setwd("/Users/Daniel/Dropbox/Teaching/CourseR/data/")
d <- read.csv("CollegeScorecard.csv", na = c("NULL", "PrivacySuppressed"))
Note the use of the na
vector, rather than an individual argument
Daniel Anderson
CourseR
setwd("/Users/Daniel/Dropbox/Teaching/CourseR/data/")
d <- read.csv("CollegeScorecard.csv", na = c("NULL", "PrivacySuppressed"))
Note the use of the na
vector, rather than an individual argument
d <- d[ ,c("INSTNM", "STABBR", "SAT_AVG_ALL", "GRAD_DEBT_MDN_SUPP", "md_earn_wne_p10")]
names(d) <- c("Institution", "State", "SAT", "Debt", "Earnings")
d$SAT_c <- d$SAT - mean(d$SAT, na.rm = TRUE)
mean(d$SAT_c, na.rm = TRUE)
## [1] -9.040443e-15
d$Debt_c <- d$Debt - mean(d$Debt, na.rm = TRUE)
mean(d$Debt_c, na.rm = TRUE)
## [1] -1.710248e-12
d[5:6, ]
## Institution State SAT Debt Earnings SAT_c Debt_c
## 5 Alabama State University AL 830 33452 27800 -231.6277 16405.389
## 6 The University of Alabama AL 1171 24000 42400 109.3723 6953.389
pairs(d[ ,3:5])
par(mfcol = c(3, 1))
hist(d[ ,3]) # SAT
hist(d[ ,4]) # Debt
hist(d[ ,5]) # Earnings
par(mfcol = c(3, 1))
plot(density(d[ ,3], na.rm = TRUE))
plot(density(d[ ,4], na.rm = TRUE))
plot(density(d[ ,5], na.rm = TRUE))
library(arm)
mA <- lm(Earnings ~ SAT, data = d)
display(mA, detail = TRUE)
## lm(formula = Earnings ~ SAT, data = d)
## coef.est coef.se t value Pr(>|t|)
## (Intercept) -9181.28 1667.70 -5.51 0.00
## SAT 49.04 1.56 31.42 0.00
## ---
## n = 1475, k = 2
## residual sd = 7791.29, R-Squared = 0.40
mB <- lm(Earnings ~ Debt, data = d)
display(mB, detail = TRUE)
## lm(formula = Earnings ~ Debt, data = d)
## coef.est coef.se t value Pr(>|t|)
## (Intercept) 21624.71 361.12 59.88 0.00
## Debt 0.68 0.02 37.75 0.00
## ---
## n = 5052, k = 2
## residual sd = 11187.05, R-Squared = 0.22
mC <- lm(SAT ~ Debt, data = d)
display(mC, detail = TRUE)
## lm(formula = SAT ~ Debt, data = d)
## coef.est coef.se t value Pr(>|t|)
## (Intercept) 1197.35 16.95 70.62 0.00
## Debt -0.01 0.00 -8.06 0.00
## ---
## n = 1502, k = 2
## residual sd = 126.70, R-Squared = 0.04
Debt
is very small, because it represents the expected
change in the outcome given a one dollar increase in debt. par(mfcol = c(3,1))
plot(d$Earnings ~ d$SAT)
abline(coef(mA)[1], coef(mA)[2],
col = "blue", lwd = 3, lty = 2)
plot(d$Earnings ~ d$Debt)
abline(coef(mB)[1], coef(mB)[2],
col = "blue", lwd = 3, lty = 2)
plot(d$SAT ~ d$Debt)
abline(coef(mC)[1], coef(mC)[2],
col = "blue", lwd = 3, lty = 2)
mAc <- lm(Earnings ~ SAT_c, data = d)
display(mAc, detail = TRUE)
## lm(formula = Earnings ~ SAT_c, data = d)
## coef.est coef.se t value Pr(>|t|)
## (Intercept) 42885.13 202.88 211.39 0.00
## SAT_c 49.04 1.56 31.42 0.00
## ---
## n = 1475, k = 2
## residual sd = 7791.29, R-Squared = 0.40
mBc <- lm(Earnings ~ Debt_c, data = d)
display(mBc, detail = TRUE)
## lm(formula = Earnings ~ Debt_c, data = d)
## coef.est coef.se t value Pr(>|t|)
## (Intercept) 33263.84 158.27 210.17 0.00
## Debt_c 0.68 0.02 37.75 0.00
## ---
## n = 5052, k = 2
## residual sd = 11187.05, R-Squared = 0.22
mCc <- lm(SAT_c ~ Debt_c, data = d)
display(mCc, detail = TRUE)
## lm(formula = SAT_c ~ Debt_c, data = d)
## coef.est coef.se t value Pr(>|t|)
## (Intercept) 38.77 5.65 6.87 0.00
## Debt_c -0.01 0.00 -8.06 0.00
## ---
## n = 1502, k = 2
## residual sd = 126.70, R-Squared = 0.04
mr <- lm(Earnings ~ SAT_c + Debt_c, data = d)
display(mr, detail = TRUE)
## lm(formula = Earnings ~ SAT_c + Debt_c, data = d)
## coef.est coef.se t value Pr(>|t|)
## (Intercept) 42308.84 365.64 115.71 0.00
## SAT_c 49.72 1.61 30.86 0.00
## Debt_c 0.09 0.05 1.99 0.05
## ---
## n = 1455, k = 3
## residual sd = 7783.43, R-Squared = 0.40
One of the best ways to visualize multiple regression models is through a predictor residual plot, which displays the relation between one of the variables and the outcome after partialing common variance with the other predictor. In the case of a model with two predictors, you would
Y
(outcome) and one as the X
(predictor). For example, Model C.X1
partialed from X2
, or vice-versa)Y
(outcome) and one as the X
(predictor). For example, Model C.mCc <- lm(SAT_c ~ Debt_c, data = d)
predSAT <- coef(mCc)[1] + coef(mCc)[2]*d$Debt_c
X1
partialed from X2
, or vice-versa)resSAT <- d$SAT_c - predSAT
plot(resSAT, d$Earnings,
main = "Predictor Residual Plot",
xlab = "Residualized SAT
(relative to Debt)",
ylab = "Earnings")
The previous plot displays the relation between Earnings
and SAT_c
while
accounting for (i.e., residualzing for) Debt_c
. To actually plot the residualzed line, you'll need to fit one additional model.
resLine <- lm(d$Earnings ~ resSAT)
coef(resLine)
## (Intercept) resSAT
## 47806 50
Note that the coefficient for the above model is essentially equivalent to the multiple regression coefficient, and if there were no missing data would be identical (though the intercept does change, because of meaning of a value of 0 on the residualized predictor).
coef(mr)
## (Intercept) SAT_c Debt_c
## 42308.842 49.719 0.092
To add the regression line, just use abline()
like normal
abline(coef(resLine)[1], coef(resLine)[2], col = "red", lwd = 3, lty = 2)
mDc <- lm(Debt_c ~ SAT_c, data = d)
predDebt <- coef(mDc)[1] +
coef(mDc)[2]*d$SAT_c
resDebt <- d$Debt_c - predDebt
resDebtLine <- lm(d$Earnings ~ resDebt)
plot(resSAT, d$Earnings,
main = "Predictor Residual Plot",
xlab = "Residualized Debt
(relative to SAT)",
ylab = "Earnings")
abline(coef(resDebtLine)[1],
coef(resDebtLine)[2],
col = "purple", lwd = 3, lty = 2)
install.packages("visreg")
library(visreg)
par(mfrow = c(2,1))
visreg(mr)
visreg2d(mr, "SAT_c", "Debt_c", plot.type = "persp")
fit <- lm(Ozone ~ Solar.R + Wind +
Temp + I(Wind^2) + I(Temp^2) +
I(Wind * Temp) + I(Wind*Temp^2) +
I(Temp*Wind^2) + I(Temp^2 * Wind^2),
data = airquality)
visreg2d(fit, "Wind", "Temp",
plot.type = "persp", col = "green")


6. The Language Specification - Control Flow¶
This section of the language specifications deals with control flow. It contains the keywords and the operators that affect which parts of the programs are run.
6.1. “#” - Exception Loop¶
Arity: Unbounded
This is the only form of error handling available in Pyth. It runs an infinite while loop until an error is reached, then breaks out of the loop.
Ex:
==================================================
#/100.T=T-T1
==================================================
while True:
try:
Pprint("\n",div(100.,T))
T=copy(minus(T,1))
except:
break
==================================================
10
11
12
14
16
20
25
33
50
100
6.2. ”)” - Close Parenthesis¶
This ends one unbounded arity. Control flow like if or for all open up an unbounded arity and this closes one of them. Also works on tuple ad list constructors.
Ex:
==================================================
I>5T"Hello")"Bye"
==================================================
if gt(5,T):
Pprint("\n","Hello")
Pprint("\n","Bye")
==================================================
Bye
6.3. ”;” - End Statement¶
This is effectively an infinite amount of close parenthesis. This closes how many ever aritys are needed to start completely afresh. This is the replacement for multiple lines in Pyth.
Ex:
==================================================
V5I>5T"Hello";"Bye"
==================================================
for N in urange(5):
if gt(5,T):
Pprint("\n","Hello")
Pprint("\n","Bye")
==================================================
Bye
6.4. “B” - Break¶
This translates into the break keyword in Python. It is used to break out of both for and while loops (and also the infinite error loop). Pyth does not have a continue statement. Break automatically puts a close parenthesis after itself.
Ex:
==================================================
#ZI>ZTB~Z1
==================================================
while True:
try:
Pprint("\n",Z)
if gt(Z,T):
break
Z+=1
except:
break
==================================================
0
1
2
3
4
5
6
7
8
9
10
11
6.5. “E” - The Else Statement¶
Arity: Unbounded
This is the else part of the if-else construct. It is pretty self explanatory and works like it would in any programing langaue. This can also be used as part of a for-else or while-else construct. The If still needs a close parenthesis after it.
Ex:
==================================================
I>5T"It's greater")E"It's less than"
==================================================
if gt(5,T):
Pprint("\n","It's greater")
else:
Pprint("\n","It's less than")
==================================================
It's less than
6.6. “F” - The For Loop¶
Arity: Variable, Sequence, Unbounded
This is the ubiquitous for loop. It works like it does in Python, with it looping through a sequence.
Ex:
==================================================
FNU5N
==================================================
for N in urange(5):
Pprint("\n",N)
==================================================
0
1
2
3
4
6.7. “I” - The If Statement¶
Arity: Boolean, Unbounded
This is the If statement from Python. If the first argument is truthy, it executes the code, else it does nothing. Requires a close paren unless it is the last piece of code.
Ex:
==================================================
I>5T"The Universe Has Exploded"
==================================================
if gt(5,T):
Pprint("\n","The Universe Has Exploded")
==================================================
6.8. “V” - Unary-Range-Loop¶
Arity: Integer, Unbounded
It is the shortest way to do a for loop. It takes an integer and translates it self to FNU. This makes it execute the following code that many times, with N being the loop variable.
Ex:
==================================================
VT*NN
==================================================
for N in urange(T):
Pprint("\n",times(N,N))
==================================================
0
1
4
9
16
25
36
49
64
81
6.9. “W” - While Loop¶
Arity: Boolean, Unbounded
This the while loop construct from Python. It executes the following code until the condition becomes False.
Ex:
==================================================
W<lYT~Y]5;Y
==================================================
while lt(Plen(Y),T):
Y+=[5]
Pprint("\n",Y)
==================================================
[5, 5, 5, 5, 5, 5, 5, 5, 5, 5]
6.10. ”?” - Ternary Operator¶
Arity: Expression, Boolean, Expression
This is the ternary operator from Python. It is a compressed version of the If-Else construct. ?abc is equivelant to the Python a if b else c which evaluates to a if b is truthy else evaluates to c.
Ex:
==================================================
?5q1ZT
==================================================
Pprint("\n",(5 if equal(1,Z) else T))
==================================================
10


Our software develompent methodology is based in computer science and mathematics. We develop highly scalable, robust and efficient web applications.
We are focused on improving the human condition by proposing, testing & developing unique technological solutions. We create technologies that will save humanity.
We believe that our success is a derivative of our willingness to lend a technical helping hand to charities and churches. God helps those who help others.


Call of Duty: Modern Warfare earned over six hundred million dollars in its first three days after release. Six hundred million well-deserved dollars.
July 1, 2015
A majority of Windows users are still avoiding the move to Windows 10 because of upgrade headaches, but there are ways around them.
June 22, 2015


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Jonathan "John" Locke is one of the surviving passengers who flew in the middle of Oceanic Flight 815. He was paralyzed in his lower torso, but after the disaster, the paralysis suddenly passed and this was the basis for Locke's belief that he has a special connection with the Island. Locke is sometimes compared to Benjamin Linus, as they both share similar traits.


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Authors: Kenji Uchino
Source: FERMAT, Volume 9, Communications 4, May Jun., 2015
Abstract: There are four factors that have influences on engineering: Social/culture/religion, Technology/science, Economics, and Politics/law. The strength of the impact of these factors becomes different according to history. Alchemy of the 16th century is an example of “Socio-Engineering”. From the Christian doctrine, “Heliocentric model” was denied, but “alchemy” was approved. Religion was controlling science. In the 17th~18th centuries, people were solved from the spell of religion and engineering based on science and technology, so-called “Techno-Engineering” is respected instead. In the 18th~19th centuries, technologies for mass production at low manufacturing cost were required and “EconoEngineering” became mainstream to enhance national strength. The intention of increasing national wealth and military strength increased friction and that led to the First and Second World War in the 20th century. Engineering of this period is mainly government-led production of war weapons, and it was a beginning of “Politico-Engineering”. After the wars, mass production technologies for the reconstruction/recovery revived, but when the 21st century began, as a consequent result, environmental degradation, resource depletion, and food famine have become major problems. Global regulations are strongly called, and the government-initiated technology (“politico-engineering”) has become important again in order to overcome the regulations. Politico-Engineering covers (1) legally-regulated normal technologies such as sustainability, and (2) crisis technologies. This paper introduces leading actuator/sensor and piezoelectric technologies, relating with the above “sustainability” and “crisis” technologies, aiming at further research expansion in this area. The sustainable society requires (a) usage of non-toxic materials (Pb-free piezoelectrics), (b) disposal technology for existing hazardous materials (high power ultrasonic transducers), (c) reduction of contamination gas (diesel injection valves), (d) new energy source creation (piezoelectric renewable energy harvesting systems), and (e) energy-efficient device development. Crisis technologies are categorized into five types: (a) natural disasters (earthquakes, tsunamis, tornadoes, hurricanes, lightning, etc.), (b) epidemic/infectious diseases (smallpox, polio, measles, and HIV), (c) enormous accident (Three-Mile-Island core meltdown accident, BP oil spill etc.), (d) intentional accidents (acts of terrorism, criminal activity, etc.), (e) civil-war, war, territorial aggression
Keywords: Crisis technology; Sustainability technology; Politico-engineering; Piezoelectric actuator; Pb-free piezoelectrics; Piezoelectric energy harvesting; Ultrasonic cavitation; Ultrasonic motor.
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Global Crisis/Sustainability Technologies


Scan Parameters (ignore if Scan Bool = false) Start frequency MHz to DDS Stop frequency MHz to DDS External factor 'm': Warning: allowed values are fmin = 125 MHz < fDDS < fmax = 275 MHz 64 x fmin = 8 GHz < 64 x fDDS < 64 x fmax = 17.6 GHz
Save/Export TSV CSV Mathematica JSON Data ready for export: right-click here & select "Save target as" to download.


GENERAL CONDITIONS FOR USE OF THE INTERNET SITE OF "Slavov detailing-auto" Sole-owned Limited Liability Company
Art. 1 These General Conditions for use of an Internet site of "Slavov detailing-auto"(Sole-owned Limited Liability Company) and the services provided through them shall regulate the relationships between "Slavov detailing-auto"(Sole-owned Limited Liability Company) (hereinafter referred to as Interior auto) and any person (hereinafter referred to as the User), who uses an Internet site of Interior auto and/or the services rendered through it. Within the meaning of these Conditions an Internet site of Interior auto shall be the site of www.interiorauto.bg
Art. 2. The users within the meaning of these Conditions are two categories:
Para. 1. Active users – making use of the contact form – users who actively use an Internet site of Interior auto through the entry of an е-mail address,name and message. The mandatory data which should be entered depend on the objectives of the use – enquiries.
Para. 2. Non-active – Users, who visit an Internet site of the Interior auto without using the contact form.
Art. 3. These rules are published on the Internet site of Interior auto and are deemed as accepted by the User by the fact of his entry into the site. The User shall be obligated to use the services in compliance with the requirements of these General Conditions.
Art. 4. By the acceptance of these General Conditions, the User shall be informed and shall agree, Interior auto to send calls, communications and electronic mail for the purposes of the direct marketing and advertisement of own services of the enterprise or of services and products of third persons, providing each User with possibility, in event of receiving a call, a communication or electronic mail for the purposes of the direct marketing, to express his disagreement with the future receipt of similar messages. Interior auto shall fulfill each refusal for receipt of future messages for marketing purposes.
Art. 5. The infringement of copyright and neighboring of www.interiorauto.bg rights, rights over trademarks or other rights of intellectual property shall be prohibited.
Art. 6. Each User who makes use of services of an Internet site of Interior auto, shall be entitled to express his opinion with regard to these General Conditions via sending a personal message through the enquiry form.
Art. 7. Questions related to the use of the offered on the Internet site of Interior auto, may be asked by a User via sending a message through the enquiry form.
Art. 8. Information referring to the manners of use of the relevant Internet site of Interior auto, as well as to the services provided through it, may be received through the enquiry form.
Art. 9. Interior auto shall be obligated to keep the secret of the correspondence as well as not to disclose the provided personal information presented by the persons without their preliminary agreement unless this follows up under the virtue of a legislative provision.
Art. 10. Interior auto shall preserve the right not to answer enquiries in the judgment of the administrator.
Art. 11. Interior auto shall not bear responsibility before the User for:
Para. 1. Losses, profits lost and other damages caused to the User as a result of use of services through an Internet site of Interior auto and the site itself on his part, as well as for the impossibility to use these services;
Para. 2. Incapability of the User to use the functionality of the Internet site;
Para. 3. Claims by third persons against the User at or on the occasion of use of the functionality of the Internet site;
Art. 12. Interior auto shall not bear responsibility if at violations of the working capacity of the software or of the technical provision of other providers in Internet or of the electronic communication connections in and/or beyond the country, a User may not use partially or fully the possibilities of the functionality provided on an Internet site of Interior auto.
Art. 13. The User shall be obligated to inform about errors, technical problems and other problems related to the use and the functionality of the Internet site, through making a call on the telephone indicated in Section Contacts or through the enquiry form.
Art. 14. Interior auto shall preserve the right unilaterally to change these General Conditions as well as the structure of its Internet site, which it shall not be obligated to inform the Users about.
Art. 15. The legislation effective in the Republic of Bulgaria shall be applied to all the issues unsettled in these Conditions.
Art. 16. At the origination of disputes the Parties shall make efforts for their voluntary settlement by mutual agreement. In event of not reaching an agreement, each of the Parties may refer the dispute for settlement by a competent Court.


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Related Website Observations
I chose a similar web page from The Bark, a dog magazine. The page is an article listing things the author loves about her dog.
Website Comparison
This web site's page has both qualities that are good and qualities that could be improved:
Good:
- The author is talking about dogs, and dogs are wonderful.
- The ordered list on the page is set up properly with a list tag, specifically <ol>.
- Each item on the ordered list mentioned above is created as a distinct list item using the semantic tag <li>.
Room for improvement:
- I think the page's main navigation should have been contained in a semantic <nav> tag. The navigation is actually setup as a table.
- In researching where the navigation table mentioned above begins, I also determined that the entire visible web page is contained within a table! It is interesting to still see a website with table layout while table-less design is widely favored these days. Tables were never intended as a layout tool--tables were intended for the display of tabular data!
- The article does not use header tags to semantically define header content. What should be created as the <h1> tag has been created as a div with a class assignment to provide meaning.
Overall, there are some areas that this web site's page could improve, namely in the area of including more semantic tags to provide additional meaning to the content.


God lets you be successful because he trusts you that you will do the right thing with it. Now, does he get disappointed often? All the time, because people get there and they forget how they got it.
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|
| def | __init__ (self, settings) |
| |
| def | a (self, t) |
| |
| def | f (self, x) |
| |
| def | g (self, x) |
| |
| def | da (self, t) |
| |
| def | df (self, x) |
| |
| def | dg (self, x) |
| |
| def | ddf (self, x) |
| |
| def | ddg (self, x) |
| |
| def | u1 (self, x1, x2, t) |
| |
| def | u2 (self, x1, x2, t) |
| |
| def | du11 (self, x1, x2, t) |
| |
| def | du12 (self, x1, x2, t) |
| |
| def | du21 (self, x1, x2, t) |
| |
| def | du22 (self, x1, x2, t) |
| |
| def | du111 (self, x1, x2, t) |
| |
| def | du122 (self, x1, x2, t) |
| |
| def | du211 (self, x1, x2, t) |
| |
| def | du222 (self, x1, x2, t) |
| |
| def | du1dt (self, x1, x2, t) |
| |
| def | du2dt (self, x1, x2, t) |
| |
◆ __init__()
| def sinusoidal_vortex.ManufacturedVortex.__init__ |
( |
|
self, |
|
|
|
settings |
|
) |
| |
◆ a()
| def sinusoidal_vortex.ManufacturedVortex.a |
( |
|
self, |
|
|
|
t |
|
) |
| |
◆ da()
| def sinusoidal_vortex.ManufacturedVortex.da |
( |
|
self, |
|
|
|
t |
|
) |
| |
◆ ddf()
| def sinusoidal_vortex.ManufacturedVortex.ddf |
( |
|
self, |
|
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|
x |
|
) |
| |
◆ ddg()
| def sinusoidal_vortex.ManufacturedVortex.ddg |
( |
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self, |
|
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|
x |
|
) |
| |
◆ df()
| def sinusoidal_vortex.ManufacturedVortex.df |
( |
|
self, |
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|
x |
|
) |
| |
◆ dg()
| def sinusoidal_vortex.ManufacturedVortex.dg |
( |
|
self, |
|
|
|
x |
|
) |
| |
◆ du11()
| def sinusoidal_vortex.ManufacturedVortex.du11 |
( |
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self, |
|
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|
x1, |
|
|
|
x2, |
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t |
|
) |
| |
◆ du111()
| def sinusoidal_vortex.ManufacturedVortex.du111 |
( |
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self, |
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x1, |
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|
|
x2, |
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t |
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) |
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◆ du12()
| def sinusoidal_vortex.ManufacturedVortex.du12 |
( |
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self, |
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|
x1, |
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x2, |
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t |
|
) |
| |
◆ du122()
| def sinusoidal_vortex.ManufacturedVortex.du122 |
( |
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self, |
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x1, |
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x2, |
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t |
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) |
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◆ du1dt()
| def sinusoidal_vortex.ManufacturedVortex.du1dt |
( |
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self, |
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x1, |
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x2, |
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t |
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) |
| |
◆ du21()
| def sinusoidal_vortex.ManufacturedVortex.du21 |
( |
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self, |
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x1, |
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|
x2, |
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t |
|
) |
| |
◆ du211()
| def sinusoidal_vortex.ManufacturedVortex.du211 |
( |
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self, |
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x1, |
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x2, |
|
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t |
|
) |
| |
◆ du22()
| def sinusoidal_vortex.ManufacturedVortex.du22 |
( |
|
self, |
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x1, |
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◆ du222()
| def sinusoidal_vortex.ManufacturedVortex.du222 |
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| def sinusoidal_vortex.ManufacturedVortex.du2dt |
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| def sinusoidal_vortex.ManufacturedVortex.f |
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| def sinusoidal_vortex.ManufacturedVortex.g |
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◆ u1()
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| sinusoidal_vortex.ManufacturedVortex.k |
| sinusoidal_vortex.ManufacturedVortex.L |
◆ nu
| sinusoidal_vortex.ManufacturedVortex.nu |
◆ omega
| sinusoidal_vortex.ManufacturedVortex.omega |
◆ rho
| sinusoidal_vortex.ManufacturedVortex.rho |
| sinusoidal_vortex.ManufacturedVortex.T |
| sinusoidal_vortex.ManufacturedVortex.U |
The documentation for this class was generated from the following file:
- /home/runner/work/Documentation/Documentation/master/applications/SwimmingDEMApplication/python_scripts/custom_body_force/sinusoidal_vortex.py


Approximation theory and approximation practice
Posted: 2016-08-08 , Modified: 2016-08-08
Tags: none
Posted: 2016-08-08 , Modified: 2016-08-08
Tags: none
Write
xx=chebpts(n+1)
(Note: from now on we will reverse the order of the \(x_j\), to go from left to right.)
The Chebyshev interpolant of \((f_j)\) is the unique polynomial of degree (\(\le\)) \(n\) going through points \(x_j,f_j\). To construct the interpolant for a function,
x = chebfun('x');
f = (function of x);
p=chebfun(f,n+1); hold on, plot(p,'.-')
(Note: x
is like a vector here. So you must write .*
for multiplication, etc.) .-
makes it point out the Chebyshev interpolation points.
Define Chebyshev polynomials.
The following are Chebyshev, Laurent, and Fourier expansions. \[\begin{align} f(x) &\approx \sumz kn a_kT_k(x), && x&\in [-1,1]\\ F(z) &= \rc 2 \sumz kn a_k(z^k+z^{-k}) & f(x)&=F\pf{z+z^{-1}}2&|z|&=1\\ \cF (\te) &\approx \rc 2 \sumz kn a_k(e^{ik\te} + e^{-ik\te})& \te&\in [-\pi,\pi] \end{align}\]One can expand a polynomial in Chebyshev basis using the FFT or Fast Cosine Transform.
Chebyshev series: If \(f\) is Lipschitz continuous on \([-1,1]\), it has a unique representation \[f(x)=\sumz k\iy a_k T_k(x),\quad a_k = \fc2\pi \int_{-1}^1 \fc{f(x)T_k(x)}{\sqrt{1-x^2}} \dx. \]
Proof. \[\begin{align} a_k &= \rc{2\pi i} \oint_{|z|=1} (z^{-1+k}+z^{-1-k})F(z)\,dz\\ &= \rc{\pi i} \int_{|z|=1} z^{-1}T_k(x) F(z)\,dz\\ &=-\rc{\pi}\fc{f(x)T_k(x)}{\Im z}\,dz & dx&=\rc 2 \pf{z-z^{-1}}{2z}dz = \rc2 i z^{-1}\Im z\\ &=\fc2\pi \int_{-1}^1 \fc{f(x)T_k(x)}{\sqrt{1-x^2}} \dx. \end{align}\]Orthonormality: \[ \fc 2\pi\int_{-1}^1 \fc{T_l(x)T_k(x)}{\sqrt{1-x^2}} = \de_{kl}.\]
There are 2 ways to approximate \(f\) by a Chebyshev expansion.
In computation, \(p_n\) are usually almost as good and easier to evaluate.
Theorem (aliasing). \(T_k\) takes the same value on the \((n+1)\)-point Chebyshev grid as \(T_m\), \(m=|(k+n-1)\bmod{2n} - (n-1)|\). (i.e., \(T_m\) takes the same value as \(T_k\) with \(k=2jn\pm m\).)
Proof. Look at \(2n\)th roots of unity.
Theorem (aliasing for Chebyshev coefficients). Let \(a_k,c_k\) be Chebyshev coefficients of \(f\) and \(p_n\). Then \[\begin{align} c_k &= \sum_{i\in \{2jn\pm k\}\cap \N} a_i. \end{align}\]So \[f(x)-p_n(x) = \sum_{k=n+1}^{\iy} a_k(T_k(x) - T_{m(k,n)}(x)).\]
In Chebfun, to get truncation, interpolation use
a = chebpoly(f) % truncation/projection
fn = chebfun(f, 'trunc', n+1) % truncation
pn = chebfun(f, n+1)
c = chebpoly(pn) % interpolation
How to evaluate a Chebyshev interpolant?
Lagrange interpolation:
\[\begin{align} p(x) &= \sumz jn f_jl_j(x)\\ l_j(x) &=\fc{\prod_{k\ne j}(x-x_k)}{\prod_{k\ne j} (x_j-x_k)} \end{align}\]The computation of \(l_j\) is unstable and takes \(O(n^2)\) operations.
Modified Lagrange formula (first barycentric formula) \[\begin{align} p(x) &= l(x) \sumz jn \fc{\la_j}{x-x_j} f_j\\ l(x) &= \prod_{k=0}^{n} (x-x_k)\\ \la_j &= \rc{\prod_{k\ne j}(x_j-x_k)} = \rc{l'(x_j)}. \end{align}\]This takes \(O(n)\) operations to evaluate. (Computing the weights takes \(O(n^2)\) but only needs to be done once.)
Theorem (Barycentric interpolation formula). \[p(x) = \left. \sumz jn \fc{\la_j f_j}{x-x_j} \right/ \sumz jn \fc{\la_j}{x-x_j}.\]
Proof. Note \(\sumz jn l_j(n)=1\). so just replace the \(l_j\) by \(\fc{\la_j}{x-x_j}\) and then normalize afterwards.
For Chebyshev points \(\la_j = (-1)^j \fc{2^{n-1}}{n} (1-\rc 2(j=0\text{ or }n))\). Obtain \[p(x) = \left. \sumz jn' \fc{(-1)^jf_j}{x-x_k}\right/\sumz jn' \fc{(-1)^j}{x-x_k} \] where \(\sum'\) means that the first and last terms are multiplied by \(\rc2\).
Proof. \[\begin{align} l(x) &= (x-x_0)\cdots (x-x_n)\\ & = (z^{2n}-1)(z^2-1)(z^{-n-1}-1) \rc{2^{n+1}} & x=\fc{z+z^{-1}}2\\ &= \rc{2^n} \pa{\fc{x^{n+1}+x^{-(n+1)}}2 - \fc{x^{n-1}+x^{-(n-1)}}}\\ \la_j &=\rc{l'(x_j)} = \fc{2^n}{T_{n+1}'(x_j) - T_{n-1}'(x_j)} = \fc{2^n}{2n(-1)^j(1+(j=0\text{ or }n))} \end{align}\]by using the recurrence relation to compute the derivatives.
This is stable, whereas polynomial interpolation via Vandemonde is exponentially unstable.
Warning:
Theorem (Weierstrass approximtion). A continuous function on \([-1,1]\) can be arbitrarily well-approximated in \(L^{\iy}\) by polynomials.
Proof. Extend \(f\) to be continuous with compact support. Take \(f\) as initial data for \(u_t=u_{xx}\). The solution is \(f*e^{-\fc{x^2}{4t}}/\sqrt{2\pi t}\). For \(t>0\) this is analytic and has uniformly convergent Taylor series.
Bernstein’s proof is a discrete analogue replacing diffusion by a random walk.
Theorem (Mergelyan). If \(f\) is continuous on compact simply connected \(K\sub \C\) and analytic in \(K^{\circ}\), then \(f\) can be approximated on \(K\) by polynomials.
(Bounded variation means \(\ve{f'}_1<\iy\) where \(f'\) is interpreted in the distributional sense.)
If \(f^{(k)}, k\le v-1\) is absolutely continuous and \(f^{(v)}\) has bounded variation, then \[\begin{align} a_k &\le \fc{2V}{\pi k\fp{v+1}} &\le \fc{2V}{\pi (k-v)^{v+1}}\\ \ve{f-f_n}_\iy &\le \sum_{k=n+1}^\iy |a_k| \le \fc{2V}{\pi v(n-v)^v}\\ \ve{f-p_n}_\iy &\le \sum_{k=n+1}^{\iy} 2|a_k|\le \fc{4V}{\pi v(n-v)^v} \end{align}\] Proof. \[\begin{align} a_k &= \rc{\pi i}\int_{|z|} f(\rc 2(z+z^{-1})) z^{k-1}\,dz\\ &=-\rc{\pi i} \int_{|z|=1} f'(\rc 2 (z+z^{-1}))\fc{z^k}{k}\dx\\ |a_k| &\le \fc{2}\pi \int_{-1}^1 |f'\Im\fc{z^k}{k}|\dx. \end{align}\]For \(v>0\), integrate by parts \(v+1\) times to get \[(-1)^{v+1} \rc{\pi i}\int_{|z|=1} f^{(v+1)}(\rc 2 (z+z^{-1})) f_{v, k}(z)\dx\] where \(f_{0,k}(z) = \fc{z^k}{k}\) and \(f_{n+1,k} = \int f_{n,k} \fc{1-z^{-2}}2\).
Proof. \(a_k = \ab{\rc{\pi i}\int_{|z|=\rh} z^{-1-k} F(z)\,dz}\).
Converse: If there exist \(q_n\), \(\ve{f-q_n}\le C\rh^{-n}\), then \(f\) is continuable to the Bernstein ellipse \(E_\rh\).
Proof. Write \(f=q_0+(q_1-q_0)+\cdots\). Use the estimate \(\deg p\le d\implies \ve{p}_{L^{\iy}(E_\rh)}\le \rh^d \ve{p}_{L^{\iy}[-1,1]}\). Proof: Let \(q(z) = \fc{p(z)}{(z+\sqrt{z^2-1})^d}\). This is analytic on \(\C\cup \{\iy\}\bs [-1,1]\). (Why is it well-defined?) (It is defined at \(\iy\) because taking \(z\leftarrow \rc z\) we get \(\fc{p_{\text{rev}}(z)}{(1+\sqrt{1-z^2})^d}\).) The maximum is attained at the boundary \([-1,1]\) where the absolute value is 1.
At discontinuities, the overshoot of a Chebyshev approximation does not \(\to 0\) as \(n\to \iy\).
For Chebyshev interpolants of \(\sgn(x)\) on \([-1,1]\), \[\begin{align} \lim_{n\to \iy,n\text{ odd}} \ve{p_n}_\iy &\approx1.282...\\ \lim_{n\to \iy,n\text{ even}} \ve{p_n}_\iy &\approx1.066... \end{align}\]For Chebyshev projections, \[\lim_{n\to \iy} \ve{f_n} = \fc 2\pi \int_0^\pi \fc{\sin x}x\dx.\]
Intuition: \(p(x) = \sum_{j=(n+1)/2}^n l_j(x)\). This is an alternating series which in the limit has finite nonzero sum.
Notes:
Theorem. A continuous \(f\) on \([-1,1]\) has a unique best approximation \(p^*\in \cP_n\). It is uniquely characterized by \(f-p\) equioscillating in \(\ge n+2\) extreme points.
Proof. The minimum is attained because it lies in \(\{\ve{f-p}\le \ve{f}\}\). (\(L^\iy\) norms.) If \(p,q\) satisfy the condition, and \(\ve{f-q}< \ve{f_p}\), then \(p-q\) has \(n+1\) zeros. If it doesn’t equioscillate, perturb by \((x_1-x)\cdots (x_k-x)\). (If \(\ve{f-q}=\ve{f-p}\), use the following argument: suppose \(p\) has equioscillation extreme points \(x_{0:n+1}\). Induct on: \(p-q\) has \(\ge j\) roots in \([x_0,x_j]\). Suppose this is first violated at \(k\) and obtain a contradiction.)
Theorem. Let \(f\) be analytic in a region \(\Om\) containing distinct points \(x_0,\ldots, x_n\) and \(\Ga\) be a contour in \(\Om\) looping once around them. The polynomial interpolant of degree \(\le n\) to \(f\) at \(\{x_j\}\) is \[p(x) = \rc{2\pi i} \int_{\Ga} \fc{f(t)(l(t)-l(x))}{l(t)(t-x)}\,dt\] and if \(x\) is enclosed by \(\Ga\), the error is \[f(x) - p(x) = \rc{2\pi i}\int_{\Ga} \fc{l(x)}{l(t)} \fc{f(t)}{t-x}\,dt.\]
This is useful because it gives an estimate for the error in terms of “analyticity” of \(f\). If \(f\) is analytic on a larger region, we can take \(\Ga\) to be bigger, and the ratio \(\fc{l(x)}{l(t)} = \prod_{j=0}^n \fc{x-x_j}{t-x_j}\) is smaller. This also tells us a property we desire for the interpolation points: they should make \(l(x)\) small. (We shouldn’t have to go far away to make the ratio \(\fc{l(x)}{l(t)}\) small.)
Proof.
We want to lower bound \(\al_n\) to get exponential convergence.
Think of \(u\) as a discrete approximation for a continuous potential \[u(s) = \int_{-1}^1 \ln |s-\tau| \,d\mu(\tau).\] On \([-1,1]\), equally spaced grids converge to \(\mu(\tau)=\rc2\) and Chebyshev grids converge to \(\mu(\tau) = \rc{\pi \sqrt{1-\tau^2}}\) in weak*.
Key property. The Chebyshev measure generates constant potential on \([-1,1]\), and so minimizes \(I(\mu)\) (proof omitted).
Some alterntive views.
The capacity is \(\min_\mu I(\mu)\); for \([-1,1]\) it is \(\log 2\). (Each grid point is at an average distance of \(\rc2\) from the others in geometric mean.)
How to generalize to other regions (compact sets of \(\C\))?
Theorem. Let \(f\in C([-1,1])\). Let \(\rh\) be the parameter of the largest Bernstein ellipse \(E_\rh\) where \(f\) can be analytically continued, and \(p_n\) be the interpolants to any sequence of grids with \(\lim_{n\to \iy}(\sup_{x\in [-1,1]}|l(x)|)^{\rc n}\). Then \(\lim_{n\to \iy} \ve{f-p_n}^{\rc n} = \rh^{-1}\).
Interpolation at equally spaced points can diverge exponentially (at the edges). Why? \([-1,1]\) is far from being a level curve. The curve \(l(x)=l(t)\) is a “football”; \(f\) needs to be analytic inside this football for convergence. The football goes to \(\approx .526i\). Ex. \(f=\rc{1+25x^2}\) is not analytic inside, so the interpolants diverge.
Even if convergence should take place in theory (\(f\) is analytic in the football), rounding errors can be amplified by \(O(2^n)\) causing divergence in practice.
Much of the literature is skeptical of high-order interpolation because people saw it doesn’t work for equispaced point. However, Chebyshev interpolation does work.
2 important issues:
The Lebesgue constant of a set of points \(S\sub [-1,1]\) is \[\La = \sup_f\fc{\ve{p}}{\ve{f}} = \sup_{x\in [-1,1]} \ub{\sumo jn |l_j(x)|}{\la(x)}\] where \(p\) is the interpolant of \(f\) through \(S\).
The largest possible interpolation error is at least \(\La-1\), and the interpolation error is at most \((\La+1) \ve{f-p^*}\).
More generally, define the Lebesgue constant of any linear projection by \(\sup_f \fc{\ve{Lf}}{\ve{f}}\). Then \(\ve{f-p}\le (\La+1)\ve{f-p^*}\).
No set of interpolation points can lead to convergence for all \(C([-1,1])\) (PROOF?) so \(\lim_{n\to \iy} \La_n\).
Theorem.
Instructive: Plot \(\la(x)\) for equispaced and Chebyshev points.
Intuition: The fastest a Lagrange polynomial can decay is \(O\prc{x}\), and adding up these alternating tails with alternating coefficients gives a harmonic series.
Related: For Taylor projection of \(f\) analytic on the unit disc, Landau constants \(\La_n \sim \rc{\pi}\log n\).


Hello! I am Lisa, a full-stack developer in Seattle. I enjoy coding, learning and creating cool stuff.
I have experience in the following: JavaScript, jQuery, MongoDB, Node.js, Angular.js, Express.js, React.js, Python, MySql, RESTful web services, AWS cloud services


Hello my name is Pierce. I am in Web Development, and I’m looking for opportunities to grow and evolve as a full-stack developer within the San Diego tech community. I come from a background in customer service and sales, I have strong interpersonal skills, and I’m most effective in a team setting.
I attended LEARN academy in 2016 to gain the foundational skills to land my first development job. I have always been fascinated by computers, and the code behind the scenes. My goal is to gain enough exposure to become a proficient developer, and make a notable impact on the community with my work.


Situation Room calls for cancellation of Kogi elections
by Azeezat AdedigbaThe Nigerian Civil Society Situation Room has called for the total cancellation of the elections held in Kogi State on Saturday due to the high level of violence and vote buying.
Governorship election was held across the state while a senatorial rerun election was held in Kogi West district.
The Situation Room, a coalition of prominent civic groups, said the Kogi election represents a major dent to Nigeria’s democracy.
The convener of the situation room, Clement Nwankwo, announced the group’s stance in a press conference in Abuja on Sunday.
According to him, if this election is allowed to stand, 2023 and Ondo State election next year will be a bloodbath.
The Situation Room is one of the accredited observers for the election.
PREMIUM TIMES reported how the Kogi State election was characterised by the late arrival of electoral materials, violence and intimidation of voters. The election was, however, also peaceful and efficient in some other areas.
A total of 24 candidates are taking part in the gubernatorial election. Although the registered voters in the state are 1,646,350, about 1,485,828 (90.2 per cent) have collected their PVCs and are thus eligible to vote in the 21 local governments of the state.
Details later…


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{% extends "base.html" %} {% block body_class %}template-homepage{% endblock %} {% block content %}
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| Package | Description |
|---|---|
| javafx.concurrent |
Provides the set of classes for javafx.task.
|
| javafx.embed.swing |
Provides the set of classes to use JavaFX inside Swing applications.
|
| javafx.event |
Provides basic framework for FX events, their delivery and handling.
|
| javafx.scene |
Provides the core set of base
classes for the JavaFX Scene Graph API.
|
| javafx.scene.canvas |
Provides the set of classes for canvas, an immediate mode style of rendering API.
|
| javafx.scene.chart |
The JavaFX User Interface provides a set of chart components that
are a very convenient way for data visualization.
|
| javafx.scene.control |
The JavaFX User Interface Controls (UI Controls or just Controls) are
specialized Nodes in the JavaFX Scenegraph especially suited for reuse in
many different application contexts.
|
| javafx.scene.control.cell |
The
javafx.scene.control.cell package is where all cell-related
classes are located, other than the core classes such as
Cell , IndexedCell ,
ListCell , TreeCell ,
and TableCell . |
| javafx.scene.image |
Provides the set of classes for loading and displaying images.
|
| javafx.scene.input |
Provides the set of classes for mouse and keyboard input event handling.
|
| javafx.scene.layout |
Provides classes to support user interface layout.
|
| javafx.scene.media |
Provides the set of classes for integrating audio and video into Java FX
Applications.
|
| javafx.scene.shape |
Provides the set of 2D classes for defining and performing operations on
objects related to two-dimensional geometry.
|
| javafx.scene.text |
Provides the set of classes for fonts and renderable Text Node.
|
| javafx.scene.transform |
Provides the set of convenient classes to perform rotating, scaling,
shearing, and translation transformations for
Affine objects. |
| javafx.scene.web |
This package provides means for loading and displaying Web content.
|
| javafx.stage |
Provides the top-level container classes for JavaFX content.
|
| Modifier and Type | Class and Description |
|---|---|
class |
ScheduledService<V>
The ScheduledService is a
Service which will automatically restart
itself after a successful execution, and under some conditions will
restart even in case of failure. |
class |
Service<V>
A Service is a non-visual component encapsulating the information required
to perform some work on one or more background threads.
|
class |
Task<V>
A fully observable implementation of a
FutureTask . |
| Modifier and Type | Class and Description |
|---|---|
class |
SwingNode
This class is used to embed a Swing content into a JavaFX application.
|
| Modifier and Type | Field and Description |
|---|---|
static EventTarget |
Event.NULL_SOURCE_TARGET
The constant which represents an unknown event source / target.
|
protected EventTarget |
Event.target
Event target that defines the path through which the event
will travel when posted.
|
| Modifier and Type | Method and Description |
|---|---|
EventTarget |
Event.getTarget()
Returns the event target of this event.
|
| Modifier and Type | Method and Description |
|---|---|
ActionEvent |
ActionEvent.copyFor(Object newSource,
EventTarget newTarget) |
Event |
Event.copyFor(Object newSource,
EventTarget newTarget)
Creates and returns a copy of this event with the specified event source
and target.
|
static void |
Event.fireEvent(EventTarget eventTarget,
Event event)
Fires the specified event.
|
| Constructor and Description |
|---|
ActionEvent(Object source,
EventTarget target)
Construct a new
ActionEvent with the specified event source and target. |
Event(Object source,
EventTarget target,
EventType<? extends Event> eventType)
Construct a new
Event with the specified event source, target
and type. |
| Modifier and Type | Class and Description |
|---|---|
class |
AmbientLight
Defines an ambient light source object.
|
class |
Camera
Base class for a camera used to render a scene.
|
class |
Group
A
Group node contains an ObservableList of children that
are rendered in order whenever this node is rendered. |
class |
LightBase
The
LightBase class provides definitions of common properties for
objects that represent a form of Light source. |
class |
Node
Base class for scene graph nodes.
|
class |
ParallelCamera
Specifies a parallel camera for rendering a scene without perspective correction.
|
class |
Parent
The base class for all nodes that have children in the scene graph.
|
class |
PerspectiveCamera
Specifies a perspective camera for rendering a scene.
|
class |
PointLight
Defines a point light source object.
|
class |
Scene
The JavaFX
Scene class is the container for all content in a scene graph. |
class |
SubScene
The
SubScene class is the container for content in a scene graph. |
| Modifier and Type | Class and Description |
|---|---|
class |
Canvas
Canvas is an image that can be drawn on using a set of graphics
commands provided by a GraphicsContext . |
| Modifier and Type | Class and Description |
|---|---|
class |
AreaChart<X,Y>
AreaChart - Plots the area between the line that connects the data points and
the 0 line on the Y axis.
|
class |
Axis<T>
Base class for all axes in JavaFX that represents an axis drawn on a chart area.
|
class |
BarChart<X,Y>
A chart that plots bars indicating data values for a category.
|
class |
BubbleChart<X,Y>
Chart type that plots bubbles for the data points in a series.
|
class |
CategoryAxis
A axis implementation that will works on string categories where each
value as a unique category(tick mark) along the axis.
|
class |
Chart
Base class for all charts.
|
class |
LineChart<X,Y>
Line Chart plots a line connecting the data points in a series.
|
class |
NumberAxis
A axis class that plots a range of numbers with major tick marks every "tickUnit".
|
class |
PieChart
Displays a PieChart.
|
class |
ScatterChart<X,Y>
Chart type that plots symbols for the data points in a series.
|
class |
StackedAreaChart<X,Y>
StackedAreaChart is a variation of
AreaChart that displays trends of the
contribution of each value. |
class |
StackedBarChart<X,Y>
StackedBarChart is a variation of
BarChart that plots bars indicating
data values for a category. |
class |
ValueAxis<T extends Number>
A axis who's data is defined as Numbers.
|
class |
XYChart<X,Y>
Chart base class for all 2 axis charts.
|
| Modifier and Type | Class and Description |
|---|---|
class |
Accordion
An accordion is a group of
TitlePanes . |
class |
Alert
The Alert class subclasses the
Dialog class, and provides support for a number
of pre-built dialog types that can be easily shown to users to prompt for a
response. |
class |
Button
A simple button control.
|
class |
ButtonBar
A ButtonBar is essentially a
HBox , with the additional functionality
for operating system specific button placement. |
class |
ButtonBase
Base class for button-like UI Controls, including Hyperlinks, Buttons,
ToggleButtons, CheckBoxes, and RadioButtons.
|
class |
Cell<T>
|
class |
CheckBox
A tri-state selection Control typically skinned as a box with a checkmark or
tick mark when checked.
|
class |
CheckBoxTreeItem<T>
TreeItem subclass that adds support for being in selected, unselected, and
indeterminate states.
|
class |
CheckMenuItem
A
MenuItem that can be toggled between selected and unselected states. |
class |
ChoiceBox<T>
The ChoiceBox is used for presenting the user with a relatively small set of
predefined choices from which they may choose.
|
class |
ChoiceDialog<T>
A dialog that shows a list of choices to the user, from which they can pick
one item at most.
|
class |
ColorPicker
ColorPicker control allows the user to select a color from either a standard
palette of colors with a simple one click selection OR define their own custom color.
|
class |
ComboBox<T>
An implementation of the
ComboBoxBase abstract class for the most common
form of ComboBox, where a popup list is shown to users providing them with
a choice that they may select from. |
class |
ComboBoxBase<T>
Abstract base class for ComboBox-like controls.
|
class |
ContextMenu
A popup control containing an ObservableList of menu items.
|
class |
Control
Base class for all user interface controls.
|
class |
CustomMenuItem
|
class |
DateCell
DateCell is used by
DatePicker to render the individual
grid cells in the calendar month. |
class |
DatePicker
The DatePicker control allows the user to enter a date as text or
to select a date from a calendar popup.
|
class |
Dialog<R>
A Dialog in JavaFX wraps a
DialogPane and provides the necessary API
to present it to end users. |
class |
DialogPane
DialogPane should be considered to be the root node displayed within a
Dialog instance. |
class |
Hyperlink
An HTML like label which can be a graphic and/or text which responds to rollovers and clicks.
|
class |
IndexedCell<T>
An implementation of
Cell which contains an index property which maps
into the data model underlying the visualization. |
class |
Label
Label is a non-editable text control.
|
class |
Labeled
A Labeled
Control is one which has as part of its user interface
a textual content associated with it. |
class |
ListCell<T>
|
class |
ListView<T>
A ListView displays a horizontal or vertical list of items from which the
user may select, or with which the user may interact.
|
class |
Menu
A popup menu of actionable items which is displayed to the user only upon request.
|
class |
MenuBar
A MenuBar control traditionally is placed at the very top of the user
interface, and embedded within it are
Menus . |
class |
MenuButton
MenuButton is a button which, when clicked or pressed, will show a
ContextMenu . |
class |
MenuItem
MenuItem is intended to be used in conjunction with
Menu to provide
options to users. |
class |
Pagination
A Pagination control is used for navigation between pages of a single content,
which has been divided into smaller parts.
|
class |
PasswordField
Text field that masks entered characters.
|
class |
PopupControl
An extension of PopupWindow that allows for CSS styling.
|
protected class |
PopupControl.CSSBridge
The link between the popup window and the scenegraph.
|
class |
ProgressBar
A specialization of the ProgressIndicator which is represented as a
horizontal bar.
|
class |
ProgressIndicator
A circular control which is used for indicating progress, either
infinite (aka indeterminate) or finite.
|
class |
RadioButton
RadioButtons create a series of items where only one item can be
selected.
|
class |
RadioMenuItem
|
class |
ScrollBar
Either a horizontal or vertical bar with increment and decrement buttons and
a "thumb" with which the user can interact.
|
class |
ScrollPane
A Control that provides a scrolled, clipped viewport of its contents.
|
class |
Separator
A horizontal or vertical separator line.
|
class |
SeparatorMenuItem
A
MenuItem that as the name suggests allows for a horizontal Separator to be embedded within it,
by assigning a Separator to the content property of the CustomMenuItem
This is provided for convenience as groups of menuitems can be separated
by a separator. |
class |
Slider
The Slider Control is used to display a continuous or discrete range of
valid numeric choices and allows the user to interact with the control.
|
class |
Spinner<T>
A single line text field that lets the user select a number or an object
value from an ordered sequence.
|
class |
SplitMenuButton
The SplitMenuButton, like the
MenuButton is closely associated with
the concept of selecting a MenuItem from a menu. |
class |
SplitPane
A control that has two or more sides, each separated by a divider, which can be
dragged by the user to give more space to one of the sides, resulting in
the other side shrinking by an equal amount.
|
class |
Tab
Tabs are placed within a
TabPane , where each tab represents a single
'page'. |
class |
TableCell<S,T>
Represents a single row/column intersection in a
TableView . |
class |
TableColumn<S,T>
A
TableView is made up of a number of TableColumn instances. |
class |
TableColumnBase<S,T>
Table-like controls (such as
TableView and TreeTableView ) are
made up of zero or more instances of a concrete TableColumnBase subclass
(TableColumn and TreeTableColumn , respectively). |
class |
TableRow<T>
TableRow is an
IndexedCell , but
rarely needs to be used by developers creating TableView instances. |
class |
TableView<S>
The TableView control is designed to visualize an unlimited number of rows
of data, broken out into columns.
|
class |
TabPane
A control that allows switching between a group of
Tabs . |
class |
TextArea
Text input component that allows a user to enter multiple lines of
plain text.
|
class |
TextField
Text input component that allows a user to enter a single line of
unformatted text.
|
class |
TextInputControl
Abstract base class for text input controls.
|
class |
TextInputDialog
A dialog that shows a text input control to the user.
|
class |
TitledPane
A TitledPane is a panel with a title that can be opened and closed.
|
class |
ToggleButton
A
ToggleButton is a specialized control which has the ability to be
selected. |
class |
ToolBar
A ToolBar is a control which displays items horizontally
or vertically.
|
class |
Tooltip
Tooltips are common UI elements which are typically used for showing
additional information about a Node in the scenegraph when the Node is
hovered over by the mouse.
|
class |
TreeCell<T>
|
class |
TreeItem<T>
The model for a single node supplying a hierarchy of values to a control such
as TreeView.
|
class |
TreeTableCell<S,T>
Represents a single row/column intersection in a
TreeTableView . |
class |
TreeTableColumn<S,T>
A
TreeTableView is made up of a number of TreeTableColumn instances. |
class |
TreeTableRow<T>
TreeTableRow is an
IndexedCell , but
rarely needs to be used by developers creating TreeTableView instances. |
class |
TreeTableView<S>
The TreeTableView control is designed to visualize an unlimited number of rows
of data, broken out into columns.
|
class |
TreeView<T>
The TreeView control provides a view on to a tree root (of type
TreeItem ). |
| Modifier and Type | Method and Description |
|---|---|
DialogEvent |
DialogEvent.copyFor(Object newSource,
EventTarget newTarget) |
DialogEvent |
DialogEvent.copyFor(Object newSource,
EventTarget newTarget,
EventType<DialogEvent> type)
Creates a copy of the given event with the given fields substituted.
|
| Constructor and Description |
|---|
ScrollToEvent(Object source,
EventTarget target,
EventType<ScrollToEvent<T>> type,
T scrollTarget)
Construct a new
Event with the specified event source, target
and type. |
SortEvent(C source,
EventTarget target) |
| Modifier and Type | Class and Description |
|---|---|
class |
CheckBoxListCell<T>
|
class |
CheckBoxTableCell<S,T>
|
class |
CheckBoxTreeCell<T>
|
class |
CheckBoxTreeTableCell<S,T>
A class containing a
TreeTableCell implementation that draws a
CheckBox node inside the cell, optionally with a label to indicate
what the checkbox represents. |
class |
ChoiceBoxListCell<T>
|
class |
ChoiceBoxTableCell<S,T>
|
class |
ChoiceBoxTreeCell<T>
|
class |
ChoiceBoxTreeTableCell<S,T>
A class containing a
TreeTableCell implementation that draws a
ChoiceBox node inside the cell. |
class |
ComboBoxListCell<T>
|
class |
ComboBoxTableCell<S,T>
|
class |
ComboBoxTreeCell<T>
|
class |
ComboBoxTreeTableCell<S,T>
A class containing a
TreeTableCell implementation that draws a
ComboBox node inside the cell. |
class |
ProgressBarTableCell<S>
A class containing a
TableCell implementation that draws a
ProgressBar node inside the cell. |
class |
ProgressBarTreeTableCell<S>
A class containing a
TreeTableCell implementation that draws a
ProgressBar node inside the cell. |
class |
TextFieldListCell<T>
|
class |
TextFieldTableCell<S,T>
|
class |
TextFieldTreeCell<T>
|
class |
TextFieldTreeTableCell<S,T>
A class containing a
TableCell implementation that draws a
TextField node inside the cell. |
| Modifier and Type | Class and Description |
|---|---|
class |
ImageView
|
| Modifier and Type | Method and Description |
|---|---|
EventTarget |
TouchPoint.getGrabbed()
Gets event target which has grabbed this touch point.
|
EventTarget |
TouchPoint.getTarget()
Gets event target on which the touch event carrying this touch point
is fired.
|
| Modifier and Type | Method and Description |
|---|---|
boolean |
TouchPoint.belongsTo(EventTarget target)
Distinguishes between touch points targeted to the given node or some
of its children from touch points targeted somewhere else.
|
ContextMenuEvent |
ContextMenuEvent.copyFor(Object newSource,
EventTarget newTarget) |
DragEvent |
DragEvent.copyFor(Object newSource,
EventTarget newTarget) |
GestureEvent |
GestureEvent.copyFor(Object newSource,
EventTarget newTarget) |
InputMethodEvent |
InputMethodEvent.copyFor(Object newSource,
EventTarget newTarget) |
KeyEvent |
KeyEvent.copyFor(Object newSource,
EventTarget newTarget) |
MouseDragEvent |
MouseDragEvent.copyFor(Object newSource,
EventTarget newTarget) |
MouseEvent |
MouseEvent.copyFor(Object newSource,
EventTarget newTarget)
Copies this event for a different source and target.
|
RotateEvent |
RotateEvent.copyFor(Object newSource,
EventTarget newTarget) |
ScrollEvent |
ScrollEvent.copyFor(Object newSource,
EventTarget newTarget) |
SwipeEvent |
SwipeEvent.copyFor(Object newSource,
EventTarget newTarget) |
TouchEvent |
TouchEvent.copyFor(Object newSource,
EventTarget newTarget) |
ZoomEvent |
ZoomEvent.copyFor(Object newSource,
EventTarget newTarget) |
MouseDragEvent |
MouseDragEvent.copyFor(Object newSource,
EventTarget newTarget,
EventType<? extends MouseEvent> type) |
MouseEvent |
MouseEvent.copyFor(Object newSource,
EventTarget newTarget,
EventType<? extends MouseEvent> eventType)
Creates a copy of the given event with the given fields substituted.
|
DragEvent |
DragEvent.copyFor(Object source,
EventTarget target,
EventType<DragEvent> type)
Creates a copy of the given drag event with the given fields substituted.
|
KeyEvent |
KeyEvent.copyFor(Object source,
EventTarget target,
EventType<KeyEvent> type)
Creates a copy of the given event with the given fields substituted.
|
RotateEvent |
RotateEvent.copyFor(Object newSource,
EventTarget newTarget,
EventType<RotateEvent> type)
Creates a copy of the given event with the given fields substituted.
|
ScrollEvent |
ScrollEvent.copyFor(Object newSource,
EventTarget newTarget,
EventType<ScrollEvent> type)
Creates a copy of the given event with the given fields substituted.
|
SwipeEvent |
SwipeEvent.copyFor(Object newSource,
EventTarget newTarget,
EventType<SwipeEvent> type)
Creates a copy of the given event with the given fields substituted.
|
TouchEvent |
TouchEvent.copyFor(Object newSource,
EventTarget newTarget,
EventType<TouchEvent> type)
Creates a copy of the given event with the given fields substituted.
|
ZoomEvent |
ZoomEvent.copyFor(Object newSource,
EventTarget newTarget,
EventType<ZoomEvent> type)
Creates a copy of the given event with the given fields substituted.
|
DragEvent |
DragEvent.copyFor(Object source,
EventTarget target,
Object gestureSource,
Object gestureTarget,
EventType<DragEvent> eventType)
Creates a copy of the given drag event with the given fields substituted.
|
static MouseDragEvent |
MouseEvent.copyForMouseDragEvent(MouseEvent e,
Object source,
EventTarget target,
EventType<MouseDragEvent> type,
Object gestureSource,
PickResult pickResult)
Creates a copy of this mouse event of MouseDragEvent type
|
void |
TouchPoint.grab(EventTarget target)
Grabs this touch point by the given target.
|
| Constructor and Description |
|---|
ContextMenuEvent(Object source,
EventTarget target,
EventType<ContextMenuEvent> eventType,
double x,
double y,
double screenX,
double screenY,
boolean keyboardTrigger,
PickResult pickResult)
Constructs new ContextMenu event.
|
DragEvent(Object source,
EventTarget target,
EventType<DragEvent> eventType,
Dragboard dragboard,
double x,
double y,
double screenX,
double screenY,
TransferMode transferMode,
Object gestureSource,
Object gestureTarget,
PickResult pickResult)
Constructs new DragEvent event.
|
GestureEvent(Object source,
EventTarget target,
EventType<? extends GestureEvent> eventType)
Deprecated.
Do not use this constructor. Constructs empty event.
|
GestureEvent(Object source,
EventTarget target,
EventType<? extends GestureEvent> eventType,
double x,
double y,
double screenX,
double screenY,
boolean shiftDown,
boolean controlDown,
boolean altDown,
boolean metaDown,
boolean direct,
boolean inertia,
PickResult pickResult)
Constructs new GestureEvent event.
|
InputEvent(Object source,
EventTarget target,
EventType<? extends InputEvent> eventType)
Creates new instance of InputEvent.
|
InputMethodEvent(Object source,
EventTarget target,
EventType<InputMethodEvent> eventType,
List<InputMethodTextRun> composed,
String committed,
int caretPosition)
Constructs new InputMethodEvent event.
|
KeyEvent(Object source,
EventTarget target,
EventType<KeyEvent> eventType,
String character,
String text,
KeyCode code,
boolean shiftDown,
boolean controlDown,
boolean altDown,
boolean metaDown)
Constructs new KeyEvent event with null source and target and KeyCode object directly specified.
|
MouseDragEvent(Object source,
EventTarget target,
EventType<MouseDragEvent> eventType,
double x,
double y,
double screenX,
double screenY,
MouseButton button,
int clickCount,
boolean shiftDown,
boolean controlDown,
boolean altDown,
boolean metaDown,
boolean primaryButtonDown,
boolean middleButtonDown,
boolean secondaryButtonDown,
boolean synthesized,
boolean popupTrigger,
PickResult pickResult,
Object gestureSource)
Constructs new MouseDragEvent event.
|
MouseEvent(Object source,
EventTarget target,
EventType<? extends MouseEvent> eventType,
double x,
double y,
double screenX,
double screenY,
MouseButton button,
int clickCount,
boolean shiftDown,
boolean controlDown,
boolean altDown,
boolean metaDown,
boolean primaryButtonDown,
boolean middleButtonDown,
boolean secondaryButtonDown,
boolean synthesized,
boolean popupTrigger,
boolean stillSincePress,
PickResult pickResult)
Constructs new MouseEvent event.
|
PickResult(EventTarget target,
double sceneX,
double sceneY)
Creates a pick result for a 2D case where no additional information is needed.
|
RotateEvent(Object source,
EventTarget target,
EventType<RotateEvent> eventType,
double x,
double y,
double screenX,
double screenY,
boolean shiftDown,
boolean controlDown,
boolean altDown,
boolean metaDown,
boolean direct,
boolean inertia,
double angle,
double totalAngle,
PickResult pickResult)
Constructs new RotateEvent event.
|
ScrollEvent(Object source,
EventTarget target,
EventType<ScrollEvent> eventType,
double x,
double y,
double screenX,
double screenY,
boolean shiftDown,
boolean controlDown,
boolean altDown,
boolean metaDown,
boolean direct,
boolean inertia,
double deltaX,
double deltaY,
double totalDeltaX,
double totalDeltaY,
ScrollEvent.HorizontalTextScrollUnits textDeltaXUnits,
double textDeltaX,
ScrollEvent.VerticalTextScrollUnits textDeltaYUnits,
double textDeltaY,
int touchCount,
PickResult pickResult)
Constructs new ScrollEvent event.
|
SwipeEvent(Object source,
EventTarget target,
EventType<SwipeEvent> eventType,
double x,
double y,
double screenX,
double screenY,
boolean shiftDown,
boolean controlDown,
boolean altDown,
boolean metaDown,
boolean direct,
int touchCount,
PickResult pickResult)
Constructs new SwipeEvent event.
|
TouchEvent(Object source,
EventTarget target,
EventType<TouchEvent> eventType,
TouchPoint touchPoint,
List<TouchPoint> touchPoints,
int eventSetId,
boolean shiftDown,
boolean controlDown,
boolean altDown,
boolean metaDown)
Constructs new TouchEvent event.
|
TouchPoint(int id,
TouchPoint.State state,
double x,
double y,
double screenX,
double screenY,
EventTarget target,
PickResult pickResult)
Creates new instance of TouchPoint.
|
ZoomEvent(Object source,
EventTarget target,
EventType<ZoomEvent> eventType,
double x,
double y,
double screenX,
double screenY,
boolean shiftDown,
boolean controlDown,
boolean altDown,
boolean metaDown,
boolean direct,
boolean inertia,
double zoomFactor,
double totalZoomFactor,
PickResult pickResult)
Constructs new ZoomEvent event.
|
| Modifier and Type | Class and Description |
|---|---|
class |
AnchorPane
AnchorPane allows the edges of child nodes to be anchored to an offset from
the anchor pane's edges.
|
class |
BorderPane
BorderPane lays out children in top, left, right, bottom, and center positions.
|
class |
FlowPane
FlowPane lays out its children in a flow that wraps at the flowpane's boundary.
|
class |
GridPane
GridPane lays out its children within a flexible grid of rows and columns.
|
class |
HBox
HBox lays out its children in a single horizontal row.
|
class |
Pane
Base class for layout panes which need to expose the children list as public
so that users of the subclass can freely add/remove children.
|
class |
Region
Region is the base class for all JavaFX Node-based UI Controls, and all layout containers.
|
class |
StackPane
StackPane lays out its children in a back-to-front stack.
|
class |
TilePane
TilePane lays out its children in a grid of uniformly sized "tiles".
|
class |
VBox
VBox lays out its children in a single vertical column.
|
| Modifier and Type | Class and Description |
|---|---|
class |
MediaView
|
| Modifier and Type | Method and Description |
|---|---|
MediaErrorEvent |
MediaErrorEvent.copyFor(Object newSource,
EventTarget newTarget) |
| Modifier and Type | Class and Description |
|---|---|
class |
Arc
The
Arc class represents a 2D arc object, defined by a center point,
start angle (in degrees), angular extent (length of the arc in degrees),
and an arc type (ArcType.OPEN , ArcType.CHORD ,
or ArcType.ROUND ). |
class |
Box
The
Box class defines a 3 dimensional box with the specified size. |
class |
Circle
The
Circle class creates a new circle
with the specified radius and center location measured in pixels
Example usage. |
class |
CubicCurve
The
CubiCurve class defines a cubic Bézier parametric curve segment
in (x,y) coordinate space. |
class |
Cylinder
The
Cylinder class defines a 3 dimensional cylinder with the specified size. |
class |
Ellipse
The
Ellipse class creates a new ellipse
with the specified size and location in pixels |
class |
Line
This Line represents a line segment in
(x,y)
coordinate space. |
class |
MeshView
The
MeshView class defines a surface with the specified 3D
mesh data. |
class |
Path
The
Path class represents a simple shape
and provides facilities required for basic construction
and management of a geometric path. |
class |
Polygon
Creates a polygon, defined by an array of x,y coordinates.
|
class |
Polyline
Creates a polyline, defined by the array of the segment points.
|
class |
QuadCurve
The
Quadcurve class defines a quadratic Bézier parametric curve
segment in (x,y) coordinate space. |
class |
Rectangle
The
Rectangle class defines a rectangle
with the specified size and location. |
class |
Shape
The
Shape class provides definitions of common properties for
objects that represent some form of geometric shape. |
class |
Shape3D
The
Shape3D base class provides definitions of common properties for
objects that represent some form of 3D geometric shape. |
class |
Sphere
The
Sphere class defines a 3 dimensional sphere with the specified size. |
class |
SVGPath
The
SVGPath class represents a simple shape that is constructed by
parsing SVG path data from a String. |
| Modifier and Type | Class and Description |
|---|---|
class |
Text
The
Text class defines a node that displays a text. |
class |
TextFlow
TextFlow is special layout designed to lay out rich text.
|
| Modifier and Type | Class and Description |
|---|---|
class |
Affine
The
Affine class represents a general affine transform. |
class |
Rotate
This class represents an
Affine object that rotates coordinates
around an anchor point. |
class |
Scale
This class represents an
Affine object that scales coordinates
by the specified factors. |
class |
Shear
This class represents an
Affine object that shears coordinates
by the specified multipliers. |
class |
Transform
This class is a base class for different affine transformations.
|
class |
Translate
This class represents an
Affine object that translates coordinates
by the specified factors. |
| Constructor and Description |
|---|
TransformChangedEvent(Object source,
EventTarget target)
Construct a new
TransformChangedEvent with the specified event
source and target. |
| Modifier and Type | Class and Description |
|---|---|
class |
HTMLEditor
A control that allows for users to edit text, and apply styling to this text.
|
class |
WebView
|
| Modifier and Type | Class and Description |
|---|---|
class |
Popup
A Popup is a special window-like container for a scene graph.
|
class |
PopupWindow
PopupWindow is the parent for a variety of different types of popup
based windows including
Popup and Tooltip
and ContextMenu . |
class |
Stage
The JavaFX
Stage class is the top level JavaFX container. |
class |
Window
A top level window within which a scene is hosted, and with which the user
interacts.
|
| Modifier and Type | Method and Description |
|---|---|
WindowEvent |
WindowEvent.copyFor(Object newSource,
EventTarget newTarget) |
WindowEvent |
WindowEvent.copyFor(Object newSource,
EventTarget newTarget,
EventType<WindowEvent> type)
Creates a copy of the given event with the given fields substituted.
|
Submit a bug or feature
For further API reference and developer documentation, see Java SE Documentation. That documentation contains more detailed, developer-targeted descriptions, with conceptual overviews, definitions of terms, workarounds, and working code examples.
Copyright © 2008, 2021, Oracle and/or its affiliates. All rights reserved. Use is subject to license terms. Also see the documentation redistribution policy.


Aegisub / Highlights
Some highlights of Aegisub:
Simple and intuitive yet powerful interface for editing subtitles
With help from such features as spell checking/thesaurus, a translation assistant, call tips for override tags, syntax highlighting and various macros, translating, editing and quality assuring subtitles is now easier than ever.
Did a mistake? Had a system crash? Don't worry, Aegisub saves your .ass with features like multi-level undo/redo, auto saving, backups and emergency recovery saving in case of system or program crashes.
- Aegisub doesn't lock you into using any specific format; importing and exporting from and to several different formats (ranging from MPEG-4 Timed Text to MicroDVD) is supported.
- Multiple language subtitles? Legacy programs without Unicode support? No problem, Aegisub has full support for both Unicode and most common legacy encodings; both reading and writing.
- Most video common video formats are supported out of the box, but if that isn't enough, Aegisub can also use your system's DirectShow environment to open any format you can play in Windows Media Player.
- Full support for variable framerate video and Matroska timecodes. Capable of reading timecodes directly from Matroska files for seamless VFR work.
- Problems with anamorphic video? Overscan? Aegisub has the tools to handle it.
- Typesetting on easy mode! No need to manually edit override tags; drag, rotate or clip the subtitles directly on the video frame using your mouse.
- Want to re-use typesetting on a video of different resolution or aspect ratio? Can't figure out what color that sign is using? Aegisub has the tools to help you deal with it.
- Time dialogue or karaoke in any way you want with the heavily customizable audio interface; less painful than ever! Use features such as the spectrum analyzer mode or the automatic timing post-processor for even more efficient timing.
- Support for any audio format your DirectShow environment knows how to decode.
- Is all the above not enough? Extend the program with your own macros or export filters using scripting in Lua.
- Comes with several ready-made scripts for quick and easy generation of your very own karaoke effects.


Logistic Maps¶
CodeSnippet
You can download all the code on this page from the code snippets directory
In this example we show MDP usage in a machine learning application, and use non-linear Slow Feature Analysis for processing of non-stationary time series. We consider a chaotic time series derived by a logistic map (a demographic model of the population biomass of species in the presence of limiting factors such as food supply or disease) that is non-stationary in the sense that the underlying parameter is not fixed but is varying smoothly in time.
The goal is to extract the slowly varying parameter that is hidden in the observed time series. This example reproduces some of the results reported in Laurenz Wiskott, Estimating Driving Forces of Nonstationary Time Series with Slow Feature Analysis (arXiv.org e-Print archive).
Generate the slowly varying driving force, a combination of three sine waves (freqs: 5, 11, 13 Hz), and define a function to generate the logistic map
>>> p2 = np.pi*2
>>> t = np.linspace(0, 1, 10000, endpoint=0) # time axis 1s, samplerate 10KHz
>>> dforce = np.sin(p2*5*t) + np.sin(p2*11*t) + np.sin(p2*13*t)
>>> def logistic_map(x, r):
... return r*x*(1-x)
Note that we define series
to be a two-dimensional array.
Inputs to MDP must be two-dimensional arrays with variables
on columns and observations on rows. In this case we have only
one variable:
>>> series = np.zeros((10000, 1), 'd')
Fix the initial condition:
>>> series[0] = 0.6
Generate the time series using the logistic equation.
The driving force modifies the logistic equation parameter r
:
>>> for i in range(1,10000):
... series[i] = logistic_map(series[i-1],3.6+0.13*dforce[i])
If you have a plotting package series
should look like this:
To reconstruct the underlying parameter, we define a Flow
to
perform SFA in the space of polynomials of degree 3. We first use a
node that embeds the 1-dimensional time series in a 10 dimensional
space using a sliding temporal window of size 10
(TimeFramesNode(10)
). Second, we expand the signal in the space
of polynomials of degree 3 using a
PolynomialExpansionNode(3)
. Finally, we perform SFA on the
expanded signal and keep the slowest feature using the
SFANode(output_dim=1)
.
In order to measure the slowness of the input time series before and
after processing, we put at the beginning and at the end of the node
sequence a node that computes the eta-value (a measure of slowness)
of its input (EtaComputerNode()
):
>>> flow = (mdp.nodes.EtaComputerNode() +
... mdp.nodes.TimeFramesNode(10) +
... mdp.nodes.PolynomialExpansionNode(3) +
... mdp.nodes.SFANode(output_dim=1) +
... mdp.nodes.EtaComputerNode() )
Since the time series is short enough to be kept in memory we don’t need to define generators and we can feed the flow directly with the whole signal:
>>> flow.train(series)
Since the second and the third nodes are not trainable we are
going to get two warnings (Training Interrupted
). We can safely
ignore them. Execute the flow to get the slow feature
>>> slow = flow(series)
The slow feature should match the driving force up to a scaling factor, a constant offset and the sign. To allow a comparison we rescale the driving force to have zero mean and unit variance:
>>> resc_dforce = (dforce - np.mean(dforce, 0)) / np.std(dforce, 0)
Print covariance between the rescaled driving force and the slow feature. Note that embedding the time series with 10 time frames leads to a time series with 9 observations less:
>>> print '%.3f' % mdp.utils.cov2(resc_dforce[:-9], slow)
1.000
Print the eta-values of the chaotic time series and of the slow feature
>>> print 'Eta value (time series): %d' % flow[0].get_eta(t=10000)
Eta value (time series): 3004
>>> print 'Eta value (slow feature): %.3f' % flow[-1].get_eta(t=9996)
Eta value (slow feature): 10.218
If you have a plotting package you could plot the real driving force is plotted together with the driving force estimated by SFA and see that they match perfectly:


Mehmet Ozdemir
Education
2015-Present: University at Buffalo
- B.S. in Computer Science(Expected May 2019), 3.4 GPA
- On the Sponsor Team for UB Hacking 2017
- On the Diversity Committee Sub Committee a part of UGAC
Experience
June 2017-Present, IT Specialist at Levittown Public Schools
- Creating and deploying images onto computers in the district
- Taking out and putting in new computers in the district
- Troubleshooting any errors or bugs on computers and tablets
September 2016-Present, Teacher's Assistant for CSE 115 at UB
- Helping students understand fundamental practices of Programming
- Grading Exams
- Holding office hours, scheduled appointments and review sessions
Skills
Computer Languages
|       • C/C++ |  • Java |  • Verilog |
|       • Python |  • SML |  • Lua |
|       • Javascript |  • HTML |  • CSS |
OS Experience
|       • Ubuntu |  • Widnows |
Projects
Website for Mental Health Hotlines
• Personal Project to bring awareness and hotlines to people.
Alien Invasion Game
• Game I made with Python's Pygame library.
Garry's Mod Gamemode
• Gamemode mod I made with Lua.
SML Interpreter
• Interpreter that I made for CSE 305.
Java Web Browser
• A Mini Java Web Browser that was made at UB Hacking with a group of four.


Wired wiki is a fiction application that was developed in some guys head for the purpose of creating a tutorial for bootstrap. The Actualization of the app would be good though
Cruising down the streets in my '64. Joking the b*tches. Slapping the hoes.       Slapping em b***hes, slaying em hoes.
Crusing down the streets in my 64. Slapping em b***hes, slaying em hoes.
Crusing down the streets in my 64. Slapping em b***hes, slaying em hoes.
Cruising down the streets in my 64.
Don't quote me boy.
Question 5 para para para para
Question 6... question 6... Question 6


Tender Matching People to Recipes
The Team
- Justin Xu<EMAIL_ADDRESS>- Makena Low<EMAIL_ADDRESS>- Joshua Dong<EMAIL_ADDRESS>Github Repo: https://github.com/justinxu421/recipe_rex
Problem Definition
You’re at the grocery store, looking through the shelves of copious options, unsure of what you’d actually enjoy cooking or eating. You have a sense of what you’re craving, but a search on Google for your latest craving can take an hour and many tabs to surface the recipes that hit it. Your cravings also keep changing. New Years’ resolutions for healthy food turn into longing for quick meals, which cascade into a phase of comfort food. Discovering new food takes a lot of effort.
Introducing Tender
Our app is like Tinder. But instead of matching people to people, it matches people to recipes with a similar focus on simplicity. When you first open the app, you’re shown the bios of 4 recipes: their profile photos, names, and who they are. After 10 rounds of choices, our app recommends the best matches to your craving from over 2000 recipes curated by blogs covering many traditional Asian recipes and fusion concepts.
As you choose, we guess your preferences for meats and starches and show them to you in graphs on the bottom of the screen. This helps narrow down our search for the most similar recipes to the ones you chose. And if you’re in the mood for desserts or sides instead of a main dish, you can choose to explore those options on the side bar.
In our next sections, we’ll describe how we evaluated our app, designed the algorithms under the hood, related works, and reflections on our work.
Related Work
Recommendations are a pretty hot topic in today’s society, from apps like Spotify and TikTok, which rely on quickly changing trends and massive amounts of input data / user information in order to build out their algorithms. As a result, many of these algorithms didn’t seem to satisfy the restrictions of our use case, as they relied on repeat user experiences and massive amounts of data.
However, inspiration for the algorithm we utilized for this project was partially taken from the original 2010 Youtube Recommendation Paper [1]. This paper showed a two-step recommendation algorithm where the first step was generating candidates based on a user’s recent activity and the second step was a ranking algorithm which was based on user preferences, which seemed to be a general interpretable approach for our problem.
Video Demo
System Evaluation
To validate the quality of our recommendations, we compare our recommendations to a random sample of recipes, and the user has to choose which they prefer the most. The percentage of their choices that we recommend is our validation score. If it’s 50%, we’re doing no better than random, giving us a natural baseline.
To perform a slice based analysis of our recommendations on different types of cravings, we designed 8 cravings for soupy and stirfry main dishes. We then asked 10 young adults in their early 20s to choose a craving, and use the app. We intentionally left the cravings up to interpretation and gave users the freedom to choose recipes.
Across our 54 user tests, our recommendation system achieved a validation score of 68%, beating our baseline by 18%. We scored 67% across soupy dishes and 71% across stir-fry dishes. Looking at the breakdown of scores, we find performance on vegetable soup and vegetarian stir-fry to be close to average, a surprise since these are the least represented dishes from our recipe websites.
System Design
Our modeling relied on libraries like FastText [2], scikit-learn [3], Pandas [4], and NumPy [5]. We chose Streamlit [6] for the front end and deployment of our app to keep our codebase in Python and for faster iteration. Below is a simple diagram of our algorithms. We’ll step through each part in the next sections.
Feature Engineering our Recipe Embeddings
Using recipe-scraper [7], we found the following features for all our recipes.
We curated recipes for main dishes, desserts, and sides, receiving recipe counts of 1737, 362, 221 respectively. For each recipe, we created a joint embedding of the nutrition and ingredients.
Our nutrition embedding gave a binary label to a recipe for exceeding the 75th percentile of fat, protein, carbohydrate, sodium, or sugar content across recipes.
Our ingredients embedding was created in a few steps. First, unigrams and bigrams were extracted from every list of ingredients. Bigrams captured words like “soy sauce” and “chicken breast”. Among the 989 which occurred over 20 times, 359 ingredient grams were manually labeled and kept. Each of these grams were mapped to a 300-dimension embedding using a pretrained FastText language model. FastText [2] forms word embeddings by averaging subword embeddings. This allows it to generalize to unseen vocabulary in our ingredient grams, unlike Word2Vec [11]. To create a sentence embedding from all the ingredients of a recipe, we took an inverse frequency weighted average of the individual ingredient embeddings based on the smooth inverse frequency method introduced by Arora et al [8]. Compared to using SentenceBERT [12], this better takes advantage of our domain specific ingredient frequency.
To create a joint embedding with a balanced influence from the nutrition and ingredients, we projected our ingredient embeddings into the subspace formed by their first 5 principal components, which explained 49% of the variance. Extending to 10 principal components would have explained an additional 12% of variance.
To evaluate the semantic understanding represented by our principal components, we examined how cuisine is clustered along the first two principal components. Below on the left includes Chinese cuisine in bright red, our dominant class. To better visualize the clustering of our minority classes, we show the same graph excluding Chinese cuisine on the right. Without explicitly including cuisine in our embedding, we find that it keeps similar cuisines close to each other while also capturing intra-cuisine variance. This supports our hypothesis that our embedding incorporates semantic understanding.
Our final joint embedding was a 5-dimensional ingredient embedding stacked on a 5 dimensional nutrition embedding.
Designing our Recommendation Algorithms
The main driver to our recommendation engine was a k-nearest neighbor [13] recommendation system. Given the fact that our dataset was relatively small, at around 2000 recipes, a nearest neighbor approach seemed to make the most sense in terms of finding similar recipes with cosine distance.
To make it a true machine learning application, our app needed to learn user preferences as it proceeded! To do this, we generated a coarser, more interpretable labeling system for every recipe to capture some taste preferences a user might have coming in. The two main categories we selected were meat and starch. These two categories were chosen given the fact that the user may have dietary restrictions. The labels were generated through a title / ingredient list keyword match.
We see that these categories are well distributed across our ingredient embedding space.
Given these taste labels, we can then restructure our search problem as a multi-armed bandit problem [10]. The goal of the algorithm is to generate a sampling procedure of the arms to find with high accuracy what the expected payout of each arm is. In this problem, our “arms” are the individuals taste preferences, and the payout is the probability given all choices that the individual will select a particular preference. Since the hypothesis is that users come into our app with a particular taste preference in mind, they will likely select recipes matching that preference.
One solution to the bandit problem with optimal regret bounds (rough amortized long term deviation from optimal) is the UCB (Upper Confidence Bound) [9] algorithm, which selects the arm with the highest upper bound to the confidence interval of the payouts.
This approach simulates exploration vs. exploitation since in the beginning, this algorithm will select taste preferences that have not been selected yet (due to high variance), but as the user proceeds, it will start to recommend more recipes matching the user’s preferences (exploitation phase), as it gains higher confidence for the value of their preferences.
Reflections
Overall, the project experience was very positive. Our team’s general dynamic and workflow worked well together. Sometimes it was a little difficult to divide up work, as some next steps were a little conditional on the previous part, so it was hard to parallelize, especially in a remote situation. On the other hand, since this project was a full application, we were able to divide work flow into the general “front end” vs. “back end” aspects that we had to handle to some extent, switching off who was working on what at different stages, and were still able to build team camaraderie by pair programming too.
The tech stack that we decided on in the beginning also worked out well, since everything was able to be in python and easily integrated together. We had to pivot a couple of times in terms of what we were designing, especially in the direction of away from black box approaches and more into the interpretable methods + UX considerations.
If given more time, we would try to incorporate more features to create a richer embedding space in combination with more recipes in our database to generate more personalized recommendations. On the engineering side, we’d also try to fully deploy our app, incorporating database storage and user memory in order to preserve information across multiple uses of our app. This would also enable many more machine learning features, including labeled data as we log users using our app, and collecting information for personalization. Streamlit’s public deploy also wasn’t able to handle multiple users using the app at the same time because of shared state space. We’d probably want to migrate our tech stack to something more robust, as well as provide more flexibility in terms of the UX design.
We were not super ambitious about the technology we used, so we’d like to also incorporate some of the concepts we learned in class, like online learning and edge computing, and setting up the general DevOps workflow (maybe if we turn our app into a startup)!
Broader Impact
We see an app like this flattening the activation energy for young adults in a hurry to plan out meals they’ll enjoy cooking and eating. Instead of many searches and open tabs to gather together a few options that satisfy one’s craving, they can come to an app like ours.
One audience we have had a challenge serving is people with dietary restrictions. For example, an early version of our app had a difficult time distinguishing red meat from non-red meat. Using filters learned by our UCB algorithm and sourcing more recipes that are kosher and vegetarian has helped. Our app could unintentionally exclude guests with dietary restrictions from the tables of users who come to use it often.
We attempted to combat this problem by being mindful of selecting recipes from a variety of sources and cuisines, including many vegetarian dishes + a variety of meats / taste profiles. However, naturally, our dataset is still heavily Chinese/Korean/Japanese skewed due to the popularity of East Asian cuisine.
References
- Davidson, James & Liebald, Benjamin & Liu, Junning & Nandy, Palash & Vleet, Taylor & Gargi, Ullas & Gupta, Sujoy & He, Yu & Lambert, Michel & Livingston, Blake & Sampath, Dasarathi. (2010). The YouTube video recommendation system
- P. Bojanowski, E. Grave, A. Joulin, T. Mikolov, Enriching Word Vectors with Subword Information
- Fabian Pedregosa, Gaël Varoquaux, Alexandre Gramfort, Vincent Michel, Bertrand Thirion, Olivier Grisel, Mathieu Blondel, Peter Prettenhofer, Ron Weiss, Vincent Dubourg, Jake Vanderplas, Alexandre Passos, David Cournapeau, Matthieu Brucher, Matthieu Perrot, Édouard Duchesnay. Scikit-learn: Machine Learning in Python, Journal of Machine Learning Research, 12, 2825-2830 (2011) 6.
- Wes McKinney. Data Structures for Statistical Computing in Python, Proceedings of the 9th Python in Science Conference, 51-56 (2010)
- Charles R. Harris, K. Jarrod Millman, Stéfan J. van der Walt, Ralf Gommers, Pauli Virtanen, David Cournapeau, Eric Wieser, Julian Taylor, Sebastian Berg, Nathaniel J. Smith, Robert Kern, Matti Picus, Stephan Hoyer, Marten H. van Kerkwijk, Matthew Brett, Allan Haldane, Jaime Fernández del Río, Mark Wiebe, Pearu Peterson, Pierre Gérard-Marchant, Kevin Sheppard, Tyler Reddy, Warren Weckesser, Hameer Abbasi, Christoph Gohlke & Travis E. Oliphant. Array programming with NumPy, Nature
- Ashish Shukla, Charly Wargnier, Christian Klose, Fanilo Andrianasolo, Jesse Agbemabiase, Johannes Rieke, José Manuel Nápoles, Tyler Richards Streamlit
- recipe-scraper https://github.com/hhursev/recipe-scrapers/
- Sanjeev Arora and Yingyu Liang and Tengyu Ma. A Simple but Tough-to-Beat Baseline for Sentence Embeddings. ICML 2017
- Sébastien Bubeck, Nicolò Cesa-Bianchi: Regret Analysis of Stochastic and Nonstochastic Multi-armed Bandit Problems. CoRR abs/1204.5721 (2012)
- Auer, Peter, et al. “The nonstochastic multiarmed bandit problem.” SIAM journal on computing 32.1 (2002): 48-77.
- Mikolov, Tomas, et al. “Efficient estimation of word representations in vector space.” arXiv preprint arXiv:1301.3781 (2013).
- Reimers, Nils, and Iryna Gurevych. “Sentence-bert: Sentence embeddings using siamese bert-networks.” arXiv preprint arXiv:1908.10084 (2019).
- Cunningham, Padraig, and Sarah Jane Delany. “k-Nearest Neighbour Classifiers–.” arXiv preprint arXiv:2004.04523 (2020).


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Gateway
BOT
17-Apr-19 03:19 PM
[dscrd-hush] <dukeleto> @juni what is your question?
[dscrd-hush] <dukeleto> @ITM airdrop works on addresses, not wallets, so most likely you have some addresses with smaller amounts of HUSH, that haven't been sent out yet
[dscrd-hush] <blankmac - BasementPool> @dukeleto The private key is the same tho, correct? Or no?
[dscrd-hush] <dukeleto> @blankmac - BasementPool no, the public and private keys have different base58 prefixes, so they look different, but they are the same key, encoded differently
[dscrd-hush] <dukeleto> @blankmac - BasementPool KMD Agama GUI wallet has a "WIF to WIF" tool in the "Tools" menu
[dscrd-hush] <dukeleto> it can translate WIFs between coins
[dscrd-hush] <blankmac - BasementPool> Ah, I see, so I can translate the private key with your script? Or another tool? Just trying to understand how to import my old address balances.
[dscrd-hush] <dukeleto> current agama only knows about old hush, so if you use an existing agama, you would say "convert this HUSH WIF to this KMD WIF"
[dscrd-hush] <dukeleto> my script only converts addresses
[dscrd-hush] <dukeleto> there is a script to convert wifs too, the Agama GUI is probably easier to use
[dscrd-hush] <dukeleto> Current HUSH3 WIF format, as an asset chain, is KMD format, like every other asset chain
[dscrd-hush] <dukeleto> KMD and all asset chains use the same base58 prefixes for addresses (normal and scripthash), public keys, and private keys
[dscrd-hush] <dukeleto> HUSH old format was exactly the same as ZEC. With the above information, it's possible to use existing tools or write new ones to do it, but it needs to be made easier
[dscrd-hush] <dukeleto> we are working on that
[dscrd-hush] <dukeleto> another simple thing, is to backup your wallet.dat
[dscrd-hush] <dukeleto> and then use an old HUSH wallet.dat on a new HUSH3 full node, with the -zapwallettxes CLI arg, which should allow you to claim funds. Obviously we need to test this more and it's only for people comfortable with the CLI
[dscrd-hush] <dukeleto> various exchanges and pools have been doing things like this, to get operational
[dscrd-hush] <dukeleto> Because all BTC forks share the same math curve, they have the same public + private keys, so your wallet.dat unlocks equivalent addresses on any chain
[dscrd-hush] <blankmac - BasementPool> Ok, my skull is thick but I think it got through...lol. So I can use the KMD agama wallet to translate the old hush priv key and then use that to import to the full node?
[dscrd-hush] <dukeleto> yes
[dscrd-hush] <dukeleto> "Tools" menu of KMD agama desktop wallet
[dscrd-hush] <dukeleto> has many things, one is "Wif to Wif"
[dscrd-hush] <dukeleto> WIF=Wallet Import Format
[dscrd-hush] <dukeleto> which is base58 of a privatey key, which some prefixes
[dscrd-hush] <dukeleto> never give a WIF to anybody! You should never give it to a website!
[dscrd-hush] <dukeleto> Only because you trust the wallet running on your computer, and it has access to all your funds already, is why putting in a WIF is ok. It's a completely local operation
[dscrd-hush] <dukeleto> You only should ever use a WIF yourself, never give it to others, is what I am trying to say
[dscrd-hush] <blankmac - BasementPool> Gotcha, I'm clear on the security aspects of the private key. I do some hardware programming as a hobby so I'm not completely out to lunch, but admittedly, my knowledge of the nuts and bolts of crypto is lacking for sure.


Users frame. More...
#include <Topsens.hpp>
Public Member Functions | |
| Vector2 | MapTo2D (const Vector3 position) const |
| Obtains a projection of a skeleton joint in a depth camera space on a two-dimensional plane. More... | |
Additional Inherited Members | |
| Public Attributes inherited from _TOPSENS_USERS_FRAME | |
| uint32_t | UserCount |
| The count of identified users. More... | |
| TOPSENS_SKELETON * | Skeletons |
| The collection of user skeleton data. More... | |
| TOPSENS_USER_MASK | UserMask |
| User mask data. More... | |
| TOPSENS_VECTOR4 | GroundPlane |
| The plane equation of the ground detected in the scene. More... | |
| TOPSENS_VECTOR4 | Projection |
| Projection parameters. More... | |
| uint64_t | Timestamp |
| The data timestamp in milliseconds. More... | |
Users frame.
Definition at line 166 of file Topsens.hpp.
Obtains a projection of a skeleton joint in a depth camera space on a two-dimensional plane.
| position | The coordinates of the skeleton joint in 3D space. |
Definition at line 174 of file Topsens.hpp.