2014). lavaan.survey: An R Package for Complex Survey Analysis
of Structural Equation Models. Journal of Statistical Software, 57(1), 1-27.
\url{http://www.jstatsoft.org/v57/i01/}.
Oberski, D. and Saris, W. (2012). A model-based procedure to evaluate
the relative effects of different TSE components on structural equation
model parameter estimates. Presentation given at the International
Total Survey Error Workshop in Santpoort, the Netherlands.
\url{http://daob.nl/publications/}
Satorra, A., & Bentler, P. M. (1994). Corrections to test statistics
and standard errors in covariance structure analysis.
Satorra, A., and Muthen, B. (1995). Complex sample data in structural
equation modeling. Sociological methodology, 25, 267-316.
Skinner C, Holt D, Smith T (1989). Analysis of Complex Surveys.
John Wiley & Sons, New York.
Stapleton L (2006). An Assessment of Practical Solutions for Structural Equation
Modeling with Complex Sample Data. Structural Equation Modeling, 13(1), 28-58.
Stapleton L (2008). Variance Estimation Using Replication Methods in Structural
Equation Modeling with Complex Sample Data. Structural Equation Modeling, 15(2), 183-210.
Yuan K, Bentler P (1998). Normal Theory Based Test Statistics in Structural Equation
Modelling. British Journal of Mathematical and Statistical Psychology, 51(2), 289-309.
}
\author{
Daniel Oberski - \url{http://daob.nl/} - \email{daniel.oberski@gmail.com}
}
\note{
1) Some care should be taken when applying multiple imputation with survey
weights. The weights should be incorporated in the imputation, and even
then the variance produced by the usual Rubin (1987) estimator may not
be consistent (Kott 1995; Kim et al. 2006).
If multiple imputation is used to deal with unit nonresponse,
calibration and/or propensity score weighting with jackknifing may be a
more appropriate method. See the \pkg{survey} package.
2) Note that when using PML or WLS, the Gamma matrix need not be positive definite.
Preliminary investigations suggest that it often is not. This may happen due to
reduction of effective sample size from clustering, for instance.
In itself this need not be a problem, depending on the restrictiveness of the model.
In such cases \code{lavaan.survey} checks explicitly whether the covariance matrix
of the parameter estimates is still positive definite and produces a warning otherwise.
3) Currently only structural equation models for continuous variables are
implemented.
}
%% ~Make other sections like Warning with \section{Warning }{....} ~
\seealso{
}
\examples{
###### A single group example #######
# European Social Survey Denmark data (SRS)
data(ess.dk)
# A saturated model with reciprocal effects from Saris & Gallhofer
dk.model <- "
socialTrust ~ 1 + systemTrust + fearCrime
systemTrust ~ 1 + socialTrust + efficacy
socialTrust ~~ systemTrust
"
lavaan.fit <- lavaan(dk.model, data=ess.dk, auto.var=TRUE, estimator="MLM")
summary(lavaan.fit)
# Create a survey design object with interviewer clustering
survey.design <- svydesign(ids=~intnum, prob=~1, data=ess.dk)
survey.fit <- lavaan.survey(lavaan.fit=lavaan.fit, survey.design=survey.design)
summary(survey.fit)
###### A multiple group example #######
data(HolzingerSwineford1939)
# The Holzinger and Swineford (1939) example - some model with complex restrictions
HS.model <- ' visual =~ x1 + x2 + c(lam31, lam31)*x3
textual =~ x4 + x5 + c(lam62, lam62)*x6
speed =~ x7 + x8 + c(lam93, lam93)*x9
speed ~ textual
textual ~ visual'
# Fit multiple group per school
fit <- lavaan(HS.model, data=HolzingerSwineford1939,
int.ov.free=TRUE, meanstructure=TRUE,
auto.var=TRUE, auto.fix.first=TRUE, group="school",
auto.cov.lv.x=TRUE, estimator="MLM")
summary(fit, fit.measures=TRUE)
# Create fictional clusters in the HS data
set.seed(20121025)
HolzingerSwineford1939\$clus <- sample(1:100, size=nrow(HolzingerSwineford1939), replace=TRUE)
survey.design <- svydesign(ids=~clus, prob=~1, data=HolzingerSwineford1939)
summary(fit.survey <- lavaan.survey(fit, survey.design))
# For more examples, please see the Journal of Statistical Software Paper,
# the accompanying datasets ?cardinale ?ess4.gb ?liss ?pisa.be.2003
# and my homepage http://daob.nl/
}
% Add one or more standard keywords, see file 'KEYWORDS' in the
% R documentation directory.
\keyword{survey}
\keyword{models}
\keyword{regression}
\keyword{robust}
\keyword{multivariate}
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• ### Characterization of a dense aperture array for radio astronomy(1602.07976)
Feb. 25, 2016 astro-ph.IM
EMBRACE@Nancay is a prototype instrument consisting of an array of 4608 densely packed antenna elements creating a fully sampled, unblocked aperture. This technology is proposed for the Square Kilometre Array and has the potential of providing an extremely large field of view making it the ideal survey instrument. We describe the system,calibration procedures, and results from the prototype.
• ### EMBRACE@Nancay: An Ultra Wide Field of View Prototype for the SKA(1504.03854)
May 4, 2015 astro-ph.IM
A revolution in radio receiving technology is underway with the development of densely packed phased arrays for radio astronomy. This technology can provide an exceptionally large field of view, while at the same time sampling the sky with high angular resolution. Such an instrument, with a field of view of over 100 square degrees, is ideal for performing fast, all-sky, surveys, such as the "intensity mapping" experiment to measure the signature of Baryonic Acoustic Oscillations in the HI mass distribution at cosmological redshifts. The SKA, built with this technology, will be able to do a billion galaxy survey. I will present a very brief introduction to radio interferometry, as well as an overview of the Square Kilometre Array project. This will be followed by a description of the EMBRACE prototype and a discussion of results and future plans.
• ### Scintillating bolometers based on ZnMoO$_4$ and Zn$^{100}$MoO$_4$ crystals to search for 0$\nu$2$\beta$ decay of $^{100}$Mo (LUMINEU project): first tests at the Modane Underground Laboratory(1502.01161)
Feb. 4, 2015 nucl-ex, physics.ins-det
The technology of scintillating bolometers based on zinc molybdate (ZnMoO$_4$) crystals is under development within the LUMINEU project to search for 0$\nu$2$\beta$ decay of $^{100}$Mo with the goal to set the basis for large scale experiments capable to explore the inverted hierarchy region of the neutrino mass pattern. Advanced ZnMoO$_4$ crystal scintillators with mass of $\sim$~0.3 kg were developed and Zn$^{100}$MoO$_4$ crystal from enriched $^{100}$Mo was produced for the first time by using the low-thermal-gradient Czochralski technique. One ZnMoO$_4$ scintillator and two samples (59 g and 63 g) cut from the enriched boule were tested aboveground at milli-Kelvin temperature as scintillating bolometers showing a high detection performance. The first results of the low background measurements with three ZnMoO$_4$ and two enriched detectors installed in the EDELWEISS set-up at the Modane Underground Laboratory (France) are presented.
• ### Axion searches with the EDELWEISS-II experiment(1307.1488)
July 4, 2013 hep-ph, astro-ph.CO
We present new constraints on the couplings of axions and more generic axion-like particles using data from the EDELWEISS-II experiment. The EDELWEISS experiment, located at the Underground Laboratory of Modane, primarily aims at the direct detection of WIMPs using germanium bolometers. It is also sensitive to the low-energy electron recoils that would be induced by solar or dark matter axions. Using a total exposure of up to 448 kg.d, we searched for axion-induced electron recoils down to 2.5 keV within four scenarios involving different hypotheses on the origin and couplings of axions. We set a 95% CL limit on the coupling to photons $g_{A\gamma}<2.13\times 10^{-9}$ GeV$^{-1}$ in a mass range not fully covered by axion helioscopes. We also constrain the coupling to electrons, $g_{Ae} < 2.56\times 10^{-11}$, similar to the more indirect solar neutrino bound. Finally we place a limit on $g_{Ae}\times g_{AN}^{\rm eff}<4.70 \times 10^{-17}$, where $g_{AN}^{\rm eff}$ is the effective axion-nucleon coupling for $^{57}$Fe. Combining these results we fully exclude the mass range $0.91\,{\rm eV}<m_A<80$ keV for DFSZ axions and $5.73\,{\rm eV}<m_A<40$ keV for KSVZ axions.
• ### Background studies for the EDELWEISS dark matter experiment(1305.3628)
May 15, 2013 hep-ex, physics.ins-det
The EDELWEISS-II collaboration has completed a direct search for WIMP dark matter using cryogenic Ge detectors (400 g each) and 384 kg$\times$days of effective exposure. A cross-section of $4.4 \times 10^{-8}$ pb is excluded at 90% C.L. for a WIMP mass of 85 GeV. The next phase, EDELWEISS-III, aims to probe spin-independent WIMP-nucleon cross-sections down to a few $\times10^{-9}$ pb. We present here the study of gamma and neutron background coming from radioactive decays in the set-up and shielding materials. We have carried out Monte Carlo simulations for the completed EDELWEISS-II setup with GEANT4 and normalised the expected background rates to the measured radioactivity levels (or their upper limits) of all materials and components. The expected gamma-ray event rate in EDELWEISS-II at 20-200 keV agrees with the observed rate of 82 events/kg/day within the uncertainties in the measured concentrations. The calculated neutron rate from radioactivity of 1.0-3.1 events (90% C.L.) at 20-200 keV in the EDELWEISS-II data together with the expected upper limit on the misidentified gamma-ray events ($\le0.9$), surface betas ($\le0.3$), and muon-induced neutrons ($\le0.7$), do not contradict 5 observed events in nuclear recoil band. We have then extended the simulation framework to the EDELWEISS-III configuration with 800 g crystals, better material purity and additional neutron shielding inside the cryostat. The gamma-ray and neutron backgrounds in 24 kg fiducial mass of EDELWEISS-III have been calculated as 14-44 events/kg/day and 0.7-1.4 events per year, respectively. The results of the background studies performed in the present work have helped to select better purity components and improve shielding in EDELWEISS-III to further reduce the expected rate of background events in the next phase of the experiment.
• ### Muon-induced background in the EDELWEISS dark matter search(1302.7112)
A dedicated analysis of the muon-induced background in the EDELWEISS dark matter search has been performed on a data set acquired in 2009 and 2010. The total muon flux underground in the Laboratoire Souterrain de Modane (LSM) was measured to be $\Phi_{\mu}=(5.4\pm 0.2 ^{+0.5}_{-0.9})$\,muons/m$^2$/d. The modular design of the muon-veto system allows the reconstruction of the muon trajectory and hence the determination of the angular dependent muon flux in LSM. The results are in good agreement with both MC simulations and earlier measurements. Synchronization of the muon-veto system with the phonon and ionization signals of the Ge detector array allowed identification of muon-induced events. Rates for all muon-induced events $\Gamma^{\mu}=(0.172 \pm 0.012)\, \rm{evts}/(\rm{kg \cdot d})$ and of WIMP-like events $\Gamma^{\mu-n} = 0.008^{+0.005}_{-0.004}\, \rm{evts}/(\rm{kg \cdot d})$ were extracted. After vetoing, the remaining rate of accepted muon-induced neutrons in the EDELWEISS-II dark matter search was determined to be $\Gamma^{\mu-n}_{\rm irred} < 6\cdot 10^{-4} \, \rm{evts}/(\rm{kg \cdot d})$ at 90%\,C.L. Based on these results, the muon-induced background expectation for an anticipated exposure of 3000\,\kgd\ for EDELWEISS-3 is $N^{\mu-n}_{3000 kg\cdot d} < 0.6$ events.
• ### A search for low-mass WIMPs with EDELWEISS-II heat-and-ionization detectors(1207.1815)
We report on a search for low-energy (E < 20 keV) WIMP-induced nuclear recoils using data collected in 2009 - 2010 by EDELWEISS from four germanium detectors equipped with thermal sensors and an electrode design (ID) which allows to efficiently reject several sources of background. The data indicate no evidence for an exponential distribution of low-energy nuclear recoils that could be attributed to WIMP elastic scattering after an exposure of 113 kg.d. For WIMPs of mass 10 GeV, the observation of one event in the WIMP search region results in a 90% CL limit of 1.0x10^-5 pb on the spin-independent WIMP-nucleon scattering cross-section, which constrains the parameter space associated with the findings reported by the CoGeNT, DAMA and CRESST experiments.
• ### Final results of the EDELWEISS-II WIMP search using a 4-kg array of cryogenic germanium detectors with interleaved electrodes(1103.4070)
Aug. 31, 2011 hep-ex, astro-ph.CO
The EDELWEISS-II collaboration has completed a direct search for WIMP dark matter with an array of ten 400-g cryogenic germanium detectors in operation at the Laboratoire Souterrain de Modane. The combined use of thermal phonon sensors and charge collection electrodes with an interleaved geometry enables the efficient rejection of gamma-induced radioactivity as well as near-surface interactions. A total effective exposure of 384 kg.d has been achieved, mostly coming from fourteen months of continuous operation. Five nuclear recoil candidates are observed above 20 keV, while the estimated background is 3.0 events. The result is interpreted in terms of limits on the cross-section of spin-independent interactions of WIMPs and nucleons. A cross-section of 4.4x10^-8 pb is excluded at 90%CL for a WIMP mass of 85 GeV. New constraints are also set on models where the WIMP-nucleon scattering is inelastic.
• ### Combined Limits on WIMPs from the CDMS and EDELWEISS Experiments(1105.3377)
July 8, 2011 hep-ex, astro-ph.CO
The CDMS and EDELWEISS collaborations have combined the results of their direct searches for dark matter using cryogenic germanium detectors. The total data set represents 614 kg.d equivalent exposure. A straightforward method of combination was chosen for its simplicity before data were exchanged between experiments. The results are interpreted in terms of limits on spin-independent WIMP-nucleon cross-section. For a WIMP mass of 90 GeV/c^2, where this analysis is most sensitive, a cross-section of 3.3 x 10^{-44} cm^2 is excluded at 90% CL. At higher WIMP masses, the combination improves the individual limits, by a factor 1.6 above 700 GeV/c^2. Alternative methods of combining the data provide stronger constraints for some ranges of WIMP masses and weaker constraints for others.
• ### Measurement of the response of heat-and-ionization germanium detectors to nuclear recoils(astro-ph/0607502)
July 21, 2006 astro-ph
The heat quenching factor Q' (the ratio of the heat signals produced by nuclear and electron recoils of equal energy) of the heat-and-ionization germanium bolometers used by the EDELWEISS collaboration has been measured. It is explained how this factor affects the energy scale and the effective quenching factor observed in calibrations with neutron sources. This effective quenching effect is found to be equal to Q/Q', where Q is the quenching factor of the ionization yield. To measure Q', a precise EDELWEISS measurement of Q/Q' is combined with values of Q obtained from a review of all available measurements of this quantity in tagged neutron beam experiments. The systematic uncertainties associated with this method to evaluate Q' are discussed in detail. For recoil energies between 20 and 100 keV, the resulting heat quenching factor is Q' = 0.91+-0.03+-0.04, where the two errors are the contributions from the Q and Q/Q' measurements, respectively. The present compilation of Q values and evaluation of Q' represent one of the most precise determinations of the absolute energy scale for any detector used in direct searches for dark matter.
• ### Final results of the EDELWEISS-I dark matter search with cryogenic heat-and-ionization Ge detectors(astro-ph/0503265)
May 26, 2005 astro-ph
The final results of the EDELWEISS-I dark matter search using cryogenic heat-and-ionization Ge detectors are presented. The final data sample corresponds to an increase by a factor five in exposure relative to the previously published results. A recoil energy threshold of 13 keV or better was achieved with three 320g detectors working simultaneously over four months of stable operation. Limits on the spin-independent cross-section for the scattering of a WIMP on a nucleon are derived from an accumulated fiducial exposure of 62 kg.d.
• ### Sensitivity of the EDELWEISS WIMP search to spin-dependent interactions(astro-ph/0412061)
April 19, 2005 astro-ph
The EDELWEISS collaboration is searching for WIMP dark matter using natural Ge cryogenic detectors. The whole data set of the first phase of the experiment contains a fiducial exposure of 4.8 kg.day on Ge-73, the naturally present (7.8%), high-spin Ge isotope. The sensitivity of the experiment to the spin-dependent WIMP-nucleon interactions is evaluated using the model-independent framework proposed by Tovey et al.
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I shamelessly realized I will be missing the Psychoco 2011 workshop. Here are some notes from the program about current research in psychometrics with R.
## Differential Item Functioning analysis
Several packages have been released on CRAN since two years or so. This includes:
• difR, from D. Magis and coll., that allows to test for uniform and non-uniform DIF effects in the case of dichotomous items. In its current stage, ten methods are implemented: Mantel-Haenszel, Standardization, Breslow-Day, Logistic regression, Lord’s chi-square test, Raju’s area, Likelihood-ratio test, Generalized Mantel-Haenszel, Generalized logistic regression, Generalized Lord’s chi-square test
• psychotree, from Carolin Strobl and coll. (after cparty) which implements a new graphical tree-based method to present DIF results based on M-Fluctuation Tests(1), but see the accompagnying vignette Using the raschtree function for detecting differential item functioning in the Rasch model.
• lordif, by Seung W. Choi, that allows to test for DIF in polytomous items within an hybrid ordinal logistic regression framework; it is not reported in the workshop program but this is the one I used in the DIF study I presented at the ISOQOL 2010 conference.
Some further references:
1. Magis, D., Beland, S., Tuerlinckx, F., and De Boeck, P. (2010). A general framework and an R pack- age for the detection of dichotomous differential item functioning. Behavior Research Methods, 42, 847-862.
2. Strobl, C., Kopf, J., and Zeileis A (2010). A New Method for Detecting Differential Item Functioning in the Rasch Model. Technical Report 92, Department of Statistics, Ludwig-Maximilians–Universität München.
3. Teresi, J.A., Ocepek-Welikson, K., Kleinman, M., Eimicke, J.P., Crane, P.K., Jones, R.N., Lai, J-S., Choi, S.W., Hays, R.D., Reeve, B.B., Reise, S.P., Pilkonis, P.A., and Cella, D. (2009). Analysis of differential item functioning in the depression item bank from the Patient Reported Outcome Measurement Information System (PROMIS): An item response theory approach. Psychology Science Quarterly, 51 (2), 148-180.
The interest of the psychotree approach is that DIF can be detected between groups of subjects created by more than one covariate. Moreover, the Rasch tree method searches for the value corresponding to the strongest parameter change and splits the sample at that value. Let’s work through the simulated dataset included in the psychotree package.
library(psychotree)
data(DIFSim)
rt <- raschtree(resp ~ age + gender + motivation, data = DIFSim)
plot(rt)
This gives the following results:
The items that are highlighted in black exhibit DIF. More to say later on.
There’s now the catR package (D. Magis and G. Raiche) for playing with CAT experiments. I didn’t try it yet.
## PLS path modeling
I am familiar with the RGCCA and plspm packages for generalized CCA, regularized PLS and PLS path mdoeling, but now I discovered that there is also semPLS (A. Monecke).
Let’s compare their respective output to a common dataset, anmely the mobi data, which comes from an European customer satisfaction index (ECSI) adapted to the mobile phone market, see Tenenhaus et al.(2).
Applying the model is as simple as
library(semPLS)
data(ECSImobi)
ecsi <- sempls(model=ECSImobi, data=mobi, E="C")
ecsi
The ECSImobi structure is a convenient wrapper holding the structural and measurement models, which I roughly show below as incidence matrices:
The figures were generated using lattice, as shown below:
levelplot(ECSImobi$M, cuts=1, col.regions=c("white","black"), xlab="", ylab="", colorkey=FALSE, scales=list(x=list(rot=45))) (idem for ECSImobi$M)
There are a lot of outputs, among which we find
• the loadings and path coefficients (LV <-> MV and LV <-> LV) in ecsi$coefficients, which is a summary of ecsi$outer_loadings and ecsi$path_coefficients or ecsi$inner_weights;
• the cross-loadings (all MV <-> LV laodings) are in ecsi$cross_loadings; • the factor scores in ecsi$factor_scores: this a 250 by 7 matrix of individual scores for each LV.
We can plot the factor scores using densityplot(ecsi):
Another very handy function is pathDiagram() which produces a Graphviz file for the PLS path model. Here is how it looks with default settings:
An equivalent formulation of this model using plspm looks like the one provided in the on-line help, with a different model specification:
library(plspm)
data(satisfaction)
IMAG <- c(0,0,0,0,0,0)
EXPE <- c(1,0,0,0,0,0)
QUAL <- c(0,1,0,0,0,0)
VAL <- c(0,1,1,0,0,0)
SAT <- c(1,1,1,1,0,0)
LOY <- c(1,0,0,0,1,0)
sat.inner <- rbind(IMAG, EXPE, QUAL, VAL, SAT, LOY)
sat.outer <- list(1:5,6:10,11:15,16:19,20:23,24:27)
sat.mod <- rep("A",6) ## reflective indicators
res2 <- plspm(satisfaction, sat.inner, sat.outer, sat.mod,
scaled=FALSE, boot.val=FALSE)
summary(res2)
plot(res2)
Again, there are useful plot methods, including the one used here to summarize the inner model (which reflects the magnitude of the links between the 6 LVs).
Finally, we could also directly use the lavaan or sem package and fit a traditional CFA/SEM model. In the latter case, there’s also a convenient function called plsm2sem() that allows to onvert a plsm object to an object of class mod for usage with interfacing with sem methods.
## Network approach
The qgraph package, which I already pointed to in an earlier post, Psychometrics, measurement, and diagnostic medicine.
In particular, there are nice illustrations on the Big Five theory of personality traits, as measured by the NEOPI, on the dedicated website. Here is the example I like best, for analysing correlation matrices, which basically show (1) an association graph with circular or (2) spring layout, (3) a concentration graph with spring layout, and (4) a factorial graph with spring layout (but see help(qgraph.panel)):
And here is an example for summarizing a standard PCA applied on the NEOPI (see help(qgraph.pca)):
## Polytomous items
Although I didn’t found any specific topic around IRT models for polytomous items, I recently tried the ordinal package. The clmm() function allows to fit an ordered logit model with a random intercept, which is also known as a proportional odds model, following McCullagh’s terminology(3) (but see Agresti, CDA 2002, pp. 275-277, or Liu and Agresti(4)). Only a single random term is allowed in the current version, but there’s a development package on R-Forge (ordinal2) that might provide extended facilities.
From the on-line help, let’s try to fit a simple model to the soup data, where respondents were asked to rate sample products on an ordered scale with six categories given by combinations of (reference, not reference) and (sure, not sure, guess), in an A-not A discrimination test. Before that, here is a quick view of the individual data (10 responses per subject, N=24 subjects, two types of stimuli):
The plot was generated as follows:
library(lattice)
xyplot(SURENESS ~ PROD | RESP, data=dat, type=c("p","g"),
col=rgb(0,0,1,.5), pch=19,
panel=function(x, y, ...) {
panel.xyplot(jitter(as.numeric(x)), y,...)
})
library(ordinal)
options(contrasts = c("contr.treatment", "contr.poly"))
data(soup)
dat <- subset(soup, as.numeric(as.character(RESP)) <= 24)
dat$RESP <- dat$RESP[drop=TRUE]
m1 <- clmm(SURENESS ~ PROD, random=RESP, data=dat, link="probit",
Hess=TRUE, method="ucminf", threshold="symmetric")
m1
summary(m1)
The results indicate a signifiant difference between the test and reference products, but also that this model performs better than a reduced (intercept-only) model
anova(m1, update(m1, location=SURENESS ~ 1, Hess=FALSE))
What does this model actually do in practical terms?
Such models are not available in lme4 at the moment, but we could use any IRT model that allows to cope with polytomous items. I should provide an example (e.g. with LPCM() from the eRm package?).
## References
1. Zeileis, A. and Hornik, K. (2007). Generalized M-Fluctuation Tests for Parameter Instability. Statistica Neerlandica, 61(4), 488–508.
2. Tenenhaus, M., Vinzi, V.E., Chatelin, Y.-M. and Lauro, C. (2005). PLS path modeling. Computational Statistics & Data Analysis, 48, 159-205.
3. McCullagh, P. (1980). Regression models for ordinal data. Journal of the Royal Society, Series B, 42, 109-142.
4. Liu, I. and Agresti, A. (2005). The analysis of ordered categorical data: An overview and a survey of recent developments. Sociedad de Estadística e Investigación Operativa, 15(1), 1-73.
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