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# Why I Hate Science Journalism

Discussion in 'Science & Society' started by BenTheMan, Feb 28, 2008.

1. ### BenTheManDr. of Physics, Prof. of LoveValued Senior Member

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http://discovermagazine.com/2008/mar/13-e-nste-n/

You know, sometimes I wonder if the people who write these articles have any clue about physics other than what they read on Wikipedia?

Lisi's Exceptionally Simple Theory of Everything'' is exceptionally incomplete and doesn't look like it can describe nature, Hawking hasn't done any physics for at least ten years, and I've never even HEARD of the rest of these people (except Witten), and I work in a closely related field.

I don't know who comes up with these lists, but if Witten isn't at the top (no matter whether string theory is right or wrong) of the list, it showcases the fact that Discover magazine seems to be hiring journalists instead of scientists.

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3. ### draqonBannedBanned

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you seem to be forgetting the type of country you are in...capitalistic or all for money. Journalism and making money is priority...than comes everything else like science

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5. ### draqonBannedBanned

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I do agree with you that Garrett Lisi is not the 1st one there on the list...more like the last on any list to do with physics/mathematics

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7. ### BenTheManDr. of Physics, Prof. of LoveValued Senior Member

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I fail to see how this has anything to do with anything. It's more about people not knowing anything about science.

8. ### zarlokBannedBanned

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You should see how bad it is in fields that have "cultural signifigance", Genetics is a complete joke. Any article you read is going to be complete garbage if the writer so much as once chooses to make a point without directly quoting the scientist who knows what he/she is talking about. For, like, uhh, 10 years we had this bogus claim of humans of all humans being essentially identical to each other(ie. 99.9% the same). Of course, the idea was completely bogus and debunked within a year of it first appearing as pseudo-science, yet even today people still believe that nonsense because it fits into their political paradigm. And why do you think? Leftist journalism have vested interest in claiming "all humans are essentially the same"-- it's nurture, not nature idiot! Ridiculous. The recent hunan origins in Africa is another steaming pile of BS that gets shoveled up daily. Sadly, in this case, the "scientists" are the ones causing the problem.

9. ### phlogisticianBannedBanned

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I reckon most Wikipedia articles would have journalists scratching their heads!

When I worked with a bunch of astronomers, one was getting interviewed by the local press over a discovery he'd made. The first thing the interviewer said was 'Right, and it's Astronomy, not Astrology, yes?' Despite having walked through a foyer, with a sign 'Department of Astronomy' in foot high letters, showing no common knowledge, no research, and no observation.

10. ### QuarkHeadRemedial Math StudentValued Senior Member

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Off-topic; I suppose the journalist in question missed the rather nice play on words in this title? Lisi's paper deals with the Lie group $\text{E_8}$, which is an exceptional Lie group (meaning it can't be classified), with a simple algebra (meaning it has no non-trivial ideals). Geddit?

I have to say, though, that the few (2) direct dealings I have had with what one might call the "heavyweight" press here (UK), I was hugely impressed by their science correspondent's ability quickly to grasp and distill what I told them of fairly complex science.

So I guess it's patchy.

11. ### iceauraValued Senior Member

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24,101
There is also the factor of scientists dismissing as trivial non-technical explanation - such as metaphor and analogy and the various techniques of rhetoric in communicating with the ignorant and the general public.

This seems to me to have fairly deep roots, affecting not only pop science but the basics of science education in early schooling, etc.

Granted the top researchers in a field don't have time, but a little more simple respect for (and cooperation with) the retired or the second tier who do take the trouble to straighten out the local media - an onerous task involving much patience, and no little rhetorical skill - might help.

I recall an account of Los Alamos (the Bomb) in which the journalist assigned by the NY Times proved incapable - and was marginalized, not seriously replaced. No one called the boss and got a better one sent out, as they would have with any other significant jobholder proven incapable. They just parceled out the communication tasks to whomever was available - people who had no journalism experience, and other things to do.

12. ### shalaykaCows are special too.Registered Senior Member

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Milgrom's MOND and Bekenstein's relativistic version TeVeS are both well known amongst those studying gravitation.

What's rather ridiculous about the article is that MOND is non-relativistic, and does not explain lensing by dark matter. Furthermore, more modern models such as MOG by Moffat (and Brownstein) do include lensing. As well, MOND does not provide any physical justification other than it makes the math add up in terms of galactic rotation curves. So really, to compare MOND to GR is a sure sign of pure ignorance on the part of the journalist. Perhaps they were running on the idea that anyone who comes up with something new is Einstein. However, that fails to be logical considering that all published manuscripts are something new (to some degree larger than none).

Markopoulou-Kalamara works with Lee Smolin at the Perimeter Institute. Not as famous as Smolin, but she's well-known in the Loop Quantum * field.

Amelino-Camelia's work is a launching pad for some of Smolin's work as well. I only knew of their work because of this relation with those at the Perimeter Institute.

Last edited: Feb 28, 2008
13. ### sowhatifit'sdarkValued Senior Member

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Well, he does have a point. You are expecting the focus to be on accurate information. Discovery is a profit making enterprise and accuracy is on the list of priorities, but only in so far as it makes money. What makes money and increases subscriptions is the goal.

This doesn't mean that communist journals will be better. But we do need to face the weaknesses of each system. Out of these a better system may develop.

The very small % of the people who know more than that journalist about the topic are probably not reading Discovery and have little impact on sales. And one can easily silence them by printing one of their letters to the editor next to another that disagrees.

14. ### BenTheManDr. of Physics, Prof. of LoveValued Senior Member

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Yes I agree. There are those who make this a priority (Brain Green) and those who do not (Witten). But I have met very few physicsts who would not talk to someone about physics, given the opportunity.

So I don't know. I see sensationalistic magazine articles (just look at the media circus surrounding Garret Lisi's E8 model), and I know that (for example) Lisi is excited about his own work, but no one else is. For example, the specific types of embeddings that Lisi NEEDS to get a realistic spectrum out of his model just don't exist. See Jaques Distler, U Texas String theorist (very technical) : http://golem.ph.utexas.edu/~distler/blog/archives/001505.html#c013271.

The same is true for MOND---which I HAD heard of, but only from people saying it was wrong. Most astrophysicsts (that I know) point to the fact that even MOND enthusiasts acknowledge the need for some dark matter to account for their observations, even though MOND was supposed to REPLACE dark matter. And (as shalayka mentioned) it doesn't explain gravitational lensing. (http://cosmicvariance.com/2006/08/21/dark-matter-exists/)

And Loop Quantum Gravity still hasn't really caught on. I have read a few of their papers out of interest, but find the whole thing to be a tad contrived. To be fair, I work on a class of models from String Theory that are extremely contrived, but the underlying physics of string theory is very beautiful and natural. (This can be debated elsewhere, but not here please!) Despite being a major research program for 10-15 years, the community is still very small, and the discoveries aren't that compelling.

I think, in retrospect, you are correct. Consumers of science information are ignorant, so you can afford to give them a bad product. Apologies to draqon for this.

15. ### BenTheManDr. of Physics, Prof. of LoveValued Senior Member

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Moved by popular demand

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16. ### cosmictravelerBe kind to yourself always.Valued Senior Member

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I'm trying to find out who this person by the name of "popular demand " is.

17. ### draqonBannedBanned

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& even if the Gods did lie to us, it is all the same to us.

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19. ### BenTheManDr. of Physics, Prof. of LoveValued Senior Member

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Well, she is quite popular with some people here, but quite unpopular with others.

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20. ### S.A.M.uniquely dreadfulValued Senior Member

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To be lexicocratic, since you moved it, you are popular demand.

Does anyone else feel that the role of science journalism in reviewing and critiquing the direction of research, including ethics, is sorely underutitlised?

21. ### cosmictravelerBe kind to yourself always.Valued Senior Member

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Not any longer!

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22. ### BenTheManDr. of Physics, Prof. of LoveValued Senior Member

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Why should we base our research programs on public opinion?

23. ### S.A.M.uniquely dreadfulValued Senior Member

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As an example, does the fact that several thousand farmers commit suicide every year due to crop failure from GM crops be a factor in future research on crops?

Similarly, does the fact that weapons are used to kill people be a factor in developing weapons that can kill larger and larger numbers of people?

Should it be a concern that vastly more amounts of money is spent on the latter than on the former?

Also, at what point does one distinguish the research conducted for getting grants from the research conducted for social benefit?

And in fact, considering the last point, who decides what research is more socially relevant and requires greater investment?


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Physics307L F08:Schedule/Week 5 agenda/Normal

Normal Distribution

The normal or Gaussian distribution is a thing of beauty, appearing in many places in nature. This probably is a result of the normal distribution resulting from the law of large numbers, by which a sum of many random variables (with finite variance) becomes a normally distributed random variable according to the central limit theorem.

Also known as the bell curve, the normal distribution has been applied to many social situations, but it should be noted that its applicability is generally related to how well or how poorly the situation satisfies the property mentioned above, whereby many finitely varying, random inputs result in a normal output.

The formula for the density f of a normal distribution with mean μ and standard deviation σ is

$f(x) = \frac{1}{\sigma\sqrt{2\pi}} \, e^{ -\frac 12 \left( \frac{x- \mu}{\sigma}\right)^2 }$.

A rather thorough article in Wikipedia could be summarized to extend the usefulness of this book: Normal distribution from Wikipedia.

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# how to prove finite subset of a countable set is countable [duplicate]

Let A be a countable set. How to prove that the set

$\mathcal A = \{X \subseteq A : |X| = n$ for some $n \in \omega \}$

of all finite subsets of A is countable?. I checked similar questions subset but they are not discussing about finite subsets. It seems the question is unclear because the finite subsets can be countable.

• (This has been answered on this site probably a dozen more times already) – MJD May 8 '14 at 12:10

If $A$ is finite, then the power set of $A$ is the set of finite subsets of $A$ and is also finite. So we can take $A$ to be countably infinite.
In this case, there exists some bijection of $A$ with the natural numbers $\mathbb{N}$. So, without loss of generality, we can think of $A$ as the natural numbers $\mathbb{N}$.
Let $S$ be the set of all finite subsets of $\mathbb{N}$. We define a map $\phi$ from $S$ to $\mathbb{N}$ as follows: Given a finite subset $X$ of $\mathbb{N}$, say $\{x_{0}, \ldots, x_{n}\}$, we place the elements in increasing order and then defin $$\phi(X) = x_{n}x_{n-1}\cdots x_{0}$$ where the term on the right refers to the decimal expansion of $\phi(X)$. Then, $\phi$ is injective, because if $X$ and $X'$ are finite subsets of $\mathbb{N}$ with different entires then $\phi(X)$ will not be $\phi(X').$
Hence, we have an injection of $X$ into a countably infinite set and hence $X$ is countable. Additionally, $X$ is obviously infinite (because every singleton is in $X$.)


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# Browsing category pi

## Futility Closet, Fibonacci and Quadratic Residues

I love Futility Closet -- it's an incredible collection of interesting bits and pieces, but it has a special place in my heart because they love and appreciate maths. Not only that, they appreciate maths that I find interesting. The internet has many interesting miscellanies, and many excellent sites specialising

## Getting closer to $\pi$

A lovely curiosity came my way via @mikeandallie and @divbyzero: In 1992 Daniel Shanks observed that if p~pi to n digits, then p+sin(p)~pi to 3n digits. For instance, 3.14+sin(3.14)=3.1415926529… — Dave Richeson (@divbyzero) July 15, 2016 Isn't that neat? If I use an estimate $p = 3.142$, then this method

## How I approximated $\pi$ for “Pi Day”

There was a post here, but it's not here any more! Instead, it's over at the Aperiodical, as part of their $\pi$ Day approximation challenge.

## Happy $\pi$ day!

Happy Pi Day! mu-tant cow pi by janemariejett In the American date format, today is 3.14 - a pretty good approximation to $\pi$, which (as any fule kno) is the ratio between a circle's diameter and circumference. It's also the focus of most of the jokes about maths, because -


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# Panel Cointegration, Moderating Effects and Multicollinearity

I am running a panel fixed effects regression on 21 countries and 16 years. Its a secondary data taken from OECD website mostly. My model looks like this:

$$\log{(GDP/Labor)}_{i} = \beta_0 +\beta_1 \log{(RnD)}_{i,t-1}+\beta_2 \log{(Human Capital)}_{i,t-1}+\beta_3 \log{(x_j*(RnD_j)}_{t-1}+\epsilon_t$$

Where,
Rndi = Research and Development expenditure of country i
Rndj = Research and Development expenditure of country j
HC = Index of Human Capital

1). I have following problems with this model:

1) all variables have strong trend and they are expected to be non-stationary however, Im-Pesaran-Shin and Levin-Lin-Chu tests are giving contradictory results about non-stationarity so I cannot conclude about non-stationarity. In your opinion, which test is better for panel regressions? Also, is there any test I can do for cointegration in stata for panel regressions in addition to Westlund test? if I dont find evidence for cointeration, do I first difference the data? I lose ALOT of information and everything becomes insignificant if I do that.

2) One of the primary goals of my paper is to test for moderation effects of human capital on knowledge spillovers and productivity nexus. Problem is that there is a serious multicollinearity problem. VIF goes as high as 1000! How can I test for moderating effects other than using interactions? Moreover, in some cases I also find strong multicollinearity between my key variables and it really makes everything significant at < 0.001 with R2 less than 50.

3) How important is it to include year dummies in regressions? I lose all significance of my variables and things become very bad in terms of signs as well for my core variables when I use year dummies.

Thanks alot

Ali

• Since there are so many forms of dynamic model, it would be useful to see the actual model equation. – Alexis May 4 '14 at 23:25
• Thank you Alexis for the comment. Here is the equation log(GDP/Labor)i = f(Log Human Capitali, Log R&D Stocki, Log (R&Dj*importsj/total imports i), log(technology gap measured relative to US), year dummies, log(capital stock/labor) All these variables are lagged one year to partially reduce endogeniety problem. I am running fixed effects models right now. – Ali-Jena May 5 '14 at 9:03
• Ali, please edit your question (edit button at lower left, between "share" and "flag") to include the formula. Also, try to use the MathJax markup (effectively LaTeX in-line math commands, bracketed by dollar signs... so $\log{(GDP/Labor)}_{i}$ gives $\log{(GDP/Labor)}_{i}$, etc.). – Alexis May 5 '14 at 14:43
• Thank you Alexis. Its so nice to be here already that I am learning bits of LaTeX. I have been planning to learni this for long long time. – Ali-Jena May 6 '14 at 16:06

Question 1

If your outcome variable is integrated, you might consider using a single-equation generalized error correction model (GECM) as per Banerjee (1993) and De Boef (2001), as this model is agnostic to the stationarity of the predictors.

You might evaluate the stationarity of your outcome using:

$\log{(GDP/Labor)_{ti}} \sim \rho_{i}\log{(GDP/Labor)_{t-1i}} + \zeta_{ti} + \mu_{\rho_{i}}$,

where:
$\zeta_{ti}$ measures all disturbances to $\log{(GDP/Labor)_{ti}}$ in each time $t$ (assumed distributed normal), and
$\mu_{\rho_{i}}$ measures state-level variation in $\log{(GDP/Labor)_{ti}}$ (assumed distributed normal).

If $|\rho_{i}| \approx 1$, then you've got nearly integrated data, and the GECM, which also has the attractive properties of disentangling long-run effects, from both instantaneous change short term effects and from lagged short term effects.

The general form of the single equation GECM is:

$\Delta y_{t} = \beta_{0} + \beta_{c}\left[y_{t-1}-\left(\mathbf{X}_{t-1}\right)\right] + \mathbf{B}_{\Delta\mathbf{X}}\Delta\mathbf{X}_{t} + \mathbf{B}_{\mathbf{X}}\mathbf{X}_{t-1} + \varepsilon$,

where: $\Delta$ is the first difference operator (e.g. $\Delta y_{t} = y_{t} - y_{t-1}$), and $\varepsilon$ may be decomposed into mixed effects (e.g. by including $\beta_{0i}$, for country-level random intercepts).

instantaneous short run effects are given by $\beta_{\Delta\mathbf{X}}$,
lagged short run effects are given by $\beta_{\mathbf{X}} - \beta_{c} - \beta_{\Delta\mathbf{X}}$, and
long run effects are given by $\left(\beta-{c}-\beta_{\mathbf{X}}\right)/\beta_{c}$.

This specification assumes a homogeneity of error correction processes. I haven't yet tried to derive a heterogeneous error correction specification...

In Stata you can perform Hadri's test for unit-root in panel data on the residuals of such a model, to check them for stationarity.

Question 2

I do not know that I can say much useful here.

Question 3

The time dummies can be included in the GECM model, and presumably other dynamic times series models, often they are used as indicators of, for example, policies going into effect. I have done something similar, but used (time-varying) proportions (rather than 0/1 indicator variables) to represent the portion of the time period during which a policy was in effect (e.g. some policies go into effect January 1, some July 1, some December 21, etc.). On the other hand: you don't have tons of data, so I suppose it depends how many new variables you are adding.

References:

Banerjee, A., Dolado, J. J., Galbraith, J. W., and Hendry, D. F. (1993). Co-integration, error correction, and the econometric analysis of non-stationary data. Oxford University Press, USA.

De Boef, S. (2001). Modeling equilibrium relationships: Error correction models with strongly autoregressive data. Political Analysis, 9(1):78–94.

• thank you very much Alexis. I will thoroughly read Benerjee GECM method and try to apply it in my case. I had a presentation today on the same paper. SOmeone suggested Hausman-Taylor method and Arellano-Bond for dynamic modelling. Do you know if this works if I want to include more than one lag in my regression? Someone also suggested multi equation VAR modelling to account for potential endogeneity problem. Do you think any of these will work? Ofcourse first I am going to study what you have suggested but I am just trying to put all possible choices on the table. – Ali-Jena May 7 '14 at 19:23
• Ali-Jena, I am largely ignorant of those methods. I suggested the GECM because there were so many similarities in your description of your data and problem to an analysis in which I found the GECM to be useful. That said, there are differences also, so you mileage may vary. :) – Alexis May 8 '14 at 1:39
• thank zou Alexis.. sems like i have a very large set of literature to read. Atleast i know the direction now. Thank you for all the help. I will come back here if I get stuck somewhere. – Ali-Jena May 9 '14 at 12:36


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# Find the only element that appears b times using C++

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In this problem, we are given an arr[] of size n and two integers a and b. Our task is to find the only element that appears b times.

All values of the array occur a time except one value which occurs b times in the array and we need to find that value.

Let’s take an example to understand the problem,

Input

arr[] = {3, 3, 3, 3, 5, 5, 5, 1, 1,1,1} a = 4, b = 3

Output

5

## Solution Approach

A simple solution to the problem is by counting the occurrence of each element and then storing it in a 2D matrix. Then traversing the matrix to find the value with occurrence frequency b.

The time complexity of this approach is O(N2) but a more effective approach that can solve the problem is by finding the sum of all unique elements of the array and then multiplying it by a. Then subtract the sum of the whole array from this value and then divide the result by (a-b). The resulting value is the value whose occurrence frequency is b.

## Example

Program to illustrate the working of our solution

#include <bits/stdc++.h>
using namespace std;
int findbFreqVal(int arr[], int n, int a, int b){
unordered_set<int> uniqueVal;
int uniqueValSum = 0, arrSum = 0;
for (int i = 0; i < n; i++) {
if (uniqueVal.find(arr[i]) == uniqueVal.end()) {
uniqueVal.insert(arr[i]);
uniqueValSum += arr[i];
}
arrSum += arr[i];
}
uniqueValSum = a * uniqueValSum;
return ((uniqueValSum - arrSum) / (a - b));
}
int main(){
int arr[] = { 4, 4, 4, 31, 8, 8, 8, 5, 5, 5};
int a = 3, b = 1;
int n = sizeof(arr) / sizeof(arr[0]);
cout<<"The value of the array that appears b times is "<<findbFreqVal(arr, n, a, b);
return 0;
}

## Output

The value of the array that appears b times is 31
Updated on 11-Feb-2022 11:41:26


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Information and Coding Theory Seminar

Abstracts of talks

Spring 2010

02/18, 02/25 Sirin Nitinawarat (UMD) , On the Deterministic Code Capacity Region of an Arbitrarily Varying Multiple-Access Channel Under List Decoding

ABSTRACT: we study the capacity region $C_L$ of an arbitrarily varying multiple-access channel (AVMAC) for deterministic codes with decoding into a list of size $L$ and for the average error probability criterion. First, we introduce the notion of symmetrizability, denoted by an integer $U \geq 0$, of the AVMAC by generalizing from a similar notion earlier defined for a point-to-point arbitrarily varying channel. It is then shown that for every $L \leq U$, $C_L$ has an empty interior, and for a fixed function $f:\{0, 1, \ldots \} \rightarrow \{0, 1, \ldots \}$ and for every $L \geq f(U)$, $C_L$ equals the capacity region of the AVMAC for random codes with a known single-letter characterization. In particular, $f(u) \leq (u+1)^2(u+2) - 1$, for every $u \geq 0,$ and, hence, the latter holds for every $L \geq (U+1)^2(U+2) - 1$.

I plan to start with some overview on the theory of the (single-input-single-output) arbitrarily varying channel and its extension to the multiple access channel before addressing the main results. If time permitted, relevant open problems will also be discussed.

03/11 Arya Mazumdar (UMD) , Coding for High-Density Magnetic Recording

ABSTRACT: We study a model of errors in binary data that arises in terabit-density magnetic recording. Under this model, several bits of the data are replaced by the values of their neighbors on the medium. We consider a simple one-dimensional version of this model, and derive several properties of codes that correct this type of error.

Joint work with Navin Kashyap and Alexander Barg.

03/25 Alexander Barg (UMD) , Codes with a strong parent-identifying property

ABSTRACT:
In the area of digital fingerprinting, one setting calls for unconditional identifying of one of the members of the "pirate coalition," while the other permits a small failure probability of the system designer. These two settings are distinguished by different types of pirate attacks. An interesting question arises if one considers an intermediate setting. It is answered by the concept of strongly IPP codes, introduced in the present work. We will prove that such codes exist, and find some exact answers for the case of size-2 pirate coalitions.

Joint work with G. Kabatiansky

04/01 Ravi Tandon (UMD) ,

ABSTRACT: We consider a secure lossless source coding problem with a rate- limited helper. In particular, Alice observes an i.i.d. source $X^{n}$ and wishes to transmit this source losslessly to Bob. A helper, say Helen, observes a correlated source $Y^{n}$ and transmits at a rate $R_{y}$ to Bob. A passive eavesdropper can observe the coded output of Alice. The equivocation $\Delta$ is measured by the conditional entropy $H(X^{n}|J_{x})/n$, where $J_{x}$ is the output of Alice. We first completely characterize the rate-equivocation region for this secure source coding model, where we show that Slepian-Wolf binning is optimal.

We next study two generalizations of this model and provide single-letter characterizations for the respective rate-equivocation regions. In particular, we first consider the case of a two- sided helper where Alice also has access to the coded output of Helen. We show that for this case, Slepian-Wolf binning is suboptimal and one can further decrease the information leakage to the eavesdropper by utilizing the side information at Alice. We finally generalize this result to the case when there are both secure and insecure rate-limited links from Helen and additional uncoded side informations $W^{n}$ and $Z^{n}$ are available at Bob and Eve, respectively. For this model, we provide a complete characterization of the rate-equivocation region when $Y^{n}\rightarrow X^{n} \rightarrow (W^{n},Z^{n})$ forms a Markov chain.

(Joint work with Sennur Ulukus and Kannan Ramchandran.)

04/08 Sirin Nitinawarat (UMD) , Maximal Error Capacity Regions Are Smaller than Average Error Capacity Regions for Multi-user Channels

ABSTRACT: The coding theorem for a discrete memoryless channel was originally proved by Shannon for the average error concept. However, a simple expurgation argument shows that the capacities for both the average and maximal error concepts are the same.

We present the results in the paper by G. Dueck (see below). In the paper, examples are given, for two-way channels and for multiple access channels, to show that the capacity regions depend on the error concept used. The author also proved that the same assertion holds with perfect feedback available to all the transmitters.

G. Dueck, Maximal Error Capacity Regions Are Smaller than Average Error Capacity Regions for Multi-user Channels,'' Problems of Control and Information Theory, Vol 7. (1), pp.11-19 (1978).

04/22 Avinash Varna (UMD) , TTT

ABSTRACT: Applications such as detection of copyright infringement and metadata services have spurred the development of efficient techniques for automated multimedia identification. Compact representations of robust and distinct multimedia features, called "fingerprints" or "robust hashes", are used for efficient multimedia identification. In this talk, we briefly review the concept of content fingerprints and present our work on modeling and analysis of multimedia content identification using binary fingerprints.

We first examine content identification using i.i.d. binary fingerprints under a detection-theoretic framework and derive a relation between the length of the fingerprint and the identification accuracy. We then model the interaction between the detector and an attacker seeking to evade detection as a two player game and obtain optimal strategies for both parties. To capture correlations among fingerprint bits, we introduce a Markov Random Field model for the fingerprint bits and noise. Under this model, we use a statistical physics inspired technique to first estimate the density of states and then utilize this estimate of the density of states to compute the probabilities of detection and false alarm.
(Joint work with Dr. Min Wu and Dr. Ashwin Swaminathan.)

05/13 Dr. S. Sandeep Pradhan (University of Michigan) , Toward a new approach to distributed information processing: Harnessing group structure

ABSTRACT: The prevalent trend in information theory has been to obtain performance limits of communication using Shannon's random coding arguments and its multi-terminal extensions, and in coding theory, the goal has been to achieve these limits using algebraic-structured codes with fast encoding and decoding algorithms.

It turns out that algebraic structure can also be used to weed out bad codes from an ensemble. In this work, we build on this observation, and look at the distributed source coding problem. We present a new approach to this problem and an achievable rate-distortion region (an inner bound to the performance limit) based on “good” structured random nested codes built over abelian groups. We demonstrate rate gains for this problem over traditional coding schemes that use random unstructured codes. For certain sources and distortion functions, the new rate region is strictly bigger than the Berger-Tung rate region, which has been the best known achievable rate region for this problem till now. Further, there is no known unstructured random coding scheme that achieves these rate gains. Achievable performance limits for single-user source coding using abelian group codes are also obtained as parts of the proof of the main coding theorem. We also show that nested linear codes achieve the Shannon rate-distortion bound in the single-user setting.


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# Electronics Handbook/Electricity Source

There are 2 sources of Electricity used in provide power to Electronic circuits to operate . DC which stands for Direct Current and AC which stands for Alternating Current

## DC

Direct Current provides constant voltage over time and the flow of electric charge is only in one direction. Mathematically DC can be represented by a function

$v(t) = v$

Direct current is generated from many sources

## AC

Alternate Current provide voltage varies sinusoidally over time with one complete cycle equals to $2\pi$

A sine wave, over one cycle (360°). The dashed line represents the root mean square (RMS) value at about 0.707

An AC voltage v can be described mathematically as a function of time by the following equation:

$v(t)=V_\mathrm{peak}\cdot\sin(\omega t)$,

where

• $\displaystyle V_{\rm peak}$ is the peak voltage (unit: volt),
• $\displaystyle\omega$ is the angular frequency (unit: radians per second)
• The angular frequency is related to the physical frequency, $\displaystyle f$ (unit = hertz), which represents the number of cycles per second , by the equation $\displaystyle\omega = 2\pi f$.
• $\displaystyle t$ is the time (unit: second).

The peak-to-peak value of an AC voltage is defined as the difference between its positive peak and its negative peak. Since the maximum value of $\sin(x)$ is +1 and the minimum value is −1, an AC voltage swings between $+V_{\rm peak}$ and $-V_{\rm peak}$. The peak-to-peak voltage, usually written as $V_{\rm pp}$ or $V_{\rm P-P}$, is therefore $V_{\rm peak} - (-V_{\rm peak}) = 2 V_{\rm peak}$.

### Power and root mean square

The relationship between voltage and the power delivered is

$p(t) = \frac{v^2(t)}{R}$ where $R$ represents a load resistance.

Rather than using instantaneous power, $p(t)$, it is more practical to use a time averaged power (where the averaging is performed over any integer number of cycles). Therefore, AC voltage is often expressed as a root mean square (RMS) value, written as $V_{\rm rms}$, because

$P_{\rm time~averaged} = \frac{{V^2}_{\rm rms}}{R}.$

For a sinusoidal voltage:

$V_\mathrm{rms}=\frac{V_\mathrm{peak}}{\sqrt{2}}.$

The factor $\sqrt{2}$ is called the crest factor, which varies for different waveforms.

$V_\mathrm{rms}=\frac{V_\mathrm{peak}}{\sqrt{3}}.$
$\displaystyle V_\mathrm{rms}=V_\mathrm{peak}.$

### Example

To illustrate these concepts, consider a 230 V AC mains supply used in many countries around the world. It is so called because its root mean square value is 230 V. This means that the time-averaged power delivered is equivalent to the power delivered by a DC voltage of 230 V. To determine the peak voltage (amplitude), we can rearrange the above equation to:

$V_\mathrm{peak}=\sqrt{2}\ V_\mathrm{rms}.$

For our 230 V AC, the peak voltage Vpeak is therefore $\displaystyle 230 V \times\sqrt{2}$, which is about 325 V. The peak-to-peak value $\displaystyle V_{P-P}$ of the 230 V AC is double that, at about 650 V.

Note that some countries use a frequency of 50 Hz, while others use a frequency of 60 Hz. The calculation to convert from RMS voltage to peak voltage is independent of the frequency.

In certain applications, different waveforms are used, such as triangular or square waves. Audio and radio signals carried on electrical wires are also examples of alternating current. In these applications, an important goal is often the recovery of information encoded (or modulated) onto the AC signal.


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Compare, Calculate, and Interpret Yield Spread Measures

Yield spread (measured in basis points) is the difference between any two bond issues and is computed as follows:

Yield spread = Yield on Bond 1 – Yield on Bond 2

When the second bond is a benchmark (i.e. Treasury), the yield spread is referred to as the absolute yield spread.

Spread can be attributed to macroeconomic factors affecting the bond issuer as well as the bond itself. These include factors such as credit risk, liquidity, and taxation. The benchmark (risk-free rate) considers the expected rate of inflation, exchange rates, the impact of fiscal/monetary policies, and general economic growth.

G-spread (nominal spread) is the difference between the yield on Treasury Bonds and the yield on corporate bonds of the same maturity.

Where:

Yc  = yield on the non-treasury bond; and

Yg = yield on the government bond of the same maturity.

The I-spread stands for interpolated spread. It represents the difference between the yield on a bond and the swap rate (the interest rate applicable to the fixed leg in the floating-for-fixed interest rate swap, say, LIBOR). A higher I-spread means that a bond has a higher credit risk.

The zero-volatility spread (Z-spread) is the constant spread that makes the price of a security equal to the present value of its cash flows when added to the yield at each point on the spot rate Treasury curve. It is the spread that must be added to each spot interest rate to equate the present value of the bond cash flows to the bond’s price.

Z-spread can be calculated using the following equation:

$$P=\frac { { CF }{ 1 } }{ { \left( 1+{ s }{ 1 }+Z \right) }^{ 1 } }+\frac { { CF }_{ 2 } }{ { \left( 1+{ s }_{ 2 }+Z \right) }^{ 2 } } +…+\frac { { CF }_{ n } }{ { \left( 1+{ s }_{ n }+Z \right) }^{ n } }$$

Where:

P is the price of the bond;

CF1, CF2, and CFn are the first, second and nth cash flows;

Si is the ith spot interest rate; and

Option-adjusted spread equals zero-volatility spread minus the value of a call option, stated in basis points. It is appropriate when measuring the yield for callable bonds.

OAS = Z-spread – Option value

Question

A 10% annual coupon corporate bond maturing in two years is trading at a price of 100.750. The two-year, 8% annual payment government benchmark bond is trading at a price of 100.950. The one-year and two-year government spot rates are 2.4% and 3.5%, respectively, stated as effective annual rates.

1. 190 bps
2.  200 bps
3.  210 bps

Solution

The yield-to-maturity for the corporate bond is 9.57%.

$$100.75=\frac { 10 }{ \left( 1+r \right) } +\frac { 110 }{ { \left( 1+r \right) }^{ 2 } } , \quad r=0.0957$$

The yield-to-maturity for the benchmark bond is 7.47%.

$$100.95=\frac { 8 }{ \left( 1+r \right) } +\frac { 108 }{ { \left( 1+r \right) }^{ 2 } } , \quad r=0.0747$$

The G-spread is 210 bps: 0.0957 – 0.0747 = 0.021

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# What definition of “LEO” does SpaceX use when specifying payload capability?

Please forgive me if I am asking a dumb question. I am a little curious about the orbital parameters of "LEO" used by SpaceX on many occasions specifically those related to payload capability. According to SpaceX's Falcon 9 newest user guide it appears, though I cannot confirm, that it refers to a 200km x 360km orbit:

Official User Guide

but on this website it hints to be a 185km x 185km circular orbit (a little dated):

spacelaunchreport

So which one is more accurate in terms of payload capability? Thanks.

• There's almost no such thing as a dumb question! This one however, is a good question. Do you mean that Table 3-2 says "LEO Direct Inject (200 km x 360 km)" for a insertion accuracy spec, but it's not clear if it also applies to a payload mass spec? – uhoh Jun 29 '16 at 3:37
• Yes that is what I meant. I just did calculaiton using an online calculator and it appears that the delta-v needed to transfer from 200x200 circular orbit into 200x360 orbit is about 50m/s, so perhaps either way it won't affect the payload capability very much? Thanks. – Peng Jun 29 '16 at 3:45
• As a rough rule of thumb, figure 0.5% payload difference per 10km of altitude difference in circular orbit. (Please do not plan an orbital launch using this information.) – Russell Borogove Jun 29 '16 at 4:26

One more thing though: While SpaceX offers a standardised orbit as a product, they operate in a very specialised niche market where missions are often custom made. As the $\Delta v$ cost of using a slightly different orbit is only minor, you could easily order another orbit for your payload, eliminating the need for having a company LEO definition. Custom orbits are of course much easier if you do not share the launch with many other satellites though.


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###### Question:

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# Prove that the sum of the squares of the diagonals of parallelogram is equal to the sum of the squares of its sides.

Let us consider, ABCD be a parallelogram. Now, draw perpendicular DE on extended side of AB, and draw a perpendicular AF meeting DC at point F.

By applying Pythagoras Theorem in $$\triangle$$ DEA, we get,

$$DE^2 + EA^2 = DA^2$$ ……………….… (i)

By applying Pythagoras Theorem in $$\triangle$$ DEB, we get,
$$\Rightarrow DE^2 + EB^2 = DB^2$$
$$\Rightarrow DE^2 + (EA + AB)^2 = DB^2$$
$$\Rightarrow(DE^2 + EA^2 ) + AB^2 + 2EA × AB = DB^2$$
$$\Rightarrow DA^2 + AB^2 + 2EA × AB = DB^2$$ ………. (ii)

By applying Pythagoras Theorem in $$\triangle$$ ADF, we get,
$$AD^2 = AF^2 + FD^2$$

Again, applying Pythagoras theorem in $$\triangle$$ AFC, we get,
$$AC^2 = AF^2 + FC^2$$
$$= AF^2 + (DC - FD)^2$$
$$= AF^2 + DC^2 + FD^2 - 2DC × FD$$
$$= (AF^2 + FD^2 ) + DC^2 - 2DC × FD (AC^2)$$
$$\Rightarrow AC^2= AD^2 + DC^2 - 2DC × FD$$ ………………… (iii)

Since ABCD is a parallelogram,
AB = CD ………………….…(iv)
And BC = AD ………………. (v)

In $$\triangle$$ DEA and $$\triangle$$ ADF,
$$\angle$$ DEA = $$\angle$$ AFD (Each 90°)
$$\angle$$ EAD = $$\angle$$ ADF (EA || DF)
$$\triangle$$ EAD $${\displaystyle \cong }$$ $$\triangle$$ FDA (AAS congruence criterion)
EA = DF ……………… (vi)

Adding equations (i) and (iii), we get,
$$DA^2 + AB^2 + 2EA × AB + AD^2 + DC^2 - 2DC × FD = DB^2 + AC^2$$
$$DA^2 + AB^2 + AD^2 + DC^2 + 2EA × AB - 2DC × FD = DB^2 + AC^2$$

From equation (iv) and (vi),
$$BC^2 + AB^2 + AD^2 + DC^2 + 2EA × AB - 2AB × EA = DB^2 + AC^2$$
$$AB^2 + BC^2 + CD^2 + DA^2 = AC^2 + BD^2$$


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### Rotating Triangle

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

### Pericut

Two semicircle sit on the diameter of a semicircle centre O of twice their radius. Lines through O divide the perimeter into two parts. What can you say about the lengths of these two parts?

### Polycircles

Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?

# Curvy Areas

### Why do this problem?

This problem offers the opportunity to practise calculating areas of semicircles and working in terms of $\pi$ and leads to a surprising result that invites students to generalise.

### Possible approach

These printable resources may be useful: Curvy Areas,
Curvy Areas.

Begin by showing one of the three diagrams on these slides for a short while, then hide it.
"Think about the image you just saw. Can you make a sketch of it? Can you describe to your partner how it was drawn?"
Show the image again so that students can compare their first impression with the actual image. Recreating the image offers students a good opportunity for practising constructions with a pair of compasses.

"Now that we can see how the images were created, talk to your partner and see if you can come up with a method for working out the shaded areas." Give students a little time to discuss, and then bring the class together to share their suggested methods. Then ask students to use these methods to work out all the areas for each curvy pattern.

Students might need prompting to choose a letter or value to represent the radius of the smallest semi-circle in order to work out the areas. There is scope for some discussion here about the merits of assigning a unit length rather than using a variable, and why this is 'allowed' in a question asking about proportion.

Surprisingly, each coloured region on a diagram is the same proportion of the total area. Once students have found that result, they could work on a pattern with more regions to see if the same result follows.

To prove the general case that all regions have equal area is quite challenging. A more accessible question to work on first of all is to show that the first region (coloured red in our diagrams) is always $\frac{1}{n}$ of the total area, for a shape with $n$ regions.

The diagram below builds a similar pattern from rectangles and could be used to develop appropriate arguments, without needing to include $\pi$ in calculations.

### Key questions

Where are the centres of semicircles in the diagrams?
What is the relationship between the different radii?
For a circle with $n$ different coloured sections, how would you work out the red area?

### Possible extension

Prove algebraically that all sections have equal area for a circle with $n$ sections

### Possible support

The problem An Unusual Shape provides practice in calculating the areas of semicircles.
The problem Blue and White investigates sequences based on the areas of circles.


text:
## Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  615.10055
Autor:  Erdös, Paul; Ivic, A.; Pomerance, C.
Title:  On sums involving reciprocals of the largest prime factor of an integer. (In English)
Source:  Glas. Mat., III. Ser. 21(41), 283-300 (1986).
Review:  Let P(n) denote the largest prime factor of n. Let \rho(u) denote the continuous solution to the differential delay equation u\rho'(u) = -\rho(u-1) with the initial condition \rho(u) = 1 for 0 \leq u \leq 1. (\rho(u) is usually called the Dickman-de Bruijn function). Let \delta(x) = intx2\rho(log x/ log t)t-2 dt. Then the authors prove

sumn \leq x(P(n))-1 = x\delta (x)(1+O((log log x/ log x) ½)).

The authors prove many other interesting results. We quote one or two results. Let w(n) = sump|n1 and \Omega (n) = sump\alpha||n. Then the authors prove a rather surprising result

sumn \leq x (P(n))-w(n) = \exp {(4+o(1))(log x) ½ (log log x)-1}

whereas (in contrast)

sumn \leq x (P(n))-\Omega (n) = log log x+D+O(1/ log x)

where D is a constant.
Another result which I would like to quote is about K. Alladi's functions \beta(n) = sump|np and \beta(n) = sump\alpha||n\alpha p. If f(n) denotes either of these functions then

sumn \leq x1/f(n) = {1+0(\exp(-C(log x log log x) ½))} sum2 \leq n \leq x1/P(n).

The reader would find many other interesting results.
Reviewer:  K.Ramachandra
Classif.:  * 11N05 Distribution of primes
11N37 Asymptotic results on arithmetic functions
Keywords:  reciprocals of largest prime factor; Dickman-de Bruijn function

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