text:
# Approximating integral of x^4 e^-x

1. Apr 28, 2005

### StatusX

I'm trying to approximate an integral of the form:

$$\int_0^{r_0} r^4 e^{-r/a} dr$$

where r0<<a. I figured I could write out the first few terms of the expansion of the exponential and integrate that, since the extra terms would quickly become negligible:

$$\int_0^{r_0} r^4 (1-\frac{r}{a}) dr$$

However, when I calculate this answer and compare it to the exact answer from mathematica, the error gets bigger the smaller r0/a gets. I can't figure out why. Specifically, with a few extra terms with the same form, but different powers of r, and r0/a of the order 10^-5, my approximated integral comes out to be about 10^-10 while the exact value is about 0.02. Could this be numerical error? I told it to algebraically come up with the ratio of the approximation and the exact integral, and there were 1/r^5 and 1/r^6 terms, but I can't figure out where they're coming from. Even as I add more terms to the taylor approximation, the answer barely changes.

2. Apr 29, 2005

### Dr Transport

express the integral in the form
$$\int^{1} _{0} x^{m} e^{-bx} dx$$ the exact answer is

$$\frac{m!}{b^{m+1}} \left[ 1 - e^{-b} \sum^{m} _{r = 0} \frac{b^{r}}{r!} \right]$$

3. Apr 29, 2005

### Hurkyl

Staff Emeritus
Have you considered that, after you've approximated the integrand, you made a mistake in your numerical computation of the integral?

format: plain


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Article Contents
Article Contents

# Shadowing for families of endomorphisms of generalized group shifts

• Let $G$ be a countable monoid and let $A$ be an Artinian group (resp. an Artinian module). Let $\Sigma \subset A^G$ be a closed subshift which is also a subgroup (resp. a submodule) of $A^G$. Suppose that $\Gamma$ is a finitely generated monoid consisting of pairwise commuting cellular automata $\Sigma \to \Sigma$ that are also homomorphisms of groups (resp. homomorphisms of modules) with monoid binary operation given by composition of maps. We show that the natural action of $\Gamma$ on $\Sigma$ satisfies a natural intrinsic shadowing property. Generalizations are also established for families of endomorphisms of admissible group subshifts.

Mathematics Subject Classification: Primary: 37B51, 37B10, 37B15; Secondary: 14L10, 68Q80.

 Citation:

•  [1] D. V. Anosov, Geodesic flows on closed Riemann manifolds with negative curvature, Translated from the Russian by S. Feder Proceedings of the Steklov Institute of Mathematics, American Mathematical Society, 90, Providence, R.I., 1967. [2] S. Barbieri, F. García-Ramos and H. Li, Markovian properties of continuous group actions: Algebraic actions, entropy and the homoclinic group, preprint, arXiv: 1911.00785. [3] G. D. Birkhoff, An extension of Poincaré's last geometric theorem, Acta Math., 47 (1926), 297-311.  doi: 10.1007/BF02559515. [4] F. Blanchard and A. Maass, Dynamical properties of expansive one-sided cellular automata, Israel J. Math., 99 (1997), 149-174.  doi: 10.1007/BF02760680. [5] R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Second Revised Edition. With A Preface by David Ruelle. Edited by Jean-René Chazottes. Lecture Notes in Mathematics, 470. Springer-Verlag, Berlin, 2008. [6] T. Ceccherini-Silberstein and M. Coornaert, Cellular Automata and Groups, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2010. doi: 10.1007/978-3-642-14034-1. [7] T. Ceccherini-Silberstein and M. Coornaert, On surjunctive monoids, Internat. J. Algebra Comput., 25 (2015), 567-606.  doi: 10.1142/S0218196715500113. [8] N. P. Chung and K. Lee, Topological stability and pseudo-orbit tracing property of group actions, Proc. Amer. Math. Soc., 146 (2018), 1047-1057.  doi: 10.1090/proc/13654. [9] F. Fiorenzi, Periodic configurations of subshifts on groups, Internat. J. Algebra Comput., 19 (2009), 315-335.  doi: 10.1142/S0218196709005123. [10] B. Kitchens and K. Schmidt, Automorphisms of compact groups, Ergodic Theory Dynam. Systems, 9 (1989), 691-735.  doi: 10.1017/S0143385700005290. [11] P. Kurka, Languages, equicontinuity and attractors in cellular automata, Ergodic Theory Dynam. Systems, 17 (1997), 417-433.  doi: 10.1017/S014338579706985X. [12] T. Meyerovitch, Pseudo-orbit tracing and algebraic actions of countable amenable groups, Ergodic Theory Dynam. Systems, 39 (2019), 2570-2591.  doi: 10.1017/etds.2017.126. [13] J. v. Neumann,  Theory of Self-Reproducing Automata, Univerity of Illinois Press, 1966. [14] P. Oprocha, Shadowing in multi-dimensional shift spaces, Colloq. Math., 110 (2008), 451-460.  doi: 10.4064/cm110-2-8. [15] A. V. Osipov and S. B. Tikhomirov, Shadowing for actions of some finitely generated groups, Dyn. Syst., 29 (2014), 337-351.  doi: 10.1080/14689367.2014.902037. [16] X. K. Phung, On dynamical finiteness properties of algebraic group shifts, to appear in Israel J. Math., arXiv: 2010.04035. [17] S. Y. Pilyugin and S. B. Tikhomirov, Shadowing in actions of some abelian groups, Fund. Math., 179 (2003), 83-96.  doi: 10.4064/fm179-1-7. [18] V. Salo, When are group shifts of finite type?, preprint, arXiv: 1807.01951. [19] A. Schlette, Artinian, almost abelian groups and their groups of automorphisms, Pacific J. Math., 29 (1969), 403-425.  doi: 10.2140/pjm.1969.29.403. [20] K. Schmidt, Dynamical Systems of Algebraic Origin, Progress in Mathematics, 128, Birkhäuser Verlag, Basel, 1995. [21] P. Walters, On the pseudo-orbit tracing property and its relationship to stability, in The Structure of Attractors in Dynamical Systems, (Proc. Conf., North Dakota State Univ., Fargo, N.D., 1977), Lecture Notes in Math., 668, Springer, Berlin, 1978,231–244.


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## 2013-05-20

### Durable Goods: Cast Iron

Cooking is one of those life skills that can very easily save you hundreds of thousands of dollars over your lifetime, for a relatively minimal initial investment of time and money.

Let's look at the numbers:

Say you're saving and investing 40% of your income and planning to retire in approximately 20 years.  If the market average return is in the vicinity of 7% (and this is very reasonable), that puts your Future Value Factors (FVFs) at approximately 4x, 40x, 500x, and 15500x for one-time, annual, monthly, and daily purchases, respectively.  Let's say that you're considering changing your lifestyle so that four days a week, you cook dinner instead of eating out ($10 saved) and you have leftovers that you can bring into work the next day ($5 saved).  At $60/week, this is equivalent to saving$8.50 a day.  At the daily-purchase FVF of 15500x, this simple act will put an extra $130,000 in your bank account at your 20-year retirement goal. Saving less than 40% and retiring in more than 20 years? Due to the power of compound interest, your savings will be even greater. Look up your Future Value Factors here. Have a significant other? If you can double the total saved on food per week, that's now$260,000 extra saved at retirement time.  If you have friends living nearby and you can coordinate regular potlucks and foodshares, the savings can be even greater for less work on your part.

Maybe it's time to learn how to cook.

### Tools For The Job

You probably already have access to the two most crucial ingredients for successful cooking: food and a heat source.  Yes yes, there are lots of fancy tools and techniques that you can make use of to accomplish all manner of tasty things, but cooking is fundamentally the application of heat to food.  And while there are some incredibly delicious things you can make with the direct application of heat (see: campfire corn-on-the-cob), in most cases you're going to want to place something between the heat source and the food itself.

Cast iron is the most inexpensive, most durable, most environmentally-friendly, and most versatile of the food-heat intermediators.  Taken together with the incredible cost savings of cooking as described above, I would venture to say that cast iron cookware is some of the most Mustachian hardware that one could obtain.  It's right up there with the bicycle.

My cast iron cookware collection consists of the following:

Lodge Logic Cast Iron Skillet, 12" (the best place to start; 10.5" or 12")
Lodge Logic Cast Iron Pizza Pan, 14" (doubles as a griddle!)
Lodge Logic Cast Iron Wok, 14"

I don't own these, but they appear to have their uses:
Lodge Logic Cast Iron Grill Griddle (20"x10.5") (turns two oven burners into a grill)
Lodge Logic Cast Iron Skillet, 17" (approaching paella pan dimensions...)
Lodge Logic Cast Iron Square Grill Pan (if you like lines on your food)
Lodge Logic Cast Iron Grill Press (press that burger, bacon, or tofu into submission)
Lodge Logic Cast Iron Loaf Pan (hello, cornbread)

Lodge's cookware is pre-seasoned and ready to go out of the box.

Drunk off the new-found economic power of my $30k/year graduate student stipend, I committed the crassly commercial and co-opted my cast iron cookware collection on Amazon. If you have more time and less money (and you almost certainly do), buy used instead! Cast iron is absolutely indestructible, so it's not surprising that Craigslist actively trades in the stuff: http://sfbay.craigslist.org/search/sss?query=cast+iron+skillet. Find a local seller and save a few bucks. Lodge is the primary manufacturer of newer cast iron cookware, but if you look on Craigslist or Ebay you can also find cookware made by Griswold, Wagner, Victor, Erie, and Iron Mountain; Griswold pans especially are now collector's items. Interestingly enough, I am related to the Griswold family who ran their cast iron manufacturing plant in Erie, PA from 1865 to 1957. Perhaps I have a little cast iron in the blood. ### Cast Iron is Awesome At$15-20 new, anyone can afford a good cast iron skillet.  Cast iron is a one-time investment, a serious heirloom purchase: it's a solid slab of metal with no welds or rivets, and you don't have to worry about it warping, cracking, or delaminating.  Drop it and you may damage your stove, countertop, floor, and foot bones, but the skillet itself will be fine.  A 12" cast iron skillet is excellent for self-defense.

While a nonstick pan is ruined when the finish begins to flake off, cast iron's finish can easily be repaired at home by a process called 'seasoning' (see 'Care and Feeding of Cast Iron' below).  The nonstick properties of the pan actually improve with the finish's age.

You can cook on the highest of high heat without fear of damaging the finish or the pan itself.  It's perfectly fine to place the cast iron directly in a campfire, on the grill, or over a high-output gas burner.  Metal utensils, which irreparably scratch nonstick, aluminium, or stainless steel, are fine too.  The metal is thick and holds a huge amount of heat, so the hot pan doesn't cool down as much when you throw cold food into it.  This is extremely important when you're trying to get a good crust of tasty browning on food, which requires that the pan's surface stay as hot as possible.  All of that retained heat also keeps the food warm when you move it to the dinner table.  If you've ever been to a restaurant that serves fajitas with a sizzling skillet of peppers and onions, you get the idea.

Lodge also makes its cast iron cookware in the US, which is pretty awesome for the economy.

### Cast Iron vs Nonstick Cookware

That said, cast iron is not perfect for everything.  It's quite heavy, so you should make sure you'll be able to handle that much metal safely before you buy one.

Lodge states that you should initially avoid highly-acidic foods containing tomatoes and citrus juices until the seasoning has had some time to develop.  Cast iron is not your best choice for boiling water, because you must also heat up the pan's considerable metal mass and it will take more time and energy than it would in a stainless steel or aluminum pot.

Some extremely delicate foods may be more difficult to cook, though this is less of an issue as the pan's non-stick properties improve with use.  Cast iron also has more stringent maintenance requirements than other pans, and should be wiped out and reheated with a bit of oil to drive off water a short time after use.

Your great great grandparents may very well have cooked ALL of their food in cast iron.  That being said, there may be times when you might personally prefer the fast heating times, reduced maintenance requirements, and unnaturally-nonstick properties of a pan coated with a halopolymer such as Teflon.  Cook's Illustrated recently evaluated these pans and found the T-fal Professional Total Nonstick Fry & Saute Pan to be among the best, at a not-terrible price of $30-40. The problem? “If you get a year to a year and a half of life out of [a new nonstick pan], we think you got a pretty good deal," says Hugh Rushing, president of the Cookware Manufacturers Association. The Environment called, and it wanted to say it hates you. Future Value Factor of an annual purchase at 7% annualized return with a 20-year retirement horizon: 40x. Total cost of this disposable pan to you at retirement:$1600.  Your wallet is on the other line.

Is your diet entirely composed of paper-thin crepes and boiled water?  No?  Then what better way to extend your nonstick pan's usable life than to use it only when it's actually necessary, leaving the heavy duty cooking jobs to an indestructible \$15-20 chunk of hot metal.

### Care and Feeding of Cast Iron

Unlike preposterously expensive enameled cookware or short-lived ceramic of Teflon nonstick pans, cast iron cookware isn't ruined if the finish is chipped; on the contrary, you can reseason the pan yourself in a few easy steps.

You can reduce the required maintenance by doing the following immediately after each use:
1. Wipe out the pan; for stirfry or meat cooking, this may be all that's required
2. If required, scrape out the pan; a plastic spatula or stiff brush works well for this
3. If there's some stuck-on stuff, add a tiny bit of water, place it on the burner, and finish the scraping
4. Once rinsed and/or wiped out, set it on the burner for a minute until the water completely evaporates
5. Add a drizzle of oil or a small glob of shortening or fat and coat the pan with a paper towel
6. Once the hot oil has soaked in to your liking, wipe out any excess and store your pan
It's fine to use some water if you need to, but never use soap.  Never ever ever put it through the dishwasher, even if you're planning on reseasoning it - harsh dishwashing detergents can cause pitting.

Worst-case scenario with cast iron?  Your roommate doesn't read this blog and doesn't know anything about cast iron, so he runs your skillet through the dishwasher (bad!).  When it comes out, much of the finish is gone and big, nasty rust spots mark the regions where bare metal was exposed to the harsh detergents.

Don't panic - it's just a flesh wound.
1. If you want to strip the finish and start over, scrub your pan with a stiff brush or steel wool
2. Dry the pan on the stovetop or in the oven - make sure the water has completely evaporated
3. Coat thinly with vegetable oil, shortening, or animal grease/fat
4. Place in the oven at 450F for at least one hour
5. Remove, recoat, repeat until the finish looks good
Don't want to waste all of that electricity or gas on your oven?  Do it directly over a gas-burning camp stove, grill, or a campfire.

More advanced methods for stripping cast iron to bare metal and removing rust include electrolysis and treatment with ammonia or lye (sodium hydroxide).  Read more about these methods at the Griswold & Cast Iron Cookware Association and the Wagner and Griswold Society.


text:
Inclusion Probabilities: Cluster Sampling

cluster_rs_probabilities(clusters = clust_var, n = NULL, prob = NULL,
simple = FALSE, check_inputs = TRUE, clust_var = NULL)

## Arguments

clusters A vector of length N that indicates which cluster each unit belongs to. Use for a design in which n clusters are sampled. (optional) Use for a design in which either floor(N_clusters*prob) or ceiling(N_clusters*prob) clusters are sampled. The probability of being sampled is exactly prob because with probability 1-prob, floor(N_clusters*prob) clusters will be sampled and with probability prob, ceiling(N_clusters*prob) clusters will be sampled. prob must be a real number between 0 and 1 inclusive. (optional) logical, defaults to FALSE. If TRUE, simple random sampling of clusters. When simple = TRUE, please do not specify n. logical. Defaults to TRUE. deprecated

## Value

A vector length N indicating the probability of being sampled.

## Examples

# Two Group Designs
clusters <- rep(letters, times = 1:26)
probs <- cluster_rs_probabilities(clusters = clusters)
table(probs, clusters)#>      clusters
#> probs  a  b  c  d  e  f  g  h  i  j  k  l  m  n  o  p  q  r  s  t  u  v  w  x
#>   0.5  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
#>      clusters
#> probs  y  z
#>   0.5 25 26
prob_mat <- cluster_rs_probabilities(clusters = clusters, n = 10)
table(probs, clusters)#>      clusters
#> probs  a  b  c  d  e  f  g  h  i  j  k  l  m  n  o  p  q  r  s  t  u  v  w  x
#>   0.5  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
#>      clusters
#> probs  y  z
#>   0.5 25 26
prob_mat <- cluster_rs_probabilities(clusters = clusters, prob = .3)
table(probs, clusters)#>      clusters
#> probs  a  b  c  d  e  f  g  h  i  j  k  l  m  n  o  p  q  r  s  t  u  v  w  x
#>   0.5  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
#>      clusters
#> probs  y  z
#>   0.5 25 26


text:
# 0.2 Learning objects for methods in java  (Page 3/6)

 Page 3 / 6
• The main method calls the method printMax ; the actual parameters are two integer literals.
• The activation record for printMax is allocated, and the actual parameters are used to initialize the formal parameters a and b .
• The variable max is allocated but not initialized.
• The method maximum is called; the actual parameters are the values of a and b , which are the formal variables of method printMax .
• An activation record is allocated for maximum . (There are now three activation in the stack.) The new activation record includesmemory for the formal parameters a and b ; note that these are new parameters not at all related to the formal parameters of the same namesin the previous method printMax because those parameters are hidden.
• The method maximum executes its body and returns a value. Just before it returns, select the tab Call Tree above the graphic display; the sequence of calls from main to printMax and then maximum is displayed. Select Theater to return to the animated display.
• When the method returns, its activation record is deallocated, uncovering the activation record of printMax .
• The value returned is assigned to the variable max and printed.
• When printMax completes its execution, its activation record is deallocated.

Note: In a call to a static method, the name of the class in which it is defined can be given as in the call to maximum . Since the method is defined in the same class as the call,the class name need not be given, as shown in the call to printMax .

Exercise Write a program to compute the maximum of six values using as few statements as possible.

## Recursion

Concept Recursion occurs when method calls itself. There is nothing at all mysterious about recursion!Each call simply creates a new activation record on the stack. However, to ensure that the recursive calls terminate,eventually, some call of the method should return without invoking itself once again.

Program: Method04.java

// Learning Object Method04 //    recursionpublic class Method04 {     static int factorial (int n) {        if (n <= 1)             return 1;        else             return n * factorial(n-1);    }      public static void main(/*String[] args*/) {        System.out.println(factorial(5));     }}

The standard example of a recursive method is one that computes the factorial function:

$n!=n·\left(n-1\right)·\cdots ·2·1=n·\left(n-1\right)!$

The recursion is terminated by defining $n!=1$ for $n\le 1$ .

• The main method calls the method factorial with the actual parameter 5. This creates an activation record with the formal parameter n initialized to 5.
• To compute the expression in the second return statement, the method factorial is called again, this time with the actual parameter equal to $5-1=4$ .
• The sequence of recursive calls continues five times, each one allocating a new activation record with a new variable n .
• Finally, factorial is called with actual parameter 1. This call creates a new activation record as usual, but does notcause factorial to be invoked again. Instead, the value 1 is returned and the activation record is deallocated.Just before the method returns, select the tab Call Tree above the graphic display; the sequence of calls from main to the sequence of recursive calls is displayed. Select Theater to return to the animated display.
• The recursive sequence unfolds : each returned value is used to compute a new value to be returned by that call of factorial .
• Finally, the value 120 is returned to the main method and printed.

#### Questions & Answers

Hi, I have a question. What factors influence social facilitation and social inhibition in groups?
Amritpal Reply
it really depends on that person on how the can task in life either they can work better with other people or you do worse working with people.
Lametra
the task
Lametra
they task
Lametra
Do you know of any studies done to show social facilitation and social inhibition
Amritpal
social facilitation is often influenced by the person's perception of the situation and their appraisal of the task. for example, a track athlete who views their competition as a challenge rather than a threat, will tend to run the fastest they have ever ran under a large crowd.
fady
Another condition is if the person has mastered the ability to perform that task. A track athlete who trains everyday, will perform above average under a large crowd, however, someone who does not run, will tend to do worse than their actual ability under a large crowd
fady
social inhibition can be explained through evolutionary biology or attachment personality theory. some people develop an avoidance personality trait, which when they feel under pressure, they tend to leave the group or avoid a gathering due to high lev of stress
fady
Does anyone know how I can transfer my higher national diploma credits in usa?
Qwanta Reply
Oh wow. I never realised there was a chat on this app!
Amritpal Reply
Then welcome dearest
Bridget
Thank you! ❤
Amritpal
thank you
Ana
Hello Ana, good afternoon from here
Philip Reply
hello im new student here.
Junalyn Reply
o sorry madm
Rai
hello
Rai
I m also student.
Rai
hi
Kavya
what is easier option to psychology?
Dhanaraj
I'm new too
Deniz
As in the the specialisation or ?
Bridget
good morning
Ana
understanding human nature is what we are going to talk about.
Ana
okay, go ahead
Philip
“ Every child is left to evaluate his experiences for himself, and to take care of his own personal development outside the classroom. There is no tradition for the acquisition of a true knowledge of the human psyche. The science of human nature thus finds itself today in the position that chemis
Ana
well, I think every individual is different and to a great extent we can't say confidently that we understand the human nature in its entirety
Philip
lack determines what we will become in life?.
Ana
Not 100% but it plays a huge role
Philip
Hi! I wasn't aware there was a chat feature on this app 😊
Ophelia
👍Philip Anyaegbu
Ana
cool
Ana
👍
Ana
yes Ana I'm here
Philip
alternatively we are different, we have basic similar qualities
Bridget
Yes true Bridget.
Philip
hello there
Ciel
Hi
Philip
hi
Ej
hi
KUNDAN
hi
Ana
who we are how we think what we do insight
Ana
@ bridget. yes that's true
Ana
Ana ioanidis? do you speak Greek?
Qwanta
Qwanta no I dont speak Greek my husband does
Ana
are you a psychologist? or your husband?
Qwanta
I need some reliable informations about my studies...
Qwanta
not a psychologist
Ana
I ask questions
Ana
so what is the cause why a person experiences a psychological disorder if it not of their own?
Junalyn Reply
it's partly genetics,culture, environment and substance abuse. generally these are the common factors which can lead to most of the disorders
war
waoo
Rai
r u proficcer
Rai
u r psychology subject
Rai
not a professor but a clinical psychologist
war
can i ask you, i keep getting headache, and had a history of hypothyroid ans diagnosed as having mild anxiety disorder. i want to finish. my undergraduate psychology thesis.. but always unable to have good ambition and energy to focus on writing the case and the theories... whats the best remedy
Astaroxche
had a headache and have a history
Ana
297 according to the DSM 5
fady
how many disorders are there
Janareon Reply
interesting question
Mahmoud
it is😅
Nelly
I'm guessing it's in the tens of thousands, maybe hundreds if you include counter interactions and stuff like it. although I'm sure it's almost impossible to know for sure, unless you're very rich and connected to the right people. but as I said: guessing.
Beenie
There are more than 200 classified forms of mental illness. Some of the more common disorders are: clinical depression, bipolar disorder, dementia, schizophrenia and anxiety disorders. Symptoms may include changes in mood, personality, personal habits and/or social withdrawal. that is what I think
Mahmoud
too difficult to number. diagnosing a disorder is just checking off boxes on a compilation of symptoms that might match any particular condition on the DSM
what is psychology of the guest
Lirilong Reply
I don't understand the question can you elaborate?
Edgar
the study of philosophy gives to the sociologist
Aman Reply
why women are viewed as far more emotional than men?
Wario Reply
because they actually are ,I guess.
Collins
May be they are biologically milder than man. It does not mean they are not equal with man. Man can also be emotional and can are oppressed with traditional norms. For example, man are not to be cry, in actual man are also emotional being and they cannot have the right to show their sentiment.
shine
sollungal bro sollungal...
Balaji
because of she has hormonal fluctuations than men..
bavi
usually women are more emotional than men and they are multi talented people
lavanya
Both men and women are capable of expressing emotions. But women has the highest percentage of doing that. Because our society is conditioned by nature in such a way that men are expected to suppress their emotions and motivate them through their acts or thoughts, which has it's side effects of....
Santos
denial of any emotion which they feel that useless at that point. Women in the other hand were encouraged/not controlled to suppress their emotions and let them out what they feel about it. I feel that's the wonderful superpower of the women.
Santos
y
Mahmoud
Men's emotion comes mostly with memories triggered by senses. That means, they thoughts have the power to decide whether to let go of emotions or not.
Santos
Q
Mark
because women tend to be more agreeable than men.
Edgar
women at a young age are conditioned to be more in tune with emotion than man should be less
David
The question is "Why women Viewed are as far more emotional than men ?" it's not a question whether women are more emotional than men. This is more an issue about the point of view from the observer, his/her assumption what emotional behavior is or what emotional behavior is.
Mehmet
The anwers are answers more to the question " Are women more emotional than men?"
Mehmet
hi are you on what'sap
Wunuji Reply
no not really a fan of social laziness
Robert
huh
Parmizan
is there any way for a Btech E.C.E. graduate to take on MSC. PSYCHOLOGY
devesh
ya you can just by cracking entrance , if in India
Mansi
Any stream in UG can go for M.Sc (Psychology)
classification of traits and how they are measured
chinedu Reply
what was Freud's first name?
Robin Reply
Sigmund
Dentriodite
sigmund
Margie
Sigismund Schlomo Freud
Mohammad
Sigmund Freud
Talal
sigmund
Ankita
Leon Vygotsky and Sergei Rubenstein please tell me contributions of these personalities in in 4 lines
Uzma
sigmund Freud
Harpreet
Lev Vygotsky was the founder of socio-cultural theory
Jo
So psychology was based off of the Greek gods I that right or no?
Tanya Reply
psychology is the study. anything -ology is the study of a certain field. Psyche is a mortal woman who becomes divine in Greek mythology. The etymology of the word "psyche" in Greek means "spirit" or "soul"
seriously there is no scope of psychology all over the world.i hear those how have psychology degrees they have no careers
Madeeha Reply
psychology degree is the waste of time qnd waste of money.is this true?...
Madeeha
at least you know people's minds
Mahmoud
hummmmm
Blaq
well, i like this subject for helping myself and others as well, not for the scope or anything. and i think we shouldn't liberate everything on the basis of outcomes etc
Natasha
Ye
Isaiah
very useful skill
Isaiah
It is not at all true that people who have psychology degree have no career scope
Aaprajita
If u complete your M.Phil then you can work in hospitals as a clinical psychologist.You can also work in school, colleges and IT companies as a counsellor or clinical psychologist.
Aaprajita
yes
aravinth
people are so stressful and tense, and they need a psychologist
aravinth
yo fr tbh lol
Isaiah
if some one have only master degree in psychology what will he/she do...where he/she utilizes degree
Madeeha
Not if you have set goals and a plan. Look into what careers are available with your degree where you live. Also it helps to have a specialty along with your psychology degree. For example a Bachelor's degree in Psychology of Science in Addictions allows for you to become an addictions counselor.
Jo
Psychology is really a valuable degree. I would like to become an "EDUCATIONAL PSYCHOLOGIST "
there is no proper society of Psychology. so it doesn't get a good exposure in our country. we along with whole student need to discuss and approach to government
Shekhar
Psychology is not only a diverse field but also one that is expected to grow tremendously in the years to come. As a subject dealing with the study of the human psyche or mind, psychology finds applications across all avenues of life, be it family, work, relationships, sports, corporate spaces
Clinical Psychology As is suggestive, this branch of psychology is associated to the understanding, diagnosis and treatment of psychological disorders in humans. Clinical psychologists help people facing difficulties in their life to get through it using different treatment methods and therapies.
These professionals work with hospitals, NGOs and even drug rehabilitation centers. As people become increasingly aware of different psychological disorders with time, the need for experts in clinical psychology is only expected to grow.
Counseling Psychology Counseling psychology is a branch of psychology that helps solve people’s personal and interpersonal issues. These issues can be problematic but are different from serious mental health issues. Counseling psychologists or counselors help people deal with such issues when they
fail to do it on their own.Career counseling, guidance counseling, marital counseling and rehabilitation counseling are among the many applications of counseling psychology. These professionals either manage their own counseling set-ups or work with therapycenters, career centers, NGOs as well as
schools and universities. Industrial or Organizational Psychology Organizational psychologists are professionals who apply the principles of psychology in organizations or workplaces. They analyze the issues of the workplace at individual as well as organizational level, and work towards resolving
them to enhance the efficiency of the employees. Those specializing in organizational psychology can choose to work as – • Human resource development specialists • HR managers • Organizational consultants With increasing pressure and stress levels at work places, the need for emotional understandi
understanding and gauging social intelligence has become stronger. Child Psychology (Development psychology) Development psychology is a branch of psychology that is dedicated to studying the psychological development of human beings over the course of their lifetime. Child psychology is one of
the more popular variants of development psychology, and deals with emotional, cognitive, social and psychomotor development in infants and children. Child psychologists work with schools, child therapy centers and also NGOs. They also play big roles in special education centers for children.
Sports Psychology This branch of psychology deals with the study of elements that influence an athlete’s performance. These elements or factors could be emotional, cognitive, psychological or motivational. Sports psychologists can go on to work with sports coaching centers, leagues, academies or
sports teams. Sports psychologists aid sportspersons to stay in their best mental forms, thus improving their performances on the ground. With the frenzy regarding sports in India, sports psychology is a promising career to pursue.
Forensic Psychology Forensic psychology offers a unique opportunity to apply psychology to the benefit of legal organizations, especially pertaining to specific contents or witness testimony. Professionals in this field utilize their skills to look deep into the psyche of criminals and figure out
the intent behind the crime. This helps define the quantum and nature of sentence to be rendered. With the onset of new legal era, forensic psychology is expected to influence policy making.
SO,THESE ARE THE CAREER SCOPE IN THE FIELD OF PSYCHOLOGY👥
psychology and the jobs in psychology are the ever growing fields. there are number of jobs available. but, yes, one needs the right qualification, such as, MPhil, PhD, NET, etc.
Paul
No. Psychology has a great scope all over world
Talal
Because of 90% people has stress or anxiety or any other mental problem. So they have a need of Psychologist.
Talal
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text:
## Thomas' Calculus 13th Edition

Start with $y=cos(x)$, stretch vertically by a factor of 2, shift right by $\pi/3$.


text:
# VECTORS mathematics

Let $$P(1, –2), Q(–2, 1), R(3, 5)$$ be three points in the cartesian plane.

(a) Calculate the vectors $PQ$ and $PR$.

(b) Draw a diagram indicating the points $P, Q$ and $R$ and the vectors and.

(c) Calculate the angle between the vectors $PQ$ and $PR$.

1. Let $P, Q$ be points with co-ordinates $P(2, 3), Q(-2, 4)$.

(a) Determine any value(s) of $k$ for which the vector $V=(K,3)$ is parallel to $PQ$.

(b) State the condition used to determine if two vectors are perpendicular.

-

To solve question 2)(b), write the scalar product $<,>$. For example $<u,v>=u_1v_1+u_2v_2$ where $u=(u_1,u_2)$ and $v=(v_1,v_2)$.


text:
# Can't see names.

The picture should be self evident.I haven't edited out the name, that is how it appeared to me. Selecting the text and right clicking showed the person's name but I can't see it without doing this.

This has happened a few times before in notes and usually happens whenever someone used asterisks. For example, I can't see this when I preview, just checked.

Is it something wrong with my computer/browser or is it site-wide? You can check if this happens for you. If you can see the following, then this doesn't happen to you.

Looks like its a problem with me only. :(

Note by Siddhartha Srivastava
6 years, 4 months ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
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Note: you must add a full line of space before and after lists for them to show up correctly
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# up as a code block.

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# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
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\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

Sort by:

- 6 years, 4 months ago

Thanks. We are currently unable to reproduce this bug.

1. What OS and browser are you using?
2. When did you first notice this occurring?
3. Does this happen every time / frequently / rarely?

Staff - 6 years, 4 months ago

1. Windows 7 and Google Chrome.
2. I can't say exactly. I guess a month or two? I used to ignore it at first since usually only a word or two were affected and not everyone wrote with asterisks.
3. This happens everytime. I can't see anything written between asterisks, even in the preview. Though if I select the space where the text should be, I can see the text in "Search google for'...' " option.
So you can actually see everything I've written between the asterisks? Even the line at the extreme bottom?

- 6 years, 4 months ago

Now I'm confused. Can you state exactly / explicitly what the issue you're getting it? I do not understand what you think is "self-evident", as there are a bunch of things happening in that screenshot.

I thought the issue was that "Names were not appearing in the notifications". But now, I do not think that's the case.

I do not understand what you meant by "For example, I can't see this when I preview, just checked."

Staff - 6 years, 4 months ago

Sorry. I'll be more clear. What's happening is that whatever is written between asterisks is not visible to me. Anywhere. Notifications, posts, questions, notes anywhere.

Imgur

So for example in the screenshot from my laptop above, I can't see the words "For example, I can't see this when I preview, just checked." which you can apparently see.I think the user @Adarsh Kumar had asterisks in before and after his name, which is why when I got a notification about him, I couldn't see his name

- 6 years, 4 months ago

Ah, now I understand.

This is indeed the first time that I've heard about this issue, and it looks like it is a problem with you only. Words in the asterisks appear as bolded or italicized (depending on the number of asterisks), and so it could be that your specific browser is unable to display that.

I will ask someone to look into the OS and Browser that you stated.

FYI, your note (without the image) looks as such:

Staff - 6 years, 4 months ago

Speaking of bugs, I wanted to report one too. The italicized text disappears at some places. Here's a screenshot.

Image

- 6 years, 3 months ago

Can you check if the following numbering bullets is visible to you:

1. This is a test
2. Testing

The above should look like this:

Staff - 6 years, 4 months ago

Yes. I can see both of them.

- 6 years, 4 months ago

Can you check if you can see this Wiki page? It should look like this:

Staff - 6 years, 4 months ago

Yes. I can see both.

- 6 years, 4 months ago

Thanks! We are narrowing down the possibilities :)

Staff - 6 years, 4 months ago

I'm using another laptop and can now see the words between the asterisks..Same OS and same browser. Must be somthing wrong with my computer. Do you have any ideas what might be wrong?

- 6 years, 4 months ago

It could be that your desktop (possibly old?) is unable to load the custom fonts that we used on the site.

Staff - 6 years, 4 months ago

Well, I can't really do anything for that. I guess I'll just have to live with it. Thank you for helping.

- 6 years, 4 months ago

Hey siddhartha, a question not related with this thread, have you received your inmo performance card, if yes how much are you scoring???

- 6 years, 4 months ago

I got 51. You?

- 6 years, 4 months ago

i haven't yet received my performance card. Hmm .. with 51 marks i think you have marginal chances to reach IMOTC. Hope for the best :)

- 6 years, 4 months ago

How many marks are you expecting?

- 6 years, 4 months ago


text:
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139 users online, thereof 1 logged in

## Definition: Extensional Relation

Let $V$ be a set and let $R\subseteq V\times V$ be a binary relation. $R$ is called extensional if all elements of $x\in V$ are uniquely determined by ordered pairs $(z,x)\in R,$ formally

$$\{z\in V\mid zRx\}=\{z\in V\mid zRy\} \Rightarrow x=y,$$

or, by contraposition,

$$\{z\in V\mid zRx\}\neq \{z\in V\mid zRy\} \Rightarrow x\neq y.$$

| | | | | created: 2019-02-01 08:03:02 | modified: 2019-02-16 17:11:14 | by: bookofproofs | references: [8055]

(none)


text:
# Parity of a system composed by 2 particles

by bznm
Tags: composed, parity, particles
 P: 70 I have read that for a system of 2 particles, the total parity is given by: $P=P_1 P_2 (-1)^L$ where - $P_1, P_2$= insisec parity of particle 1, 2 - L= relative angular moment what's the meaning of "relative angular moment"? Do I have to add the $l$ numbers of the two particles? And what if I have 3 particles? Many thanks
 P: 305 L is the "relative" angular momentum, which means that is the momentum of the system of the two particles "orbiting around each other" if considered as a whole. If you have three particles you need to first study two of them and obtain the corresponding system and then compose this last system with the third particle.
P: 70
 Quote by Einj L is the "relative" angular momentum, which means that is the momentum of the system of the two particles "orbiting around each other" if considered as a whole. If you have three particles you need to first study two of them and obtain the corresponding system and then compose this last system with the third particle.
Thanks for your answer. But I have no ideas about what I have to do in practice... For example, let's consider a pion and a deuterium. I know that the pion is captured in s-wave by the deuterium and it was told me that $(-1)^L$ =1, but I don't understand why. Could you help me?

 P: 305 Parity of a system composed by 2 particles The nomenclature is S-wave (L=0), P-wave (L=1), D-wave (L=2), etc.
 P: 70 I imagined it... but I haven't understood what is a "S-wave". The fist - and last - time that I have heard it, the prof said "The deuterium captures the pion in S-wave". Could you explain me briefly in which way "S-wave" and L (relative angular moment) are related? Does "S-wave" imply that the relative angular moment is 0?
 P: 305 Yes, it's just a way of saying it. If you say that a system is in S/D/P-wave you are simply saying that the relative angular momentum of this system is L=0/1/2, nothing more. It's a nomenclature borrowed from atomic physics.
 P: 70 Oh, so many thanks!! :) And so, if the prof hadn't said that the pion is captured in S-wave, I wouldn't be able to say that L=0, isn't it?
 P: 305 Generally speaking yes. In some cases the relative angular momentum is constrained by total angular momentum and parity conservation. However, most of the times, a certain process can happen with different L. The distinction between the different cases must be made experimentally.
 P: 70 Thanks again!

 Related Discussions General Physics 8 High Energy, Nuclear, Particle Physics 2 Quantum Physics 0 High Energy, Nuclear, Particle Physics 9 General Physics 3


text:
When a body falls freely towards the earth,
Question:

When a body falls freely towards the earth, then its total energy

(a) increases

(b) decreases

(c) remains constant

(d) first increases and then decreases,

Solution:

(c) Total energy = K.E. + P.E.

When a body falls freely, its K.E. increases and P.E. decreases but the sum of K.E and P.E. remains the same.


text:
# Gauss' law question

It's actually a teaching conflict at my school. They said that $$\text{Flux}=\frac{q}{\varepsilon_0}.$$ Say for a point charge at the centre of the sphere and let's say we not put water into the sphere, so now $E/ \varepsilon_0=K$. Thus $E= \varepsilon_0 K$. So flux becomes $q/\varepsilon_0 K$. That means that any change in medium changes the flux.

However, in FIITJEE I was told that the addition of a medium won't change the flux since the number of electric field lines remains constant for any medium. So changing medium won't change the formula, $\text{flux}=q/\varepsilon_0$.

So, does flux actually change with change in medium or not?

$K$ is the dielectric constant.

• Think about what you said ....'for a given medium'. – Shubham Apr 19 '14 at 13:09
• I think there might be a confusion with what do you mean by q – evil999man Apr 19 '14 at 13:13
• @WetSavannaAnimalakaRodVance I am talking about the place where we live(same country) and here teacher in schools don't get much money and are teachers because they didn't get another job not because they want to teach... although there are some institutes do have good teachers like OP mentioned. – evil999man Apr 21 '14 at 10:21

## 2 Answers

The answer depends on the vector field whose flux you are talking about. There are two vector fields that describe the electric part of electromagnetism: the electric field vector $\vec{E}$ and the electric displacement $\vec{D}$ (see Wiki page) - don't get too caught up in the name of the latter: it was named by James Clerk Maxwell (I believe) and its name is not too meaningful to a modern English speaker.

The fundamental relationship here is

$$\vec{E} = \frac{\vec{D}-\vec{P}}{\epsilon_0}\tag{1}$$

The flux of $\vec{D}$ through the bounding surface $\partial V$ of a volume $V$ is always related to the nett charge $q_{nett}$ enclosed in the volume $V$ in exactly the way you state whether there be mediums or vacuum inside the volume. So

$$\text{flux of }\vec{D} \text{ through }\partial V = q_{nett}\tag{2}$$

This is the famous Gauss law. So, if you if you have a handful of electrons or other charged particles in your pocket and put them into a volume where there was formerly no nett charge, the flux of $\vec{D}$ through the volume's boundary will be equal to this charge regardless what mediums or other stuff there happens to be in that volume.

Now, however, the stuff inside the volume before you put $q_{nett}$ in there is made up of charges, even though the nett charge was nought before your handful went in. This stuff reacts to the displacement field of the nett charge: dipoles align, atomic orbitals and chemical bonds subtly change shape in the presence of the displacement field. There is a kind of "back reaction", a "neutralising displacement vector" which we call $\vec{P}$: this one is called the electric polarisation and this name (IMO) is a good one: it evokes the shifting or "parting of ways" or "poalrisation" of "bound charges" (the charge making up the no-nett-charge matter) to weaken the effect of $\vec{D}$.

So now, if you put a tiny test charge into the volume - so small that it does not measurable affect the electrostatic field configuration - and then measure the force on it, you can calculate the "effective" displacement $\vec{E}$, which is (i) that owing to the nett charge less (ii) that arising to the polarised bound charge: your force per unit test charge is (conceptually) $\vec{E} = \vec{D}-\vec{P}$. However, this isn't quite the full story, because we don't measure force and charges in the same units in SI, we need to put a dimension-correcting constant in. This constant, $\epsilon_0$, defines the force on a charge that produces unit displacement $\vec{D}$ in a vacuum: so we get the fundamental relationship (1) above.

You can simplify things by "hiding" the polarisation in many cases. A iostropic, homogeneous, linear medium is defined by a polarisation, or "reaction displacement", that is proportional to the displacement: in this case, we can simply summrise the effect in one constant of proportionality, which you call $K$ in your question. So $\vec{D} = \epsilon_0\,K\,\vec{E}$ and you accordingly have:

$$\text{flux of }\vec{E} \text{ through }\partial V = \frac{q_{nett}}{K\,\epsilon_0}\tag{3}$$

You should read the Wiki page I cited carefully.

The confusion is what you mean by $Q$.

Flux is still $$\frac{q_{in}}{\epsilon_0}$$

But, the numerator has changed. If you take into account the negative charge $$-q(1-\frac 1 K)$$

induced, you will reach the result :

$$\frac{q}{K\epsilon_0}$$

Remember, this $q$ is only the charge $q$, not accounting any other induced charges. It is denoted by $q_{free}$


text:
# RBA paper investigates post-crisis leap in currency demand

A research discussion paper, published by the Reserve Bank of Australia today, investigates why the demand for currency "increased abnormally quickly" following the collapse of Lehman Brothers in 2008.

By the end of the year, an additional A$5 billion worth of banknotes ($5.21 billion) – 12% of the banknotes in the system at the time – was on issue, the paper says.

The authors, Tom Cusbert and Thomas Rohling, say up to 80% of the increased demand may reflect an increase in precautionary holdings

Only users who have a paid subscription or are part of a corporate subscription are able to print or copy content.

To access these options, along with all other subscription benefits, please contact [email protected] or view our subscription options here: http://subscriptions.centralbanking.com/subscribe


text:
# Math Help - find function

1. ## find function

If a function f:R->R satisfies the inequalities f(x) <=x, f(x+y)<=f(x), for all real numbers x and y, show that f(x)=x.

2. Originally Posted by kamaksh_ice
If a function f:R->R satisfies the inequalities f(x) <=x, f(x+y)<=f(x), for all real numbers x and y, show that f(x)=x.
Why can't $f(x) = \frac{1}{3}x$? Seems to me that one works as well.

Edit: Ah wait! That doesn't work for negative x, does it?

-Dan

3. Originally Posted by kamaksh_ice
If a function f:R->R satisfies the inequalities f(x) <=x, f(x+y)<=f(x), for all real numbers x and y, show that f(x)=x.
Wait a minute.

If $f(x) = x$ then $f(x + y) = x + y \not \leq x ~ \forall y$. So $f(x) = x$ isn't correct.

I'm beginning to think there is no such function because of the second condition. If I'm seeing this correctly it implies that $f(x)$ is an absolute maximum for the function for all x, which is a contradiction, unless we want to use the trivial $f(x) = \text{constant}$.

-Dan


text:
Hindi,English,Punjabi

# Case Of The Ex

100 Hits20113 min 56 sec
Case Of The Ex

## About Case Of The Ex Song

Listen to Mya Case Of The Ex MP3 song. Case Of The Ex song from the album 100 Hits is released on Nov 2011. The duration of song is 03:56. This song is sung by Mya.

Related Tags - Case Of The Ex, Case Of The Ex Song, Case Of The Ex MP3 Song, Case Of The Ex MP3, Download Case Of The Ex Song, Mya Case Of The Ex Song, 100 Hits Case Of The Ex Song, Case Of The Ex Song By Mya, Case Of The Ex Song Download, Download Case Of The Ex MP3 Song

Released onNov 25, 2011
Duration03:56
LanguageHindi


text:
# Integration question

1. Apr 22, 2006

### dan greig

I have a question asking me to find the area under a curve, the curve is,

y=10/x^2

I know the process to find the area but I can't find how to integrate the fraction, some help would be appreciated,

thanks, dan

2. Apr 22, 2006

### HallsofIvy

Staff Emeritus
Are you aware that $\int x^n dx= \frac{1}{n+1}x^{n+1}+ C$?

Are you aware that $\frac{1}{x^2}= x^{-2}$?

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook


text:
Question: "set genotype" function for gds?
0
2.3 years ago by
Lna0
Lna0 wrote:

I'm using GWASTools for my GWAS analysis. It turned out that there are some genotyping problems with a few hundred SNPs on the X-chromosome. I already have all my data stored in gds files for use in GWASTools and I want to change the genotypes of the erroneous SNPs directly in the gds file. I was hoping there is kind of a "setGenotype" function with works exactly like the "getGenotype" function that I use to obtain specific SNP genotypes, but couldn't find anything like that.

Did I miss anything? How can genotype changes of specific SNPs be done in gds files without going back to raw data file and creating a new gds file based on them?

gwastools gds • 457 views
modified 2.3 years ago • written 2.3 years ago by Lna0
Answer: "set genotype" function for gds?
1
2.3 years ago by
University of Washington
Stephanie M. Gogarten640 wrote:

You need to use the gdsfmt package to modify GDS files directly.

library(gdsfmt)

file <- system.file("extdata", "illumina_geno.gds", package="GWASdata")
gdsfile <- tempfile()
file.copy(file, gdsfile)

# open file in write mode

# get node of the genotype variable
node <- index.gdsn(gdsobj, "genotype")

# uncompress node so we can write to it
compression.gdsn(node, "")

# change some values for 100 SNPs
nsnp <- 100
nsamp <- 77
newsnps <- matrix(sample(c(0,1,2), size=nsnp*nsamp, replace=TRUE), nrow=nsnp, ncol=nsamp)

# write new values for SNPs 101:200
write.gdsn(node, newsnps, start=c(101,1), count=c(100,77))

# close
closefn.gds(gdsobj)
cleanup.gds(gdsfile)

file.remove(gdsfile)

There's one thing... When I read an entry for one SNP which includes "NA"s

(like: NA   NA   NA   NA   NA   NA   NA   NA    2    NA    NA    NA    NA    NA    NA    NA     1    NA    NA    NA     2    NA     2   2  NA    NA    NA    NA)

from a gds file and try to write it with write.gdsn to another, the "NA"s are exchanged by "0"s when I read the same data from the changed gds file
(0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 1 0 0 0 2 0 2 2 0 0 0 0)

I checked the help entry for write.gdsn, because I hoped I can choose what happens to missing entries and it says:

"GDS format does not support missing characters NA, and any NA will be converted to a blank string "". "

I don't really get it. In general there can be missing values in a gds file (that is where my data came from), but how can I set them with write.gdsn?

The standard missing code for genotype gds files is 3. The GWASTools getGenotype function takes care of converting a value of 3 to NA, but the gdsfmt package does not. When writing the new genotype values, set the missing genotypes to 3 before calling write.gdsn. For example:

geno[is.na(geno)] <- 3

write.gdsn(node, geno, ...)

Thank you! Now everything seems to work. Maybe it would make sense to include this information in the help text for write.gdsn...

Answer: "set genotype" function for gds?
0
2.3 years ago by
Lna0
Lna0 wrote:

Thank you! That worked fine!


text:
# Golden Ratio

While traveling through Tuscany, I was photographed in front of the Torre di Pisa. My intention was to get a unique picture of me and the tower. There are thousands of pictures with tourists that pretend to hold/push the tower with their hands. To add some irony, I wanted a picture of me kicking the bell tower. Here it is:

Recently, I had a second look at the picture taken in June. Inspired by the fine art in Pisa and Florence I posed, unconsciously, in divine proportion aka Golden Ratio.

The Golden Ratio is defined as a sectioning of a line where the ratio between smaller and larger subsections equals the ratio of the larger subsection to the complete line segment:

$\frac{a}{b} = \frac{a+b}{a}$

The Golden Ratio can be found in various paintings from Da Vinci or other painters of Italian renaissance. But also in architecture, and in the nature as well. Just type it into google or wikipedia to see some examples.I depicted the Golden Ratio in my picture with red:

Golden Ratio

(remark, a’= b)

There is also the Golden Angle in my photo. I have painted it in orange:

Golden Angle

Honestly, I did not pose intentionally in the Golden Ratio or the Golden Angle. There is even more:

I sectioned the picture into further squares in order to approximate the Golden Spiral. I have brushed the golden spiral into the picture below with blue color – sorry to the colorblind for being ‘not accessible’, but you should be able to differ between straight lines and curved lines anyway 😉

Golden Spiral

Best regards from your Renaissance man ;-)>


text:
Enter the line voltage (volts) into the calculator to determine the Line to Phase Voltage.

## Line to Phase Voltage Formula

The following formula is used to calculate the Line to Phase Voltage.

Vphase = VL-L / 1.732

Variables:

• Where Vphase is the Line to Phase Voltage (volts)
• VL-L is the line voltage (volts)

To calculate the phase voltage from line to line voltage, divide the line-to-line voltage by 1.732.

## How to Calculate Line to Phase Voltage?

The following two example problems outline how to calculate the Line to Phase Voltage.

Example Problem #1:

1. First, determine the line voltage (volts). In this example, the line voltage (volts) is measured to be 47.
2. Finally, calculate the Line to Phase Voltage using the formula above:

Vphase = VL-L / 1.732

Inserting the values from above and solving the equation with the imputed values gives:

Vphase = 47 / 1.732 = 27.136 (volts)

Example Problem #2:

Using the same process as example problem 1, we first define the variables outlined by the formula. In this case, the values are:

line voltage (volts) = 69

Entering these values into the formula or calculator above gives us::

Vphase = 69 / 1.732 = 39.83 (volts)


text:
## Department of Mathematics

Indian Institute Of Technology Madras , Chennai

### The Kadison Singer problem and Anderson's Paving conjecture - II

#### Abstract :

This is a continuation of last week's talk on the Kadison Singer problem and Anderson's Paving conjecture. In the fifties, Kadison and Singer conjectured the following : Any pure state on $D$ extends uniquely to a state on $B(l^2)$ where $B(l^2)$ is the set of all bounded operators on the Hilbert space $l^2$ and $D$ is the set of all diagonal operators in $B(l^2)$. In this talk, we will see how Anderson's Paving conjecture implies the Kadison-Singer conjecture.

Key Speaker Jayakumar Ravindran, IMSc, Chennai
Place NAC 522
Start Time 3:00 PM
Finish Time 4:00 PM


text:
# On a restaurant sign, 14 light bulbs must be replaced. These light bulbs represent 3/8 of the total number of light bulbs on the sign. What is the total number of light bulbs?

Aug 5, 2016

$= 37$

#### Explanation:

$14 = \frac{3}{8} \left(T o t a l\right)$
or
$T o t a l = \left(14\right) \frac{8}{3}$
or
$T o t a l = 37$

Aug 5, 2016

$37$ bulbs

#### Explanation:

This is a direct proportion, showing a comparison between the number of dead bulbs and the total number of bulbs.

$\frac{3}{8} = \frac{14}{x}$

$3 x = 8 \times 14$

$x = \frac{8 \times 14}{3}$

=$37.33333$

The number of bulbs obviously cannot be a fraction so there are 37 or 38 bulbs.


text:
# Astro 585 discussion 3

05 February 2014

Bottom lines:

• If you are going to be running a code a lot - benchmark it.

Not so much. The thing is: in a few years you will be running your code on a different chip on a different system, maybe somewhere on the cjoud. So at this point, don't worry too much about the low level hardware side of the coding. Moreover, ignore RISCs and CISCs - except if you are planning on buying a supercomputer!

## When should we use vector processors?

The most common vector processors today are graphics chips. If you are doing the same operations on the same data again, and again, and again, then you might be better off using a graphics card, letting it perform these operations. It is not uncommon to get around 2x performance or more that way, with little effort.

Make your compiler optimize for your computer? Can get around 10x performance.

## Jobs on a supercomputer

If the supercomputer is homogeneous, i.e. has the same type of chips as computing nodes, then it might be very advisable to compile your code for that exact chip. It might just be worth your while to spend those 5 minutes reading that man page to check what flags you need to use in order to optimize the code, to get that performance increase you are looking for!

If your supercomputer is heterogeneous, i.e. has different types of chips as computing nodes, some AMD over here, and some Intel chips over there. Then you have to two choices:

1. You compiled it and optimized it for one particular chip. Then it won't run on the other types (it will probably crash!). The code might run faster, but you might just be spending your time waiting in the queue line!

2. You compiled it more generally, not optimizing for a particular chip. Then the code will probably run slower, but you'll be quicker out of the queue line!

## Real world testing vs micro-benchmarking

Where you are blazingly fast at multiplying a bunch of numbers, but Microsoft Word performs differently.

In practice a computer has multiple cache levels. Normally what you do is specify the L2 cache size, as the L1 is usually more constrained in size, and sometimes you see the effect of the computer moving data around in these different levels.

#### Can cache sometimes be too big - so that it might actually slow you down?

Yes, this applies to L1 caches. For a larger cache it is harder to have a fast clock speed; it takes longer to move electrons over a bigger distance, than a smaller distance.

#### Is there an optimal ratio of processor clock speed, and cache size?

Yes, the fastest, and the biggest L2 cache size! Well, still its not exactly that simple. The chip manufacturers are kind of trying to figure this out for you - they want to make chips that people buy.

Example (see graph in last class): If I were to go from 2mb to 8mb in L2 cache size, the range of which it took the same amount of time while still increasing the data size steadily, would probably be around 4 times as big (see graph in last class).

## Using SSD drives - does it mean performance increase vs. using magnetic disks?

It depends on what you want to do.

For sequential reading, and sequential writing the old magnetic disk actually perform quite well with respect to the SSD drives (the platter is reading of a very fast spinning disk), and the old fashioned ones are still a cheaper option if you are working with huge amount of data.

However, for random reading the old fashioned disks are much slower, while SSD are much better - physically moving things like the platter needle in the old hard drives is much slower than moving electrons around in an SSD.

## Are there hybrid systems, that combine a normal processor, and a vector processor?

Yes, there are; usually it is a CPU processor, bundled with a graphics co-processor.

## Two different parallelisms

#### Structure-level-parallelism

When you can have your code such that is making use of structure-level-parallelism; you can get the benefit of the hardware doing different instructions at the same time - meaning performance increase via pipelining.

#### Data-level-parallelism

Write your code so that is easy for the compiler to find ways to do data-level-parallelism. Modern compilers, have instruction level cache, and are constantly trying to figure out how they can use its computation units effectively. They break the instructions into smaller chunks, and try to order them in a smart way.

Write the working set data small enough so that it can fit into the cache - this way you can potentially get an increase the performance several times.

## When optimizing - optimize the slowest part!

Still you have to be aware that the total execution time will still depend on all the parts of the program. For example:

• You have a program that is 10 parts, each of which takes 10% of the time to run. You choose one part to optimize, making it effectively free to perform. - This way, you only make the program 10% faster.

• You have a program that is 10 parts, where one of the part takes 90% of the time to run. You choose this part to optimize, making it effectively free to perform. - This way, you make the program 10x faster!

## Branch predictions

Pretty cool way to make your compiler to work for you - Need to look better into this! You can speed things up by reducing the instructions performed on your branch. Still sometimes the only thing to do is: compile, and compile, and hope!

# Astro 585 discussion 2

03 February 2014

One of the general themes of this course (and perhaps in real life as well?);

Try not to do work that you don't need to do

RISC-y chips, and CISC-y chips

#### Coding habits in Julia

Put an exclamation mark at the end of a function if your function modifies some of the input arguments.

#### Performance checking

People who did memory allocation in the for loop:

1. asserts didn't really make any difference in time

2. making generic function calls didn't really make a difference either

People who didn't do memory allocation in the for loop:

1. asserts didn't really make any difference in time

2. making generic function calls did really make a difference

## Explaining performance curves in homework 2

Check the following code:

    using PyPlot
n_list = [ 2^i for i=1:24 ] #Increasing i from 1:10 to 1:24 to see further
elapsed_list = map(calc_time_log_likelihood,n_list)
plot(log10(n_list), log10(elapsed_list), color="red", linewidth=2, marker="+", markersize=12);
xlabel("log N"); ylabel("log (Time/s)");

Note that we are using map - next it might be cool to check out pmap. This gives the following result on my computer:

Sometimes things that you think should take longer don't: look at the first part from 0.5 to around 2 - the curve is almost flat. There we are probably making good use of the caches. Then as we keep using bigger and bigger arrays, we see a linear increase in time: we are starting to use the main memory.

Note: Some people saw strange bumps/spikes in their curves; probably due to memory-cache interactions, where the computer is trying to be smart, but pays a price in performance for it.

## What are caches though?

Caches, are a small amount of memory that is better accessible to the CPU; the memory access is much, much faster, than accessing the main memory. Accessing the memory is slow, and expensive. Smaller caches are relatively fast, while bigger ones are slower.

# Discussion on chapter 6: Computer Organization

## When do we need queues, and when do we need stacks?

If you wanna get a Starbucks - you stand in line and get your coffee the last. However, if you are the last one to check in your flight-luggage, then there is a good chance that you are the first to get it back (bags are usually stacked on top of each other).

Queues: - Well if you need to do things that require you to do them in a particular fixed order.

Stacks: - Function calls for small variables. They are not efficient when you have dynamic memory allocation. Moreover, you have to be careful with using stacks and recursive functions - can lead to stack overflows!

Check out tail recursion though: The ability to implement neat recursive algorithms without doing terrible things.

## Registers, stacks, and heaps

Registers
Registers are a property of the hardware, while the stacks, and heaps are software constructs. And accessing the registers is basically free - this is what you would like to do in an ideal world.

stack vs heap
If its dynamically allocated, it is almost certain that the compiler will put it into the heap - its safer, and a reasonable thing to do. Still however, it costs time and performance.

A function can return data types that are small, on the stack, or return a pointer to a memory location on the heap (if the return data is big).

## Language choices

Some languages were written a long time ago. Ideas like "I would like to access the web" were non-existent when the people were developing the initial versions of Fortran. If you are doing text processing - then it makes sense to use Python or Perl - don't really try to do it in Fortran or C; you have to do some real acrobatics.

In general if you use a higher level language - then hopefully you need a fewer lines of code; and hopefully you have less bugs, and are quicker to get things done. However using an interpreted language you have to live with the overhead it has to go through when interpreting.

One of the nice things about Julia - is that it combines some of the best of the ides of high-level language, as high performance, but its syntax is similar to Python's.

## Higher level language parallelism

Macro-use-framework Sometimes referred to as embarrassingly parallel - still, this is often the best parallelization you can come up with. Why? A) its easy for you, and B) its easy for the computer to do.

# Astro 585 discussion 1

29 January 2014

I'm taking Eric's class: Astro 585, topics in Astronomy and Astrophysics; High-Performance Scientific Computing for Astrophysics. Its a very discussion based class, and I thought I might try to post my notes here.

These notes are typed quite quickly during class - but I'll try my best to minimize wrong spelling!

Anyways, lets see how it goes!

# Discussion Wed Jan 29, 2014

### Q: IDL precision, single or double?

IDL's default is single precision - many oblivious grad students have suffered through history because of this.

I myself, a grad-student am started to be exposed to this! - Why are we still using a thing born in the 70s of which you can almost physically see the rust covering it? - Not even mentioning the digital handcuffs... Stallman, are you picking your feet about this?

### Automating processes

#### Using scripts like make

Often if you find yourself doing stuff again, and again (3 or 4 times). Then automating might be useful. Say you have a humongous table that lists lots of things about a new planet you found. For the next planet you find, you might want to have this table be automated.

You can automate things pretty easily in Julia.

### Reusing code

#### The difference between writing astronomical software and developing drugs for a pharmaceutical company

The readings were pretty supportive of reusing code. However, you have to have two things in mind:

Beware of Licenses - This can be troublesome, and can become very hindering for the expansion of projects. - Remember Eric's story about Numerical Recipes - sort of like: All of your thoughts belong to us type of deal.

Libraries - Be sure to know that they are actually doing what you want them to do!

### Any tips about refactoring code, or start from scratch?

Difficult to answer, depends on the problem. Rather than rewrite everything maybe focus on rewrite a few functions. And do it in a ridiculously incremental level. Use assertions, debuggers, warnings, print statements etc.

### Q: Top-Down vs. Bottom-Up type programming

#### Difference between academic programming and commercial programming

In the old days, everybody had these massive plans (in the Extreme Programming movement) to make everything perfect from the beginning. Then it sort of transitioned to the quick-and-dirty movement (sometimes making programs that didn't even work!). Nowadays its a kind of pendulum between the two extremes.

For an academic setting: Its very good to make small incremental changes. Still you have to have some overview. So maybe actually programming from the middle might be the right thing to do. Do keep in mind Donald Knuth's words: "Premature optimization is the root of all evil"

Somebody suggested: Bottom up, but keep it general.

### Q: Functional programming vs. Object oriented programming

#### Reusing objects as containers, or making functions do all the work.

For example, you can have a galaxy-class and you can make it do photometry, redshifts, etc.

Object oriented Languages like C++, and Java, make it easy to think in that way. Once you start writing functions that have. You don't need classes really, you can do things you want in C!

Template meta programming (still not exactly sure what this is - you can do it, but supposedly it is a little bit obnoxious).

Say you have a function, an abstract integrator say, and you are gonna pass it a variable. But what if your function doesn't know what type you are gonna pass it? Those types have different internal data structures. If you had a pre-compiled language, the compiler wouldn't really know what type you are gonna pass it - and it might barf. Julias approach is to compile everything at runtime, so it then knows the type, and does it right. So it is a way of getting a compile-type function arguments.

# Northern Lights

19 January 2014

"The prospects are at 6! The prospects are at 6!! Have you seen what's happening outside? It's green! Everything! I'm heading out in 5. Are you with me?"

I'm quite impressed of those of my friends that decided spontaneously leave the things they were doing after receiving such an abrupt phonecall without any other notice, then quickly put on a jacket and an extra pair of socks, grab a snack and to join me to drive into the night in an attempt to capture the Aurora. Different ways were used: some tried filming; other took handheld pictures; others pictures on a tripod; and still others on a dolly; some wrote short stories and poems; some stood and leaned their head gaping just a little bit too much, straining their neck; others lay down on the ground on the cold winter snow, laying absolutely still to see if they could hear them; others tried running around and dancing, either dancing with their rhythm or plainly just to keep warm. Some of my friends were irritated, hung up and went right back to sleep. I tended to call back the former.

In particular I remember the expressions of my friends who were seeing them for the first time. Becoming active in the Erasmus community back home was a logical extension of my own exchange program, and I made many international friends, all of which absolutely adored the place - and probably even more than us Icelanders! - haha!). They came to Iceland to study (some I think were more inclined on the parties, and having a swell time; but that is another story), also hoping to see the Northern Lights - at least once; "Solamente una vez!" - that would be enough for me, one of my friend said. And all of them did! - those that took the time to look for them at least!

I sometimes think if capturing the expressions they showed when seeing them for their first time, along with the plethora of foreign words and slang they used to describe them as they saw them (I believe I still remember some of the Italian ones!), might have been a worthier material to capture than the lights themselves. The Aurora will come again, but those first time expressions only happen once.

The northern lights do not wait for anybody. Although various websites that try to predict their visibility they are not always that accurate as viewing conditions depend on many dynamic factors; cloud cover, seeing, time of day, and solar activity, capriciousnes of Icelandic weather, etc.

Still, as 2013 was at the peak of the sun-spot cycle, the trips added up, and over the course of last year I ended up accumulating quite a few timelapse scenes - some of which made use of a homemade wooden Arduino+car-battery-dolly - sometimes referred to as the "Icebox", or "Bomb Slider". I decided to make a video-project out of it. Below you can see the result:

# Plotting Planck's Law

18 January 2014

The Planck function or Planck's law describes the electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature $$T$$. Max Planck - the originator of quantum theory - proposed it in 1900, solving the Ultraviolet catastrophe. It remains a very important in physics (and particularly so in astrophysics) to this day.

Planck's law can be formulated in terms of frequency, $$\nu$$ in the following way

\begin{align} B_\nu(T) = \frac{2 h \nu^{3} /c^{2}}{\exp\left( h\nu/kT \right)-1} \label{eq:planck} \end{align}

and equivalently, in terms of wavelength $$\lambda$$

\begin{align} B_{\lambda}(T) =\frac{2 h c^{2} / \lambda^{5}}{\exp\left( hc/\lambda kT \right) -1}. \label{eq:bL} \end{align}

In the figure below I plot the latter equation for two temperatures. Here is the Python script, planck.py, which I used to produce the plot.

# Fossá - (The River of Waterfalls)

27 December 2013

"Lets cut to the case we talked about: lets go somewhere!", I told my friends upon arriving back at the Iceberg.

"Alright, where then?", they answered back.

We kind of worked out a loose plan: To go to Snæfellsnes a peninsula in the West of Iceland sometimes known for containing a pathway to the center of the Earth (ask Jules Verne!). We also knew that it offers quite a few scenic places. Still, however, it is also renowned for its capricious weather this time of year (commonly called algjört vindrassgat in Icelandic; for English speakers: it has bad connotations with wind). And sure enough we heard:

"Its gonna be windy out there, perhaps a storm - so watch out!". Our plans changed. Instead of going North-West, East it was instead. The journey to the center of the Earth had to wait a better time.

The plan: No plan really, lets just go to our friend's house in the countryside and take it from there, taking care to bring the following things with us:

• Cameras, tripods, lenses and other camera equipment
• Clothes, lots of them - its gonna be cold!
• Sleeping bags
• Food
• A thermocup to keep our coffee warm - again, its gonna be cold!
• A copy of the whole Hitchhiker's guide (The Big Blue Bundle-edition, containing all the books)
• Towel (recommended by The Guide)
• Showels

"What kind of car do you guys have?" my friend's dad asked.

"Good", he nodded while bringing a book of Icelandic roads loaded with pictures of iconic places near them.

"See those waterfalls here? Háifoss (Literally: Tall-Waterfall), and Granni (either; neighbour or something thin), where the former one is the second tallest waterfall in all Iceland. Also, do notice that this picture is taken during summer. I've never seen it during winter - it might be worth for you to take a look at and see how it looks like. What do you think?"

And indeed, we took it from there. Resolving to start the journey before sunrise the following day to get some sunrise time-lapses. This might sound more ambitious than it was - twilight was at around 10 am, and sunrise at 11:15 am - it really wasn't that hard.

Still, on our way there we managed to get our jeep stuck in the snow- the type of stuck that all crew members had to get out of the car and start showeling - at least 4 times. Intelligent as we were, we only brought one showel, so the ones not showeling defaulted to using their hands and boots to help out. When you got tired you had fun by photographing the others working their asses off.

In retrospect we did learn a few things after the trip: bring at least two shovels, and definitely more coffee - in the cold you drain it much faster than you thin!

Eskimos had over two hundred different words for snow, without which their conversation would probably have got very monotonous. So they would distinguish between thin snow and thick snow, light snow and heavy snow, sludgy snow, brittle snow, snow that came in flurries, snow that came in drifts, snow that came in on the bottom of your neighbor’s boots all over your nice clean igloo floor, the snows of winter, the snows of spring, the snows you remember from your childhood that were so much better than any of your modern snow, fine snow, feathery snow, hill snow, valley snow, snow that falls in the morning, snow that falls at night, snow that falls all of a sudden just when you were going out fishing, and snow that despite all your efforts to train them, the huskies have pissed on.

-- The Guide

# A trip to the North; Canada

01 December 2013

"What are you doing for Thanksgiving break, and more importantly: where are you eating turkey?" a friend asked me. "Who, me? I'm heading North, to Canada - I might not eat any Thanksgiving-turkey this year. Don't worry though, I'll just eat twice as much next year!"

We don't celebrate Thanksgiving in Iceland, so I didn't really mind missing out on the turkey (also: my family eats it during New Years Eve). And yes, my Thanksgiving dinner ended up being a quick wrap-sandwich on the cold road, somewhere in the province of Quebéc.

We headed out, a crew of 4; three French, and one Icelander, travelling over 1800km in 5 days, covering 2 states, 2 provinces, in 2 countries. We had a rough destination outline: A) Niagara Falls, from there swing up to B) Toronto to check out the CN-Tower; and then spend the remainder of the holidays in C) Montreal. It was an ambitious goal. It took some resiliance (mostly on the driver's part), some enthusiasm, and some power-music, but we did it.

As anticipated, the journey itself was a large part of the trip. However, for me - the co-pilot and one of two master DJs - the time passed relatively quickly; for the driver I'm not as sure. We did come prepared with a carefully crafted music playlist, consisting largely of songs made by indie and electronic groups that originate from an island a part of the Mid-Atlantic Ridge. Judging by the fact that we all had certain songs playing in our mind for the rest of the trip, I might have played some of them once or twice too often. Moreover, countless stories were told (some in French with English subtitles) about things that first came to our minds. Those stories will not be listed here - they would fill volumes.

As we were heading straight to the capital of Québec, the French-speaking state of Canada, I felt I had to shape up my (totally non-existent) French skills. And sure I did: I learned some very crucial first words, providing me with a diverse and lucid vocabulary, forming a sturdy basis to further build on. In return, I provided an equally descriptive vocabulary in my own mother tongue; words that ended up forming an effective and encrypted code language used in the midst of the French speaking Canadians - nobody speaks Icelandic, right?

I immediately felt that there was something about Canada that I resonated with. Maybe it was the chilly weather, temperatures routinely dropping to -8C or -10C, and sometimes to -15C. It was very interesting to see the Mediterranians' expressions seeing the temperature drop by one degree for every hour we drove North. The Icelander grinned. Or maybe, maybe I was just glad to be finally travelling again.

Having only a rough outline of what to do, this trip - like all good trips are - was largely characterized by on-the-fly decisions and last minute finalizations. Despite a few minor delays, everything went quite smoothly. Living in a digital age where your smartphone has a better idea where you are going than yourself, and where you can find, read reviews, book, and pay for a hostel in less than 5 minutes, it is getting exceedingly easy to travel. So what are you waiting for dear reader, give yourself the time (and some money - but money is best invested in travelling), open your door and step out!

# Mt. Nittany

21 November 2013

Every time I walk up the stairs in Davey Lab, I get an exceptionally good view of a prominent geographic feature in Centre County, Pennsylvania, called Mount Nittany. One day, walking up those flight of stairs, from the 4th floor to the 5th, with a warm cup of coffee in my hand, I noticed that there was something different about the old hill. She had changed colors; the copious green blanket that she usually wears, she had swapped for a gleaming yellow and red coat! Postponing my duties, leaving them to cool off with my undrunk coffee; I stepped off into the outdoors.

According to local legend the mountain was formed in a very dramatic way; I summarized the lore surrounding its formation below, but you can read the whole legend here.

The legend says that Nit-A-Nee (the wind-breaker) an Indian Princess, fell in love with a handsome Indian Brave of the tribe called Lion's Paw. This fearless Brave was killed in a fierce battle with the wicked Wind from the North.

When Princess Nit-A-Nee heard of Lion's Paw's death, she carried his body to the center of the Valley where she laid the fierless warrior in his grave, and built a mound of honor to commemorate his strength. On the last night of the full moon, after she had finally raised the last of the soil and stone over his high mound, a terrible storm came unleashing itself with thunder and lightening and the wailing of a horrendous wind from the depths of the Earth. Every Indian in the Valley shuddered and all eyes were directed to Lion's Paw's high mound upon which the beautiful maiden Princess Nit-A-Nee was mounted with arms outstretched to touch the sources of the lightning bolts in the sky.

Through the night they watched with awe as the Indian Brave’s burial mound grew and rose into a Mountain penetrating the center of the big valley between the two legs of the Tussey and Bald Eagle ridges. When the dawn finally came a huge mountain was found standing erect in the center of the Valley.

A legend had been born. The mound and the maiden had given place to a Mountain, and standing on its summit was a Lion surrounded by eleven orphaned male cubs, each of whom had the courage of the fearless Indian Brave and the heart of the mysterious Indian Princess. From that day forward every place in the valley was safe, and the Wind wrested nothing from the fields on which these Lions strode as fearless heroes from the Mountain - the Mountain which still stands as a breaker against the wicked Wind of the North.

10 November 2013

"I wonder how tall people feel in long flights?" my friend once asked me. Generously speaking she is only around 165cm, not a centimeter more. I'm 192cm. Upon arrival in a new country, 8 and a half hours of flight-time later, my legs felt like a pair of stiff logs. Those logs somehow got me past the gate, for my next flight.

I remember sleeping, or dozing off, with my head leaning to the brown fabric off the airline seat in front of me. It smelled a bit, I couldn't place of what. Lemon peanut butter? Anyways, - "... dear passengers, we will be arriving in Reno, Nevada, in approximately 1 hour and 50 minutes - we want to remind you to remain seated... ". When I woke up, I was already there.

It definitely felt different. As I walked the tapered isles of the airport, I saw a box covered with flashy and colorful lights, spinning wheels. The box played joyful tunes, the kind you quickly get tired of if you have nothing better to do. I however wasn't bored at all; some of the lights even blinked in sync as the tunes played. Yes, this was a slot machine: a box that keenly takes in bills or coins, that never seems to give anything in return, except for the pretty lights and playful tunes.

For a moment my right brain hemisphere wondered; should I? My left hemisphere then thought about negative expectation values combined with The Law of Large Numbers - I walked on. As I walked, I noticed other boxes - they were everywhere, some neatly arranged in groups; 4 over here, 16 symmetrically placed over there; dozens and dozens along the isles you walked. Waiting passengers tried their luck, with that gleam in their eye that said, this time, this time it will work. The wheels spinned.

I remembered my friend telling me that you will never find a clock in a casino, as they don't want you to be able to tell the time. But wait, this was in an airport, one of those places you really, really want to be able to tell the time! As I sunk into ideas about the distribution of clocks in this peculiar airport; wondering if the combination of singing slot boxes and the lack of clocks could potentially lead people to miss their flights, I heard Icelandic! 2 friends, and surely enough I had met one of them before. We left the airport.

The next days were packed. I was in the midst of the internationals, and there were quite a few of us. A typical introduction went like this:

"Hi! Where do you come from?
What do you study?
What school are you going to?"

"Well, I come from Iceland, and I'm going to PSU to study the stars. Next!" - This perhaps might sound superficial, but all of us immediately became good friends. We were in the honeymoon stage: we came from all around the world, with our own cultural luggage; everything and everybody looked interesting.

One thing I immediately noticed how few of us where going into science related fields. Management, Law, Economics, Fine Arts, Economics, Political Theory, and Public Administration seemed more popular career choices. For a while I introduced myself as a student of astronomy, which in some rare cases was confused with astrology. A bit disappointed, I quickly corrected them. I wondered; how does this miscommunication happen? Was it purely a language error (being nonnative English speakers), or was it the plain misconception that astronomy and astrology deal with the same thing? I hoped for the first. I then tried a few variations; Hi, I'm the Icelander with the unpronounceable name that studies law: the laws of the universe. Well.., I quickly just defaulted to plain astrophysics.

I had a hell of a time, my lenses and my vague colloquial S-American Spanish skills did too. We travelled, we visited places, we took pictures, we told stories, and shared jokes about our respective countries and cultures, we got our personality traits analyzed (supposedly I'm an extrovert analyzer with a very unclean desk - those who have ever my desk will be quick to know if I was classified correctly or not!), we all caught a cold with the ultra-cool air-conditioning, we ate & drunk well, and took various on-the-fly decisions that in the end turned out pretty good.

What I took most from these days was not necessarily the seminars I attended (although those were very good, I won't complain at all!), but rather getting to meet the other students. Even though we knew we came from such vastly different places, we had more things in common than we thought; we were all starting out a big trip in a new place. I think a good measure of your friendship is how long you are willing to stay up with people on the night before you have a long flight (or a chain of flights for that matter): With that as a measure, I can surely say I made many. Leaving to the strange airport-casino again, direction first West and then a lot more East, I knew I would be making good use of of sofas in various locations around the US, hopefully sooner rather than later.

A chain of flights later, I arrived in central PA; a place I noticed that is is characterized with having the word Nittany in front of everything. "Spontaneously, your luggage decided to take a trip to the edge of the universe" - What? Of course it hadn't, not that far, it was still somewhere in the western spiral arm of our Galaxy, still orbiting our small unregarded Sun, it had just taken a ride to the third largest city of a very remote state, I daydreamed in a Douglas Adam-ish fashion.

On that note, without luggage, without a towel, I Hitchhiked a ride, I hit the road again.

# Kóperníkus

28 October 2013

Ég er að læra stjarneðlisfræði. Í íslenskutíma í MR var eitt ljóð sem stóð upp úr; ég hef ekki gleymt því síðan:

Á kvöldin undir kveiktu tungli og stjörnum
koma þeir heim af ökrunum. Lágan óm
ber vindur frá klukku er álútu höfði og hljóðir
halda þeir stíginn hjá veðruðum róðukrossi með
feðranna gömlu, gnúðu amboð á herðum
en glaðir að allt skuli bundið svo föstum skorðum:
sjá þarna tungl og vindar, hér vegur og blóm.

Þeir vita' ekki að hann sem heilsar þeim oft á daginn
hjó þessa jörð af feyskinni rót - og henti
sem litlum steini langt út í myrkur og tóm.

Kvæðið virðist kannski einfalt við fyrstu sýn; auðskyld orð og tákn (róðukross - ítök kirkjunnar), smá rím, ljóðstafir (yfirleitt) og einfaldar myndlíkingar.

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Ergonomically handwritten code, with a little help from my friends; vim, jekyll and twitter bootstrap


text:
# simultaneous equations

Discussion in 'Math' started by amilton542, Feb 22, 2011.

1. ### amilton542 Thread Starter Active Member

Nov 13, 2010
494
64
i dont have great difficulty in rearranging simultaneous equations with an x and y value equals a number but when a third value is put in things confuse me : im trying to rearrange this formula

y = 8 - 2x
x + y + 7 = 0

ive rearranged the top one to y + 2x = 8

the second one i dont no what to do with the zero ? my attempt is x + y = 0 - 7

2. ### Georacer Moderator

Nov 25, 2009
5,142
1,266
Quite right. Can you solve the system now?

3. ### amilton542 Thread Starter Active Member

Nov 13, 2010
494
64
maths guru is that a yes your answer is right ( keep all cons together) then i can solve the "system"

4. ### Georacer Moderator

Nov 25, 2009
5,142
1,266
Yes, I said that your assumption about putting the '7' on the right hand expression was correct. Your new system should be:

$\left\ \begin{array}{l} y+2x=8 \\ x+y=-7\\
\end{array} \right}$

Can you handle that system? Do you need any more help?

Last edited: Feb 22, 2011
5. ### amilton542 Thread Starter Active Member

Nov 13, 2010
494
64
just what i was looking for


text:
# pathway.var.test

0th

Percentile

##### Testing the concentration matrices of a pathway.

Test the equality of concentration matrices in two experimental conditions for a pathway

##### Usage
pathway.var.test(y1,y2,dag,alpha,variance=FALSE,s1=NULL,s2=NULL)
##### Arguments
y1
a matrix with n1 individuals (rows) in the first experimental condition and p genes (columns).
y2
a matrix with n2 individuals (rows) in the second experimental condition and p genes (columns). The genes in the two experimental conditions must be the same.
dag
graphNEL object, directed acyclic graph (DAG) corresponding to the pathway of interest. See package gRbase for more details.
alpha
significance level of the test.
variance
logical flag. If TRUE the estimates of the covariance matrices are included in the result.
s1
y1 covariance matrix estimation.
s2
y2 covariance matrix estimation.
##### Details

The graph of a pathway is first converted into a DAG and then into a moral graph. The data is modelled with two Gaussian graphical models with zero mean and graph provided by the moral graph. The function tests the equality of the two concentration matrices (inverse of the covariance matrices).

The expression data may contain some genes differing from those in the pathway: in such case the function automatically takes the intersection between the two gene sets.

A necessary condition for the existence of the covariance estimates is that the number of statistical units (samples) is greater than the number of variables. If this is not the case, penalized techniques for estimating $s1^(-1)$ and $s2^(-1)$ have to be employed, that are currently not provided by the package. In theses cases, one can perform penalized estimation of $s1^(-1)$ and $s2^(-1)$ outside topologyGSA, and then provide such estimates as input arguments to the function pathway.var.test to compute the value of the test for homogeneity. In this case, computation of the p-value deserves attention, as standard results on the asymptotic distribution of the test statistic may no longer be valid. Therefore, computation of the p-value has to be dealt with by the user.

This function requires gRBase and qpgraph packages.

##### Value

lambda.value
the observed value of the test statistic.
qchisq.value
the 1 - alpha quantile value of the null distribution of the test statistic on the variance.
p.value
the observed value of the significance level of the test.
cli.moral
a list containing the cliques of the moral graph.
var.equal
logical flag. If TRUE variances are heteroschedastic.
graph
a graphNEL object representing the moral graph.
df
the degrees of freedom of the null distribution.
s1
if variance=TRUE, the estimate of y1 covariance.
s2
if variance=TRUE, the estimate of y2 covariance.

##### References

Massa, M.S., Chiogna, M., Romualdi, C. (2010). Gene set analysis exploiting the topology of a pathway. BMC Systems Biology, 4:121 http://www.biomedcentral.com/1752-0509/4/121

Lauritzen, S.L. (1996). Graphical models. Clarendon Press, Oxford.

pathway.mean.test, clique.var.test, clique.mean.test.

##### Aliases
• pathway.var.test
##### Examples
data(examples)

pathway.var.test(y1, y2, dag_bcell, 0.05)

Documentation reproduced from package topologyGSA, version 1.4.5, License: GPL-3

### Community examples

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