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## Sunday, November 16, 2014 ... /////

### Lightnings may increase by 12% per 1 °C of warming

David M. Romps, Jacob T. Seeley (Berkeley), David Vollaro, and John Molinari (Albany) published a report in Nature whose title reads

Projected increase in lightning strikes in the United States due to global warming
that was quoted in hundreds of media outlets.

Let me tell you: I find this number conceivable.

They decided that the lightning frequency is approximately equal to the product of the precipitation rate and a potential energy (CAPE). It probably isn't exact but it's probably good enough for some estimates. Combined with some empirical data, 1 °C of warming adds 12% to the warming strikes. When combined with some nonsensically overrated projections about the rise of the mean temperature in the rest of the century, they may get a 50% increase of lightnings.

More realistically, the Earth may experience at most something like additional 0.8 °C of warming by 2100 so the increase of the lightnings will be about 10%.

It's interesting to see how many people are killed (click) by lightnings in the U.S. (the same country that the paper analyzes). Since the beginning of 2014, there have been 25 casualties. So in a climate warmer by 1 °C, there would be about 2 more deaths in the U.S. each year – unless something else changes, of course.

This should be compared with the thousands that freeze to death and whose lives could be saved if there's some warming. Obviously, lightnings are negligible relatively to those. But despite the small numbers, lightnings are interesting because it's a rare example of a process by which "warming may indirectly kill people".

You may see that only 1/5 of the 2014 fatalities are women (pink color). This percentage actually isn't true just in this year – you find a similar percentage of 80% of men in previous years, too. Why is that? Is Nature misandrist or feminist? Or do penises act as lightning rods? Well, both of these explanations are unikely.

It's more likely that the explanation hides in the activities of the victims. Women are probably less likely to be closing car windows on a construction site, roofing car dealerships and other things, fishing, riding motorcycles, fixing windshield wipers, swimming, building tree house, doing a maintenance work, sheltering in storm, and (to explain some previous years) playing golf. So even though women are competitive in horseback riding, picking blueberries, walking, perhaps swimming, trimming hedges, the "men's excess" can't be eliminated.

Incidentally, you could argue that this ratio of deaths – four-to-one "favoring" men – roughly represents the ratio how much the two sexes work, especially when it comes to risky jobs (although you shouldn't forget that they're less likely in doing various types of work at home). So the "apparent meritocratic gender gap" is actually larger than the 1.5-to-1 gap in their average salaries.

But back to the lightnings. It's likely that the lightning rate increases with the temperature and is of order 100% already for temperature changes comparable to 10 °C. We could find some alternative methods to get this dependence from looking at the weather in different seasons – or different climatic zones – and do some regression. I am convinced that the dependence would be "comparable".

Lightnings are examples of phenomena where the warming matters; and where there are some fatal consequences, too. In principle, all the necessary conditions are fulfilled for the climate change hysteria to be relevant. But when we look at the problem quantitatively, we see that the casualties are tiny and negligible in comparison with the casualties of freezing that may be avoided with a degree of warming.

#### snail feedback (20) :

I read a Los Angeles Times article on it today, and it addressed the problem of brush/forest fires. If I recall correctly, there was no mention of people being struck by lightning. I imagine that other media published similar things.

I once saw lightning strike hit a metal fence post at the top of a hill that's behind my house. There were horses up there. After the strike, four horses went to the post and spent a few minutes examining it closely. Horse scientists, I guess.

Haha, horse scientists or maybe just electrically charged horses attracted to the opposite charge. ;-)

This danger to forests can't be allowed to continue. Something must be done!

Quick! We gotta ...

STAMP OUT THESE FOREST FIRES! :)

http://news.sciencemag.org/climate/2014/11/slideshow-seven-types-lightning-common-bizarre
Note bottom comment.

If the following is the result of Klimate Kaos, everybody will be wanting their own Lichtenberg figures. Either that, or a Darwin Award,

http://asset-a.soup.io/asset/3205/6108_a886_390.jpeg

Hmmm, Great!--I love dramatic lightning storms...the ozone generated will help to patch the ozone hole, and the ozone and negative ions act on our brains to produce a nice euphoric feeling. Now, if we could only influence whom the lightning will strike---that would be gravy. :)

"I once saw lightning strike a metal fence post at the top of a hill behind my house..."

That would explain your name "Smoking Frog"
:)

"Horse scientists, I guess."--I just hope they weren't wearing blankets with naked mares on them...

As for the gender ratio when it comes to work: maybe, if you stick to rural areas, trucks and the kitchen. But during the great US economic recovery since 2009 most jobs created were in the service sector. According to some, we hired way more waitresses and bartenders than workers in manufacturing. Bottom line, I would expect that employed women outnumber men and I've read some stats that imply so, but can't find the link at the moment.

You must be right - waitresses are also hard-working and mostly women. They're just safer against lightning than golf players, for example. ;-)

As long as humans aren't consumed, forest fires are actually beneficial to the ecosystem---
--just a quick google search will reveal many articles.

OT. I am still shaking my head about the Matt Taylor brouhaha. It is hard to believe and pathetic that humans have evolved into such caviling toxic nit-pickers who are allowed (and encouraged) to cause pain and suffering to the decent and interesting. And, of course, Sean Carrol joins in...he seems to be in the running for the most politically correct human on earth---the Nobel Prize must be waiting...

Can't this lightning be harnessed to produce energy and displace the fossil fuels that create the global warming?

A charger is a horse! Just to make sure you know how extra word-wise witty you were!😉😊

Speaking of gender ratios and death, in the US the occupational fatality ratio for men to women is about 13.6 to 1:

http://www.aei.org/publication/equal-pay-day-this-year-fell-on-april-14-the-next-equal-occupational-fatality-day-will-occur-on-july-31-2025/

The idea that warming may increase thunderstorm activity doesn't seem implausible to me. The world distribution looks something like this:

http://geology.com/articles/lightning-map.shtml

That being said, in principle we should be able to measure lightning frequency using satellites and test to see what the real magnitude of any such dependency is.

One should also keep in mind that any such connection is likely linked to various feedback mechanisms, since such systems play a keep part in the planet's energy balance, especially in the tropics, through the associated cloud systems.

Smoking Frog was a 4th-century Mayan warlord. Actually his name was "Born of Fire," but scholars used to call him "Smoking Frog," either because they didn't understand the glyphs very well, or as a joke, or both. His name was written as two glyphs, an iguana looking upward, and a set of wavy lines. Supposedly the scholars mistook the iguana for a frog, and didn't know it meant "born," and they misread the wavy lines as "smoke," whereas actually it means "fire."

No, the horses weren't wearing pictures of naked mares. They're only at the Ben Franklin stage of development.

"Electrically charged horses" - you're such a reductionist! :-)

As to the upper limit, yes, but where is it?

Do alarmists pay for new ideas? I'm thinking of advising them to say there's a tipping point after which lightning electrocutes the entire human race.

The article was pretty calm. It only said something about an increase of the cost of fire-fighting.

It's just an old joke, SF. I'll tidy it up to make it clearer.

Hmmm, SF, my take on your name was my attempt at a joke :) You explained the supposed origin of your nick to me once before.
Also, those horses may have been further evolved than you knew---Houyhnhnms are everywhere...

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A binomial probabilistic inequality [duplicate]

Let $n$ and $1\leq k \leq n$ be natural numbers. Prove the inequality $$\sum_{i=k}^n \binom{n}{i}\bigg(\frac{k}{n+1}\bigg)^i\bigg(1-\frac{k}{n+1}\bigg)^{n-i} \leq 1 - \frac{1}{e}$$

Equivalently, if $X\sim$ Bin($n$,$\frac{k}{n+1}$), prove that $\mathbb{P}[X\geq k] \leq 1 - \frac{1}{e}$.

My attempt: It may be helpful to show that the LHS tends to a limit less than $1-\frac{1}{e}$ as $n \to \infty$ (already did that) and that the LHS is an increasing function on $n$ (have not done that).

marked as duplicate by Mike Earnest, Isaac Browne, Chris Custer, NCh, JonMark PerryApr 14 '18 at 2:33

• In fact, it's exactly the same question, asked by the same OP. What gives? – saulspatz Apr 13 '18 at 22:28

1) $\binom{n}{k} \leq \frac{n^k}{k!}$
2) $\sum_{k=0}^{n}\frac{z^k}{k!} < e^z \ \text{if} \ z>0$
3) $\sum_{i=k}^{n} p(k) = 1 - \sum_{i=0}^{k-1}p(k)$


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Table 1

Comparison between the properties of the model cilia and experimental data

ParameterDimensionsData*Model
Beat durationms35.7≈34
Beat frequencycycles/s28≈29.4
Angular range of the effective stroke°110110–115
Duration of the effective strokems≈9≈7–8
Duration of the recovery strokems≈26≈26
Ratio of durations (recovery/effective)2.93.25
Duration of basal swing during the recovery strokems6≈7


text:
• 安全与环保 •

### 高压静电场中粉尘静电力及收集的研究

1. 江西理工大学
• 出版日期:2009-03-14 发布日期:2012-01-30
• 基金资助:

* 国家自然科学基金项目(编号：50167001)。

### Electrostatic Forces and Dust Collection in High Electrostatic Field

Zhi Xueyi，Jiang Xiaohua，Tang Minkang

1. Jiangxi University of Science and Technology
• Online:2009-03-14 Published:2012-01-30

Abstract: Electrostatic forces consisting of corona electrostatic force, polarization electrostatic force, contact electrostatic force & faradic electrostatic force are of great importance to dust adhesion on the plate and collection in electrostatic precipitator.The theoretical equations for all kinds of electrostatic forces of particles from microcosmic aspect are derived by setting up a model.By simulating the electrostatic field in electrostatic precipitator, the magnitude of the electrostatic forces of dust with different applied pulse electrostatic fields are measured，and the conditions for the air re-entrainment of particles under rapping are proposed.The experiment result shows that the electrostatic forces of dust is proportional to the applied pulse electrostatic field and the dust can not be re-entrained easily because of high electrostatic forces at a great current density .It is indicated that the charging bar is also beneficial to controlling the re-entrainment of precipitated particles.


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First Order Ordinary Differential Equation by Any Method (1R-24)

I just need for someone to check my work and suggest a better way to solve this if one exists. I can use any method but not numerical or any other iterative series approximation. The following documents my process of attempting to solve this problem. It does not appear to be separable, reducible to separable such as with an appropriate change of variable like the u-substitution $u=\tfrac{y}{x}$, or linear, or reducible to linear? But is it exact or can it be made to be exact?

$$y' = \frac{y}{x + (y + 1)^2}$$

Rearrange terms and expand then test for total differential (exactness):

$$Mdx + Ndy = 0$$

$$-ydx + (x + y^2 + 2y + 1)dy = 0$$

$$\frac {\partial M}{\partial y} = -1, \frac {\partial N}{\partial x} = 1$$

It is not exact but can it be made to be exact with an integrating factor in x? Here $P$ is $M$ and $Q$ is $N$. $P$ and $Q$ are used to imply that ODE is not exact but is being worked on to find an integrating factor.

$$\frac {1}{F} \frac {dF}{dx} = \frac {1}{Q} \left[ \frac {\partial P}{\partial y} - \frac {\partial Q}{\partial x} \right]$$

$$\frac {1}{F} \frac {dF}{dx} = \frac {1}{x + y^2 + 2y + 1} \left[ -1 - 1 \right] = \frac {-2}{x + y^2 + 2y + 1}$$

This will not work because of the y-terms. Plus it would be far too complex to use. We need to find a simpler integrating factor. How about deriving one in y? Like before $P$ is $M$ and $Q$ is $N$.

$$\frac {1}{F} \frac {dF}{dy} = \frac {1}{P} \left[ \frac {\partial Q}{\partial x} - \frac {\partial P}{\partial y} \right]$$

$$\frac {1}{F} \frac {dF}{dy} = \frac {1}{-y} \left[ 1 - (-1) \right] = - \frac {2}{y}$$

It appears we may have made a breakthrough in finding an integrating factor in y.

$$\int \frac {dF}{F} = -2 \int \frac {dy}{y}$$

$$ln|F| = -2 \ln|y|$$

$$F = y^{-2}$$

So far so good. Let us now multiply the rearranged ODE by $F$ and test once more for exactness. As before $P$ is $M$ and $Q$ is $N$.

$$FPdx + FQdy = 0$$

$$y^{-2}(-y)dx + y^{-2}(x + y^2 + 2y + 1)dy = 0$$

$$-\frac {1}{y}dx + \left(\frac {x}{y^2} + 1 + \frac {2}{y} + \frac {1}{y^2}\right)dy = 0$$

$$\frac {\partial M}{\partial y} = \frac {1}{y^2}, \frac {\partial N}{\partial x} = \frac {1}{y^2}$$

The integrating factor worked. We now have exactness and can finally proceed in solving this ODE. We may begin with either term $M$ or $N$.

$$u(x,y) = \int Mdx = - \int \frac {1}{y}dx = - \frac {x}{y} + k(y)$$

$$\frac {\partial u}{\partial y} = \frac {\partial \left[-\frac{x}{y} + k(y)\right]}{\partial y} = \frac {x}{y^2} + k(y)' = N = \frac {x}{y^2} + 1 + \frac {2}{y} + \frac {1}{y^2}$$

We are now at the home stretch. We just need to isolate and solve for $k(y)$ and insert it back into our premature solution $u(x,y)$.

$$k(y)' = 1 + \frac {2}{y} + \frac {1}{y^2}$$

$$k(y) = \int \left[1 + \frac {2}{y} + \frac {1}{y^2}\right]dy = y + 2\ln|y| - \frac {1}{y} + c$$

$$u(x,y) = - \frac {x}{y} + k(y) = - \frac {x}{y} + y + 2\ln|y| - \frac {1}{y} + c$$

$$y + 2\ln|y| - \frac {1}{y}(x + 1) = c$$

I believe I may have solved it but I just need someone to check my work.

You could check by yourself your result : $$y+2\ln|y|-\frac{1}{y}(x+1)=c$$ $$x=y^2-2y\ln|y|-cy-1$$ $$dx=(2y-2\ln|y|-2-c)dy$$ Bringing it back into the ODE : $$-ydx + (x + y^2 + 2y + 1)dy = 0$$ leads to : $$-y\big((2y-2\ln|y|-2-c)dy\big) + \big((y^2-2y\ln|y|-cy-1) + y^2 + 2y + 1\big)dy =$$ after simplification $$=0$$ So, the result is correct.
I think you could go faster to the solution rewriting $$\frac{dy}{dx} = \frac{y}{x + (y + 1)^2}$$ as $$\frac{dx}{dy} = \frac{x + (y + 1)^2}{y}$$ that is to say $$\frac{dx}{dy}-\frac{x}{y} =\frac{ (y + 1)^2}{y}=y+2+\frac{1}{y}$$ which gives for the homogeneous equation $x=Cy$. So, the equation write now $$y \frac{dC}{dy}=y+2+\frac{1}{y}$$ that is to say $$\frac{dC}{dy}=1+\frac{2}{y}+\frac{1}{y^2}$$ and then $$C=-\frac{1}{y}+y+2 \log (y)+K$$ So, finally $$x=K y+y^2+2 y \log (y)-1$$


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# Dragon Balls

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 32768/32768 K (Java/Others)

## Description

Five hundred years later, the number of dragon balls will increase unexpectedly, so it's too difficult for Monkey King(WuKong) to gather all of the dragon balls together.

His country has N cities and there are exactly N dragon balls in the world. At first, for the ith dragon ball, the sacred dragon will puts it in the ith city. Through long years, some cities' dragon ball(s) would be transported to other cities. To save physical strength WuKong plans to take Flying Nimbus Cloud, a magical flying cloud to gather dragon balls.
Every time WuKong will collect the information of one dragon ball, he will ask you the information of that ball. You must tell him which city the ball is located and how many dragon balls are there in that city, you also need to tell him how many times the ball has been transported so far.

## Input

The first line of the input is a single positive integer T(0 < T <= 100).
For each case, the first line contains two integers: N and Q (2 < N <= 10000 , 2 < Q <= 10000).
Each of the following Q lines contains either a fact or a question as the follow format:
T A B : All the dragon balls which are in the same city with A have been transported to the city the Bth ball in. You can assume that the two cities are different.
Q A : WuKong want to know X (the id of the city Ath ball is in), Y (the count of balls in Xth city) and Z (the tranporting times of the Ath ball). (1 <= A, B <= N)

## Output

For each test case, output the test case number formated as sample output. Then for each query, output a line with three integers X Y Z saparated by a blank space.

## Sample Input

2
3 3
T 1 2
T 3 2
Q 2
3 4
T 1 2
Q 1
T 1 3
Q 1

## Sample Output

Case 1:
2 3 0
Case 2:
2 2 1
3 3 2

lcy

## Source

2010 ACM-ICPC Multi-University Training Con


text:
## Friday, August 09, 2013

### Skyrmions could make hard disks 100 times smaller

Remotely related: sci-fi gets real: tech junkies should look at 27 science-fiction concepts that morphed into reality in 2012.
Nature's Ron Cowen reviewed a technical paper in Nature that is one month old,
Writing and Deleting Single Magnetic Skyrmions (Niklas Romming and 7 co-authors from Hamburg).

Skyrmions, some topologically non-trivial solutions of non-linear sigma-models first described by Tony Skyrme in the 1960s, may be thought of as tiny vortices of atoms. Because in this very recent breakthrough, Romming et al. became able to create and destroy them at will, it's plausible that they may be used in future magnetic information storage technologies.

I've been in love with skyrmions decades before I knew their name.

It really began when I was 15. I was obsessively reading Albert Einstein's book "My World View" ("Mein Weltbild", in a Czech translation) that I had found somewhere in the bookshelves (I guess that it would originally belong to my paternal grandfather, a professional painter/artist and geometry teacher).

In this book, one that probably overlaps with "Ideas and Opinions" heavily, Einstein popularly presents his views and insights about relativity, religion, socialism, Jewish questions, Nazism, meanders, Max Planck, alleged incompleteness of quantum mechanics, and other things.

Einstein wrote many inspiring things, many things that looked deeply ethical, many political ideas I would later find myself in disagreement with, many ideas about physics that were right, and some ideas about physics that were wrong.

Those nearly 25 years ago, I was only beginning to be exposed to quantum mechanics and for a year, I was an employee of Einstein's dream to construct the unified field theory de facto as a classical field theory, if you allow me to use the standard terminology. After some months, I had to begin to steal ideas from proper quantum mechanics to explain the hydrogen atom, before I was forced to steal all of quantum mechanics, of course, but let me avoid the hydrogen atom here.

While its quantum dynamics implies that some quantum numbers are discrete, there are also other observables that have to be discrete in the real world (because they were observed as discrete!) although such a quantization rule seems hard to get in a classical field theory. In one of the essays, Einstein wrote something like (using a modernized terminology):
Quantum mechanics is probably incomplete and a complete description should still be looked for. There is no proof that an old-fashioned, realist, classical theory may not account for the quantum phenomena. For example, the quantization of the electric charge could follow from a classical field theory. There could be a classical field theory that allows us to derive that whenever the charge density vanishes on the boundary of a region, the region contains a charge that is an integral multiple of the elementary charge.
I took that as a homework and apparently found a solution. Imagine that in each point of the spacetime, there is a field that takes values on a three-sphere. If $$\vartheta(x,y,z,t)=0$$ corresponds to a conventionally preferred point of the sphere (the North Pole) in the same way that we know from the two-sphere, we may add a potential energy term to our action such as$S_{\rm pot}\sim - C \int \dd^4 x\,\vartheta^2$ that will place the value of $$\vartheta$$ in the majority of the spacetime close to the value zero. However, in a limited three-dimensional region, the field $$\vartheta$$ may probe all points of the target three-sphere. We may figure out that in those regions, the real space may be "wrapped" on the target space three-sphere.

The charge density may be calculated as the "solid angle" spanned by the infinitesimal region of space in the three-sphere. That means that the charge current is proportional to the Hodge dual of a Jacobian of a sort,$j^\kappa = \frac{e}{6}\cdot\frac{1}{2\pi^2} \varepsilon^{\kappa\lambda\mu\nu} \partial_\lambda V^a \partial_\mu V^b \partial_\nu V^c \varepsilon_{abcd} V^d$ where $$V^a$$ is the four-vector embedding the three-sphere pointer into a four-dimensional Euclidean space of a sort; we always have $$V^a V_a=1$$. I hope that I inserted the right normalization factor above; $$1/6$$ avoids the multiple counting over the permutations of $$a,b,c$$ while the other factor divides by the "full solid hyperangle" i.e. the surface/volume of the unit three-sphere $$2\pi^2$$ for the integral of $$j^0$$ over the regions where something happens to be an integer multiple of $$e$$.

This seemed like a cute idea. Later, I learned that the magnetic (monopole) charge density actually is represented by a similar topological trick. However, the electric charge is quantized for purely quantum mechanical reasons. Due to the quantization of energy in the quantum harmonic oscillators, one may only add energy to charged fields by creation operators whose electric charges are quantized. There's nothing wrong about this intrinsically quantum explanation for the electric charge.

In the 1990s, the discovery of dualities (and S-duality in particular) showed that these two constructions or explanations for the charge quantization are equivalent although the proof is in no way obvious.

In 1998, I still didn't know the word "skyrmion" although my adviser Tom Banks was telling me that I should have found out what the word meant. ;-) But when I and Ori Ganor asked how the cylindrical M2-branes stretched between pairs of M5-branes are represented at the Coulomb branch of the 6-dimensional (2,0) theory, they are represented by skyrmions, too. The fivebranes become knitted.

This 6-dimensional construction differs from the 4-dimensional construction above by some changes to the dimension only. First, the pointer field isn't labeling a three-sphere but a four-sphere. You may obtain the corresponding vector $$V^a$$ from the 5-dimensional transverse Euclidean space as the separation of the corresponding points of the two M5-branes normalized so that it is a unit vector, i.e. as$V^a = \frac{\Phi^a_M - \Phi^a_N}{|\Phi_M -\Phi_N|}$ where the index $$a=1,2,3,4,5$$ labels the transverse dimensions to the M5-branes and $$M,N$$ label the M5-branes themselves (Chan-Paton indices of a sort).

There's one more difference between the six-dimensional and four-dimensional case. The six-dimensional theory has five and not just four spatial dimensions. So the four-sphere may only be wrapped by four spatial dimensions and the solution remains constant in 1 remaining spatial dimension (plus 1 temporal dimension). That's why the resulting skyrmionic objects are strings rather than point-like objects. They become tensionless strings ("the" tensionless strings known in this theory) in the $$\Phi_M-\Phi_N\to 0$$ limit where the Coulomb-branch-based description of the theory breaks down.

In 2000, Ken Intriligator used some nice anomaly considerations to derive structurally similar terms in the six-dimensional theory. I've tried to see that the equations are equivalent to the skyrmion-based ones but the two papers always seemed slightly inequivalent at the end.

In various effective descriptions of nuclear physics, one encounters nonlinear sigma-models and the baryon number seems to be exactly given by the skyrmionic wrapping number. I guess that the detailed implementation of the nonlinear sigma-models is inequivalent in the condensed-matter-physics setup by Romming et al. but the mathematics is going to be analogous. In a foreseeable future, this 50-year-old piece of mathematical physics that has appeared at various places of real physics may dramatically improved magnetic information storage systems.

1. Dear Lubos,

2. Ha ha,

this is an additional cute point against sourpusses who loudly demand that all legitimate physics has to have direct every-day implications for their close minded view of the world, high energy theoretical physics is therefor no good, etc ... :-D.

This is really a cute application of some serious physics, thanks for explaining this even though I do not get all the fine grained details of course :-)

3. kashyap vasavadaAug 9, 2013, 6:14:00 PM

I agree with Dilaton and "and?" that mathematical content of Lubos' blog is superior to any other physics blog around. So Lubos, keep it up!

4. I saw also you cite some very good arxiv papers. I worked through some algebraic topology, mainly Hatcher and for the geometry part Griffiths. Of course, I still have some parts to read from the huge book about "mirror symmetry" and Baker & Baker on string theory but I would like to know if you know a shorter introduction to the way in which topology and group theory connects to string theory... That could help me now. Thanks in advance and keep the good work :)

5. *Becker&Becker ... sorry

7. Why the inertia? ;)

8. I first silently lurked around here too, before I dared to post my first TRF comment, believe it or not ... ;-) !

9. I have an obsession with 6d (2,0) SCFT. This paper was on my radar for quite some time and I think now is the time to read it.
BTW I still can't use the Disqus with Chrome to log on to TRF (the Disqus log on window disappears). Each time I want to log on to TRF I must use IE. Maybe because I have Windows 8? Does anyone else have a similar problem with Chrome and Windows 8?

10. What is the setting in your Chrome for "Allow third-party cookies to be set"? If the setting is "No" then you must exempt disqus.com explicitly. Try it and let us know if it works.

11. It worked!

Thanks Eugene!

12. Well, you will laugh but I found this blog searching for "Sean Carroll, nonsense" so I cannot really start posting here in a less anonymous way :)) I nevertheless share many ideas I found here and I like string theory although I might have things to learn about it before reaching Lubos's skills of argument. All the posts on this blog about quantum mechanics are right and it brings some sort of relief to see that not everyone is into "many worlds interpretation of Quantum Mechanics"... it is funny thinking that everyone used ghosts in doing some QFT calculations but nobody ever went to the public screaming "Ghosts are real!!!" well, anyhow, great blog!

13. In SQCD, for example Seiberg duality, can one still see the Baryon number as being given by the skyrmion wrapping number?

14. Dear any, SQCD - theories subject to Seiberg dualities - are gauge theories with polynomial Lagrangians.

The Skyrmions are solitions in nonlinear sigma-models, e.g. in effective field ttheory descriptions that involve pion and rho-meson fields.

15. right, like the magnetic description of SQCD. which too is an effective field theory after adding an irrelevant operator of mass dimension. Give the magnetic squarks a vev and the magnetic gauge bosons become your massive rho-meson (and mesino). Still not sure how to see the skyrmions :) best, any.

16. I may be ignorant of something about the Lagrangians you mention but just to be sure that we're on the same frequency, do you understand that the skyrmions only appear in non-linear - and therefore non-polynomial and non-renormalizable - sigma-models? See

http://www.scholarpedia.org/article/Nonlinear_Sigma_model

for some explanation of the NLSMs. The kinetic terms have field-dependent "metric tensor" prefactors in NLSMs. You may have pions and rho but the configuration space has to be compact - a sphere of a sort.

17. i agree with what you are saying, and i will have to think about your comments on config. space and field dependent metric tensor, although if i understand it correctly the NLSM may be related (is gauge equivalent) to a linear one. i.e. there is a G/H lagrangian that is relatable to a linear one with gauged H. hence the rho mesons....may i mention this http://arxiv.org/abs/1202.2863v3 and the introduction.

My feeling is that some sort of gauged bosonic skyrmion should be present by using certain field configurations of the magnetic description.

18. Hi Lubos,

I was thinking how the free SCFT theory in 6d may arise in this picture. Since we must retain CF invariance the M5 branes should coincide of course; so my intuition says that the way to go from a strongly coupled (2,0) SCFT to a free SCFT (i.e. to switch off the interactions of the tensionless strings) is the width of the M2 brane (i.e. the M2 dimension in the worldvolume of the M5 brane) to collapse and thus M2 to become a thin stringy like membrane. This way the Wilson surface on M5 would collapse to a Wilson loop.

But I’m not sure if I got it right. Do you know if there are
any papers on this issue?

19. Dear Giotis, I am not sure I understand what you want the papers to be about.

First, yes, the conformal symmetry is broken by the separation of the M5-branes. In the (2,0) theory, the separation scalars have dimension mass^2 - it's from the kinetic terms being mass^6 - so one can see that the transverse thickness in the 4 dimensions that belong to the 5+1 dimensions in which the (2,0) theory is defined is given by Thickness = scalarvev^{-1/2} by dimensional analysis.

The cylindrical M2-branes considered here are strings simply because 1 of the dimensions is in the transverse dimensions to the M5-branes, so it's "internal" from the (2,0) viewpoint, while the remaining 1 spatial and 1 temporal dimension is along the M5-branes. There is never any Wilson surface inside the (2,0) or M5 world volume theory. When M2-branes are fully parallel to M5-branes, they dissolve into the electromagnetic flux of the self-dual 3-form field strength H fields in the (2,0) theory.

A way to get a free theory limit is to have the large scalarvevs in the (2,0) theory. In that limit, the transverse (4D) thickness of the strings goes to zero, mass goes to infinity, and they don't affect low-energy physics. The interactions in this low-energy theory are weak in this limit and may be viewed as effects of integrating out the heavy thin strings.

20. Thanks Lubos,

There was a misunderstanding then; I was talking about the Wilson surfaces which appear in the 6d theory (see e.g. http://arxiv.org/abs/hep-th/9809188).
Probably you have some other configuration that I didn't quite understand.

The question was generally, how can I get a free SCFT in the M5/M2 picture i.e. without breaking CF invariance.

21. I see. Just be careful, the Wilson surfaces from the 1998 paper aren't really "object" that last in time. They're localized in time, i.e. generalized instantons.

The same is true for the Wilson loops, of course, but I didn't understand how you reduced the surfaces to the loops. In general, the reduction from (2,0) to N=4 Super Yang-Mills proceeds by compactification of 2 dimensions on a small torus.

22. My aim is to switch off the interactions of the tensionless
strings while retaining conformal invariance (in order to get a free SCFT in 6d). So I was thinking if I could make the membranes thin (stringy like with zero width) then in 6d the tensionless strings will become point like and thus their paths won’t be able to intersect.

But I’m not sure if these things have already been solved. That’s why I was asking if there are any papers on this issue i.e. how to get a
free SCFT in 6d.

23. Just a correction:

What I wrote above for Wilson surfaces turning into Wilson loops is complete nonsense of course. Sorry for that; I got confused due to AdS7/CFT6 duality. The Wilson surface of 6d (2,0) *is not* the world sheet of the tensionless string.

Thanks for the correction Lubos.


text:
# Are lagrangians based on physical observation or mathematics?

1. Aug 15, 2007

### captain

are lagrangians based on physical observation or mathematical reasoning?

2. Aug 16, 2007

### Thrice

yes.

3. Aug 16, 2007

### PhysiSmo

In the same question, "Why do we use THIS Lagrangian, or THAT, and HOW did we derive it?", I have been told that "it just suits the corresponding problem, it just works out!".

I guess that the first one who came up with a working Lagrangian had tried a lot, before he got there. One may be able to recognize several proper terms in a Lagrangian, such as the kinetic terms, or mass terms, or interactions between the sources and the fields, which have imply physical meaning. But I don't think there is a "standard" way to create a working Lagrangian, or a step by step proof of the procedure to get there!

4. Aug 16, 2007

### mjsd

in classical mechanics L = T-V, kinetic energy - potential energy of the system.
in QM, and QFT we just push this idea further

5. Aug 16, 2007

### LHarriger

I am not sure what you are driving at when you say "it just works out".
It is not a difficult matter to prove the equivalance of newtonian and lagrangian dynamics. You can find this proof in just about all undergraduate classical mechanics texts, see Marion. Given this proof, it doesn't just work out for some mysterious reason, rather it is simply a reformulation of mechanics in terms of energy instead of forces. If anything about the langrangian is mysterious, I would consider it to be the fact that the langrangian formulation implies that nature always minimizes the time integral of action. Which is a topic that has been beat to death on this forum with no real consensus.

6. Aug 17, 2007

### PhysiSmo

When I answered the original question posted, the thread was in the "Quantum Mechanics" section, not the "Classical Mechanics" that has been moved now.

Anyway, in C.M., Lagrangian is always L= T - V, and one can derive it easily. In QFT, one cannot use a similar path, since, as far as I know, it doesn't exist.

The fact that the Lagrangian minimizes the time integral action does not push one further to find the correct corresponding Lagrangian to his problem.

Say, i.e., we need to find the Lagrangian from which Klein-Gordon equation arises. We cannot "prove" the satisfying Lagrangian by means of a "law", such as T-V, as in C.M., but only by means of minimizing the action time integral. Which means that the procedure requires a lot of effort, trying and fantasy to get the proper result!

7. Aug 17, 2007

### captain

i am curious to know how can you couple the field A with the dirac field with the use of a coupling constant. I am not quite sure how that works out?


text:
# Continuity of the function

1. Nov 13, 2008

### l46kok

1. The problem statement, all variables and given/known data
$$f(x) = x^2 - 4x + a$$
$$g(x) = \lim_{n\rightarrow\infty} \frac {2|x-b|^n + 1}{|x-b|^n + 1}$$

let $$h(x) = f(x)g(x)$$

Find the sum of a+b that makes h(x) continuous for all x.

2. Relevant equations
Power Series??? Derivation to test continuity???

3. The attempt at a solution

Well I know a function is continuous if

1)f(c) exists
2)Limit as x goes to c of f(x) exists
3)#1 is equal to #2

2. Nov 13, 2008

### Office_Shredder

Staff Emeritus
How does it fail to be continuous? f(x) is continuous for all a, but g(x) has a jump from when |x-b| < 1 (in which case g(x)=1) to when |x-b|>1 (in which case g(x)=2). So you need to figure out how to take care of it.

3. Nov 13, 2008

### l46kok

I understood why the discontinuity occurs, since |x-b|^n of n to the infinity could take you to 0 or a huge value (I think it was related to geometrical sum) depending on whether it's smaller than 1 or bigger than 1. I still do not have a clue how to get the specific values of a and b from it...

Last edited: Nov 13, 2008
4. Nov 13, 2008

### Office_Shredder

Staff Emeritus
So, for f(x)g(x) to be continuous, you know that when |x-b| isn't near 1, the function's continuous. You should realize this gives us that the only two points of concern are x=b+1 and x=b-1. You have that as x approaches b+1 and b-1 from different sides, g is either 2 or 1. So you need f(b+1) and f(b-1) to be values such that f(b-1)*2=f(b-1)*1 and f(b+1)*2=f(b+1)

5. Nov 13, 2008

### l46kok

Then that simply means

f(b-1) = 1
f(b+1) = 1

So we have

$$1 = (b-1)^2 - 4(b-1) + a$$
$$1 = (b+1)^2 - 4(b+1) + a$$

$$0 = (b-1)^2 - 4(b-1) - (b+1)^2 + 4(b+1)$$
$$0 = (b-1)^2 - (b+1)^2 + 8$$

$$b = 2$$

Then,

$$1 = (2+1)^2 - 4(2+1) + a$$
$$1 = 9 - 12+ a$$
$$a = 4$$

a + b = 6 is what I get, but supposedly this isn't the answer. I don't see what went wrong here, everything seems right.

Actually, I thought about it, but for the two distinct points of x = b-1 and x = b+1 to be continuous, shouldn't that mean that
f(b-1) = f(b+1) ?

6. Nov 13, 2008

### Office_Shredder

Staff Emeritus
f(b-1)=1. Then 2*f(b-1)=f(b-1) gives us 2=1. Are you sure that's the right value?

f(b-1) and f(b+1) have nothing to do with each other really (although it is correct that f(b-1)=f(b+1) is necessary, this is more by coincidence than any deep connection).

7. Nov 13, 2008

### l46kok

Oh, it's actually

f(b-1) = 0
f(b+1) = 0

Doh! Thx


text:
# Gravitational Waves and Potential

1. Nov 9, 2008

### Naty1

What's the relationship between gravitational waves and (traditional/stationary) gravitational potential?

Does the (traditional/stationary) potential become a "wave" under acceleration? Or do both exist under acceleration? Do both use energy from the source? I think I saw somewhere that GR predicts gravitational waves...true? Is this related in any way to the Unruh (acceleration) effect? Are these effects (waves, Unruh) evidence of the "absolute" nature of acceleration?

(http://en.wikipedia.org/wiki/Bill_Unruh)

Wiki says:

2. Nov 9, 2008

### tiny-tim

Hi Naty1!

Here's another wiki link (about the decomposition of the Riemann curvature tensor into the Ricci tensor and the Weyl tensor) which may help: http://en.wikipedia.org/wiki/Ricci_decomposition#Physical_interpretation
EDIT: and this link from John Baez's website:

Last edited: Nov 9, 2008
3. Nov 10, 2008

### Naty1

Tiny-tim...great descriptions to get me started...thanks..

4. Nov 13, 2008

### Antenna Guy

An electromagnetic wave that needn't have any source???

How does one rationalize something like that?

Regards,

Bill

Last edited: Nov 13, 2008
5. Nov 13, 2008

### spidey

will an accelerated observer also emits gravitational waves?

6. Nov 14, 2008

### Naty1

It's a wave originating from other than the source description reflected in the Ricci tensor. Like an initial condition.

7. Nov 14, 2008

### Naty1

Sure. Although extremely,extremely small as even massive bodies emit only small amounts of gravitational radiation (power).

And an accelerating observer, in the absence of external gravity, also observes curved space time via the equivalence principle (I think). I think this is why special relativity (no gravity) requires inertial frames to keep space time observations flat.

I still not quite sure whether an accelerating observer measures local light at "c". I believe I read there is a theory that basically says instantaneous readings while accelerating measure "c". These would apparently be inertial observers.
But there are so many references which say "free falling observers" (non accelerating) in general relativity measure light at "c" that I am still suspicious...it may be a matter of context. I know Einstein came close to relying exclusively on free falling (local) frames and there had to be a good reason.

8. Nov 14, 2008

### tiny-tim

Weyl curvature tensor is not related to sources

Yup!

The source tensor (the stress-energy tensor) only has ten independent parameters,

but the Riemann curvature tensor has twenty

Einstein's field equations ("matter tells space how to curve") only relate the source tensor to the Ricci tensor, which of course also has ten parameters (natch ) …

the remaining ten parameters of the Riemann curvature tensor (in other words, the ten parameters of the Weyl tensor) are entirely independent of the source tensor, and therefore independent of all sources (assuming Einstein is right! )

9. Nov 17, 2008

### DrGreg

I'd just like to remind you of this reply I gave you in another thread. "Curvature of spacetime" is an intrinsic property of spacetime and does not depend on the observer. In the absence of gravity, spacetime is always "flat" whether you are an inertial observer or not. It's just that (to use the analogy of that other post) non-inertial observers draw a curved grid on flat graph paper.

Non-inertial observers in the absence of gravity do indeed see some (but not all) of the effects that "stationary" observers see near black holes, but you shouldn't attribute those effects to "spacetime curvature" -- attribute them to a non-inertial frame instead.

This is more a question of the established terminology than anything else.

(For the benefit of other readers: as for your last paragraph, we are currently discussing that in another thread.)

10. Nov 19, 2008

### Naty1

I just read your "this reply"...which was # 11 on the other thread .....don't believe I saw that ...excellent description and likely the source of my confusion.....

I'll think about it and post tomorrow...


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# UG calling on large number of samples (>2,000) : IO issues

Member Posts: 78

Hi there

I am trying to run UG across just over 2,200 individuals (exome sequencing). I have successfully done this on our computing cluster with just over 1,000 samples without issues (apart from having to get the limit on no. of open files (ulimit) increased).

I got another increase in ulimit to allow me to run UG on the larger set. However, our IO is being pushed over the edge with the 2,200 input samples. I have two questions:

• does UG open all of the input bam files at the same time? It seems like it, since a ulimit of 2048 was not sufficient for 2,200 input files.
• is there a way to optimise this, possibly by getting UG to open files sequentially - or do they have to be all open at the same time? I suspect this will become more of a problem as the size of the datasets available increases.

Would appreciate any advice you would have on getting this to run on this size of data.
Thanks!

Tagged:


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This equation implies two things. First buying one more unit of good x implies buying {\displaystyle {\frac {P_{x}}{P_{y}}}} less units of good y. So, {\displaystyle {\frac {P_{x}}{P_{y}}}} is the relative price of a unit of x as to the number of units given up in y. Second, if the price of x falls for a fixed {\displaystyle Y} , then its relative price falls. The usual hypothesis is that the quantity demanded of x would increase at the lower price, the law of demand. The generalization to more than two goods consists of modelling y as a composite good.

## I enjoy how you lay out real numbers. A lot of people wouldn’t do that. While you admit that you are somewhat conservative, I think the $1M in CD’s is just too conservative. Assuming you don’t need the cash flow now (which you say you just save anyways) then all that could be invested for potentially higher returns. For example, what if you bought San Francisco real estate along the way instead of CD’s. Or, an SP500 Index fund. I bet your average return would have been higher than 3.75%. Sure you could lose it, but the point is if you don’t need the cash flow now, you should try to increase that nut as high as possible until the day you actually need it. Your nut could be$5M right now if you had invested in asset classes other than CD’s for the last 14 years. Don’t get me wrong, you have done far better than me, but I guess I would take a little more risk if you don’t rely on that cash flow.

Doesn’t it sound awe-inspiring to have more than one income source? You already have one source of work with a steady flow of income and then you are creating more and more work for you with more income for you. Who does not want to have lots of money in their bank accounts floating all around? For the person who values financial security and their ultimate dream is financial freedom, creating more than one source of income becomes a necessity not just desire.

The reason I consider dividends artificial and believe they don’t matter is because you can just as easily reinvest your dividends. If a stock is worth $100/share, I don’t care if it issues a$1/share dividend or if the share price instead increases to $101/share – either way, I have the same amount of money, because there’s no difference to my net worth whether I take the dividend or sell part of a stock.  The Indian economy was large and prosperous under the Mughal Empire, up until the 18th century.[71] Sean Harkin estimates China and India may have accounted for 60 to 70 percent of world GDP in the 17th century. The Mughal economy functioned on an elaborate system of coined currency, land revenue and trade. Gold, silver and copper coins were issued by the royal mints which functioned on the basis of free coinage.[72] The political stability and uniform revenue policy resulting from a centralised administration under the Mughals, coupled with a well-developed internal trade network, ensured that India–before the arrival of the British–was to a large extent economically unified, despite having a traditional agrarian economy characterised by a predominance of subsistence agriculture,[73] with 64% of the workforce in the primary sector (including agriculture), but with 36% of the workforce also in the secondary and tertiary sectors,[74] higher than in Europe, where 65–90% of its workforce were in agriculture in 1700 and 65–75% were in agriculture in 1750.[75] Agricultural production increased under Mughal agrarian reforms,[71] with Indian agriculture being advanced compared to Europe at the time, such as the widespread use of the seed drill among Indian peasants before its adoption in European agriculture,[76] and higher per-capita agricultural output and standards of consumption.[77] Doesn’t it sound awe-inspiring to have more than one income source? You already have one source of work with a steady flow of income and then you are creating more and more work for you with more income for you. Who does not want to have lots of money in their bank accounts floating all around? For the person who values financial security and their ultimate dream is financial freedom, creating more than one source of income becomes a necessity not just desire. You can uses tools such as Wordpress for your website platform. MailChimp to collect email addresses. Clickfunnels to create funnels and landing pages that are completely automated. Stripe to process payments. These are just a few tools I use but there are many more options for each part of your business. Find the ones that work for you and help you create systems. (Disclaimer: I was not paid to mention any of these companies). "But for our jobs, for how we make money, I think many of us — most of us — have one way we make money. It can be very risky. I've really come to believe, and have done a lot of research over the years, that one of the best ways that we can create real, legitimate professional stability for ourselves is by choosing to cultivate multiple income streams. In India Freelancing is synonym with Journalism but trust me its a very big industry abroad. Freelancing is full time career for many professionals. In India its at nascent stage and Freelancing is not a highly paid job. Positive way to look at it is that if you start today then you will have 1st mover advantage. Freelancing jobs are available in various domains. One of dedictaed Indian site for freelancing job is worknhire.com I came across your site and I love it! My husband and I work in corporate America and I own a consulting/coaching business. I have a goal to gross 1 MIL within the next 10 years I’ll be 40 then. How can I begin now? How do I find a millionaire mentor? We live in Philadelphia, PA all of our friends and family are mostly employed some with small businesses however i have huge goals I am working so hard to become a full time entrepreneur. Seems like everyone we know are all on the same level and I fear we’ll stay here of we don’t meet someone willing to show us how to level up. Any suggestions? The type of business you should start depends on your passion and existing skill set. If you love baking, for example, you could consider starting a home-based cake or brownie business. Love to sew? Spend your free time creating the perfect crafts, then turn around and sell them with your own Etsy store. Love dogs? Consider watching dogs out of your own home and marketing your services on a website like Rover.com. **The information contained herein neither constitutes an offer for nor a solicitation of interest in any securities offering; however, if an indication of interest is provided, it may be withdrawn or revoked, without obligation or commitment of any kind prior to being accepted following the qualification or effectiveness of the applicable offering document, and any offer, solicitation or sale of any securities will be made only by means of an offering circular, private placement memorandum, or prospectus. No money or other consideration is hereby being solicited, and will not be accepted without such potential investor having been provided the applicable offering document. Joining the Fundrise Platform neither constitutes an indication of interest in any offering nor involves any obligation or commitment of any kind.  Almost all of these ideas require starting a personal blog or website. But the great thing about that is that it's incredibly cheap to do. We recommend using Bluehost to get started. You get a free domain name and hosting starts at just$2.95 per month - a deal that you won't find many other places online! You can afford that to start building a passive income stream.
As for me, I started focusing on passive income last year, but have owned rentals for 5 years. $25k now outside retirement accounts in mostly real estate. Looking to invest another$500k cash into real estate to get about $65k, and then 1031 under performers next year to hopefully boost that a bit higher. Heavy in real estate, but feels lower risk than the stock market to me if you have cashflowing properties. Real estate is inflation adjusted, and built in cashflow raise when the loan pays off. "That's certainly true for entrepreneurs, but even for people who work inside a company, cultivating a side income stream of some sort — whether it's having an Etsy store on the side, or doing a little bit of coaching or having a workshop now and then, whatever it is, doing a little bit of paid speaking — having that sideline gives you additional protection against uncertainty and also has a lot of other benefits. I’m still a big fan of InfoBarrel, Eric, even though I haven’t been able to write much. With what I am earning there, I’ve actually shifted to outsourcing quite a bit of content…call it a “respite” from writing, I had just needed a break. Even if one pays$5-$10 per article, IF the keywords are researched properly and effectively, one can easily turn that one article and earn several hundred off of it in it’s lifetime. Right now, one of my friends had written a single article that, already this month, has earned over$83 on InfoBarrel. Not too shabby at all…


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# No Leaf Clover (Live)

## Features of This Track

hard rock roots
repetitive melodic phrasing
demanding instrumental part writing
minor key tonality
melodic string accompaniment
orchestral arranging
mixed acoustic and electric instrumentation
dirty electric guitar riffs
a gravelly male vocalist
emphasis on instrumental arranging

These are just a few of the hundreds of attributes cataloged for this track by the Music Genome Project.

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ASWOME!!!!!! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !
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